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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.