Eddy-viscosity Turbulence Model Research Articles

Computations of post-trip reactor core thermal hydraulics using a strain parameter turbulence model

Coolant flows in the cores of nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be modified strongly from the forced convection condition by the action of buoyancy, in particular exhibiting impaired levels of heat transfer with respect to corresponding forced convection cases. The heat transfer performance of these ‘mixed convection’ flows is investigated here using two physically distinct eddy viscosity turbulence models: the recent ‘strain parameter’ (or k– ε– S) model of Cotton and Ismael [A strain parameter turbulence model and its application to homogeneous and thin shear flows. Int. J. Heat Fluid Flow 19 (1998) 326] is examined against the benchmark low-Reynolds-number k– ε model of Launder and Sharma [Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfer 1 (1974) 131]. Comparison is made with three sets of heat transfer data for ascending mixed convection flows, and it is demonstrated that both turbulence models are generally successful in resolving the Nusselt number distributions occurring along the lengths of mixed convection flow passages. The mechanisms by which the strain parameter model generates reduced turbulence levels, and hence impaired heat transfer rates, is explored in comparison with a fourth set of experimental data for mixed convection flow profiles.

Realizability for the Reynolds Stress in Nonlinear Eddy-Viscosity Model of Turbulence

The non-negativeness of the normal stress is one of the realizability conditions for the Reynolds stress. This condition is investigated to improve turbulence models. A statistical theory called th...

A modeling of in-tube condensation heat transfer for a turbulent annular film flow with liquid entrainment

An analytical model is developed for condensation heat transfer coefficients for a turbulent annular film flow in tubes. This calculation model not only incorporates a new turbulent eddy viscosity profile modified from the Blangetti and Schlunder model but also liquid entrainment effect. In order to assess the prediction capability of the calculation model, an experiment was performed for measurement of condensation heat transfer coefficients of R22 in horizontal smooth tubes. The calculated condensation heat transfer coefficients of R22 were compared with present experimental data and some existing correlations. From the present analysis and experiment it is found that incorporating the effect of liquid entrainment into the calculation model gives better prediction capability for in-tube condensation heat transfer coefficients. Also, the proposed turbulent eddy viscosity model gives better prediction capability for the condensation heat transfer coefficients than that of the Blangetti and Schlunder model.

Numerical investigation of the adverse effect of wind on the heat transfer performance of two natural draft cooling towers in tandem arrangement

This article reports the findings on the adverse effect of the crosswind on the performance of natural draft cooling towers through numerical computation with thek-e eddy-viscosity turbulence model. It is observed here that the cause of the adverse effect of the crosswind on the cooling towers can be attributed to the around flow effect which destroys the radial inflow into the cooling towers when the wind is absent. Hence, a significant deterioration in the heat transfer from the heat exchangers at lateral sides occurs.

The Modeling of Variable Density Turbulent Flows. A review of first-order closure schemes

The paper is intended as a review of where eddy-viscosity turbulence models have reached in accounting for the several distinct effects of variable density and high-Mach number behaviour on the development of turbulent shear flows. Three generations of ``compressible models'' are depicted: a first one based on variable density and compressible adjustments of ``incompressible'' schemes, a second one in which it is presumed that explicit dilatational terms can account for variable density and compressibility effects, and a third one, where such effects are taken implicitly in association with structural changes of the turbulent field. The latter are hardly tractable when using first-order closure schemes, but more reliable than the former in accounting for most observed variable density and compressibility effects in turbulent shear flows.

Assessment of turbulence model performance for transonic flow over an axisymmetric bump

AbstractA computational study has been performed to evaluate the predictive capabilities of some existing eddy-viscosity (both linear, LEVM, and non-linear, NLEVM) and Reynolds stress transport turbulence models (RSTM) by reference to a transonic shock-induced separated flow over a 10% axisymmetric bump. The calculations have been carried out during the course of a collaborative research programme including both UK universities and industry. The findings of the project demonstrate that improved results can be obtained for such flows by using more advanced turbulence models. For linear eddy-viscosity models, only the SST approach gave good predictions of shock location, recirculation size and pressure recovery, although this was accompanied by deficiencies in the prediction of post-shock velocity profile shape. Non-linear eddy-viscosity models, particularly at the cubic level, provided a more consistent level of agreement with experiments over the range of shock location, wall pressure and velocity profile parameters. Some improvement was also seen in the prediction of turbulence quantities, although only a move to an RSTM closure model reproduced the measured peak stress levels accurately. It was notable that the use of low-Re variants of the models (instead of wall functions) produced no significant improvement in predictions. There are, however, some shortcomings in all models, particularly in the development of flow after reattachment, which was always predicted to be too slow.

An assessment of k–ε and k–l turbulence models for a wide range of oscillatory rough bed flows

The k–ε and k–l eddy viscosity turbulence models are now used extensively in environmental flow modelling. In the present work computations for oscillatory flows are examined over a broader range of experimental parameters than considered previously. Comparisons are made with field measurements and laboratory data, including new measurements reported here for the first time. It is confirmed that the bed friction velocity and mean flow profiles are, in general, adequately predicted by both models (the k–ε model is, however, somewhat more accurate than the k–l formulation). Reynolds shear stress, turbulent kinetic energy, and eddy viscosity are less well predicted, although the k–ε model again gives more accurate results than the k–l model. An attempt has been made to assess the uncertainty in the experimental data for Reynolds stress and eddy viscosity: it is found that the k–ε model computations for both quantities more frequently lie within the estimated uncertainty bounds. Those bounds are nonetheless wide, emphasizing the need for improved experimental resolution of rough bed flows. Such an improvement would assist in the evaluation of proposed refinements to commonly used turbulence models such as those under investigation here and, indeed, to greater reliability in the development and assessment of more sophisticated schemes.

Unsteady vorticity–streamfunction algorithm for external flows

A non-inertial vorticity–streamfunction algorithm of the Reynolds-averaged Navier–Stokes equations is developed for studying unsteady and turbulent flows past airfoils. The equations are solved on a non-orthogonal C-grid using a combined finite-difference/finite-volume technique. Comparative computations are carried out employing three different turbulence models. These are the algebraic zero-equation model of Baldwin and Lomax [1], and the one-equation models of Baldwin and Barth [2] and Spalart and Allmaras [3]. The performance of the models is evaluated against experiments of the Aérospatiale-A airfoil at incidences up to 40° and against two cases of an oscillating NACA 0015 airfoil experiencing light and deep stall. The computations demonstrate that the vorticity–streamfunction formulation combined with standard eddy-viscosity turbulence models is capable of predicting accurately unsteady and turbulent flows past airfoils.

Depth-Averaged Simulation of Supercritical Flow in Channel with Wavy Sidewall

Supercritical flow in a channel with a wavy sidewall is numerically simulated by solving the two-dimensional (2D) depth-averaged equations using two different second-order accurate finite-difference schemes: ADI and MAC. ADI is an implicit model that uses an alternating-direction-implicit (ADI) scheme to solve the governing equations. MAC is an explicit model employing the MacCormack two-step predictor-corrector scheme. To accurately simulate the wavy sidewall, both models solve the governing equations in transformed computational coordinates. Bottom friction is computed using the Manning formula and the effective stresses are modeled with a constant eddy-viscosity turbulence model. As is customary, the stresses due to depth-averaging are neglected. The computed water depth in the channel is compared with experimental data obtained by Mizumura. The effect of bottom friction, effective stresses, artificial viscosity, grid geometry, boundary conditions, and the Courant-Friedrichs-Lewy (CFL) number are investigated. Similarities and differences in the behavior of the models are observed and discussed.

Flowfield characteristics of swept struts in supersonic annular flow

Abstract Supersonic flow over four, circumferentially equidistant, diamond-shaped swept struts positioned between a concentric cylindrical cowl and centerbody is examined from both experimental and numerical points of view. Experimental cross flow vectors and cross-planar pitot pressure and static pressure contours are compared with their numerical counterparts downstream of the strut trailing edge. Numerical results are also presented which show shock wave and expansion fan patterns generated at each strut/endwall intersection in order to demonstrate the full complexity of the flow. The numerical results are analyzed to show that computed limiting streamlines on the strut, cowl and centerbody surfaces are compatible with corner and shock generated vortices observed in the flow. Comparisons between predicted and measured contours downstream of the strut trailing edge indicate that the prescribed zero-equation (isotropic eddy viscosity) turbulence model performs well outside the wake region behind a strut, but not within the wake itself.

Investigation of Nonlinear Eddy-Viscosity Turbulence Models in Shock/Boundary-Layer Interaction

Validation of nonlinear two- and three-equation, eddy-viscosity turbulence models (NLEVM)in transonic e ows featuring shock/boundary-layer interaction and separation is presented. The accuracy of the models is assessed againstexperimentalresultsfortwotransonice owsoverbumpgeometries.Moreover,theaccuracyandefe ciencyof NLEVMsisalsoassessedincontrasttonumericalpredictionsobtainedbyavarietyofothermodelsemployedinthis study. These include two linear eddy-viscosity k‐≤ models, the k‐! shear-stress transport model, and a nonlinear version of the k‐! model. Discretization of the mean e ow and turbulence transport equations is obtained by a characteristics-based scheme (Riemann solver ) in conjunction with an implicit unfactored method. The study shows that NLEVMs improve the numerical predictions in shock/boundary-layer interaction, compared to the linear models, but they require longer computing times. Nomenclature A = Lumley’ s e atness parameter, ´ 1 i 9 (A2 i A3) A2 = second invariant of Reynolds-stress anisotropy, ´ a ija ij A3 = third invariant of Reynolds-stress anisotropy, ´ a ika kja ji c

Investigation of nonlinear eddy-viscosity turbulence models in shock/boundary-layer interaction

Investigation of nonlinear eddy-viscosity turbulence models in shock/boundary-layer interaction

Nonlinear Eddy-Viscosity Turbulence Model and Its Application

Nonlinear Eddy-Viscosity Turbulence Model and Its Application

Development and assessment of computer methods for three-dimensional turbulent boundary layers

AbstractThis paper describes the development of a finite difference method that solves the boundary-layer equations for three-dimensional compressible turbulent flows. The most prominent achievements are the employment of a Newton technique for the simultaneous solution of all governing equations, an option to choose an algebraic or a k-ε eddy-viscosity turbulence model, and the flexible use of curvilinear coordinates. The method is validated by comparisons with a number of experimental and theoretical data sets of three-dimensional, compressible and incompressible, steady and unsteady boundary layers. In parallel, the performance of a three-dimensional compressible industrial integral boundary-layer technique is evaluated by comparisons with experimental test cases and with the results of the field method.

Solving incompressible internal flow fields in turbomachinery with time marching algorithms

A time marching algorithms, which is used to solve incompressible internal flow fields in turbomachinery, has been developed. By using Chorin’s method of artificial compressibility, the governing equations are transformed from elliptic type into hyperbolic form in order to extend the time marching technique to very low Mach number flows. Viscous effects can be predicted by using the distributed body force method and Baldwin-Lomax eddy viscosity turbulence model. Some accelerating convergence techniques such as multi-grid and local time step method are employed. The application to a flow field within a low-solidity rocket pump inducer is presented and discussed.

Nonlinear eddy-viscosity turbulence model and its application

Nonlinear eddy-viscosity turbulence model and its application

Pressure-Based Compressible Calculation Method Utilizing Total Variation Diminishing Schemes

A pressure-based implicit procedure to solve the Euler and Navier ‐Stokes equations on a nonorthogonal mesh withcollocated e nitevolumeformulation is described. The boundedness criteria forthisprocedurearedetermined from total variation diminishing (TVD) schemes, which are based on characteristic variables and are applied to the e uxes of the convected quantities, including mass e ow rate. The procedure incorporates the k‐ eddy-viscosity turbulence model. Thealgorithm ise rsttested for inviscid e owsat differentMach numbers ranging from subsonic to supersonic on a bump in a channel geometry, where the results are compared with other existing numerical solutions.Themethodisthenvalidatedagainstexperimentandanothernumericalsolutionforthecaseofturbulent transonic e ow through a gas turbine rotor blade cascade for which wind-tunnel experimental data exist. The comparisons show that the quality of the resolution of the TVD scheme, as implemented in the pressure-based procedure, is similar to that obtained when applied in density-based methods.

Flowfield characteristics of struts in supersonic annular flow

Abstract This paper describes a combined experimental and numerical study of supersonic flow over four, circumferentially equidistant, diamond-shaped struts positioned within an annular flow passage formed by a cylindrical cowl and centerbody. The experimental results include static pressure, pitot pressure, total pressure, and Mach number distributions at two streamwise locations downstream of the strut trailing edge. Resultant cross flow vectors based on yaw and pitch angle measurements in the flow are also presented at these two locations. The experimental results are compared with numerical predictions based on a combined version of the Baldwin–Lomax and P.D. Thomas turbulence models. Experimental and numerical results are in good agreement throughout wall-bounded regions of the flow, including regions that contain propagating shock and expansion waves. The predictions do not simulate, however, the presence of vortices in the wake region downstream of the strut trailing edge and their distorting influence on flow in this region. This discrepancy is attributed to the prescribed zero-equation (isotropic eddy viscosity) turbulence model, which apparently cannot simulate the effects of streamwise vorticity in a supersonic wake.

Prediction of High-Lift Flows Using Turbulent Closure Models

The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.

A stable algorithm for Reynolds stress turbulence modelling with applications to rectilinear and circular tidal flows

This paper employs one-point, linear eddy viscosity and differential second-moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non-staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non-linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schröder (Tech. Rep. GK55 87/E/16, GKSS-Forshungszentrum Geesthacht, 1983) and McClean (Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade), Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones (Int. j. numer. meth. fluids,12, 17 (1991)) and Davies (Continental Shelf. Res., 11, 1313 (1991)), who employed the one-equation, k–l, eddy viscosity turbulence model to simulate rectilinear and circular tidal flows. © 1998 John Wiley & Sons, Ltd.