Spatial Stability of Stagnation Water Boundary Layer with Heat Transfer

Abstract

Neglecting temperature fluctuations, assuming viscosity is only temperature dependent, and assuming all other fluid properties are constant, the two-dimensional linearized parallel flow stability problem is adequately treated by modifying the Orr-Sommerfeld equation to include viscosity variations with temperature. The resulting equation is used to study the spatial stability of stagnation water boundary layer with heat transfer. The mean flow with free-stream temperature T∞ = 60°F and wall temperature Tw ranging from 32 to 200°F is computed numerically, from the boundary layer equations with variable fluid properties. It is found that heating stabilizes the boundary layer and cooling destabilizes it. At Tw≅196°F the neutral curve degenerates to a singular point at frequency ω = 5×10−7 and Reynolds number Rδ* = 30.7×103. All disturbances become completely damped for Tw>196°F. It appears that the effect of viscosity μ is larger than the effect of its first derivative μ′ on stability, and that the effect of μ″ is negligible compared with the effect of μ′.

Onset of convection in the Rayleigh-Bénard flow with temperature dependent viscosity: An asymptotic approach

“…Wazzan et al [6] for water flowing over a heated flat plate, for example, found the critical Reynolds number to vary between 520 and 16000. In forced convection as well as in free convection flows the strongest effects on flow stability often come from changes in viscosity.…”

Stability analysis of plane laminar Poiseuille flow with constant heat flux across the wall: asymptotic methods

“…(2) and (3) it immediately foIlows, that we have introduced T = (T* -T~)/(q~L~/k~) and p = (F -P*a)/(P~U~ 2) as dimensionless temperature and pressure, respectively. Here LR, U~, PR and T R are reference quantities, q~ is a constant heat flux across the wall.…”

“…For a heated flat plate boundary layer in water, for example, Wazzan et al [2] found that ~e critical Reynolds number varies between 520 and nearly t6 000 (based on the displacement thickness). Thus there is a considerabIe potential for transition control with technical applications in various fieIds, see Morkovin and Reshotko [3] for a review on transition control for drag reduction.…”

Numerical Study of Coherent Structures of Turbulence with Large Wall-Normal Gradients in Thermophysical Properties

“…However, the details of the physical mechanisms by which spatial gradients in density and viscosity affect the development and concentration of turbulence structures remain poorly understood, largely because of the relatively disorganized state of the coherent turbulence structures in a fully-turbulent boundary layer (Azih et al, 2012). Conversely, studies which focus on the influence of spatial gradients in thermophysical properties on boundary layer stability are limited to using linear stability analysis and experimentally determining the point of transition in flows that are heated or cooled near standard atmospheric pressure and temperature (Wazzan et al, 1972;Özgen, 2004). In these studies, the property gradients in the boundary layer are several orders of magnitude lower than in flows which are heated at a thermodynamic state near the pseudocritical point.…”

“…The boundary layers developing on the two sides of the splitter plate merge downstream of the splitter plate forming a free shear layer. Since the initial roll-up of a free shear layer properties on flow instability have been established to be several orders of magnitude lower than those of density and viscosity (Azih and Yaras, 2013;Wazzan et al, 1972;Schäfer et al, 1995;Özgen, 2004).…”