Abstract
In developing turbulence models, different authors have proposed various model constraints in an attempt to make the model equations more general (or universal). Most recent of these are the realizability principle (Lumley 1978, Schumann 1977), linearity principle (Pope 1983), rapid distortion theory (Reynolds 1987) and material indifference principle (Speziale 1983). In this paper we will discuss several issues concerning these principles and will pay special attention to the realizability principle raised by Lumley (1978). Realizability (defined as the requirement of non-negative energy and Schwarz’ inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. In this paper we will describe in detail the principle of realizability, derive the realizability conditions for various turbulence models, and propose the model forms for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models (Launder et al 1975, Craft et al 1989, Zeman and Lumley 1976, Shih and Lumley 1985 and the one proposed here) with experiments and direct numerical simulations will be presented. As a special case of turbulence, we will also discuss the two-dimensional, two-component turbulence modeling.
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© 1992 Springer-Verlag New York, Inc.
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Shih, TH., Shabbir, A. (1992). Advances in Modeling the Pressure Correlation Terms in the Second Moment Equations. In: Gatski, T.B., Speziale, C.G., Sarkar, S. (eds) Studies in Turbulence. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2792-2_7
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