Advancements in Synthetic Jet for Flow Control and Heat Transfer: A Comprehensive Review

Abstract

Synthetic jets, generated through the periodic suction and ejection of fluid without net mass addition, offer distinct benefits, such as compactness, ease of integration, and independence from external fluid sources. These characteristics make them well-suited for flow control and convective heat transfer applications. However, conventional single-actuator configurations are constrained by limited jet formation, narrow surface coverage, and diminished effectiveness in the far field. This review critically evaluates the key limitations and explores four advanced configurations developed to mitigate them: dual-cavity synthetic jets, single-actuator multi-orifice jets, coaxial synthetic jets, and synthetic jet arrays. Dual-cavity synthetic jets enhance volume flow rate and surface coverage by generating multiple vortices and enabling jet vectoring, though they remain constrained by downstream vortex diffusion. Single-actuator multi-orifice designs enhance near-field heat transfer through multiple interacting vortices, yet far-field performance remains an issue. Coaxial synthetic jets improve vortex dynamics and overall performance but face challenges at high Reynolds numbers. Synthetic jet arrays with independently controlled actuators offer the greatest potential, enabling jet vectoring and focusing to enhance entrainment, expand spanwise coverage, and improve far-field performance. By examining key limitations and technological advances, this review lays the foundation for expanded use of synthetic jets in practical engineering applications.

1. Introduction

Jets are fluid streams formed by the discharge of fluid through an orifice or nozzle into a surrounding medium, resulting in a momentum-driven flow that entrains and interacts with the ambient fluid. Due to their ability to deliver high momentum fluid, jets are widely employed in practical applications across various engineering domains (Figure 1). They play a pivotal role in propulsion systems, including aircraft engines, rocket propulsion, and marine thrusters (Figure 1a), where high velocity fluid ejection generates thrust [1]. Jets are also extensively used in heat and mass transfer applications, such as impinging jets for localized cooling, spray cooling in electronics, and industrial drying processes (Figure 1b), where enhanced convective transport is critical [2]. Additionally, they are used in flow control and mixing to improve combustion efficiency, reduce noise, and mitigate pollution (Figure 1c) by actively manipulating flow fields and enhancing fluid mixing [3,4,5].

Figure 1. Illustration of engineering applications of jet flows: (a) propulsion, (b) heat and mass transfer, and (c) flow control and mixing.

Jets can be broadly classified based on different criteria, as shown in Figure 2. Depending on the flow regime, jets can be classified as laminar, transitional, or turbulent, with each regime distinguished primarily by the Reynolds number (Figure 2a). Laminar jets exhibit smooth flow [6,7], transitional jets show emerging instabilities [8], and turbulent jets display chaotic motion with strong mixing [9,10]. Classifications based on working fluid (Figure 2b) are air jets [11], liquid jets [12], and plasma jets [13]. Each type varies in fluid properties and energy requirements, influencing their suitability for specific thermal and flow control applications. Jet classification based on exit geometry (Figure 2c) includes round jets [14], slot jets [15], coaxial jets [16], and jet arrays [17]. Each geometry produces distinct flow patterns and spatial coverage, affecting mixing efficiency and heat transfer characteristics. Jets, based on the surrounding flow environment (Figure 2d), can also be categorized into free jets [18], impinging jets [19], crossflow jets [20], wall jets [21], and confined jets [22]. These categories reflect differences in boundary interactions and flow confinement, which significantly influence jet behavior and performance. Additionally, jets based on their temporal characteristics (Figure 2e) can be classified as steady jets (Figure 2(e1)) [18] and unsteady jets (Figure 2(e2)). The latter includes pulsating [23], flapping [24], sweeping [25], modulated pulse jet [26,27], and synthetic jet (SJs) [28]. Steady jets provide consistent flow conditions, while unsteady jets exhibit time-varying dynamics that enhance mixing and flow control capabilities [29]. Recently, modulated pulse jets have been introduced as an extension of unsteady jet actuation, employing burst modulation that combines a high-frequency carrier with a low-frequency modulation [26]. This approach enhances vortex generation while reducing air consumption compared to continuously pulsed jets, and has demonstrated effective flow separation control in high-lift airfoil applications [27].

Figure 2. Classification of jets based on various criteria: (a) flow regime, (b) working fluid, (c) geometry of jet exit, (d) flow environment, and (e) flow temporal characteristics, further divided into (e1) steady jet and (e2) unsteady jet.

Among unsteady jets, synthetic jets are unique in generating periodic vortices through alternating suction and blowing without net mass input [28]. Their compact design [19], non-requirement of external fluid to form the jet [28], precise control over operating parameters [16], energy efficiency [30], and easy integration into complex circuits [31] make synthetic jets well-suited for a wide range of engineering applications.

1.1. Overview of Synthetic Jets

Over the last two decades, SJs, also referred to as zero-net-mass-flux (ZNMF) actuators [28], have gained significant attention as an innovative approach in the fields of fluid mechanics [32,33] and aerodynamics [34,35]. Unlike conventional jet systems that rely on bulky mechanical components such as rotors or blades, synthetic jets are generated by oscillating actuators such as diaphragms or loudspeakers. Although these actuators involve mechanical motion and may experience wear or fatigue over time, the absence of large moving parts generally leads to lower maintenance requirements compared to traditional jet systems [30,36].

Synthetic jets are typically generated using a fluidic device called a synthetic jet actuator (SJA) (Figure 3), which consists of a cavity enclosed by a vibrating membrane on one side and an orifice on the other [28]. The vibrating medium can be a piston-cylinder arrangement [37], a speaker [38], or a diaphragm [16]. When an alternating current (AC) is applied, the diaphragm undergoes oscillatory motion, drawing surrounding fluid into the cavity during the suction stroke (Figure 3a) and ejecting fluid along with a pair of counter-rotating vortices during the ejection stroke (Figure 3b). This cyclic process generates a series of vortex rings, which collectively form the synthetic jet [39]. Typically, the ejection phase produces a high-velocity jet that dominates the region downstream of the orifice, while the suction phase induces inward flow toward the orifice. These opposing phases create distinct flow regions, with a saddle point often observed near the orifice exit, separating the suction-influenced zone from the ejection-dominated region (Figure 3). The resulting SJs exhibit high-momentum [40] and turbulent characteristics [31].

Figure 3. Illustration of synthetic jet components during (a) suction stroke and (b) ejection stroke.

1.2. Comparative Analysis of Synthetic Jets and Continuous Jets

Unlike continuous jets (CJs), which require an external fluid source, SJAs utilize the surrounding fluid, eliminating the need for additional airflow [31]. For a fixed Reynolds number ($Re$), synthetic jets exhibit stronger entrainment of the surrounding fluid [18,31], leading to a wider and more rapidly spreading jet (Figure 4a) compared to continuous jets (Figure 4b). Here, the Reynolds number, calculated based on the time-averaged jet velocity $U_o$, is defined as [28]

$${Re}_{U_o}=U_{o}d/\vartheta$$

(1)

where $d$ is the orifice diameter (or slot width), and $\vartheta$ is the kinematic viscosity of the working fluid. The detailed methodology used to calculate the Reynolds number is discussed in Section 2.4.1.

Hot-wire anemometry and Schlieren visualizations confirm that these vortex structures dominate the early development of SJs before transitioning into turbulence downstream [28,41]. Under identical operating conditions, SJs generate approximately 1.414 times higher eddy viscosity than CJs, promoting stronger momentum transfer and enhanced mixing due to their pulsatile nature [29].

In terms of thermal performance, SJs produce broader and more uniform thermal distributions during impingement cooling. Under identical flow conditions (${Re}_{U_o}$ ≈ 1700), the Nusselt number ($Nu$), which quantifies heat transfer, for SJs exceeded that of CJs by approximately 34% (Figure 4c). This improvement is attributed to the dynamic entrainment and mixing characteristics of the synthetic jets [42]. The Nusselt number is defined as

$$Nu={\displaystyle \frac{hd}{k}}$$

(2)

where $h$ is the convective heat transfer coefficient and $k$ represents the thermal conductivity of the working fluid.

Figure 4. Evolution of synthetic and continuous jets along with their heat transfer characteristics. Flow development of (a) synthetic jets and (b) continuous jets, reproduced with permission from [18]; (c) variation in Nusselt number with Reynolds number at a jet-to-heated-plate distance of $Y/d$ = 10 for both jet types, reproduced with permission from [42].

Figure 4. Evolution of synthetic and continuous jets along with their heat transfer characteristics. Flow development of (a) synthetic jets and (b) continuous jets, reproduced with permission from [18]; (c) variation in Nusselt number with Reynolds number at a jet-to-heated-plate distance of $Y/d$ = 10 for both jet types, reproduced with permission from [42].

The enhancement in the Nusselt number remains significant across a range of $Re$ [43]. Additional studies support these findings, consistently demonstrating improved convective cooling by SJs relative to CJs under similar operational regimes [44,45]. The enhanced entrainment and increased eddy viscosity make synthetic jets a compelling alternative to continuous jets.

1.3. Applications of Synthetic Jets in Various Fields

Due to their unique design and operational advantages discussed earlier, synthetic jets have progressed beyond laboratory investigations and are increasingly utilized in various engineering applications. The major applications of synthetic jets are illustrated in Figure 5. One of the most prominent areas is flow control (Figure 5a), where synthetic jets inject momentum into the boundary layer, energizing near-wall fluid, generating coherent vortices, and suppressing flow separation. This leads to enhanced lift, reduced drag, and improved maneuverability in aerospace systems [33,40,46,47,48,49,50,51,52,53,54,55,56,57,58,59]. Synthetic jets are widely used to enhance mixing by introducing unsteady disturbances that intensify turbulence and promote entrainment. This is demonstrated in Figure 5b, which shows the coaxial jet without synthetic jet actuation (Figure 5(b1)) and with actuation (Figure 5(b2)). The synthetic jets disrupt the potential core and broaden the shear layer, leading to a thickened outer shear layer and a reduced radial velocity gradient, clear indicators of enhanced entrainment (Figure 5(b2)) compared to the case without synthetic jet actuation (Figure 5(b1)) [60]. The enhanced mixing leads to improved combustion efficiency and reduced emissions [61,62,63,64,65,66,67,68,69]. They are also widely adopted in thermal management applications, where their unsteady nature disrupts thermal boundary layers and enhances convective heat transfer [70]. During the cyclic operation of synthetic jets, the suction stroke draws in cool ambient air (Figure 5(c1)), while the ejection stroke expels hot air (Figure 5(c2)). This periodic jetting action improves entrainment, increases near-wall turbulence, and significantly enhances convective heat removal from the surface. This is particularly effective for cooling electronic components such as CPUs and GPUs [15,22,45,71,72,73,74,75]. Additionally, synthetic jets are employed in unmanned aerial vehicles (UAVs) (Figure 5d), where their compactness and controllability contribute to aerodynamic efficiency and flight control [76,77,78,79].

Figure 5. Applications of synthetic jets in (a) flow control, reproduced with permission from [46]; (b) mixing enhancement, figure reproduced from [60], licensed under CC BY 4.0; (c) heat transfer, reproduced with permission from [70]; and (d) unmanned aerial vehicles (UAVs), reproduced with permission from [77].

Together with these major areas, synthetic jets have also been explored for underwater propulsion and maneuvering in marine robotics, offering a compact and efficient solution for submerged environments [76,78,79,80,81]. These diverse implementations highlight the versatility of synthetic jets and their potential to impact a wide spectrum of engineering domains.

1.4. Review Scope and Objectives

As discussed previously, SJs exhibit strong potential for flow control and thermal management applications, owing to their compact design, ZNMF, ease of integration into miniaturized systems, and independence from external fluid sources. However, a detailed review of the literature highlights three fundamental limitations affecting the practical deployment of synthetic jets, namely restricted jet formation, limited spanwise coverage, and rapid loss of momentum and coherence in the far field due to vortex diffusion. These core issues remain largely unaddressed in the existing literature. Several existing review articles have primarily focused on understanding the flow physics of synthetic jets, examining the influence of geometric and non-dimensional parameters on their flow and heat transfer behavior, and discussing application-oriented aspects, particularly in heat transfer enhancement and flow control. However, these reviews largely treat these topics independently, without explicitly identifying the inherent limitations of synthetic jets. A summary of these review works and their respective scopes is provided in Table 1. In contrast, the present review is the first to explicitly identify the fundamental drawbacks of single-actuator synthetic jets and to systematically evaluate the technological advancements proposed to overcome these limitations.

Table 1. Summary of key review papers on synthetic jets and their scope.

Author(s)	Focus Area	Research Gaps	Relevance to Present Review
Murugan et al. [82]; Walimbe et al. [30]; Bharghava et al. [83]	Fundamental flow physics, formation criteria, and applications of SJs	Limited understanding of vortex dynamics and a lack of systematic identification of fundamental drawbacks of SJs	Provides a foundation in SJ flow physics and applications, extended here by identifying key limitations and reviewing technological solutions
Chiatto et al. [84]; Ja’fari et al. [36]; Ho et al. [85]; Hong et al. [53]	Synthetic jet actuator modeling, design, and operating parametric influence in quiescent and cross-flow	Primarily actuator- and parameter-centric, with limited connection to actual synthetic jet performance limits and corresponding mitigation strategies	Provides actuator-level insights that support the present review
Krishan et al. [86]; Arshad et al. [87]; Ariffin and Ahmad [88]; Ikhlaq et al. [89]; Sharma et al. [90]	Synthetic jet heat transfer for electronics cooling, with emphasis on the effects of geometric parameters and operating conditions	Focuses on synthetic jet heat transfer and empirical correlations, with limited coverage of fundamental limitations at large jet to surface spacings or mitigation strategies	Provides a heat transfer foundation that the present review advances by identifying and addressing unresolved key drawbacks of synthetic jets
Ahmed et al. [91]	Comprehensive review of multiple-orifice synthetic jets with emphasis on flow interaction, heat transfer enhancement, and integration with passive and active cooling systems.	Focuses on performance gains of multi-orifice synthetic jets over single-actuator designs, with limited attention to limitations and solutions for single-actuator jets	Informs advanced configurations, which the present review evaluates from a drawback-mitigation perspective
Present Review	Identification of fundamental drawbacks of SJs and technological advancements to address them	—	Synthesizes key unresolved synthetic jet issues and critically reviews technologies to overcome them

The review categorizes and evaluates four major SJ configurations, namely dual cavity jets, single-actuator multi-orifice jets, coaxial jets, and synthetic jet arrays, based on their ability to mitigate these limitations. Each configuration is analyzed in terms of momentum delivery, spatial coverage, and vortex structure sustainability. Performance improvements through design modifications, actuator arrangements, and control of operating parameters are critically examined alongside unresolved challenges. By establishing a clear link between the observed limitations in single-actuator configurations and the functional enhancements achieved through more advanced arrangements, this review offers a solid foundation for future research and design optimization. This assessment is crucial due to the rising demand for compact, efficient flow control along with thermal management solutions in miniaturized electronics, aerospace, and next-generation energy systems.

To provide a quantitative overview of the literature surveyed in this review, Figure 6 presents the distribution of cited papers by country (a) and by year of publication (b). This illustrates the geographical spread and temporal evolution of research in synthetic jet technologies, highlighting growing international interest and increasing publication trends over the past two decades. In addition, Figure 6c presents a categorical breakdown of the cited literature based on research focus and application areas, including heat transfer, aerodynamic flow control, jet fundamentals and vortex dynamics, actuator design and modeling, mixing, propulsion and robotics, and noise and acoustics. This quantitative classification highlights the dominant research emphasis on heat transfer and flow control, while revealing comparatively fewer studies in propulsion and robotics, mixing, and noise and acoustics, indicating underexplored areas with significant potential for future research. In recent years, greater emphasis has been placed on the practical implementation of synthetic jets in cooling and flow control applications, reflecting a shift toward real-world applicability and system-level integration. This review offers a comprehensive synthesis of existing knowledge that not only clarifies key challenges and technological progress but also provides a valuable foundation for guiding future research and development efforts toward more effective and practical synthetic jet solutions.

Figure 6. Distribution of cited literature included in this review: (a) country-wise percentage of cited papers, (b) year-wise distribution of cited publications, and (c) classification of the reviewed studies based on research focus and application areas.

2. Key Parameters Governing Flow and Heat Transfer in Synthetic Jets

The performance of synthetic jets, encompassing both flow dynamics and heat transfer, is strongly governed by a combination of geometric, operational, and fluid parameters (Figure 7). Additionally, various non-dimensional numbers (Figure 8) are critical in describing the development and interaction of synthetic jets with the surrounding flow and thermal fields. This section outlines the key parameters that influence the overall behavior and effectiveness of synthetic jets.

Figure 7. Key parameters influencing the flow and heat transfer characteristics of synthetic jets, classified into (a) geometric parameters, (b) operating parameters, and (c) fluid parameters.

Figure 8. Nondimensional parameters governing the flow and heat transfer characteristics of synthetic jets: (a) Reynolds number, (b) Strouhal number, (c) Stokes number, and (d) Nusselt number.

2.1. Geometric Parameters of SJA

The geometry of an SJA plays a crucial role in defining its flow behavior and performance. Two primary geometric aspects govern this behavior, namely the orifice configuration, referring to its shape, size, and edge, and the cavity parameters (Figure 7a). The orifice shape, size, and edge configuration directly influence the exit jet’s velocity profile, directionality, and coherence [92]. Circular, rectangular, and slit-shaped orifices generate distinct vortex structures and entrainment characteristics. Smaller orifices produce faster, more focused jets due to concentrated momentum, while larger ones yield slower, higher-volume jets with broader coverage [93]. However, an increase in peak jet velocity resulting from a reduced orifice size does not necessarily lead to a proportional increase in Reynolds number or entrainment capability [94]. The orifice edge configuration significantly affects vortex formation and jet performance; sharp edges enhance vortex roll-up and momentum flux, while rounded edges improve entrainment and mixing but reduce axial velocity and impingement strength [95,96].

The cavity parameters largely affect the actuator’s resonant behavior and energy transfer efficiency. Together with the orifice, the cavity forms a system that closely resembles a Helmholtz resonator, where the air inside the cavity acts as a compressible spring, and the slug of air oscillating through the orifice behaves as an inertial mass [97]. A larger cavity volume enhances compressibility, lowering the natural oscillation frequency, while a larger orifice area reduces inertial resistance, thereby raising the frequency [98]. Optimal actuator performance typically occurs near the resonant frequency, where stronger vortex formation and higher jet velocities enhance flow control and heat transfer [99].

2.2. Operating Parameters of SJA

A critical aspect of synthetic jet actuator operation is the membrane oscillation. The key input parameters controlling this oscillation include the driving frequency, oscillation amplitude, and actuation waveform (Figure 7b), which govern jet formation and vortex dynamics, and influence both flow control and heat transfer performance.

2.2.1. Driving Frequency ($f$)

The actuation frequency of the oscillating membrane determines the rate at which SJs are produced during each oscillatory cycle. An increase in frequency typically leads to higher jet velocities and the formation of stronger vortex structures, which can be beneficial in applications requiring rapid and dynamic flow control. In contrast, lower frequencies tend to generate more stable jets with reduced turbulence, making them more suitable for conditions where steady flow behavior is desired [98].

2.2.2. Oscillation Amplitude ($a$)

Amplitude reflects the extent of membrane displacement during each oscillation cycle. A larger amplitude typically induces greater fluid movement, resulting in stronger jet formation. This parameter significantly influences the evolution and spreading characteristics of the jet [100]. Moreover, variations in amplitude influence the formation and spreading of vortices within the flow, which directly impacts the mixing efficiency and heat transfer performance of the jet.

2.2.3. Actuation Waveform

Synthetic jet actuators can be operated using various waveforms, including sinusoidal, square, and triangular signals. The choice of waveform influences the jet’s temporal behavior, leading to differences in velocity profiles and vortex dynamics. These waveforms affect the rate of diaphragm acceleration and deceleration during each cycle, which in turn alters the strength and structure of the expelled vortices. Square waveforms tend to produce sharper transitions and more abrupt vortex shedding, whereas sinusoidal signals generate smoother, more continuous flow development [101,102]. These variations affect the balance between suction and expulsion phases, altering the jet’s symmetry, strength, and temporal characteristics, which collectively impact its overall performance. By modifying the waveform, the thermal and momentum transport characteristics of the jet can be adjusted to meet specific application requirements [103].

2.3. Fluid Parameters in SJA

The thermophysical properties of the working fluid, including density, viscosity, velocity, and temperature, play a critical role in shaping the behavior of synthetic jets (Figure 7c). These properties govern the momentum and heat transport mechanisms that influence the formation, evolution, and stability of vortical structures during each actuation cycle, particularly under varying thermal conditions [33]. Density determines the inertial response and penetration capability of the flow [13]. Viscosity affects the rate of vorticity diffusion, thereby influencing the coherence and dissipation of the jet [104]. Fluid velocity contributes directly to the jet momentum and the vortex strength [28,105]. Temperature variations not only modify the intrinsic properties of fluid but also influence key dimensionless numbers, such as the Reynolds and Prandtl numbers, which are critical to both flow dynamics and thermal transport [92]. These effects become increasingly significant in applications involving strong thermal gradients, where precise control of jet behavior is essential for optimal performance.

2.4. Characteristics of Dimensionless Numbers Governing Synthetic Jet Behavior

The dimensionless parameters simplify the influence of operating conditions and fluid properties into meaningful quantities that help understand patterns in vortex motion, jet development, and heat transfer. Various key dimensionless quantities, such as the Reynolds number ($Re$), Strouhal number ($St$), Stokes number ($Stk$), and Nusselt number ($Nu$), as illustrated in Figure 8, provide insight into the fundamental physics governing jet behavior and thermal transport.

2.4.1. Reynolds Number ($Re$)

The Reynolds number is a fundamental dimensionless parameter that characterizes the flow behavior of SJs (Figure 8a). It indicates the nature of the flow regime, distinguishing whether the flow remains laminar or transitions to turbulence. In SJ applications, the Reynolds number affects vortex formation, jet penetration, and overall mixing behavior [39]. The Reynolds number directly depends on dimensional parameters such as the jet velocity, which is influenced by the driving frequency and oscillation amplitude of the diaphragm, as well as the orifice diameter and fluid properties.

In the Reynolds number expression defined in Equation (1) in Section 1.2, the time-averaged jet velocity $U_o$ is related to the stroke length and the actuation frequency as

$$U_o=L_{o}f,$$

(3)

where

$$L_o={\int }_o^{T/2}\mathrm{V}\left(t\right)dt.$$

(4)

The $L_o$ denotes the stroke length, representing the effective displacement of the jet during the blowing half-cycle. The $\mathrm{V}\left(t\right)$ is the instantaneous centerline velocity at the orifice exit, and $T=1/f$ represents the period of one complete actuation cycle, where $f$ is the diaphragm frequency.

To account for the distributed nature of the exit velocity, Utturkar et al. [106] later proposed a Reynolds number formulation based on the average velocity over time and space across the orifice area, i.e.,

$${Re}_{\overline{U}}=\overline{U}d/\vartheta ,$$

(5)

where $\overline{U}$ is defined as

$$\overline{U}={\displaystyle \frac{2}{TA}}{\int }_A{\int }_0^{T/2}V\left(t,x\right)dt dA.$$

(6)

In this formulation, $V\left(t,x\right)$ represents the local velocity at the orifice exit as a function of time and transverse coordinate $x$, and $A$ is the orifice area. The two velocity scales are related as

$$\overline{U}=2U_o.$$

(7)

Both definitions are commonly used, depending on the experimental approach or modeling requirements. A higher Reynolds number typically correlates with increased jet momentum, enhanced vortex strength, and improved mixing and heat transfer performance [107].

2.4.2. Strouhal Number ($St$)

The Strouhal number (Figure 8b) is a dimensionless parameter that relates the actuation frequency, orifice size, and the time-averaged jet velocity, which itself depends on the frequency and amplitude of oscillation of the diaphragm.

It can be expressed as [28]

$$St=fd/U_o$$

(8)

This parameter characterizes the interaction between periodic actuation and the inertia of the fluid, which plays a significant role in shaping the formation and spacing of vortical structures. It influences the generation of discrete vortex pairs during each actuation cycle by relating the actuation frequency and orifice geometry to the resulting fluid motion. According to Smith and Glezer [28], the $St$ is the inverse of the nondimensional stroke length and controls the axial distance from the orifice where vortex pairs or rings are shed. Experimental results indicate that at lower $St$ values, vortex rings form farther apart, reducing mutual interaction and shifting the breakdown location downstream [39]. On the other hand, high $St$ values prevent proper vortex separation, resulting in flow being drawn back into the cavity during the suction phase, thereby disrupting jet formation. The vortex formation condition that incorporates the combined effects of Reynolds number, $St$, and Stokes number ($Stk$) was introduced by Holman et al. [108]. For jets issuing from planar orifices, formation is observed when

$${\displaystyle \frac{1}{St}}={\displaystyle \frac{{Re}_{U_o}}{{Stk}^2}}>1.0,$$

(9)

and for axisymmetric jets, the corresponding criterion is

$${\displaystyle \frac{1}{St}}={\displaystyle \frac{{Re}_{U_o}}{{Stk}^2}}>0.16.$$

(10)

These expressions define the minimum conditions required for effective vortex roll-up and sustained jet formation during the ejection phase.

2.4.3. Stokes Number ($Stk$)

The Stokes number (Figure 8c) is an important dimensionless parameter that captures the combined effects of the actuation frequency, orifice size, and fluid viscosity on the unsteady behavior and evolution of vortices in synthetic jet flows. For synthetic jets, the Stokes number is defined as [109]

$$Stk=\sqrt{{\displaystyle \frac{2\pi f{d}^2}{\vartheta }}}.$$

(11)

This quantity plays a crucial role in determining whether coherent vortices can form and separate from the orifice. Earlier investigations reported that the strength of the vortex roll-up mechanism diminishes as $Stk$ decreases [109]. Experimental results showed that when the $Stk$ falls below 7, the shear layer cannot produce well-defined vortex structures [109]. Generally, a Stokes number around or above 10 is considered necessary to ensure the formation of distinct vortex rings that can detach and propagate downstream, contributing to effective SJ formation.

2.4.4. Nusselt Number ($Nu$)

The Nusselt number (Figure 8d), defined in Equation (2) in Section 1.2, is a key dimensionless parameter for evaluating the convective heat transfer performance of synthetic jets, as it relates the convective heat transfer coefficient $h$ to the characteristic length scale $d$ and the thermal conductivity $k$ of the working fluid. In synthetic jet flows, the heat transfer coefficient is influenced by dimensional parameters such as the jet velocity, actuation frequency, oscillation amplitude of the diaphragm, and the orifice-to-heated surface spacing, thereby indirectly linking the Nusselt number to the operating and geometric conditions of the actuator.

The area-average Nusselt number ($\overline{Nu}$) can be expressed as

$$\overline{Nu}={\displaystyle \frac{{\int }_0^{A_f}Nu d{A}_f}{{\int }_0^{A_f}d{A}_f}}.$$

(12)

Here, $A_f$ is the surface area of the heated object.

Synthetic jets enhance convective heat transfer by periodically ejecting and ingesting fluid, disrupting the thermal boundary layer and promoting vortex-induced mixing. The resulting Nusselt number is governed by vortex strength, actuation frequency, oscillation amplitude, and the orifice-to-surface spacing. Several studies [11,99,110] have shown that careful adjustment of these operating conditions can significantly increase both local and average Nusselt numbers. This makes SJs particularly effective for thermal management applications.

3. Flow Characteristics of Synthetic Jets

A comprehensive overview of the geometric configurations, operating conditions, fluid properties, and non-dimensional parameters influencing synthetic jet behavior has been presented earlier. This section reviews key experimental and numerical studies that examine the effects of these factors on vortex dynamics and flow characteristics. In addition to offering deeper insight into the relevant flow phenomena, the discussion also highlights limitations and challenges related to synthetic jets, particularly in engineering applications with specific performance requirements.

3.1. Influence of Geometric Parameters on SJ Flow Characteristics

The geometric configuration of SJA exerts a critical influence on jet formation, flow development, and downstream momentum transfer. For the same orifice area, actuation frequency, and actuation amplitude, a comparison of circular, square, slot, and triangular orifices revealed that the triangular orifice performs best in terms of peak centerline velocity ($V_{cl}/U_o$) [93]. The percentage enhancement of peak $V_{cl}/U_o$ for the triangular orifice is approximately 6%, 24%, and 31% compared to the circular, slot, and square orifices, respectively. However, the triangular orifice exhibits the highest decay in $V_{cl}/U_o$ among all the orifice shapes. For instance, the triangular orifice shows a decay of approximately 42% in $V_{cl}/U_o$ between $y/d_h\approx 1$ (where $V_{cl}/U_o$ reaches its peak) and $y/d_h\approx 4$ [93]. Here, $d_h$ is the hydraulic diameter, defined as $d_h$ = 4 × orifice area/perimeter. This significant reduction in $V_{cl}/U_o$ is attributed to the pronounced weakening of jet strength in the downstream direction [93]. A similar drastic reduction in $V_{cl}/\overline{U}$ for circular, square, and slot orifices can also be observed in Figure 9, indicating that all orifice shapes experience substantial weakening of jet strength with downstream distance [111]. Moreover, studies have shown that rectangular orifices generate broader vortex structures and enhanced lateral spreading; however, rapid diffusion of vortex strength in the far field remains a significant drawback [81,100].

Figure 9. Variation in jet centerline velocity ($V_{cl}/\overline{U}$) along the streamwise direction ($y/d_h$) for different orifice shapes. Figure reproduced from [111], licensed under CC BY 4.0.

The orifice edge geometry significantly influences vortex roll-up and near-field evolution during the ejection phase of synthetic jets by altering shear-layer separation and pressure drop at the orifice exit [39,112,113,114]. Sharp inner orifice edges promote abrupt boundary-layer separation at the orifice lip, producing a thin shear layer that quickly rolls up into compact vortex rings dominating the near field during the expulsion phase [39]. These coherent vortex structures convect downstream with higher axial momentum than those generated by rounded or beveled-edge orifices [114]. In contrast, rounding the inner lip reduces adverse pressure gradients and flow losses, resulting in smoother exit flow but weaker shear-layer roll-up [96,113,114]. Consequently, vortex rings formed from rounded edges tend to have lower coherence, enhanced lateral entrainment, increased jet spreading, and a more rapid decay of axial velocity as they propagate downstream [96]. Nani and Smith [114] quantified the impact of inner edge rounding, showing that it reduces acoustic power input up to a radius of $0.5d$. Beyond this threshold, power consumption increases due to loss of wall attachment and suction inefficiency.

Internal cavity dimensions further modulate jet characteristics, especially through their interaction with the acoustic response of the actuator. A reduced cavity height strengthens vortex shedding and improves near-field momentum transfer [96,115,116,117,118,119]. Conversely, under resonance conditions, larger cavities can support enhanced jet velocities by amplifying acoustic oscillations [117]. This resonance-based performance improvement has been extensively documented [98,118,119] and is often associated with peak output occurring at or near the actuator’s Helmholtz frequency [97,120]. These studies collectively highlight the importance of tuning cavity dimensions to balance jet strength, frequency response, and energy efficiency.

Along with poor far-field performance, another primary limitation of single-actuator configurations is that the generated stroke volume is inherently constrained by physical displacement and chamber size of the actuator. As a result, the time-averaged mass flow rate remains relatively low when considered for various engineering applications [21,121,122,123].

3.2. Effect of Non-Dimensional Parameters on SJ Flow Dynamics

As discussed earlier, the flow characteristics of synthetic jets are governed by several dimensionless parameters, including the Reynolds number, $St$, and $Stk$, along with $L_o/d$ that is inherently related to both Reynolds number (Equations (1) and (3)) and $St$ (Equation (8)) through its dependence on $U_o$. These dimensionless parameters encapsulate the effects of actuation frequency, oscillation amplitude, and fluid properties, thereby governing jet flow behaviors.

Operation of the SJA at low $L_o/d$ limits SJ formation by preventing vortices from moving far enough from the orifice during the blowing phase. This causes stronger suction effects that disrupt coherent vortex development, resulting in weaker jets and reduced fluid mixing, which are major drawbacks restricting effective jet formation [21]. As $L_o/d$ increases, the spacing between successive vortices grows, significantly affecting the jet’s spatial development. In rectangular configurations, a higher $L_o/d$ enhances lateral spreading but causes a transition from a discrete vortex train to a more continuous jet flow, resulting in a weakened jet due to increased vortex diffusion [29]. The best performance occurs in the range 4 ≤ $L_o/d$ < 8, where a balance is achieved between vortex strength and stability. In contrast, for $L_o/d$ > 8, the primary vortices become unstable and eventually lose coherence, giving rise to trailing jets that dominate the downstream flow [124].

A higher $Re$ produces stronger and more stable vortex rings, thereby enhancing momentum flux [125]. However, as the jet propagates away from the orifice, vortex diffusion causes a rapid decay in jet velocity. For example, Shuster and Smith [39] showed that synthetic jets operating at ${Re}_{U_o}$ = 10⁴ experience a 33% drop in peak streamwise velocity between $y/d$ = 2 and 5, and nearly a 50% reduction between $y/d$ = 5 and 10, highlighting the significant impact of vortex diffusion in the far field. In flow control applications, moderate Reynolds numbers combined with a low-frequency actuation have shown improved flow reattachment using less momentum input than high-frequency strategies [126]. Nonetheless, maintaining jet effectiveness at higher Reynolds numbers remains challenging due to enhanced turbulence and diffusion losses in the far field.

The St integrating actuation frequency, flow velocity, and jet size (Equation (8)) characterizes jet formation and behavior. In two-dimensional and axisymmetric jets, the $Re/{Stk}^2=1/St$ ratio governs the onset of vortex shedding and the development of coherent flow structures [106,108]. Operating outside the optimal $St$ range can inhibit the formation of discrete vortex rings or lead to unstable and ineffective flow regimes. For instance, in high Reynolds number impinging jets, lower Strouhal numbers shift the flow dominance from the primary jet to trailing jets, thereby weakening the actuator control capability and effectiveness [127]. Additionally, spanwise instabilities and secondary flow structures, such as rib-like vortices, emerge under certain operating conditions, further contributing to the decay of jet strength. The $St$ plays a pivotal role in dictating the onset, scale, and evolution of these flow features, as it influences both the initial vortex formation and the subsequent development of three-dimensional instabilities [128].

The excitation frequency of the actuator is a crucial parameter in aerodynamic applications, as it determines the effectiveness of flow control, influencing separation suppression, vortex formation, and lift enhancement [85]. In aerodynamic applications, the excitation frequency is typically non-dimensionalized as a dimensionless frequency, $F^{+}=fc/U_{\infty }$, where $c$ is the chord length and $U_{\infty }$ is the freestream velocity. The parameter $F^{+}$ is equivalent to a Strouhal number based on the airfoil chord length [85]. When the actuator operates at a low dimensionless frequency ($F^{+}$ ≈ 1), the excitation frequency closely matches the natural instability frequencies of the flow, such as those in the wake or the separated shear layer [129,130]. Under this resonance condition, the actuator effectively amplifies existing vortical structures, promoting large-scale coherent vortices that interact with the boundary layer [129,130]. These vortices enhance momentum exchange between the free stream and the near-wall flow, increasing mixing and facilitating unsteady reattachment of separated regions [129,130]. As a result, the flow over the surface becomes more organized, circulation is modulated in a time-periodic manner, and aerodynamic performance is improved through increased lift and delayed flow separation [130].

Abdolahipour et al. [131] systematically investigated low- and high-reduced-frequency pulsed-jet actuation (0.2 ≤ $F^{+}$ ≤ 12) for separation control over an airfoil at a high Reynolds number of 1 × ${10}^6$ and an angle of attack of $16°$. Their results demonstrated that low actuation frequencies ($F^{+}$ = 0.2–1.2) produced strongly time-dependent aerodynamic forces and generated larger and more intense near-wall vorticity patches due to the longer blowing and suction phases [131]. These low-frequency excitations resulted in the largest time-averaged lift enhancement, with the maximum aerodynamic efficiency achieved at $F^{+}$ = 1, corresponding to a lift-to-drag ratio improvement of 28.62% [131]. In contrast, high-frequency actuation, particularly at $F^{+}$ = 12, generated smaller and less intense vortical structures due to the shorter duration of the blowing phase [131]. As a result, the aerodynamic forces became nearly time-invariant over an actuation cycle, and the highest time-averaged drag reduction of 15.7% was achieved [131].

The importance of excitation frequency is also closely linked to actuator performance. Arafa et al. [132] showed that the mean jet velocity produced by synthetic jet actuators depends strongly on the excitation frequency relative to the acoustic resonance modes of the cavity. Multiple resonant peaks were observed in large unified cavities, leading to non-uniform jet velocity and phase variations across orifice arrays, whereas compartmentalized cavities exhibited a single dominant resonance and more uniform jet output [132].

Murillo-Rincón and Duque-Daza [133] showed that synthetic jet actuation influences vortex evolution and turbulence in a frequency-dependent manner. Lower actuation frequencies produced stronger disturbances and enhanced turbulence levels near the jet exit, whereas higher frequencies led to weaker flow modification and reduced velocity fluctuations downstream [133].

The Stokes number has emerged as a particularly important nondimensional parameter for evaluating synthetic jet coherence. Coherent jets typically form only when the Stokes number exceeds a critical threshold, often around 8.5, and when the stroke length ratio is greater than 4 [109]. Below these values, vortex formation is weak or suppressed entirely, leading to low-momentum jets incapable of effective flow control or heat transfer. As the jet moves downstream, the increasing Kolmogorov length scale reflects vortex breakdown and reduced mixing efficiency [51]. Research has shown that counter-rotating vortex pairs near the orifice dissipate rapidly, becoming indistinct beyond one wavelength and causing significant velocity decay beyond $y/d$ $\approx$ 10, thereby highlighting challenges to long-range jet effectiveness [134]. This rapid jet diffusion in the far field has also been demonstrated earlier (Figure 4a) by Cater and Soria [18].

Another important parameter, the momentum coefficient $C_{\mu }$, defined as the ratio of synthetic jet momentum to the freestream momentum, plays a crucial role in aerodynamic applications such as flow separation control on lifting surfaces [135,136]. The methodology for estimating the momentum coefficient has been discussed in detail in the literature [135]. Increasing $C_{\mu }$ enhances jet penetration into the boundary layer, promoting flow reattachment, reducing separation, and improving lift and aerodynamic efficiency [135]. However, studies indicate the presence of a saturation threshold of $C_{\mu }$, beyond which further increases provide minimal additional benefits to flow control [135,136]. For example, for a NACA0015 airfoil studied at a chord Reynolds number of 1.1 × 10⁵, an excitation frequency of 175 Hz, angles of attack of 0°, 6°, and 12°, and momentum coefficients in the range 0.0044 ≤ $C_{\mu }$ ≤ 0.0688, it is reported that up to $C_{\mu }$ < 0.017, the mean lift coefficient increases almost linearly with $C_{\mu }$ [136]. This behavior suggests that, in the low-momentum regime, the injected jet momentum primarily compensates for momentum deficits associated with vortex shedding and enhances circulation without significantly altering the overall boundary-layer structure [135,136]. As $C_{\mu }$ increases beyond $C_{\mu }$ ≈ 0.017, the diminishing lift increment indicates that the boundary layer approaches a reattached or near-reattached state, such that additional momentum input increasingly contributes to local turbulence amplification, vortex breakdown near the jet slot, and unsteady mixing rather than further circulation enhancement [135,136].

While appropriate values of $Re$, $St$, $Stk$, and $L_o/d$ enhance near-field entrainment and vortex coherence, these advantages progressively weaken downstream due to vortex breakdown and diffusion. The combined limitations of insufficient jet formation and reduced jet strength beyond the near field represent fundamental challenges to employing SJs in applications demanding sustained and spatially extensive flow control.

3.3. Impact of Waveform on Flow Dynamics of SJs

The shape of the actuation waveform directly impacts the dynamic response of SJs, influencing the suction and ejection of fluid through oscillatory membrane motion. This, in turn, affects vortex formation and the momentum of the jet. In the region close to the wall, sine wave excitation typically leads to optimal performance, as it facilitates smoother transitions between the suction and blowing cycles, supporting stable vortex formation [69]. However, as the jet moves farther from the orifice, square waves prove more effective in delivering momentum due to their higher power input, enhancing jet strength. On the other hand, triangular waveforms fail to effectively stabilize the flow, resulting in weaker jet performance and a higher tendency for wake unsteadiness [69].

The type of actuator used further affects the jet velocity. With piezoelectric actuators, square and pulse waveforms generate stronger jets compared to sine wave excitations, which produce lower peak velocities [14]. The way the waveform is modulated also plays a significant role. Dual sine waves, when modulated at low frequencies and voltages, result in higher velocity ratios than single sine inputs at higher voltages, providing a more energy-efficient approach to generating momentum [137]. Similarly, square and sawtooth waveforms enhance the velocity profiles, with square waveforms producing the most robust jets in terms of peak output [138,139]. For a sinusoidal input signal, Ceglia et al. [140] systematically investigated the influence of the ejection duty cycle by varying it from 0.3 to 0.7, where a duty cycle of 0.5 corresponds to the baseline case of a standard symmetric sinusoidal waveform. Duty cycles lower than 0.5 shorten the ejection phase relative to suction, whereas higher duty cycles extend the ejection phase, thereby increasing the duration of fluid expulsion from the actuator [140]. At $St$ = 0.056, increasing the duty cycle enhanced heat transfer, reaching an improvement of about 8% at a duty cycle of 0.7, due to accelerated axial velocity growth and earlier shear-layer roll-up that strengthened vortex-ring formation and radial wall-jet development [140]. In contrast, at $St$ = 0.11, higher duty cycles degraded heat transfer, with the maximum enhancement of approximately 4.3% occurring at a duty cycle of 0.3 [140]. This behavior was linked to increased radial velocity fluctuations and turbulent dissipation at higher duty cycles, which weakened vortex coherence and reduced momentum preservation during wall spreading [140].

3.4. Flow Physics of Impinging Synthetic Jets

The flow field of a synthetic jet impinging normally on a flat surface is illustrated in Figure 10. The flow field can be broadly divided into four distinct regions, namely the near-field coherent vortex region, the free jet region, the impingement region, and the wall jet region [141]. In the near field of the orifice (Figure 10), the flow is characterized by the formation of discrete, coherent vortices and exhibits strongly periodic behavior [90,141]. Further downstream, these vortices interact and progressively lose coherence as the flow transitions into a synthetic free jet with turbulent characteristics, exhibiting self-similar behavior comparable to that of a continuous turbulent free jet but with an enhanced spreading rate [90,141]. As the jet approaches the impingement region near the surface, the axial velocity decreases rapidly and reduces to zero at the stagnation point [141]. Beyond this point, the flow is redirected radially outward along the surface, forming a characteristic wall jet, as shown in Figure 10 [90,141]. Building upon these observations, several studies have further elucidated the complex flow dynamics of impinging synthetic jets and their implications for heat transfer [142,143]. The near-wall flow is dominated by vortex ring dynamics, adverse pressure gradients, and the development of stagnation and wall jet regions, which together regulate momentum redistribution and turbulence generation at the surface [141]. The interaction of vortex structures with the impingement surface often results in characteristic velocity profiles, such as the formation of double-peak axial velocity distributions at short nozzle-to-plate distances ($Y/d$ < 4) and bell-shaped profiles at larger distances ($Y/d$ > 6) [143]. The impingement flow characteristics are strongly influenced by actuation parameters such as frequency and waveform. Sinusoidal waveforms produce smoother, wider velocity profiles and more coherent vortex formation, whereas square waveforms generate narrower profiles with less effective vortex development, thereby affecting vortex interactions and local turbulence intensity near the wall [101]. Additionally, Singh et al. [101] found that increasing the actuation frequency from 100 Hz to 175 Hz enhances vortex shedding rates and flow unsteadiness, leading to intensified turbulence and mixing near the impingement surface. Greco et al. [127] observed that at higher Strouhal numbers ($St$ = 0.044), the synthetic jet produces distinct vortex rings that impact the wall directly. In contrast, at lower Strouhal numbers ($St$ = 0.011), the flow is primarily influenced by the pronounced trailing jet, and the primary vortex ring triggers the formation of secondary vortex rings close to the wall following impingement. In configurations with multiple jets, such as twin [144] and quadruple synthetic jets [145], inter-jet interactions significantly modify the impingement flow by increasing axial momentum, turbulence levels, and generating complex coherent vortex structures, which directly enhance convective heat transfer by disrupting thermal boundary layers and promoting mixing [144,145].

Figure 10. Flow dynamics of a synthetic jet impinging on a flat surface.

A summary of the parameters influencing synthetic jet flow characteristics is presented in Table 2.

Table 2. Summary of parameters influencing synthetic jet flow characteristics.

Category	Parameter	Key Influence on Flow/Vortices
Geometry	Orifice shape [93,111]	Controls peak centerline velocity and vortex spreading; triangular orifices yield higher peak velocity but exhibit faster downstream decay compared to circular, square, and slot orifices.
	Orifice edge [39,96,113,114]	Sharp edges promote abrupt shear-layer separation, enhancing vortex roll-up and axial momentum; rounded edges reduce losses but produce weaker, less coherent vortices with increased spreading.
	Cavity dimensions [96,98,116,117,118,119]	Smaller cavity heights strengthen near-field vortex formation; resonance-sized cavities can maximize jet velocity under acoustic resonance conditions near the Helmholtz frequency.
Non-dimensional	Stroke length ($L_o/d$) [21,29,124]	Optimal vortex formation occurs for 4 ≤ $L_o/d$ < 8; larger values cause vortex instability and transition to trailing jets, reducing jet coherence.
	Reynolds number ($Re$) [39,125]	Higher $Re$ strengthens near-field vortex rings and momentum flux, but enhances vortex diffusion, leading to accelerated decay of jet velocity in the far field.
	Strouhal number ($St$) [106,108,127,128]	Governs vortex shedding, jet stability, and formation; for planar synthetic jets, jet formation requires ${\displaystyle \frac{1}{St}}={\displaystyle \frac{Re}{{Stk}^2}}>1.0$, while for axisymmeric jets, the threshold is ${\displaystyle \frac{1}{St}}={\displaystyle \frac{Re}{{Stk}^2}}>0.16$. Operation outside the optimal $St$ range suppresses coherent vortex formation and reduces control effectiveness.
	Stokes number ($Stk$) [51,109,134]	Coherent synthetic jets form only above a critical $Stk$ (≈8.5); low $Stk$ suppresses vortex roll-up and results in weak, ineffective jets.
Waveform	Waveform shape [14,69,137,138,139,140]	Sine wave excitation stabilizes near-field vortex formation; square wave excitation enhances jet momentum delivery and improves far-field jet strength.
	Waveform modulation [137,138,139]	Dual and modified waveforms improve jet velocity output and energy efficiency compared to single-frequency sine excitation.

4. Heat Transfer Characteristics of Synthetic Jets

Here, we focus on the heat transfer behavior of SJs under various geometric and nondimensional configurations, providing a comprehensive understanding of the mechanisms through which SJs enhance heat transfer. Additionally, the effectiveness of SJs in various cooling applications is examined, along with the challenges and limitations associated with their use for thermal enhancement.

4.1. Influence of Geometric Parameters on Heat Transfer Characteristics

A synthetic jet impingement configuration illustrating the jet-to-surface spacing ($Y$) is shown in Figure 11a. Among the common orifice shapes, such as circular, square, and rectangular, square orifices exhibit strong heat transfer performance in the near field but experience a significant decline as $Y/d_h$ increases, showing approximately a 46% drop in $\overline{Nu}$ between $Y/d_h\approx 6$ (where heat transfer peaks) and $Y/d_h\approx 20$ [92]. This significant drop in heat transfer is attributed to the drastic loss of jet strength at larger spacings [92]. A similar trend is observed for circular and rectangular orifices, where thermal enhancement diminishes noticeably with increasing $Y/d_h$ [92]. Nonconventional orifice shapes, such as diamond and oval, have demonstrated superior thermal performance compared to the traditional circular configuration (Figure 11b). At 200 Hz, diamond orifices provide up to 17% higher area-average heat transfer coefficient ($\overline{h}$) than circular ones (Figure 11b). However, a significant decline of approximately 40% in thermal performance is observed as the jet-to-surface distance increases from $Y/d_h\approx 6$ to $Y/d_h\approx 16$ [146]. Oval orifices perform better at smaller $Y$ and are particularly effective in compact configurations (Figure 11b), but like others, their efficiency deteriorates with $Y$ [146]. For the same hydraulic diameter ($d_h$ = 8 mm) and identical operating conditions (Stokes number $Stk$ = 71.78), a comparison of circular, square, rectangular, diamond, and oval orifices shows that square and rectangular orifices consistently outperform other geometries over a wide range of axial distances ($Y/d_h$ > 3) [146]. This superior performance is attributed to enhanced entrainment, which results in a higher mass flux impinging on the heated surface [146]. In contrast, oval and diamond orifices exhibit superior heat transfer primarily in the near field ($Y/d_h$ < 2), where axis switching and corner-induced azimuthal distortions promote early vortex breakdown, increased turbulence intensity, and enhanced local mixing [93]. However, this premature deformation of coherent vortex structures leads to rapid jet spreading and momentum loss, causing a marked reduction in thermal performance at larger axial distances ($Y/d_h$ > 6), where their entrainment rates asymptotically approach those of circular jets [143]. Circular orifices, while maintaining coherent vortical structures over longer distances due to uniform curvature, exhibit the lowest heat transfer because reduced vortex breakdown limits mixing and entrainment [93]. Despite variations in geometry, the overall trend remains a consistent decline in thermal performance with increasing $Y/d$ [43].

Figure 11. (a) Schematic of a synthetic jet impingement setup illustrating the jet-to-surface spacing ($Y$). (b) Area-average heat transfer coefficient ($\overline{h}$) as a function of axial distance for circular, diamond, and oval orifices with a hydraulic diameter of 8 mm at 200 Hz excitation frequency, reproduced with permission from [146].

The roles of orifice diameter, aspect ratio, and cavity depth are equally significant. Among these, the aspect ratio significantly influences near-wall behavior and jet development. Elliptical orifices with moderately low aspect ratios around 1.4 have been shown to enhance heat transfer at smaller $Y/d$ (<6) [147]. Increasing the aspect ratio tends to produce elongated vortex structures that improve mixing and momentum exchange near the surface compared to circular jets, thereby further enhancing heat transfer. However, increasing the aspect ratio beyond a certain threshold does not necessarily yield further improvement. In fact, doubling the aspect ratio has been associated with a decline in heat transfer performance by approximately 15%, highlighting that the geometric advantage is limited to specific operating conditions [147]. Similarly, increased cavity depth and hydraulic diameter contribute positively to heat transfer, with maximum Nusselt numbers typically occurring around $Y/d$ = 6 [148]. Additionally, optimizing the cavity design to operate at the actuator’s resonance frequency can significantly enhance heat transfer; however, this improvement diminishes as the jet-to-surface spacing increases beyond an optimal range [149]. These findings are consistent with previous studies showing that, although geometric optimization can significantly enhance thermal performance in the near field, the rapid decay of jet strength and coherence at greater distances remains a fundamental limitation [89,150,151,152].

Extensive investigations into orifice shape, size, and cavity configuration have demonstrated that thermal performance can be optimized under specific conditions. However, a consistent pattern emerges across the literature as synthetic jets are fundamentally limited by a rapid decline in momentum and vortex structure beyond the near field. This leads to a marked drop in heat transfer performance, typically in the range of 40–46% as spacing increases. The degradation is due to vortex diffusion, which disrupts the coherence of the jet and limits its effectiveness in the far field.

4.2. Influence of Dimensionless Parameters on Heat Transfer

The thermal performance of SJs is closely tied to their unsteady vortex dynamics and governed by $L_o/d$, $Re$, $St$, and $Stk$. These parameters collectively influence the formation, strength, and coherence of vortex structures, thereby modulating both local and global heat transfer behavior.

4.2.1. Nondimensional Stroke Length

The $L_o/d$ serves as a governing parameter for the thermal performance of SJs by regulating the formation, strength, and propagation of vortex rings. The dynamics of the vortices and the impingement heat transfer behavior of the synthetic jet operated at low, moderate and high $L_o/d$ are illustrated in Figure 12. At low values of $L_o/d<4$ (Figure 12a), the strong suction effect during the suction stroke disrupts vortex formation, resulting in underdeveloped primary vortices that dissipate rapidly. This leads to weak impingement and limited heat transfer enhancement (Figure 12a) [124]. As $L_o/d$ increases to a moderate range between 6 and 8, coherent vortex structures develop, enabling more effective momentum transfer and improved convective transport (Figure 12b). Within this regime, a marked increase in heat transfer at the stagnation region is observed, consistent with phase-resolved measurements that identify a transition in vortex behavior around $L_o/d\approx 5$ [110]. However, at higher $L_o/d$ values (Figure 12c), the unstable trailing jet promotes vortex instabilities and the formation of small secondary vortical structures, which reduce the coherence of the primary vortices before they impinge on the heated surface, leading to diminished thermal performance [124].

Figure 12. Variation in heat transfer characteristics of the synthetic jet actuator under (a) low-, (b) medium-, and (c) high-stroke-length conditions.

Experimental findings further support this trend, showing an enhancement of approximately 105% in the peak $\overline{Nu}$ at $Y/d$ = 2 when the stroke length ratio is reduced from $L_o/d$ = 13.75 to 7.86 [149]. However, even at the optimal $L_o/d$ = 7.86, a substantial 64% drop in $\overline{Nu}$ is observed between the near field ($Y/d$ = 2 corresponding to the peak) and the far field ($Y/d$ = 14), which is attributed to the pronounced reduction in jet strength with increasing $Y/d$. This decline in far-field performance, despite operating at the optimal $L_o/d$, aligns with findings reported by other researchers [149,153]. Ineffective heat transfer in the far field was also observed by Chaudhari et al. [149] for synthetic jets operating at ${Re}_{U_o}$ = 1500–4200. A similar trend was reported by Persoons et al. [154] across varying Strouhal numbers ($St$ = 0.15–0.35), indicating that the diminished thermal performance in the far field is largely insensitive to changes in these parameters.

Even when operated at a moderate $L_o/d$ (=10), synthetic jets exhibit another primary drawback, namely limited spanwise coverage (Figure 13). The radial distribution ($r/d$) of the time averaged Nusselt number ($\underset{\_}{Nu}$) at ${Re}_{U_o}$ = 5250 demonstrates a consistent decline in heat transfer intensity away from the jet centreline [155]. Regardless of $Y/d$ (Figure 13), the heat transfer performance reduces noticeably with increasing radial distance. For instance, at $Y/d$ = 4, $\underset{\_}{Nu}$ decreases by approximately 52% between $r/d$ ≈ 0 and 3.5 (Figure 13a), indicating a significant loss in thermal effectiveness across the surface. This observation reflects the concentrated nature of vortex-induced momentum transfer in synthetic jets, which remains dominant near the core but weakens rapidly with lateral distance. As a result, the inability to maintain strong radial coverage limits the suitability of synthetic jets for applications requiring broad and uniform thermal control [155]. This limitation is further highlighted in the work of Rylatt and O’Donovan [156], where thermal enhancement was predominantly confined to the core region.

Figure 13. Radial distribution of time-averaged Nusselt number ($\underset{\_}{Nu}$) for the synthetic jet operated at ${Re}_{U_o}$ = 5250, $L_o/d$ = 10 at (a) $Y/d$ = 4 and (b) $Y/d$ = 8, derived from data in [155].

Although operating at optimal stroke lengths enhances near-field heat transfer due to coherent vortex formation, SJs exhibit poor thermal performance in the far field as jet strength rapidly deteriorates with distance. Moreover, the spanwise coverage remains limited, as the influence of coherent structures is largely confined near the jet axis, restricting the effective cooling of large surface areas.

4.2.2. Influence of Oscillation Frequency

Frequency, though dimensional, is often characterized by dimensionless parameters like the Stokes number (Equation (11)), which relates frequency, orifice diameter, and fluid viscosity. SJAs perform optimally when operating near resonant frequencies, including mechanical or diaphragm resonance frequency ($f_d$) and fluidic or Helmholtz resonance frequency ($f_h$). The diaphragm resonance is primarily determined by the physical properties of the actuator membrane and its geometry [155], while Helmholtz resonance is influenced by cavity and orifice dimensions [157]. At these resonant conditions, membrane displacement and pressure oscillations are maximized, thereby enhancing the volume and strength of fluid ejection [97,98,99]. Previous studies have reported that for both circular and square orifices, the heat transfer increases with excitation frequency and reaches a maximum at the Helmholtz resonant frequency, after which it begins to decline [92,149]. However, even at the optimal resonant frequency, the area-averaged heat transfer coefficient in the far field ($Y/d_h$ = 20) shows a substantial decrease, with a reduction of about 40% for the circular orifice and about 45% for the square orifice compared with their respective peak values ($Y/d_h\approx 6.25$ for both orifices) [92,149]. Similarly, SJAs operated under different Reynolds numbers and heat flux conditions reveal that although resonance improves local mixing and impingement, the strength of the vortices deteriorates rapidly with increasing axial distance [11].

The frequency of oscillation significantly influences the near-field, far-field, and overall performance of SJAs [158,159]. Even beyond the resonance frequency (>$f_h$), SJAs demonstrate enhanced heat transfer in the near field ($Y/d$ ≈ 5) at a higher excitation frequency. This improvement is attributed to the more rapid generation and accumulation of coherent vortices near the orifice, which impinge collectively and enhance local mixing [158]. Ghaffari et al. [159] made a similar observation and further reported that the high frequency leads to increased power consumption and noise. This, in turn, reduces the coefficient of performance (COP), particularly in configurations operating above the diaphragm or Helmholtz resonance. Despite marginal gains in convective enhancement, the associated energy inefficiency and acoustic penalties make such operating conditions less favorable for practical applications [159]. Moreover, these densely packed vortices lose coherence rapidly as they propagate downstream, breaking into smaller, less effective structures, and consequently diminishing far-field performance [158,160]. In contrast, at lower frequencies, the spacing between successive vortex rings is larger, allowing each vortex to impinge independently on the target surface. This improves coherence retention and leads to better heat transfer further downstream [158].

To extend synthetic jet functionality beyond conventional frequency limits, operating in the ultrasonic regime (above 20 kHz) has shown promise in enhancing heat transfer by generating densely packed vortices that behave like a quasi-steady jet [19]. Piezoelectric-driven ultrasonic SJAs offer compactness and low noise, making them well-suited for micro-scale thermal applications [161,162]. Even with these advantages, far-field ineffectiveness in heat transfer is still observed due to the rapid decay of jet momentum downstream [19]. Together with this, excessively short stroke lengths at ultrasonic frequencies can limit net fluid displacement and volumetric flow rate [163], while thermal loading and material fatigue pose additional reliability concerns. Although operating SJAs at optimal (resonant) or ultrasonic frequencies enhances near-field performance, the steep decline in far-field effectiveness remains a concern for synthetic jets.

4.2.3. Jet-to-Heated Plate Distance ($Y/d$)

The behavior of synthetic jets at different $Y/d$ values has been extensively studied, revealing distinct regions of performance [11,23,42,44,110,150,154,158,164,165,166,167]. Based on previous findings [149], the relationship between heat transfer and $Y/d$ can be classified into three stages: increasing heat transfer ($Y/d$ < 5), maximum heat transfer ($Y/d$ = 5–9), and decreasing heat transfer ($Y/d$ > 9). These three trends are linked to three stages of jet development: premature (small $Y/d$), matured (intermediate $Y/d$), and over-matured (large $Y/d$), as explained in Figure 14.

Figure 14. Heat transfer characteristics of synthetic jets at different nondimensional jet to heated plate distances ($Y/d$): (a) small $Y/d$, (b) intermediate $Y/d$, and (c) large $Y/d$.

When $Y/d$ is small, the limited spacing between the orifice and the target surface prevents the vortices from fully developing before reaching the surface. In addition, the confined spacing traps hot air and promotes recirculation (Figure 14a). The heat transfer thus increases with increasing $Y/d$ in this regime [72,153]. The intermediate values of $Y/d$ (Figure 14b) allow for the full development of the primary vortices, with the impingement of coherent vortical structures on the surface resulting in the highest heat transfer [11]. On the other hand, when $Y/d$ is large (Figure 14c), the primary vortices lose significant coherence and even break into small vortical structures before impingement, leading to a sharp decline in cooling performance. Such behavior is consistently reported across multiple studies [92,149,158,159,167,168,169,170]. Gillespie et al. [11] noted up to a 36% drop in heat transfer between $Y/d$ = 18 (intermediate) and $Y/d$ = 23 (large).

In addition to heat transfer decay with increasing $Y/d$, synthetic jets suffer from significant limitations in spanwise coverage. For the single-orifice SJA at $Y/d$ = 6, a pronounced reduction in heat transfer is observed across the span, with the Nusselt number dropping by approximately 58% from the stagnation point ($r/d$ = 0) to the outer region ($r/d$ = 4) [171]. This is attributed to the rapid spanwise decay in jet strength [171]. A summary of the key parameters influencing synthetic jet heat transfer performance is presented in Table 3.

Table 3. Summary of key parameters influencing synthetic jet heat transfer performance.

Category	Parameter	Key Influence on Heat Transfer/Thermal Performance
Geometry	Orifice shape [92,146]	Square and rectangular orifices provide higher heat transfer over a wide axial range ($Y/d_h$ > 3), while oval and diamond orifices enhance heat transfer mainly in the near field ($Y/d_h$ < 2). Circular orifices yield more uniform but comparatively lower heat transfer. Irrespective of orifice shape, a significant decay in heat transfer is observed in the far field due to vortex weakening and increased jet spreading.
	Cavity parameters [148,149]	Cavity depth has little to no influence on the average heat-transfer coefficient once a sufficiently deep cavity is ensured (typically $H/d_h\ge 1$); beyond this point, the jet velocity and thermal performance remain nearly unchanged. While resonance-tuned cavities can enhance near-field heat transfer by maximizing jet velocity, their influence diminishes at larger jet-to-surface spacings.
Non-dimensional	Stroke length ($L_o/d$ = ${\displaystyle \frac{1}{2St}}$) [110,124,149,153]	Maximum heat transfer occurs at $L_o/d$ ≈ 6–8 due to coherent vortex formation; $L_o/d$ < 4 weakens vortex generation, while $L_o/d$ > 8 causes vortex instability and reduced performance. Even at the optimal $L_o/d$ ≈ 7.86, heat transfer exhibits a significant decay in both axial and radial directions.
	Reynolds number (${Re}_{U_o}$) [149,154]	Increasing ${Re}_{U_o}$ (1150–4180) enhances heat transfer, but higher ${Re}_{U_o}$ accelerates far-field decay due to vortex breakdown.
	Frequency of oscillation (linked to Stokes number; see Equation (11)) [97,98,99,149,155,157]	Heat transfer peaks when the SJA is operated near the Helmholtz resonance frequency; however, even at resonance, far-field performance still drops significantly by approximately 40–45%. Operating the SJA in the ultrasonic regime (>20 kHz) generates dense vortices, improving near-field heat transfer, but significant far-field decay still exists.
	Jet-to-surface distance ($Y/d$) [11,72,149,153,158,167]	Heat transfer increases for $Y/d$ < 5, peaks at $Y/d$ ≈ 5–9, then decreases sharply beyond $Y/d$ > 9 due to vortex diffusion and loss of coherence; typical 40–46% drop from near to far field.
Waveform	Waveform shape [92,103]	At low $St$ (<0.06), square and rectangular waves enhance stagnation-point heat transfer via stronger instantaneous ejection; at critical $St$ (≈0.24–0.48), triangular waveforms maximize heat transfer through coherent vortex formation and accelerated impingement; sinusoidal waves yield higher area-averaged heat transfer at intermediate $St$ (≈0.06–0.24); excessively high $St$ (>1.2) lead to premature vortex breakdown and reduced thermal performance.

5. Technological Advancements of Synthetic Jets

A detailed flow and heat transfer study identified three fundamental drawbacks of SJs: (a) limited jet formation, particularly when driven by a single actuator; (b) reduced spanwise effectiveness, which limits their applicability in scenarios requiring wide area coverage; and (c) diminished far field performance due to the rapid decay of jet strength caused by strong vortex diffusion. Collectively, these limitations constrain the practical implementation of synthetic jets in real-world applications. Here, various technological advancements aimed at addressing these limitations are discussed in detail, with a focus on their effectiveness in enhancing SJ performance.

5.1. Dual Cavity Synthetic Jets (DSJs)

Dual synthetic jets (Figure 15), consisting of two actuators adjacent to each other and operating either in phase or out of phase, offer greater control over vortex interactions compared to a single SJ [121]. When the DSJ operates in phase ($\varnothing$ = 0°), each actuator generates a pair of counter-rotating vortices, namely vortices $1^{-}$ and $1^{+}$ from SJA 1, and $2^{-}$ and $2^{+}$ from SJA 2 (Figure 15a). Due to their opposite sense of rotation, the inner vortices ($1^{+}$ and $2^{-}$) undergo destructive interaction near the centerline, while the outermost vortices ($1^{-}$ and $2^{+}$) evolve through interaction with the ambient fluid to form merged vortices, denoted as $M^{-}$ and $M^{+}$, respectively (Figure 15a). These merged vortices convect in a straight downstream direction (Figure 15a and Figure 16a). Studies have reported that under in-phase operation, the volume flow rate produced by the DSJ is approximately twice that of a single synthetic jet actuator (Figure 16c) [121].

Figure 15. Schematic representation showing (a) dual synthetic jets operated in phase ($\varnothing =0°$), (b) DSJ operated with a phase difference where SJA 2 leads SJA 1, and (c) demonstration of vectoring angle ($\beta$) calculation.

Figure 16. Schlieren visualization of DSJ operated at (a) $\varnothing =0°$ and (b) $\varnothing =60°$. (c) Streamwise variation (y*) of normalized volume flow rate for single (${Q_s}^{*}$, ○) and DSJs (${Q_a}^{*}$, □). (d) Decay of centerline velocity ($V_{cl}/U_o$) for a single synthetic jet (○) and DSJs (□) operated at $\varnothing =0°$. The solid line shows the $y^{-1/2}$ decay law. Reproduced with permission from [121].

In contrast, when a phase difference ($\varnothing$) is introduced between the actuators (Figure 15b), with SJA 2 leading SJA 1, vortices $2^{-}$ and $2^{+}$ form earlier and convect with their self-induced velocities. The wake generated by the leading vortices entrains the lagging vortices $1^{-}$ and $1^{+}$, which share the same rotational direction. This interaction leads to momentum transfer from the lagging to the leading vortices, which in turn causes vectoring of the resultant jet toward the leading actuator (Figure 15b and Figure 16b). This directional control, or vectoring, was later attributed to a mechanism known as the “attract impact causing deflection” (AICD) [172]. The vectoring angle ($\beta$) is typically measured as the angle between the vertical axis ($y$ = 0) and the direction of convection of the resultant jet (Figure 15c and Figure 16b). The angle is considered positive when the jet vectors toward the leading actuator and negative when it vectors toward the lagging actuator [123]. Further studies have shown that the vectoring angle increases with increasing phase difference [121,173].

DSJs offer advantages over single-actuator SJs by generating multiple vortices that entrain more surrounding fluid, thereby increasing the volume flow rate [121]. Additionally, their vectoring capability enables wider spanwise coverage [121,173,174]. However, far-field ineffectiveness remains a key drawback of DSJs. For $\varnothing$ = 0° (Figure 15a), the counter-rotating inner vortices ($1^{+}$ and $2^{-}$) lead to significant destructive interference in the near field. This interaction diminishes vortex coherence and results in a noticeable reduction in jet strength downstream [121]. The centerline velocity decay ($V_{cl}/U_o$), plotted against the non-dimensional streamwise distance ($y^{*}$), is shown in Figure 16d. For the single SJA, $y^{*}=y/d$, whereas for the DSJ, $y^{*}=y/2d$, where $2d$ represents the total orifice width of the dual configuration. This scaling is adopted to enable a direct comparison of the streamwise evolution of the single jet and the merged jet pair based on their respective total exit widths [121]. It can be interpreted from Figure 15d that, beyond $y^{*}\approx 15$, although the DSJs retain a modest advantage in velocity magnitude over the single SJs, both configurations exhibit significant decay.

Berk et al. [175] investigated effects of ${Re}_{U_o}$ (171–856), Strouhal number ($St$ = 0.02–0.12), orifice spacing ($s/d$ = 2–3), and phase difference ($\varnothing$ = 100–150°) on the flow behavior of DSJs, while maintaining a fixed aspect ratio ($AR$ = 13). While the Reynolds number showed limited influence on vectoring, greater $St$ amplified jet deflection. For smaller orifice spacings ($s/d$ = 2.2 and 2.4), the vectoring angle increases noticeably with higher phase differences (Figure 17a). However, these conditions also intensified vortex interactions, diminishing jet momentum. For example, at $s/d$ = 2.2 and $\varnothing$ = 100–140°, jet vectoring angle increased by ~31° (Figure 17a), but the normalized jet momentum flux ($J/J_o$) dropped by nearly 45% (Figure 17b). Here, the jet momentum flux $J$ is defined as [175]

$$J={\int }_{-90°}^{90°} \rho {V_n}^2 \left(r,\alpha \right) r d\alpha .$$

(13)

Here, $\rho$ is the air density, $V_n$ is the normal velocity, $r$ is the radial distance from the origin, and $\alpha$ is the angle measured from the vertical axis. The momentum flux is normalized by $J_o$, the reference momentum flux, which is calculated using the time-averaged velocity at the orifice exit. This decline in normalized momentum flux is attributed to enhanced vortex interaction, where destructive interference and the formation of smaller secondary vortices disrupt the primary flow structures [175]. Similar reductions in jet strength due to strong inner vortex interactions have also been reported at small orifice spacings [176], with the merged structure mimicking a single jet rather than two distinct sources. For DSJs, research has reported that while cavity geometry has minimal influence on jet dynamics, stroke length and Reynolds number play a crucial role in jet development and deflection [173]. The influence of phase difference and actuator spacing on the vectoring and mixing characteristics of DSJs in both quiescent and crossflow environments has been extensively investigated [20,174,177,178,179,180,181,182,183,184,185,186,187,188,189].

Figure 17. (a) Vectoring angle ($\beta$) and (b) normalized momentum flux ($J/J_o$) as functions of phase difference at $St=0.06$ and ${Re}_{U_o}=342$, reproduced with permission from [175]. (c) Comparison of time-averaged and area-averaged Nusselt number $\left(\underset{\_}{\overline{Nu}}\right)$ variation with $Y/d_h$ between a single-actuator SJ and a DSJ, reproduced with permission from [190].

Figure 17. (a) Vectoring angle ($\beta$) and (b) normalized momentum flux ($J/J_o$) as functions of phase difference at $St=0.06$ and ${Re}_{U_o}=342$, reproduced with permission from [175]. (c) Comparison of time-averaged and area-averaged Nusselt number $\left(\underset{\_}{\overline{Nu}}\right)$ variation with $Y/d_h$ between a single-actuator SJ and a DSJ, reproduced with permission from [190].

Luo et al. [191] introduced a novel synthetic jet actuator featuring two adjacent cavities driven by a single piezoelectric diaphragm, with a slide block separating the two slot orifices. They demonstrated that jet vectoring can be achieved by varying the position of the slide block. This design produces dual synthetic jets that merge downstream into a larger, combined synthetic jet. Greco et al. [144] studied the near-field flow behavior of single and twin synthetic jets. They found that at larger spacings between the two orifices ($s$ = $3d$ and $5d$), the twin jets behaved similarly to single jets. However, at close spacing ($s$ = $1.1d$), strong interactions between the jets produced a double vortex ring structure, resulting in increased centerline velocities and a reduced jet width.

DSJs have proven effective in aerodynamic flow control applications due to their ability to generate synchronized or phase-shifted vortex pairs, which enable precise manipulation of boundary layer behavior [192]. This makes them well suited to delaying flow separation, enhancing lift, and suppressing wake instabilities [187,188,193]. In particular, DSJs have demonstrated greater control effectiveness in managing flow over airfoils and bluff bodies compared to single actuators, owing to enhanced momentum addition [194].

In heat transfer applications, DSJs operated out of phase have demonstrated improved heat transfer performance compared to in-phase operation [195,196,197]. Specifically, DSJs with phase differences between 60° and 120° show enhanced heat transfer compared to all other phase configurations, primarily due to the vectoring effect and improved mixing characteristics with the surrounding fluid [197]. Furthermore, in applications requiring localized cooling, such as hot spot mitigation, phase differences between 135° and 180° have been found to be most effective [197]. The heat transfer benefits of DSJs over single SJs have also been reported in the literature [150,190]. At $Y/d_h$ = 6, the heat transfer enhancement between the DSJ and single SJ is approximately 32% (Figure 17c) [190]. However, this enhancement drastically reduces to about 10% at $Y/d_h$ = 8, with further decrease in performance as $Y/d_h$ increases (Figure 17c). This suggests that DSJs exhibit superior heat removal capabilities at lower jet-to-surface distances, facilitated by the formation of twin vortex rings and strong inter-jet interactions, a phenomenon also noted by other researchers [150]. In the far downstream, DSJs resemble single SJs (Figure 17c, $Y/d_h$ > 20), demonstrating their ineffectiveness in the far field. This decline in performance is attributed to extensive vortex diffusion, a phenomenon well documented in the literature [150,190]. Greco et al. [144] found that at lower jet-to-plate spacing ($Y/d$ < 4), the impinging flow of twin synthetic jets exhibits higher axial velocities and turbulence levels near the plate compared to single jets, due to strong jet interactions. They also observed that when a phase difference of 180° is introduced between the actuators, significant destructive interaction occurs between the jets, drastically reducing the jet strength [145].

5.2. Single-Actuator Multi-Orifice Synthetic Jets

Another advancement in SJ technology is the single-actuator multi-orifice configuration (Figure 18a), in which a single actuator simultaneously drives multiple orifices [198]. The multi-orifice design, typically featuring a central orifice encircled by satellite orifices (Figure 18b), enhances fluid entrainment and mixing near the surface, thereby significantly improving convective heat transfer [198]. Under the same jet operating parameters (${Re}_{U_o}$ = 2600), multi-orifice synthetic jets with the C5 × S3 × 8 configuration (where 5 mm is the diameter of the central orifice, 3 mm is the diameter of the satellite orifices, and 8 is the number of satellite orifices) achieve higher heat transfer than single-orifice synthetic jets (Figure 19) [198]. The heat transfer enhancement measured at $Y/d$ = 8 (Figure 19a) for the C5 × S3 × 8 jets at ${Re}_{U_o}$ = 2600 is approximately 20% percent greater than that of conventional single-orifice synthetic jets with an 8 mm diameter under identical conditions (${Re}_{U_o}$ = 2600) [198]. For the same hydraulic diameter ($d_h$ = $d$ = 14 mm) and the same operating parameters ($f$ = 125 Hz and $a$ = 4 V), the heat transfer enhancement achieved with multi-orifice synthetic jets, compared to a single orifice, is also observed along the spanwise direction in the near field ($Y/d$ = 2) (Figure 20a) [171].

Figure 18. Schematic representation of a multi-orifice synthetic jet actuator: (a) 3D view of a synthetic jet actuator with five circular orifices and (b) front view of the orifice plate illustrating the central and satellite orifices arranged along a defined pitch circle radius (PCR).

Figure 19. (a) Variation of $\overline{Nu}$ with $Y/d$ showing (a) heat transfer enhancement of multi-orifice synthetic jets over single-orifice, and (b) significant performance degradation of multi-orifice SJs in the far field. Data derived from [198]. Configuration C5 × S3 × 4 denotes center orifice diameter × satellite orifice diameter × number of satellite orifices.

Figure 20. Comparison of local Nusselt number distribution along the radial direction between multi-orifice synthetic jets and single-orifice SJs with the same hydraulic diameter of 14 mm, operated at 125 Hz frequency and 4 V amplitude, at (a) $Y/d$ = 2 and (b) $Y/d$ = 6, based on data from [171].

Chaudhari et al. [198] investigated the effect of Reynolds number (1000–2600) on heat transfer in multi-orifice synthetic jets. They found that increasing the Reynolds number consistently raises the peak $\overline{Nu}$ across all configurations. Configurations with fewer satellite orifices, such as 5 × 3 × 2 and 5 × 3 × 4 (where 5 mm and 3 mm are the central and satellite orifice diameters, respectively), show two distinct $\overline{Nu}$ at normalized axial distances of approximately $Y/d$ ≈ 2 and $Y/d$ ≈ 9, regardless of Reynolds number [198]. In contrast, the 5 × 3 × 8 configuration with more satellite orifices exhibits a single $\overline{Nu}$ peak that increases monotonically up to $Y/d$ ≈ 10 before declining, independent of Reynolds number. The percentage increase in $\overline{Nu}$ is due to the Reynolds number rise being greater at the first peak (about 85%) than the second peak (about 38%) for the 5 × 3 × 2 case between ${Re}_{U_o}$ = 1400 and 2600 [198]. Additionally, increasing the Reynolds number from 1450 to 2600, the maximum $\overline{Nu}$ enhancement between low (5 × 3 × 2) and high (5 × 3 × 8) satellite orifice configurations differs by approximately 12%, indicating a stronger Reynolds number influence in configurations with more satellite orifices [198].

The influence of Stokes number on the heat transfer behavior of multi-orifice synthetic jets revealed a small increment of peak $\overline{Nu}$ by approximately 4–8% for a 15–30% increase in Stokes number, within the considered range of 50.75 to 80.25 [199]. The peak positions of $\overline{Nu}$ also remain nearly unchanged across the range of Stokes numbers studied [199].

For different orifice shapes, including circular, oval, and diamond configurations, the pitch ratio $R$, defined as the pitch circle radius (Figure 18b) normalized by the hydraulic diameter of the central orifice, plays a significant role in governing the heat transfer behavior of multiple orifice synthetic jets [199]. Within the investigated range ($R$ = 1 to 1.75), the maximum $\overline{Nu}$ is consistently observed at $R$ = 1.25, irrespective of orifice shape, and is accompanied by the appearance of two distinct $\overline{Nu}$ peaks located at $Y/d$ ≈ 2 and $Y/d$ ≈ 6, respectively [199]. At lower pitch ratios ($R$ = 1.25), strong interactions between the central and satellite jets give rise to secondary maxima $\overline{Nu}$. As the pitch ratio increases further to $R$ = 1.5, these secondary peaks disappear due to weakened inter-jet interactions [199].

Research has also reported that a configuration consisting of a central orifice surrounded by satellite orifices provides improved cooling performance for compact electronic components that require localized heat dissipation [198]. Interestingly, such heat transfer enhancements occur without increasing input power. The multi-orifice configuration can slightly reduce power consumption compared to single-orifice actuators [198].

When integrated into electronic cooling systems such as heat sinks, multi-orifice synthetic jets have demonstrated superior thermal performance [17,200]. During impingement on the heat sink surface, these jets showed a 12% increase in the maximum heat transfer coefficient compared to single-orifice jets, and an overall heat transfer enhancement nearly six times greater than that achieved by natural convection [200]. Despite these benefits, multi-orifice jets, like single-orifice SJs, exhibit ineffective performance in the far field [198]. For example, the $\overline{Nu}$ for satellite orifices (C5 × S3 × 4) at ${Re}_{U_o}$ = 2440 decreases by approximately 50% between $Y/d$ = 10 and 24 (Figure 18b), which Chaudhari et al. [198] attributed to rapid vortex diffusion in the far downstream region. This decline in far-field performance has been observed across various multi-orifice shapes, including circular, oval, and diamond configurations, as well as different waveforms [102,199,201,202].

Single-actuator multi-orifice synthetic jets exhibit superior heat-transfer performance in the near field (Figure 20a, $Y/d$ = 2) compared to single-orifice SJs; however, this advantage progressively diminishes at larger orifice-to-surface spacings (Figure 20b, $Y/d$ = 6) due to changes in vortex dynamics and turbulence evolution [171,198]. As reported by Kumar et al. [171], at low axial spacings ($Y/d$ ≈ 2), the multi-orifice configuration generates higher vorticity with a larger radial spread. In addition, the satellite vortices impinge separately on the heated surface, which limits the accumulation of hot fluid near the stagnation region and enables continuous replacement by cooler jet fluid. This strengthened wall–jet interaction enhances local mixing and convective transport, resulting in a higher average Nusselt number compared to a single-orifice synthetic jet in the near field.

In contrast, as the axial distance increases ($Y/d$ > 5), the vortices generated by the center and satellite orifices in a multi-orifice jet begin to interact and merge, forming larger composite vortex structures. As reported by Kumar et al. [171], these merged structures become unstable and break down earlier (4 < $Y/d$ < 6) than those in a single-orifice jet, resulting in reduced vorticity, weaker entrainment, and lower turbulence intensity. Consequently, the multi-orifice configuration exhibits reduced surface heat transfer compared to a single-orifice synthetic jet, in which more coherent vortical structures persist farther downstream and sustain effective mixing near the heated surface. This suggests that the performance benefits of multi-orifice arrangements are primarily limited to the near field [171].

5.3. Coaxial Synthetic Jets (CSJs)

Coaxial synthetic jets, another technological advancement based on their structural configuration and actuation method, are categorized into three types: (a) double acting synthetic jets with concentric cavities driven by a common actuator (Figure 21); (b) concentric orifice single-actuator synthetic jets, which use one actuator to supply multiple concentric orifices (Figure 23); and (c) independently controlled coaxial synthetic jets, featuring separate actuators for each element (Figure 24).

Figure 21. Operating principle of a DASJs showing (a) ejection from the inner cavity and suction into the annular cavity during the forward stroke, and (b) suction from the inner cavity and ejection from the annular cavity during the backward stroke.

5.3.1. Double-Acting Synthetic Jets (DASJs)

In the DASJ configuration, both the inner and annular cavities are actuated by a common mechanism operating in anti-phase (Ø = 180°). During one half-cycle, the inner cavity expels fluid while the annular cavity simultaneously draws it in (Figure 21a). This flow pattern reverses in the subsequent half-cycle, with the annular cavity ejecting fluid and the inner cavity inducing suction (Figure 21b).

Particle image velocimetry studies reveal that the vortex formed by the inner cavity during the ejection phase develops within a strong opposing suction field generated by the annular cavity. This suction suppresses radial momentum diffusion, keeps the forming vortex attached close to the orifice exit, and extends the vortex growth phase before pinch-off. As a result, circulation accumulates more efficiently within the shear layers, leading to significantly higher instantaneous and peak vorticity levels in DASJs compared to single-acting configurations [12].

The suction-induced confinement mechanism is responsible for the time-averaged velocity fields, which exhibit narrow, flat-top axial velocity profiles that remain highly concentrated along the centerline. This results in significantly reduced jet spreading compared to single-acting synthetic jets [12]. This confinement significantly enhances vortex strength and preserves axial momentum over longer distances, making DASJs particularly advantageous for applications that require high localized momentum delivery, deep flow penetration, or targeted actuation, such as boundary-layer reattachment, localized flow control, and impingement on confined surfaces. However, the elevated vorticity and concentrated momentum flux associated with DASJs are accompanied by pronounced jet narrowing, which inherently limits lateral coverage. Consequently, in applications such as surface cooling, where a uniform spatial distribution of momentum and heat transfer is desired, the confined nature of DASJs may reduce overall effectiveness [12].

To address the limitation of the jet narrowing effect and less spanwise coverage, researchers modified the geometric configuration of DASJs [203]. Ahmed and Bangash [203] reported that when the radial spacing ($S_r$) between the inner orifice and the outer annular opening (as shown in Figure 21b) is maintained at $1d$, the jet width is significantly enhanced compared to a single orifice synthetic jet. At this spacing ($S_r$ = 1), the interaction between the vortices from the inner and annular cavities promotes vortex stretching and instability, which increases lateral spreading and broadens the jet. However, when the radial spacing is reduced (e.g., to 0 or $0.5d$), the strong suction effect from the annular cavity suppresses radial momentum diffusion, causing the jet to remain narrower and reducing its spanwise coverage.

In a coaxial jet configuration, where the inner jet is continuous, and the annular jet is a synthetic jet, it has been observed that at lower inner jet Reynolds numbers (${Re}_{U_o}$ = 1600), where the inner jet remains laminar, synthetic jet actuation at Strouhal numbers ranging from 0.28 to 0.6 significantly accelerates the transition to turbulence. This results in enhanced jet spreading and increased entrainment [204]. This effect occurs because the synthetic jet introduces perturbations near the jet’s natural preferred frequencies, triggering early vortex formation and promoting mixing. In contrast, at higher Reynolds numbers (${Re}_{U_o}$ = 5500), where the inner jet is already turbulent, the synthetic jet still enhances spreading and entrainment, but the effect is less pronounced due to the reduced sensitivity of turbulent flow to additional excitation [204].

While manipulating the design and operating parameters of DSJs enhances jet spreading [203], this improvement often comes at the expense of a significant reduction in the centerline velocity (Figure 22) [60]. Specifically, the centerline velocity $(V_{cl}/U_i)$ decreases by approximately 56% between $y/d_i$ = 0.5 and $y/d_i$ = 10 (Figure 22), where $U_i$ and $d_i$ are the time-averaged velocity and diameter measured at the inner orifice exit, respectively [60]. This reduction is due to the weakening of vortex structures downstream [60,203].

Figure 22. Variation in jet centerline velocity $(V_{cl}/U_i)$ along the streamwise direction ($y/d_i$) of the DASJs operated at Reynolds number ${Re}_{U_i}=1.3\times {10}^4$ for nozzle B configuration with inner diameter $d_i$ = 10 mm and outer diameter $d_o$ = 25 mm. Figure adapted from [60], licensed under CC BY 4.0.

5.3.2. Concentric Orifices Single-Actuator Synthetic Jets (COSASJs)

In the COSASJs configuration (Figure 23), both the inner and outer orifices operate simultaneously, generating coordinated vortex structures that enhance jet formation and increase the overall flow volume [205]. Studies using infrared thermography and smoke wire visualization at ${Re}_{U_o}$ = 3490, 5830, and 7360, corresponding to actuation amplitudes of 2 V, 4 V, and 6 V, respectively, and different orifice-to-surface spacings, have demonstrated significant improvements in convective heat transfer when this configuration operates close to the heated surface [205]. It has been observed that increasing the Reynolds number from 3490 to 7360 leads to an approximate 56% increase in the peak $\underset{\_}{\overline{Nu}}$. This enhancement is primarily attributed to the stronger vortex structures and increased jet momentum generated at higher Reynolds numbers, which promote better mixing and more effective disruption of the thermal boundary layer, thereby intensifying convective heat transfer [205]. Research reported that at smaller spacings ($Y/d$ = 2), the COSASJ configuration with dimensions 1.5_4_10.6 (where $w_s$ = 1.5 mm, $d_i$ = 4 mm, and $d_{o1}$ = 10.6 mm) achieves an approximately 20% increase in the time- and area-averaged Nusselt number ($\underset{\_}{\overline{Nu}}$) compared to conventional single-orifice synthetic jets of 12 mm diameter [205]. The equivalent diameter $d$ used for normalization is defined such that the total discharge area of the coaxial configuration equals the area of a 12 mm single orifice [176]. The enhancement in $\underset{\_}{\overline{Nu}}$ for the COSASJ at $Y/d$ = 2 is primarily attributed to independent vortex generation from the inner and outer orifices, which strengthens local mixing, disrupts the thermal boundary layer, and suppresses hot-air recirculation near the heated surface [205].

Figure 23. Comparison of time-averaged Nusselt number distribution along the radial direction between COSASJs and single-orifice SJs with the same hydraulic diameter of 12 mm, operated at ${Re}_{U_o}$ = 5830 at $Y/d$ = 10, based on data from [205].

However, for $Y/d$ ≥ 6, the thermal performance of COSASJs begins to deteriorate, becoming lower than that of single-orifice jets [205]. This decline is attributed to rapid vortex energy dissipation, which weakens momentum transport in the far field and reduces the effectiveness of jet-surface interaction [205]. This decline in heat transfer occurs because the larger vortex structures generated by the coaxial synthetic jets do not travel as far downstream and break down earlier compared to the vortices formed by single-orifice jets [205]. As a result, the momentum and coherence of these vortices dissipate more rapidly, weakening momentum transport and reducing the effectiveness of jet-surface interaction [205]. Flow visualization confirms that while single-orifice jets maintain vortex rings and trailing jets over longer distances, the coaxial jet’s larger vortices entrain surrounding fluid quickly, become bulky, and dissipate sooner, limiting their heat transfer performance at larger surface spacings [205]. A similar trend is observed in the radial distribution of heat transfer (Figure 23), where COSASJs demonstrate inferior performance compared to single-orifice jets at $Y/d$ = 10 [205].

5.3.3. Independently Controlled Coaxial Synthetic Jets (IC-CSJs)

Among all coaxial synthetic jet configurations, independently controlled coaxial synthetic jets (Figure 24) stand out for their ability to precisely regulate frequency, amplitude, and phase of each actuator separately, enabling fine-tuned control over jet behavior [206]. Such independent control enables precise modulation of vortex interactions, leading to more efficient momentum transfer and enhanced entrainment [16,206]. The flow dynamics of IC-CSJs involve the formation, evolution, and interaction of the inner vortex ring (IVR) generated by the inner actuator and the annular vortex ring (AVR) formed by the annular actuator [206,207]. In a two-dimensional representation, the annular actuator produces a pair of counter-rotating vortices, denoted as $A^{-}$ and $A^{+}$, corresponding to anticlockwise and clockwise rotations, respectively, while the inner actuator generates vortices $I^{-}$ and $I^{+}$ with the same rotational convention (Figure 24). The dynamics of these vortex structures under varying jet operating conditions have been extensively reported in the literature [206,207].

Figure 24. Schematic of IC-CSJs illustrating key components.

A crucial parameter governing IC-CSJ behavior is the mass flux ratio ($M_r$), defined as the ratio of the mass flux of the inner jet ($M_{inn}$) to that of the annular jet ($M_{ann}$) [206]. The mass flux for each jet is expressed as $M_{inn}$ = $\rho {\left(U_o\right)}_{inn}$ and $M_{ann}$ = $\rho {\left(U_o\right)}_{ann}$, where ${\left(U_o\right)}_{inn}$ and ${\left(U_o\right)}_{ann}$ are the time-averaged velocities of the inner and annular jets, respectively. This ratio is typically varied by modifying the annular jet’s frequency and amplitude of oscillation [206]. Panda et al. [206] performed a detailed numerical investigation at ${Re}_{U_o}$ = 150 to examine the influence of mass flux ratio ($M_r$ = 0.25–3) on the flow behavior of IC-CSJ and compared the results with those of independently operated inner and annular actuators. According to their findings, when the IC-CSJ is operated at the lower end of this range ($M_r$ = 0.25), the resulting jet exhibits superior flow characteristics compared to other mass flux ratios, as well as to the inner and annular jets operating individually (Figure 25). Specifically, the jet maintains a stronger volume flux ($Q/Q_o$) throughout the streamwise domain (Figure 25a), a wider half-width ($b_{1/2}/d_h$) (Figure 25b), and a significantly higher centerline velocity (Figure 25c). For the three-dimensional simulated case, the detailed methodology for estimating the volume flux and jet half-width has been comprehensively documented in the literature [206]. Here, the hydraulic diameter ($d_h$) is maintained at 1.5 mm for both the inner and annular orifices [206]. The enhanced volume flux corresponds to the generation of a larger flow rate, while the wider jet half-width and higher centerline velocity indicate greater spanwise coverage and sustained jet strength in the far field, respectively, for IC-CSJs compared to single-actuator synthetic jets [206]. The enhanced performance of the IC-CSJ at the lower mass flux ratio ($M_r$ = 0.25) arises from an effective interaction between the strong annular jet momentum and the inner jet, which promotes intensified vortex interactions, improved mixing, and a coherent, sustained jet structure [206].

Figure 25. Variation in normalized (a) jet volume flux ($Q/Q_o$), (b) jet half-width ($b_{1/2}/d_h$), and (c) centerline velocity ($V_{cl}/U_o$) along the streamwise direction ($y/d_h$) for the ICASJs operated at different mass flux ratios ($M_r$) and ${Re}_{U_o}$ = 150. Results are compared with inner and annular cavity synthetic jets operated individually, reproduced with permission from [206]. The solid lines show the slope of their corresponding distributions.

This advantage becomes even more pronounced when the phase difference between the actuators is varied [207]. Introducing a phase difference between the inner and annular jets, where the annular jet leads in phase relative to the inner jet, facilitates constructive vortex interactions [207]. For instance, at $\varnothing$ = 180°, vortex pairing enhances the coherence and strength of the jet core, while intermediate phase differences such as $\varnothing$ = 90° and 135° induce azimuthal instabilities that enhance entrainment and volumetric growth [207]. The progressive increase in centerline velocity and jet volume flux with increasing $\varnothing$ is evident in Figure 26a and Figure 26b, respectively. These trends underscore the critical role of phase control in optimizing the full potential of IC-CSJ configurations [207].

Figure 26. Streamwise variation in independently controlled coaxial synthetic jets. (a) Normalized centerline velocity ($V_{cl}/U_o$) and (b) normalized jet volume flux ($Q/Q_o$) for different phase differences ($\varnothing$ = 0°, 45°, 90°, 135°, 180°) at ${Re}_{U_o}$ = 150, reproduced with permission from [207]. (c) Influence of mass flux ratio ($M_r$ = 0.7, 1.0, and 2.0) and (d) effect of phase difference ($\varnothing$ = 0°, 45°, 90°, 135°, 180°) at $M_r$ = 0.7 on centreline velocity at ${Re}_{U_o}$ = 1100, reproduced with permission from [16].

When operated at ${Re}_{U_o}$ = 1100, the IC-CSJ configuration demonstrates superior performance compared to single-actuator counterparts, as revealed through hotwire anemometry measurements (Figure 26c,d) [16]. The study considered $M_r$ = 0.7, 1, and 2. At the lower $M_r$ (=0.7), the centerline velocity attains a peak value that exceeds those of the inner and annular jets by 184% and 113%, respectively (Figure 26c). Furthermore, introducing a phase difference of 180° produces a 28.5% increase in peak centerline velocity compared with the in-phase case (Figure 26d) [16].

In thermal applications, IC-CSJ performance exhibits a similar trend with changes in $M_r$ (=0.5, 1, and 2) and phase difference ($\varnothing$ = 0–180°) [208]. Maximum heat transfer rates were achieved at the smaller $M_r$ (=0.5) with $\varnothing$ = 135°, indicating that the flow behavior strategies observed at lower $M_r$ for momentum transfer also contributes to enhanced thermal transport [208].

However, a comparison between the numerical and experimental results offers additional insights into Reynolds number sensitivity. Despite similar trends in flow structure and jet enhancement across both studies, the decay rate of the normalized centerline velocity $V_{cl}/U_o$ is significantly higher in the experimental case (Figure 26c). The numerical simulations, conducted at ${Re}_{U_o}$ = 150, exhibit a more gradual decay (Figure 25c), while the experimental study at ${Re}_{U_o}$ = 1100 reveals a steeper decline (Figure 26c). This difference is attributed to increased vorticity diffusion and turbulence intensity at higher Reynolds numbers, which accelerate the breakdown of vortex rings and cause earlier momentum dissipation in the far field [16,207]. Such behavior can constrain the far-field effectiveness of IC-CSJs, especially under high Reynolds number conditions.

5.4. Synthetic Jet Array (SJ Array)

The synthetic jet array (Figure 27) is composed of multiple independently controlled actuators placed adjacent to each other. Unlike multi-orifice SJs driven by a common diaphragm with uniform operating conditions [198], the SJ array allows individual control over frequency, amplitude, and phase difference for each actuator [123]. This precise control facilitates spatial and temporal modulation of the flow field, which enhances jet interaction and offers greater flexibility for flow manipulation and thermal management [123,209].

Figure 27. Schematic representation of a synthetic jet array.

5.4.1. Vectoring of Jets

Controlling the direction of synthetic jet propagation through phase manipulation has emerged as an effective strategy for achieving broader surface coverage compared to single-actuator synthetic jets [123]. Research has shown that when the actuators in a synthetic jet array operate in phase (Ø = 0°) (Case 1, Figure 31a), the resulting jet remains symmetric and directed along the streamwise axis (Figure 28). However, introducing a uniform linear phase difference between the actuators (Case 2, Figure 31a) causes the jet to deflect toward the actuator leading in phase [123] (Figure 28), with the extent of deflection strongly dependent on the operating Strouhal number [123]. In this configuration, the actuators from SJA 1 to SJA 4 operate with progressively increasing phase lag (Case 2, Figure 31a). At a low Strouhal number ($St$ = 0.028) and a phase difference of 90° (Figure 28a), the jet attained its maximum vectoring angle of 78°. At an intermediate Strouhal number ($St$ = 0.086), the vectoring angle was observed to vary with changes in the phase difference (Figure 28c). Notably, for $St$ = 0.086, a 90° phase difference produced a vectoring angle of 36°, while at $\varnothing$ = 180°, the jet curved toward the lagging actuator ($\beta$ = 10°), demonstrating the reversibility of jet direction based on phase configuration (Figure 28c) [123].

Figure 28. Directivity plots illustrating the resultant jet direction for various Strouhal numbers—(a) 0.028, (b) 0.057, (c) 0.086, (d) 0.115, (e) 0.130, and (f) 0.172—at a fixed Reynolds number (${Re}_{U_o}$) of 300, reproduced with permission from [123].

The dynamics of vortices originating from the SJ array, when operated at ${Re}_{U_o}$ = 300, $St$ = 0.086, and with different linear phase differences, is illustrated in Figure 29. For the SJ array operated at Ø = 0°, the phase-averaged vorticity field shows that vortices 2⁻ and 3⁺ are attracted toward the same-signed remnant vortices $R^{1-}$ and $R^{4+}$, respectively, which were formed during the previous actuation cycle (Figure 29a, $t/T$ = 0.5) [210]. This attraction drives the inner vortices $2^{+}$ and $3^{-}$ toward the jet centerline (Figure 29a, $t/T$ = 0.5), where they undergo destructive interaction due to their opposite sense of rotation, leading to a rapid loss of vorticity by $t/T$ = 0.75 (Figure 29a) [210]. In contrast, the outer primary vortices 1⁻ and 4⁺ continue to grow through interaction with the surrounding fluid and convect downstream under their induced velocities (Figure 29a, $t/T$ = 1) [210]. Consequently, for Ø = 0°, the downstream transport of the resultant jet is primarily governed by the evolution and convection of vortices $1^{-}$ and $4^{+}$ [210].

Figure 29. Phase-averaged visualization of vortex formation and interaction for the SJ array operated at ${Re}_{U_o}=300$, $St=0.086$ under different linear phase differences: (a) $\varnothing =0°$; (b) $\varnothing =60°$; (c) $\varnothing =90°$; (d) $\varnothing =180°$ [210].

When a linear phase difference of Ø = 60° is introduced between the actuators, with the actuators lagging in phase from SJA 1 to SJA 4, vortex $1^{-}$ interacts with vortex $2^{-}$ at $t/T$ = 0.75 (Figure 29b) and subsequently merges to form a combined structure $M^{-}$ at $t/T$ = 1 (Figure 29b) [210]. Similarly, vortex $3^{+}$ interacts with vortex $4^{+}$ and merges to form $M^{+}$ at $t/T$ = 1 (Figure 29b) [210]. During this merging process, momentum transfer from the lagging vortices ($2^{-}$ and $4^{+}$) to the leading vortices ($1^{-}$ and $3^{+}$) vectors the resultant jet toward the leading actuator, which becomes evident at $t/T$ = 1 (Figure 29b) [210].

For Ø = 90°, the remnant vortices $R^{(3^{-}+4^{-})}$ exert a strong repulsive influence on vortices $1^{-}$ and $1^{+}$ generated by SJA1, causing them to vector toward the leading actuator (SJA1) at $t/T$ = 0.5 (Figure 29c) [210]. Simultaneously, vortex 4⁻ interacts with the remnant vortex pair $R^{(3^{-}+4^{-})}$, transferring additional momentum to the evolving merged structure (Figure 29c, $t/T$ = 0.5) [210]. The combined effects of vortex repulsion, interaction, and momentum transfer result in the strongest jet vectoring observed at $St$ = 0.086 for Ø = 90° (Figure 28c) [123].

At Ø = 180°, adjacent actuators operate in alternating ejection and suction phases. At $t/T$ = 0.25, vortices generated by SJA1 ($1^{-}$,$1^{+}$) and SJA3 ($3^{-}$,$3^{+}$) experience strong suction induced by the neighboring actuators SJA2 and SJA4, respectively, causing the vortical structures to bend toward the lagging actuators (Figure 29d) [210]. This bending becomes more pronounced by $t/T$ = 0.5, as vortices $1^{-}$ and $3^{-}$ are additionally attracted toward the remnant vortices $R^{2-}$ and $R^{4+}$, leading to significant momentum transfer (Figure 29d) [210]. As a result, the resultant jet is vectored toward the lagging actuator, SJA4, which is clearly observed at $t/T$ = 1 in Figure 29d and is consistent with the overall jet deflection shown in Figure 28c [210].

The variation in the non-dimensional jet momentum flux ($J/J_o$) for the SJ array operated at ${Re}_{U_o}$ = 300, $St$ = 0.086, and for various phase differences is shown in Figure 30a. It can be seen from Figure 30a that the peak $J/J_o$ decreases progressively as the phase difference increases up to Ø = 90° [123]. This reduction is attributed to the enhanced interaction and mutual interference among neighboring vortical structures (observed in Figure 29a–c), which weakens coherent momentum transport in the streamwise direction. For larger phase differences, particularly at Ø = 180°, the jet momentum flux partially recovers (Figure 30a) [123]. This recovery occurs because the direct interaction between vortices generated by adjacent actuators is significantly reduced, as the actuators operate in opposite phases (Figure 29d). Nevertheless, the recovered momentum flux remains lower than that observed at Ø = 0°, since vortices formed during the ejection phase experience a strong suction effect from neighboring cavities (Figure 29d) [123]. In addition, the streamwise decay of $J/J_o$ from the peak location to the far field ($y/d$ = 20) (Figure 30a) is considerably steeper for Ø = 0° compared to all other phase differences [123]. This behavior suggests that, although the near field jet appears strong at zero phase difference, intense destructive vortex interactions in the near field accelerate momentum dissipation, leading to a substantially weaker jet in the far field [123].

Figure 30. (a) Streamwise variation in the normalized jet momentum flux ($J/J_o$) for the SJ array operating at ${Re}_{U_o}$ = 300 and $St$ = 0.086 under different phase differences, reproduced with permission from [123]. (b) Streamwise variation in cross-stream velocity fluctuations along the square cylinder centerline, reproduced with permission from [211].

The effectiveness of jet vectoring for bluff body flow control has been extensively investigated by Mittal and Arumuru [211]. A pronounced peak in $V_{avg}/U_o$ near the cylinder reflects the influence of SJ actuation, in contrast to the case without actuation (Figure 30b) [211]. Compared to all other operated phase differences, at Ø = 60°, where the vectoring effect is most prominent, two distinct peaks appear (Figure 30b), which Mittal and Arumuru [211] identified as indicative of asymmetric vortex shedding from the upper and lower shear layers. This asymmetry, induced by the vectoring effect, modifies the vortex formation length and alters the wake structure, highlighting the ability of jet vectoring to manipulate shear layer dynamics and improve flow control effectiveness [211].

From a thermal management perspective, vectoring significantly improves heat transfer performance [212]. Maximum vectoring, achieved at a phase difference of 90°, results in a substantially larger cooling surface area on the heated plate compared to the in-phase operation (Ø = 0°) of the SJ array [212]. The phenomenon of enhanced heat transfer when the SJ array is operated out of phase has also been reported in the literature [213]. This demonstrates that phase control can be strategically employed to target and cool specific surface regions based on application requirements. Together with this, the multiple vortices generated by each actuator interact with the surrounding fluid as they propagate outward, promoting greater entrainment and enhancing overall jet formation [123,214].

5.4.2. Focusing of Jets

While the use of independently controlled SJ arrays and jet vectoring effectively addresses the primary limitations of single-actuator SJs, such as restricted jet formation [123,214] and limited spanwise coverage [123,210,212], the degradation of jet strength in the far field remains a significant challenge [214]. When the synthetic jet array operates in phase ($\varnothing$ = 0°), the inner counter-rotating vortices in the near field interact destructively, similar to the behavior observed in dual synthetic jets in Figure 15a [214,215,216]. This interaction breaks the primary vortices into smaller secondary structures, which dissipate rapidly as they convect downstream, resulting in a pronounced reduction in jet momentum [214,217]. To address this issue, a novel focusing technique has been introduced, where a nonlinear phase delay, specifically a trapezoidal distribution (Case 3, Figure 31a), is applied across the actuators. In this configuration, the inner actuators (SJA 2 and SJA 3) lead in phase compared to the outer actuators (SJA 1 and SJA 4) (Case 3, Figure 31a). This approach reduces destructive vortex interactions and promotes coherent vortex evolution along with constructive merging, thereby enhancing jet strength in the far field [214,218].

Figure 31. (a) Schematic diagram showing the phase difference between actuators for the formation of straight, vectored, and focused jets. Focusing characteristics of SJ array operated at ${Re}_{U_o}$ = 300, $St$ = 0.086, and varying non-linear phase differences: (b) directivity plot showing enhancement or reduction of $V_{avg}/U_o$ measured at $y/d$ = 20, (c) normalized jet momentum flux ($J/J_o$) variation, and (d) jet half-width, reproduced with permission from [214].

The study revealed that for the SJ array operated at ${Re}_{U_o}$ = 300, maximum focusing was achieved at an intermediate Strouhal number ($St$ = 0.086) and a moderate nonlinear phase difference of 90° (Figure 31b) [214]. A quantitative assessment indicates that in the far field at $y$ = $20d$, maximum focusing ($\varnothing$ = 90°) leads to an increase of approximately 52% in ${\mathrm{V}}_{avg}/U_o$ compared to $\varnothing$ = 0° (Figure 31b). Additionally, under maximum focusing conditions, $J/J_o$, which also characterizes the jet strength measured in the far field ($y$ = $20d$), increased by nearly 35% compared to Ø = 0° (Figure 31c). Notably, contrary to the expectation that focusing would confine the flow near the centerline and reduce the jet width, the jet instead displayed lateral expansion (Figure 31d). This broadening is attributed to the development of larger and more coherent vortical structures capable of entraining greater volumes of surrounding fluid [214]. A further quantitative analysis revealed that maximum focusing at $\varnothing$ = 90° led to a reduction of approximately 43% in destructive vortex interactions compared to the in-phase operation of the synthetic jet array [214].

The phase-averaged vorticity fields of the SJ array operated at $St$ = 0.086 for different nonlinear phase delays are shown in Figure 32 [214]. For in-phase operation ($\varnothing$ = 0°), vortices $2^{-}$ and $3^{+}$ are attracted toward the identically rotating remnant vortices $R^{1-}$ and $R^{4+}$ (formed in the previous cycle), respectively, and merge at $t/T$ = 0.5 (Figure 32a) [214]. This interaction induces pronounced stretching of vortices $2^{+}$ and $3^{-}$, which subsequently break down into smaller-scale structures by $t/T$ = 0.75 (Figure 32a) [214]. For $\varnothing$ = 0°, the downstream convection of the resultant jet is primarily governed by the acceleration of the outer vortices $1^{-}$ and $4^{+}$, as observed at $t/T$ = 1 (Figure 32a) [214].

Figure 32. Phase-averaged evolution of vortical structures generated by the synthetic jet array operating at ${Re}_{U_o}$ = 300 and $St=0.086$, illustrating vortex formation, growth, and interaction for different non-linear phase differences: (a) $\varnothing$ = 0°; (b) $\varnothing$ = 90°; (c) $\varnothing$ = 120°; and (d) $\varnothing$ = 180° [214].

For the intermediate Strouhal number ($St$ = 0.086), remnant vortices play a dominant role in jet focusing. Maximum focusing is achieved at $\varnothing$ = 90° (Figure 32b) [214]. Under this condition, vortices $2^{-}$ and $3^{+}$ (shown in Figure 32b at $t/T$ = 0.25) merge with the remnant vortices $R^{1-}$ and $R^{4+}$ at $t/T$ = 0.5 (Figure 32b) [214]. Although the initial momentum of vortices $2^{-}$ and $3^{+}$ displaces the merged vortex pairs ($2^{-}$ + $R^{1-}$ and $3^{+}$ + $R^{4+}$) away from the centerline, the subsequent attraction and momentum transfer from the lagging vortices $1^{-}$ and $4^{+}$ reorient the merged structures toward the centerline (Figure 32b, $t/T$ = 0.75) [214]. This constructive interaction strengthens the coherent vortex system and leads to maximum jet focusing [214]. As a consequence of this enhanced focusing at $\varnothing$ = 90°, ${\mathrm{V}}_{avg}/U_o$ increases by approximately 52% (Figure 31b), while $J/J_o$ increases by nearly 35%, measured at $y/d$ = 20 (Figure 31c), compared with $\varnothing$ = 0° [214]. At $\varnothing$ = 90°, constructive merging between adjacent vortices results in the formation of larger vortical structures compared to all other phase differences [214]. These larger vortices enhance jet entrainment of the surrounding fluid. Consequently, rather than convecting toward the jet centerline, the increased entrainment at $\varnothing$ = 90° prevents jet contraction [214]. For $\varnothing$ = 120° (Figure 32c), although the overall vortex dynamics remain similar to those observed at $\varnothing$ = 90°, the increased phase difference causes suction effects to become more pronounced [214]. As a result, the jet focusing effect is less significant compared to that at $\varnothing$ = 90° (Figure 31b,c) [214]. For $\varnothing$ = 180°, suction-induced interactions between adjacent actuators become even more dominant (Figure 32d, $t/T$ = 0.75), leading to severe disruption of coherent vortex formation [214]. As a result, vortex strength weakens substantially, causing a further reduction in ${\mathrm{V}}_{avg}/U_o$ and $J/J_o$, as shown in Figure 31b and Figure 31c, respectively.

Flow control applications benefit considerably from this focusing effect [211]. By delaying vortex shedding and shortening the vortex formation length, focused synthetic jets contribute to a more stable and narrower wake [211]. These alterations promote earlier and stronger interactions with bluff body vortices, leading to reduced velocity fluctuations and suppression of turbulent structures. At optimal focusing ($\varnothing$ = 90°), the root-mean-square values of both streamwise and transverse velocities reach their minimum, resulting in a 43% reduction in the drag coefficient ($C_D$) (Figure 33a) [211].

Figure 33. Effect of nonlinear phase delay ($\varnothing °$) on (a) drag coefficient ($C_D$) for a bluff body with synthetic jet actuation, reproduced with permission from [211] and (b) $\underset{\_}{\overline{Nu}}$ distribution at various $Y/d$ values, reproduced with permission from [209].

Thermal performance also benefits from this focused configuration [209]. For the SJ array operated at Reynolds numbers (${Re}_{U_o}$ = 600) and Strouhal number ($St$ = 0.1), constructive merging of the leading and lagging vortices in a nonlinearly phased synthetic jet array significantly enhances convective heat transfer [209]. The intermediate region ($Y/d$ = 14) exhibits enhanced heat transfer (Figure 33b), with the peak $\underset{\_}{\overline{Nu}}$ increasing by approximately 21% under maximum focusing (Ø = 120°), compared to the in-phase operation of the SJ array [209]. Moreover, the drop in heat transfer from the intermediate region ($Y/d$ = 14) to the far field ($Y/d$ = 28) under maximum focusing (Ø = 120°) is only 17% (Figure 33b) [209], which represents a substantial improvement compared to a single-actuator SJ operated at ${Re}_{U_o}$ = 396, where a drop of approximately 36% is observed between the intermediate field ($Y/d$ = 18) and the far field ($Y/d$ = 23) [11]. These outcomes underscore that jet focusing, achieved through nonlinear phase delay, directly addresses the loss of jet coherence and strength in the far field [209,214].

Similarly, Paolillo et al. [219,220] developed a novel quadruple synthetic jet (QSJ) device consisting of four synthetic jets arranged in a square configuration, each driven independently with controllable phase shifts. They found that the phase differences between the actuators strongly influence the formation and interaction of large coherent vortex structures, which significantly affect the heat transfer performance [220]. For example, when the actuators operate in phase ($\varnothing =0°$), the least heat transfer is observed compared to other phase difference settings, although the heat transfer is uniformly distributed across the heated plate [220]. This is because, in the in-phase configuration, the jets produce large, long-lived vortex rings that merge to create a more uniform but less turbulent flow [220]. In contrast, the highest heat transfer is observed when a 90° phase difference is applied between the actuators [145]. This configuration generates swirling flow patterns that enhance mixing and turbulence near the impingement surface, leading to stronger local vortex interactions and more effective disruption of the thermal boundary layers [145].

Table 4 summarizes the fundamental drawbacks of single-actuator synthetic jets along with the effectiveness of various technological advancements in overcoming these limitations. While some configurations address one or two drawbacks, the synthetic jet array with independently controlled actuators emerges as the most promising solution, offering comprehensive improvement across all critical performance aspects.

Table 4. Summary of performance assessment of recent synthetic jet technologies in addressing key limitations of single-actuator jets.

Technological Advancement	Restricted Jet Formation	Limited Spanwise Coverage	Ineffective Far-Field Performance	Remarks
Dual-cavity SJs	√	√	×	Doubles flow rate and expand coverage via vectoring, while near-field interactions reduce far-field performance
Single-actuator multi-orifice SJs	√	∆	×	Generates multiple vortices, improving near-field heat transfer, while vortex diffusion limits far-field performance
Double-acting coaxial SJs	√	√	×	Improves jet formation and spanwise influence, while far-field strength remains weak
Concentric orifice single-actuator coaxial SJs	√	×	×	Improves jet formation but ineffective in spanwise and far-field behavior
Independently controlled coaxial SJs (Low $Re$)	√	√	√	Enhances jet formation, wide coverage and sustained far-field strength
Independently controlled coaxial SJs (High $Re$)	√	√	∆	Enhances jet formation and wide coverage, but only partial improvement in far-field
SJ array with independent actuator control	√	√	√	Offers best performance overall, with enhanced jet formation, wide coverage, and sustained far-field

Legend: √ = fully addressed; ∆ = partially addressed; × = not addressed.

6. Conclusions

Synthetic jets generate zero net mass flux through periodic suction and blowing, offering compactness, ease of integration, and eliminating the need for an external fluid supply. These features make them well-suited for applications such as flow control and heat transfer enhancement. Despite their promise, SJs are not without limitations. This review presents a detailed assessment of the primary limitations associated with single-actuator SJs and examines the technological developments that have emerged to overcome these challenges. Our findings reveal that key drawbacks, such as restricted jet formation capacity, limited spanwise coverage, and diminished far-field effectiveness, significantly constrain their broader application in practical scenarios. To mitigate these limitations, several technological advancements have been proposed, including dual-cavity synthetic jets, single-actuator multi-orifice synthetic jets, coaxial synthetic jets, and synthetic jet arrays, each aiming to enhance the flow and thermal performance of SJ systems.

Dual-cavity synthetic jets, comprising two side-by-side actuators operated either in phase or with a phase difference, enable enhanced jet formation and controllable vectoring. When actuated in phase, the jet remains symmetric and convects straight downstream, while a phase difference causes deflection toward the leading actuator, allowing directional control. Experimental studies have shown that DSJs can nearly double the flow rate and expand the effective coverage area, addressing key limitations of conventional SJs related to restricted jet formation and limited spanwise influence. However, destructive interactions in the near field significantly degrade the far-field performance of DSJs.

Single-actuator multi-orifice synthetic jets, which utilize a single actuation chamber connected to multiple orifices, address the limitation of restricted jet formation observed in single-orifice designs by generating multiple coherent vortices. In this configuration, higher near-field heat transfer performance has been observed compared to conventional single orifice jets. Together with this, experimental studies have reported two distinct peaks in the average Nusselt number distribution, with the first occurring near the orifice exit ($Y/d$ = 2), highlighting the effectiveness of this configuration for localized or spot cooling applications. Despite these advantages, ineffective performance in the far field due to significant vortex diffusion remains a limiting factor for this configuration.

Among all coaxial synthetic jet configurations, independently controlled coaxial jets show the most promise, offering precise control over vortex dynamics through the modulation of frequency, amplitude, and phase. This configuration significantly enhances jet volume flux and promotes greater jet spreading. The resulting jets also retain their strength in the far field. However, at higher Reynolds numbers, intensified vortex diffusion limits their performance in the far field.

A synthetic jet array, comprising multiple independently controlled actuators, facilitates two powerful strategies: vectoring and focusing of jets. Formation of multiple vortices from the SJ array entrains more surrounding fluid, which enhances jet formation, and precise control of the jet direction using phase modulation increases spanwise coverage. Focusing, achieved through nonlinear phase delays, reduces destructive vortex interactions, allows the primary vortices to evolve effectively, and constructive merging between vortices enables them to retain their strength in the far field. These capabilities have demonstrated substantial improvements in both flow control and thermal management. Overall, the strategic use of phase modulation in the SJ array effectively addresses the key limitations of SJs, including limited jet formation, restricted surface coverage, and ineffective performance in the far field, making it a promising solution for advanced fluidic and thermal applications.

7. Future Scope

Among the various technological advancements, independently controlled coaxial synthetic jets and synthetic jet arrays demonstrate significant potential to overcome the fundamental limitations of conventional synthetic jets. Therefore, future research should place greater emphasis on these promising configurations to fully harness their capabilities.

• The steering and focusing behavior of independently operated SJ arrays strongly depends on geometric parameters such as actuator geometry, spacing between orifices, and the number of actuators, as well as operating parameters including oscillation frequency, amplitude, and phase difference between actuators. Future research is needed to systematically assess the impact of these factors on jet vectoring and focusing, with a particular focus on optimizing the performance of synthetic jet arrays for improved flow control and thermal management.
• Moreover, the feasibility of achieving simultaneous vectoring and focusing in synthetic jet arrays remains an open area of exploration. Achieving this would significantly enhance directional flow manipulation while maintaining jet coherence and intensity in the far field.
• For IC-CSJs, detailed flow analysis is essential, especially at high Reynolds numbers ($Re$ ≈ 1100), to understand the vortex dynamics responsible for the significant reduction in jet strength in the far field. The performance of IC-CSJs deteriorates significantly under these conditions. Gaining a deeper understanding of these flow structures could provide valuable insights for optimizing design and operating parameters, thereby mitigating far-field performance degradation.