Heat Transfer Enhancement in Heat Exchangers by Longitudinal Vortex Generators: A Review of Numerical and Experimental Approaches

Abstract

Heat exchangers are critical components in various industrial applications, requiring efficient thermal management to enhance thermal performance and energy efficiency. Longitudinal vortex generators (LVGs) have emerged as a potent mechanism to enhance heat transfer within these devices. A precise knowledge of the thermal performance enhancement of HE through LVGs is missing in the literature. Therefore, this study aims to provide a critical review of both numerical simulations and experimental studies focusing on the enhancement of heat transfer through LVGs to further enhance the knowledge of the field. It begins with elucidating the fundamental principles behind LVGs and delineating their role in manipulating flow patterns to augment heat transfer. This is followed by an exploration of the various numerical methods employed in the field, including computational fluid dynamics techniques such as Reynolds-Averaged Navier–Stokes (RANS) models, Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). Various experimental methods are then summarised, including differential pressure measuring instruments, temperature measurements, velocity measurements, heat transfer coefficient measurements, and flow visualisation techniques. The effectiveness of these methods in capturing the complex fluid dynamics and thermal characteristics induced by LVGs is critically assessed. The review covers a wide range of LVG configurations, including their geometry, placements, and orientations, and their effects on the thermal performance of heat exchangers. Different from previous reviews that mainly focus on classical configurations and historical studies, this review also emphasizes recent developments in computational fluid dynamics and progress in interdisciplinary fields such as innovative materials, additive manufacturing, surface finishing, and machine learning. By bridging the gap between fluid dynamics, thermal enhancement, and emerging manufacturing technologies, this paper provides a forward-looking, comprehensive analysis that is valuable for both academic and industrial innovations.

1. Introduction

To achieve high energy efficiency and performance optimization, the engineering community continues to seek innovative methods to enhance heat transfer mechanisms in thermal systems. Heat exchangers, as critical components in industrial, automotive, and HVAC applications, are the focal point of such innovations due to their significant role in energy conservation and system efficiency. The efficiency of heat exchangers is pivotal in minimizing energy consumption and improving the overall thermal performance of systems. Traditional methods, such as increasing surface area or operational adjustments, often lead to higher costs and complex operational strategies [1]. Among various enhancement techniques, the integration of longitudinal vortex generators (LVGs) in heat exchanger design has emerged as a promising solution to enhance thermal performance without substantially increasing the pressure drop or the footprint of the equipment. LVGs are typically designed as small protrusions aligned with the flow direction and are integrated into heat transfer surfaces through various methods such as embossing, mounting, attaching, stamping, and punching [2]. Their main function is to generate longitudinal vortices, thus swirling flows that effectively mix fluid layers. This mixing action disrupts the thermal boundary layer, a thin layer of fluid that normally acts as a thermal insulator, thereby enhancing the overall heat transfer rate [2,3]. Numerous studies have demonstrated that the incorporation of LVGs in heat exchangers can increase the Nusselt number compared to baseline configurations, depending on their geometry, positioning, and Reynolds number range, leading to more compact, energy-efficient, and effective systems [2,3,4,5]. However, this enhancement is often accompanied by a rise in the friction factor, which can result in increased pumping power and operational costs if not carefully evaluated and optimized. Despite this trade-off, systems equipped with LVGs can still achieve energy savings, particularly when optimized for specific applications. While several previous reviews have explored classical LVG configurations and their historical development, a more comprehensive, contemporary, and forward-looking review is still needed. The special feature of this review is that it not only integrates numerical and experimental research methods and findings on traditional LVG designs but also emphasizes the latest advances in CFD, including topology optimization and multi-objective algorithms. In addition, this review highlights progress in interdisciplinary areas, such as the use of innovative materials (e.g., shape memory alloys) for generating adaptive vortex generators, additive manufacturing techniques for fabricating complex LVG geometries, surface adjustment methods (e.g., surface abrasive finishing) for reducing flow resistance, and machine learning algorithms for design optimization and surrogate models. By integrating these advances, this review provides a comprehensive and up-to-date perspective on the heat transfer enhancement role of LVGs in heat exchangers. It aims to serve as a fundamental reference for researchers and engineers exploring the next generation of thermal management technologies.

2. Longitudinal Vortex Generators

2.1. Heat Transfer Enhancement Characteristics

Vortices can be classified by their rotational axes: transverse vortices (TVs) have perpendicular axes to the main flow direction; longitudinal vortices (LVs), also referred to as streamwise vortices, on the other hand, have parallel ones. LVs are typically more efficient at improving heat transfer while only causing a minimal rise in pressure drop compared to TVs [2,6,7]. LVGs are utilized as a passive technique for augmenting heat transfer, involving the generation of streamwise vortices, as depicted in Figure 1, which induces heightened turbulence within the fluid flow across heat transfer surfaces [8].

When the fluid traverses LVGs, a potent secondary swirling flow is induced, where the tangential velocity of the vortices may reach twice that of the main flow. This high-velocity swirling action not only facilitates the fluid mixing within the main and peripheral flow regions but also introduces high-energy fluid into the boundary layer, which effectively suppresses and postpones the separation of the boundary layer, consequently leading to the profile drag reduction and heat transfer enhancement. Conventional heat transfer augmentation methods like louvered, slit, and wave fins operate by disrupting the flow, reducing the thickness of boundary layer or halting its progression, and generating small transverse vortices. However, the contribution of these transverse vortices to heat transfer enhancement is somewhat limited under conditions of steady-state laminar flow, whereas longitudinal vortices have a pronounced effect on increasing both the average and local heat transfer coefficients throughout the channel [9]. Consequently, LVGs are markedly advantageous in augmenting heat transfer within heat exchangers operating under laminar flow regimes.

2.2. Types of Longitudinal Vortex Generators Studied in Recent Decades

Due to the significant effect of LVGs on the heat transfer capacity of heat exchangers, more and more geometrical and positional parameters of LVGs have been investigated to obtain optimal design configurations of LVGs to achieve maximum heat transfer enhancement.

Four prevalent LVGs are illustrated in Figure 2, encompassing delta wings, delta winglets, rectangular wings, and rectangular winglets [10,11,12]. In addition to the primary four types, a variety of other LVGs have been explored and studied extensively in recent years. Studies on a range of winglet VGs were conducted by Zhou and Feng [13], Lu and Zhou [14], including delta, trapezoidal, and rectangular shapes, plane and curved designs, with and without holes, as depicted in Figure 3a. Wang et al. [5], and Lin et al. [15] proposed the application of annular winglet VGs to finned-tube heat exchangers, as shown in Figure 3b. Gholami et al. investigated the heat transfer enhancement in a finned-tube heat exchanger with wavy rectangular winglet VGs, as illustrated in Figure 3c [16]. He et al. introduced arrays of V-deployed VGs, inspired by animal locomotion in nature, as illustrated in Figure 3d [17]. Lotfi et al. explored the use of four distinct VG designs on wavy-finned elliptical-tube heat exchangers, including the wheeler wishbone (WW), angle rectangular winglet (ARW), curved angle rectangular winglet (CARW), and rectangular trapezoidal winglet (RTW), depicted in Figure 3e [18,19]. In addition to WW, ARW, and RTW, Samadifar and Toghraie also investigated the effect of the intended vortex generator (IVG) and waved vortex generator (WVG) on heat transfer in finned plate heat exchangers, as shown in Figure 3f [20].

Representative numerical studies focusing on LVGs in recent decades are thoroughly investigated in this paper. The author(s) of these studies, year of publication, LVG type, application, and Reynolds number range are summarized in

Table 1. Representative numerical studies of LVGs in recent decades.

Author(s)	Year	Application	VG Type	Reynolds Number
Biswas et al. [21]	1989	Flat plate	Delta wings	500–1815
Fiebig et al. [22]	1989	Flat plate	Delta winglets and delta wings	500–2000
Biswas et al. [23]	1992	Flat plate	Delta wings and punched holes	500–1815
Zhu et al. [24]	1993	Flat plate	Delta wings, rectangular wings, DWPs and RWPs	50,000
Zhu et al. [25]	1993	Flat plate	DWPs	67,000
Biswas et al. [26]	1994	Flat plate	Delta wings and DWPs	500–3000
Biswas et al. [27]	1994	FTHE (plate fins and circular tubes)	DWPs	500–1000
Deb et al. [28]	1995	Flat plate	DWPs	400–1000
Biswas et al. [29]	1996	Flat plate	Delta winglets	1580
Vasudevan et al. [30]	2000	Triangular duct	Delta winglet	100, 200
Chen et al. [31]	2000	FTHE (plate fins and oval tubes)	Punched delta winglets	300
Sohankar and Davidson [32]	2001	Flat plate	Inclined block shapes	400–1500
Jain et al. [33]	2003	FTHE (plate fins and circular tubes)	DWPs	1000
Prabhakar et al. [34]	2003	FTHE (plate fins and oval tubes)	DWPs	1300
Tiwari et al. [35]	2003	FTHE (plate fins and oval tubes)	DWPs	500, 1000, 1500
Leu et al. [36]	2004	FTHE (plate fins and circular tubes)	RWPs	400–3000
Sohankar [37]	2004	Plate-fin heat exchanger	RWPs	2000
Srikanth and Biswas [38]	2005	Rectangular channel	DWPs	10000
Ferrouillat et al. [39]	2006	Rectangular channel	RWPs and DWPs	2000–8000
Sohankar [40]	2007	Rectangular channel	RWPs	200–2000
Wu and Tao [41]	2007	FTHE (plate fins and circular tubes)	DWPs	800–2000
Joardar and Jacobi [42]	2007	FTHE (plate fins and circular tubes)	DWPs	330–850
Wu and Tao [7,43]	2008	Rectangular channel	Rectangular winglets	800–3000
Song et al. [44]	2008	FTHE (plate fins and flat tubes)	DWPs	200–1900
Tang et al. [45]	2009	FTHE (plate fins and circular tubes)	DWPs	4000–100,000
Chang et al. [46]	2009	FTHE (plate fins and flat tubes)	DWPs	300–1700
Tian et al. [47]	2009	FTHE (wavy fins and circular tubes)	DWPs	500–5000
Tian et al. [48]	2009	Plate-fin heat exchanger	RWPs and DWPs	470–1700
Chu et al. [49]	2009	FTHE (plate fins and circular tubes)	RWPs	500–880
Chu et al. [50]	2009	FTHE (plate fins and oval tubes)	DWPs	500–2500
Lei et al. [51]	2010	FTHE (plate fins and circular tubes)	DWPs	600–2600
Onishi et al. [52]	2010	Finless flat-tube heat exchanger	Rectangular winglets	710–2130
Zeng et al. [53]	2010	FTHE (plate fins and circular tubes)	DWPs	4200–12,200
Lemouedda et al. [54]	2010	FTHE (plate fins and circular tubes)	DWPs	200–1200
Wu and Tao [55]	2011	FTHE (plate fins and circular tubes)	DWPs	800–2000
Aris et al. [56]	2011	FTHE (plate fins and circular tubes)	Delta wings	300
Hwang et al. [57]	2012	FTHE (plate fins and circular tubes)	DWPs	130–5180
Pal et al. [58]	2012	FTHE (plate fins and circular tubes)	DWPs	800
He et al. [59]	2012	FTHE (plate fins and circular tubes)	DWPs	600–2600
He et al. [60]	2013	FTHE (plate fins and circular tubes)	RWPs	550–880
Sinha et al. [61]	2013	Plate-fin heat exchanger	DWPs	250–1580
Huisseune et al. [62]	2013	FTHE (louvred fins and circular tubes)	DWPs	220–915
Huisseune et al. [63]	2013	FTHE (louvred fins and circular tubes)	DWPs	140–1220
Song and Wang [64]	2013	FTHE (plate fins and flat tubes)	DWPs	200–1600
Hu et al. [65]	2013	FTHE (plate fins and circular tubes)	DWPs	200–1900
Jang et al. [66]	2013	FTHE (plate fins and circular tubes)	Inclined block-shape VG pairs	400–1200
Saha et al. [67]	2014	Flat plate	DWPs and RWPs	50–200
Gholami et al. [16]	2014	FTHE (plate fins and circular tubes)	Wavy RWPs	400–800
Lotfi et al. [18]	2014	FTHE (wavy fins and elliptical tubes)	Plane and curved angle rectangular winglet, rectangular trapezoidal winglet, and wheeler wishbone	500–3000
Wu et al. [68]	2014	FTHE (plate fins and circular tubes)	DWPs	304–2130
Zhao et al. [69]	2014	FTHE (H-type fins and oval tubes)	RWPs	22,504–40,509
Lin et al. [15]	2014	FTHE (plate fins and circular tubes)	Interrupted annular groove fins	600–2500
Lin and Wang [70]	2014	FTHE (plate fins and flat tubes)	DWPs	1300–2400
Gong et al. [71]	2015	FTHE (plate fins and circular tubes)	Curved RWPs	800–3000
Li et al. [72]	2015	FTHE (plain fins and ellipse flat tubes)	RWPs and DWPs	450–3000
Lin et al. [73]	2015	FTHE (plate fins and circular tubes)	Curved DWPs	1100–3000
Behfard and Sohankar [74]	2016	FTHE (plate fins and circular tubes)	DWPs	1000
Lotfi et al. [19]	2016	FTHE (wavy fins and elliptical tubes)	Plane and curved angle rectangular winglet, and rectangular trapezoidal winglet	500–3000
Lu and Zhou [14]	2016	Rectangular channel	Plane and curved TWPs, DWPs, RWPs	700–26,500
Sinha et al. [75]	2016	FTHE (plate fins and circular tubes)	RWPs	250–1500
Song and Wang [76]	2016	FTHE (plate fins and flat tubes)	Delta winglets	400–2200
Oneissi et al. [77]	2016	Parallel plate-fin heat exchanger	DWPs	270–30,000
Tang et al. [78]	2016	FTHE (plate fins and circular tubes)	DWPs	4500–9500
Esmaeilzadeh et al. [79]	2017	Flat plate	Plane and curved TWPs	7000–35,000
Sarangi and Mishra [80]	2017	FTHE (plate fins and circular tubes)	RWPs	643–1286
Chimres et al. [81]	2018	FTHE (plate fins and circular tubes)	Elliptical winglets	/
Song and Tagawa [82]	2018	FTHE (plate fins and flat tubes)	Delta winglets	200–1600
Abdelatie et al. [83]	2018	Wing-shaped tubes-bundle heat exchanger	RWPs	1850–9700
Chamoli et al. [84]	2018	Solar air heater	DWPs, TWPs and RWPs	3500–16,000
Samadifar and Toghraie [20]	2018	Fin–plate heat exchanger	Rectangular trapezoidal winglet, rectangular, angle rectangular winglet, Wheeler wishbone, waved vortex generator, and intended vortex generator	200
Han et al. [85]	2018	Rectangular channel	Punched RWPs	214–10,703
Naik et al. [86]	2018	Rectangular channel	Plane and curved rectangular winglets	3000
Zeeshan et al. [87]	2019	FTHE (plate fins and circular tubes)	RWPs	500–900
Lu and Zhai [88]	2019	FTHE (plate fins and circular tubes)	Curved RWPs, TWPs	405–4050
Luo et al. [89]	2019	Fin–plate heat exchanger (wavy fins)	Delta winglets	100–3000
Song et al. [90]	2019	Plate heat exchanger	Curved delta winglets	200–1400
Tang et al. [91]	2019	FTHE (H-type fins and elliptical tubes)	RWPs	10,676
Bjerg et al. [92]	2019	Rectangular channel	RWPs	700
Jeong et al. [93]	2019	Dimpled cooling channel	Crescent-shaped protrusion VG	2800
Zhang et al. [94]	2020	Helical channel with rectangular cross section	Streamlined winglet pairs	2000–17,000
Sun et al. [95]	2020	Circular heat exchanger tube	Rectangular winglets	10,000
Gupta et al. [96]	2020	FTHE (plate fins and circular tubes)	Punched RWPs	1500–9000
Modi et al. [97]	2020	FTHE (plate fins and circular tubes)	Punched RWPs	400–2000
Oh and Kim [98]	2021	FTHE (plate fins and circular tubes)	Curved DWPs and RWPs	2680
Promvonge et al. [99]	2021	Solar air heater	Punched delta winglets and flapped delta winglets	4000–24,000
Shi et al. [100]	2021	FTHE (plate fins and circular tubes)	Curved DWPs	600–5000
Naik and Tiwari [101]	2021	FTHE (plate fins and circular tubes)	RWPs	2000–10,000
Naik et al. [102]	2022	Rectangular channel	Curved RWPs	2000–4000
Pérez et al. [103]	2022	Rectangular channel	Delta winglets	120–1440
Pérez et al. [104]	2022	FTHE (louver fins and circular tubes)	Delta winglets	208
Sharma et al. [105]	2023	FTHE (plate fins and circular tubes)	Curved trapezoidal winglets	634.5
Saini et al. [106]	2023	FTHE (plate fins and circular tubes)	Curved TWPs with circular holes	400–2000
Saini et al. [107]	2023	FTHE (plate fins and circular tubes)	Curved DWPs with circular holes	400–2000
Hu et al. [108]	2023	FTHE (wavy fins and circular tubes)	Curved DWPs	500–3000
Feng et al. [109]	2023	FTHE (H-type fins and circular tubes)	RWPs	4650–28,300

Note: FTHE is finned tube heat exchanger; DWP is delta winglet pair; RWP is rectangular winglet pair; TWP is trapezoidal winglet pair.

as shown below. This paper also provides a comprehensive review of representative experimental studies focusing on LVGs in recent decades, as listed in

Table 2. Representative experimental studies of LVGs in recent decades.

Author(s)	Year	Application	VG Type	Reynolds Number
Garimella and Eibeck [110]	1991	Horizontal channel	Half-delta wings	700–5200
Fiebig et al. [111]	1991	Flat plate	Delta and rectangular wings and winglets	1360–2270
Tiggelbeck et al. [112]	1992	Rectangular Channel	DWPs	1300–8000
Mitra and Fiebig [113]	1993	Rectangular Channel	DWPs	2000–8000
Fiebig et al. [114]	1993	FTHE (plate fins and circular tubes)	DWPs	600–2700
Tiggelbeck et al. [115]	1994	Flat plate	Delta wings, rectangular wings, DWPs and RWPs	2000–9000
Fiebig et al. [116]	1994	FTHE (plate fins and circular/flat tubes)	DWPs	600–3000
Valencia et al. [117]	1996	FTHE (plate fins and circular/flat tubes)	DWPs	2360–2440
Gentry and Jacobi [118]	1997	Flat plate	Delta wings	600, 800, 1000
Kotcioğlu et al. [119]	1998	Rectangular Channel	RWPs	3000–30,000
Wang et al. [2]	2002	FTHE (plate fins and circular tubes)	Wave-type VGs	500, 1500, 3300
Wang et al. [5]	2002	FTHE (plate fins and circular tubes)	Annular and delta winglets	500, 1500, 2500
Torii et al. [120]	2002	FTHE (plate fins and circular tubes)	DWPs	350–2100
Kwak et al. [121]	2002	FTHE (plate fins and circular tubes)	DWPs	300–2700
Gentry and Jacobi [122]	2002	Flat plate	Delta wings	300–2000
Yoo et al. [123]	2002	FTHE (plate fins and circular/flat tubes)	RWPs	800–4500
Yuan et al. [124]	2003	Flat plate	RWPs	5000–47,000
Kwak et al. [125]	2003	FTHE (plate fins and circular tubes)	DWPs	350–2100
Chen and Shu [126]	2004	Flat plate	Delta wings	4430–11,820
Leu et al. [36]	2004	FTHE (plate fins and circular tubes)	RWPs	400–3000
O’Brien et al. [127]	2004	FTHE (plate fins and oval tubes)	DWPs	670–6300
Sommers and Jacobi [128]	2005	FTHE (plate fins and circular tubes)	Delta wings	500–1300
Kwak et al. [129]	2005	FTHE (plate fins and circular tubes)	DWPs	350–2100
Pesteei et al. [130]	2005	FTHE (plate fins and circular tubes)	DWPs	2250
Shi et al. [131]	2006	FTHE (plate fins and flat tubes)	DWPs	<3000
Allison and Dally [132]	2007	FTHE (plate fins and flat tubes)	DWPs	2600, 3400, 4600
Wang et al. [133]	2007	Rectangular channel	RWPs	3000–20,000
Joardar and Jacobi [134]	2008	FTHE (plate fins and circular tubes)	DWPs	220–960
Tang et al. [135]	2009	FTHE (plate fins and circular tubes)	DWPs	4000–10,000
Tang et al. [45]	2009	FTHE (plate fins and circular tubes)	DWPs	4000–10,000
Hernon and Patten [136]	2009	Flat plate	DWPs	/
He et al. [17]	2010	FTHE (plate fins and circular tubes)	DWPs	1400–3400
Yang et al. [137]	2010	Flat plate	Dimple wings, triangular wings, semi-circular wings, and delta wings	120–600
Promvonge et al. [138]	2010	Triangular ribbed channel	DWPs	5000–22,000
Chompookham et al. [139]	2010	Wedge-ribbed channel	DWPs	5000–22,000
Min et al. [140]	2010	Rectangular channel	Modified RWPs	5000–17,500
Aris et al. [56]	2011	FTHE (plate fins and circular tubes)	Delta wings	330–960
Aris et al. [10]	2011	Flat plate	Delta wings	1573–3712
Wu and Tao [141]	2012	Flat plate	DWPs	500–2000
Zhou and Ye [142]	2012	Flat plate	RWPs, TWPs, DWPs, and Curved TWPs	700–26,800
Wu et al. [143]	2012	FTHE (plate fins and circular tubes)	DWPs	/
Du et al. [144]	2013	FTHE (wavy fins and flat tubes)	DWPs	500–4500
Zhou and Feng [13]	2014	Flat plate	Plane and curved RWPs, TWPs, DWPs with and without holes	650–21,000
Caliskan [145]	2014	Rectangular channel	Delta winglets and rectangular winglets	3288–37,817
Khoshvaght-Aliabadi et al. [146]	2015	Circular tube	DWPs	3485–8715
Khoshvaght-Aliabadi et al. [147]	2015	Plate–fin heat exchanger	Rectangular wings	200–1600
Wang et al. [148]	2015	FTHE (plain/louvre fins and circular tubes)	Semi-dimple winglet pairs	/
Deshmukh et al. [149]	2016	Circular tube	Curved delta wings	250–1500
Sawhney et al. [150]	2017	Rectangular channel	Wavy-up DWPs	4000–17,300
Wu et al. [151]	2017	FTHE (plate fins and circular tubes)	Curved DWPs	500–4200
Abdelatie et al. [83]	2018	Wing-shaped-tubes-bundle heat exchanger	RWPs	1850–9700
Xu et al. [152]	2018	Circular tube	DWPs	6000–33,000
Zhai et al. [153]	2019	Circular tube	DWPs	5000–25,000
Sun et al. [95]	2020	Circular heat exchanger tubes	Rectangular winglets	10,000
Dogan and Igci [154]	2021	Rectangular channel	DWPs and a novel type of VG	5000–25,000
Zhang et al. [155]	2021	Rectangular channel	DWPs and tetrahedron pairs	20,000–100,000
Berber et al. [156]	2022	Rectangular channel	Curved winglets	6000–20,000
Modi and Rathod [157]	2022	FTHE (plate fins and circular tubes)	RWPs with or without holes	8000–25,000
Dogan and Erzincan [158]	2023	Rectangular channel	A novel type of VG	5000–25,000

below.

3. Numerical Methods

Computational Fluid Dynamics (CFD) analysis of LVGs in heat exchangers involves a complex process that depends on several numerical elements such as solver selection, assumptions on the model used to analyse LVGs, modelling strategies employed and discretization methods. Each of these elements is critical to produce accurate and reliable simulation results.

3.1. Solvers

CFD analysis relies heavily on its solver, which numerically solves fluid flow and heat transfer equations to produce results. Selecting an optimal solver depends on multiple variables, including flow state (laminar or turbulent), geometry complexity, and available computational resources. Solvers optimized for incompressible turbulent flows tend to be preferred when performing LVG analysis in heat exchangers. Solvers typically employ the Finite Volume Method (FVM), which is known for conservation of fluxes within the control volume, or the Finite Element Method (FEM), which excels at handling complex geometries. Common computational solvers for CFD analysis include Solution Algorithm (SOLA), Modified Marker-and-Cell (MAC) algorithm, FORTRAN code, and FLUENT, CFX, and STAR-CD.

Table 3. Comparative overview of representative computational solvers used in CFD studies and their applications.

Solver	Description	Studies Applied
Solution Algorithm (SOLA)	SOLA uses finite difference methods and iterative solvers to solve the Navier–Stokes equations governing incompressible flow, specifically for pressure/velocity coupling issues [159]. Since its creation, this solution algorithm has gained popularity due to its simplicity and efficiency.	[22,24,25]
Modified Marker-and-Cell (MAC) algorithm	The MAC method was developed by Harlow and Welch in 1965 [160,161]. The MAC method is a numerical approach commonly used to simulate the behaviour of incompressible, viscous fluids. It is based on a Eulerian staggered grid system, where velocity components are calculated at the cell faces, and pressure is computed at the cell centres. This arrangement enhances numerical stability and reduces errors, particularly in the coupling of pressure and velocity fields. The MAC method solves the governing equations of fluid flow, including the Navier–Stokes equations, using finite difference techniques.	[21,23,26,27,28,29,61,67]
FORTRAN code	FORTRAN (FORmula TRANslation) is a high-level programming language commonly used in engineering and scientific applications. Due to its numerical computing capabilities, FORTRAN is frequently used to develop custom solvers, algorithms, and simulation programs in CFD applications.	[76,90]
FLUENT solver	Known for its user-friendly interface and powerful solver capabilities, ANSYS FLUENT offers comprehensive modelling options, including laminar and turbulent flow, multiphase flow, combustion simulation, fire modelling, etc.	[7,14,16,20,37,38,39,40,41,42,43,45,46,47,48,49,50,51,52,53,55,58,59,60,62,63,66,71,74,75,77,78,79,80,83,84,85,86,87,88,89,92,94,95,96,97,99,100,101,102,103,104,106,107]
CFX solver	CFX, the computational fluid dynamics software in the ANSYS suite, is known for its advanced solver technology. CFX supports polyhedral meshes, powerful multigrid methods, and sophisticated turbulence modelling, making it an indispensable CFD solution for many different applications.	[18,19,72,98]
STAR-CD solver	STAR-CD is known for its robustness, flexibility and extensive physical modelling capabilities. The program offers a wide range of turbulence models, multiphase flow capabilities, and solvers designed to efficiently solve complex flow problems.	[54]

offers an in-depth review of computational solvers used in numerical studies of LVGs, along with examples of numerical studies conducted using these solvers. Ideal solvers would allow for coupled heat transfer and fluid flow simulation as well as managing turbulent interactions associated with LVGs.

3.2. Assumptions

Assumptions in CFD are necessary to simplify real-world scenarios into computationally manageable models. Common assumptions for LVG analysis include steady-state or transient flow, incompressible flow, or neglect of gravity effects, depending on the specific application and analysis objectives.

3.3. Models

Numerous numerical solvers and turbulence models have been used to simulate heat transfer enhancement induced by LVGs. These models range from simplified laminar assumptions to highly detailed Direct Numerical Simulation (DNS), each with its own advantages and disadvantages in terms of accuracy, computational cost, and applicability to real-world conditions. For low Reynolds number flows, the laminar model can provide reasonable predictions, especially in microchannel heat exchangers, where the flow remains steady, and vortex shedding is minimal. However, this model neglects turbulence effects and becomes unreliable in transitional or turbulent flows, where secondary flow interactions play a dominant role in heat transfer enhancement. For LVGs in heat exchangers, the flow is often turbulent due to the vortex generation. Thus, a turbulence model is generally more appropriate. RANS models, such as the standard k–ε model, the RNG k–ε model, and the SST k–ω model, are widely used due to their low computational requirements and acceptable accuracy in steady-state simulations. The RNG k–ε model is more suitable for the swirling flows and recirculation regions generated by LVGs, while the SST k–ω model is better at predicting vortex structures near walls and under adverse pressure gradients. However, RANS models are usually unable to resolve the unsteady vortex structures that are critical to LVG performance. To obtain higher fidelity, Large Eddy Simulation (LES), and Detached Eddy Simulation (DES) can more effectively capture large-scale unsteady vortex dynamics and flow anisotropy. LES shows good agreement with experimental results in predicting turbulent kinetic energy and local heat transfer enhancement, albeit at a significantly increased computational cost. LES requires substantially more computational resources, typically one to two orders of magnitude higher than RANS models. DNS resolves all scales of turbulence with the highest accuracy, without the need for turbulence models. DNS comprehensively captures the entire spectrum of eddies, including integral, Taylor scale, and Kolmogorov scales. DNS provides unparalleled insight into vortex-wall interactions, boundary layer behaviour, and local Nu variations induced by LVGs. However, the computational power of DNS limits its use in practical applications, which are usually limited to low Reynolds numbers, simplified geometries, and fundamental studies. The comparative properties of these models are summarized in

Table 4. A detailed comparison of the laminar and various turbulence models used for numerical investigations of LVGs.

Model	Accuracy for Prediction	Computational Cost	Strengths	Limitations	Study Applied
Laminar Model	Low (in turbulent flows)	Very Low	Suitable for Re < 500 or microchannels	Not suitable for turbulent or transitional flows	[7,15,16,21,22,23,26,27,28,29,30,31,32,33,34,35,41,42,43,44,46,48,49,50,51,52,54,55,56,58,59,60,61,62,63,64,65,66,67,68,70,71,73,75,76,77,80,82,87,88,89,90,103,104]
Standard k–ε Model	Low-Moderate	Low	Robust, fast, widely available	Poor for separation and swirling flows	[24,25,28,36,39,45,53,78]
RNG k–ε Model	Moderate	Low	Better for recirculating and swirling flows	Still lacks accurate near-wall resolution	[14,39,47,57,69,83,84,85,89,91,97,100,106,107,108,109]
Realizable k–ε Model	Moderate-High	Low-Moderate	Improved viscosity modelling; better for complex strain and shear	Less widely validated for LVG-specific cases	[39,86,94,99,101,102]
Standard k–ω Model	Moderate	Low-Moderate	Accurate in near-wall regions	Sensitive to inlet and boundary conditions	[72]
SST k–ω Model	Moderate-High	Moderate	Good for separation and wall heat transfer	May overpredict eddy viscosity in certain flows	[18,19,20,74,77,81,88,95,96,98,105]
DES	High	High	Balances accuracy and cost; can be applied in large industrial areas	Transition between RANS and LES regions must be managed carefully
LES	Very High	Very High	Captures unsteady vortex shedding and turbulence	Requires fine mesh and high computational power	[37,38,39,40,92]
DNS	Extremely High (benchmark)	Extremely High	Full turbulence resolution; used for validation and insight	Not suitable for complex or large-scale systems	[37,40,93]

, providing guidance for model selection in future studies of LVG-based heat exchangers. The choice of these models depends on the available computational resources and the level of detail required.

3.4. Boundary Conditions

CFD simulations rely on boundary conditions to provide an operating environment for the physical model and obtain realistic and reliable results. When simulating heat exchangers equipped with LVGs, setting accurate boundary conditions becomes particularly important due to their huge impact on fluid dynamics and heat transfer characteristics. Accurate boundary conditions are essential in describing the flow behaviour around LVGs, which create secondary flows with complex dynamics. They can accurately predict heat transfer rates in regions with steep temperature gradients and validate experimental data by accurately replicating physical setups. Most researchers assume a constant velocity and temperature at the flow channel inlet; however, a few studies utilize periodic fully developed fluid flow conditions at both computational domain inlets and outlets. In order to save computing resources, the physical model needs to be simplified, and periodic boundary conditions are usually adopted in the simulation domain, such as symmetric boundary conditions or periodic boundary conditions.

Table 5. A detailed overview of the discretization methods used in CFD studies of LVGs in heat exchangers.

Type	Importance	Method	Description
Spatial Discretization	Spatial discretization involves dividing the computational domain into small control volumes or cells where the governing equations are approximated. This process is crucial to capturing the gradients and complex flow characteristics introduced by LVGs.	Finite Volume Method (FVM)	FVM is widely used due to its conservative nature. This ensures that the fluxes entering and leaving the control volume are accurately represented, which is crucial when simulating heat exchangers. Second-order upwind schemes generally achieve an ideal balance between precision and computational cost. Their steep sharp gradient resolution reduces numerical diffusion more efficiently than first-order schemes.
		Higher-Order Schemes	Schemes such as QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and central differencing provide higher accuracy but can be more computationally expensive and more prone to instability. These schemes are particularly beneficial in capturing the detailed flow structures generated by LVGs [162].
Temporal Discretization	Time discretization is crucial in transient simulations to study time-dependent phenomena. The choice of time-stepping method affects the accuracy and stability of the solution.	Explicit Methods	These methods are conditionally stable and require smaller time steps to maintain stability, making them computationally intensive for large-scale simulations.
		Implicit Methods	Implicit methods, such as the Crank–Nicolson scheme, are unconditionally stable and allow for larger time steps. They are the preferred method in simulations where resolving the transient behaviour of LVG-induced flows is critical [163].
		Adaptive Time-Stepping	Adaptive time-stepping methods dynamically adjust the time step based on the local flow conditions, ensuring accuracy while optimizing computational resources [164].
Grid Independence Studies	Ensuring grid independence is critical to verify that simulation results are not affected by the discretised grid.	Grid Refinement	Successive grid refinement studies are conducted to ensure that further refinement does not significantly change the results. This practice confirms that the solution is grid-independent and accurate.
		Non-Uniform Grids	Non-uniform grids are often used to concentrate grid points in regions with large gradients, such as near LVGs, thereby improving accuracy without an excessive increase in computational cost [165].

offers an overview of some common boundary conditions used in CFD simulations of heat exchangers with LVGs.

3.5. Discretization Techniques

Discretization techniques are an important part of CFD, as it transforms continuous partial differential equations into discrete algebraic equations that can be solved numerically.

Table 6. A detailed comparison of typical experimental techniques used for experimental investigations of LVGs.

Technique	Development	Description	Application	Studies Applied
Thermocouples	The fundamental principle was discovered in 1821 by Thomas Johann Seebeck, with practical development occurring in the late 19th and early 20th centuries.	Thermocouples are temperature-measuring devices that consist of two different types of metal wires joined at one end. When the junction of the two metals is heated or cooled, it produces a temperature-dependent voltage, which can be interpreted to measure temperature.	Measurement of temperature.	[10,13,17,45,56,83,95,110,117,119,124,126,128,130,133,134,135,137,138,139,140,141,142,143,144,145,146,147,149,150,151,152,153,154,157,158]
Resistance Temperature Detectors (RTDs)	Became popular in the 1900s for industrial and scientific use because they are very precise.	RTDs are precision temperature sensors that measure temperature based on the principle that the electrical resistance of a metal changes predictably with temperature. Platinum is the most widely used material due to its stability and wide temperature range.	Measurement of temperature.	[2,5,120,121,125,129,134,142,148,154,157]
Differential Pressure Meter/Gauge/Transmitter/Transducer/Micro-Manometer	Developed in the 20th century.	These devices are all designed to measure and manage pressure differences, though they operate in subtly distinct manners or serve varied objectives. Some display the pressure difference directly to the user (Differential Pressure Meter, and Differential Pressure Gauge), others relay this information to a computer (Differential Pressure Transmitter and Differential Pressure Transducer), and some are tailored for highly sensitive measurements where even minimal changes are significant (Differential Micro-Manometer).	Measurement of pressure drop.	[2,5,10,13,95,114,116,117,128,130,133,134,137,138,139,142,143,144,145,146,147,148,150,152,153,154,157,158]
Hot-Wire Anemometry	The fundamental principles were established in the early 20th century, with significant developments in the 1910s and 1920s.	A thin wire is heated and exposed to the fluid flow. The cooling effect of the fluid on the wire is proportional to its velocity. This technique is sensitive and provides high-resolution measurements but is generally limited to small-scale applications.	Measurement of fluid velocity.	[10,36,114,116,117,136,138,139,140,144,154,158]
Dye-Injection Technique	The use of dyes for flow visualization dates back to the early 20th century, with significant advancements in the mid-20th century.	This technique involves injecting a coloured dye into a fluid flow and recording its movement using a digital video camera. The dye, which is typically brightly coloured for high visibility, acts as a tracer, visually highlighting the flow patterns, turbulence, and mixing processes within the fluid.	Flow visualization.	[2,5,36,119,132]
Naphthalene Sublimation Technique	Gained popularity in the mid-20th century, particularly in the 1950s and 1960s.	Naphthalene is coated on a surface exposed to airflow. As the air passes over the surface, naphthalene sublimates (changes from solid to gas). The rate of sublimation is related to the local heat transfer coefficient. By measuring the mass loss of naphthalene over time, the heat transfer characteristics of the flow can be determined.	Measurement of heat transfer coefficients, particularly in gas-solid interfaces.	[118,122,123,131]
Infrared Thermography	Infrared imaging technology began in the 1950s, with significant advancements in the 1970s and 1980s.	An infrared camera detects the infrared radiation emitted by objects. The intensity of this radiation is related to the temperature of the object. This technique allows for the visualization and measurement of temperature distributions on surfaces without physical contact.	Non-contact measurement of surface temperature.	[10,36,127,140,144,145,149]
Laser Doppler Velocimetry (LDV)	Developed in the late 1960s and early 1970s.	LDV uses the Doppler shift in laser light scattered by particles moving in the flow. Two laser beams intersect at a point in the flow field, and the frequency shift of the scattered light from particles passing through this point is proportional to their velocity.	Measurement of the velocity of particles in a fluid.	[126]
Laser Light Sheets (LLS)	Became prominent with the advancement of laser technology in the 1960s and 1970s.	A laser light sheet illuminates a plane within a fluid flow. Particles seeded in the flow scatter the light, allowing for visualization and analysis of flow patterns. This technique is often used in conjunction with Particle Image Velocimetry (PIV).	Flow visualization.	[111,112,113,118,122,152,153]
Liquid Crystal Thermography (LCT)	Became widely used in the 1970s and 1980s.	Liquid crystals that change colour based on temperature are applied to a surface. When the surface is heated or cooled, the colour change in the liquid crystals can be observed and correlated to temperature changes. This method provides a visual, full-field map of surface temperatures.	Measurement of surface temperature distribution.	[111,112,113,114,115,116,117,155]
Particle Image Velocimetry (PIV)	Began to take shape in the 1980s, with significant advancements in the 1990s due to improvements in laser and imaging technology.	The fluid is seeded with tracer particles, and a laser light sheet illuminates these particles. A camera captures their movement over a short interval. By analysing the displacement of particles between images, the velocity field of the flow can be determined.	Flow visualization and measurement of flow velocities.	[140,154]

offers an in-depth review of discretization methods employed in LVG studies of heat exchangers using CFD. Table 5 contains spatial and temporal discretization as well as grid independence studies to illustrate their importance in discussing the modelling results.

4. Experimental Methods

The comprehensive experimental analysis of LVGs covers a wide range of measurements and techniques. This includes pressure difference assessments using tools like differential pressure meters, gauges, transmitters, transducers, and micro-manometers; temperature evaluations employing thermocouples, Resistance Temperature Detectors (RTDs), infrared thermography, and Liquid Crystal Thermography (LCT); velocity determinations via hot-wire anemometry, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV); calculations of heat transfer coefficients through methods such as the naphthalene sublimation technique; and flow visualization utilizing dye-injection technique, Laser Light Sheets (LLS), and PIV. Table 6 compiles a summary of the experimental techniques outlined above, detailing their development, fundamental principles, applications, and research conducted applying these methods.

5. Different Configurations of Longitudinal Vortex Generators in Heat Exchangers and Their Effects

5.1. Geometric Parameters

5.1.1. Plane Longitudinal Vortex Generators

There are many studies focusing on the difference in the effect of different shapes of plane VGs on heat transfer enhancement. For a specified heat load, DWPs have significant potential to substantially decrease the mass and size of heat exchangers. Fiebig et al. experimentally determined that in an inline tube configuration, the use of DWPs resulted in a 55–65% enhancement in heat transfer, accompanied by a 20–45% increase in the apparent friction factor [114]. Tiggelbeck et al. found that winglets outperformed wings in terms of heat transfer enhancement, with a DWP capable of enhancing heat transfer by 46% at a Reynolds number of 2000, and up to 120% at a Reynolds number of 8000, compared to the heat transfer on a flat plate [115]. Fiebig et al. investigated the performance differences of DWPs used in FTHEs with different tube shapes (circular tubes and flat tubes). [116]. Study findings indicated that in a staggered fin-and-tube configuration, longitudinal vortices generated by DWPs led to a modest heat transfer increase of about 10% for circular tubes, but a significant 100% increase for flat tubes [116]. A heat exchanger element equipped with flat tubes and DWPs achieved nearly double the heat transfer and only half the pressure loss compared to an equivalent element with circular tubes [116]. In the study carried out by Torii et al., for staggered tube banks, the addition of delta winglets resulted in a heat transfer augmentation ranging from 30% to 10%, and a pressure loss reduction of 55% to 34%, across Reynolds numbers from 350 to 2100; for in-line tube banks, the heat transfer augmentation was observed to be between 20% to 10%, with a corresponding pressure loss reduction of 15% to 8% [120]. Kwak et al. discovered that in an in-line fin–tube bundle configuration, the application of delta winglets led to an overall heat transfer enhancement of 10–25% and a pressure loss increase of 20–35%, across a range of Reynolds numbers from 300 to 2700 [121]. In a follow-up study, they observed that in a configuration with three rows of tubes and a single transverse row of delta winglets adjacent to the front row of tubes, heat transfer increased by 30–10%, while pressure loss decreased by 55–34% as the Reynolds number rose from 350 to 2100 [125]. O’Brien et al. conducted research on the effect of DWPs on finned oval-tube heat exchangers, and they revealed that incorporating a single DWP into the oval-tube geometry resulted in a notable average heat transfer enhancement of 38% compared to the setup without DWP, with only a modest increase in the friction factor observed [127]. The experimental results of Pesteei et al. showed that utilizing DWPs led to a significant enhancement of the heat transfer coefficient, on the order of 46%, accompanied by an 18% increase in pressure drop compared to a plain fin–tube heat exchanger [130]. Wang et al. experimentally determined that the application of RWPs can increase heat transfer rate by 10–45% across the investigated Reynolds number range of 3000 to 20,000 [133]. Joardar and Jacobi compared the performance difference between a single DWP and three DWPs, and they identified that within the Reynolds number range of 220 to 960, the air-side heat transfer coefficient experienced an increase of 16.5–44% with the arrangement of a single DWP and 30–68.8% with the arrangement of 3 DWPs [134]. Although the 3 DWP array demonstrated superior heat transfer performance over the single DWP, it incurred a greater pressure drop penalty, which notably diminished as the Reynolds number increased [134]. In comparison to the wavy fin without delta winglets, Tian et al. noted that the wavy fin using delta winglets in staggered and in-line setups experienced respective Colburn factor and friction factor enhancements of 13.1%, 7.0% and 15.4%, 10.5%, while the delta winglet amplified the fin channel’s pressure drop, the heat transfer saw a greater increase [47]. Chu et al. found that for Reynolds numbers between 500 and 880, the introduction of RWP to the baseline configuration resulted in a substantial increase in the air-side heat transfer coefficient, ranging from 28.1% to 131%, accompanied by a corresponding increase in pressure drop between 11.3% and 121.4% [49]. Experimental findings of Promvonge et al. [138] and Chompookham et al. [139] revealed a notable impact of the ribs and DWPs on both the heat transfer rate and friction loss, compared to a smooth wall channel. The Nusselt number and friction factor values for configurations employing both the ribs and DWPs were significantly higher than those using either the ribs or DWPs alone [138,139]. Hwang et al. found that the presence of delta winglet VGs on fins enhanced heat transfer performance, particularly at high Reynolds numbers or air velocities, while also maintaining a lower pressure loss compared to plain fins, primarily due to improved flow mixing and delayed flow separation [57]. According to Du et al., when 6 DWPs were punched onto the wavy fin surface, the average friction factor rose by 13–83% with the Reynolds number varying from 500 to 4500, while the average Nusselt number exhibited an increase of 21–60% as the Reynolds number ranged from 1500 to 4500 [144]. Additionally, the average Performance Evaluation Criteria (PEC) reached a value of up to 1.31 [144]. As illustrated in Figure 4, Huisseune et al. numerically explored the impact of integrating delta winglet VGs into the surfaces of louvered fins, specifically in each tubes near wake region. They pointed out that the incorporation of delta winglets resulted in an elevated net core pressure drop and a more efficient heat transfer compared to the baseline design devoid of delta winglets [63]. Three significant mechanisms contributing to the enhancement of heat transfer were identified: improved fluid mixing, thinned boundary layer, and delayed flow separation from tube walls [63]. Tian et al. [48] and Caliskan [145] indicated that the DWP-equipped channel outshone the one with RWPs in heat transfer performance. The use of delta winglet VGs in pipes can also significantly enhance heat transfer [146,152,153]. Khoshvaght-Aliabadi et al. stated that using a specialized arrangement of delta-winglets on the VG insert of circular pipes, an ideal balance between enhanced heat transfer and friction can be attained, yielding the highest heat transfer coefficient and a peak PEC value of 1.41 at a Reynolds number of 8715 [146]. Zhai et al. observed that the Nusselt number (Nu) tended to rise with an increase in Reynolds number (Re), whereas the friction factor showed a decreasing trend with Re [153].

5.1.2. Curved Longitudinal Vortex Generators

Zhou and Ye compared the thermohydraulic performance of curved TWPs and plane RWPs, TWPs, DWPs in the Reynolds number range of 700–26,800, indicating that in laminar and transitional flow regions, plane DWPs performed optimally, while in fully turbulent regions, curved TWPs stood out for their excellent thermohydraulic performance, primarily due to their streamlined configuration that led to reduced pressure drop [142]. They also revealed that a greater angle of inclination (α = 20°), a larger curvature ratio (b/a = 1/2), and a smaller attack angle (β = 0° and 15°) led to improved thermohydraulic performance for curved TWPs [142]. Among six winglet VGs without holes (plane and curved RWPs, TWPs, DWPs) investigated by Zhou and Feng, the curved DWPs exhibited the best thermohydraulic performance across Reynolds numbers from 650 to 21,000 [13]. The experimental outcomes of Wu et al. also demonstrated that curved DWPs were highly effective in improving heat transfer when compared to equivalent plain fin geometries [151]. In the study carried out by Gong et al., under working conditions encompassing a range of Reynolds numbers (800–3000), optimal heat transfer performance was achieved by curved RWPs when the leading edge of VGs was aligned with the transversal axis of the tube, the fin spacing to tube outer diameter ratio was 0.239, the height of VGs was about 0.8 times the fin spacing, and the base arc length diameter of VGs was approximately 3.8 times their optimal height [71]. According to Lin et al., at a Reynolds number of 2000, optimal heat transfer performance was observed when the fin spacing was 0.293 times the fin collar outer diameter and the base arc diameter of curved DWPs was 1.95 times the fin collar outer diameter [73]. Curved VGs, due to their streamlined design, outperform plane VGs in heat transfer and pressure loss by 8.2–15.8% under identical conditions [14]. Deshmukh et al. conducted a study on curved delta wings and pointed out that the implementation of curved delta wings resulted in Nusselt number enhancements ranging approximately from 5.0 to 15.0 times greater than those observed with smooth tubes [149]. According to Esmaeilzadeh et al., curved TWPs demonstrated a superior overall performance and a lower pressure drop in comparison to the plane one [79]. In the study conducted by Naik et al., curved rectangular winglet VGs exhibited a maximum heat transfer enhancement of 3% and a notable 32% decrease in friction factor when contrasted with plane rectangular winglet VGs, as indicated in Figure 5 [86]. Among the variants, concave rectangular winglet VGs led in heat transfer enhancement and pressure loss, with a 75° arc angle concave rectangular winglet VGs achieving a peak heat transfer enhancement of 22% relative to the channel without rectangular winglet VGs [86]. However, convex rectangular winglets VGs demonstrated superior thermodynamic efficiency and overall thermal performance, surpassing both plane and concave rectangular winglet VGs [86].

Lu and Zhai showed that curved VGs possessing a curvature of 0.25 and oriented at an angle of attack of 15° demonstrated superior thermal hydraulic performance [88]. They also observed that curved VGs featuring decreased inclination angle and increased height exhibited improved thermal hydraulic performance at high Reynolds numbers (Re > 1620), while those with greater inclination angle and reduced height yielded enhanced thermal hydraulic performance at low Reynolds numbers (Re < 1620) [88]. As depicted in Figure 6, Song et al. conducted a numerical analysis on the enhancement of heat transfer in plate heat exchangers using concave and convex curved delta winglet VGs, examining the impacts of varying central angles (θ = 10–80°) and angles of attack (β = 20°, 30°, 40°) on thermal hydraulic performance across Reynolds numbers ranging from 200 to 1400 [90]. Compared to plane VGs, concave curved VGs proved to be advantageous for enhancing heat transfer, with the Nusselt number increasing alongside both the attack angle and the central angle [90]. Conversely, convex curved VGs were found to be less effective for heat transfer enhancement relative to plane VGs, with Nu rising as the attack angle increased but decreasing as the central angle increased [90]. Concave curved delta winglet VGs exhibited a 19.7% higher Nu and an 11.35% greater surface goodness factor (JF) compared to those measured for convex curved delta winglet versions within the examined parameter range [90]. An optimal configuration for concave curved VGs was found to significantly enhance heat transfer performance, with the highest efficiency achieved at a β of 30° for θ less than 60°, and for θ greater than 60°, VGs with a β of 20° were markedly more effective, particularly at an optimal θ of around 70° [90]. Naik et al. examined how variations in the arc angle of curved rectangular winglet VGs affected the flow dynamics and thermal properties, while maintaining a constant chord length [102]. They found that the concave rectangular winglet VGs with a 90-degree arc angle produced the strongest longitudinal vortices and the highest heat transfer augmentation of 39.4% at a Reynolds number of 2000, compared to the channel without VGs [102]. However, the convex rectangular winglet VGs with a 30-degree arc angle offered a better thermal performance factor due to lower friction losses [102]. Hu et al. revealed that concave curved VGs created robust longitudinal vortices that intensified fluid mixing and enhanced heat transfer, resulting in maximum increases of 30.4% in the Nusselt number and 25.9% in the surface goodness factor compared to a smooth wavy channel [108]. While curved VGs can enhance heat transfer performance, they are not inherently superior to traditional VGs and require specific positional and geometric criteria to achieve optimal performance [98].

5.1.3. Wavy Longitudinal Vortex Generators

Gholami et al. numerically examined the impact of pressure loss and heat transfer enhancement in finned circular-tube heat exchangers featuring wavy-down and wavy-up rectangular winglets, focusing on flows with relatively low Reynolds numbers (400–800) [16]. As shown in Figure 7, wavy-up rectangular winglets yielded the highest heat transfer enhancement, outperforming conventional and wavy-down rectangular winglets, while wavy-down rectangular winglets were associated with lower friction factor and pressure drop penalty compared to both conventional and wavy-up rectangular winglets [16]. Sawhney et al. investigated wavy delta winglets with different wave numbers (3, 5, and 7) as depicted in Figure 8, and they concluded that these winglets offered superior thermal performance compared to smooth channels, with the inline setup achieving a higher Nusselt Number than the staggered arrangement [150]. Using five-wave delta winglets (ϕ = 5) with a relative longitudinal pitch of 3 (P/H = 3) at a Reynolds number of 4000, the Nusselt number enhancement reached 223% over a flat plate, accompanied by a 10.3-fold increase in the friction factor, resulting in a thermohydraulic performance of 2.09 for this configuration [150].

5.1.4. Other Innovative Geometries

Wang et al. introduced wave-type VGs and identified that the application of these VGs significantly improved mixing characteristics [2]. When compared to plain fin geometry, the frictional penalty associated with these VGs was approximately 25–55% higher, with their pressure drop penalty exhibiting relatively low sensitivity to Reynolds number changes [2]. Wang et al. then compared the performance of annular and delta winglets, and they indicated that with identical winglet heights, the delta winglet induced more intense vortical motion and flow unsteadiness compared to the annular winglet, resulting in superior mixing [5]. Despite this enhanced mixing, the delta winglet incurred lower pressure drops than the annular winglet [5]. Additionally, when compared to plain fin geometry, the extra pressure drop penalty associated with these winglet VGs showed relatively little sensitivity to Reynolds number changes [5]. Wang et al. also investigated the heat transfer performance of semi-simple winglets, comparing their effectiveness to that of louvered fins [148]. The louver fin geometry exhibited superior heat transfer coefficients compared to the semi-dimple winglet geometry, largely attributed to enhanced fluid mixing [148]. For heat exchangers with 2 or 4 tube rows, the louver fin’s heat transfer coefficients were about 2–15% greater than those of the semi-dimple winglet setup [148]. As shown in Figure 9, Min et al. introduced modified RWPs created by cutting off the four corners of rectangular winglets, and the experimental findings demonstrated that these modified RWPs possess superior flow and heat transfer properties compared to traditional RWPs [140].

Oneissi et al. conducted numerical simulations on the classical DWP as a baseline, and then examined a novel vortex generator configuration, the inclined projected winglet pair (IPWP), which exhibited superior performance [77]. The IPWP configuration demonstrated a 50% reduction in peak friction magnitude, a 30% improvement in vorticity, and a 6% increase in the thermal enhancement factor relative to the DWP [77]. Zhang et al. investigated five different types of VGs, which are streamlined winglet pairs (SWPs), isosceles right-angled triangular winglet pairs (IRATWPs), equilateral triangular winglet pairs (ETWPs), spline curve winglet pairs (SCWPs), and semicircle winglet pairs (SEWPs) [94]. They observed that SWPs exhibited the lowest pressure drop, and utilizing these VGs resulted in a 46% increase in heat transfer coefficients compared to a heat exchanger without VGs [94]. As illustrated in Figure 10, Dogan and Igci conducted experimental research on a novel type of VG (NTVG) and revealed that NTVG delivered both a lower friction factor and a higher Nusselt number compared to DWP across all tested Reynolds numbers, indicating that NTVG achieved superior heat transfer enhancement relative to DWP [154]. The highest thermal enhancement factor (TEF) reached approximately 1.15 for DWP and was recorded at about 1.34 for NTVG at a Reynolds number of 5000 [154]. At a transverse pitch ratio of 0.4, the NTVG achieved its highest TEF value [154]. A single delta winglet was able to generate one longitudinal vortex, while a single NTVG was capable of generating two longitudinal vortices; the creation of longitudinal vortices persistently interfered with the thermal boundary layer, promoting the intermingling of cold and hot fluids and consequently leading to improved heat transfer [154].

5.1.5. Height, Length, and Thickness

The influence of height, length, and thickness of VGs on heat transfer and flow structure has also been extensively studied. Wu and Tao noted that the thickness of rectangular winglets marginally impacted heat transfer near VGs and negligibly affected the channel’s total pressure drop [7,43]. Tang et al. identified that enhancing the heat transfer performance of a vortex-generator fin can be achieved by increasing the length of DWPs or by decreasing their height [45]. However, Zeng et al. presented a differing observation, exhibiting that elevating the height and length of DWPs significantly boosts heat transfer intensity, albeit with a corresponding rise in pressure drop [53]. Sharma et al. observed that the escalation in the dimensions of the winglets resulted in a more pronounced diversion of the primary flow towards the thermal isolation region, thereby intensifying thermal mixing and mitigating the formation of large eddies, leading to a marked improvement in heat transfer at the cost of a moderate increase in pressure losses [105]. Lotfi et al. revealed that wheeler wishbone (WW) VGs with a width-to-length aspect ratio of 0.5 achieved the most effective heat transfer performance [18]. As indicated in Figure 11, Zeeshan et al. examined four VG heights (40%, 50%, 60%, and 70% of the channel height), employing the Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) method to identify the optimal performance configuration [80]. Based on the area goodness factor, VGs with a height constituting 60% of the channel’s height demonstrated superior thermal hydraulic performance in comparison to alternative height configurations considered [87]. At this height, heat transfer was enhanced by 27.40% to 35.42%, albeit with a 17.79% to 25.76% higher pressure loss, relative to the baseline case across the examined Reynolds number range from 500 to 900 [87]. Tang et al. demonstrated that heat transfer intensity was significantly enhanced by lessening the position of VGs and by raising their height, although this was accompanied by an increased pressure drop [78]. Additionally, they also observed that both the friction factor and Nusselt number exhibited an initial increase followed by a decrease as the length of VGs was extended [78]. Sun et al. found that the Nusselt number and friction factor both escalated with the quantity and height ratio of rectangular winglets, with the thermal enhancement factor reaching a maximum value of up to 1.27 at a height ratio of 0.05 [95]. However, the height of the winglet exerted a negligible influence on the Colburn factor across varying Reynolds numbers [83].

5.2. Positional Parameters

5.2.1. Common-Flow-Down and Common-Flow-Up Setups

Various studies have demonstrated that the placement and alignment of VGs in a heat exchanger or a channel significantly influence its heat transfer efficiency. Kwak et al. discovered that in a staggered three-row tube bundle, a single transverse row of DWPs arranged in the common-flow-down (CFD) setup enhanced heat transfer by 5–15% and increased pressure loss by 2–10%, while DWPs arranged in the common-flow-up (CFU) setup improved heat transfer by 10–30% and decreased pressure loss by 34–55%, both compared to fin–tube bundles without winglets and measured across Reynolds numbers from 350 to 2100 [129]. However, Tian et al. noted that in the channel with DWPs, there is a minimal distinction between the CFU and CFD setups, whereas in the channel with RWPs, the CFD configuration notably surpassed the CFU configuration in overall performance [48]. Sinha et al. evaluated five distinct strategic placements of the VGs: common-flow down in series (CFD–CFD), common-flow up in series (CFU–CFU), combined (CFD–CFU), staggered rows of winglet (SRW), and inline rows of winglet (IRW) as illustrated in Figure 12 [61]. They indicated that, among the various VG arrangements, the CFU–CFU configuration excelled in both quality factor and heat transfer performance at Reynolds numbers in the range of 250–1580 [61]. According to Abdelatie et al., maximum heat transfer efficiency, characterized by elevated values of efficiency index (η), area goodness factor (G), and effectiveness (ε), alongside minimized fluid-flow parameters such as the friction factor, is attained at orientations of +5° counterclockwise common-flow down (CFDn) downstream and −15° clockwise common-flow up (CFUp) downstream [83]. Zhang et al. found that DWPs set up in the CFD configuration consistently delivered the best overall thermal performance across various Reynolds numbers, achieving up to a 5.51% improvement in heat transfer performance compared to setups featuring five continuous ribs [155].

5.2.2. Angle of Attack

Fiebig et al. stated that longitudinal vortices remained stable at higher angles of attack [111]. Within a Reynolds number spectrum of 500 to 2500, the three-row fin-and-oval-tube heat exchanger equipped with VGs demonstrated a 13.6–32.9% enhancement in the average Nusselt number and a 29.2–40.6% increase in pressure loss compared to the baseline scenario, and optimal heat transfer performance was attained with VGs positioned downstream, set at an angle of attack of 30°, and configured with the minimum number of tube rows [50]. Zeng et al. [53], Promvonge et al. [138], and Zhai et al. [153] noted that elevating the attack angle of VGs significantly boosted heat transfer intensity, albeit with a corresponding rise in pressure drop and friction factors. As represented in Figure 13, the experimental findings of Wu and Tao indicated that the average Nusselt number on the surface of a flat plate with DWP increased as the attack angle was raised, compared to a flat plate without DWP within the tested Reynolds number range of 500–2000 [141]. Lotfi et al. found that rectangular trapezoidal winglet (RTW) VGs excelled in heat transfer enhancement at larger attack angles between 15° and 75°, outperforming angle rectangular winglet (ARW) and curved angle rectangular winglet (CARW) VGs, due to their larger surface area interacting with airflow and inducing robust streamwise vortices [18]. Conversely, at smaller attack angles, CARW VGs demonstrated superior thermo-hydraulic performance [18]. Li et al. noted that rectangular winglets outperformed delta winglets in heat transfer enhancement at identical angles of attack, with the former achieving optimal performance between 20° and 30°, and the latter at 45° [72]. Samadifar and Toghraie identified that rectangular winglet VGs had the optimal effectiveness in enhancing heat transfer at the angle of attack of 45° [20]. Luo et al. pointed out that the optimal attack angle for delta winglet VGs in wavy fin plate heat exchangers was 45°, which, along with the integration of wavy fins, boosted the thermal performance factor by 26.4% [89]. The results of Zhai et al. showed that a peak thermal enhancement factor of 1.44 can be obtained at an angle of attack of 30° for a Reynolds number of 5000 in a circular pipe equipped with DWPs [153]. The effect of angle of attack on the heat transfer enhancement properties of curved winglets was evaluated by Berber et al., and they observed that the increase in the attack angle of curved winglets led to higher Nusselt numbers, performance evaluation criteria values, and friction factors [156]. Specifically, curved winglets at attack angles of 0°, 30°, and 60° enhanced heat transfer by 217.39–291.30%, 260.86–465.21%, and 278.26–476.08%, respectively, compared to a plain tube [156]. The PEC values for curved winglets at these angles were in the ranges of 1.22–1.78, 1.28–1.86, and 1.32–1.89, respectively [156]. Correspondingly, the friction factors in the inner rectangular channel for these attack angles were about 8.93–10.33, 10.66–14.16, and 14.96–19.13 times higher than that of a plain tube [156].

5.2.3. Location

Mitra and Fiebig stated that aligned double rows of delta winglets demonstrated a greater enhancement in heat transfer compared to their staggered counterparts [113]. Longitudinal vortices induced by DWPs can markedly boost the heat transfer performance of finned flat-tube heat exchangers, but this enhancement is reliant on the positioning of DWPs [117]. Among the three locations evaluated by Valencia et al., the optimal one resulted in a 50% increase in heat transfer and a 36% rise in pressure loss [117]. The experimental research conducted by Pesteei et al. exhibited that the optimal placement for the delta winglets was at a streamwise distance (Δx) of 0.5D (where D was the tube diameter) and a spanwise distance (Δy) of 0.5D from the tube [130]. The positioning of delta winglet VGs adjacent to circular tubes fosters stronger longitudinal vortices and creates nozzle-like flow passages that accelerate the flow, significantly enhancing heat transfer by eliminating zones of poor heat transfer [58]. Whereas delta winglets positioned entirely within tube wakes failed to contribute to heat transfer enhancement [62]. Song and Wang indicated that the transverse pitches of VGs were associated with the interaction between longitudinal vortices, and this interaction significantly impacted both the intensity and the heat transfer performance of the longitudinal vortices [76]. Thus, selecting the optimal transverse pitch for VGs is crucial for achieving peak heat transfer performance while avoiding transverse pitches that could lead to suboptimal results [76]. Sarangi and Mishra found that positioning winglets near the central tube proved to be more efficacious in heat transfer, with a significant boost observed when the streamwise and spanwise distances were determined to be −3.201 mm and 7.2 mm, respectively, resulting in a 60% improvement in the Nusselt number compared to the baseline [80]. Chimres et al. revealed that elliptical winglets, featuring a vertical distance of 6 mm, a horizontal distance of 0 mm, a 30° angle of attack, and a 120° trailing angle, delivered the highest performance [81]. Relative to the baseline plain fin, these configurations yielded pressure drops and heat transfer coefficients that were elevated by approximately 35% and 13%, respectively [81]. Song and Tagawa examined the impact of the transverse distance of VGs on the heat transfer performance and the interaction of longitudinal vortices, revealing that for the highest Reynolds number investigated (Re = 1600), the maximal variations in the increments of friction factor, Nusselt number, and longitudinal vortex intensity across different VG transverse distances are 18.5%, 33.9%, and 34.0%, respectively [82]. Shi et al. noted that the vortex generator had an ideal longitudinal position for maximum heat transfer performance, where the Nusselt number rose by 43.9% compared to the plain fin and 9.8% over its original position; additionally, the thermal performance factor at this optimal spot grew by 8.1% from its original location, achieving a value of 1.38 [100]. Naik and Tiwari numerically investigated how various locations of RWPs affect the thermodynamic and thermohydraulic performances of staggered finned circular-tube heat exchangers [101]. As displayed in Figure 14, adjacent RWP locations yielded a higher augmentation in heat transfer but incurred a higher friction loss, resulting in a lower thermal performance factor [101]. In contrast, upstream RWP locations, with stronger longitudinal and horseshoe vortices, enhanced fluid mixing and transport, leading to a notable improvement in heat transfer augmentation and a higher JF due to a reduced friction loss penalty [101]. Hu et al. employed a neural network and a multi-objective genetic algorithm to optimize the arrangement of VGs and used the Pareto optimal strategy to determine the ideal transverse distances, leading to an optimal configuration that enhances heat transfer power by up to 34.6% [108]. Dogan and Erzincan determined that the ratios of transverse and longitudinal pitch play crucial roles in determining thermal performance, with an inline arrangement proving more effective for heat transfer than a staggered one [158]. The optimal thermal enhancement factor was attained with a transverse pitch ratio of 0.16, a longitudinal pitch ratio of 1.5, and an inline arrangement [158].

5.3. Punched Holes

To figure out the effect of punching holes in winglet VGs on heat transfer enhancement, many studies have been conducted to investigate the punched winglet VGs and the parameters of holes, including hole shape, size, location, and number of holes. Wu and Tao [7,43], Modi and Rathod [157] indicated that compared to unpunched setups, rectangular winglets with punched holes exhibited superior heat transfer enhancement near VGs and a decreased flow frictional coefficient. Zhou and Feng noted that the introduction of punched holes significantly reduced flow resistance and enhanced the thermohydraulic performance across all cases [13]. However, the optimal diameter of these holes should correspond to the face area of VGs, with smaller VGs benefiting from relatively smaller holes [13]. Holes punched lower in the vertical direction and at the lateral centreline yield better thermohydraulic performance and heat transfer enhancement [13]. Nonetheless, the positioning of these holes had a minimal impact on the VGs’ flow resistance [13]. As indicated in Figure 15, Lu and Zhou also conducted research on the dimensions of holes and their placement, identifying that punched VGs boosted heat transfer and lessened flow resistance, with an optimal hole-to-vortex generator area ratio of 0.06 for best overall performance [14]. Holes placed lower vertically and near the leading-edge enhanced heat transfer, but their positioning had minimal effect on flow resistance [14].

According to Han et al., rectangular winglet VGs with a hole excelled in thermo-hydraulic performance compared to those without, and based on PEC, Colburn factor and friction factor values, the optimal hole diameter was 5 mm, with its position mildly affecting heat transfer enhancement but greatly influencing VGs’ flow resistance [85]. For the given Reynolds number range (1500–9000), using rectangular winglets with a punched hole in the CFU configuration at an upstream location in a FTHE resulted in a heat transfer increase of up to 34% compared to its non-punched counterpart in the same setup [96]. The punched delta winglet increased the Nusselt number by 78.21 times compared to the plain flat plate and offered a peak thermal enhancement factor of 2.1, while the flapped delta winglet’s thermal enhancement factor was approximately 2.16, which was about 2.9% higher than the punched version [99]. As shown in Figure 16, Modi et al. conducted numerical studies to assess the thermo-hydraulic performance of finned circular-tube heat exchangers outfitted with rectangular winglet VGs with different numbers of circular punched holes (1, 2, 4, and 6) [97]. They noted that rectangular winglet VGs featuring circular punched holes significantly enhanced FTHE’s thermo-hydraulic performance, with the 6-hole variant outshining others by raising the Nusselt number approximately 45.95% at a Reynolds number of 400 and 57.37% at 2000 [97]. Among various configurations of rectangular winglet VGs, the version with 6 holes demonstrated the highest values for both Hydro Thermal Performance Factor (HTPF = (Nu/Nu0)/(f/f0)^(1/3)) and Performance Evaluation Criteria (PEC = (j/j0)/(f/f0)), indicating a superior thermo-hydraulic performance for the 6-hole variant [97]. Using curved trapezoidal winglet VGs with circular punched holes notably boosted FTHE’s thermo-hydraulic performance, with the 6-hole variant excelling other curved trapezoidal winglet vortex generator designs, showing a Nusselt number increase of approximately 75.25% and 40.10% at Reynolds numbers of 400 and 2000, respectively [106]. In addition to punched curved trapezoidal winglet VGs, Saini et al. also conducted research on punched curved delta winglet VGs. They observed that FTHE’s thermo-hydraulic performance was notably enhanced by curved delta winglet VGs with circular punched holes, especially the 6-hole variant, which elevated the Nusselt number by about 77.25% and 42.51% at Reynolds numbers of 400 and 2000, compared to the heat exchanger without VGs [107].

6. Recent Advances and Emerging Technologies in Heat Transfer Enhancement

Heat transfer enhancement technologies have made significant progress in recent years, integrating innovative materials, manufacturing techniques, computational methods, and multidisciplinary approaches. This section briefly explores these advanced solutions and highlights potential synergistic applications with LVGs.

6.1. Shape Memory Alloys (SMAs)

Shape memory alloys are smart materials that can deform significantly under thermal stimulation and return to their original shape after heating. In recent years, SMAs have been explored as adaptive vortex generators in heat exchangers [56,166,167,168,169,170,171]. SMA-based vortex generators can passively respond to temperature fluctuations and dynamically change their shape to optimize the vortex strength and turbulence intensity according to operational requirements. This adaptive capability allows active and autonomous control of heat transfer performance without the need for external mechanical actuation, thereby significantly improving thermal efficiency and operational stability. Aris et al. introduced a memory-alloy-based vortex generator for active regulation of heat transfer performance [166]. Subsequently, Aris et al. extended this approach by integrating this vortex generator into a fin-and-tube heat exchanger, performing comprehensive experimental investigations and numerical simulations [56]. Their findings demonstrated that the device achieved a 16% improvement in heat transfer performance under the activated state, and a 19% decrease in pressure losses when deactivated [56]. Vilarrubi et al. introduced a self-adaptive vortex generator made of SMA, showing its effectiveness in sustaining a steady wall temperature under increasing heat flux conditions [167]. Chu et al. conducted both experimental and numerical analyses to evaluate the heat transfer performance of microchannel heat exchangers equipped with SMA-based vortex generators [168]. The microchannel equipped with the SMA vortex generator demonstrated enhanced localized disturbance effects. At a heat flux of 100,000 W/m², the Nusselt number improved by 112% compared to the plain channel and was 9% higher than that of the channel featuring a non-deformed vortex generator [168]. According to Regany et al., implementing a self-adaptive vortex generator enhances wall temperature uniformity by 63.1% compared to a plain channel configuration [169]. Wang et al. [170] and Li et al. [171] introduced a heat exchanger design incorporating SMAs, where a two-way SMA strip functions as a self-adaptive vortex generator to improve heat transfer performance. As fluid temperature rises, heat transfer enhancement ranges between 110% and 125%. Conversely, when thermal demand decreases, the Darcy friction factor drops by 74% to 90%, in line with their proposed mechanism.

6.2. Soft Abrasive Flow (SAF) Finishing Methods

Curved thin-walled structures, such as winglet-type vortex generators, are likely to experience brittle failure or deformation during fabrication because of their complex stress distribution. Traditional processing techniques often struggle to deliver high precision in both geometric accuracy and surface finish. The SAF surface finishing methods offer a more effective solution by establishing flexible contact with the surface, making it particularly suitable for machining complex structure surfaces [172]. The process involves flowing a semi-solid abrasive media through complex internal geometries, smoothing surface roughness without destroying structural integrity. By lowering surface roughness, the SAF finishing techniques can reduce flow friction and inhibit boundary layer separation, significantly improving convective heat transfer and thermal hydraulic performance. Applying the SAF finishing methods to LVG surfaces can further enhance heat transfer efficiency by optimizing vortex shedding characteristics and minimizing undesirable pressure drops.

6.3. Additive Manufacturing (AM) Technologies

The advancement of additive manufacturing technologies, particularly Selective Laser Melting (SLM) [173,174,175,176], Electron Beam Melting (EBM) [177,178], and Fused Deposition Modelling (FDM) [179,180,181,182,183,184,185,186,187,188,189,190,191], has provided new perspectives for the fabrication of vortex generators and heat exchanger surfaces. The FDM technology, also referred to as Fused Filament Fabrication (FFF) technology, is widely recognized for its advantages in rapid prototyping, including affordability, broad material compatibility, ease of operation, and a high level of design flexibility [179,180,181,182,183,184]. This layer-by-layer additive process enables the fabrication of complex geometries. However, it also has several challenges during the extrusion deposition process. Insufficient contact pressure, inadequate interfacial temperature, or limited molding time can affect interlayer healing strength. Weak interlayer healing strength between layers can substantially reduce the mechanical strength of the printed object, thereby restricting the use of FDM in applications requiring high-performance structural components [185,186]. As a result, considerable research has recently focused on improving the interlayer healing strength of components produced by FDM [187,188,189,190,191]. For example, Xu et al. investigated the underlying mechanisms influencing interlayer healing strength in multi-path deposition configurations and demonstrated that optimizing nozzle geometry can significantly improve interlayer healing strength [191]. In summary, additive manufacturing technologies provide design flexibility and the ability to produce complex three-dimensional geometries that are difficult or impossible to achieve using traditional manufacturing methods. Novel structures such as triply periodic minimal surfaces, lattice-based fins, and integrated vortex generators can be easily manufactured and contribute to enhanced heat transfer performance by increasing the surface-to-volume ratio and optimizing the flow channel structure.

6.4. Topology Optimization

Originally introduced by Bendsøe and Kikuchi in 1988 [192], topology optimization reformulates structural optimization as a problem of material distribution. In this approach, design variables indicate the presence or absence of material at specific locations within the design space. Through iterative updates of these variables using mathematical programming techniques, the optimal configuration is achieved. This method has found widespread application across numerous areas of physics [193,194,195,196,197,198,199,200,201,202,203,204,205]. Zeng et al. developed a simplified 2D model to approximate a 3D conjugate heat transfer model for the design of a heatsink and validated the resulting optimized configuration through both experimental testing and numerical simulations [206]. Sun et al. employed topology optimization in the development of a fin-and-tube heat exchanger, proposing an innovative fin configuration featuring surface embossments [207]. These features were optimized to reduce pressure drop, and the approach allowed extensive flexibility in fin geometry design [207]. However, employing topology optimization to the tube-and-fin heat exchanger design presents certain challenges. Firstly, the optimized fin structures are often impractical for direct use due to manufacturing restrictions. Secondly, conventional topology optimization methods typically neglect the influence of heat transfer in the design process. To address these issues, Kobayashi et al. developed a method for designing freeform winglets that incorporates both heat transfer performance and manufacturability of the topology-optimized fin [208]. As a result, the proposed configuration achieved a 16% improvement in the performance factor j/f compared to a fin equipped with traditional rectangular winglet pairs [208]. In conclusion, topology optimization employs advanced computational techniques to determine the optimal material layout within a given design domain, maximizing performance under specified constraints. Applying topology optimization to LVGs can generate innovative designs that maximize vortex strength and heat transfer performance while minimizing pressure losses. Integrating these optimized geometries into heat exchangers can lead to significant improvements in energy efficiency and compactness.

6.5. Machine Learning (ML) Integration with CFD

Recent advancements integrate machine learning algorithms with CFD, creating hybrid frameworks that rapidly predict flow behaviour and heat transfer characteristics with high accuracy. ML-driven CFD approaches can efficiently explore extensive design spaces for LVGs, rapidly identifying optimal configurations. Furthermore, predictive models trained on CFD simulation data could accelerate the design cycle and enhance real-time operational adaptability. Various ML models are employed, including supervised learning algorithms such as Random Forest (RF), Gradient Boosting (GB), Support Vector Regression (SVR), and Artificial Neural Network (ANN) to approximate CFD outputs such as temperature distribution, velocity profiles, and Nusselt number predictions. For example, Berber et al. used ANN algorithms to explore the effects of the innovative fin configuration and different attack angles of winglets (30°, 60°, and 90°) on convective heat transfer in a rectangular channel, considering variations in Reynolds number and plate temperature [209]. Kang et al. employed three machine learning techniques, that is, RF, ANN, and SVR, to predict average heat transfer and net energy loss [210]. The input features included gap distance, bending rigidity, and inclination angle of flexible vortex generators [210]. Among all the models, SVR and ANN delivered the most accurate predictions on both thermal performance and mean energy loss [210]. Wu et al. conducted a study utilizing four machine learning methods, that is, SVR, GB, RF, and XGBoost regression, to develop prediction models for dimensionless heat transfer coefficients in microchannel heat sinks equipped with flexible vortex generators [211]. Xie et al. proposed using Response Surface Methodology (RSM) and ANN for optimizing the design of fin-and-tube heat exchangers equipped with vortex generators [212]. The findings indicated that while both methods provided reliable predictions, ANN demonstrated superior accuracy in predicting the friction factor and Nusselt number compared to RSM [212]. Liang et al. also applied RSM and ANN to analyse how design variations influence the Nusselt number and pressure drop in microchannel heat sinks, and they obtained similar results, that is, ANN provided more accurate predictions than the RSM approach [213]. Li et al. proposed a multi-objective optimization method for designing microchannels featuring a delta winglet pair to achieve optimal hydrothermal performance under conditions of high heat flux [214]. The optimization integrated Non-dominated Sorting Genetic Algorithm II (NSGA-II), ANN, and grey relational analysis [214]. Among the models tested, the genetic algorithm-enhanced back-propagation neural network demonstrated superior accuracy and generalization capabilities in predicting both the friction factor and Nusselt number, outperforming the conventional back-propagation neural network model [214]. Deep learning models, especially Convolutional Neural Network (CNN) algorithms, are increasingly applied to capture spatial features from CFD-generated flow fields, enabling efficient surrogate modelling and flow regime classification. For example, Seal et al. achieved over 98% accuracy in predicting flow pattern images of R-134a refrigerant condensation using CNN algorithms [215]. In this study, principal component analysis and multilayer perceptron neural networks were also employed to visualize the dataset and reduce computational requirements [215]. Reinforcement learning is emerging as a tool to optimize flow control strategies. For example, Ren et al. integrated various machine learning techniques, including reinforcement learning based on the non-Oberbeck-Boussinesq (NOB) approximation and proximal policy optimization (PPO) approximation [216]. An intelligent active flow control approach was developed to enhance fluid heat transfer under laminar flow conditions [216]. Following extensive training, the method demonstrated a 76.7% improvement in heat transfer performance [216]. Unsupervised learning methods like clustering and dimensionality reduction are also used to discover patterns in high-dimensional simulation outputs.

6.6. Potential Synergistic Applications with LVGs

The integration of SMA materials with AM technologies presents a promising pathway for the development of advanced LVG designs in heat exchangers. AM technologies facilitate the fabrication of complex and optimized geometries that can be precisely tailored to enhance thermal efficiency, while SMA materials offer dynamic shape adaptability, enabling components to passively respond to changing thermal conditions. This synergy has the potential to produce self-adaptive LVGs that can adjust vortex strength and distribution in real time, thereby significantly improving both thermal performance and operational flexibility. Future research should focus on improving AM techniques, embedding SMA wires or layers into printed LVGs, investigating the adaptive thermal response mechanisms of these SMA-integrated structures under actual operating conditions, and conducting long-term evaluations to assess their fatigue behaviour and overall durability.

Integrating ML algorithms into topology optimization frameworks provides a novel and powerful approach to enhance LVG designs. By quickly predicting flow behaviour and heat transfer characteristics, ML significantly speeds up the optimization process, allowing topology optimization algorithms to more effectively explore complex design spaces. This synergistic effect helps create efficient, lightweight, and turbulence-optimized LVG configurations to meet specific thermal and fluid conditions. Future research should focus on developing hybrid ML-based topology optimization frameworks specifically for LVG design, validating ML-predicted CFD results against experimental benchmarks to ensure robustness and accuracy, and conducting comparative studies to evaluate the performance and manufacturability of ML-optimized LVGs in contrast to those produced by traditional methods.

SAF applied to AM vortex generators offers an attractive solution for improving surface finish, thereby significantly reducing friction losses and minimizing boundary-layer disruptions. By enhancing the surface properties of complex AM-fabricated vortex generators, SAF contributes to improved aerodynamic performance, greater turbulence generation efficiency, and ultimately more effective heat transfer enhancement. Future research should include experimental investigations into the effects of SAF-treated AM vortex generators on flow turbulence and thermal enhancement, optimization of SAF process parameters specifically for complex AM geometries, and comprehensive evaluations of long-term performance gains and structural durability resulting from SAF application.

7. Recommendations for Future Research

Despite the significant progress in the application of LVGs for heat transfer enhancement in heat exchangers, there are still some research gaps that deserve further investigation. The following suggestions are proposed to guide future research work:

• Develop more sophisticated numerical models that incorporate complex geometric structures and fluid dynamics phenomena. These models should aim to reduce the existing differences between simulation results and experimental data. Attention should be paid to combining actual operating conditions to improve the predictive ability of the model.
• Investigate the application and effectiveness of LVGs in miniaturized heat exchangers commonly used in portable and microscale devices. Research focus should be on optimizing LVG design to minimize space occupation without affecting efficiency, including exploring microfabrication techniques for LVG manufacturing.
• Study the integration of LVGs with other heat transfer enhancement methods, including active techniques such as spray cooling, electrohydrodynamic techniques, fluid vibration, magnetic fields, etc., and passive techniques such as nanofluids, extended surfaces, rough surfaces, porous materials, dimples and protrusions, other inserts, etc. Such integrative approaches could potentially lead to breakthroughs in heat transfer rates and efficiency.
• Design adaptive LVG systems equipped with sensors and actuators that can dynamically adjust their behaviour based on real-time feedback from the heat exchanger’s performance. This approach allows for continuous optimization of energy consumption and performance under a wide range of operating conditions.
• Explore the use of advanced materials in LVGs, such as composites or metamaterials that can withstand extreme conditions while maintaining performance. Research into environmentally friendly materials that are both effective and sustainable for long-term use is also crucial.
• Conduct a comprehensive cost–benefit and environmental impact analysis to evaluate the feasibility of implementing LVGs in industrial settings. The study should include a lifecycle assessment to fully understand the environmental impacts of widespread LVG adoption.
• Expand experimental methods to include long-term performance studies under varying operating pressures. Such studies will help to understand the durability and maintenance requirements of LVGs in industrial applications.

8. Conclusions

This literature review systematically examines a large number of numerical and experimental studies on the enhancement of heat transfer in heat exchangers through the use of LVGs. The review highlights the effectiveness of LVGs in improving heat exchanger performance by generating coherent vortex structures that augment the thermal boundary layer mixing, thereby significantly enhancing heat transfer rates while minimally impacting pressure drop. A comprehensive review of the results from numerous studies indicates that the geometry, size, orientation, and location of LVGs play a key role in optimizing heat transfer enhancement. Numerical simulations are essential to understand the complex fluid dynamics and thermal characteristics induced by LVGs, providing insights into the mechanisms of heat transfer enhancement and facilitating the design of more efficient heat exchanger configurations. Experimental activities, on the other hand, validate the numerical models and provide empirical data that are crucial for the practical application and further development of LVG technologies. Despite some progress, gaps remain in the current knowledge base, particularly regarding the long-term performance, fouling resistance, and economic feasibility of heat exchangers equipped with LVGs. In addition, more comprehensive studies are needed to explore the integration of LVGs in various types of heat exchangers and their performance under different operating conditions. Future research should aim to address these gaps, including developing more sophisticated numerical models, conducting long-term performance studies, and exploring innovative materials and manufacturing techniques for LVGs. Additionally, the environmental impact and sustainability of LVG-enhanced heat exchangers warrant further investigation to ensure that these technologies can actively contribute to energy efficiency goals and carbon footprint reduction. In summary, the use of LVGs presents a promising avenue for enhancing the performance of heat exchangers. Based on the foundation laid by the extensive numerical and experimental activities reviewed in this paper, future advances are expected to lead to more efficient, reliable, and sustainable heat exchange technologies.