Range Of Mach Numbers Research Articles

Kinetic modeling of fluid-induced interactions in compressible, rarefied gas flows for aerodynamically interacting particles

In the study of gas-particulate multiphase systems, the flow of high-speed gas through a distribution of solid particulates is of utmost importance. While these aerodynamically interacting systems have been extensively studied for low-speed gas flows in the gas continuum regime, less attention has been given to high-speed systems where non-continuum effects are significant due to the high flow gradients. To address this, the flow of rarefied gas through an aerodynamically interacting monodisperse spherical particle system is studied using the Direct Simulation Monte Carlo (DSMC) gas-kinetic approach. Since the method provides the best resolution of shocks at supersonic Mach numbers it is used to classify the weak separated shocks and strong collective shocks in these systems based on particle spacing in a two-particulate system at different orientation angles. The study used the two-particle system to help analyze more complex particle distributions of volume fractions, 1%, 5%, and 15%, exposed to gas flows in the slip and transitional gas regime for a free-stream Mach number range of 0.2<Ma∞<2.0. We observe that the weak separated shocks in the 1% distribution allow a higher degree of gas penetration and shock-particle interactions or “hypersonic-surfing”, exposing a major fraction of the particulates to higher force magnitudes. In contrast, the strong collective shock in the 5% and 15% distributions only generates high particulate forces on the flow-facing particles. Finally, a simple stochastic model is proposed for use in large-scale Eulerian–Lagrangian simulations that captures the non-monotonic behavior of average drag and force variability generated by the complicated gas particulate interactions in the compressible gas regime.

Optimization of transonic low-Reynolds number airfoil based on genetic algorithm

A 2-D airfoil shape optimization in transonic low-Reynolds number regime is conducted. A Navier–Stokes flow solver with a transition model (k-ω SST γ-Reθ) is used to evaluate the fitness function. Single-point and multi-point formulations of the optimization results are compared. In addition, the effects of Mach number and angles of attack on aerodynamic characteristics of the optimized airfoils are investigated under low Reynolds number (Re = 17,000) and high-subsonic-flow ([Formula: see text]) conditions. The results show that the corresponding drag divergence Mach number curves of the conventional airfoil present almost a parallel shifting at the entire Mach number range. By contrast, the unconventional airfoil starts showing a significant drag reduction when Mach number is greater than 0.75. Besides, the maximum lift-to-drag ratio is highly influenced by the Mach number because of the formation, movement, type, and strength of a shock wave. In addition, the distinguishing difference in the conclusion between two airfoils is that the lift fluctuation of the conventional airfoil amplifies with the increase of the Mach number. However, the unconventional airfoil shows an opposite trend.

State switching in the wake of a transverse circular cylinder in the transonic regime

The flow past a circular cylinder in a cross-flow configuration was investigated using a wind tunnel experiment across a range of Mach numbers M∞ from 0.30 to 0.85 and corresponding Reynolds numbers, based on diameter, ranging from 2×105 to 5×105. The boundary layer at the cylinder surface is either free or fixed turbulent using artificial tripping at azimuth 12.5°, 25°, and 50°. Measurements combine temporal recordings of the wall pressure and schlieren high-speed visualizations of the flow past and downstream of the cylinder. First, by attaching the tripping strips to the cylinder at the different azimuthal positions, the effect of the boundary layer state on the cylinder wake is found to be strong at subsonic speeds but much smaller in the transonic regime. Multiple flow states are observed depending on the value of M∞. Of particular interest was the narrow region between M∞=0.80 and =0.85, which yields three different states, namely the vortex shedding state, the parallel shear layer state, and the crossed shear layer state. By precisely managing back and forth travels in Mach number with the wind tunnel, it is found that the transitions between these states have a hysteresis behavior. This sub-critical behavior could explain the surprisingly variable threshold values between these different states reported in the literature.

Supersonic Flow past a Sharp Plate with Surface Anomalous Glow Discharge in a Magnetic Field

The electrodynamic structure of an anomalous glow discharge between two plane electrodes located on the surface of a sharp plate in supersonic flow of molecular nitrogen is studied numerically in a wide range of Mach numbers using a modified ambipolar model of quasi-neutral electric-discharge plasma. The ambipolar diffusion coefficient and the effective ionization rate are modified while taking into account the external magnetic field. The problem is solved in the two-dimensional x–y formulation, when the external magnetic field strength is directed in the positive or negative direction of the z axis. The parameters of anomalous glow discharge are numerically studied in the pressure range p = 0.14–5 Torr and the voltage drops on the quasineutral current column of discharge plasma V = 30–320 V. The main problem parameters which make it possible to obtain a reasonable agreement with the available experimental data are determined.

A low diffusion flux-split scheme for all Mach number flows

A low diffusion version of the Harten–Lax–Leer convective pressure split (HLL-CPS) scheme for resolving the shear layers and the flow features at low Mach numbers is presented here. The low diffusion HLL-CPS scheme is obtained by reconstructing the velocities at the cell interface with the face normal Mach number and a pressure function. Asymptotic analysis of the modified scheme shows a correct scaling of the pressure at low Mach numbers and a significant reduction in numerical dissipation. The robustness of the HLL-CPS scheme for strong shock is improved by reducing the contribution of the contact wave in the vicinity of the shock. The improvement in robustness for strong shock is demonstrated analytically through linear perturbation and matrix stability analyses. A set of numerical test cases are solved to demonstrate the efficacy of the proposed scheme over a wide range of Mach numbers.

A new type of non-polynomial based TENO scheme for hyperbolic conservation laws

For classical WENO/TENO reconstructions, the high-order polynomial interpolation is one of the main building-blocks for constructing the numerical fluxes. However, due to the inherent characteristics of polynomials, the polynomial interpolation is not suitable to represent the flow scale with sharp transitions such as high-wavenumber fluctuations or discontinuities. In this work, based on a new candidate stencil arrangement with explicit detection of non-smooth regions, a new shock-capturing framework is proposed by combining the infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with the jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme not only achieves the desired high-order accuracy for smooth flow scales but also resolves the genuine discontinuities with a sub-cell resolution. Moreover, with the observation that the built-in parameter has a significant impact on the basic shape of the Gaussian RBF kernel function, a nonlinear adaptation strategy for the shape parameter is proposed to incorporate the local features of the flow field and further minimize the numerical dissipation errors for smooth flow scales. In order to demonstrate the robust shock-capturing and high wave-resolution properties of the proposed non-polynomial based scheme, a set of challenging benchmark cases with a wide range of Mach numbers is simulated without the necessity of parameter tuning case by case.

Study on Ground Experimental Method of Stagnation Point Large Heat Flux of Typical Sharp Wedge Leading Edge Structure

In this paper, aimed at the problem of large temperature gradient thermal testing with the typical sharp wedge leading edge structure of a hypersonic vehicle, a subsonic high-temperature combustion gas heating (SHCH) test device is used to conduct a series of experiments on the heat flux simulation ability of subsonic high-temperature combustion gas in the stagnation point region. Firstly, for a hypersonic vehicle with a flying height of 24 km and Mach number range of 4~6.5, the stagnation point heat flux in the head area is obtained by numerical calculation of a typical leading edge structure, which is used as the experimental target of the thermal structure test. Secondly, an experimental specimen with a Gardon heat flux meter is designed with the same shape and size as the specimen in the numerical simulations to prepare for the subsequent SHCH test. Thirdly, a method to determine the combustion gas temperature based on a Kriging surrogate model is proposed. CFD numerical simulation is conducted using the SHCH test model, and the numerical calculation results are used as the training dataset. The Kriging surrogate model is used to establish an approximate fitting relationship between the stagnation point heat flux and experimental parameters under SHCH conditions. The corresponding combustion gas temperature values are found, respectively, with the hypersonic aerodynamic heat flux at Mach 5.0~5.4 as the target value. Finally, stagnation point heat flux testing of low-speed and high-temperature combustion gas is performed at different combustion gas temperatures. The experimental and target values obtained from hypersonic aerodynamic thermal simulations are compared and analyzed to verify the heating capacity of SHCH and the feasibility of hypersonic aerothermal simulation testing.

Calculation of Dynamic Derivatives for High-Speed Vehicles Based on the National Numerical Windtunnel Software

Based on the NNW-HyFLOW high-speed numerical simulation software, the forced-oscillation dynamic derivatives module has been constructed using the unsteady implicit method, dual time stepping and rigid rotary grid deformation. The code has been validated by the calculation of Finner, HBS, blunt cone and OV-102 vehicle in the range of Mach number 1.85∼6.85 and angle of attack 0∼20°. Compared with the results from experiments, engineering methods and other software, all predicted dynamic derivatives have the same sign as experimental values, and the overall error is within 15%, which illustrate the effectiveness of the dynamic derivative module. Due to the difference of numerical and experimental environment and error bands of both, the numerical predictions of the damping derivatives and cross-coupling derivatives are consistent with the experimental values, which means that the proposed module has the capacity to calculate dynamic derivatives for complex engineering vehicles.

A unified explanation of energy growth sources for unstable modes in flat-plate boundary layers

The detailed energy sources that sustain the eigenmodal exponential growth in boundary layers are currently unclear. In the present study, the phase of each term in the linear stability equation is examined to identify the significant physical sources for a wide range of Mach numbers and wall temperature ratios. The Tollmien–Schlichting mode for incompressible flows, the oblique first mode for supersonic flows and the Mack second mode and supersonic mode for hypersonic flows share some similar features. The unique appearance of obliqueness for the most unstable first mode is accompanied by the enhancement of Reynolds shear stress. By contrast, the weakened Reynolds thermal stress prevents the oblique second mode from being the most unstable state. Wall cooling stabilises the oblique first mode by rendering Reynolds thermal stress and dilatation fluctuations out of phase with the internal energy fluctuation. It destabilises the second mode by a newly generated pronounced region of wall-normal internal energy transport beneath the second generalised inflection point. In comparison, the porous coating destabilises the oblique first mode by significantly enhancing the mean-shear production while it stabilises the second mode similarly to wall heating. Finally, the relatively weak supersonic mode has the feature that the phase destruction of wall-normal transport near the critical layer results in a low contribution to the internal energy growth. Connections and consistencies are also highlighted with the previous inviscid thermoacoustic interpretation for the second mode (Kuehl, AIAA J., vol. 56, 2018, pp. 3585–3592) and for the supersonic mode. The pronounced sources along the critical layer and near-wall regions provide a unified understanding of the local energy amplification mechanisms of the inviscid modes in hypersonic boundary layers.

The influence of Mach number and overpressure on the structure of supersonic gas jets

ABSTRACT The Mach number is the primary parameter in determining the intrinsic driving properties, and effect on the environment of a supersonic jet. In the most basic form, a jet is released when a wall of a large high-pressure gas reservoir is punctured. The resulting high-pressure jet contains a configuration of shocks that continue to disturb the environment after the initial bow shock has passed. Here, we perform numerical simulations to determine the properties attributable to pure adiabatic hydrodynamic effects, taking a uniform stream out of a circular nozzle. We take a range of Mach numbers that, along with the jet overpressure, determine the flow pattern and shock locations. We distinguish conditions that generate Mach shock discs rather than a diamond pattern of oblique regular reflections. Potential observational diagnostics explored include the disc size, the distance from the nozzle, and oscillations in shock positions. Rapid oscillations occur in the divergent–convergent pattern through a feedback/hysteresis effect promoted by the ambient medium. The underlying flow patterns are independent of relative jet density, but heavy jets display both lower amplitude and lower frequency oscillations. We also study the energy transferred into the environment. Overpressured jets may contribute to noise and sound wave generation through screeching. However, these oscillations in the near-field are not sufficiently significant to regulate star and galaxy formation. We expect that upcoming high dynamic range and resolution observations will increasingly detect the shock patterns as jet gas transits from protostellar and galactic cores.

Aerodynamic Control of an Inlet Flow in Crosswind Using Peripheral Bleed Actuation

The flow within the inlet of an engine nacelle model in the absence of a fan and the presence of crosswind is investigated in wind-tunnel experiments, with specific emphasis on the effects of separation over the inlet’s inner windward surface on the flow distortion and pressure recovery. The inlet’s entrance plane is tilted forward, and its cross section is asymmetric about the horizontal centerline. The flow topology within the inlet is characterized over a range of Mach numbers and crosswind speeds up to M=0.72 and Uo=18 m/s, respectively. It is shown that in the presence of sufficiently high crosswind to the inlet speed ratio, a three-dimensional horseshoe-like separation domain is formed over the inlet’s inner windward surface. Owing to the cross-sectional asymmetry of the entrance plane, the separation domain migrates azimuthally downward and expands azimuthally with increased crosswind to the inlet speed ratio. The present investigations demonstrate the utility of flow control for mitigating the adverse effects of the separation. The actuation is based on controllable distributed aerodynamic air bleed that is driven by the pressure differences across the nacelle’s inner and outer surfaces and reattaches the separated base flow up to crosswind speeds of 15.4 m/s, resulting in a gain of up to 38% in total pressure recovery and a decrease of up to 55% in total pressure distortion. The efficacy of the bleed actuation can be further improved by tailoring the bleed distribution to the topology of the separated flow domain.

Effects of Periodic Incoming Wakes on the Aerodynamics of a High-Speed Low-Pressure Turbine Cascade

The influence of unsteady wakes incoming from the upstream stages is of high relevance in modern high-speed, low-pressure turbines (LPT) operating at transonic exit Mach numbers and low Reynolds numbers for their potential to trigger transition and influence the separation of the boundary layer on the blade suction side. The aim of this paper is the experimental characterization of the influence of incoming wakes on the 2D aerodynamics of a high-speed LPT cascade operating at a low Reynolds number and transonic exit Mach number. A detailed analysis of the status of the flow along the blade under investigation and its impact on the profile loss are presented for a range of Mach numbers from 0.70 to 0.95 and Reynolds numbers from 70k to 120k under steady and unsteady inflow conditions. Tests were conducted at on- and off-design engine realistic conditions in the VKI S-1/C wind tunnel on the SPLEEN C1 transonic cascade. The wakes incoming from an upstream blade row have been replicated using a set of rotating bars, which shed wakes at an engine-representative reduced frequency (f+=0.95) and flow coefficient (Φ=0.80). A set of densely instrumented traversable blades were used to sample the surface pressure distributions. The development of the boundary layers along the blade suction side is examined through quasi-wall shear stress obtained with surface-mounted hot-film sensors. Wake traverses were carried out downstream of the cascade with a miniaturized L-shaped five-hole probe to characterize the blade losses. The introduction of periodic incoming wakes promotes variations in the flow topology over the blade. The effect on the suction side separation bubble is shown to depend on the exit flow conditions. At low Mach numbers, the incoming wakes determine a reduction in the size of the bubble; in contrast, this effect is not registered as the exit Mach number increases. Consistently, a high dependence of the unsteady wake effect on the profile loss on the exit Reynolds and Mach numbers is demonstrated.

Intelligent variable strut for combustion performance optimization of a wide-range scramjet engine

This paper investigates an intelligent strut design scheme for achieving high-performance combustion of a combustion chamber under wide-ranging flow conditions. The design process involves optimizing the base strut configuration for the design point and obtaining the Pareto front. The subsequent selection of the optimal configuration is followed by analyzing and interpreting the optimization results using single-factor analysis rules. The findings reveal that the selected optimal configuration enhances the combustion efficiency by 8.22% and reduces the force by 66.12% compared to the traditional DLR combustion chamber. Additionally, a surrogate model is constructed to investigate the influence of the rotation angle of the intelligent strut's rotating blades on the combustion efficiency and force at a Mach number range of 2–3.5. Results indicate that the intelligent strut is capable of improving combustion efficiency via regulation, and the efficiency can quickly reach a desirable level. These findings suggest that the proposed design scheme has potential applications in achieving high-performance combustion in combustion chambers exposed to wide-ranging flow conditions.

Flow Topology of a Slanted Cylinder with Rounded-Edges Under Compressible Conditions

In this study, the slanted afterbody was modified to more closely represent cargo aircraft afterbodies through the addition of a basal edge fillet. Two slant angles ( and ) were explored over two Mach numbers ( and ) and two Reynolds numbers ( and ) using oil flow visualization and pressure-sensitive paint to identify surface flow phenomena, while the spanwise shadowgraph enabled the observation of mean wake phenomena. The rounded-edge afterbody surface measurements displayed a centerline-separated vortex state with flow features and regions of suction qualitatively similar to those of the baseline sharp-edge case, with some notable differences. For example, a separation bubble at the slant leading edge is nearly twice the size of the baseline sharp-edge model. This is accompanied by the presence of a “source point,” indicated by a region of high pressure where the flow reattaches, and a tighter counter-rotating vortex pair in comparison to the baseline. The rounded-edge prevented the previously seen compressible transition to a fully separated wake state within the Mach number range studied while showing an increase in separation bubble size with increasing Mach number. Also noteworthy was the existence of a new vortex state for the model, where the flow remains attached at the model centerline. This is in contrast to the previously observed flow topology of the centerline-separated vortex state in the sharp-edge model, which formed a separation bubble at the model centerline. The transition between the new centerline-attached vortex state and the traditional centerline-separated vortex state was shown to be dependent on both Mach number and Reynolds number, revealing the importance of boundary-layer development on the rounded afterbody flowfield. Overall, these observations indicate that the rounded afterbody produces flowfields with distinct features that vary from the previously described sharp-edge afterbody wake field under certain conditions.

Flow pattern diagram of compressible non-equilibrium gas flow around a circular cylinder

An investigation into the non-equilibrium gas flow around a circular cylinder within the Knudsen number (Kn) range of 0.001–1 and the free-stream Mach number (Ma) range of 0.01–6 is presented using the unstructured grid unified gas kinetic scheme. The primary objective is to examine the impact of Kn and Ma on flow patterns. The flow pattern diagram illustrating seven flow patterns in the Ma-Kn space is provided, including the transition boundary between bow shock-wave with laminar flow (BS+L) and bow shock-wave with vortex flow (BS+V). The relationships between Re-Kn and Ma-Re both follow the power function: y=eβxα, where α and β are constants. The study also provides a more precise critical curve of vortex shedding in subsonic inflow, the boundary of tailing shock-wave, and the boundary of vortex shedding in a transonic inflow. The flow pattern diagram indicates that the variation of flow separation with Kn is non-monotonic across the entire Ma range but is monotonic at Ma&amp;gt;1. In the subsonic inflow, the critical Re of flow separation (Rec) increases with Ma, while Rec initially increases and then decreases with Kn. The critical Ma at the turning point is about 0.72. In supersonic inflow, the critical Re associated with the onset of flow separation either increases or decreases with the increase in Ma or Kn. The critical Re of vortex shedding is non-monotonic with Kn. The critical Re of the trailing shock-wave decreases with both Kn and Ma. In the transonic inflow, the critical Re and critical Ma of vortex shedding decrease with Kn. As rarefaction increases, the type of flow patterns decreases. The flow pattern diagram provides a visual representation of the impact of rarefaction and compressibility effects on flow pattern transitions and assists in determining the applicable range of the drag coefficient model.

Hybrid Lattice Boltzmann Approach for Simulation of High-Speed Flows

A lattice Boltzmann approach utilizing hybrid lattices for accurate simulation of high-speed transonic (TS) flows is presented in this study. Single-layer lattice models, such as D3Q19, are computationally efficient with low numerical dissipation, but are limited to simulate weakly compressible flows within subsonic Mach regime. Multilayer lattice models, such as D3Q33, are capable of simulating thermal and high-speed compressible flows in TS Mach regime, but suffer from a higher numerical dissipation and higher computational cost. To take full advantages of these two types of lattices, a simulation domain is divided into two regions, high-subsonic (HS) flow regions to be solved by single-layer lattices and TS flow regions to be solved by multilayer lattices. The interface connecting the HS and TS flow regions are represented by double-sided surfels to realize smooth flow transition and ensure satisfaction of fundamental conservation laws. The hybrid lattice Boltzmann approach is stable and robust, and it allows multiple HS/TS flow regions with arbitrary shapes. Extensive validation studies demonstrate that the proposed approach is capable of obtaining accurate aerodynamic prediction of flows with a wide range of Mach numbers, and preserving the low numerical dissipation advantage of single-layer lattices in aeroacoustic computations.

Piston problem for the generalized Chaplygin Euler equations of compressible fluid flow

We study the piston problem for the compressible fluid flow of generalized Chaplygin gas, for both cases that the piston rushes into or recedes from the uniform still gas at a constant speed. The global existence of a solution to the piston problem is established. For the proceeding piston problem, we find that the front shock can be detached or adhered to the surface of the piston depending on the range of Mach numbers. Then, a Radon measure solution, with density containing a Dirac measure supported on the piston is rigorously defined and proved to be a reasonable solution to deal with the concentration of mass on the piston. When the piston recedes from the gas, we show strictly that only a first-family rarefaction wave exists in front of the piston and that concentration will never occur. Moreover, we also analyzed the occurrence of the vacuum state and the degeneration of the compressible fluid flow in the receding case as the Mach number tends to infinity.

Аналіз впливу мотогондоли на силу тяги вентиляторного контуру турбовентиляторної приставки

The subject of this study is the interaction between the engine nacelle of a three-circuit turbojet engine and a turbofan attachment. The object of this research is a model of a cylindrical engine nacelle and a fan part of the impeller of a turbofan attachment. The aim of this study was to evaluate the influence of the engine nacelle on the thrust force of the fan circuit of a three-circuit turbojet engine, taking into account the influence of the operation of the turbofan attachment. Tasks: to simulate the flow around the engine nacelle with a turbofan attachment and without a turbofan attachment; calculate the thrust force of the turbofan attachment. The studies were carried out using the method of numerical experiment. The system of Navier-Stokes equations was closed by the turbulent viscosity model SST Gamma Theta Transitional No. 4. The results of the study showed that the reactive thrust of the fan circuit of the turbofan attachment increases by 0.87-6.15% when operating at an altitude of 0 km, 9 km, 11 km and the range of Mach numbers at the input from 0.2 to 0.5. When flowing around the engine nacelle without taking into account the influence of the turbofan attachment, it is characteristic that the velocity field at the inlet is uniform, except for the zone with a boundary layer near the surface of the engine nacelle. However, during operation of the turbofan attachment, the flow pattern changes radically and the thickness of the boundary layer decreases, and the flow in front of the fan is uneven. A characteristic feature of the turbofan attachment, which is associated with the heating of the intermediate housing between the turbine and fan housings, has a positive effect on reducing the thickness of the boundary layer, wall heating contributes to an increase in the stagnant flow velocity due to viscous forces. The presence of a boundary layer on the engine nacelle does not adversely affect the flow in the fan circuit of the turbofan attachment, and the fan of the turbofan attachment does not adversely affect the engine gas generator. The scientific novelty and practical significance of this work lies in obtaining new data on the effect of the engine nacelle on the thrust force of the fan circuit of a three-circuit turbojet engine, taking into account the influence of the operation of the turbofan attachment. The results obtained can be used to optimize the turbofan attachment of a three-circuit turbojet engine.

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Computational Study of Supersonic Flow Over a Flat Plate With Protrusion

Motivated by a developmental approach of using micro-actuated surface protrusions to control/maneuver slender bodies in supersonic flight, this paper presents a detailed study of a two dimensional laminar supersonic flow over a flat plate with a surface protrusion. The flow field is computed by solving the Navier-Stokes equations using the finite difference method with the particle velocity upwinding scheme (PVUS) for spatial discretization, and the explicit Mac Cormack scheme for temporal integration. A range of free stream Mach numbers (2.0 - 4.5), Reynolds numbers (1000 - 100000) and protrusion heights (0.866% to 8.66% of the characteristic length) has been considered for a thorough parametric study. The parametric study indicates that the oblique shock structure and strength are influenced by all the variables to varying extents. However, the shock location is substantially altered by the protrusion height, Reynolds number, and protrusion shape, while the influence of Mach number is only marginal. An increase in the protrusion height results in an increased wall pressure as well as increased separation lengths on both sides of the protrusion. In contrast, an increase in Mach number increases the wall pressure, but moves the separation point marginally towards the protrusion. Increase in Reynolds number and protrusion bluffness (triangular → trapezoidal → rectangular) increases separation lengths on both sides of the protrusion. In addition to taking a close look at the flow physics, particularly in the protrusion vicinity, considerable attention has also been devoted to important design parameters such as wall pressure, skin friction and the overall normal and tangential force coefficients.