Computation of rotating turbulent flow with an algebraic Reynolds stress model

Abstract

Rotation has a strong effect on the structure of turbulent flows. Turbulence models based on isotropic eddy viscosity are ineffective at predicting such flows. An algebraic Reynolds stress model has been implemented to modify the Kolmogorov-Prandtl eddy-viscosity relation to produce an anisotropic turbulence model. The eddyviscosity relation becomes a function of the local turbulent production-dissipation ratio and local turbulence/rotation parameters. A three-dimensional model is presented, and a two-dimensional form is utilized to predict fully developed rotating channel flow over a wide range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with available experimental data. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (ft greater than 0.10), where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, laminarization on the trailing side of the channel represents a complex effect of rotation that is difficult to predict with the described models. NomenclatureA, C = constants in law of wall relation C^ = eddy-viscosity coefficient d = channel width gjj km = mean velocity derivative ratios defined in Eq. (18) k = turbulence kinetic energy = (w, w ; ) /2 p = static pressure normalized by pU 2 P = production of kinetic energy, defined in Eq. (4) q = unknown vector = [p t U, V] Re -Reynolds number = U m d/v r k» r ijk -turbulence parameters defined in Eq. (18) U it U, V -mean velocities normalized by U m U* = wall shear velocity = (T O ) 1/2 U+ = wall velocity variable = U/U* u if u,v = velocity fluctuations u t Uj = Reynolds stress tensor normalized by Lfa Xj = coordinate directions y = distance normal to leading side (Fig. 1) normalized byd y+ = wall length variable =yU*Re djj = Kronecker delta e = dissipation of turbulence kinetic energy e ijfc = alternating tensor K = von Karman constant v = kinematic viscosity v t = eddy viscosity p = density a = small negative coefficient for space marching r 0 = normalized wall shear stress = [dU/dy] Q Re a? = rotation rate, 1/s fi = rotation number = ud/U m Subscripts 8 = values at edge of boundary layer e = dissipation equation k = kinetic energy equation m = average p = modification of pressure for space marching s = slip a = modification of vector for space marching 0 = wall value 1 = first grid point from wall

A Comparison Between Measurements and Turbulence Models in a Turbine Cascade Passage

“…In the present analysis, the values of k and E are not updated because, in the examined part of the passage, the production minus dissipation terms are small compared with the convective terms and therefore a correction of their values is believed to affect only weakly the k and £ distributions. Following (20), eqs. (7) are reduced to linear form, by assuming that the production term P is known, and the numerical solution is obtained by iterations.…”

Calculation of a Three-Dimensional Turbomachinery Rotor Flow With a Navier-Stokes Code

“…The model (Warfield and Lakshminarayana (1987)) is a three-dimensional extension of the model presented by Warfield and Lakshminarayana (1986) and is derived from the Algebraic Reynolds Stress Model (ARSM) of Galmes and Lakshminarayana (1984), given by:…”

High Reynold Number LES of a Rotating Two-Pass Ribbed Duct

“…, where λ is a constant and Ri acts as a local stability parameter with a negative value denoting an unstable region. Other than modifications such as these [72,73] to sensitize EVMs to rotation, the other choices are to solve for the full Reynolds stress model (RSM) [74] or its algebraic equivalent (ASM) [75].…”