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Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow

Published online by Cambridge University Press:  26 April 2006

U. Karnik  and
S. Tavoularis
U. Karnik
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada
S. Tavoularis
Affiliation:
Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada
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Abstract

The diffusion of a passive scalar (heat) from a continuous line source placed in a uniformly sheared, nearly homogeneous, turbulent shear flow is examined. Measurements indicate that the mean temperature profile is approximately Gaussian near the source but, further downstream, it becomes asymmetric and its peak shifts towards the region of lower velocity. The r.m.s. temperature fluctuation profile is double peaked close to the source, it is single peaked at intermediate distances and it demonstrates a re-emergence of double peaks which grow in relative magnitude far away from the source. In comparison to similar experiments in isotropic turbulence, the centreline mean temperature appears to have a comparable decay rate, whereas the centreline mean-square temperature fluctuations appear to decay at a faster rate. The spread of the plume is faster than that in isotropic turbulence. The measured turbulent heat fluxes and triple temperature-velocity correlations demonstrate self-similar features. The development of temperature integral lengthscales and microscales is comparable to that in other heated, uniformly sheared flows, while the temperature p.d.f. and the temperature-velocity joint p.d.f. are distinctly non-Gaussian, especially away from the centreline. The relative magnitudes of the two measured components of the turbulent diffusivity tensor are in agreement with earlier measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 233 - 261
Copyright
© 1989 Cambridge University Press

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References

Alexopoulos, C. C. & Keffer, J. F., 1971 Turbulent wake in a passively stratified field. Phys. Fluids 14, 216.Google Scholar
Anand, M. S. & Pope, S. B., 1983 Diffusion behind a line source in grid turbulence. In Proc. Fourth Symp. Turb. Shear Flows, Karlsruhe (ed. L. J. S. Bradbury et al.), p. 17.11. Springer.
Budwig, R., Tavoularis, S. & Corrsin, S., 1985 Temperature fluctuations and heat flux in grid generated isotropic turbulence with streamwise and transverse mean temperature gradients. J. Fluid Mech. 153, 441.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S., 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81.Google Scholar
Collis, D. C.: 1948 The diffusion process in turbulent flow. Rep. A55. Div. Aero. Australian Council Sci. and Indus. Res.
Corrsin, S.: 1952 Heat transfer in isotropic turbulence. J. Appl. Phys. 23, 113.Google Scholar
Corrsin, S.: 1957 Some current problems in turbulent shear flow. In Naval Hydrodynamics, Proc. 1st Symp. on Naval Hydrodynamics, Publication 515, p. 373.Google Scholar
Deissler, R. G.: 1962 Turbulent heat transfer and temperature fluctuations in a field with uniform velocity and temperature gradients. Intl J. Heat Mass Transfer 6, 257.Google Scholar
Elrick, D. E.: 1962 Source functions for diffusion in uniform shear flow. Austral. J. Phys. 15, 283.Google Scholar
Fox, J.: 1964 Turbulent temperature fluctuations and two dimensional heat transfer in a uniform shear flow. NASA Tech. Note D2511.Google Scholar
Frenkiel, F. N.: 1950 On turbulent diffusion. Symp. on Turbulence, Naval Ord. Lab., Rep. 1136, p. 67.Google Scholar
Harris, V. G., Graham, J. A. & Corrsin, S., 1977 Further experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 81, 657.Google Scholar
Hinze, J. O.: 1975 Turbulence, 2nd edn. McGraw-Hill.
Huang, C. H.: 1979 A theory of dispersion in turbulent shear flow. Atmos. Environ. 13, 453.Google Scholar
Jones, W. P. & Musonge, M., 1983 Modelling of scalar transport in homogeneous turbulent flows. In Proc. Fourth Symp. on Turbulent Shear Flows, Karlsruhe (ed. L. J. S. Bradbury et al.), p. 17.18. Springer.
Karnik, U. & Tavoularis, S., 1987 Generation and manipulation of uniform mean shear with the use of screens. Exp. Fluids 5, 247.Google Scholar
Kistler, A. L.: 1956 Measurement of joint probability in turbulent dispersion of heat from two line sources. PhD dissertation, part II, The Johns Hopkins University, Baltimore, USA.
Kistler, A. L., O'Brien, V. & Corrsin, S. 1956 Double and triple correlations behind a heated grid. J. Aero Sci. 23, 96.Google Scholar
Kyong, H. N. & Chung, K. M., 1987a Measurements of turbulent diffusion field behind a line heat source in a homogeneous shear flow. Korean Soc. Mech. Engrs J. 1, 24.Google Scholar
Kyong, H. N. & Chung, K. M., 1987b Turbulent scalar transport correlation behind a line heat source in a uniform shear flow. Korean Soc. Mech. Engrs J. 1, 95.Google Scholar
Libby, P. & Scragg, C., 1972 Diffusion of heat from a line source downstream of a turbulence grid. Amer. Inst. Aeron. Astron. J. 562.Google Scholar
Lin, S. C. & Lin, S. C., 1973 Study of strong temperature mixing in subsonic grid turbulence. Phys. Fluids 16, 1587.Google Scholar
Lumley, J. L.: 1978 Computational modelling of turbulent flows. Adv. Appl. Mech. 18, 123.Google Scholar
Lumley, J. L.: 1983 Turbulence modelling. Trans. ASME E: J. Appl. Mech. 105, 1097.Google Scholar
Lumley, J. L. & Van Cruyningen, I. 1985 Limitations of second order modelling of passive scalar diffusion. In Frontiers in Fluid Mechanics (ed. S. H. Davis & J. L. Lumley), p. 199. Springer.
Mills, R., Kistler, A. L., O'Brien, V. & Corrsin, S. 1958 Turbulence and temperature fluctuations behind a heated grid. NACA Tech. Note 4288.Google Scholar
Mills, R. R. & Corrsin, S., 1959 Effect of contraction on turbulence and temperature fluctuations generated by a warm gird. NASA Memo. 5-5-59W.Google Scholar
Monin, A. S. & Yaglom, A. M., 1973 Statistical Fluid Mechanics. MIT Press.
Nakamura, I., Sakai, Y., Miyata, M. & Tsunoda, H., 1986 Diffusion of matter from a continuous point source in uniform mean shear flows. Bull. JSME 29, 1141.Google Scholar
Newman, G. R., Warhaft, Z. & Lumley, J. L., 1977 The decay of temperature fluctuations in isotropic turbulence. Proc. 6th Australasian Hydraulics and Fluid Mech. Conf., Adelaide.Google Scholar
Novikov, E. A.: 1958 Turbulent diffusion in a shear flow. Prikl. Mat. Mekh. 22, 412.Google Scholar
Okubo, A. & Karweit, M. J., 1969 Diffusion from a continuous source in a uniform shear flow. Limnol. Oceanogr. 14, 514.Google Scholar
Pope, S. B.: 1981 Transport equation for the joint probability density function of velocity and scalars in turbulent flow. Phys. Fluids 24, 588.Google Scholar
Pope, S. B.: 1983 Consistent modelling of scalars in turbulent flows. Phys. Fluids 26, 404.Google Scholar
Riley, J. & Corrsin, S., 1971 Simulation and computation of dispersion in turbulent shear flow. Proc. Conf. on Air Pollut. Met., Amer. Met. Soc., p. 16.Google Scholar
Riley, J. & Corrsin, S., 1974 The relation of turbulent diffusivities to Lagrangian statistics for the simplest shear flow. J. Geophys. Res. 79, 1768.Google Scholar
Rogers, M. M., Moin, P. & Reynolds, W. C., 1986 The structure and modeling of hydrodynamic and scalar fields in homogeneous turbulent shear flow. Dept. of Mech. Engng Rep. TF-25. Stanford University, Stanford, California.
Sakai, Y., Nakamura, I., Miyata, M. & Tsunoda, H., 1986 Diffusion of matter from a continuous point source in uniform mean shear flows (2nd report). Bull. JSME 29, 1149.Google Scholar
Schubauer, G. B.: 1935 A turbulence indicator utilizing the diffusion of heat. NACA Rep. 524.Google Scholar
Sepri, P.: 1976 Two-point turbulence measurements downstream of a heated grid. Phys. Fluids 19, 1876.Google Scholar
Shih, T. H. & Lumley, J. L., 1986 Influence of timescale ratio on scalar flux relaxation: modelling Sirivat and Warhaft's homogeneous passive scalar fluctuations. J. Fluid Mech. 162, 211.Google Scholar
Shirani, E., Ferziger, J. H. & Reynolds, W. C., 1981 Mixing of a passive scalar in isotropic and sheared homogeneous turbulence. Dept. Mech. Engng Rep. TF-15, Stanford University, Stanford, California.
Shlien, D. J. & Corrsin, S., 1974 A measurement of Lagrangian velocity autocorrelation in approximately isotropic turbulence. J. Fluid Mech. 62, 255.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, 323.Google Scholar
Sreenivasan, K. R., Tavoularis, S. & Corrsin, S., 1981 A test of gradient transport and its generalizations. In Turbulent Shear Flows, vol. 3 (ed. L. J. S. Bradbury et al.), p. 96. Springer.
Sreenivasan, K. R., Tavoularis, S., Henry, R. & Corrsin, S., 1980 Temperature fluctuations and scales in grid turbulence. J. Fluid Mech. 100, 597.Google Scholar
Stapountzis, H. & Britter, R. E., 1987 Turbulent diffusion behind a heated line source in a nearly homogeneous turbulent shear flow. Proc. Sixth Symp. on Turbulent Shear Flows, Toulouse, p. 9.2.1. Springer.
Stapountzis, H., Sawford, B. L., Hunt, J. C. R. & Britter, R. E. 1986 Structure of the temperature field downwind of a line source in grid turbulence. J. Fluid Mech. 165, 401.Google Scholar
Sullivan, P.: 1976 Dispersion of a line source in grid turbulence. Phys. Fluids 19, 159.Google Scholar
Tavoularis, S.: 1978 A circuit for the measurement of instantaneous temperature in heated turbulent flows. J. Sci. Instrum. 11, 21.Google Scholar
Tavoularis, S.: 1985 Asymptotic laws for transversely homogeneous turbulent shear flows. Phys. Fluids 28, 999.Google Scholar
Tavoularis, S. & Corrsin, S., 1981a Experiments in a nearly homogeneous shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311.Google Scholar
Tavoularis, S. & Corrsin, S., 1981b Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure. J. Fluid Mech. 104, 349.Google Scholar
Tavoularis, S. & Corrsin, S., 1985 Effects of shear on the turbulent diffusivity tensor. Intl J. Heat Mass Transfer 28, 265.Google Scholar
Tavoularis, S. & Karnik, U., 1989 Further experiments on the evolution of turbulent stresses and scales in uniformity sheared turbulence. J. Fluid Mech. (submitted).Google Scholar
Taylor, G. I.: 1921 Diffusion by continuous movements. Proc. Lond. Math. Soc. A 20, 196.Google Scholar
Townsend, A. A.: 1951 The diffusion of heat spots in isotropic turbulence. Proc. R. Soc. Lond. A 209, 418.Google Scholar
Townsend, A. A.: 1954 The diffusion behind a line source in homogeneous turbulence. Proc. R. Soc. Lond. A 224, 487.Google Scholar
Uberoi, M. S. & Corrsin, S., 1952 Diffusion from a line source in isotropic turbulence. NACA Tech. Note 2710 (also NACA Rep. 1142).Google Scholar
Venkataramani, K. S. & Chervay, R., 1978 Statistical features of heat transfer in grid generated turbulence: constant gradient case. J. Fluid Mech. 86, 513.Google Scholar
Warhaft, Z.: 1981 The use of dual injection to infer scalar covariance decay in grid turbulence. J. Fluid Mech. 104, 93.Google Scholar
Warhaft, Z.: 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363.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, 659.Google Scholar
Wiskind, H. K.: 1962 A uniform gradient turbulent transport experiment. J. Geophys. Res. 67, 3033.Google Scholar
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated grid turbulence. J. Fluid Mech. 58, 233.Google Scholar