Prediction Of Separated Flows Research Articles

Energy thickness in turbulent boundary layer flows

In this study, we investigate the properties of energy thickness $\delta _3$ in turbulent boundary layer (TBL) flows, a parameter derived solely from the mean streamwise velocity ( $U$ ) profile. Through an analysis of the energy integral equation for zero pressure gradient TBLs, we establish a close relationship between turbulent kinetic energy (TKE) production and $\delta _3$ , offering a practical method to estimate TKE production, which is particularly useful in physical experiments where direct measurements are challenging. The significance of $\delta _3$ becomes even more pronounced in TBLs under pressure gradient. Through extensive analysis of numerical and experimental data, we show that the ratio between $\delta _3$ and the momentum thickness $\delta _2$ is a promising criterion for predicting flow separation. Moreover, we derive a new energy integral equation for TBLs under arbitrary pressure gradients, and provide approximations for TKE productions terms by $R_{uv}\,\partial U/\partial y$ and $R_{uu}\,\partial U/\partial x$ , and dissipation term by the mean shear. Here, $x, y$ represent the streamwise and wall-normal directions, respectively, and $R_{uu}$ and $R_{uv}$ are the Reynolds normal and shear stresses. The accuracy and robustness of the new energy integral equation and the approximation equations are validated using direct numerical simulations data. Our results show that the TKE production by $R_{uv}\,\partial U/\partial y$ and the overall productions consistently remain positive, reflecting a continuous conversion of mean kinetic energy into TKE across all TBLs. However, under strong favourable pressure gradients, TKE production by $R_{uu}\,\partial U/\partial x$ becomes negative, indicating a reverse energy transfer from TKE to mean kinetic energy.

Investigating the Effects of Labeled Data on Parameterized Physics-Informed Neural Networks for Surrogate Modeling: Design Optimization for Drag Reduction over a Forward-Facing Step

Physics-informed neural networks (PINNs) are gaining traction as surrogate models for fluid dynamics problems, combining machine learning with physics-based constraints. This study investigates the impact of labeled data on the performance of parameterized physics-informed neural networks (PINNs) for surrogate modeling and design optimization. Different training approaches, including physics-only, data-only, and several combinations of both, are evaluated using fully connected (FCNN) and Fourier neural network (FNN) architectures. The test case focuses on reducing drag over a forward-facing step through optimal placement and sizing of an upstream obstacle. Results demonstrate that the inclusion of labeled data significantly enhances the accuracy and convergence rates of FCNNs, particularly in predicting flow separation and recirculation regions, and improves the stability of design optimization outcomes. Conversely, FNNs exhibit inconsistent responses to parameter changes when trained with labeled data, suggesting limitations in their applicability for certain design optimization tasks. The findings reveal that FCNNs trained with a balanced integration of data and physics constraints outperform both data-only and physics-only models, highlighting the importance of optimizing the training approach based on the specific requirements of fluid mechanics applications.

Study on cross effect of mesh and turbulence model on separated flow prediction using a tandem cylinder case

Abstract Low dissipative separated flow prediction is still a great challenge in aeronautics engineering. An open-source CFD code named SU2 is employed to study the cross effect of mesh as well as turbulence model on the numerical resolution of separated flow for a tandem cylinder case. Firstly, a nonlinear variation of the numerical resolution for the separated flow is found by comparing the mean surface pressure distribution, mean streamwise velocity profile, the instantaneous vorticity magnitude as well as the aerodynamic forces on the rear cylinder. The resolution of separated flow from the medium mesh is the best compared to those getting from the coarse and fine mesh. Secondly, the reason causing the nonlinear variation of flow resolution is analyzed considering the influence of spatial discretization error and turbulent viscosity locally. A finer mesh would lead to a low spatial discretization error and then a high turbulent viscosity and then causes nonlinear variation of flow resolution. Finally, the existence of a “density boundary” of the mesh is proposed which could balance the spatial precision as well as turbulent viscosity and achieve the prediction of separated flow with a good resolution employing the RANS method.

A Comparison of Local and Global Strategies for Exploiting Field Inversion on Separated Flows at Low Reynolds Number

The prediction of separated flows at low Reynolds numbers is crucial for several applications in aerospace and energy fields. Reynolds-averaged Navier–Stokes (RANS) equations are widely used but their accuracy is limited in the presence of transition or separation. In this work, two different strategies for improving RANS simulations by means of field inversion are discussed. Both strategies require solving an optimization problem to identify a correction field by minimizing the error on some measurable data. The obtained correction field is exploited with two alternative strategies. The first strategy aims to the identification of a relation that allows to express the local correction field as a function of some local flow features. However, this regression can be difficult or even impossible because the relation between the assumed input variables and the local correction could not be a function. For this reason, an alternative is proposed: a U-Net model is trained on the original and corrected RANS results. In this way, it is possible to perform a prediction with the original RANS model and then correct it by means of the U-Net. The methodologies are evaluated and compared on the flow around the NACA0021 and the SD7003 airfoils.

Experimental and numerical comparison of aerodynamics for a wind turbine rotor model under turbulent inflow conditions

Computational prediction of aerodynamics for a two-bladed wind turbine rotor model at the profile, blade, and rotor scale are compared to wind tunnel experimental data. Wind tunnel tests are carried out in the large subsonic wind tunnel at the University of Orleans with an instrumented rotor model to obtain power and thrust coefficients, bending moments and pressure chordwise distributions. A passive uniform turbulence grid is used to obtain a turbulence intensity of 3.8% at the front of the rotor. A k − ω SST unsteady Reynolds-averaged Navier-Stockes (URANS) simulation with the ISIS-CFD flow solver is conducted with a fully resolved rotor, with and without automatic grid refinement. The focus of this study is to examine the prediction capabilities of the simulation for various physical variables. The simulation demonstrates a relatively good prediction of power and thrust coefficients compared with experimental data with a maximum scatter of 8.5%. The prediction of the pressure coefficient distribution at three different radial positions is satisfactory, but shows discrepancies when it comes to accurately predicting flow separation and Reynolds effects.

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Validation of helicity-corrected Spalart-Allmaras model for corner separation prediction in incompressible flow with OpenFOAM

Steady Reynolds-averaged Navier-Stokes (RANS) computations save significant computational resources compared to unsteady RANS and large eddy simulation (LES). However, the ability of most RANS models to accurately predict flow separation in compressor/fan blade rows is limited. Recent research focused on reducing the computational cost of predicting compressor/fan stall points with steady computations has shown that the helicity-corrected Spalart-Allmaras (SA) turbulence model is able to avoid over-predicting corner separations and thus lead to converged RANS up to the actual stall point. To date, this model has mostly been implemented in in-house codes or in commercial codes as a user add-on, where the source code is not available. In a recent paper, the authors implemented the helicity-corrected SA model in OpenFOAM, an open-source CFD package. In this paper, the differences in the flow field for RANS solutions with the original SA model, the helicity-corrected SA model, and Menter’s shear stress transport (SST) model are highlighted for a linear cascade with incompressible flow. A NACA 65-1810 cascade is used, and computational results are compared to experimental data.

Improved SST turbulence model for supersonic flows with APG/separation

A goal in modeling the turbulent flows in computational fluid dynamics is to find an empirical yet universal model to address the complex scenarios. Menter's Shear Stress Transfer (SST) [1] is a Reynolds-Averaged Navier-Stokes (RANS) based two-equation turbulence model and has been one of the most widely used turbulence models for numerical simulation of viscous flows. However, in some practical cases on supersonic, the standard SST model shows unsatisfactory prediction of flow separation and the often underestimation of Reynolds stress. The error mainly comes from the inappropriate use of Bradshaw's assumption which is proposed under turbulent kinetic energy (TKE) equilibrium flow conditions. This paper proposes an improved SST turbulence model which combines the structural parameter with the ratio of the turbulence generation term to the dissipation term and imposes a mixing function to correct the logarithmic and wake parts of the region. Several supersonic test cases are carried out to verify the new model. The calculation results show that the new model exhibits better performance in capturing the separation zones than the baseline model (BSL) and the standard SST model.

Progressive augmentation of turbulence models for flow separation by multi-case computational fluid dynamics driven surrogate optimization

In the field of data-driven turbulence modeling, the consistency of the a posteriori results and generalizability are the most critical aspects of new models. In this study, we combine a multi-case surrogate optimization technique with a progressive augmentation approach to enhance the performance of the popular k−ω shear stress transport (SST) turbulence model in the prediction of flow separation. We introduce a separation factor into the transport equation of a turbulent specific dissipation rate (ω) to correct the underestimation of the turbulent viscosity by the k−ω SST model in the case of flow separation for two-dimensional cases. The new model is optimized based on their performance on the training cases including periodic hills and curved backward-facing step flow. Simulation of the channel flow is likewise included in the optimization process to guarantee that the original performance of k−ω SST is preserved in the absence of separation. The new model is verified on multiple unseen cases with different Reynolds numbers and geometries. Results show a significant improvement in the prediction of the recirculation zone, velocity components, and distribution of the friction coefficient in both training and testing cases, where flow separation is expected. The performance of the new models on the test case with no separation shows that they preserve the successful performance of k−ω SST when flow separation is not expected.

Assessment of the DDES-γ Model for the Simulation of a Highly Loaded Turbine Cascade

Abstract The flow over the linear low-pressure turbine cascade MTU-T161 at Re = 90,000 is analyzed using delayed detached eddy simulations (DDES). At this operating point, the low Reynolds number and the high loading of the blade result in a separation bubble and a separation-induced transition of the flow over the suction side. The utilized DDES method is based on a vorticity-based formulation to calculate the subgrid length scales, and it incorporates the one-equation γ-transition model. The computational model of the MTU-T161 cascade consists of one blade passage, including the diverging viscous sidewalls. To reproduce realistic operating conditions and to mimic the experiments, synthetic turbulence is prescribed at the inlet of the computational domain. Several studies are performed to assess the accuracy and performance of the DDES one-equation γ-transition model against experimental data and a benchmark large eddy simulations (LES). The primary focus is on the prediction of the separation and the separation-induced transition mechanism. First of all, a systematic grid convergence study is conducted and grid criteria are derived in order to ensure a satisfactory agreement of the flow metrics, such as isentropic Mach number, friction coefficient distribution, and total pressure wake losses at mid-span with experimental data. Furthermore, a detailed analysis of the DDES model parameters, such as shielding function and subgrid length scale, is presented and the effect of these parameters on the prediction accuracy of the separation bubble region is analyzed. The analysis of the suction side boundary layer indicates that the turbulent kinetic energy should be resolved and modeled properly in order to represent the separation bubble correctly. In particular, the correct prediction of the separated shear layer above the separation bubble is of utmost importance. The results of the simulations reveal higher demands on grid resolution for such transitional flows than typically have been reported in the literature for turbulent boundary layers. This higher demand on grid resolution results in more expensive simulations than Reynolds-averaged Navier–Stokes (RANS). Nevertheless, DDES requires less computing time than wall-resolved LES. Additionally, the results of the transitional DDES model are compared to DDES without a transition model, an RANS eddy viscosity model, and a reference LES. The results show that the DDES approach needs to be coupled with a transition model, such as the one-equation γ-transition model, in order to capture the flow topology over a highly loaded turbine blade correctly. The benefit of the DDES one-equation γ-transition model becomes particularly evident when predicting the separated shear layer, the transition process, and the subsequent reattachment. The RANS eddy viscosity turbulence and transition models applied within our study are not able to predict the aforementioned mechanisms accurately. For highly loaded turbine blades in particular, the accurate prediction of flow separation and potential reattachment is crucial for the aerodynamic design of turbines, since large parts of the total pressure loss are generated in the separated region. For this reason, the DDES one-equation γ-transition model can be a good compromise in terms of predictive accuracy and computational costs.

On the extension of k−ω−SST corrections to predict flow separation on thick airfoils with leading‐edge roughness

AbstractModern wind turbines employ thick airfoils in the outer region of the blade with strong adverse pressure gradients and high sensitivity to flow separation, which can be anticipated by leading‐edge roughness. However, Reynolds average Navier‐Stokes simulations currently overpredict the Reynolds shear stresses near the surface, and the flow separation is not correctly predicted. Hence, these methods are not representative enough to optimize the blade design to avoid flow separation, which becomes relevant for rough blades. While several eddy‐viscosity corrections in the turbulence model have been previously studied to predict flow separation over smooth airfoils, the present study aims to extend their applicability to airfoils with leading‐edge roughness. Two corrections, whose effect on flow physics has not been empirically quantified, are addressed. Particle image velocimetry measurements have been performed on a 30% thick airfoil to quantify the impact of these corrections. The reduction of the eddy viscosity introduced by the corrections leads to a shift of the peak location of the Reynolds shear stresses away from the surface, which, in turn, promotes flow separation and improves the prediction of the mean velocity and the pressure‐coefficient distribution. Besides, the ratio between the main turbulent shear stress and turbulent kinetic energy is demonstrated to be lower than the standard value used in the turbulence model at the boundary‐layer outer edge. Adjusting this ratio for an angle of attack of 0° decreases the error on the predicted lift and drag coefficients from 75% to 3% and from 58% to 39%, respectively.

Forced Response Due to Vane Stagger Angle Variation in an Axial Compressor

Abstract Recent developments in turbomachinery design require an improved prediction accuracy of blade vibrations to maintain safe operations. This article aims to investigate the accuracy of numerical aeroelastic approaches for the calculation of blade vibrations. For validation, extensive aerodynamic and forced response measurements in an 1.5-stage axial compressor with a blade integrated disk (Blisk) are presented. The excitation intensity of the vibration is controlled by varying the stagger angle of the inlet guide vane (IGV). In addition, a second engine order is imposed by a nonsymmetric circumferential vane angle distribution to simulate a multistage behavior. Experimental validated Reynolds-averaged Navier–Stokes (RANS) simulations in both the frequency and the time domain are compared to assess the prediction accuracy of the numerical approaches. The numerical results agree with the experiments for low and intermediate vane angles. However, at high IGV stagger angles and when exciting multiple engine orders, the inaccuracy in the prediction of flow separation by the RANS simulations leads to an overprediction of vibration amplitudes. This exaggeration becomes even more pronounced in the frequency domain simulations. Time domain methods with a time lag formulation tend to be efficient and more accurate approaches for large separated flow regimes.

Application of Linear and Nonlinear Two-Equation Turbulence Models in Hypersonic Flows

A nonlinear two-equation model has been implemented in the OpenFOAM framework and has been assessed for the computation of hypersonic flows with shock-wave boundary-layer interactions (SWBLIs), together with two other linear, low-Reynolds number models, namely the Launder–Sharma model and the shear stress transport model. Supersonic and hypersonic flow computations resulting from the use of these three models have been compared with experimental benchmark cases over a range of conditions. The three original models tested do generally return reasonable predictions of wall pressure in most cases, with the nonlinear model resulting in the best capability among the three in predicting flow separation. The wall heat flux in the interaction region, however, is overpredicted, in most cases by all three models (sometimes showing quite a dramatic overprediction). While the overall wall heat flux predictions of the nonlinear model are closer to the measured values, it is nevertheless evident that there is a need for further improvement. To address this need, the inclusion of a new source term in the dissipation rate equation is proposed, which aims to restrict the turbulent length scales in the shock-wave boundary-layer interaction region. This is inactive in incompressible flows and exerts only a minor influence in supersonic SWBLI cases. Computations of a range of supersonic and hypersonic flows with SWBLI show that this inclusion of the proposed source term in the dissipation rate equation, of both the nonlinear and the linear models, has significant effects only in hypersonic flows. These effects are mainly confined to the thermal predictions of these models. In the nonlinear model predictions, the overestimation of the wall heat flux in the SWBLI region is largely eliminated, while, in the corresponding predictions of the linear model, the overestimation is substantially reduced. The cubic nonlinear model tested, with the proposed new source term to the dissipation rate equation, is thus shown to be a very reliable and cost-effective tool for the Reynolds-averaged Navier–Stokes modeling of supersonic and hypersonic flows.

The prediction of the flow separation occurring in a steam control valve by unsteady CFD simulation

The large flow separation in a steam control valve is a problematic phenomenon because it causes unstable conditions such as oscillation and the noise. However, there are many challenges in predicting flow separation by CFD simulation, and it is difficult to estimate the conditions under which unstable behavior occurs. Therefore, the unsteady simulation using the correction function which works to correct the turbulence source term in the separated region was performed in this research. Also, the air test using the quasi-3D model of the steam control valve was conducted in order to quantitatively evaluate the CFD simulation result. As a result, the simulation result shows the good agreement with the test result about the oil flow and the pressure amplitude. It was suggested the simulation method using the correction function is effective for the prediction of the flow separation.

Mechanism and Performance Differences between the SSG/LRR-ω and SST Turbulence Models in Separated Flows

Accurate predictions of flow separation are important for aerospace design, flight accident avoidance, and the development of fluid mechanics. However, the complexity of the separation process makes accurate predictions challenging for all known Reynolds-averaged Navier–Stokes (RANS) methods, and the underlying mechanism of action remains unclear. This paper analyzes the specific reasons for the defective predictions of the turbulence models applied to separated flows, explores the physical properties that impact the predictions, and investigates their specific mechanisms. Taking the Menter SST and the Speziale-Sarkar–Gatski/Launder–Reece–Rodi (SSG/LRR)-ω models as representatives, three typical separated flow cases are calculated. The performance differences between the two turbulence models applied to the different separated flow calculations are then compared. Refine the vital physical properties and analyze their calculation from the basic assumptions, modeling ideas, and construction of the turbulence models. The numerical results show that the underestimation of Reynolds stress is a significant factor in the unsatisfactory prediction of separation. In the SST model, Bradshaw’s assumption imposes the turbulent energy equilibrium condition in all regions and the eddy–viscosity coefficient is underestimated, which leads to advanced separation and lagging reattachment. In the SSG/LRR-ω model, the fidelity with which the pressure–strain term is modeled is a profound factor affecting the calculation accuracy.

Numerical analysis for wake flow field of Ahmed model based on a nonlinear-LRN/DES turbulence model

PurposeThis paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately.Design/methodology/approachAs the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the detached Eddy simulation (DES) model, this paper proposes a nonlinear-low-Reynolds number (LRN)/DES turbulence model. The turbulence model is verified in a backward-facing step case and applied in the flow field analysis of the Ahmed model. Several widely applied turbulence models are compared with the nonlinear-LRN/DES model and the experimental data of the above cases.FindingsCompared with the experimental data and several turbulence models, the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately.Research limitations/implicationsThe nonlinear-LRN/DES model proposed in this paper suffers from separation delays when simulating the separation flows above the rear slant of the Ahmed body. Therefore, more factors need to be considered to further improve the accuracy of the model.Practical implicationsThis paper proposes a turbulence model that can more accurately simulate the wake flow field structure of automobiles, which is valuable for improving the calculation accuracy of the aerodynamic characteristics of automobiles.Originality/valueBased on the nonlinear eddy viscosity method and the scale resolved simulation, a nonlinear-LRN/DES turbulence model including the nonlinear Reynolds stress terms for separation and reattachment prediction, as well as the wake vortex structure prediction is first proposed.

Low-Reynolds Number Behavior of the Leading-Edge Suction Parameter at Low Pitch Rates

Small unmanned aerial vehicles (UAVs) are becoming increasingly popular as low-cost observation and research platforms. However, these aircraft operate low in the atmosphere, exposed to the turbulent wakes of man-made and natural roughness features. As such, it is important to estimate their unsteady aerodynamic performance. The leading-edge suction parameter (LESP) is one criterion used in vortex methods for predicting flow separation, which can arise in both steady and unsteady flows. The critical LESP represents the maximum suction supported in the leading-edge region, equivalent to the flat-plate behavior of thin airfoil theory. This parameter was investigated at low pitch rates for a NACA0012 airfoil at Reynolds numbers applicable to small UAVs, to examine the hypothesis of a constant critical value existing for an arbitrary motion. It is seen that the critical LESP shows a strong dependence on pitch rate, with a piecewise linear fit being obtained. A higher pitch rate induces a greater pressure-field lag, promoting a higher peak LESP for flow separation, and a lower value for reattachment. These peaks in the LESP agree well with the instances of separation and reattachment. Raising the Reynolds number also acts to raise the critical LESP for a given reduced pitch rate.

Bayesian model evaluation of three k–ω turbulence models for hypersonic shock wave–boundary layer interaction flows

Shock wave–boundary layer interaction (SWBLI) is one of the most prevalent challenges in the field of fluid mechanics. Excessive interaction may lead to strong flow separation, which is an important factor causing the deterioration of aircraft performance. Reynolds averaged Navier–Stokes (RANS) models remain the primary methods for predicting flow separation for engineering applications. RANS simulation results typically have uncertainty owing to the drawbacks of the model structure and the variability of the parameters. Therefore, evaluation of a turbulence model based on nominal predictions may be insufficient for reflecting its actual simulation capabilities. In this study, the Bayesian method is employed to re-evaluate the simulation capabilities of three k–ω models for hypersonic SWBLI flows: the original k–ω model and two k–ω models with compressibility corrections (Wilcox's and Zeman's corrections). This is achieved by perturbing the model parameters and combining with experimental data. Bayesian model evaluation based on different datasets is performed using the embedded model error method, and the three turbulence models are compared from three aspects: posterior mean of the quantities of interests, model error, and Bayesian evidence. The results show that the Bayesian calibration can effectively improve the predictive abilities of the three models for wall pressure and wall heat flux. Different from the large differences in the nominal results, the performance of the two calibrated k–ω models with compressibility corrections are very close and superior to that of the original model. Moreover, the evaluation results of this study are also proven to be applicable to other similar flows.

One-equation turbulence models applied to practical scramjet inlet

Abstract Reynolds-averaged Navier–Stokes equations are used to simulate a practical scramjet inlet geometry using the shock-unsteadiness modified Spalart–Allmaras (SA) turbulence model. The geometry consists of fore-body ramps, expansion corners, and inlet ducts. The focus is to study the impingement of the cowl shock on the opposite wall boundary-layer. The resulting separation bubble can lead to blockage and inlet unstarts. The shock-unsteadiness correction is employed and is found to improve the computational fluid dynamics (CFD) prediction of flow separation in shock/boundary-layer interactions. The shock-unsteadiness parameter is calibrated against available experimental data of canonical flows, and the predicted flow-field is analyzed in detail. A large separation bubble size normalized to the upstream boundary-layer thickness of 4.6 is observed in the interaction region. Across the reattachment region in the interaction region, a peak value of wall pressure is observed. The inlet performance parameters are also calculated. The total pressure losses of 62% are observed across different shock waves, with an additional loss of 15% due to viscous boundary-layer effects.

One-equation turbulence models applied to practical scramjet inlet

Abstract Reynolds-averaged Navier–Stokes equations are used to simulate a practical scramjet inlet geometry using the shock-unsteadiness modified Spalart–Allmaras (SA) turbulence model. The geometry consists of fore-body ramps, expansion corners, and inlet ducts. The focus is to study the impingement of the cowl shock on the opposite wall boundary-layer. The resulting separation bubble can lead to blockage and inlet unstarts. The shock-unsteadiness correction is employed and is found to improve the computational fluid dynamics (CFD) prediction of flow separation in shock/boundary-layer interactions. The shock-unsteadiness parameter is calibrated against available experimental data of canonical flows, and the predicted flow-field is analyzed in detail. A large separation bubble size normalized to the upstream boundary-layer thickness of 4.6 is observed in the interaction region. Across the reattachment region in the interaction region, a peak value of wall pressure is observed. The inlet performance parameters are also calculated. The total pressure losses of 62% are observed across different shock waves, with an additional loss of 15% due to viscous boundary-layer effects.