Shock Wave Boundary Layer Interaction Research Articles

Modal Analysis on MVG Controlled Supersonic Flow at Different Mach Numbers

Modal analysis on micro-vortex generator (MVG)-controlled supersonic flow at different Mach numbers is performed in this paper. The purpose of this investigation is to clarify the different properties of streamwise and ring-like vortical modes, and the effects of different Mach numbers on these modes, to further understand the vortical structures as they travel from MVG down to the shock wave/boundary-layer interaction (SWBLI) region. To this end, a high order and high resolution large eddy simulation (LES) was carried out, which identified the vortical structures behind the MVG and in the shock wave/boundary-layer interaction (SWBLI) region in the supersonic ramp flow with flow speeds of three different Mach numbers 1.5, 2.0, and 2.5. The proper orthogonal decomposition (POD) then was adopted to investigate the modes of the fluctuation flow field. It emerged that the streamwise and ring-like vortical modes were disparate in energy distribution, structural order, frequency and amplitude. Furthermore, it showed that as the Mach number increased, the energy of the streamwise modes increased while the opposite was true for ring-like modes; and the streamwise modal structures were altered more significantly than the ring-like modes, and the frequency of each mode scarcely varied. It was also found that the streamwise vortices absorbed energy from the ring-like vortices while they traveled from the MVG down to the SWBLI region, but the dominant frequency of each mode rarely changed during this process.

Hypersonic shock wave and turbulent boundary layer interaction in a sharp cone/flare model

A direct numerical simulation of hypersonic Shock wave and Turbulent Boundary Layer Interaction(STBLI) at Mach 6.0 on a sharp 7° half-angle circular cone/flare configuration at zero angle of attack is performed. The flare angle is 34° and the momentum thickness Reynolds number based on the incoming turbulent boundary layer on the sharp circular cone is Reθ = 2506. It is found that the mean flow is separated and the separation bubble occurring near the corner exhibits unsteadiness. The Reynolds analogy factor changes dramatically across the interaction, and varies between 1.06 and 1.27 in the downstream region, while the QP85 scaling factor has a nearly constant value of 0.5 across the interaction. The evolution of the reattached boundary layer is characterized in terms of the mean profiles, the Reynolds stress components, the anisotropy tensor and the turbulence kinetic energy. It is argued that the recovery is incomplete and the near-wall asymptotic behavior does not occur for the hypersonic interaction. In addition, mean skin friction decomposition in an axisymmetric turbulent boundary layer is carried out for the first time. Downstream of the interaction, the contributions of transverse curvature and body divergence are negligible, whereas the positive contribution associated with the turbulence kinetic energy production and the negative spatial-growth contribution are dominant. Based on scale decomposition, the positive contribution is further divided into terms with different spanwise length scales. The negative contribution is analyzed by comparing the convective term, the streamwise-heterogeneity term and the pressure gradient term.

Control mechanism of micro vortex generator and secondary recirculation jet combination in the shock wave/boundary layer interaction

Shock wave/boundary layer interaction (SWBLI) is a common phenomenon occurring in the supersonic/hypersonic flow fields, and it can constrain the performance of the vehicle. In the current study, a combined control device of a micro vortex generator (MVG) and a secondary recirculation jet is numerically simulated by using three-dimensional Reynolds-averaged Navier-Stokes equations (RANS) coupled with the SST k-ω turbulence model to control the SWBLI flow field at the incoming Mach number being 2.9. From the obtained results, the combination is able to significantly reduce the volume of the separation zone while maintaining little change in the peak heat flux, and the volume of separation bubble is reduced by 87.81%. At the same time, the flow field details and control mechanism are also clearly captured. Six combined models of MVG and secondary recirculation jets are considered, and the design parameters are optimized based on the model with the best control performance. The results of the orthogonal experimental design and the range analysis provide the relationship between the geometric design variables and the performance parameters of the combination.

Quantitative flow diagnostics of shock trains by rainbow schlieren deflectometry

AbstractA new measurement technique to reconstruct the density field of the shock-wave/boundary-layer interaction (SWBLI) in a confined duct is proposed. With this technique, it is possible to quantitatively capture in detail the structures of the density field both in the regions of the shock-systems in the central core and boundary-layer flows near the duct wall concurrently. The novel feature of the proposed technique is to make use of the schlieren images with the rainbow filters of the vertical and horizontal cutoff settings and then to reconstruct the two-dimensional density field integrated over the line-of-sight direction using the corresponding filter calibration curves. The proposed technique is applied for the first time to a shock train in a constant-area straight duct under the upstream condition of the shock train: the freestream Mach number is 1.42, the incoming boundary layer thickness normalised by the duct half height is 0.175, and the corresponding unit Reynolds number $Re/m$ is $2.99 \times 10^7$ m-1. The calculated isopycnic field depicts the streamwise and transverse density variations inside the shock train, the mixing region after the shock train, and the boundary-layer of the interaction region. This technique is shown to be capable of identifying the locations of shocks in a shock train more precisely than a conventional approach measuring the static pressure distribution along the duct wall. In addition, various quantitative visual representations such as a shadowgraphy and a bright-field schlieren can be extracted from the density field acquired by the present approach, and the spatial evolution of the shape and strength of each shock constituting the shock train as well as the boundary layer flow properties can be quantitatively clarified.

Experimental Investigation of Fluid-Structure Interaction in Mach 2 Flow Using Simultaneous High-Speed PIV and DIC

The fluid-structure interaction (FSI) of a compliant panel under a compression-ramp-induced shock-wave/boundary-layer interaction (SBLI) has been studied in Mach 2 flow. Simultaneous high-speed measurements of the velocity field and the panel displacement were conducted using 50 kHz particle image velocimetry (PIV) and 5 kHz stereoscopic digital image correlation (DIC). The mean effect of the panel displacement has been evaluated by monitoring the change in velocity profiles along the streamwise direction (x), upstream of the separated flow region. Streamwise (u) velocity near the panel surface has been shown to change its magnitude in response to the wall shape. Furthermore, the strong cross-correlation between fluctuations of the wall-normal panel displacement and the transverse (v) velocity can be explained by the flow remaining tangent to the wall surface as the panel deforms. This latter result is consistent with the panel motion being sufficiently low frequency compared to flow convective time scales that the flow is quasi-steady. In addition, assessment of the correlation between the separation shock position and panel displacement seems to suggest that when the panel is bulged down (concave up) at the downstream end of the panel, a larger separated flow is generated and the shock moves upstream. This observation remains speculative, but is consistent with the flow undergoing greater compression for the bulged down case.

Numerical Study of Stream-wise and Span-wise Nanosecond DBD Plasma Actuators Effects on Supersonic Flow Separation

The current paper aimed to investigate the primary control mechanism of various Nanosecond Dielectric Barrier Discharge (NS-DBD) plasma actuators on the Shock Wave/Boundary Layer Interaction (SWBLI). For this purpose, the effects of the NS-DBD actuator have been investigated on an M=2.8 supersonic flow numerically. The Reynolds Averaged Navier-Stokes (RANS) equations and SST turbulence model were used as the governing equations to simulate the supersonic flow characteristics. The numerical simulation of the baseline flow (without plasma actuator) was verified using an investigation on wall pressure distribution and the size of SWBLI. Then, NS-DBD phenomenological model based on the energy deposition model in accordance with experimental data was applied to the baseline simulation. Moreover, various stream-wise and span-wise NS-DBD plasma actuator models were used to investigate the actuator effects on the studied flow’s low-density separation zone. Comparing the numerical results of the stream-wise and span-wise actuations revealed that both actuator types cause a momentum transferred to the flow, consequently decreasing the SWBLI region’s size and the boundary layer’s thickness. The results showed that the presence of the NS-DBD actuator increased the local temperature of flow over the insulated electrode. In this regard, a stream-wise NS-DBD actuator with a length of 90 mm upstream of the SWBLI increased the separation flow velocity by 33.7% and decreased the length of the separation region by 5 mm. Also, in this case, after 170 microseconds from the start of actuation, the size of SWBLI decreased by 4.2 mm. Therefore, it can be concluded that the stream-wise type of actuation was more effective in reducing the flow separation and SWBLI size than the span-wise type due to vortex generation into the inlet flow and suppressing the SWBLI region. The proposed NS-DBD actuators were mainly capable of applying the momentum to the boundary layer and reducing the velocity of separated flow in the SWBLI zone. The micro shock wave propagation through the flow associated with the NS-DBD discharge of the actuators can produce more effective high-speed flow control.

A Streamline-Upwind Petrov–Galerkin formulation for the analysis of hypersonic flows in thermal non-equilibrium

This work presents a Streamline-Upwind Petrov–Galerkin (SUPG) framework with finite elements discretization for the prediction of non-ionized hypersonic flows in thermal non-equilibrium. The formulation is enhanced with a residual-based discontinuity-capturing (DC) operator. The numerical framework solves the set of Navier–Stokes equations for the compressible reacting flows with an additional equation for the vibrational–electronic energy conservation. The set of equations, which involves one continuity equation for each chemical species considered, is solved in the pressure-primitive variables. The numerical framework capabilities are assessed through several benchmark cases, including validation of the chemical model and its coupling with the two-temperature model in the context of critical flow features such as shock–shock and shock wave–boundary layer interactions. The accuracy of the results is assessed through the comparison with the numerical and experimental data available in the literature for all the test cases presented. The numerical results demonstrate the suitability of the formulation in predicting non-ionized reacting hypersonic flows in thermal non-equilibrium.

Investigations on Turbulence Model Uncertainty for Hypersonic Shock-Wave/Boundary-Layer Interaction Flows

Shock-wave/boundary-layer interaction (SWBLI) is a fundamental scientific problem that restricts the breakthrough of high-speed flight technology. Owing to the complex shock structure and boundary-layer separation in the interaction region, the widely used eddy-viscosity turbulence models have large uncertainties and model errors in the simulation of such flows. To make more reasonable aerodynamic/aerothermal predictions and identify the critical parameters affecting the prediction results, Bayesian uncertainty quantification and sensitivity analysis are conducted for the three turbulence models [Spalart–Allmaras (SA), SA with quadratic constitutive relation (SA-QCR), and shear-stress transport (SST) models] and the hypersonic SWBLI cases. First, the prior variances and Sobol indices are calculated to obtain a preliminary understanding of the parameter variability for turbulence models. Then, the posterior distributions of the model closure coefficients and posterior uncertainties of the wall pressure and thermal flux are systematically analyzed and compared. The results indicate that the prediction performances of the three models can be effectively enhanced by Bayesian estimation. The peak of the posterior uncertainty of the SST model is the largest among the three models, whereas that of the SA-QCR model is the smallest. The results of the Bayesian model evaluation demonstrate that the SA-QCR model has the highest reliability.

Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$ . This damping rate is found to scale as $1/L$ , leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$ , a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

Experimental investigation of expansion effect on shock wave boundary layer interaction near a compression ramp

The experiment is conducted to investigate the effect of expansion on the shock wave boundary layer interaction near a compression ramp. The small-angle expansion with an angle degree of 5° occurs at different positions in front of the compression ramp. The particle image velocimetry and flow visualization technology show the flow structures, velocity field, and velocity fluctuation near the compression ramp. The mean pressure distribution, pressure fluctuation, and power spectral density are measured by high-frequency response pressure transducers. The experimental results indicate that the expansion before the compression ramp position affects the shock wave boundary layer interaction to induce a large-scale separation. But the velocity fluctuation and pressure fluctuation are attenuated near the large-scale flow separation region. When the expansion occurs closer to the compression ramp, the expansion has a more significant impact on the flow. The fluctuation of velocity and pressure is significantly attenuated, and the wall pressure rise of the separation point is reduced obviously. And the characteristic low-frequency spectrum signal related to the unsteadiness of the shock wave boundary layer interaction is significantly suppressed. In addition, variation of the separation region scale at different compression angle degrees is distinctive with the effect of expansion.

Combined application of passive and active boundary layer aspiration in a transonic compressor rotor for shock wave/boundary layer interaction control

Shock wave/boundary layer interaction (SWBLI) is one of the key factors that limits the improvement of aerodynamic performance and stability for supersonic/transonic compressors. In this research, a combined flow control device (CFCD) was designed for controlling SWBLI in the NASA transonic compressor Rotor 35. The original flow fields for Rotor 35 were numerically analyzed first. The results show that the SWBLI is severe, resulting in much flow loss and partly leading to the compressor instability. Based on this phenomenon, the CFCD was designed with a novel three-dimensional passive self-recirculation flow channel and an active suction slot. The flow channel is mounted on the rotor blade suction surface to connect the low- and high-pressure regions ahead of and behind the shock, respectively. The effect of the CFCD on the rotor performance and corresponding working mechanism are then researched as well. With the help of CFCD, the rotor-achieved total pressure ratio (TPR) is maximally increased by 3.0%, and the stall margin (SM) is improved by 4.1% as well. But the rotor isentropic efficiency (IE) considering additional energy expenditure caused by active suction flow has the maximum increment at choke point of 0.27% and highest reduction at near-stall point of 0.54%. The working mechanisms of CFCD include two aspects: one is forming a stable and low-entropy generated lambda shock wave and the other one is reducing the magnitude of flow separation. The dominant mechanism varies with the rotor working condition and depends on whether the leading-edge shock moves upstream of the passive bleed slot.

Study of shock wave/boundary layer interaction from the perspective of nonequilibrium effects

Shock wave/boundary layer interaction (SWBLI) is a widespread phenomenon in supersonic flows and has received extensive attention. The boundary layer is generated due to viscous stress, which is a kind of macroscopic manifestation of molecular nonequilibrium motion, namely, nonequilibrium effects. In this paper, an investigation is conducted on SWBLI from the perspective of nonequilibrium effects. A method is proposed for studying nonequilibrium effects based on the Navier–Stokes (NS) equations and the Reynolds-averaged NS (RANS) equations. The SWBLI at Mach 2 and Mach 6 is concerned. The results show that nonequilibrium effects associated with the incident shock wave are weaker than that in the boundary layer for a Mach 2 incoming flow. Neither the separation shock wave nor the incident shock wave has an obvious interaction with nonequilibrium effects in the boundary layer. However, the nonequilibrium effects of the incident shock wave are stronger for a Mach 6 incoming flow, and it has an obvious interaction with the nonequilibrium effect in the boundary layer. We also discuss the relation between nonequilibrium effects and energy conversion in the boundary layer. The analysis reveals that changes in the gradients of total energy-related nonequilibrium effects contribute to the change in total energy by influencing the gradient of the heat flux and the power of viscous stress. Thus, this work provides the flow characteristics of boundary layer separation and energy conversion mechanism of SWBLI from the perspective of nonequilibrium effects, as well as the interaction of nonequilibrium effects between the shock wave and boundary layer.

CFD simulation of shockwave-boundary layer interaction induced oscillation in NACA SC2-0714 transonic airfoil

Abstract To develop an advanced way of designing transonic airfoils for industry, a reliable and user-friendly mesh generator and a robust CFD solver are necessary. Especially, the prediction of unsteady shock buffet phenomenon is always a focus for the CFD simulation of transonic airfoils. In this study, BOXERmesh (an automatic mesh generator) and NEWT (a robust CFD solver), which are developed by CFS (Cambridge Flow Solutions) in collaboration with MHI (Mitsubishi Heavy Industries), are used to perform the CFD simulation of NACA SC2-0714 transonic airfoil. CFD simulation is conducted at two different attack angles with Mach number as 0.74 and Reynold number as 1.5×107 (non-buffet: α=2°; shock buffet: α=3°). A hexahedral dominant mesh is generated by BOXERmesh with the cell number as 5.52 million. Both unsteady RANS (URANS) and LES are performed using the CFD solver NEWT. Specifically, the governing equation is discretized by central differencing scheme with 2nd order accuracy in space by applying Swanson and Turkel type artificial viscosity, and the Adams-Bashford time integration with the dual-time stepping method is applied for temporal discretization in the density-based solver. Results show CFD simulation could reproduce the time averaged chordwise distribution of pressure coefficient at the two conditions. Both URANS and LES successfully capture the unsteady shock buffet phenomenon when increasing attack angle from 2° to 3°. However, the calculated peak oscillation location and the shock buffet frequency are different between URANS and LES. Applying the same mesh resolution, URANS performances better than LES, with the deviation of the shock buffet frequency less than 6% (Exp.: 69 Hz; URANS: 73 Hz). The reason is considered as the wall-normal mesh refinement near the airfoil surface (y+∼66) being not enough for LES to accurately resolve the turbulence scale and capture the boundary layer separation behavior. On the other hand, URANS is thought to be enough to reproduce the periodic moving of the onset of boundary separation and to predict the main characteristics of the shock buffet phenomenon.

Volumetric Velocity Measurements of a Three-Dimensional Shock-Wave/Boundary-Layer Interaction with Flow Actuation Using Two-Camera Plenoptic Particle Image Velocimetry

Two-camera plenoptic particle image velocimetry is used to study a three-dimensional (3-D) shock-wave/boundary-layer interaction (SBLI) generated by a single unswept fin. The SBLI considered was the swept interaction induced by a sharp fin at an angle of attack of 15 deg in Mach 2 flow. The fin generates an oblique shock with a wave angle of approximately 45 deg that interacts with the boundary layer on the incident flat plate. As an extension of previous work, these experiments were conducted to examine the effects of momentum-based flow actuation on the 3-D flowfield, as well as reduce the data uncertainty and improve the overall data quality via addition of a second camera. The following three cases are presented for this work: 1) the baseline interaction with the presence of the inactive microjet actuators (physical insert present), 2) the mean SBLI flowfield under the influence of microjet actuation upstream of the oblique shock, and 3) the mean flowfields corresponding to phase-locked images captured at four different phases of the actuator pressure cavity signal. The results show good correlation with the literature of the SBLI with actuation, including a possible shift or rotation of the shock feature during actuation, and an increased velocity deficit and boundary-layer height. The resonance-enhanced microjet actuation also had a notable impact on the low-speed flow region near the fin. This work presents one of the first 3-D measurements of a fin-generated SBLI influenced by flow actuation.

Experimental Study of the Unstart/Restart Process of a Two-Dimensional Supersonic Inlet Induced by Backpressure

Unstart/restart phenomena induced by backpressure in a general inlet with a freestream of M = 2.7 are investigated in an in-draft supersonic quiet wind tunnel. The boundary layers are turbulent on the forebody while are laminar on the lip wall, which could mimick real flight conditions. The high-speed Schlieren imaging system and the nanoparticle-based planar laser scattering (NPLS) method are used to visualize the inlet flowfield. The inlet wall pressure is measured by high-frequency pressure transducers. The backpressure is reproduced by downstream transverse jets other than mechanical throttlers, which is more suitable to mimic backpressure caused by combustion. The high spatio-temporal resolution full-view images of inlet flow features during the complete unstart/restart process are captured, which are seldom seen before. The formation and disappearance process of massive boundary layer separation at the entrance of the unstarted inlet is observed. The backpressure transmits upstream through the shock wave/boundary layer interaction (SWBLI) regions. The shock structures change the angles and merge upstream to balance the pressure rise. The Mach shock reflection configuration is observed in both unstart/restart process, accompanied by the boundary layer separation extending to the leading edge. The experiment also revealed notable hysteresis in the unstart/restart process.

Capsule aerodynamics and shock-wave boundary layer interaction (SBLI) in supersonic and transonic flow

Static force and moment measurements are performed on the MarcoPolo-R aero shape in the trisonic wind tunnel TMK. The static stability behaviour of the capsule is characterized in the Mach number range 0.5le Mle 3.5 reproducing the Mach and Reynolds conditions of the flight trajectory in the supersonic regime. An aerodynamic database is built based on the experimental results. The flow structure around the capsule is visualised in supersonic tests by means of schlieren imaging. Under certain conditions, development of a complex shock system on the leeward side of the inclined capsule is observed. Oil film technique is used to visualise boundary layer phenomena in connection to this shock system. Numerical simulations with the DLR TAU code are performed to support the interpretation of the flow phenomena under these conditions.Graphical abstractSchlieren imaging visualisation of density gradients in supersonic flow. Depending on the test conditions and angle of incidence, a complex shock system is observed on the leeward side of the inclined capsule. Analysis of the shock structure and its impact on aerodynamic coefficients is one subject of the present investigation.

Numerical investigation of unswept and swept turbulent shock-wave boundary layer interactions

Hybrid turbulence model and large-eddy simulations of turbulent shock-wave boundary layer interactions at a freestream Mach number of 2.3 were carried out for sweep angles of 0 and 40 deg. The simulations for the unswept interaction reveal the shedding of spanwise coherent structures as well as intermittent spanwise deformations of the separation line. The frequencies associated with the spanwise deformations are in the low- to mid-frequency band. By adding a cross-flow component to the approach flow, a comparable turbulent interaction with 40 deg sweep was obtained. For the swept interaction, the overall level of the pressure fluctuations is higher than for the unswept case but the spanwise structures are absent. Instead, traveling oblique structures are observed downstream of the interaction.

Investigation on the three-dimensional shock wave/turbulence boundary layer control induced by the secondary recirculation jets

The interaction between the shock wave and the turbulence boundary layer induces a separation, and this is an undesired phenomenon for the flow field performance. The control work of the separation is pretty important. In the current study, the passive control is carried out. The three-dimensional coupled with the implicit Reynolds Averaged Navier-Stokes (RANS) equations and the two-equation shear stress transport (SST) k-ω turbulence model have been used to simulate the shock wave/boundary layer interaction (SWBLI) flow control induced by the secondary recirculation jet numerically. Four different configurations of the secondary recirculation jet device are put into investigation. The obtained results show that the control induced by the secondary recirculation jet has pretty good effect to decrease the projected area and the volume of the separation zone, as well as the wall heat flux. The projected area and the volume can be reduced by 24.68%.and 29.31%, respectively, and the wall heat flux can be reduced by 17.92%. The case with the best effect equips with two blow or bleed holes and proper spacing. The high heat flux distribution is closely related to the reattached node.

Transitional shockwave/boundary layer interaction experiments in the R2Ch blowdown wind tunnel

Transitional shockwave/boundary layer interactions (SBLI) are studied experimentally. Experiments are conducted on a hollow-cylinder flare model in the R2Ch blowdown facility at a Mach number of 5 for three different Reynolds numbers in the transitional regime. Unsteady wall pressure measurements are conducted along with mean and unsteady heat flux measurements and high-speed Schlieren imaging. The images are then processed using Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition (SPOD) to extract relevant information. Two main phenomena are identified and documented: the oblique modes traveling in the shear layer above the recirculation region and the streaks appearing in the reattachment region. New results illustrating the multiple physical origins of the streaks, either linked with globally unstable modes and convectively unstable mechanisms, are discussed.Graphical Abstract

Uncertainty Analysis of Parameters in SST Turbulence Model for Shock Wave-Boundary Layer Interaction

Shock wave-boundary layer interactions (SWBLIs) have a tremendous influence on the performance of hypersonic vehicles. For the numerical simulation of such engineering flows, Reynolds averaged Navier-Stokes (RANS) still occupies an irreplaceable role. However, parameters of turbulence models in RANS have substantial uncertainties, which impact the reliability of simulation results. Thus, the aim of the present study is to conduct an uncertainty analysis on parameters in the shear-stress transport (SST) turbulence model for the simulation of SWBLIs. In the current work, uncertainty quantification was performed first. A surrogate model was constructed by the non-intrusive polynomial chaos (NIPC) method to propagate uncertainties from model parameters to the quantities of interests (QoIs) and quantify them. In the subsequent sensitivity analysis, the key parameters were identified for such flow by calculating the Sobol index of each parameter for various QoIs. The results indicate that uncertainties of model parameters led to non-negligible uncertainties in those QoIs, particularly in skin friction and wall heat flux. The parameters α1, σω1, β1 were identified as primary contributors through the sensitivity analysis. Moreover, the specific effects of the three parameters on the flow prediction were analyzed by changing the parameters’ values separately.