High Mach Number Flows Research Articles

Enhancing improved advection upstream splitting method on triangular grids: A hybrid approach for improved stability and accuracy in compressible flow simulations

This paper introduces NAUSM+M+AUFS (New Improved Advection Upstream Splitting Method Plus Artificially Upstream Flux Vector Splitting), a novel hybrid computational scheme for simulating compressible flows on triangular grids. The AUSM+M (Improved Advection Upstream Splitting Method) method is enhanced through two key modifications to boost numerical stability and robustness in high Mach number and hypersonic flows. The first modification redefines the interfacial numerical sound velocity, reducing shock anomalies and improving shock-capturing by integrating velocity and characteristic sound speed parameters. The second modification addresses the insufficiency of the pressure flux dissipation term at supersonic speeds by introducing a formulation that increases dissipation proportionally to the Mach number, thereby enhancing performance in high-speed flows. These enhancements constitute the NAUSM+M method. The NAUSM+M+AUFS scheme combines the strengths of NAUSM+M and AUFS (Artificially Upstream Flux Vector Splitting) methods, particularly in overcoming the limitations of NAUSM+M in handling shock instabilities and the carbuncle phenomenon on structure triangular grids. A dynamic switching function adjusts the weighting between NAUSM+M and AUFS, optimizing accuracy and stability based on local flow conditions. Numerical tests demonstrate that NAUSM+M+AUFS significantly outperforms AUSM+M, NAUSM+M, and AUFS, effectively eliminating the carbuncle phenomenon and providing smooth shock wave contours. In steady flow analysis, the new hybrid method achieves convergence speeds comparable to AUFS and shows 15% to 45% superior convergence accelerating than AUSM+M, depending on the convergence rate. In addition, in steady flow analysis, the accuracy of NAUSM+M+AUFS is 46% better than that of AUFS. This approach represents a significant advancement, offering a robust, accurate, and efficient solution for high-speed aerodynamic simulations, with broad applicability across various compressible flow challenges.

A GPU-Based Lattice Boltzmann Method for Predicting Near- and Far-Field Jet Noise

Jet flow and noise are simulated using the lattice Boltzmann method (LBM). The D3Q19 lattice model calculates the flow field with a high-order distribution function to overcome LBM limitations in solving high Mach number flows. Multiple relaxation times (MRT) and large eddy simulation (LES) are used in this study. Compressible LBM was applied to the simulation jet flow to demonstrate the ability of the fifth-order equilibrium distribution function to simulate compressible flows efficiently. The results from the LBM simulation were then employed in Kirchhoff's surface integral approach to predict far-field jet noise. In this research, we used the compute unified device architecture (CUDA) to implement the LBM in a graphics processing unit (GPU), thus creating a hybrid code, LBM-MRT-LES. The obtained results agreed with the experimental and numerical results in the literature.

An implicit adaptive unified gas-kinetic scheme for steady-state solutions of nonequilibrium flows

In recent years, nonequilibrium flows have been frequently encountered in various aerospace engineering and micro-electro-mechanical systems applications. To understand nonequilibrium physics, multiscale effects, and the dynamics in these applications, a reliable multiscale scheme for all flow regimes is required. Following the direct modeling methodology, the adaptive unified gas-kinetic scheme employs discrete velocity space to accurately capture the nonequilibrium physics, recovering the original unified gas-kinetic scheme (UGKS). By adaptively employing continuous distribution functions based on the Chapman–Enskog expansion, it efficiently handles near-equilibrium flow regions. The two regions are dynamically coupled at the cell interface through the fluxes from the discrete and continuous gas distribution functions, thereby avoiding any buffer zone between them. In this study, an implicit adaptive unified gas-kinetic scheme (IAUGKS) is constructed to further enhance the efficiency of steady-state solutions. The current scheme employs implicit macroscopic governing equations and couples them with implicit microscopic governing equations within the nonequilibrium region, resulting in high convergence efficiency in all flow regimes. To validate the efficiency and robustness of the IAUGKS, a series of numerical tests were conducted for high Mach number flows around diverse geometries. The current scheme can capture the nonequilibrium physics and provide accurate predictions of surface quantities. In comparison with the original UGKS, the velocity space adaptation, unstructured discrete velocity space, and implicit iteration significantly improve the efficiency by one or two orders of magnitude. Given its exceptional efficiency and accuracy, the IAUGKS serves as an effective tool for nonequilibrium flow simulations.

A Structure-Preserving Semi-implicit IMEX Finite Volume Scheme for Ideal Magnetohydrodynamics at all Mach and Alfvén Numbers

We present a divergence-free semi-implicit finite volume scheme for the simulation of the ideal magnetohydrodynamics (MHD) equations which is stable for large time steps controlled by the local transport speed at all Mach and Alfvén numbers. An operator splitting technique allows to treat the convective terms explicitly while the hydrodynamic pressure and the magnetic field contributions are integrated implicitly, yielding two decoupled linear implicit systems. The linearity of the implicit part is achieved by means of a semi-implicit time linearization. This structure is favorable as second-order accuracy in time can be achieved relying on the class of semi-implicit IMplicit–EXplicit Runge–Kutta (IMEX-RK) methods. In space, implicit cell-centered finite difference operators are designed to discretely preserve the divergence-free property of the magnetic field on three-dimensional Cartesian meshes. The new scheme is also particularly well suited for low Mach number flows and for the incompressible limit of the MHD equations, since no explicit numerical dissipation is added to the implicit contribution and the time step is scale independent. Likewise, highly magnetized flows can benefit from the implicit treatment of the magnetic fluxes, hence improving the computational efficiency of the novel method. The convective terms undergo a shock-capturing second order finite volume discretization to guarantee the effectiveness of the proposed method even for high Mach number flows. The new scheme is benchmarked against a series of test cases for the ideal MHD equations addressing different acoustic and Alfvén Mach number regimes where the performance and the stability of the new scheme is assessed.

An all Mach number scheme for visco-resistive magnetically-dominated MHD flows

In this work we present a novel conservative, semi-implicit, finite-volume scheme, designed for the numerical simulation of magnetically-dominated plasma rapidly evolving from a near-equilibrium state into a time-dependent compressible regime. The proposed scheme utilises a well-studied flux vector splitting approach, where the ideal magnetohydrodynamic (MHD) system is partitioned into two sub-systems, one containing all the advective terms and the other containing the rest of the terms, including not only the gas pressure but also magnetic pressure terms. The former is discretised explicitly as part of a standard finite-volume update, while the latter is treated implicitly by means of a nested Picard algorithm. As a result, the algorithm is constrained only by a mild velocity CFL stability condition, rendering it highly suitable for low Mach number flows in both gas and magnetic pressure dominated conditions, and for the incompressible limit of the MHD equations. The visco-resistive dissipative terms are also treated implicitly so that the numerical stability of the algorithm remains dependent only on the fluid velocity, maintaining its efficiency even for visco-resistive dominated problems. The divergence constraint of the magnetic field is handled through either staggered or unstaggered adaptations of the constrained transport methodology, which are both shown to preserve the divergence error up to machine precision levels. The algorithm is validated thoroughly by means of several benchmark problems for high and low Mach number flows, as well as multiple visco-resistive test cases. The scheme is found to perform well for both regimes, providing accurate and computationally efficient results in low Mach number flows in both gas and magnetic pressure dominated scenarios, while also demonstrating excellent shock-capturing capacity. A novel test case is finally introduced to truly demonstrate the all Mach number capabilities of the proposed scheme.

Sensors Layout Optimization Design of Rocket Sled Test System.

The rocket sled, as a ground dynamic test system, combines the characteristics of the wind tunnel test and the flight test. However, some practical factors, such as shock wave interference, ground effect, and high-intensity aerodynamic noise will cause serious interference and even failure of the uniformly distributed sensors during horizontal sliding in a wide speed range. The AGARD HB-2 standard model is employed as the payload to simulate the aerodynamic and aeroacoustic characteristics during the variable acceleration period, aiming to optimize the test sensors layout. It is observed that in the high Mach number flow fields, strong coupling behaviors among complex waves will occur. The peak of wake vortex strength will appear at 1.5 s and gradually diminish over time. In addition, when the vortex between the load and the booster is monitored, its position shifts forward in the subsonic stage, then gradually moves backward and expands in the supersonic stage. Acoustic directivity is pronounced at subsonic and transonic speeds, pointing towards 75° and 135° relative to the sliding speed, respectively. These results can provide technical support for sensor layout and high-precision testing in rocket sled tests.

Numerical stability analysis of Godunov-type schemes for high Mach number flow simulations

Modern shock-capturing schemes often suffer from numerical shock instabilities when simulating strong shocks, limiting their application in supersonic or hypersonic flow simulations. In the current study, we devote our efforts to investigating the shock instability problem for second-order schemes, which has not gotten enough attention in previous research but is crucial to address. To this end, we develop the matrix stability analysis method for the finite-volume Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) approach, taking into account the influence of reconstruction. With the help of this newly developed method, the shock instability of second-order schemes is investigated quantitatively and efficiently. The results demonstrate that when second-order schemes are employed, whether shock instabilities will occur is closely related to the property of Riemann solvers, just like the first-order case. However, enhancing spatial accuracy still impacts the shock instability problem, and the impact can be categorized into two types depending on the dissipation of Riemann solvers. Furthermore, the research emphasizes the impact of the numerical shock structure, highlighting both its role as the source of instability and the influence of its state on the occurrence of instability. One of the most significant contributions of this study is the confirmation of the multidimensional coupled nature of shock instability. Both one-dimensional and multidimensional instabilities are proven to influence the instability problem, and they have different properties. Moreover, this paper reveals that increasing the aspect ratio and distortion angle of the computational grid can help mitigate shock instabilities. The current work provides an effective tool for quantitatively investigating the shock instabilities for second-order schemes, revealing the inherent mechanism and thereby contributing to the elimination of shock instability.

Design, Multi-Point Optimization, and Analysis of Diffusive Stator Vanes to Enable Turbine Integration Into Rotating Detonation Engines

Abstract Pressure gain combustion is considered a possible path toward improved thermal cycle efficiency and reduced carbon emissions. However, ad hoc turbine designs are required to maximize the thermodynamic potential; the new turbomachinery should be suited for the oscillations in flow conditions generated by the detonation combustor, which are very different from conventional gas turbines. This paper investigates the design, optimization, and analysis of diffusive stator vanes operating under large inlet flow angles in the high-subsonic regime. First, the design methodology is outlined, focusing on the geometric requirements to ingest high Mach number flow and the parametric modeling of the endwall and the 3D vane pressure and suction sides. Then, the impact of the inlet flow angle on the flow field and vane design is studied through a multi-point, multi-objective optimization with three different inlet angles, performed using steady Reynolds-averaged Navier–Stokes simulations. Remarkable reductions in pressure loss and stator-induced rotor forcing are attained while maintaining an extensive operating envelope and high flow turning. Moreover, several design guidelines are provided based on the analysis of the optimized geometries. Finally, the effectiveness of the proposed methodology is verified with an unsteady assessment of the baseline and optimized vane designs.

Quasi all-speed schemes for magnetohydrodynamic flows in a wide range of Mach numbers

We present novel numerical schemes for ideal magnetohydrodynamic (MHD) simulations aimed at enhancing stability against numerical shock instability and improving the accuracy of low-speed flows in multidimensions. Stringent benchmark tests confirm that our scheme is more robust against numerical shock instability and is more accurate for low-speed, nearly incompressible flows than conventional shock-capturing schemes. Our scheme is a promising tool for tackling MHD systems, including both high and low Mach number flows.

Relative entropy inequality for capillary fluids with density dependent viscosity and applications

We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak–strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.

A shock-stable numerical scheme accurate for contact discontinuities: Applications to 3D compressible flows

The low-dissipation Roe scheme is a popular shock capturing scheme but the shock instability, such as the infamous carbuncle phenomenon, seriously affects its application in high Mach number flows. Although considerable research has been undertaken in two dimensions, mechanism analysis of the three-dimensional shock instability is relatively scarce. Numerical simulations of the Sedov blast wave indicate that the shock instability is more prominent in three dimensions, so it has theoretical and practical significance to analyze and heal the numerical instability. The mechanism for three-dimensional shock instability has been thoroughly studied by means of the linearized stability analysis and the dissipation-controlling approach which introduces the required transverse dissipation in the numerical shock layer and is adopted to enhance the Roe scheme’s shock stability. Furthermore, the unphysical expansion shock resulting from the violation of entropy condition is eliminated by a simple modification of numerical signal speed. For the improvement of the resolution for contact discontinuities and shear waves, an algebraic method which combines the THINC reconstruction scheme and the BVD algorithm is employed to minimize the density difference in the numerical diffusion term. A series of benchmark numerical experiments fully demonstrate that the proposed scheme is endowed with excellent robustness against the shock instability and high accuracy for contact discontinuities and shear waves.

Effect of combustion chamber diameter size on scramjet rotating detonation under high Mach number flow conditions

This study conducted 3D numerical simulations to investigate the impact of combustion chamber diameter on the combustion characteristics of liquid kerosene scramjet rotating detonation under high Mach number flow conditions (Ma6/28 km). After ignition, a local hotspot near the contact surface between the combustion product and fresh reactant facilitates the generation of new detonation wave heads, resulting in a co-directional multi-wave mode in the detonation combustion flow field. The higher total temperature of the incoming flow restricts the accumulation of a substantial fuel gas layer in the axial direction of the combustion chamber, resulting in a smaller fuel distribution area and a lower wave head. Increasing the inner diameter of the combustion chamber leads to an increase in the number of wave heads but a decrease in overall height. Specifically, when using diameters of 125 and 150 mm, we observed significant periodic low-frequency oscillations in the peak pressure of the detonation wave during stable propagation. The specific impulse of the fuel does not vary significantly across different combustion chamber diameters. However, when the inner diameter is 75 mm, periodic oscillations occur, which reduce thrust stability. These findings provide valuable insights into optimizing combustion chamber design and improving the efficiency and stability of liquid kerosene scramjet rotating detonation propulsion systems under high Mach number flow conditions.

High temperature non-equilibrium flow characteristics of impinging shock/flat-plate turbulent boundary layer interaction at Mach 8.42

There are fewer reports on the impinging shock/boundary layer interaction in the high Mach number and high-temperature flow than that in the supersonic flow. High-temperature flow characteristics of the impinging shock/flat-plate turbulent boundary layer interaction (IS/FTBLI) at Mach 8.42 are numerically investigated by solving two-dimensional Reynolds averaged Navier–Stokes equations coupling with the thermal–chemical non-equilibrium model. An impinging shock is formed by the wedge with a 10° deflection angle. The inviscid flow parameters ahead of the cowl of a Mach 12 inlet are selected as the free-stream condition of this study. The primary emphasis of this study lies in understanding the thermal–chemical non-equilibrium effects in the IS/FTBLI. Moreover, the chemical non-equilibrium effects similar to previous reports from others are utilized for the comparative analysis. Our findings reveal that the vibrational or thermal non-equilibrium effects exhibit maximum prominence subsequent to the intersection of the impinging shock with separation shock, as well as in the convergence area of compression waves during the flow reattachment. On the other hand, the chemical non-equilibrium effects predominantly result from oxygen dissociation and atomic nitrogen production within the boundary layer; the chemical reactions are most intense within the separation zone. By comparing with a thermally perfect gas, a reduction in the flow separation is observed in the chemical non-equilibrium effects, but the flow separation is enhanced in the thermal–chemical non-equilibrium effects. The insights gained from our research are expected to contribute to the development of flow control technology in hypersonic IS/FTBLI scenarios and aid in configuring wave structures in the inner compression section of high Mach number scramjet inlets.

RAM: Rapid Advection Algorithm on Arbitrary Meshes

The study of many astrophysical flows requires computational algorithms that can capture high Mach number flows, while resolving a large dynamic range in spatial and density scales. In this paper we present a novel method, RAM: Rapid Advection Algorithm on Arbitrary Meshes. RAM is a time-explicit method to solve the advection equation in problems with large bulk velocity on arbitrary computational grids. In comparison with standard upwind algorithms, RAM enables advection with larger time steps and lower truncation errors. Our method is based on the operator splitting technique and conservative interpolation. Depending on the bulk velocity and resolution, RAM can decrease the numerical cost of hydrodynamics by more than one order of magnitude. To quantify the truncation errors and speed-up with RAM, we perform one- and two-dimensional hydrodynamics tests. We find that the order of our method is given by the order of the conservative interpolation and that the effective speed-up is in agreement with the relative increment in time step. RAM will be especially useful for numerical studies of disk−satellite interaction, characterized by high bulk orbital velocities and nontrivial geometries. Our method dramatically lowers the computational cost of simulations that simultaneously resolve the global disk and potential well inside the Hill radius of the secondary companion.

Dissipation and time step scaling strategies for low and high Mach number flows

Aircraft aerodynamic design often involves evaluating flow conditions that span low subsonic to transonic or even supersonic Mach numbers. Compressible flow solvers are a natural choice for such design problems, but these solvers suffer from reduced accuracy and efficiency at low Mach numbers. In addition, simulations with supersonic conditions can be challenging to converge because of large gradients in the flow field. This paper presents three contributions to address these issues in the context of an approximate Newton–Krylov solver for the Reynolds-averaged Navier–Stokes equations. First, we propose a method for scaling the artificial dissipation terms in the Jameson–Schmidt–Turkel scheme to improve its accuracy at low Mach numbers while retaining the simplicity of the original scalar dissipation formulation. Second, we show that characteristic time-stepping combined with an approximate Newton method can accelerate convergence for low Mach number flows by reducing the stiffness in the linear system for each Newton iteration. Third, we introduce a dissipation-based continuation method for flows with shocks that improves robustness and accelerates convergence without sacrificing accuracy. These methods can make compressible flow solvers more accurate and efficient across low and high Mach number regimes.

Benchmarking the face-centred finite volume method for compressible laminar flows

Purpose This study aims to assess the robustness and accuracy of the face-centred finite volume (FCFV) method for the simulation of compressible laminar flows in different regimes, using numerical benchmarks. Design/methodology/approach The work presents a detailed comparison with reference solutions published in the literature –when available– and numerical results computed using a commercial cell-centred finite volume software. Findings The FCFV scheme provides first-order accurate approximations of the viscous stress tensor and the heat flux, insensitively to cell distortion or stretching. The strategy demonstrates its efficiency in inviscid and viscous flows, for a wide range of Mach numbers, also in the incompressible limit. In purely inviscid flows, non-oscillatory approximations are obtained in the presence of shock waves. In the incompressible limit, accurate solutions are computed without pressure correction algorithms. The method shows its superior performance for viscous high Mach number flows, achieving physically admissible solutions without carbuncle effect and predictions of quantities of interest with errors below 5%. Originality/value The FCFV method accurately evaluates, for a wide range of compressible laminar flows, quantities of engineering interest, such as drag, lift and heat transfer coefficients, on unstructured meshes featuring distorted and highly stretched cells, with an aspect ratio up to ten thousand. The method is suitable to simulate industrial flows on complex geometries, relaxing the requirements on mesh quality introduced by existing finite volume solvers and alleviating the need for time-consuming manual procedures for mesh generation to be performed by specialised technicians.

A discrete unified gas kinetic scheme on unstructured grids for viscid compressible flows and its parallel algorithm

<abstract><p>In this paper, we present a discrete unified gas kinetic scheme (DUGKS) on unstructured grids for high-speed viscid compressible flows on the basis of double distribution function (the density and the total energy distribution functions) Boltzmann-BGK equations. In the DUGKS, the discrete equilibrium distribution functions are constructed based on a D2Q17 circular function. In order to accelerate the simulation, we also illustrate a corresponding parallel algorithm. The DUGKS is validated by two benchmark problems, i.e., flows around the NACA0012 airfoil and flows past a circular cylinder with the Mach numbers range from 0.5 to 2.5. Good agreements with the referenced results are observed from the numerical results. The results of parallel test indicate that the DUGKS is highly parallel scalable, in which the parallel efficiency achieves $ 93.88\% $ on a supercomputer using up to $ 4800 $ processors. The proposed method can be utilized for high-resolution numerical simulation of complex and high Mach number flows.</p></abstract>

Wall-modeled LES of shock-wave/boundary layer interaction

The present paper discusses the physical reliability of turbulence modeling in an adverse pressure gradient wall flow setup at moderate/high Reynolds number by comparing wall-modeled and wall-resolved LES with DNS and experimental data. A canonical configuration of shock-wave/boundary-layer interaction is used to illustrate the wall modeling behavior. In particular, a standard equilibrium-based wall-modeling approach, combined with an innovative strategy to keep active the no-slip velocity and adiabatic/isothermal temperature constraints at the wall, is adopted. The method, in particular, does not rule out flow separations from the description of the near-wall dynamics and automatically reverts to a wall-resolved LES approach if the spatial resolution allows it. The paper demonstrates how the proposed wall modeling strategy accurately describes the incoming and recovering boundary layers. On the other hand, the recirculation region appears oversized compared to wall-resolved LES and the experimental references. However, bubble shape and morphology are always well described, almost independently from the adopted resolution, well-fitting the experimental results. Thus, the present methodology seems a promising strategy to deal with high Reynolds and Mach number flow with adverse pressure gradient conditions.

Numerical Investigation of Aerodynamic and Aeroheating Characteristics of Blunted Cone and Wedge for High Mach Number Flow

Numerical Investigation of Aerodynamic and Aeroheating Characteristics of Blunted Cone and Wedge for High Mach Number Flow

Lattice Boltzmann Method for high Reynolds number compressible flow

We employ a Lattice Boltzmann Method (LBM) for modelling high Reynolds number (Re) compressible supersonic flow using D2Q9 lattice. In this model, a two-population thermal lattice Boltzmann (LB) is utilized in order to allow varying Prandtl number and adiabatic exponent. The equilibrium population fieq term for mass and momentum conservation is matched analytically with order of accuracy O(Ma4), while the equilibrium population gieq term for energy conservation is solved numerically through Lagrange multipliers method. By using more accurate equilibrium population gieq, the present numerical method shows the enhancement of stability, especially at high Reynolds and Mach number flows. To simulate high Reynolds and Mach number (Ma) flows efficiently, we adopt a shifted lattice scheme, stabilized by relaxation time depending on the Knudsen number. The LBM show excellent accuracy through 1D Riemann examples, capable of handling expansion shock waves and discontinuity. Our results for supersonic flow past a cylinder also find excellent agreement with experimental data in literature. Separately, we benchmark results for transonic and supersonic flows past a NACA0012 aerofoil as a demonstration of its simplicity, versatility for applications involving high Reynolds and Mach numbers (Ma∞=1.5,Re=107).