Cebeci-Smith Model Research Articles

Computational approach to the turbulent boundary layer of a rotating porous cylinder with strong suction based on an algebraic turbulence model

Many important technical systems operate according to the principles of momentum transfer, heat transfer and mass transfer near the surface of a cylinder rotating in a confined space. Numerical study of the Taylor–Couette flow with an imposed inward radial throughflow in the rotating inner cylinder demonstrates the possibility of flow stabilization to prevent large-scale vortices up to high rotation rates. The fluid is involved in rotation by the inner rotating cylinder only in a thin layer (boundary layer) near the cylinder surface with strong radial throughflow. Turbulence in the boundary layer may occur before the centrifugal instability, and there is a way to control the thickness of the layer as well as shear intensity and turbulence intensity near the surface of the rotating cylinder. The present work develops a compact and robust approach for the turbulent boundary layer calculation on the surface of a rotating cylinder based on an algebraic turbulence model. The generalized Cebeci–Smith model was supplemented with Richardson number-based corrections to address the centrifugal force action. It also generalized the correction used for accounting for wall suction. Analytical corrections and empirical coefficients of the model were tuned to reflect the coupled influence of the specific flow conditions. The approach, comprehensively verified in the preliminary research, was adapted to the desired geometric configuration and checked. The modified algebraic turbulent model was incorporated into an iterative calculation method developed especially for the case of axisymmetric boundary layers. The results of the algebraic turbulence model with different combinations of rotational speed and suction velocity agree well with the simulation results of the Reynolds stress turbulent model. The method proposed provides efficient practical engineering calculations and can be applied up to approaching the centrifugal instability in the boundary layer.

Runge–Kutta time‐stepping schemes with TVD central differencing for the water hammer equations

AbstractIn the present study, Runge–Kutta schemes are used to simulate unsteady flow in elastic pipes due to sudden valve closure. The spatial derivatives are discretized using a central difference scheme. Second‐order dissipative terms are added in regions of high gradients while they are switched off in smooth flow regions using a total variation diminishing (TVD) switch. The method is applied to both one‐ and two‐dimensional water hammer formulations. Both laminar and turbulent flow cases are simulated. Different turbulence models are tested including the Baldwin–Lomax and Cebeci–Smith models. The results of the present method are in good agreement with analytical results and with experimental data available in the literature. The two‐dimensional model is shown to predict more accurately the frictional damping of the pressure transient. Moreover, through order of magnitude and dimensional analysis, a non‐dimensional parameter is identified that controls the damping of pressure transients in elastic pipes. Copyright © 2006 John Wiley & Sons, Ltd.

Forced convection in a composite parallel plate channel: modeling the effect of interface roughness and turbulence utilizing a k– ε model

In this paper, a composite parallel plate channel whose central part is occupied by a clear fluid and whose peripheral part is occupied by a fluid-saturated porous medium is considered. The modeling is based on the assumption that the flow in the clear fluid region is turbulent while in the porous region the flow remains laminar. The turbulent and laminar flow solutions are matched at the porous/fluid interface, which is assumed rough. Two different models are utilized for calculating turbulent viscosity in the clear fluid region, the algebraic Cebeci–Smith model and a k– ε model. Numerical results obtained utilizing both models are compared and analyzed in detail.

Numerical Simulation of Dynamic Stall Around an Airfoil in Darrieus Motion

The objective of this study is to investigate the two-dimensional unsteady flow around an airfoil undergoing a Darrieus motion in dynamic stall conditions. For this purpose, a numerical solver based on the solution of the Reynolds-averaged Navier-Stokes equations expressed in a streamfunction-vorticity formulation in a non-inertial frame of reference was developed. The governing equations are solved by the streamline upwind Petrov-Galerkin finite element method (FEM). Temporal discretization is achieved by second-order-accurate finite differences. The resulting global matrix system is linearized by the Newton method and solved by the generalized minimum residual method (GMRES) with an incomplete triangular factorization preconditioning (ILU). Turbulence effects are introduced in the solver by an eddy viscosity model. Our investigation centers on an evaluation of the algebraic Cebeci-Smith model (CSM) and the nonequilibrium Johnson-King model (JKM). In an effort to predict dynamic stall features on rotating airfoils, first we present some testing results concerning the performance of both turbulence models for the flat plate case. Then, computed flow structure together with aerodynamic coefficients for a NACA 0015 airfoil in Darrieus motion under dynamic stall conditions are presented.

A Note on the Baldwin-Lomax Turbulence Model

An analytic expression is obtained for the constant Ccp in the Baldwin-Lomax model by comparing self-similar solutions for velocity in a constant pressure incompressible flow that are based on the Cebeci-Smith and Baldwin-Lomax models; both models are shown to give identical results when the model Ccp has a specific analytical form.

COMPUTATION OF TWO-DIMENSIONAL INCOMPRESSIBLE TURBULENT BOUNDARY LAYER FLOWS WITH EQUILIBRIUM AND NONEQUILIBRIUM TURBULENCE MODELS

Two-dimensional incompressible turbulent boundary layer flows over a flat plate were predicted using turbulent boundary layer equations. Reynolds stresses were calculated using Cebeci-Smith, Baldwin-Lomax, and Johnson-King eddy viscosity models. Computational results of mean-flow properties based on Cebeci-Smith model and Baldwin-Lomax model are in excellent agreement with experimental data, and, those based on Johnson-King model are not as accurate as the other two models.

On turbulent separation in the flow past a bluff body

The basic model problem of separation as predicted by the time-mean boundary-layer equations is studied, with the Cebeci-Smith model for turbulent stresses. The changes between laminar and turbulent flow are investigated by means of a turbulence ‘factor’ which increases from zero for laminar flow to unity for the fully turbulent regime. With an attached-flow starting point, a small increase in the turbulence factor above zero is found to drive the separation singularity towards the trailing edge or rear stagnation point for flow past a circular cylinder, according to both computations and analysis. A separated-flow starting point is found to produce analogous behaviour for the separation point. These findings lead to the suggestion that large-scale separation need not occur at all in the fully turbulent regime at sufficiently high Reynolds number; instead, separation is of small scale, confined near the trailing edge. Comments on the generality of this suggestion are presented, along with some supporting evidence from other computations. Further, the small scale involved theoretically has values which seem reasonable in practical terms.

A modified Cebeci-Smith model for sedimentsuspending flow

A modified Cebeci-Smith model for the velocity profile in sediment-suspending flow has been developed. Measured velocity profiles from two different data sets have been used as a basis of comparison to determine the degree of validity of the model. The model proves to be an asymptote toward which data trend for low values of y +.

Computation of viscous transonic flow over porous airfoils

The viscous effects on transonic flow past an airfoil which contains a shallow cavity beneath a porous surface are studied numerically. The porous region occupies a small portion of the total airfoil surface, and is located near the shock. Both an interactive boundary layer (IBL) algorithm and a thin-layer Navier-Stokes (TLNS) algorithm have been modified for use in studying the outer flow, whereas a stream-function formulation has been used to model the inner flow in the small cavity. The coupling procedure at the porous surface is based on Darcy's law and on the assumption of a constant total presusre in the cavity. In addition, a modified Baldwin-Lomax turbulence model is used to consider the transpired turbulent boundary layer in the TLNS approach, and the Cebeci-Smith turbulence model is used in the IBL approach. According to the present analysis, a porous surface can reduce the wave drag appreciably, but it can also increase viscous losses. As has been observed experimentally, the numerical results indicate that the total drag is reduced at higher Mach numbers and increased at lower Mach numbers when the angles of attack are small. Furthermore, the streamline patterns of passive-shock and boundary-layer interaction are revealed in this study.

Algebraic turbulence models for the computation of two‐dimensional high‐speed flows using unstructured grids

AbstractThe incorporation of algebraic turbulence models in a solver for the 2D compressible Navier–Stokes equations using triangular grids is described. A practical way to use the Cebeci–Smith model and to modify it in separated regions is proposed. The ability of the model to predict high‐speed perfect‐gas boundary layers is investigated from a numerical point of view.

Comparison of turbulence models for the natural convection boundary layer along a heated vertical plate

With a numerical code for solving the boundary-layer equations, the performance of different turbulence models for the natural convection boundary layer for air along a heated vertical plate is tested. The algebraic Cebeci-Smith model, the standard k- ε model with wall functions for k and ε and different low-Reynolds number k- ε models are tested. The Cebeci-Smith model calculates a too low wall-heat transfer and turbulent viscosity. The standard k- ε model with wall functions gives a too high wall-heat transfer, but the velocity and temperature profiles agree reasonably with experiments. Accurate wall-heat transfer results require the use of low-Reynolds number k- ε models; the models of Lam and Bremhorst, Chien, and Jones and Launder perform best up to a Grashof number of 10 11. For larger Grashof numbers the Jones and Launder model is best. A sensitivity study shows that the wall-heat transfer with the standard k- ε model largely depends on the choice of the wall functions for k and ε. Replacing these wall functions by zero wall conditions for k and ε and adding the functions D and ƒ μ of the Chien model to the standard k- ε model gives a simple, but accurate low-Reynolds number k- ε model for the natural convection boundary layer.

Calculation of two-dimensional turbulent boundary layers using the Baldwin-Lomax model

THE algebraic turbulent eddy-viscosity model of Baldwin and Lomax is critically evaluated for a class of twodimensional, nonseparated, turbulent boundary-layer flows exhibiting adverse and favorable pressure gradients, and boundary-layer bleed. The flows are computed using the twodimensional, mass-averaged, boundary-layer equations. Overall, the results obtained using the Baldwin-Lomax model compare favorably with the experimental data. Two quantities in the outer eddy-viscosity formulation are examined by comparison with the eddy-viscosity model of Cebeci and Smith. Contents The present capabilities for numerical simulation of highspeed turbulent flows are based on a variety of turbulence models. Algebraic eddy-viscosity models are still among the most popular. Certain algebraic models require the determination of the boundary-layer edge velocity and thickness, which can result in large variations in the computed outer eddy viscosity due to the uncertainty in determining the boundarylayer edge.1 Baldwin and Lomax1 have developed a two-layer, algebraic eddy-viscosity model in an attempt to eliminate this difficulty. This model has been patterned after the model of Cebeci and Smith2; however, it does not require the determination of the boundary-layer edge. The Baldwin-Lomax turbulence model was evaluated by its originators for several cases, including a shock-wave, turbulent boundary-layer interaction on a flat plate, a supersonic turbulent compression corner, and a transonic airfoil.1 Visbal and Knight3 noted that the constants Ccp and CKleb in the Baldwin-Lomax outer formulation were dependent on flow Mach number. They also identified difficulties with the determination of the length scale in the outer eddy viscosity. Similar difficulties have been encountered by other computers.4 Despite the difficulties identified with the BaldwinLomax model, and its increasing popularity and extensive application to two- and three-dimensional flows with strong viscous-inviscid interaction, a critical evaluation of this model for nonseparated, two-dimensional, turbulent boundary-layer flows has not been performed. The present investigation seeks to contribute to the evaluation of the model by critically examining its performance for a class of turbulent boundarylayer flows. Baldwin and Lomax determined the constants Ccp and CKleb appearing in the outer formulation1 by comparison with the Cebeci-Smith model for transonic, constant-pressure,