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The interference of thermal fields from line sources in grid turbulence

Published online by Cambridge University Press:  20 April 2006

Z. Warhaft
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853

Abstract

The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross-correlation coefficient ρ between the temperature fluctuations produced by the sources. The evolution of ρ as a function of downstream distance, for 0.075 < d/l < 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that ρ may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line-source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar-variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements.

Type
Research Article
Copyright
© 1984 Cambridge University Press

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References

Anand, M. S. & Pope, S. B. 1983 Diffusion behind a line source in grid turbulence. In Proc. 4th Symp. on Turbulent Shear Flows, Karlsruhe, Germany, 13–16 Sept. 1983.
Antonopoulos-Domis, M. 1981 Large-eddy simulation of a passive scalar in isotropic turbulence. J. Fluid Mech. 104, 5579.Google Scholar
Durbin, P. A. 1980 A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence. J. Fluid Mech. 100, 279302.Google Scholar
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411437.Google Scholar
Hinze, J. T. 1975 Turbulence, 2nd edn. McGraw-Hill.
Kistler, A. L. 1954 Ph.D. thesis, The Johns Hopkins University.
Lundgren, T. S. 1981 Turbulent pair dispersion and scalar diffusion. J. Fluid Mech. 111, 2757.Google Scholar
Paranthoen, P., Petit, C. & Lecordier, J. C. 1982 The effect of the thermal prong-wire interaction on the response of a cold wire in gaseous flows (air, argon and helium). J. Fluid Mech. 124, 457474.Google Scholar
Pope, S. B. 1981 Transport equation for the joint probability density function of velocity and scalars in turbulent flow. Phys. Fluids 24, 588596.Google Scholar
Pope, S. B. 1983 Consistent modeling of scalars in turbulent flows. Phys. Fluids 26, 404408.Google Scholar
Sawford, B. L. 1983 The effect of Gaussian particle-pair distribution functions in the statistical theory of concentration fluctuations in homogeneous turbulence. Q. J. R. Met. Soc. 109, 339354.Google Scholar
Sawford, B. L. & Hunt, J. C. R. 1984 Effects of turbulence structure, molecular diffusion and source size on fluctuations of concentration in homogeneous turbulence. Submitted to J. Fluid Mech.Google Scholar
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323346.Google Scholar
Sreenivasan, K. R., Tavoularis, S., Henry, R. & Corrsin, S. 1980 Temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 100, 597623.Google Scholar
Stapountzis, H., Sawford, B. L., Hunt, J. C. R. & Britter, R. E. 1984 Structure of the temperature field downwind of a line source in grid turbulence. Submitted to J. Fluid Mech.Google Scholar
Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196212.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. IV - Diffusion in a turbulent air stream. Proc. R. Soc. Lond. A 151, 465478.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Townsend, A. A. 1954 The diffusion behind a line source in homogeneous turbulence. Proc. R. Soc. Lond. A 224, 487512.Google Scholar
Uberoi, M. S. & Corrsin, S. 1953 Diffusion of heat from a line source in isotropic turbulence. NACA Rep. 1142.Google Scholar
Warhaft, Z. 1981 The use of dual heat injection to infer scalar covariance decay in grid turbulence. J. Fluid Mech. 104, 93109.Google Scholar
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659684.Google Scholar