A. O. Demuren

Calculation of turbulence-driven secondary motion in non-circular ducts

Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate e of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it.

Calculation of flow and pollutant dispersion in meandering channels

Experiments on and calculation methods for flow and pollutant spreading in meandering channels are reviewed. The shortcomings of existing calculation methods are discussed in the light of the complex three-dimensional nature of the flow situation. A mathematical model is presented which takes full account of the three-dimensionality of the flow and pollutant concentration fields. This model is based on the solution of the momentum equations governing the flow in the lateral, vertical and longitudinal directions with a three-dimensional numerical procedure together with the continuity equation.

Numerical calculations of steady three-dimensional turbulent jets in cross flow

This paper presents calculations of the steady flow of a row of turbulent jets issuing normally into a nearly uniform cross flow, using three-dimensional finite-difference numerical procedures. One procedure uses a quadratic upstream weighted (QUICK) difference scheme in representing the convection terms, while the other uses a hybrid central/upwind difference scheme. The calculations with the former are shown to be superior to those with the latter for all grid distributions. Fine grid calculations with the QUICK scheme are shown to agree fairly well with experimental measurements of total pressure distributions immediately downstream of the jet discharge. The agreement becomes worse further downstream, and it is shown that this may be due to the inablility of the k-e turbulence model to correctly reflect the complex turbulent structure in the wake region. Estimates are provided of the relative magnitudes of the three-dimensional false or numerical diffusivities, resulting from the use of upwind differencing. The QUICK and hybrid schemes are shown to produce closer results when these false diffusivities are not much higher than the physical diffusivity.

Modeling near-wall effects in second-moment closures by elliptic relaxation

The elliptic relaxation method for modeling near-wall turbulence via second-moment closures (SMC) is compared to direct numerical simulation (DNS) data for channel flow at Reτ=395. The agreement for second-order statistics, and the terms in their balance equation is quite satisfactory, confirming that essential kinematic effects of the solid boundary on near-wall turbulence are accurately modeled by an elliptic operator. Additional viscous effects, immediately next to the surface, can be added via Kolmogoroff scales. In combination, elliptic relaxation and Kolmogorov scaling provide a general formulation to extend high Reynolds number SMC to wall-bounded flows. This formulation was easily applied to the nonlinear Craft-Launder and Speziale-Sarkar-Gatski (SSG) pressure-strain models. It is observed that the boundary conditions of the relaxation operator dominate the homogeneous pressure-strain model in the near-wall region. While looking at high-Reynolds number channel flows, it was found necessary to modify the effect of the relaxation operator throughout the log-layer by accounting for gradients of the turbulent lengthscale; this brings the velocity gradient into perfect agreement with the von Karman constant. The final form of the model based on the SSG homogeneous closure was then successfully applied to rotating channel flows, including relaminarization. The paper merges and updates two contributions by the five authors to the 10th Turbulent Shear Flow Conference.

Perspective: Systematic Study of Reynolds Stress Closure Models in the Computations of Plane Channel Flows (Data Bank Contribution)

Abstract : This paper investigates the roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models. Three turbulent diffusion and five pressure- strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the direct numerical simulation are used to further clarify this behaviour of the models.

A numerical model for flow in meandering channels with natural bed topography

A finite-volume numerical model is presented for the calculation of three-dimensional turbulent flow in meandering channels with natural bed configuration. The governing equations are written in a general curvilinear coordinate system so that all singly connected geometrical configurations can be accommodated. For simplicity, the Cartesian velocity components are retained as dependent variables. The numerical procedure is very general so that it can deal with complex cross sections and separated flow. Turbulence closure is through the standard k-ϵ model. Computed results show good agreement with experimental data in meandering channels with rectangular and natural bed configurations. This work provides a hydrodynamic basis for the study of the mechanisms for the formation of river meanders.

Characteristics of three-dimensional turbulent jets in crossflow

Abstract Three-dimensional turbulent jets in crossflow at low to medium jet-to-crossflow velocity ratios are computed with a finite-volume numerical procedure which utilizes a second-moment closure model to approximate the Reynolds stresses. A multigrid method is used to accelerate the convergence rate of the procedure. Comparison of the computations to measured data shows good qualitative agreement. All trends are correctly predicted, though there is some uncertainty on the height of penetration of the jet. The evolution of the vorticity field is used to explore the jet-crossflow interaction.

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross-sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. Model predictions are compared to experimental data for developed flow in triangular duct, trapezoidal duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with the measured data.

Numerical simulation of turbulent jets with rectangular cross-section

Three-dimensional turbulent jets with rectangular cross-section are simulated with a finite-difference numerical method. The full Navier-Stokes equations are solved at low Reynolds numbers, whereas at the high Reynolds numbers filtered forms of the equations are solved along with a subgrid scale model to approximate effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporal discretization and a fourth-order compact scheme is used for spatial discretization. Computations are performed for different inlet conditions which represent different types of jet forcing. The phenomenon of axis-switching is observed, and it is confirmed that this is based on self-induction of the vorticity field. Budgets of the mean streamwise velocity show that convection is balanced by gradients of the Reynolds stresses and the pressure.

Higher-order compact schemes for numerical simulation of incompressible flows. Part I: theoretical development

A higher-order-accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization. New insights are presented on the elimination of the odd-even decoupling problem in the solution of the pressure Poisson equation. For consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Accuracy and robustness issues are addressed by application to several pertinent benchmark problems in Part II.A higher-order-accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth- and sixth-order compact finite-difference schemes for spatial discretization. New insights are presented on the elimination of the odd-even decoupling problem in the solution of the pressure Poisson equation. For consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Accuracy and robustness issues are addressed by application to several pertinent benchmark problems in Part II.