Effects of Synthetic Jets on Swirl Inflow in a Variable-Geometry Twin Air-Intake

Air intakes are an integral part of contemporary passenger and military aircraft engines. Their impact on aerodynamic performance across the entire flight envelope is critical to aircraft flight safety, efficiency, and manoeuvrability, especially at high Mach numbers due to shock waves. The high demand for reductions in aircraft weight and size and enhancements in durability, comfort, and thermal and radar signatures compel researchers and engineers to explore new designs and develop efficient air intakes for high-performance aircraft engines. Although a number of studies on air intake have been conducted and reported in the open literature, there is little information available in the public domain on bifurcated twin air intakes using synthetic jet. As a result, the primary goal of this research is to use computational fluid dynamics modelling to investigate the effects of synthetic jets on swirl inflow variable geometry twin air intake aerodynamic performance over a range of Reynolds numbers. Some important parameters (distortion coefficient, non-uniformity index, swirl coefficient, and static and total pressure coefficients) were investigated. Both static and total pressure recovery have been increased at all swirl numbers. A significant decrease in distortion coefficient and swirl coefficient has also been achieved, reaching a 53% reduction in the distortion coefficient and a 62% reduction in the swirl coefficient. The reduction in the non-uniformity index is achieved by 62% for the controlled flow case. The findings show that synthetic jets are effective in controlling the flow separation in the twin air intakes and enhancing aerodynamic performance.


Introduction
Most modern-day passenger and military aircraft are powered by gas turbine (jet) engines that have inlets to bring freestream air into the engine.Sitting upstream of the compressor and not having any work done on the flow, the performance of the air-inlet (also called air-intake) significantly influences engine net thrust.The shapes and sizes of air intakes are constrained by the speed of aircraft (NASA Glenn Research Center 2021).Aircraft engines for below-sonic speeds (i.e., subsonic) generally have a simple, straight, and short inlet (intake).However, the air intake design of an aircraft engine for supersonic speeds becomes significantly complicated due to using a sharpened inlet lip to minimise performance losses from shock waves and the requirement of slowing supersonic air speed to subsonic speed before reaching the compressor using the complex inlet's physical shape.Figure 1 shows a range of air intakes used in modern fighter aircrafts manufactured by the USA, Russia, China, and the European Union (EU).
Single military aircraft engines typically use twin air intakes (transitional, double-offset, diffusing) with two inlet limbs merged downstream to form a common outlet connected to the engine's compressor inlet (Singh et al. 2008).Due to space constraints and other technical requirements, these diffusing ducts need to be curved, causing flow distortion and an adverse pressure gradient on the curved surface, resulting in flow separation (Hegde et al. 2013;Hickling and Ingram 2020;O'Neill 2020).This flow distortion creates early engine rush and flow non-uniformity, which cause irregular loading on the compressor vanes (Kim et al. 2001;Kurzke 2008;Saiz 2020).Friction on air-intake walls and flow separation due to adverse pressure gradients at air-intake bends are considered the major sources of losses (Sagar et al. 2011).An air intake must operate efficiently over the entire flight envelope, including take off, flight, maneuvering at different altitudes, landing, etc. (NASA Glenn Research Center 2021).Two important indicators ensure this: (a) intake distortion, which is a ratio of local pressure variation to average pressure at the compressor face, and (b) total pressure recovery, which is a ratio of average total pressure at the compressor face to the free stream total pressure.The intake distortion shows the amount of airflow disruption, while the total pressure recovery indicates the engine's performance; the higher the value, the better the design of the inlet (the US term for intake).However, for hypersonic intakes (inlets), the value of pressure recovery is almost constant and negligible due to shock wave-induced losses.Hence, a third parameter, "kinetic energy efficiency", is used to characterise the performance of hypersonic air intakes (inlets) of fighter aircraft engines (Sen et al. 2018).
Due to the high demand for reduction in aircraft size, weight, efficiency, durability, comfort, thermal signature, and radar signature, the design of air intakes has now become more challenging (Chopra and Walia 2020).During mid-air operations, an aircraft must be prepared to deal with sudden changes in the atmosphere caused by rapid maneuvering and/or foreign object ingestion.These incidents may create high turbulence and high swirl flow at the twin air intakes, and the aircraft may face engine flameout (due to a lack of oxygen), abrupt failure of compressor blades (due to uneven impact), and a narrow surge margin (indicating engine stall), creating a catastrophe during flight conditions (Sheard and Corsini 2012;Kerres 2017).Subsequently, the aircraft's aerodynamic performance is to be affected.
The steady flow behaviour in twin air intakes for different pre-swirl flow conditions was reported by Ramazan (2015) and Anand et al. (2008).However, the effect of passive flow control techniques in air intakes and their impact on engine performance are not well reported in the open literature except for some preliminary work by (Paul et al. 2010(Paul et al. , 2011a(Paul et al. , 2011b(Paul et al. , 2020;;Yadav et al. 2021).The focus is gradually shifting from passive flow control techniques to active flow control techniques, which offer flexible and innovative ways to control air flow in hypersonic aircraft engines (Paul et al. 2013a, b), thanks to emerging technologies, advanced materials, and manufacturing processes.Among various active flow control techniques, the synthetic jet presents a novel and innovative approach due to some of its features.Simple evaluation studies of synthetic jets without any application in jet engines have been reported by Smith and Glezer ( 1998), Seifert and Pack (1999), McCormick (2000), Glezer and Amitay (2002), Rediniotis et al. (2002), Smith and Swift (2003), Mathis et al. (2007Mathis et al. ( , 2008)), You and Moin (2008), Aram andMittal (2010, 2011), Mohseni and Mittal (2019), Singh et al. (2021).The synthetic jet was used for a plethora of applications by the researchers, namely, Smith and Glezer (1998) for thrust vectoring, Utturkar et al. (2002Utturkar et al. ( , 2003)), Gallas et al. (2003) for heat transfer enhancement, Zhang et al. (2273), Kim andKim (2009), andLin et al. (2016) for turbomachinery, and Yadav et al. (2021Yadav et al. ( , 2022) ) for flow control in air-intake ducts.These studies indicate that the pre-swirl at the inlet is the main energising agent in variable and complicated geometry.However, the present literature review summarised in Table 1 reflects the need for a comprehensive study on the effects of various degrees of inflow swirl on the aerodynamic performance of a realistic (dual offset, transitional cross-section with a high turning angle) twin air-intake duct and the application of a robust active flow control technique thereto.
Table 1 summarises the notable work on various air intakes.It is noticed from the table that although the researchers used air intakes of various shapes, area ratios, and curvatures, the duct geometry was not realistic (i.e., no vertical offset, no transitional cross-section).Moreover, these studies were based on uniform inflow conditions, which are far from the real conditions that prevailed with the combat aircraft, especially during sharp manoeuvring during aerial combat.A few researchers have, however, used active and hybrid flow control techniques.But the supremacy of slotted synthetic jets over circular jets, as established by Leschziner and Lardeau (2011), has not been used in the air intakes so far.
Given the importance of agility in modern combat aircraft, the lift-to-drag ratio needs to be maintained across all manoeuvring conditions.High inflow swirl and asymmetric conditions at the inlet of the air intakes can cause a sharp deterioration of the aerodynamic performance.Hence, the use of robust flow control techniques is essential in the air intakes of these aircraft.Therefore, the objective of this study is to investigate the performance of a variable-geometry twin air intake under a range of swirl inflow conditions and to determine the efficacy of the twin air intake under these inflow conditions.The swirling inflow conditions, including the boundary layer of air that forms around the aircraft's fuselage as it flies, are the problem.Contrary to the air that is offset from the aircraft's surface and is freely sucked up by the aircraft's intakes, the turbulent boundary layer air spreads around the fuselage of an aircraft at a different velocity and flow direction.The combined effect of the two results in significant reductions in engine performance, thrust instability, or even worse.The turbulent boundary layer and swirling air can become extremely turbulent during different flight regimes, affecting the engine's performance and/or choking it.Understanding airflow through the entire intake opening with a very turbulent and swirling boundary layer is crucial.Additionally, the air flow problems are exacerbated at supersonic speeds, especially for stealth aircraft, because their design limitations prevent them from having variable-shaped inlets, big bleed air doors, vents, manoeuvre ramps, and cones.The absence of these qualities prevents supersonic air intake by the aircraft's engines from being slowed down, which is essential for supplying massive volumes of stable air to highpower engines.Therefore, this study's uniqueness lies in figuring out how to address the swirling air and turbulent boundary layer problems of a variable geometry twin air intake.
The research methodology applied to this study is in-house developed, computational fluid dynamics (CFD) modelling.The findings of the modelling would be validated by experimental data from closely related fields available in the open literature.The following is the order of this article: A summary of the research techniques and modelling programmes used for the study is presented in Sect. 2. Results from the computational modelling are presented in Sect.3. Section 4 provides an elaborate discussion of the major findings and limitations.Finally, Sect. 5 summarises the findings and suggestions.

Computational Methodologies
The present study was carried out computationally using CFD modelling.The following sub-sections briefly describe the computational methodology used in the present study.The model geometry and grid generation are discussed in the following sub-sections.Further details can be found in Rajnath et al. (2019Rajnath et al. ( , 2020)).

Geometry and Grid Generation
The geometry of a typical twin air intake used in the present study, with the major dimensions in mm, is shown in Fig. 2a.The cross-section of the air-intake at its inlet was of super-elliptic shape, which is transformed continuously from the inlet and becomes circular at the aerodynamic interface plane (AIP), maintaining an area-diffusion ratio of 2, hence it is called a variable geometry air intake.The limbs of the twin air intakes are S-shaped, having a double curvature of θ = 60°/60°, thereby creating a horizontal offset.To avoid the radar signature, a vertical offset of 1.375 times the inlet hydraulic diameter of the air intake was also provided.
According to Leschziner and Lardeau (2011), the use of slotted synthetic jets results in a significantly higher momentum and vorticity flux that extends across the entire spanwise direction of the flow.As a result, the control of flow separation is improved due to enhanced sensitivity.This helps to maintain the lift-to-drag ratio across all manoeuvring conditions of the aircraft.A slotted synthetic jet of 70 mm length and 1 mm width was provided just upstream of the point of inflexion at each limb of the air intake, which is used to employ synthetic jets (Fig. 2b).
An unstructured grid containing both hexahedral and tetrahedral grid elements was used for the grid generation in the twin air-intake (Fig. 3).Wilcox (2006) recommended a y + value of 0.5-1.0 for wall-bounded turbulent flows.He noted that this value ensures that the near-wall region is well resolved and that the turbulence model can accurately capture the effects of the wall on the flow.In line with this, Shukla et al. ( 2012) used a y + value as low as 0.2 for the wall treatment to compute turbulent flow in a curved duct.Hence, a low y + value of 0.5 was used for near wall meshing to computationally capture the laminar sub-layer.A close-up view of the grid in and around the slot provided for the synthetic jet is shown in Fig. 3c, d.A grid independence test (GIT) was carried out to determine the final grid that was eventually used Fig. 3 Computational grid in the twin air-intake for the CFD simulation.A patch-independent algorithm with the multizone technique was used for the present study.The value of the static pressure recovery coefficient (C PR ) was calculated for each mesh type.It is noticed from Table 1 that at around 1.5 million mesh elements, the value of C PR becomes independent of the number of grid elements.The grid convergence index (GCI) was determined using the approach recommended by Roache (2009), and the results are displayed in Table 2.

Governing Equations and Boundary Conditions
Three-dimensional, unsteady continuity equations and momentum equations are solved using the finite volume method based on the Ansys-Fluent code.Large eddy simulations (LES) are best suited to capture the turbulent flow phenomena in such highly curved air-intakes.However, LES involves high computational power, cost, and time, which compels the authors to rely on a RANS-based turbulence modelling technique.Conventional one-and two-equation RANS-based turbulence modelling is less accurate, and the turbulence structure in the flow is lost due to averaging.However, due to the limitation of computational resources, the authors decided to carry out the CFD simulation with the advanced transition shear stress transport (Transition-SST) k − ω equations.Turbulent equations are applied for the present CFD simulation.The transition SST k − ω model is based on the combination of the SST k − ω transport equations with two other transport equations, one for the transition onset criteria (intermittency, γ) and another for separation-induced transition in terms of momentum thickness Reynolds number ( Rẽ t ).It is used to solve the flow near the wall.The SST k − ω turbulence model was invented by Menter (1994) for the precise creation close to the wall region of adverse pressure gradient flows that cause flow separation.In addition to the transport equations for turbulent kinetic energy TKE (k) and dissipation rate of TKE (ω), two additional transport equations incorporated in the transition SST k − ω turbulence model are shown in Eq. (1-2).These two additional transport equations helped the authors capture better flow physics in the twin air intake.
Transport equation for intermittency (γ): Transport equation for Reynolds number based on transition momentum thickness ( Rẽ t ): Boundary conditions (1) Velocity is set as the boundary condition at both the inlets of the twin air intakes, while atmospheric pressure is imposed at the outlet.The swirl number (S) is used to indicate the degree of swirls in the flow.It is defined as the ratio of the axial flux of tangential momentum to the axial flux of axial momentum of flows flowing into a pipe (Chen et al. 1999).Swirl numbers were imposed at inlet-2 of the twin air intake with a range of swirl numbers (S = 0.1, 0.2, 0.5, and 0.7), while a set of average uniform velocities (U avi = 20, 60, and 90 m/s) were maintained at inlet-1 of the twin air intake for CFD simulation.Zero-gauge pressure was imposed at the outlet of the air intake.The superiority of a rectangular slotted synthetic jet over a circular slotted jet in an air intake was discussed in Yadav et al. (2020).Hence, a sinusoidal periodic velocity (U = U amp sin (2πft) was set at the rectangular slot of the synthetic jets attached to the twin air intakes.
The operating parameters of the synthetic jet are furnished in Table 3. Velocity ratio (VR) is defined as the ratio of the average maximum velocity at the exit of the slot of the synthetic jet to the mass-averaged velocity at the inlet of the air intake (U j /U avi ).The velocity ratio (VR) characterises the relative strength between the jet and free stream velocity of air intake.VR values have varied from 2.0 to 6.0 in the present study.
The Reynolds number based on a synthetic jet (Re j ) is calculated on the basis of jet velocity (Uj), which is generated through a rectangular slot of the synthetic jet having a size of 70 mm × 1 mm.If Re j < 50, the jet created by synthetic jet is not separated from the slot.It results in the fact that the momentum of the jets coming out of the slot does not have the control authority to delay the boundary layer flow separation in the main flow of a fluid system (Dahalan et al. 2012).
When Re j > 50, flow separation can, however, be prevented.The Re j values in Table 3 ensured that the synthetic jet seemingly possessed the ability to prevent flow separation in the twin air intakes.The Strouhal number (St) is the ratio of the unsteady inertial power that is emitted due to oscillation inside the cavity of a synthetic jet actuator to the inertial forces that are associated with acceleration that cause convection of fluid elements away from the slot of a synthetic jet.
During the operation of the synthetic jet actuator, the oscillating membrane has a certain frequency, causing the movement of the air in the cavity through the orifice.The relationship between the rate of airflow and the membrane frequency is used to assess the Strouhal number.The relationship between the rate of mass-averaged velocity at inlet, hydraulic diameter, and frequency gives a Strouhal number.The jet momentum coefficient (C μ ) is defined as the ratio of the total jet momentum imparted by the synthetic jets to the mass flow's average main flow momentum j U 2 j A j 0.5 ∞ U 2 avi A i .Reduced frequency narrates the distinctive advection period over the detached flow field with the period of the operating cycles, which relates to average inlet velocity.Non-dimensional reduced frequency (F + ) is based on mass flow average flow inlet velocity ( U avi )and the length of the rectangular slot ( ) and is expressed as F + = 2 f U avi .The value of F + = for U avi = 20 m/s and f = 200 Hz is 12.56.
The synthetic jets operated at a velocity ratio (VR) of 4.0 and a frequency (f) of 200 Hz, which was found to be optimal for the present flow conditions after conducting an optimisation study.

CFD Solver Settings
The second-order upwind scheme was used for the discretization of the governing equations, whereas SIMPLE algorithm was used for the pressure-velocity coupling.Convergence criteria was set for 1 × 10 −5 for the governing equations.A time-step size of 5 × 10 −5 s was maintained for all the unsteady simulations after carrying out a detailed time independence test shown in Table 4.The mass-averaged value of static pressure recovery (C PR ) was monitored for each time step till the solution is converged around 40,000 iterations.
The second-order upwind scheme was used for the discretization of the governing equations, whereas the SIMPLE algorithm was used for the pressure-velocity coupling.The convergence criteria were set at 1 × 10 -5 for the governing equations.A time-step size of 5 × 10 -5 s was maintained for all the unsteady simulations after carrying out the detailed time independence test shown in Table 4.The mass-averaged value of static pressure recovery (C PR ) was monitored for each time step until the solution converged around 40,000 iterations.

Validation of the Computational Scheme and Development of Synthetic Jet
The numerical results of the bare (uncontrolled) twin air-intake were validated against the experimental results reported in Yadav et al. (Rajnath et al. 2020).Validation of the controlled twin air-intake was carried out by comparing the numerical results with the experimental results reported by Mathis et al. (2007Mathis et al. ( , 2008)).The validation graph and table were described in detail in Rajnath et al. (2019Rajnath et al. ( , 2020)).
For the validation of twin air-intake with synthetic jets, experimental results reported by Mathis et al. (2007Mathis et al. ( , 2008) ) for S-shaped air-intake is used.The experiments were conducted at average inlet velocity (U avi ) of 12.4 m/s, corresponding to a Reynolds number at the S-shaped leading edge of about Re (U avi )h c /ν = 4.1 × 10 4 ), where h c = 0.1h 1 , whereash 1 being the height of the inlet section of the S-shaped duct.The turbulence intensity of the flow at the inlet of the S-duct was reported to be about 1.35%.The geometry corresponds to Mathis et al. (2007Mathis et al. ( , 2008) ) is of S-shaped diffusing duct.Same geometry was used in the present study to validate CFD model with the experimental results reported in Mathis et al. (2007).The flow separation point and the boundary layer thickness during suction and blowing are calculated.It is noted that the boundary layer thickness is calculated at a point just before the flow separation beginscorresponds to 0.99U avi located at x/C L = 0.65 based on computational data.In the uncontrolled case, the velocity profile showed a wake region and massive flow separation zone due to adverse pressure gradient as revealed in Figs. 4 and 5a.
The synthetic jet is located just before the point of flow separation (Fig. 5a, b).The operation of a typical synthetic jet consists of blowing and suction in a cycle.At the onset of blowing (Fig. 5b), a small mass with high momentum enters the decelerated flow region.More momentum is mixed with the decelerated flow as the blowing cycle progresses (Fig. 5c), and finally the highest momentum is delivered (Fig. 5d) when blowing is at its peak.It is interesting to notice that when the synthetic jets are applied, the flow domain in the air intake does not exhibit any wake region in the downstream, as exhibited in Fig. 5b-d.The computational results varied 9-15% from the experimental results, which were considered acceptable.The variation is due to the limitations of the RANS turbulence model used in predicting the near-wall flow features as compared to large-eddy simulation (LES).Further details on the flow physics associated with synthetic jets can be found in Smith and Glezer (1998) and Glezer and Amitay (2002).

Results
The performance of the variable-geometry twin air intake in the presence of inlet swirl was computed at the aerodynamic interface plane (AIP) of the air intake for a wide range of inflow conditions.Swirl numbers were imposed at inlet-2 of the twin air intake with a range of swirl numbers (S = 0.1, 0.2, 0.5, and 0.7), while a set of average uniform velocities (U avi = 20, 60, and 90 m/s) were maintained at inlet-1 of the twin air intake for CFD simulation.Flow control techniques are used for the selected cases that were reported as the aerodynamically worst.
The performance parameters for the twin air intake system with and without synthetic jets and their variations are furnished in this section.It includes static pressure recovery, total pressure loss, total pressure distortion, and secondary and axial non-uniformity.It is worth noting that the cases where synthetic jets are used in the twin air intake are referred to as "controlled" cases throughout the study, whereas everything else is referred to as "uncontrolled" cases.

Mean Velocity Distribution at Longitudinal Plane
The mean velocity distribution at the longitudinal plane of the twin air intake for various pre-swirl inflow conditions is shown in Figs. 6, 7, and 8.A set of average uniform velocities of 20, 60, and 90 m/s is maintained at inlet-1, while varying inflow velocities with swirl numbers (S = 0.1, 0.2, 0.5, and 0.7) are imposed at inlet-2 of the air intake.Due to the strong manoeuvring of the aircraft and the strong turbulence present in the atmosphere, the twin air intakes of the aircraft sometimes ingest airflows with a strong swirl component.Once this inlet swirl flow enters the twin air intakes, it is further subjected to the curvature and area diffusion of the air intakes.These effects can either increase or decrease the strength of the swirl in the flow, depending on the direction (clockwise or anti-clockwise) and strength of the inlet pre-swirl.In this study, a clockwise pre-swirl is imposed at the inlets of the twin air intakes.The energy carried out with the pre-swirl inflows, which supplied the energy to the decelerating boundary layer negotiating the positive pressure gradient downstream of the twin air intake, could be one of the possible reasons.
The self-generated secondary inflows are subjected to the air-intake curvature while flowing downstream.As a result, the extent of the flow separation in both limbs is reduced when it flows downstream.Thus, the extent of the flow separation in both limbs is significantly reduced.Moreover, the wake region in the post-merger plane is also decreasing, as evident from these figures, especially at high swirl numbers.The no flow-control technique is used in the twin air in these cases.
Figure 9 shows that a pre-swirl inflow profile invigorates the flow in the air-intake limbs, creating a high-velocity thin boundary layer near its sidewalls, while the low-velocity flow core is divided into two segments due to the pre-swirl effects.This is the case when a high pre-swirl (S = 0.7) is imposed on both inlets.However, with the use of slotted synthetic jets, the inception of flow separation is delayed and reduced to a great extent.It is evident from Fig. 10 that the slotted jets enabled the inception of flow separation to move further downstream (s/C L = 0.61), indicating the efficacy of slotted synthetic jets.

Axial Velocity Vectors at Longitudinal Plane
Axial velocity vectors for various types of swirl flow at inlet-2 with swirl numbers (S = 0.1, 0.2, 0.5, and 0.7) and an average uniform velocity of 20, 60, and 90 m/s at inlet-1 imposed at the inlet of the air intake are discussed in this section.For brevity, a few representative cases are shown in Figs.11, 12, as they have almost identical natures.The effect of inlet pre-swirl can be seen in the axial velocity vectors in these figures, particularly a little downstream from the twin air-intake inlets.The flow performance of the twin air-intake system becomes more uniform at the AIP with the increase in swirl number imposed at one of its inlets because of self-generated secondary flow generated from the air-intake curvature.But in this process, a significant amount of energy is also wasted in swirl flows due to the higher shear involved.Figure 12 shows the case when high swirl inflows are employed at both of its inlets.In this case, the downstream wake region has been found to reduce in the post-merger plane because of more mixing involved due to pre-swirl inflows.However, when synthetic jets are used as an effective flow control technique, flow separation and flow reversal are suppressed, as shown in these figures.Flow non-uniformities after the merger plane are also reduced to a great extent, as shown in Fig. 13.

Secondary Velocity Vectors at Transverse Plane
The secondary flow velocity vectors at the transverse plane are presented in Figs. 14,15,and 16.While introducing the pre-swirl at the inlet of the air intake, the variation in the velocity vectors at the AIP is found.As per Facciolo (Facciolo 2006), the swirl number S = 0.5 is considered the moderate swirl number, S < 0.5 is the low swirl, and S > 0.5 is the high swirl, and all the cases are computed in the present study.Better flow uniformity is achieved with a higher inflow swirl, as shown in the figures.Table 4 shows the quantification of flow uniformity (in terms of S io ).However, the use of a high-strength swirl causes high shear, and hence the increment in total pressure loss coefficient (C TL ) is also observed.Therefore, there is a trade-off between flow uniformity and total pressure loss coefficient while imposing a pre-swirl inflow.
Figure 17a-c depicts the secondary flow vectors at the AIP when a swirl number S = 0.7 pre-swirl is imposed at both inlets of the twin air intake.Due to the strong pre-swirl that exists beginning at the inlets, the self-generated vortex pairs created by the double curvature of the limbs in the twin air intake are not identified at the AIP.This eventually leads to flow uniformity at the AIP as well.The use of synthetic jets, however, removed those vortices, and the secondary flow at the AIP has become more uniform, as evident from Fig. 17d.

Turbulent Kinetic Energy
Figure 18a-c shows the effects of turbulent kinetic energy (TKE) at pre-swirl inflows for a range of swirl strengths for U avi = 20, 60, and 90 m/s.It is revealed that the TKE value remains higher up to s/C L = 0.6 as compared to the non-swirl cases due to the strong presence of inflow swirl and the TKE contained in it.However, after the merger of the two flow jets from the two limbs of the twin air intake at its merger plane, the value of TKE dropped gradually, even below that of non-swirl cases.When synthetic jets are used, the TKE is significantly reduced after the post-merger plane of the twin air intake.However, due to the use of synthetic jets, a local increase of TKE is observed around s/C L = 0.425 in Fig. 18d.

Vorticity Dynamics and Q-Criterion
The Q-criterion as proposed by Hunt et al. (1988) and mathematically formulated by Chong et al. (Chong et al. 1990) is defined as.
It indicates the comparative supremacy of the rotational component over the stretching component while a fluid element is subjected to deformation.The Q-criterion is used to represent the connected region of the coherent vortical structure (eddy) in a turbulent flow where the pressure is lower than the atmospheric pressure.Aref et al. (2018) used the Q-criterion to explain the vortical structure formation in a RAE-M2129 air intake.A value of Q > 0.1 is chosen in this study to generate iso-surfaces for visualising the vortices generated by the synthetic jets during the blowing (Fig. 19) and suction phases (Fig. 20).The iso-surfaces are coloured with normalised velocity, which is the ratio of the phase-averaged streamwise velocity component (u) and the mass-averaged jet velocity (U j ).When synthetic jets generate successive vortex rings during their blowing phase, the leading vortex rings are widened by reducing velocity due to the influence of the trailing (following) vortex ring.The trailing vortex ring, on the other hand, reduces its size and thereby increases its velocity, eventually merging into the leading vortex ring.This phenomenon is termed "leapfrogging," which weakens both the primary and secondary Q = 1∕2 vorticity 2 − strain rate 2 > 0.
vortex rings.As a result, both rings break down even after merging.Meanwhile, the jet sheds more vorticity, and highly unstable tertiary rings are seen in the flow domain.However, the life span of these tertiary vortex rings is short, and they degrade immediately after formation (Rajnath et al. 2020;Fischer 2012).
At the onset of the blowing phase (Fig. 19a), primary vortices are seen generated from the slots of the synthetic jets attached to the twin air-intakes.These vortices are mostly rectangular in shape and elongated in a streamwise direction because of the shape of the jet slots.As the primary vortices convect downstream of the twin air-intakes under the influence of the bulk flow, the vortices break down owing to the spanwise instability and the vortex stretching (Fig. 19b).Consequently, a secondary vortex structure appeared in the flow, connecting opposite ends of each primary vortex, thereby forming a rib-like vortex structure in the flow (Fig. 19c).The secondary vortex structure is, however, much smaller in size as compared to the primary vortex, and its growth is hindered due to highly accelerating primary vortex rings (Fig. 19d).It is pertinent to note that these secondary vortex structures cause transitions in the turbulent flow and are usually seen appearing in the central flow core, contributing to flow non-uniformity at the AIP of the twin air intakes.
At the end of the blowing phase, the suction phase started (Fig. 20), and the nearby air was sucked into the cavity of the synthetic jets.Here, streamwise rib-like secondary vortex structures are mostly seen encircling the primary vortex core (Fig. 20a).The vortex stretching increases the size of these secondary vortex structures (Fig. 20b-d), and the primary vortex core is transitioned to a turbulent jet near the slot.Counter-rotating vortices are also generated during the suction phase.

Performance of Uncontrolled Twin Air-Intake with Swirl Inflow Conditions
The performance parameters of the twin air intake duct are calculated at the aerodynamic interface plane (AIP) and are discussed in detail in the following sub-sections.

Coefficient of Static Pressure Recovery (CPR)
The difference in static pressure between a cross-section and the inlet of the air intake normalised by the average inlet dynamic pressure is called the coefficient of static pressure recovery.Mathematically, it is expressed in Eq. (3). Figure 21a-c depicts an increase in the static pressure recovery coefficient (C PR ) at U avi = 20, 60, and 90 m/s at inlet-1, with swirl of varying magnitudes (S = 0.1, 0.2, 0.5, and 0.7) imposed at inlet-2.This enhancement is mainly due to the dominance of self-generated secondary flows generated from the air-intake curvature due to the pre-swirl carried into the air-intake from inlet 2. In these figures, it is also observed that as the swirl number increases, so does the static pressure recovery.Figure 21d reveals an increase in static pressure recovery due to the effective control of flow separation using the synthetic jets.An increase of 4.33% in the C PR value is recorded, as shown in Fig. 21d.The difference in total pressure between a cross-section and the inlet of the air intake, normalised by the average inlet dynamic pressure, is called the coefficient of total pressure loss, expressed in Eq. ( 4).
The distribution of the total pressure loss coefficient in the twin air intake for preswirl inflow conditions is presented in Fig. 22a-c.It was noticed from the preceding sub-section that the pre-swirl in the inflow helps in increasing the static pressure recovery.However, in this process, the total pressure loss is also increased due to higher shear, and a significant amount of energy is wasted in the swirl inflows.This is the case without the flow control technique used in the twin air intakes.Total pressure loss can be minimised by injecting additional energy into the already slowing boundary layer in the twin air intakes by means of synthetic jets.The C TL distribution in the twin airintake for U avi = 90 m/s at inlet-1 and S = 0.7 as compared to the uncontrolled case is found to be 65.59% in Fig. 22d.53%, as a high pre-swirl inflow can suppress the effect of the self-generated secondary flow vortices created inside the air intake.

Swirl Coefficient (SC 60 )
The swirl coefficient (SC 60 ) is the ratio of the change in secondary flow velocity and secondary flow worst velocity to the average velocity at the engine face, i.e., at the AIP.It is expressed in Eq. ( 6).
The values of the swirl coefficient for various cases are tabulated in Tables 4, 5, and 6.It is seen that the presence of pre-swirl inflow at the inlet of the twin air-intakes reduced the value of the swirl coefficient.For low-value swirl numbers, the reduction in SC 60 is between 11 and 31%if compared with the uniform inflow conditions.However, for a swirl number of S = 0.5, the reduction in SC 60 could be as high as 62% as shown in Table 6.

Secondary Flow Non-uniformity (S io )
The secondary flow non-uniformity is defined as the sum of all secondary (or cross flow) velocities computed at n points in the aerodynamic interface plane (AIP) and normalised by the average inlet velocity.Formula-wise, it is shown in Eq. ( 7).
Here V yz is secondary velocity, U avi is mass-averaged velocity at inlet of the airintake, and n = computational nodes on the AIP.Secondary non-uniformity in the twin air-intake system coupled with area diffusion downstream is caused by the curvature 1 3 effect.Tables 5, 6, and 7 present secondary flow non-uniformity (S io ).A drop between 7 and 35% is observed in the S io values for the swirl number, S = 0.5), and the reduction in S io could be as high as 51%, as shown in Table 8 if compared with the uniform inflow conditions.

Discussion
The mean and axial velocity distributions in the twin air-intake duct at all inflow velocities revealed that increasing the swirl number (S) from 0.1 to 0.7 further delays flow separation.The clockwise pre-swirl inflows are imposed at the duct inlets, which convected energy to the energy-deficient boundary layer, encountered the adverse pressure gradient downstream, and thus stopped the flow separation.However, the use of slotted synthetic jets further reduced the flow separation, and as a result, separation inception points were moved further downstream.Secondary flow vectors indicated better flow uniformity at higher swirl numbers, but at the cost of higher total pressure loss in the air intake.The use of synthetic jets removed the vortices and made the flow more uniform as it appeared downstream of the duct while limiting total pressure loss.
The greater the pre-swirl number, the lower the turbulent kinetic energy (TKE) in the twin air intakes.However, the use of synthetic jets caused an increase in TKE locally.In the presence of synthetic jets, the flow in a twin air intake generates vortices and their subsequent convection with the bulk flow downstream of the air intake.The Q-criterion was used in this article to explain the formation of vortex structures in the twin air intakes.The iso-surface contours are drawn with Q = 0.1 for both the blowing and suction phases of the synthetic jets that visualise the vortices.The generation, growth, and pattern of the vortices (namely, primary, secondary, and tertiary vortices) and the Fig. 16 Secondary velocity vector at AIP for swirl inflows (U avi = 90 m/s at inlet-2) 1 3 transformation of these vortices in the presence of bulk flow are described in detail.It shows that the secondary vortices caused transition and mostly appeared in the core flow, leading to flow non-uniformity at the AIP of the air intake during the blowing phase, while counter-rotating vortices are present in the suction phase.
The most important performance parameter of the air intake, static pressure recovery, increased with the increase in swirl number.Using synthetic jets in the air intake, static pressure recovery was increased even further.It was seen that the total pressure distortion as well as flow non-uniformity computed at the aerodynamic interface plane (AIP) were reduced with the pre-swirl.The swirl coefficient computed at the AIP was also reduced with the introduction of pre-swirl.These findings indicate the greater control authority of the synthetic jets used in air intakes.Fig. 17 Secondary velocity vector in twin air-intake for S = 0.7 at both inlets Air intake, being a critical component of the air induction system of all air-breathing aircraft, has immense practical applications.Air intakes are used for a variety of purposes, including air conditioning, ventilation of hydraulic and fuel lines, and engine cooling (Almeida et al. 2021).The study enumerated in this article can be considered an engineering tool to design air intakes for aerospace engineers under swirl inflow conditions.It also demonstrates how powerful computational modeling tools can be used for the engineers' aid in designing complex components in an aircraft.The present study is sufficiently exhaustive and covers various swirl conditions and flow control using synthetic jets.However, flow control in the air-intakes using other flow control techniques, namely hybrid jets and plasma jets, investigation of structural analysis of the air-intakes, and shape optimization of the air-intakes are some of the areas where further studies can be carried out by the researchers.

Conclusion
In the work presented here, an investigation of the flow field in an uncontrolled and controlled (i.e., using synthetic jets) twin air intake was undertaken.The study's key findings are summarised below: The flow behaviour at the aerodynamic interface plane (AIP) is found to be more uniform with the pre-swirl imposed at one inlet of the twin air intakes than with the uniform flow maintained at both inlets, as depicted from the performance parameters.
An increase in the swirl number causes an increment in the coefficient of static pressure recovery as a result of the self-generated secondary flow created due to duct curvature.Static pressure recovery is also found to be greater at all swirl numbers than that of uniform flow imposed at both inlets.
The use of slotted synthetic jets increases static pressure recovery up to 4.33% as compared to uncontrolled jets while reducing the total pressure loss coefficient by 65.59%.
The distortion coefficient is used to determine the primary distortion caused by unequal (asymmetric) pressure.The employment of slotted synthetic jets shortly before the separation point results in a 53% reduction in the distortion coefficient and a 62% reduction in the swirl coefficient.These decreases suggest that the dual air intakes will perform better aerodynamically.
The secondary flow cross velocity is defined in terms of the secondary flow non-uniformity index as compared to both uncontrolled and controlled flow with the use of slotted  synthetic jets.In this study, a maximum reduction of 62% in the non-uniformity index has been achieved for uncontrolled twin air intake.Since the robustness of the synthetic jet is still under question, the study of the performance characteristics of pulsating jets (a combination of continuous and synthetic jets) may be explored further by interested researchers.Overall, the findings of the present study are expected to have a substantial impact on the aerospace sector and allied industries as manufacturers will be able to develop more efficient, durable, and reliable air intakes that can function in a variety of flight scenarios and environments.

Fig. 2 a
Fig. 2 a Geometry of a twin air-intake model.b Schematic of a synthetic jet (left), Close-up view of the slot marked with red arrow (right)

Fig. 12
Fig. 12 Longitudinal velocity vector in twin air intake for S = 0.7at both inlets (U avi = 20 m/s)

Fig. 18
Fig. 18 Turbulent kinetic energy (TKE) variation in twin air intake under various conditions

Fig. 19
Fig. 19 Vortical structure emancipated from synthetic jets in a twin air-intake visualised by Q = 0.1 isosurface coloured with normalised velocity during the blowing phase

Fig. 22
Fig. 22 Total loss coefficient along centreline of twin air-intake under various conditions

Table 3
Operating parameters of the synthetic jet for jet frequency (f) = 200 Hz and reduced frequency (F + ) = 12.56

Table 4
Time independency test

Table 6
Performance parameters of twin air-intake for various pre-swirl inflows at U avi = 60 m/s