Numerical Investigation on Flow Separation Control for Aircraft Serpentine Intake with Coanda Injector

Abstract

Modern military aircraft integrate a large number of high-power-density electronic devices, which leads to a rapid increase in thermal load and poses significant challenges for heat dissipation. A promising thermal management approach is to intake ram air through a fuselage-mounted S-duct inlet and utilize it as a heat sink for the downstream heat exchanger. However, the S-duct’s geometry can induce significant flow separation and total pressure distortion, thereby limiting the mass flow rate. To address these challenges, this study investigates three flow-control strategies—vortex generators (VGs), Coanda injectors, and their combination—using high-fidelity three-dimensional numerical simulations validated against experimental data. The results indicate that VGs effectively suppress local separation and improve flow uniformity, although additional losses limit pressure recovery. The Coanda injector enhances boundary-layer momentum, substantially increasing mass flow throughput and pressure recovery. The combined VGs and Coanda injector approach achieves a lower distortion coefficient and provides a favorable balance between pressure recovery and flow uniformity. These findings demonstrate the potential of hybrid passive–active flow control in improving inlet aerodynamic quality and supporting integrated thermal management systems for future aircraft.

1. Introduction

As the power demand of onboard systems in modern aircraft continues to rise, the associated heat dissipation requirements have increased accordingly [1]. Employing the inlet to introduce external airflow as a cooling medium represents an effective solution [2]. Among various configurations, the S-duct inlet is widely adopted owing to its superior stealth characteristics and compact integration within constrained fuselage space [3]. However, compared with straight ducts, the pronounced curvature and cross-sectional variations in S-duct inlets induce boundary-layer separation, which degrades total pressure recovery and intensifies flow distortion [4]. These effects ultimately compromise engine intake quality and overall aerodynamic performance [5]. Consequently, the effective control of flow separation in S-duct inlets is of significant importance.

Active flow control involves injecting energy into the fluid system or applying external interventions to mitigate boundary-layer thickening [6]. In contrast, passive flow control leverages the inherent properties of the fluid to reduce boundary-layer thickness and enhance aerodynamic performance [7]. Common passive techniques include vortex generators [8] and aerodynamic bumps [9], while active methods mainly adopt boundary-layer suction [10] and blowing [11]. Saad et al. [12] experimentally and numerically investigated the flow separation mechanisms in S-duct inlets. Similarly, Reichert et al. [13] demonstrated that vortex generators can energize low-velocity flow, delaying separation. In addition, Wan et al. [14] confirmed their effectiveness in reducing cyclonic flow distortion within intake ducts. Chen et al. [15] further established that vortex generators can mitigate secondary flow losses. Marco Debiasi et al. [16] numerically verified that boundary-layer jetting and suction effectively improve the total pressure recovery coefficient in S-duct inlets. Similarly, Hamed et al. [17] proposed a hybrid suction strategy combining cross-flow and downstream slits, demonstrating its efficacy in suppressing flow separation. Wang [18] conducted combined experimental and numerical investigations on hypersonic inlets, analyzing their flow mechanisms, startup processes, and performance enhancement methods. Furthermore, Liu et al. [19] demonstrated that combined blowing/suction strategies significantly enhance aerodynamic performance. Huang [20] computationally validated the efficacy of boundary-layer blowing in suppressing shock-induced boundary-layer separation. Among passive techniques, aerodynamic bumps have attracted a lot of attention recently. Bumps modify the local surface geometry to accelerate airflow, thereby increasing boundary-layer kinetic energy and delaying flow separation [9]. Zhang et al. [21] developed an innovative two-dimensional bump configuration and a corresponding design methodology. Hamstra et al. [22] further advanced the inlet design by integrating wave-rider principles, optimizing flow control and enhancing overall inlet performance. In emerging technologies, Liu [23] successfully developed an adjustable plasma actuator system for active flow control through electric field modulation.

Active flow control technology offers the advantage of flight performance optimization through the real-time adjustment of control devices in response to varying flight conditions [7]. However, its implementation is often constrained by system complexity, which may increase an aircraft’s weight and compromise structural layouts [24]. On the other hand, passive flow control techniques feature simpler installation and lower maintenance requirements, but their fixed configurations typically lead to performance degradation under off-design conditions, making them insufficient for comprehensive flow control demands [24]. Consequently, developing cost-effective flow control solutions that maintain efficiency across complex operational scenarios remains a critical research focus in aerodynamics [25]. Vortex generators, though effective in directing airflow to targeted regions or modifying flow angles, demonstrate strong dependence on operating conditions in S-duct inlets. Their geometric parameters and installation positions are typically optimized for specific design points, potentially increasing flow losses during off-design operation [26].

To address these challenges, this study proposes a hybrid flow control strategy that synergistically combines both techniques. For a specified S-duct inlet configuration, we employ a Coanda injector to transform high-pressure engine-bleed air into a high-velocity, low-temperature injector stream. Flow control strategies such as vortex generators and Coanda-based actuators have also been applied to boundary-layer control and propulsion optimization [27,28]. The control methodology incorporates the combined use of VGs and Coanda injector outlets, aiming to enhance flow control effectiveness under the investigated operating condition.

2. Simulation Validation

2.1. S-Duct Inlet Geometry

The geometry used in this study is the S-duct inlet published by the Propulsion Aerodynamics Workshop (PAW), which is organized by the American Institute of Aeronautics and Astronautics [29]. The integrated geometry consists of a horn-shaped constriction duct, a duct adapter, an S-duct inlet, an Aerodynamic Interface Plane (AIP) section, and an intake duct extension section (Figure 1). Tests were conducted in the Georgia Tech Transonic Wind Tunnel, where air is sucked through a vacuum pump to generate low pressure downstream. The airflow is controlled by a pump and measured using a calibrated mass flow detector. The S-duct inlet has an AIP diameter (D) of 5 inches. The S-duct inlet is offset vertically by 1.09 D, and it has an aspect ratio L/D of 3.106, where L (15.53 in) refers to the effective duct length. To evaluate the impact of flow control measures, a row of 10 vortex generators (VGs) is installed near the duct inlet (Figure 2). Each VG featured a chord length of 19 mm and a height of 12.5 mm and was rotated isotropically at a fixed angle of 12.9° [29].

2.2. Grids

In this study, the meshes were generated using the commercial software ANSYS 2024 Fluent Meshing [30]. In order to resolve complex geometries and flow fields with a large gradient, a prismatic mesh was applied in the boundary layer, and a polyhedral mesh was used in the inner region of the flow field. A mesh independence study was first conducted by setting different mesh sizes and refinement schemes. The number of elements in the coarse, medium, and fine meshes was 3 million, 9 million, and 20 million, respectively. The calculated bottom wall’s static pressure curves at the meridional plane are shown in Figure 3. The abscissa $X$ in the figure represents the coordinate along the flow direction, with the unit being in meters. The ordinate $P/P_{i0}$ denotes the ratio of the wall static pressure to the incoming flow total pressure. It can be observed that the results obtained from the coarse mesh are significantly higher than those from the other two meshes, while the results from the medium mesh and fine mesh are almost identical. Therefore, it can be concluded that the solution using 9 million meshes is basically convergent, and this mesh configuration was adopted for subsequent calculations. To accurately capture the possible flow separation that occurs inside the S-duct inlet, the y+ value of the first layer mesh along the wall is less than 1, with a height set to 0.00464 mm. And the number of boundary-layer mesh layers is 20, with a growth rate of 1.2 for the baseline smooth mesh without VGs. The maximum mesh size is 5 mm, and the number of mesh elements is 9 million (Figure 4). For the mesh with VGs, local refinement was applied in the vicinity of the generators. The height of the first mesh layer is 0.00343 mm, the geometric growth rate of the boundary layer is 1.2, the number of boundary-layer mesh layers is 15, and the number of meshes is 9 million (Figure 5).

2.3. Solver

The three-dimensional Navier–Stokes equations were solved with the $k-\omega SST$ turbulence model for compressible flow [28]. This method is chosen as it provides a reasonable trade-off between accuracy and computational efficiency, making it suitable for parametric studies [30]. The mass conservation equation can be expressed as follows:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla ·\left(\rho \overrightarrow{v}\right)=0,$$

(1)

where $\rho$ denotes the density, and $\overrightarrow{v}$ is the velocity vector. The momentum equation is written as follows:

$${\displaystyle \frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}}+\nabla ·(\rho \overrightarrow{v}\overrightarrow{v})=-\nabla p+\nabla ·\left(\overrightarrow{\tau }\right)+\mathsf{\rho }\overrightarrow{g},$$

(2)

where p is the static pressure, $\overrightarrow{\tau }$ represents the viscous stress tensor, and $\rho \overrightarrow{g}$ is the gravitational acceleration.

The energy equation is solved in the following form:

$${\displaystyle \frac{\partial \left(\rho E\right)}{\partial t}}+\nabla ·(\overrightarrow{v}(\rho E+p))=\nabla ·(k_{eff}\nabla T+\stackrel{̿}{{\tau }_{eff}}·\overrightarrow{v}),$$

(3)

where $k_{eff}$ is the effective thermal conductivity, T is the temperature, and $\stackrel{̿}{{\tau }_{eff}}·\overrightarrow{v}$ denotes viscous dissipation.

This study obtained the time-averaged results of the flow field distribution from transient calculation solutions. In the transient calculation’s setup, the time step size was set to 0.0001 s, and the number of iterations per time step was configured to 10 to ensure that the solution converges sufficiently within each individual time step.

For both cases (i.e., the case with and without VGs), the inlet boundary conditions were specified using the experimental total pressure (99,254.86 Pa) and total temperature (293.35 K) [29]. The static pressure at the outlet surface of the computational domain was adjusted to match the mass flow across the intake with the experimental measurement. The mass flow rates were 2.509 kg/s and 2.464 kg/s for the case without and with VGs, respectively. It can be seen that the mass flow with VGs is smaller due to flow blockage. The mass flow at the outlet is monitored during a simulation to ensure the convergence of the flow field. All solid surfaces are set to be no-slip, adiabatic walls (Figure 6).

2.4. Case Validation

The static pressure distribution along the flow direction on the upper and lower walls of the meridional surface of the inlet channel is extracted and compared with the experimental data, which is noted as φ = 0° and φ = 180° (Figure 7). In Figure 7, the coordinate X represents the position along the flow direction.

Comparisons between the simulated pressure distributions and experimental measurements reveal good agreement (Figure 8 and Figure 9); the maximum deviation does not exceed 3%, which validates the accuracy and reliability of the present computational methodology.

Figure 10 shows the Mach contours on the meridional plane and the total pressure distribution at AIP for the S-inlet. Airflow accelerates through the transition’s constriction, reaching a maximum Mach number of 0.77 at the beginning of the S-duct inlet and an average Mach number of 0.59 at the AIP. The pressure gradient increases due to rapid changes in the local curvature and the duct’s diameter, resulting in flow separation near the upper wall downstream of the AIP.

The computational results for the case with VGs are demonstrated in Figure 11, Figure 12 and Figure 13. Figure 11 presents the Mach number distribution at the meridional plane, demonstrating peak values of 0.77 at the inlet. The corresponding total pressure distribution at the AIP is quite different from the contour in Figure 9. While the low-pressure region near the bottom surface is obviously larger with VGs, another two meridional low-pressure regions (denoted with the black boxes) can be observed at the AIP. Flow visualizations with Q-criterion (Figure 12) illustrate the wake vortex formation when the fluid encounters the VGs array. These vortices subsequently convect downstream and ultimately form the vortex pairs near the duct walls, as indicated by the streamtraces in Figure 13, which directly reduces the total pressure observed at the AIP.

Calculations reveal that the addition of VGs results in a reduction in the total pressure at the AIP, as indicated by the recovery factor (where $P_0$ refers to the total pressure at the AIP, and $P_{i0}$ is total pressure of the freestream) in

Table 1. Total pressure recovery factor of the validation case.

Location	Inlet	${\mathit{P}}_0/{\mathit{P}}_{\mathit{i}0}$
AIP	Smooth S-duct inlet	0.9706
	S-duct inlet with VGs	0.9654
Outlet	Smooth S-duct inlet	0.9543
	S-duct inlet with VGs	0.9507

, which is due to the blockage of the inlet flow caused by the VGs, as well as the energy loss caused by the vortex wake created by the VGs. It has been demonstrated that the VGs may not be effective in generating the required vortex strength and controlling the flow separation under non-designed conditions, and they can even cause additional pressure losses [31]. The observed performance of the VGs in this work highlights the need for optimized VG geometries or alternative flow control approaches to mitigate these adverse effects while maintaining separation control capability.

3. Results and Discussion

3.1. Flow Separation in the S-Duct Inlet

Given the absence of flow separation in the baseline PAW4 configuration under the experimental conditions, we implemented geometric modifications to the S-duct inlet profile to test the control effect of different measures. Figure 14 presents a comparative visualization of the original (orange contours) and modified (black contours) geometries. With the same simulation strategies, the flow field obtained from the present geometry is shown in Figure 15. It can be seen that there is an obvious flow separation at the bottom of the S-duct inlet due to the steep curvature. The airflow near the top region at the AIP is subjected to centrifugal forces, which lead to the formation of a transversal pressure gradient, thus forming a flow separation at the AIP, as shown in Figure 16. In this study, only the flow separation near the lower wall of the intake is considered. In order to rule out the influence of flow separation near the upper wall, the AIP2 plane is selected as another axial position to demonstrate the total pressure deficit caused by flow separation near the bottom wall, as shown in Figure 17 and Figure 18. The total pressure distribution at the AIP of the S-duct inlet (Figure 17) demonstrates the highly unsteady nature of the flow field, and a time-accurate simulation may be needed to capture this oscillation; however, in steady-state simulations, the mass flow has already converged.

Here, we adopt ${DC}_{60}$ to represent the flow distortion strength of the flow separation region, which is defined as follows:

$${DC}_{60}={\displaystyle \frac{{\overline{P}}_{t,AIP}-{\overline{P}}_{t,60}}{{\overline{P}}_f}},$$

(4)

where ${\overline{P}}_{t,AIP}$ is the average value of total pressure at AIP, ${\overline{P}}_{t,60}$ is the area-averaged total pressure in the worst 60° circumferential sector, and ${\overline{P}}_f$ is the average dynamic head at the AIP.

3.2. S-Duct Inlet Flow Separation Control with Vortex Generators

As illustrated in Figure 19, the VGs were installed on the lower surface of the inlet duct at the position of X = 0.231 m. The axial positions of Plane 1 to Plane 4 are located at X = 0.137 m, X = 0.252 m, X = 0.350 m, and X = 0.493 m, respectively. Compared with the smooth S-duct inlet, the installation of VGs substantially reduces the low-pressure region at the AIP, indicating the effective suppression of flow separation. Quantitatively, the total pressure recovery coefficient increases to 0.9439, while the total pressure distortion coefficient decreases to 0.1439, both superior to the baseline configuration without VGs. The flow-control mechanism can be attributed to the streamwise vortices generated by the VGs, which entrain high-momentum fluid from the core into the near-wall region (Figure 20 and Figure 21). This momentum transfer strengthens the boundary layer, enabling it to better withstand the adverse pressure gradient and thus delay or suppress separation. In addition, the secondary flow induced by the vortices redistributes low-energy fluid near the inner wall, thereby shrinking the separation bubble, reducing the low-pressure area at the AIP, and improving flow uniformity (Figure 22).

In conjunction with the PAW4 case, it is evident that VGs are conditionally effective. Under attached-flow conditions, their presence introduces additional losses and increases the total pressure deficit; however, under separated-flow conditions, they re-energize the boundary layer, effectively mitigate separation, and slightly enhance aerodynamic performance. The current VG configuration is in accordance with the PAW-4 experiment. Under off-design conditions, the flow control capability of the VGs may decrease.

Numerical simulations under various operating conditions reveal that the flow control effectiveness of the VGs deteriorates as the Mach number increases (Mach = 0.18, 0.19, and 0.2, as shown in Figure 23). This performance degradation at higher Mach numbers suggests that the current VG configuration may not provide sufficient vortex strength to counteract intensified adverse pressure gradients. To address this issue, increasing the VG’s blade height, length, and installation angle is necessary to enhance vortex intensity and boundary-layer momentum exchange. Furthermore, to improve robustness, variable VGs could be employed. Such a design would enable the VGs to actively adjust their geometric parameters in response to varying flow conditions, thereby maintaining optimal aerodynamic effectiveness across a wide operational envelope. This adaptive approach ensures sustained suppression of flow separation, leading to higher total pressure recovery and reduced flow distortion even under off-design conditions.

3.3. Flow Control with Coanda Injector in S-Duct Inlet

3.3.1. Geometric Design of Coanda Injector

When designing the Coanda jet nozzle’s geometry, the inlet pipeline diameter should be selected appropriately based on the actual flow rate, avoiding cross-sectional changes in order to reduce total pressure loss. When the pipeline diameter changes, it should be designed with a smooth transition. The geometry of the Coanda injector is shown in Figure 24, where a smooth transition from a circular cross-section to a narrow rectangular exit area can be seen. This can reduce the separation and vortex caused by the sudden expansion or contraction of fluids, thus reducing the total pressure loss. The exit of the Coanda injector is designed as a curved surface to ensure that the injector flow attaches to the wall’s surface.

A three-dimensional numerical simulation was conducted, and the total pressure distribution contour on the nozzle’s meridional plane is shown in Figure 25. The inlet boundary conditions were specified as a Mach number of 0.2, static temperature of 288.85 K, and static pressure of 101,325 Pa. The numerical results indicate that the outlet velocity increased to 0.47 Mach, corresponding to a total pressure recovery coefficient of 0.9823.

3.3.2. Control of S-Duct Inlet Flow Separation by Coanda Injector

In the present study, the designed Coanda injector nozzle was located at X = 0.253 m, with the nozzle exit attached to the S-duct inlet (Figure 26). This configuration was designed to maximize the Coanda attachment effect while minimizing flow disturbance. Due to the Coanda effect, a high-velocity jet placed at an appropriate location on the surface of the inlet can keep the flow close to the surface in such a way that boundary-layer separation can be reduced or avoided (Figure 27). The use of the Coanda jet creates a more stable airflow in the inlet, reducing drag and flow separation and improving the overall performance of the engine or other aerodynamic systems [32].

The calculation conditions adopted in the numerical simulation of this section are consistent with those in Section 3.1. Figure 27 and Figure 28 reveal substantial suppression of the separation zone in the inlet’s meridional plane, with only a minimal recirculation region persisting downstream of the nozzle’s exit. The total pressure recovery coefficient is 0.9515, and the total pressure distortion index at the AIP is 0.1530 (Figure 29).

3.4. Control of S-Duct Inlet Flow Separation by Combination of Coanda Injector and Vortex Generator

Considering various spatial configurations between the VGs and the Coanda injector, such as the axial spacing and relative positioning (Figure 30), the total pressure contours at the AIP are illustrated in Figure 31. The VGs are fixed at X = 0.245 m, while the Coanda injector is moved to three different positions: (a) X = 0.250 m (Location 1), (b) X = 0.253 m (Location 2), and (c) X = 0.256 m (Location 3). The comparison reveals that the flow field characteristics are highly sensitive to the spatial arrangement of these flow-control devices. After evaluating multiple configurations, the optimal spatial layout that achieves the most effective flow control performance was selected at Location 2 (X = 0.253 m), as shown in Figure 32. Only a small region of flow separation can be observed below the injector in Figure 33. A comparison of the numerical simulation results for different flow control techniques in

Table 2. Total pressure recovery factor.

Condition	σ	DC
Baseline	0.9405	0.1634
VGs	0.9439	0.1439
Coanda	0.9515	0.1530
VGs and Coanda	0.9465	0.1366

indicates that the combined flow control approach employing VGs and Coanda jet increases the total pressure recovery coefficient of the inlet and achieves the lowest total pressure distortion coefficient, with the total pressure contour at the AIP shown in Figure 34. The flow field with and without VGs using the Coanda injector is compared in Figure 28 and Figure 33. The velocity curve of the flow field at a position 1 mm away from the lower wall of the S-inlet on the meridional plane is presented in Figure 35. In the baseline case, the flow separation region is in the range of X = 0.45~0.66 m. For the case with VGs, the flow separation region is located between X = 0.48 m and X = 0.53 m. In contrast, no flow separation region is observed in cases using the Coanda injector alone and the combined configuration of the Coanda injector with VGs.

This improvement arises because the hybrid flow control strategy mitigates flow separation through two complementary mechanisms: The Coanda injector enhances boundary-layer momentum via direct momentum injection, while the VGs generate vortices that strengthen momentum exchange within the boundary layer, further improving flow attachment. The combination of these methods effectively energizes the boundary layer, stabilizes airflow attachment, reduces separation, and thereby lowers pressure loss in the S-duct inlet while enhancing overall pressure recovery efficiency and aerodynamic performance. In this configuration, the total pressure recovery coefficient is slightly lower than that achieved with the Coanda injector alone due to additional losses introduced by the VGs. This reduction originates from the blockage and additional mixing losses caused by the VGs. Future optimization could focus on adjusting VG geometry (height, thickness, and angle) to balance vortex strength and total pressure loss. Nevertheless, considering the overall improvements in separation control and pressure recovery, this trade-off is acceptable.

4. Conclusions

To reduce flow separation in the S-duct and mitigate flow distortion in downstream areas, some flow control strategies were tested, including vortex generators (VGs), Coanda injectors, and their combination. The results are summarized as follows:

(1)

The CFD simulations are validated against experimental data, showing good agreement and confirming the accuracy of the numerical approach.

(2)

With the VGs inside the S-duct inlet, flow separation is suppressed, the recirculation region is reduced, and the total pressure distortion coefficient at the AIP decreases, while improvements in total pressure recovery remain limited. The current VGs configuration proves beneficial under specific conditions but may require optimization for broader operational envelopes to maximize its aerodynamic effectiveness.

(3)

With the Coanda injector installed in the S-duct inlet, direct momentum injection energizes the boundary layer, significantly improving pressure recovery and mass flow supply, while moderately reducing distortion though less effectively than VG.

(4)

With the combined VGs and Coanda injector, the method achieves the lowest total pressure distortion coefficient and a higher total pressure recovery coefficient than VGs alone. Although the recovery is slightly lower than the Coanda injector case due to additional flow blockage from VGs, the coupled strategy provides the most balanced performance by minimizing flow distortion, increasing the mass flow rate across the S-duct.

The combined flow control strategy is beneficial for configurations with strong curvature or severe flow distortion. Since modern aircraft often integrate engine bleed systems for thermal management, implementing Coanda injections through existing bleed ports adds minimal structural complexity while providing substantial aerodynamic improvements. The present study is limited to fixed VG geometries. Future work will explore the effects of VG geometry parameters on flow control, as well as the influence of Coanda air-bleed extraction on engine performance and integration.