Effect of Coriolis and Centrifugal Forces at High Rotation and Density Ratios

Abstract

Numerical simulation of fluid flow and heat transfer of high rotation and density ratio flow in internal cooling channels of turbine blades with smooth walls is the main focus of this study. The flow in these channels is affected by rotation, buoyancy, bends, and boundary conditions. On the basis of comparison between two-equation (k− −ε and k− −ω) and Reynolds-stress (RSM) turbulence models, it is concluded that the two-equation turbulence models cannot predict heat transfer correctly, whereas RSM showed improved prediction. Thus RSM model was validated against available experimental data (which are primarily at low rotation and buoyancy numbers). The model was then used for cases with high rotation numbers (as much as 1.29) and high-density ratios (up to 0.4) not studied previously. Particular attention was given to how Reynolds stresses, turbulence intensity, and transport are affected by coriolis and buoyancy/centrifugal forces caused by high levels of rotation and density ratio. The results obtained are explained in view of physical interpretation of Coriolis and centrifugal forces. It has been concluded that the heat-transfer rate can be enhanced rapidly by increasing rotation number to values that are comparable to the enhancement caused by introduction of ribs inside internal cooling channels. It is possible to derive linear correlation for the increase in Nusselt number as a function of rotation number. Increasing density ratios at high rotation number does not necessarily cause an increase in Nusselt number. The increasing thermal boundary-layer thickness near walls is the possible reason for this behavior ofNusselt number. Nomenclature a ce = acceleration caused by centrifugal force a co = acceleration caused by Coriolis force D h = hydraulic diameter f ce = centrifugal force f co = Coriolis force N u = local Nusselt number, h D h /k N u 0 = Nusselt number in fully developed turbulent nonrotating tube flow Pr = Prandtl number Pr t = turbulent Prandtl number R = radius from axis of rotation Re = Reynolds number, ρW 0 D h /µ Ro = rotation number, D h /W 0 r = inner radius of bend S = distance in streamwise direction T = local coolant temperature T b = coolant bulk temperature T 0= coolant temperature at inlet T w = wall temperature W 0 = inlet velocity ρ/ρ = density ratio, (T w − T 0 )/T w θ = dimensionless temperature, (T − T 0 )/(T w − T 0 ) µ = dynamic viscosity of coolant ρ = density of air

Heat Transfer in Channels in Parallel-Mode Rotation at High Rotation Numbers

“…All these researchers have concentrated on low rotation number and low-density ratios cases. The authors in [10][11][12] investigated smooth-wall and ribroughened channels using Reynolds stress model (RSM) turbulence models for the cases of high rotation number and high-density ratios cases.…”

Heat transfer study in a rotating ribbed two-pass channel with engine-similar cross section at high rotation number

“…And the trailing edge Nu/Nu 0 ratios increase consistently from unity as Ro increases but their responses toward the increase of AR are less systematic than those found along the leading edge. Sleiti and Kapat [25] numerically studied the fluid flow and heat transfer of high rotation (Ro: 0-1.30) in internal cooling channels. Results obtained were explained in view of physical interpretation of Coriolis and centrifugal forces.…”

Effect of Coriolis and centrifugal forces on turbulence and transport at high rotation and density ratios in a rib-roughened channel

“…They concluded that a second-moment closure is necessary to predict the high anisotropy produced by secondary flows induced by the angle ribs, rotating buoyancy and Coriolis forces. Using RSM with both standard wall functions and with enhanced wall treatment, the authors in Sleiti and Kapat [30][31][32][33][34][35][36] investigated the flow and heat transfer for different configurations: smooth channels with curvature at high Ro and DR, ribbed-roughened channels, parallel mode rotation and compared RSM to two-equation models. The results showed the advantages of using RSM with enhanced wall treatment in predicting the high anisotropy, additional secondary flows caused by high level of rotation and density ratios and the changes in Nusselt's number.…”