DNS of Wall-Bounded Turbulent Flows by Tapan K. Sengupta & Swagata Bhaumik

Author:Tapan K. Sengupta & Swagata Bhaumik
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

3.7 Equilibrium Solution for Mixed Convection Flows: Isothermal Wall Case

In [42] the formulation used in [49] has been generalized for flow past isothermal wedge. This flow does not exhibit singular heat transfer at the leading edge. The governing equation transforms to ordinary differential equation for the external flow given by , with the new independent variable, . The wall temperature distribution is given by . The choice of provides a wall-temperature distribution which is independent of X, which corresponds to a wedge angle of . Despite similarity, flow and heat transfer at the wall are completely different in [42], as compared to that in [49]. However, as the boundary layer edge velocity in [42] is a function of X, none of these velocity profiles directly represents similar solution. Both these flows are considered to study spatial and temporal viscous instabilities by solving NSE with different heat transfer at the wall, and help identify the active instability mechanisms for mixed convection flows.

Heat transfer modeled by Boussinesq approximation for mixed convection flows induces pressure gradient of the equilibrium flows. Such mean flows display flow instabilities, including inviscid instability, similar to that given by Rayleigh’s equation for flows without heat transfer [19, 53]. This is shown here and new theorems stated with necessary conditions for temporal instability by linear inviscid mechanism. Also DNS of flows with heat transfer are provided, which show viscous and inviscid mechanisms simultaneously. In such a scenario, it is essential that we show predominance of one mechanism over the other.

The wedge flow given in [42] is a general equilibrium flow. In defining the governing equations for mixed convection flows, a buoyancy parameter is introduced as in [42] and K in [49], these symbols will be used here as and , respectively, with the subscript indicating isothermal and adiabatic conditions for flow over the general wedge flow defined as,

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