Prediction Of Turbulent Flow Research Articles

Particle Dispersion in Flowing Gases—1994 Freeman Scholar Lecture

Particle-laden gas flows are common in many man-made and natural environments. Their importance to industrial processes, agriculture, and human health has made them of great theoretical and practical interest over the past 50 years. Because particles are often carried by a turbulent gas stream, progress in understanding and predicting behavior of particle-laden flows has closely followed developments in understanding and prediction of turbulent flow. The motion of a particle in a gas flow is governed by gravity and the particle`s interaction with the turbulent fluid surrounding it. However, to determine the location and thus the local turbulence surrounding the particle, the trajectory of the particle must be known. It is this nonlinear coupling between the particle motion and the turbulence that makes predicting particle dispersion in gas flow difficult. During the past two decades, fundamental understanding of the dispersion of particles in simple turbulent gas flows has been reached, and the capability of predictive tools has increased exponentially as a result. This review is an attempt to summarize the current state of knowledge about gas-particle flows, and to highlight areas where more research is needed.

Development of Multiple Production $\varepsilon$ Equation Model in Low Reynolds Number $\kappa$-$\varepsilon$ Model with the Aid of DNS Data

A multiple production .epsilon. equation model was developed in the low Reynolds number - model with the aids of DNS data. We derived the model theoretically and avoided the use of empirical correlations as much as possible in order for the model to have generality in the prediction of complex turbulent flow. Unavoidable model constants were, however, optimized with the aids of DNS data. All the production and dissipation models in the equation were modified with damping functions to satisfy the wall limiting behavior. A new function, turbulent diffusion and pressure diffusion model for the k and .epsilon. equations were also proposed to satisfy the wall limiting behavior. By, computational investigation on the plane channel flows, we found that the multiple production model for .epsilon. equation could improve the near wall turbulence behavior compared with the standard production model without the complicated empirical modification. Satisfication of the wall limiting conditions for each turbulence model term was found to be most important for the accurate prediction of near wall turbulence behaviors.

Prediction of turbulent flows in dredged trenches

Data from turbulent flows over steep-sided trapezoidal trenches and a backward-facing step in an open channel were used to assess the performance of three alternative models of turbulence viz. the industry-standard k-∊ model, a second-order closure which is linear in the Reynolds stresses and another which is quadratic in the same quantities. The computations were carried out on body-fitted coordinates and were carefully checked for numerical accuracy. It is demonstrated that the mean-flow parameters are predicted equally well by all models but that the details of the turbulence structure are best captured by the second-order closures. The significance of these results to the practical prediction of trench flows is discussed.

Prediction of nonequilibrium turbulent flows with explicit algebraic stress models

An explicit algebraic stress equation, developed by Gatski and Speziale, is used in the framework of the K-UJ and K-e formulations to predict two-dimensional separated turbulent flows. The nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains. The proposed models were implemented in the Courant-Friedrichs-Lewy three-dimensional Navier-Stokes code. Comparisons with the experimental data are presented, which clearly demonstrate that explicit algebraic stress models improve the response of standard two-equation models to nonequilibrium effects. I. Introduction

Heat transfer and flow structure in laminar and turbulent flows in a rectangular channel with longitudinal vortices

Heat transfer characteristics and flow structure in laminar and turbulent flows through a rectangular channel containing built-in vortex generators have been analyzed by means of solutions of the full Navier-Stokes and energy equations. The geometrical configuration of interest is representative of single element of a plate-fin cross-flow heat exchanger. Each winglet-pair induces longitudinal vortices behind it. These vortices swirl the flow around the axis parallel to the mainstream direction and strongly enhance the exchange of fluid between the wall and the core region which causes high heat transfer augmentation. A detailed evaluation of the performance parameters in the laminar flow regime with regard to the enhancement of heat transfer using winglet-type vortex generators has been accomplished in this study. It may be mentioned that for some special applications the fluid velocity becomes very high and one may encounter turbulent flows in plate-fin heat exchangers. In the present study, the predictions for turbulent flows have been made and an effort has been undertaken to compare the accuracy of the predictive procedure with well documented experiments of another research group. The computational results agree reasonably well with their experimental counterpart.

The Effect of Turbulence on Solidification of a Binary Metal Alloy With Electromagnetic Stirring

Electromagnetic induction is considered as a means of altering convection during the solidification of a Pb–19 wt pct Sn alloy. Application of a time-varying magnetic field induces Lorentz forces, which augment thermal buoyancy forces in the melt and oppose solutal buoyancy forces in the mushy zone. A continuum model for binary solid–liquid phase change is extended to account for turbulence, and laminar and turbulent flow predictions are contrasted. Results indicate that turbulence decreases the propensity for channel development and macrosegregation by enhancing mixing and reducing the effective Lewis number from 8600 to near unity.

Numerical laminar and turbulent fluid flow and heat transfer predictions in tube banks

Numerical predictions of laminar and turbulent fluid flow and heat transfer around staggered and in‐line tube banks are shown to agree closely with seven experimental test cases. The steady state Reynolds‐averaged Navier‐Stokes equations are discretised by means of a cell‐centred finite‐volume algorithm. Two‐dimensional results include velocity vectors and streamlines, surface shear stresses, pressure coefficient distributions, temperature contours, local Nusselt number distributions and average convective heat transfer coefficients, and indicate very good agreement with experimental data. It is found that a relatively fine grid is required to be able to predict the surface heat transfer behaviour accurately. Also, three‐dimensional simulations are shown, which are physically consistent. The numerical procedure presented here is robust, accurate and time efficient, making it suitable as a design tool for tube banks in heat exchangers.

Prediction of Turbulent Flow and Heat Transfer in a Ribbed Rectangular Duct With and Without Rotation

The present study deals with the numerical prediction of turbulent flow and heat transfer in a 2:1 aspect ratio rectangular duct with ribs on the two shorter sides. The ribs are of square cross section, staggered and aligned normal (90 deg) to the main flow direction. The ratio of rib height to duct hydraulic diameter equals 0.063, and the ratio of rib spacing to rib height equals 10. The duct may be stationary or rotating. The axis of rotation is normal to the axis of the duct and parallel to the ribbed walls (i.e., the ribbed walls form the leading and the trailing faces). The problem is three dimensional and fully elliptic; hence, for computational economy, the present analysis deals only with a periodically fully developed situation where the calculation domain is limited to the region between two adjacent ribs. Turbulence is modeled with the k–ε model in conjunction with wall functions. However, since the rib height is small, use of wall functions necessitates that the Reynolds number be kept high. (Attempts to use a two-layer model that permits integration to the wall did not yield satisfactory results and such modeling issues are discussed at length.) Computations are made here for Reynolds number in the range 30,000–100,000 and for Rotation number = 0 (stationary), 0.06, and 0.12. For the stationary case, the predicted heat transfer agrees well with the experimental correlations. Due to the Coriolis-induced secondary flow, rotation is found to enhance heat transfer from the trailing and the side walls, while decreasing heat transfer from the leading face. Relative to the corresponding stationary case, the effect of rotation is found to be less for a ribbed channel as compared to a smooth channel.

Prediction of turbulent flow over rough asymmetrical bed forms

This paper is concerned with a numerical investigation of the turbulent flow over a train of immobilized two-dimensional asymmetric bed forms. The results from a differential second moment (DSM) closure turbulence model, together with two simpler eddy-viscosity based models, are compared with experimental data. The DSM model is then used to calculate the drag coefficient over bed forms of varying steepness, and the result is compared with a number of empirical formulas that have previously been proposed. Finally, the partitioning of the total drag into form drag and skin friction contributions as a function of bed form steepness is investigated.

Invariant discretization of the k-ϵ model in general co-ordinates for prediction of turbulent flow in complicated geometries

An invariant formulation and finite volume discretization of the standard k-ϵ turbulence model in general curvilinear co-ordinates is presented. The k-ϵ model is implemented together with the incompressible Navier-Stokes equations on staggered grids with contravariant flux components as unknowns. A proof that k and ϵ are non-negative is given. Positive schemes in the implementation of the k-ϵ model are evaluated. Discretization of boundary conditions is considered. The numerical method is applied to a turbulent flow across a staggered tube bank.

Numerical Analysis of Developing Turbulent Flow in a Square-Sectioned Bend. Prediction of Turbulent Flow with the Secondary Flow of the First and the Second Kind.

A numerical analysis has been performed on developing turbulent flow in a square-sectioned 180 deg bend. The ratio of bend mean radius of curvature to hydraulic diameter is 3.35 and straight ducts of 31 hydraulic diameter long are attached to the inlet and outlet planes of the bend. In calculation, an algebraic stress model was adopted in order to predict Reynolds stresses precisely, and a boundary fitted coordinate system was introduced to briefly set boundary conditions. Calculated results were compared with the experimental data available. Moreover, the transition from the secondary flow of the second kind to that of the first kind and vice versa are examined. It was found that the present method predicted the mean flow velocity with a minimum at 90 deg of bend without much discrepancy. In a straight duct of a bend inlet, the secondary flow of the second kind transforms into that of the first kind at 1.0∼1.6 hydraulic diameter upstream from the bend inlet. In contrast, in a straight duct of a bend outlet, the secondary flow of the first kind is accelerated downstream from bend outlet by increasing the pressure gradient of the square cross section. After this acceleration, the secondary flow of the first kind decays and gradually transforms into the secondary flow of the second kind.

Numerical prediction of turbulent flow around a three-dimensional surface-mounted obstacle

A numerical model is presented for the computation of general three-dimensional incompressible turbulent flow. The turbulence is modelled by use of a standard two-equation ( k − ε) model. The numerical formulation is a Galerkin finite element method, and a fractional step algorithm is applied for the solution of the advection-diffusion equations. The pressure is computed from a derived Poisson equation, and the solution of this equation system is performed by the use of an efficient incomplete Cholesky conjugate gradient (ICCG) algorithm. Computations are performed for flow around a three-dimensional surface-mounted cube, and predictions are compared with available measurements. The predicted results show encouraging agreement with the experiments.

Prediction of turbulent wall shear flows directly from wall

AbstractThe fully elliptic Reynolds‐averaged Navier–Stokes equations have been used together with Lam and Bremhorst's low‐Reynolds‐number model, Chen and Patel's two‐layer model and a two‐point wall function method incorporated into the standard k‐ϵ model to predict channel flows and a backward‐facig step flow. These flows enable the evaluation of the performance of different near‐wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non‐equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ϵ‐transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low‐Reynolds‐number model has wider applicability and performs better than the two‐layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ϵ equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ϵ‐equation, one can still predict satisfactorily some simple turbulent flows.

Prediction of turbulent flow through a transition duct using second-moment closure

The near-wall, full Reynolds-stress closure of Launder and Shima is employed to calculate the three-dimensional turbulent flow through a circular-to-rectangular transition duct. The solutions are compared with the recent experimental data of Davis and Gessner. Dowstream of the transition region, however, the computed Reynolds stresses appear to decay at a much caster rate than observed in the measurements. These results point to the need for further refinement of Reynolds-stress models to correctly predict the relaxation of rapidly strained turbulence towards equilibrium

Two-equation turbulence model for unsteady separated flows around airfoils

HE prediction of turbulent unsteady separated flows around airfoils is currently a priority in the domain of aeronautics. There are numerous studies in this domain, but the accurate prediction of the flow structure and aerodynamic parameters, especially near stall conditions, remain open questions, and considerable efforts have to be made to suggest an efficient way to resolve this problem. The majority of the studies devoted to the problem use different classes of turbulence models employing the steady Reynolds-averaged equations. A widely used turbulence model in the context of the eddy-viscosity concept is the two-equation model (Launder and Spalding1) and its various versions (Jones and Launder2 and Chien3 among others). However, this kind of model was originally conceived for free shear flows and then adapted for boundary-layer flows. It is not evident whether this model may be directly applicable in the elliptic flows around airfoils, as often discrepencies in the flow parameters appear when comparing with the physical experiments (see numerous papers reported in Ref. 4). One of the well-known reasons is that the various applications of the k-£ model provide generally too high a level of the eddy viscosity and of the turbulent kinetic energy production. In this study, we simulate the turbulent incompressible flow around an airfoil NACA 0012 at a Reynolds number range of 1$, by an unsteady approach, using the phase-averaging decomposition (Hussain and Reynolds5), in the form suggested by the experimental work of Cantwell and Coles.6 This decomposition provides the phase-averaged Navier-Stokes equations, as reported in the works of Ha Minh et al., 7 Chassaing,8 Braza and Nogues,9 and Franke and Rodi,10 among others. Furthermore, we introduce the unsteady vorticity into the production term of turbulent energy to improve the behavior of the two-equation model with respect to the physics of the flow.

Incompressible flow calculations with a consistent physical interpolation finite volume approach

The computation of incompressible three-dimensional viscous flow is discussed. A new physically consistent method is presented for the reconstruction for velocity fluxes which arise from the mass and momentum balance discrete equations. This closure method for fluxes allows the use of a cell-centered grid in which velocity and pressure unknowns share the same location, while circumventing the occurrence of spurious pressure modes. The method is validated on several benchmark problems which include steady laminar flow predictions on a two-dimensional cartesian (lid driven 2D cavity) or curvilinear grid (circular cylinder problem at Re = 40), unsteady three-dimensional laminar flow predictions on a cartesian grid (parallelopipedic lid driven cavity) and unsteady two-dimensional turbulent flow predictions on a curvilinear grid (vortex shedding past a square cylinder at Re = 22,000).

Velocity Distribution in Compound Channel Flows by Numerical Modeling

The paper examines the problem of prediction of uniform turbulent flow in a compound channel with the nonlinear k‐ε model. This model is capable of predicting the secondary currents, caused by the anisotropy of normal turbulent stresses, that are important features of the flow in compound channels, as they determine the transverse momentum transfer. The model is applied to reproduce experimental runs available in the literature. The comparison shows that the model predicts with accuracy the distribution of the primary velocity component, the secondary circulation, and the discharge distribution. The numerical results are used to search a subdivision surface between main channel and floodplain on the basis of the flow field and to compare different subdivision surfaces on the basis of the discharge distribution by a simple uniform flow formula. The better subdivision surfaces as predicted by the model are the diagonal surface going from the corner between main channel and floodplain to the free surface on the symmetry plane and the bisector of the same corner.

Multiple-Scale Turbulence Model for Wall and Free Turbulent Flows.

It is well known that turbulence models based on the eddy viscosity assumption have been quite successful in the numerical predictions of various kinds of turbulent flows. In particular, the k-εmodel is the most popular and has been proven to be effective in predicting wall shear layer turbulence. The k-ε models, however, show poor performance in the prediction of free shear flows. Such inconsistency is not caused by the crudeness of the eddy viscosity approximation, but by the inappropriate estimation of the relevant time scale of turbulence. Thus, in order to settle this problem, we propose a low-Reynolds-number-type "multiple-scale" turbulence model on the basis of the original model of Hanjalic et al. (Turbulent Shear Flows 2, 1980, Springer), in which multiple scales characterizing a turbulent flow are introduced by dividing the turbulence energy spectrum into two wave-number regions. In the present study, much emphasis is put on making a proposed model applicable to the prediction of near-wall turbulent flows without the controversial wall functions and reproduce the wall-limiting behavior of turbulence quantities. The proposed model has been tested in canonical wall and free shear flows and are found to work quite well regardless of the flow regimes.

Prediction of Turbulent Flows in Rotating Rectangular Ducts

This paper reports on progress made in the development of a numerical predictive procedure for turbulent flows in rotating rectangular ducts. The unknown turbulent stresses were approximated with the k–ε model of turbulence while Speziale’s (1987) nonlinear stress-strain relationship was utilized to capture the turbulence-driven secondary motions. Data from stationary rectangular ducts of aspect ratios in the range 1:1 to 10:1 were used to check the model. It was found that the occurrence and consequences of these motions were well reproduced. Application of the model to rotating rectangular ducts yielded results which suggest that the interactions between the pressure and turbulence-driven motions are far more important than hitherto suspected.

Computation of unsteady viscous flow using a pressure-based algorithm

The objective of this research is the development of an efficient and accurate numerical analysis for the prediction of unstready turbulent flows using a Navier-Stokes solver. The technique developed is to be used for incompressible flow and is an extension of the pressure-based method. The finite volume approach and a nonstagger grid formulation are used. A predictor-corrector type algorithm is applied to the governing equations to ensure time accuracy. The convergence is improved using a multigrid scheme