Asymptotic Preserving Property of a Semi-implicit Method

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.

We design and analyse a first-order accurate implicit–explicit (IMEX) scheme for the two-dimensional wave equation system in the low Mach number limit. It has been shown by Dellacherie [S. Dellacherie, Analysis of Godunov-type schemes applied to the compressible Euler system at low Mach number. J. Comput. Phys., 229(4): 978–1016, 2010, [1]] that the standard Godunov-type numerical schemes suffer from a severe loss of accuracy at low Mach numbers. This inaccuracy arises due to the inability of schemes to preserve the incompressible space of constant densities and divergence-free velocities. Guided by this principle, we design an IMEX scheme which possess the invariance property, and analyse its stability. The proposed scheme has been shown to be stable under a usual CFL-like condition, independent of the Mach number. The results of numerical experiments confirm the accuracy and stability of the new scheme when applied to low Mach number problems.

Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number

Context. Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. Aims. While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Methods. Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Results. Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Conclusions. Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.

Features of the simulation of low-velocity inviscid and viscous compressible gas flows are considered, and a finite-volume discretization of gas dynamics equations at low Mach numbers on unstructured meshes is discussed. Preconditioning based on the use of physical variables is used to speed up the convergence of time marching to a steady state and to improve the accuracy of the steady-state solution. The structure of the preconditioning matrix and the diagonalization of the Jacobian of the preconditioned system of equations are discussed. The capabilities of this approach are demonstrated using model gasdynamic simulations ing a wide range of Mach numbers.

This study comprehensively investigates the response of a combusting droplet during its interaction with a high-speed transient flow imposed by a coaxially propagating blast wave. The blast wave is generated using a specially designed miniature shock generator that produces blast waves using the wire-explosion technique, facilitating a wide range of Mach numbers (1.03 < Ms < 1.8). The experiments are performed in two configurations: open field and focused blast wave. The charging voltage and the configuration determine the Mach number (Ms) and flow characteristics. The flame is found to exhibit two major response patterns: partial extinction followed by reignition and full extinction. Increasing the Mach number (Ms > 1.1) makes the droplet flame more vulnerable to extinction. Additionally, the flame exhibits stretching and shedding, followed by reignition at lower Mach numbers (Ms < 1.06). In all cases, the flame base lifts off in response to the imposed flow, and the advection of the flame base interacting with the flame tip results in flame extinction. The entire interaction occurs in two stages: (i) interaction with the blast wave and the decaying velocity profile associated with it, and (ii) interaction with the induced flow behind the blast wave as a result of the entrainment (delayed response). Alongside the flame's response, the droplet also interacts with the flow imposed by the blast wave, exhibiting different response modes including pure deformation, Rayleigh–Taylor piercing bag breakup and shear-induced stripping.

Godunov-type schemes with an inertia term for unsteady full Mach number range flow calculations

Combustion noise is becoming increasingly important as a major noise source in aeroengines and ground based gas turbines. This is partially because advances in design have reduced the other noise sources, and partially because next generation combustion modes burn more unsteadily, resulting in increased external noise from the combustion. This review reports recent progress made in understanding combustion noise by theoretical, numerical and experimental investigations. We first discuss the fundamentals of the sound emission from a combustion region. Then the noise of open turbulent flames is summarized. We subsequently address the effects of confinement on combustion noise. In this case not only is the sound generated by the combustion influenced by its transmission through the boundaries of the combustion chamber, there is also the possibility of a significant additional source, the so-called ‘indirect’ combustion noise. This involves hot spots (entropy fluctuations) or vorticity perturbations produced by temporal variations in combustion, which generate pressure waves (sound) as they accelerate through any restriction at the exit of the combustor. We describe the general characteristics of direct and indirect noise. To gain further insight into the physical phenomena of direct and indirect sound, we investigate a simple configuration consisting of a cylindrical or annular combustor with a low Mach number flow in which a flame zone burns unsteadily. Using a low Mach number approximation, algebraic exact solutions are developed so that the parameters controlling the generation of acoustic, entropic and vortical waves can be investigated. The validity of the low Mach number approximation is then verified by solving the linearized Euler equations numerically for a wide range of inlet Mach numbers, stagnation temperature ratios, frequency and mode number of heat release fluctuations. The effects of these parameters on the magnitude of the waves produced by the unsteady combustion are investigated. In particular the magnitude of the indirect and direct noise generated in a model combustor with a choked outlet is analyzed for a wide range of frequencies, inlet Mach numbers and stagnation temperature ratios. Finally, we summarize some of the unsolved questions that need to be the focus of future research.

Entropy-based viscous regularization for the multi-dimensional Euler equations in low-Mach and transonic flows

The increasing demand for the wide-range aircraft technique requires the ground test facilities with continuous variation of the Mach number. Owing to the rigorous aerodynamic foundation and simple operation, the single-jack flexible nozzle is widely used. However, there are still some problems in the original single-jack flexible nozzle, such as low Mach number and insufficient flow uniformity. This paper presents a novel design of the single-jack flexible nozzle with high flow uniformity and continuous variable Mach number, adopting flow field inverse design and elasticity inverse design. The new nozzle adopts a three-order transonic asymptotic solution and a B-spline axial velocity distribution, designed by the method of characteristics. By comparing with the original nozzle, the new nozzle no longer requires the conical flow assumption, and the flow fields are more uniform. Another improvement is the continuous contour curvature to ensure the coincidence of the aerodynamic profile and the elastic profile, avoiding the negative Mach waves generated by the curvature discontinuity. In addition, the new nozzle has the advantage of two Mach number design points. Similar to the squeeze theorem, the flow fields are uniform at the non-design points between two design points. The numerical results show that the new nozzle eliminates the Mach waves at different Mach number cases. Within the design range of Mach 2.0–4.0, the flow angle's maximum deviations do not exceed 0.2°, and the average deviations do not exceed 0.1°, meeting the national standard of 0.3°. The Mach number's maximum deviations are around 0.5% of Ma¯, the average deviations are less than 0.2% of Ma¯, and the standard deviations meet the national advanced standard. Even at Mach 1.5 and Mach 4.5 outside the design range, the new nozzle still performs well. The evaluation results validate the feasibility of the novel design, supporting the future construction of the variable Mach number facility.

This paper discusses the sound generated when an inhomogeneity in density is convected in a low Mach number steady flow through a contraction in a duct of infinite extent, and also when the inhomogeneity exhausts through a nozzle into free space. The analyses of Candel (1972) and Marble (1973) for the case of duct flow were based on a frequency decomposition of the incident inhomogeneity and cannot adequately deal with sharp-fronted inhomogeneities and entropy spots. However, the practical difficulties of this earlier work can be avoided at low flow Mach numbers by conducting the analysis in terms of an approximate expression for the acoustic Green's function in the manner described by Howe (1975). This method also permits a considerable extension of the range of the earlier investigations to the determination of the sound generated when the inhomogeneity is swept out of a nozzle orifice into free space. It is shown that the acoustic pressure perturbations developed in a duct at a contraction are in general proportional to the fractional difference between the density of the inhomogeneity and that of the mean flow times a typical mean flow pressure level, and are due principally to the fluctuation in thrust accompanying the passage of the inhomogeneity through the region of variable pressure gradient. The pressure waves generated at a nozzle orifice and radiated into free space are O(M0) smaller, where M0 is a mean flow Mach number based on the speed of sound in the jet.

This article verifies the low Mach number and non-resistive limit of local strong solutions to non-isentropic compressible magnetohydrodynamic (MHD) equations in general three-dimensional bounded domains when the temperature variation is large but finite. The uniform estimates of strong solutions are obtained in a short time interval independent of the Mach number and the magnetic resistivity coefficient, provided that the initial data are well prepared. Previous results on this multi-scale singular limit of compressible MHD equations are either for the cases of the weak solutions or for the cases of small temperature variations or for the cases of flat boundary where the mechanisms are essentially different. The new ingredient of this article is that we develop a new approach of weighted energy to establish the uniform estimates for high-order spatial derivatives of solutions.

A preconditioning scheme has been implemented into a three-dimensional viscous computational fluid dynamics code for turbomachine blade rows. The preconditioning allows the code, originally developed for simulating compressible flow fields, to be applied to nearly-incompressible, low Mach number flows. A brief description is given of the compressible Navier-Stokes equations for a rotating coordinate system, along with the preconditioning method employed. Details about the conservative formulation of artificial dissipation are provided, and different artificial dissipation schemes are discussed and compared. The preconditioned code was applied to a well-documented case involving the NASA large low-speed centrifugal compressor for which detailed experimental data are available for comparison. Performance and flow field data are compared for the near-design operating point of the compressor, with generally good agreement between computation and experiment. Further, significant differences between computational results for the different numerical implementations, revealing different levels of solution accuracy, are discussed.

The simulation of low Mach number (Ma) flows, including those with combustion, using a simple implementation of Roe's flux-difference splitting on unstructured grids is described. Roe's scheme is modified to reduce numerical diffusion at low Ma. Time integration of the primitive variables is performed by implicit time-marching with an artificial compressibility which is approximately equal to the true compressibility. The implicit equations are solved using symmetric Gauss-Seidel iteration, which is convergent with large CFL numbers (scaling with Ma ) because of the strong diagonal dominance provided by Roe's scheme. The procedure is used to simulate a variety of flow types and speeds, including combustion in a complex gas turbine combustor, to demonstrate its potential.

In this paper, radiated sound from low Mach number turbulent boundary layers is studied using Lighthill’s analogy. The focus is to investigate the behavior of wall pressure fluctuations on a flexible wall boundary. Comparisons are made between the results from rigid and flexible walls. At low frequencies, the flexible wall results have shown much higher levels of power spectra. At high frequencies, the spectra of the flexible wall sound radiation and those of the rigid wall sound radiation merge. These trends are in agreement with other experimental and theoretical results in literature. This theoretical study of the two-dimensional turbulent boundary layer can clarify the effects of a flexible wall on radiated sound in low Mach number flows.