Algebraic Turbulence Model Research Articles

Development of an explicit algebraic turbulence model for buoyant flows – Part 1: DNS analysis

An analysis of DNS databases of vertical plane channel flow for forced, mixed and natural convection is proposed. This analysis aims to assess the main features needed to develop an algebraic model for buoyant flows. First, the weak equilibrium assumption, at the root of algebraic models, is investigated. This hypothesis is shown to fail near the velocity maximum and close to the walls but remains valid otherwise, whatever the convection regime. The models for the redistribution term and the pressure scrambling term are then analyzed on the same configurations. A linear form of the Speziale et al. (1991) model is retained for the redistribution term. No model for the pressure scrambling term is fully satisfactory; nevertheless some models are recommended. The buoyant contributions to the pressure term are investigated. Finally, the generalized gradient diffusion hypothesis, which could be used to model the turbulent heat fluxes in order to avoid the coupling with the Reynolds stresses, is shown to be inaccurate.

Numerical Simulation of Supersonic Mixing Layers for Parallel and Non-parallel Streams

Abstract In this study supersonic mixing of two-parallel and non parallel gaseous streams has been simulated numerically. The streams are of air and hydrogen, which come into contact after passing over a finite thickness base. Two gas streams are considered from a high-pressure reservoir and entering into the domain with atmospheric pressure. Two-dimensional unsteady state Navier-Stokes equations, energy, mass diffusion and species continuity equations are numerically simulated to analyze the two-dimensional mixing layer in supersonic flow field. An explicit Harten-Yee Non-MUSCL Modified flux-type TVD (total variation diminishing) scheme has been used to solve the system of equations. An algebraic turbulence model is used to calculate the eddy viscosity coefficient. Keeping constant the inlet pressure and velocity of the streams, the merging angle is varied to observe the physics of flow fields, mixing fields of two-streams and mixing efficiency. The result shows that when merging angle increases interaction between two streams, high momentum exchange occurs and eventually enhances the mixing of two streams.

Algebraic Turbulent Heat Flux Model for Prediction of Thermal Stratification in Piping Systems

The effect of stratification on the flow in bounded geometries is studied through computational fluid dynamics and two different modelings of the turbulent heat flux: constant turbulent Prandtl number and Algebraic Heat Flux Model (AHFM). The main feature of the work is evaluation of the effect of buoyancy on the thermal quantities, velocity field, and related pressure drop. For evaluation of the turbulent heat flux and temperature field, AHFM has been demonstrated to be superior to the simple eddy diffusivity approach. However, serious concerns remain for the prediction of the velocity field in both isothermal and nonisothermal conditions, since greater uncertainties for the obtained pressure drop and related Fanning friction factor can be introduced. Incremental pressure drop is also investigated in conditions deviating from fully developed flows, in order to study stratification effects qualitatively using an engineering method.

Normal-Velocity Relaxation and Higher Order Algebraic Heat Flux Models Applicable to an Axisymmetric Impinging Jet

The present article encompasses an effort on the prediction of flow and heat transfer characteristics in the turbulent axisymmetric impinging jet. This is achieved by applying the realizability constraint in the normal-velocity relaxation (v 2 − f) model and algebraic turbulent heat flux models to flow and thermal fields, respectively. The realizable v 2 − f model is capable of improving the predicted velocity and Reynolds stress and consequently the local Nusselt number as compared with the available experimental data. Applying the higher order algebraic turbulent heat flux models, namely, GGDH and HOGGDH results in a larger wall jet heat diffusion. This causes an improvement in the predicted local Nusselt number through its reduction in both the stagnation and wall jet regions. For the local Nusselt number prediction, the realizable v 2 − f model in combination with HOGGDH model is shown to be in reasonably good agreement with the available experimental data. This is also regarded as an overall progress compared with the results reported by other workers.

Modeling and Simulation of Cold Flow Fluidized Bed Reactors

Simulations of cold flow fluidized gas-solid systems have been conducted for both riser and bubbling bed reactors, alone and combined in a circulating fluidized bed reactor. An Eulerian continuum two-fluid model with the Constant Particle Viscosity closure for the stresses term was employed for the granular phase whereas an algebraic turbulence model was used for the gas phase. An in-house code was developed, based upon the Finite Volume Method applied to the governing equations with a staggered grid arrangement. The velocities for both gas and solid phases are obtained solving the 1D Reynolds averaged Navier-Stokes equations using the Partial Elimination Algorithm (PEA) algorithm and a coupled solver, while a pressure correction equation allows to solve for pressure based on gas continuity.The void fraction profile is computed from the solid continuity. Cold flow simulations of fluidized systems form the basis for the modeling of chemical processes such as Sorption-Enhanced Steam Methane Reforming (SE-SMR).

Application of the Algebraic Subgrid Turbulent Kinetic Energy Model in LES Model

In this study the dynamic Smagorinsky model (DSM model) and an algebraic model for the subgrid turbulent kinetic energy have been implemented into KIVA3VLES code to investigate the atomization and evaporation processes of diesel spray in a constant volume vessel. Based on the experimental results of the liquid and vapor phase distributions as well as the results obtained by the differential subgrid scale kinetic energy (K-equation) model, the paper reveals the influence of the turbulent kinetic energy model on the fuel spray prediction. Computational results show that by combining the DSM model and the algebraic subgrid turbulent energy model, the turbulent diffusion of droplets can be reasonably simulated, the liquid penetration and the predicted liquid and fuel vapor mass fraction contours are close to the experiment results. At the same time, the turbulent kinetic energy given by the DSM model is in agreement with the results by the K-equation model, but with less computational cost..

Development and Validation of an Algebraic Turbulence Model for Outdoor Airflow and Contaminant Simulations around a Building

The design of outdoor environment requires a tool that could provide fast and reliable simulations for outdoor airflow and contaminant dispersions. This investigation has developed and validated a new algebraic turbulence model for outdoor environment design. The new model was tested by a natural ventilation case and two contaminant dispersion cases. The computed air velocities and contaminant concentrations agree well with the wind tunnel measurements. The computation time for the new model is about two times faster than the time needed by the standard k-ε model with an even better accuracy for the three validation cases.

Algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic and evaporating annular two-phase flow, focusing in particular on momentum and heat transfer (so-called ‘convective boiling’) through the annular liquid film. In contrast with single-phase wall-bounded flow theory, shear-driven annular liquid films are assumed here to behave as fluid-bounded flows, mostly interacting with the shearing gas-entrained droplets core flow. Besides providing velocity and temperature profiles through the liquid film, the turbulence model proposed here predicts key parameters such as the average liquid film thickness, the void fraction and the convective boiling heat transfer coefficient with accuracies comparable or better than those of leading design correlations. This turbulence model is part of a unified annular flow modeling suite that includes methods to predict the entrained liquid fraction and the axial frictional pressure gradient. The underlying heat transfer database covers nine fluids (water, two hydrocarbons and six refrigerants) for vertical and horizontal tubes of 1.03–14.4 mm diameter and pressures of 0.1–7.2 MPa. Importantly, this study shows that there appears to be no macro-to-microscale transition when it comes to annular flow. Simply better physical modeling is required to span this range.

Unsteady compressible flow simulation around low-aspect-ratio rectangular flat wings

Unsteady compressible flow solutions around a sharp-edged rectangular flat wing of an aspect ratio of 1.0 are obtained using a parallel Reynolds-averaged Navier–Stokes algorithm. The simulated cases are obtained for Mach numbers of 0.42–0.87 and Reynolds numbers of the order of 200 000–300 000 in the transitional flow regime up to an angle of attack of 15°. A Degani–Schiff modification for the Baldwin–Lomax turbulence model is used to distinguish between the boundary layers and the primary and secondary vortices over the flat plate. Unsteady vortex shedding frequencies and Strouhal number variation with the angle of attack are obtained by using the fast Fourier transform. The flow around the low-aspect-ratio rectangular flat wing is strongly dominated by the leading- and side-edge vortices and flow separations. The numerical results are compared with the prior experimental data acquired at the von Karman Institute that shows a mix of laminar/transitional flow. In the simulations, top surface pressures of the rectangular flat wing are well predicted except in the leading-edge region. Time-mean averaged surface flow topologies are also found to be in good agreement with the experiment. Complex flow structures, including the primary and secondary separation bubbles and the footprints of the primary and secondary vortex cores, are well captured through the use of the modified algebraic turbulence model.

Validation of Arbitrary Unstructured CFD Code for Aerodynamic Analyses

An unstructured grid CFD code capable of handling arbitrary polyhedra, named ‘‘LS-FLOW,’’ is developed for aerodynamic analyses of complex geometries. Through a series of numerical test cases, it is demonstrated that LS-FLOW can handle both structured and body-fitted/Cartesian hybrid unstructured grids successfully. Then, the code is validated by comparison with experimental data and theoretical solutions. In addition, it is shown that when a Baldwin-Lomax algebraic turbulence model is employed on the body-fitted/Cartesian grid, the portion of the body-fitted grid should be large enough to contain the whole boundary-layer. Finally, LS-FLOW is applied to a rocket configuration, and its future prospects are addressed.

An efficient solver for the RANS equations and a one-equation turbulence model

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. Using the algebraic turbulence model of Baldwin and Lomax, this scheme has been used to solve the compressible Reynolds-averaged Navier–Stokes (RANS) equations for transonic and low-speed flows. In this paper we focus on the convergence of the RK/Implicit scheme when the effects of turbulence are represented by the one-equation model of Spalart and Allmaras. With the present scheme the RANS equations and the partial differential equation of the turbulence model are solved in a loosely coupled manner. This approach allows the convergence behavior of each system to be examined. Point symmetric Gauss-Seidel supplemented with local line relaxation is used to approximate the inverse of the implicit operator of the RANS solver. To solve the turbulence equation we consider three alternative methods: diagonally dominant alternating direction implicit (DDADI), symmetric line Gauss-Seidel (SLGS), and a two-stage RK scheme with implicit preconditioning. Computational results are presented for airfoil flows, and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and a transport-type equation for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses RK/Implicit schemes.

Shape Optimization for Navier–Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

Void Fraction Prediction in Annular Two-Phase Flow Using an Algebraic Turbulence Model

The study considers the prediction of the main flow parameters of adiabatic annular two-phase flows, focusing in particular on the void fraction. Recently developed models to predict the entrained liquid fraction, the wall shear stress and the velocity profile in the annular liquid film are discussed and integrated to provide a unified annular flow model that is used to predict the void fraction. A comparison with experimental void fraction data shows that the unified annular flow model slightly outperforms some of the most accurate void fraction empirical correlations currently available.

Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness of a simplified model, by application of the linearization principle for non-linear parabolic equations. We finally present some numerical tests for realistic flows in tropical seas that reproduce the formation of mixing layers in time scales of the order of days, in agreement with the physics of the problem. We conclude that the typical mixing layers are transient effects due to the variability of equatorial winds. Also, that these states evolve to steady states in time scales of the order of years, under negative surface energy flux conditions.

熱線流速計による垂直大口径管内の気液二相流の計測

In this study, local measurements of flow parameters, such as void fraction, liquid velocity and turbulence intensity were performed in a vertical upward air-water two-phase flow in a 200 mm inner diameter and 24 m in height pipe by using a hot-film anemometer. The measured mean void fraction and mean liquid velocity agreed well with those by the differential pressure method and the liquid Venturi flow meter respectively. The experimental results are summarized as follows: (1) The radial profile of void fraction changes from a wall peak shape to a core peak shape and the radial profile of liquid velocity changes from a flat shape to a core peak shape as the flow develops. (2) When the average void fraction increases, the shape of void fraction radial profile changes from a wall peak to a core peak and the radial profile of liquid velocity shows a gradually increasing core peak shape. (3) The turbulence intensity increases with the increase in void fraction, flow direction and radial direction. The predicted liquid velocities by using existing algebraic turbulence models of Sato et al. and Kataoka and Serizawa were compared with the present experimental data. The comparison indicates that those models do not reasonably predict the liquid velocity distribution in a two-phase flow in a large diameter pipe mainly due to the defect in the predictive model of the liquid shear stress. It is necessary for us to establish a new model for the radial pressure distribution when we predict the liquid velocity distribution by using the measured void fraction distribution and algebraic turbulence models in a large diameter pipe. (author)

Prediction of second-order concentration statistics for dispersing plumes in obstacle arrays

In this paper, the turbulent dispersion of a passive scalar released from a continuous ground-level point-source in two obstacle arrays is simulated using the Reynolds-averaged Navier-Stokes (RANS) method. An explicit algebraic nonlinear turbulent stress model and a tensor-diffusivity scalar-flux model are used for the closure of the ensemble-averaged momentum and scalar transport equations, respectively. The principal physical mechanisms governing the transport of the second-order concentration statistics of a passive scalar are modelled following Yee et al. (2009). The results of the simulation for the flow and concentration statistics are compared against two sets of high-quality water-channel measurement data obtained using laser induced fluorescence (for concentration) and laser Doppler anemometry (for velocity).

A methodology to quantify the nonlinearity of the Reynolds stress tensor

Turbulent models provide closure equations that relate the Reynolds stress with kinematic tensors. In this study, we present a methodology to quantify the dependence of the Reynolds stress tensor on mean kinematic tensor basis. The methodology is based upon tensor decomposition theorems which allow to extract from the anisotropic Reynolds stress tensor the part that is linear or nonlinear in the strain rate tensor D, and the parts that are in-phase (sharing the same eigenvectors) and out-of-phase with the strain rate. The study was conducted using direct numerical simulation (DNS) data for turbulent plane channel (from Reτ=180 to Reτ=1000) and square duct flows (Reτ=160). The results have shown that the tensorial form of the linear Boussinesq hypothesis is not a good assumption even in the region where production and dissipation are in equilibrium. It is then shown that the set of tensor basis composed by D, D2 and the persistence-of-straining tensor D·(W-ΩD)-(W-ΩD)·D, where W is the vorticity tensor and ΩD is the rate of rotation of the eigenvectors of D, is able to totally reproduce the anisotropic Reynolds stress. With the proposed methodology, the scalar coefficients of nonlinear algebraic turbulent models can be determined, and the adequacy of the tensorial dependence of the Reynolds stress can be quantified with the aid of scaled correlation coefficients.

Numerical simulation of unsteady flows with transient regimes

Self-oscillatory flows in aerodynamics and astrophysics are studied. The two-dimensional compressible gas equations are solved using the implicit Runge-Kutta scheme of the third order with respect to the inviscid terms and of the second order with respect to the viscous terms. An algebraic Cebeci-Smith turbulence model is used. Weakly unsteady and strongly unsteady flow regimes are observed. The former occur in a supersonic flow past a cylinder with a front projection and in the heliosphere. Such flows became stable when the turbulent diffusion is taken into account. The latter flows occur when a supersonic jet meets an obstacle and when such a jet penetrates a cavity. In these flows, the amplitude of oscillations slightly decreases when the turbulent diffusion is taken into account.

Implicit algebraic model for predicting turbulent heat flux in film cooling flow

AbstractThe present study addresses a new effort to improve the prediction of turbulent heat flux in the film cooling flow by applying the implicit algebraic flux (IAF) model of Rogers et al. A three‐dimensional symmetry case is investigated using a film hole length‐to‐diameter ratio of 1.75 and an injection angle of 35∘. The low Reynolds number second moment closure (SMC) model with a wall‐reflection term is employed for simulating the turbulent flow field right up to the wall. Results obtained from the IAF model are compared with two other algebraic turbulent heat flux models, namely, the simple eddy diffusivity (SED) with a constant turbulent Prandtl number and the generalized gradient diffusion hypothesis (GGDH). Comparisons of the turbulent heat flux components calculated by these models show that the major difference appears in the streamwise turbulent heat flux. These models demonstrate a significant effect on the prediction of film cooling effectiveness. The SED model with a constant prescribed value for the turbulent Prandtl number fails to predict the cooling air spreading in the lateral direction while by employing the GGDH and IAF models, the spreading of the cooling air and the decay of the effectiveness in the core region are reasonably predicted. A combination of the SMC and IAF models for simulating the turbulent flow and heat transfer is capable of predicting the streamwise and lateral film cooling effectiveness in very good agreement with the available experimental data. Copyright © 2009 John Wiley & Sons, Ltd.

Algebraic turbulence modeling in adiabatic gas–liquid annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic gas–liquid annular two-phase flow. After reviewing the existing literature, two new algebraic turbulence models are proposed for both the liquid film and the droplet laden gas core of annular two-phase flow. Both turbulence models are calibrated with experimental data taken from the open literature and their performance critically assessed. Although the proposed turbulence models reproduce the key parameters of annular flow well (average liquid film thickness and pressure gradient) and the predicted velocity profiles for the core flow compare favorably with available core flow velocity measurements, a more accurate experimental database is required to further improve the models accuracy and range of applicability.