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Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number

  • C. Cambon (a1), G. N. Coleman (a2) and N. N. Mansour (a3)

The effect of rapid mean compression on compressible turbulence at a range of turbulent Mach numbers is investigated. Rapid distortion theory (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes – the nearly solenoidal and the ‘pressure-released’ – are defined by a single parameter involving the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is proposed as a means of improving turbulence models for compressible flows. In contrast to the well-documented observation that ‘compressibility’ (measured, for example, by the turbulent Mach number) is often associated with a decrease in the growth rate of turbulent kinetic energy, we find that under rapid distortion compressibility can produce an amplification of the kinetic energy growth rate. We also find that as the compressibility increases, the magnitude of the pressure–dilation correlation increases, in absolute terms, but its relative importance decreases compared to the magnitude of the kinetic energy production.

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Batchelor, G. K. & Proudman, I.1954The effect of rapid distortion on a fluid in turbulent motion. Q. J. Mech. Appl. Maths7, 83.

Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433.

Hayes, W. D. 1957 The vorticity jump across a gasdynamic discontinuity. J. Fluid Mech. 2, 595.

Herring, J. R.1974Approach of axisymmetric turbulence to isotropy. Phys. Fluids17, 859.

Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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