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Velocity and vorticity in weakly compressible isotropic turbulence under longitudinal expansive straining

Published online by Cambridge University Press:  25 July 2007

SAVVAS XANTHOS ,
MINWEI GONG  and
YIANNIS ANDREOPOULOS
SAVVAS XANTHOS
Affiliation:
Experimental Aerodynamics and Fluid Mechanics Laboratory, The City College of the City University of New York, NY 10031, USA
MINWEI GONG
Affiliation:
Experimental Aerodynamics and Fluid Mechanics Laboratory, The City College of the City University of New York, NY 10031, USA
YIANNIS ANDREOPOULOS
Affiliation:
Experimental Aerodynamics and Fluid Mechanics Laboratory, The City College of the City University of New York, NY 10031, USA
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Abstract

The response of homogeneous and isotropic turbulence to streamwise straining action provided by planar expansion waves has been studied experimentally in the CCNY shock tube research facility at several Reynolds numbers. The reflection of a propagating shock wave at the open endwall of the shock tube generated an expansion fan travelling upstream and interacting with the induced flow behind the incident shock wave which has gone through a turbulence generating grid.

A custom-made hot-wire vorticity probe was designed and developed capable of measuring the time-dependent highly fluctuating three-dimensional velocity and vorticity vectors, and associated total temperature, in non-isothermal and inhomogeneous flows with reasonable spatial and temporal resolution. These measurements allowed the computations of the vorticity stretching/tilting terms, vorticity generation through dilatation terms, full dissipation rate of kinetic energy term and full rate-of-strain tensor. The longitudinal size of the straining zone was substantial so that measurements within it were possible. The flow accelerated from a Mach number of 0.23 to about 0.56, a value which is more than twice the initial one.

Although the average value of the applied straining was only between S11 = 130 s−1 and S11 = 240 s−1 and the gradient Mach number was no more than 0.226, the amplitude of fluctuations of the strain rate S11 were of the order of 4000 s−1 before the application of straining and were reduced by about 2.5 times downstream of the interaction. This characteristic of high-amplitude bursts and the intermittent behaviour of the flow play a significant role in the dynamics of turbulence.

One of the most remarkable features of the suppression of turbulence is that this process peaks shortly after the application of the straining where the pressure gradient is substantial. It was also found that the total enthalpy variation follows very closely the temporal gradient of pressure within the straining region and peaks at the same location as the pressure gradient.

Attenuation of longitudinal velocity fluctuations has been observed in all experiments. It appears that this attenuation depends strongly on the characteristics of the incoming turbulence for a given straining strength and flow Mach number. The present results clearly show that in most of the cases, attenuation occurs at large times or distances from the turbulence generating grids where length scales of the incoming flow are high and turbulence intensities are low. Thus, large eddies with low-velocity fluctuations are affected the most by the interaction with the expansion waves. Spectral analysis has indicated that attenuation of fluctuations is not the same across all wavenumbers of the spectrum. The magnitude of attenuation appears to be higher in cases of finer mesh grids.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 584 , 10 August 2007 , pp. 301 - 335
Copyright
Copyright © Cambridge University Press 2007

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