Range Of Freestream 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.

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.

Transonic Flow Computation Over A Heat Shield Using Three Dimensional Finite Element Method

A three dimensional finite element method is employed for solution of the transonic full potential equation in mass conservation form. The finite element analysis allows the boundary conditions to be treated in simple and exact manner, without the use of a mapping scheme. The full potential equation is based on the assumption of irrotational flow and density of the fluid is calculated using isentropic relation and it is applicable for upstream local Mach number upto 1.6. The nonlinear full potential equation is reduced to a set of nonlinear algebraic equation using Galerkin’s formulation. An iterative scheme in conjunction with the artificial viscosity term is used to solve the set of algebraic equations. The artificial viscosity term stabilizes the numerical scheme and captures the shock very well. An appropriate grid arrangement is selected in the algorithm to maintain proper and continuous linkage between upstream and downstream of the flow at the centroid of the hexahedral element. The surface pressure distribution in the freestream Mach number range 0.80 - 0.95 and at an angle of incidence 5 degree shows a fairly good agreement with the experimental data. The present finite element discretization can be coupled with the commercially available software.

Numerical Simulation of Flow Field Over a Sharp-Tipped Double Cone at High Speed

The flowfield over a sharp-tipped double cone axisymmetric configuration is carried out by solving time dependent axisymmetric laminar compressible Navier-Stokes equations for freestream Mach number range of 2.0 - 6.0. The fluid dynamics equations are discretized in spatial coordinates using integral formulation in conjunction with finite volume method which reduces the governing equations to semi-discretized ordinary differential equations. Temporal integration is performed employing multistage Runge-Kutta time-stepping scheme. A local time step is used to achieve steady-state solution. The numerical computation is carried out on a mono-block with structured grids. The flowfield features over the sharp-tipped double cone configuration such as conical shock wave, separation region, separation and reattachment shock wave and bow shock wave in the cone region, expansion fan, and recirculation flow in the base region are well captured at Mach number 3 and 6 which are identical to the Edney VI type shock interaction. The velocity vector, Mach contours plots and variations of surface pressure coefficient along the sharp-tipped double cone configuration are analyzed at various Mach numbers. The fore-body aerodynamic drag is calculated employing computed pressure distribution. The paper presents the influence of the freestream Mach number on the flows with shock interactions over the sharp-tipped double cone geometry.

High order discontinuous Galerkin simulation of hypersonic shock-boundary layer interaction using subcell limiting approach

Numerical simulation of shock-boundary layer interactions in the hypersonic regime has for long been a challenge, plagued by high sensitivity of the surface predictions to grid and numerical details. In the course of developing adaptive high order methods to mitigate this issue, discontinuous Galerkin method has emerged as a promising alternative to the conventionally used finite volume method. However, till date, among the reported finite element method-based simulations of these flows, only a few have presented high order simulations using a higher than linear basis. In this work, a subcell limiting technique devised for the compressible Navier-Stokes equations is extended for use in the hypersonic regime. The proposed extension is tested by performing simulations of several shock-boundary layer interaction cases in the freestream Mach number range 6 to 14 using a quadratic basis. For a set of cases at Mach 6, grid converged simulations are presented that agree reasonably well with experimental data and other numerical solutions. More importantly, simulations of a Mach 11 case that are performed using two different flux schemes are shown to yield nearly identical predictions of the surface pressure and heat transfer, suggesting that high order solutions can reduce the sensitivity of numerical predictions to the computational details. Grid convergence studies of two cases at Mach numbers 11 and 14 led to observing large scale oscillations in the separation bubble in finer grid simulations, suggesting that explicit time integration may not always be suitable for high order computation of hypersonic separated flows at very high Mach numbers.

Computational Fluid Dynamics Analysis and Design of Payload Shroud of Satellite Launch Vehicle

The main focus of the present paper is to computational fluid dynamics analysis and design of payload fairing of satellite launch vehicle at freestream Mach number range of 0.6 - 3.0. Initially, time-dependent compressible three-dimensional Euler equations are solved employing a finite volume discretization method with a multi-stage Runge-Kutta time-stepping scheme to compute surface pressure and aerodynamic coefficients at various payload fairing and at angle of attack up to 5o with an increment of 1o. Payload fairing dimensions are selected that satisfies permissible structure load on satellite launch vehicle. Detailed flowfield simulation is carried out on the selected payload fairing employing axisymmetric compressible Reynolds-average Navier-Stokes equations to assess unsteady flowfield characteristics. The numerical simulations are used to locate terminal shock on the payload fairing at transonic Mach number. Unsteady flow characteristics are used to compute acoustic load. Shock standoff distances at supersonic speeds are tabulated and compared with the analytical solution. Schlieren images and oil flow pictures are compared with experimental results and in good agreement. Aerodynamic shape optimization of satellite launch vehicle payload fairing shape has been performed to satisfy structural load at maximum drag and dynamic pressure.

SPARK: Implicit Time-Accurate Algorithm for All-Speed Viscous Flows

A new pressure-based finite volume algorithm is developed for simulating all-speed viscous flows. In this algorithm, the semidiscretized transport equations are integrated in the framework of stiffly accurate diagonally implicit Runge–Kutta methods. At each stage of time integration, the density–pressure–velocity coupling is fully solved, and mass conservation is ensured. The algorithm is verified and validated for several canonical cases over a wide range of freestream Mach number, from incompressible to supersonic flow. The performance and accuracy of the proposed algorithm are benchmarked against established methods for simulating unsteady flow, namely, SIMPLE and SIMPLER.

Linear stability analysis of hypersonic boundary layers computed by a kinetic approach: a semi-infinite flat plate at $$\varvec{4.5\le \mathrm{M}_\infty \le 9}$$

Linear stability analysis is performed using a combination of two-dimensional Direct Simulation Monte Carlo (DSMC) method for the computation of the basic state and solution of the pertinent eigenvalue problem, as applied to the canonical boundary layer on a semi-infinite flat plate. Three different gases are monitored, namely nitrogen, argon and air, the latter as a mixture of 79\% Nitrogen and 21\% Oxygen at a range of free-stream Mach numbers corresponding to flight at an altitude of 55km. A neural network has been utilised to predict and smooth the raw DSMC data; the steady laminar profiles obtained are in very good agreement with those computed by (self-similar) boundary layer theory, under isothermal or adiabatic wall conditions, subject to the appropriate slip corrections computed in the DSMC method. The leading eigenmode results pertaining to the unsmoothed DSMC profiles are compared against those of the classic boundary layer theory. Small quantitative, but no significant qualitative differences between the results of the two classes of steady base flows have been found at all parameters examined. The frequencies of the leading eigenmodes at all conditions examined are practically identical, while perturbations corresponding to the DSMC profiles are found to be systematically more damped than their counterparts arising in the boundary layer at the conditions examined, when the correct velocity slip and temperature jump boundary conditions are imposed in the base flow profiles; by contrast, when the classic no-slip boundary conditions are used, less damped/more unstable profiles are obtained, which would lead the flow to earlier transition. On the other hand, the DSMC profiles smoothed by the neural network are marginally more stable than their unsmoothed counterparts.

Numerical investigation of impact of fixed-exit boundary-layer bleed on supersonic intake performance

Results of numerical investigation of flow and performance characteristics of a rectangular supersonic intake with boundary-layer bleed system are presented. The effects of several flush slot bleed geometric parameters including entrance and exit area, plenum size, rear edge vertical displacement and the position relative to the incident shock have been studied to clarify their effects on the compression performance. The viscous flowfield has been obtained by solving Favre averaged Navier-Stokes equations with shear stress transport (SST) k-ω turbulence model. Moreover, the numerical methodology deployed is validated with the experimental data from literature. The analysis has been carried out in the freestream Mach number range of 1.8-2.5 and at 00 angle-of-attack, corresponding to a unit Reynolds number of approximately 1.9−2.7×107 m−1. The results show that with the use of bleed, the exit flowfield uniformity as well as the critical and peak total pressure recovery (TPR) improves considerably at all operating conditions. Furthermore, the analysis indicates that the exit throat area of a slot bleed operating at a particular design condition can be increased up to a point such that it is just sufficient to eliminate the upstream boundary-layer at its peak operation. The variation in the bleed entrance area or its position relative to the throat entrance only alters the critical performance depending on the supercritical boundary-layer mass flow loss; however, the peak TPR or the sustainable backpressure remains the same at all upstream conditions, controlled by the fixed-exit throat area. Further, it is found that for the removal of comparable amount of boundary-layer mass flow, the effects of pure flush slot or of a configuration with slight vertical displacement at its rear edge, located at the same position are similar.

Numerical simulation of hypersonic flow with non-equilibrium chemical reactions around sphere

High-temperature effects have a significant impact on the characteristics of aircraft moving at super- and hypersonic speeds. Due to the complexity of setting up a physical experiment, methods of mathematical modelling play an important role in finding the characteristics of hypersonic aircraft. Numerical modelling of super- and hypersonic air flow around the sphere is carried out taking into account high-temperature effects and non-equilibrium chemical reactions. The mathematical model includes equations of gas dynamics, equations of the turbulence model and equations of chemical kinetics. A critical review of the various models that are used to find the stand-off distance is provided. The results of numerical calculations on the distribution of flow quantities in the shock layer and the stand-off distance at different freestream Mach numbers are presented. The results of numerical calculations in a wide range of freestream Mach numbers are compared with the experimental data and computational results of other researchers. Standoff distance is computed at various Mach number and heights during a flight in the atmosphere at hypersonic speed.

Computational evaluation of geometric effects on aerodynamic performance of circulation control airfoils

The geometric effects of Coanda trailing edges on the aerodynamic performance of an airfoil are numerically evaluated for a range of different freestream Mach numbers and momentum coefficients. A Circulation control (CC) airfoil with a circular trailing edge (ACTE) proves to have better control effectiveness at low subsonic freestream speeds (Mach = 0.1). A CC airfoil having an elliptic trailing edge (AETE) outperforms the ACTE at high subsonic flow conditions. The occurrence of C μ-stall for the AETE is greatly postponed, and meanwhile the maximum net lift coefficient increment achieved for the AETE (Δ C L = 0.51) is slightly higher than that of the ACTE (Δ C L = 0.50) at Mach 0.6. Compared to the ACTE, the AETE is found to have better control consistency at different operating velocities and better control stability when the Coanda jet is supersonic. Through careful consideration of the aerodynamic performance and the control effects, the most appropriate axial ratio for an AETE ellipse is within the interval from 1.5 to 2. Finally, the flow field instability phenomenon and the jet detachment induced by the supersonic Coanda jet are investigated. A self-sustained shock-wave instability phenomenon without jet detachment is first observed in this paper.

Prediction of plateau and peak of pressure in a compression ramp flow with large separation

Based on the Helmholtz–Rayleigh minimal dissipation theorem, a theoretical model is proposed to predict both the plateau and peak of pressure in a compression ramp flow with large separation (CRFLS). Since the total dissipation of CRFLS is mainly contributed by the shock waves, the steady flow pattern can be determined by minimizing the shock dissipation among all the possible configurations. The predictions agree well with both experimental data and numerical simulations, covering a wide range of free-stream Mach number and ramp angle. This method could be applied to other flow systems where the dissipation is dominated by shock waves.

Numerical investigation of nanoporous evaporation using direct simulation Monte Carlo

Evaporation is an effective cooling mechanism widely exploited in the thermal management of modern electronic devices, with a growing interest in the evaporation process in thin film based nanoporous membrane technologies. At such scales, classical approaches fail and one requires solutions of the Boltzmann equation; these are obtained here using the direct simulation Monte Carlo method. In particular, the evaporation from representative nanoporous meniscus shapes, corresponding to different operating conditions, has been investigated. Evaporation rates for the different conditions have been characterized as a function of a wide range of Knudsen numbers and free-stream Mach numbers. Additionally, the influence of porosity and evaporation coefficient on the nanoporous evaporation rates has been assessed. Investigations have also been carried out to consider cases where the meniscus has sunk within the pore, and cooling efficacy compared with cases where the meniscus is pinned to the top of the pore. This work demonstrates that the net evaporative mass flux is ultimately determined by the interplay between various physical effects, whose dominance is quantified by the Knudsen number, porosity, evaporation coefficient and the meniscus shape. This work thus provides useful information for the design of nanoporous membrane-based cooling devices.

Suppression of transonic buffet with plasma vortex generators

In the present paper, we report on the results of an experimental study of the possibility to control the transonic buffet on a rectangular wing using plasma vortex generators. The influence of the developed device on the flow consists in creating a longitudinal vortex in the boundary layer as a result of asymmetric energy supply at the surface of a small vertical wedge. The experiments were performed using a wing model with a supercritical airfoil in the range of free-stream Mach numbers 0.73 to 0.78 and Reynolds numbers Re = (2.64-2.8)·106. The experimental data obtained using the method of high-speed schlieren visualization and pressure distribution measurements in the wake of the model show that the technique allows one to control both the average flow characteristics and the characteristics of shock-wave oscillations.

A cure for numerical shock instability in HLLC Riemann solver using antidiffusion control

Various forms of numerical shock instabilities are known to plague many contact and shear preserving approximate Riemann solvers, including the popular Harten-Lax-van Leer with Contact (HLLC) scheme, during high speed flow simulations governed by the Euler system of equations. In this paper we propose a simple and inexpensive novel strategy to prevent the HLLC scheme from developing such spurious solutions without compromising on its linear wave resolution ability. The cure is primarily based on a reinterpretation of the HLLC scheme as a combination of its well-known diffusive counterpart, the HLL scheme, and an antidiffusive term responsible for its accuracy on linear wavefields. In our study, a linear analysis of this alternate form indicates that shock instability in the HLLC scheme could be triggered due to the unwanted activation of the antidiffusive term appearing in its mass and interface-normal momentum flux component discretizations on interfaces that are not aligned with the shock front. This inadvertent activation results in weakening of the favourable dissipation provided by its inherent HLL scheme and causes unphysical mass flux variations along the shock front. To mitigate this, we propose a modified HLLC scheme that employs a simple differentiable pressure-ratio based multidimensional shock sensor to achieve smooth control of these critical antidiffusive terms near shocks. Using a linear perturbation analysis and a matrix based stability analysis, we establish that the resulting scheme, called HLLC-ADC (Anti-Diffusion Control), is shock stable over a wide range of freestream Mach numbers. Results from standard numerical test cases demonstrate that the HLLC-ADC scheme is indeed free from the most common manifestations of shock instability including the Carbuncle phenomenon without significant loss of accuracy on shear dominated viscous flows.

The initiation and propagation of detonation in supersonic combustible flow with boundary layer

Adaptive simulations solving the Navier-Stokes equations have been conducted in order to get a better understanding on the detonation initiation and propagation in a stoichiometric H2/O2/Ar supersonic mixture with boundary layer. The detonation is initiated by a continuous hot jet. When reflecting on the wall, the jet induced bow shock interacts with the boundary layer and forms the shock boundary layer interaction phenomena, while in Euler result the bow shock forms Mach reflection. The investigation shows that the Navier-Stokes simulation result is structurally in better agreement with the experiment compared with that of the inviscid Euler simulation result. The bow shock interacts with the separation shock, forming the shock induced combustion behind the interaction zone. Then the combustion front couples with shock and forms Mach stem induced detonation. The Mach stem induced detonation continues to getting higher and propagating upstream, initiating the main flow. The initiated partial detonation exists with the separation shock induced combustion front, forming an “oblique shock induced combustion-partial detonation” structure in the main flow. The investigation on the influence of free stream Mach number further confirms that the boundary layer has an important influence on detonation initiation. The parametric studies also show that there exists a free stream Mach number range to initiate the partial detonation in supersonic combustible flow successfully.

Transonic buffet control research with two types of shock control bump based on RAE2822 airfoil

Current research shows that the traditional shock control bump (SCB) can weaken the intensity of shock and better the transonic buffet performance. The author finds that when SCB is placed downstream of the shock, it can decrease the adverse pressure gradient. This may prevent the shock foot separation bubble to merge with the trailing edge separation and finally improve the buffet performance. Based on RAE2822 airfoil, two types of SCB are designed according to the two different mechanisms. By using Reynolds-averaged Navier-Stokes (RANS) and unsteady Reynolds-averaged Navier-Stokes (URANS) methods to analyze the properties of RAE2822 airfoil with and without SCB, the results show that the downstream SCB can better the buffet performance under a wide range of freestream Mach number and the steady aerodynamics characteristic is similar to that of RAE2822 airfoil. The traditional SCB can only weaken the intensity of the shock under the design condition. Under the off-design conditions, the SCB does not do much to or even worsen the buffet performance. Indeed, the use of backward bump can flatten the leeward side of the airfoil, and this is similar to the mechanism that supercritical airfoil can weaken the recompression of shock wave.

Effects of viscosity and conductivity stratification on the linear stability and transient growth within compressible Couette flow

Accurate prediction of laminar to turbulent transition in compressible flows is a challenging task, as it can be affected by a combination of factors. Compressibility causes large variations in thermodynamic as well as transport properties of a gas, which in turn are known to affect flow stability. We study the stratification of individual transport properties and their combined behavior. We also examine the effect of a change in the magnitude of viscosity and conductivity on flow stability. The Couette flow of a perfect gas is our model problem and both modal and non-modal analyses are carried out. We notice a large destabilizing role of the increase in the conductivity value and a dramatic stabilizing effect of mean viscosity stratification, over a range of free-stream Mach number, Reynolds number, Prandtl number, and disturbance wavenumber. In the combined case, viscosity stratification plays a dominant role. We find this to be the case for finite-time transient growth in the parameter regime below linear instability as well as asymptotically at large time. A budget of the transient growth energy amplification is also shown to identify the effects of transport properties on the constituents of perturbation energy. The extensive results presented in this paper, we believe should motivate those studying more realistic flows to examine how these contrasting effects of stratification come together.

Compressibility effects in the shear layer over a rectangular cavity

The influence of compressibility on the shear layer over a rectangular cavity of variable width has been studied in a free stream Mach number range of 0.6–2.5 using particle image velocimetry data in the streamwise centre plane. As the Mach number increases, the vertical component of the turbulence intensity diminishes modestly in the widest cavity, but the two narrower cavities show a more substantial drop in all three components as well as the turbulent shear stress. This contrasts with canonical free shear layers, which show significant reductions in only the vertical component and the turbulent shear stress due to compressibility. The vorticity thickness of the cavity shear layer grows rapidly as it initially develops, then transitions to a slower growth rate once its instability saturates. When normalized by their estimated incompressible values, the growth rates prior to saturation display the classic compressibility effect of suppression as the convective Mach number rises, in excellent agreement with comparable free shear layer data. The specific trend of the reduction in growth rate due to compressibility is modified by the cavity width.

Reynolds and Mach Number Dependence of Hypersonic Blunt Body Laminar Near Wakes

Laminar separation on the aftbody of an adiabatic circular cylinder was numerically investigated over a range of freestream Mach and Reynolds numbers using the free open-source program OpenFOAM. Simulations were performed assuming laminar, continuum, thermally perfect flow of nitrogen gas. Simulation predictions have been compared to various empirical correlations in the literature. Empirical formulations were presented for the pressure minimum location, separation location, and separation length on the cylinder aftbody. The effects of both Mach and Reynolds numbers on the separation location were examined by correcting for the change in viscosity across the shock wave. This was accounted for explicitly in the presented empirical formulations by deriving an expression for the viscosity change across the shock. A free-interaction theory was used to examine the wall-pressure distribution due to lip-shock formation on the aftbody. Over a range of Mach and Reynolds numbers, it was found that the profile of a free-interaction parameter was predictable and nearly Reynolds number and Mach number independent. This free-interaction parameter was a correlation between the properties at the onset of the interaction and the ensuing pressure rise. This provided a means to predict the lip-shock formation, provided the boundary-layer properties at the pressure minimum were known.