Direct numerical simulation of high–temperature supersonic turbulent channel flow of equilibrium air

Xiaoping Chen,Heuy-Dong Kim,Hua-Shu Dou,Zuchao Zhu

doi:10.1063/1.5050657

Xiaoping Chen, Heuy-Dong Kim + Show 2 more

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https://doi.org/10.1063/1.5050657

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Abstract

Direct numerical simulations (DNS) of high–temperature supersonic turbulent channel flow of equilibrium air are conducted at constant dimensional wall temperature 1733.2 K. The Mach number based on the bulk velocity and the speed of sound at the isothermal wall is 3.0, and the Reynolds number based on the bulk density, bulk velocity, channel half–width, and viscosity at the isothermal wall is 4880. Bidirectional coupling (BC) and unidirectional influence (UI) conditions are investigated, conditions which take account, respectively, of the influence of turbulence on chemistry and the influence of chemistry on turbulence, and just the influence of turbulence on chemistry. The reliability of the DNS data for the UI condition is verified by comparison with the results of Coleman et al. [J. Fluid Mech. 305, 159–183 (1995)]. The results of present research show that the many turbulent statistics and instantaneous structures which hold for calorically perfect gas also hold for equilibrium air, even for the BC condition. The coupling condition has no significant influence on the van Driest transformed mean velocity and turbulent kinetic energy budget. The magnitudes of the mean and fluctuating specific heat and enthalpy for the BC condition are larger than those for the UI condition. An inverted trend is observed for the temperature and dissociation degree. Compared with the UI condition, the near–wall streaks for the BC condition are arranged in a more spanwise manner, owing mainly to the increase in anisotropy ratios. The large–scale structures become small, sharp, and chaotic for the BC condition.

Highlights

Supersonic turbulent channel flows, which induce substantially higher frictional resistance and heat flux in comparison with laminar flows, have critical importance in engineering applications and gas dynamics
In a turbulent flow simulation, compared with large–eddy simulation (LES) and Reynolds–averaged Navier–Stokes (RANS), direct numerical simulation (DNS) is a powerful tool to study the mechanisms of turbulent flow because it solves the Navier–Stokes equations directly and does not involve any modeling errors.[2]
We have developed a high–order computational fluids dynamics (CFD) code to simulate high-temperature supersonic and hypersonic flows of equilibrium air, whose thermodynamic properties are calculated from the data of McBride and Zehe[37] and whose equilibrium composition is determined by using the method of Dong.[35]

Summary

Introduction

Supersonic turbulent channel flows, which induce substantially higher frictional resistance and heat flux in comparison with laminar flows, have critical importance in engineering applications and gas dynamics. For supersonic turbulent channel flows, the temperature near the wall may be very high and the assumption of calorically perfect gas is no longer applicable. When the temperature is greater than 500 K, a new thermodynamic environment will be established, in which what are generally known as “real gas effects1” become important. Gases under these conditions include thermally perfect gas, equilibrium air (chemically reacting gas in equilibrium) and nonequilibrium air (chemically reacting gas in nonequilibrium).

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