scholarly journals Asymptotic behaviour at the wall in compressible turbulent channels

2021 ◽  
Vol 933 ◽  
Author(s):  
Akanksha Baranwal ◽  
Diego A. Donzis ◽  
Rodney D.W. Bowersox
Keyword(s):  
Mach Number ◽  
Asymptotic Behaviour ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Turbulent Channel Flow ◽  
Turbulent Fluxes ◽  
Reynolds Stresses ◽  
Compressible Turbulent Flow ◽  
High Mach ◽  
Near Wall

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

scholarly journals High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yanqun Jiang ◽  
Xun Chen ◽  
Xu Zhang ◽  
Tao Xiong ◽  
Shuguang Zhou
Keyword(s):  
Mach Number ◽  
Gas Dynamics ◽  
Compressible Flows ◽  
Time Discretization ◽  
Euler System ◽  
High Order ◽  
Shock Capturing ◽  
Third Order ◽  
High Mach ◽  
Fifth Order

AbstractThe computation of compressible flows at all Mach numbers is a very challenging problem. An efficient numerical method for solving this problem needs to have shock-capturing capability in the high Mach number regime, while it can deal with stiffness and accuracy in the low Mach number regime. This paper designs a high order semi-implicit weighted compact nonlinear scheme (WCNS) for the all-Mach isentropic Euler system of compressible gas dynamics. To avoid severe Courant-Friedrichs-Levy (CFL) restrictions for low Mach flows, the nonlinear fluxes in the Euler equations are split into stiff and non-stiff components. A third-order implicit-explicit (IMEX) method is used for the time discretization of the split components and a fifth-order WCNS is used for the spatial discretization of flux derivatives. The high order IMEX method is asymptotic preserving and asymptotically accurate in the zero Mach number limit. One- and two-dimensional numerical examples in both compressible and incompressible regimes are given to demonstrate the advantages of the designed IMEX WCNS.

An appraisal of ‘flat plate’ closure for the approximate solution of boundary layer problems

1987 ◽  
Vol 91 (908) ◽  
pp. 373-389
Author(s):  
D. I. A. Poll ◽  
C. M. Hellon
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mach Number ◽  
Flat Plate ◽  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Similarity Solutions ◽  
Laminar Flows ◽  
Reynolds Analogy

SummaryThe usefulness of zero pressure gradient, flat plate closure relations in providing approximate solutions for the boundary layer momentum and energy integral equations is examined. Expressions are obtained for skin friction, surface heat transfer rate and local Reynolds analogy factor under general compressible flow conditions. For laminar flows the predictions are compared with well known similarity solutions, with some exact solutions for non-similar flows and with experimental heat transfer data for high speed flow over a blunt cone. Consideration is also given to situations in which the surface temperature is a function of position. For turbulent flow situations comparisons are made with experimental data obtained from two-dimensional and axi-symmetric tests. Conditions vary from low Mach number incompressible flows through to high Mach number compressible flows with highly cooled walls. Some comparisons are also made with other prediction techniques.

scholarly journals The use of shock-detecting sensor to improve the stability of Lattice Boltzmann Model for high Mach number flows

2015 ◽  
Vol 26 (01) ◽  
pp. 1550006 ◽  
Author(s):  
Mohsen Ghadyani ◽  
Vahid Esfahanian ◽  
Mohammad Taeibi-Rahni
Keyword(s):  
Mach Number ◽  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Recent Decade ◽  
Numerical Results ◽  
Lattice Boltzmann Model ◽  
Rarefaction Waves ◽  
High Mach ◽  
The Stability ◽  
Improved Model

Attempts to simulate compressible flows with moderate Mach number to relatively high ones using Lattice Boltzmann Method (LBM) have been made by numerous researchers in the recent decade. The stability of the LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. The present study proposes an approach for simulation of inviscid flows by a compressible LB model in order to enhance the robustness using a combination of Essentially NonOscillatory (ENO) scheme and Shock-Detecting Sensor (SDS) procedure. A sensor is introduced with adjustable parameters which is active near the discontinuities and affects less on smooth regions. The validity of the improved model to capture shocks and to resolve contact discontinuity and rarefaction waves in the well-known benchmarks such as, Riemann problem, and shock reflection is investigated. In addition, the problem of supersonic flow in a channel with ramp is simulated using a skewed rectangular grid generated by an algebraic grid generation method. The numerical results are compared with analytical ones and those obtained by solving the original model. The numerical results show that the presented scheme is capable of generating more robust solutions in the simulation of compressible flows and is almost free of oscillations for high Mach numbers. Good agreements are obtained for all problems.

Direct Numerical Simulation Of Turbulent Flows

1996 ◽  
Author(s):  
Anthony Leonard
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Spectral Element ◽  
Von Neumann ◽  
Eddy Simulation ◽  
Parallel Supercomputers

The numerical simulation of turbulent flows has a short history. About 45 years ago von Neumann (1949) and Emmons (1949) proposed an attack on the turbulence problem by numerical simulation. But one could point to a beginning 20 years later when Deardorff (1970) reported on a large-eddy simulation of turbulent channel flow on a 24x20x14 mesh and a direct simulation of homogeneous, isotropic turbulence was accomplished on a 323 mesh by Orszag and Patterson (1972). Perhaps the arrival of the CDC 6600 triggered these initial efforts. Since that time, a number of developments have occurred along several fronts. Of course, faster computers with more memory continue to become available and now, in 1994, 2563 simulations of homogeneous turbulence are relatively common with occasional 5123 simulations being achieved on parallel supercomputers (Chen et al., 1993) (Jimenez et al., 1993). In addition, new algorithms have been developed which extend or improve capabilities in turbulence simulation. For example, spectral methods for the simulation of arbitrary homogeneous flows and the efficient simulation of wall-bounded flows have been available for some time for incompressible flows and have recently been extended to compressible flows. In addition fast, viscous vortex methods and spectral element methods are now becoming available, suitable for incompressible flow with complex geometries. As a result of all these developments, the number of turbulence simulations has been increasing rapidly in the past few years and will continue to do so. While limitations exist (Reynolds, 1990; Hussaini et al., 1990), the potential of the method will lead to the simulation of a wide variety of turbulent flows. In this chapter, we present examples of these new developments and discuss prospects for future developments.

The Zero-Mach Limit of Compressible Euler Equations

2013 ◽  
Vol 275-277 ◽  
pp. 518-521
Author(s):  
Shu Wang
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Initial Velocity ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Compressible Euler Equations ◽  
Time Interval ◽  
Compressible Euler ◽  
Three Space ◽  
Incompressible Euler

The aim of this paper is to prove that compressible Euler equations in two and three space dimensions converge to incompressible Euler equations in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the initial velocity, or the time interval. We assume instead that the incompressible flows exists and is reasonably smooth on a given time interval, and prove that compressible flows converge uniformly on that time interval.

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