Computation Of Turbulent Flows Research Articles

Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests

This article reports on the potential of application of LES in the calculation of turbulent two-phase flows, in the case where each phase is resolved and interfaces remain much larger than the mesh size. In comparison with single-phase flow, successful application of LES to resolve two-phase flow problems should account for the complex interaction between turbulence and interfaces. Non-linear transfers of turbulent energy across the interface have to be accurately modeled. The derivation of the complete filtered two-phase flow governing equations has been formulated to deal with turbulence at the interface in a comprehensive and practical way. Explicit filtering of 2D direct numerical simulations has been employed to evaluate the order of magnitude of the new subgrid contributions. A parametric study on the academic test case of two counter-rotative vortices and a more complex test case of phase inversion in a closed box have been utilized to perform an order of magnitude analysis of different transport mechanisms. Important features of turbulent energy transfer across the interface have been discussed. Analyses of the numerical results have been conducted to derive conclusions on the relative importance of the different subgrid scale contributions, and modeling issues and solutions are provided.

Modelling and computation of unsteady turbulent cavitation flows

Unsteady turbulent cavitation flows in a Venturi-type section and around a NACA0012 hydrofoil were simulated by two-dimensional computations of viscous compressible turbulent flow model. The Venturi-type section flow proved numerical precision and reliability of the physical model and the code, and further the cavitation around NACA0012 foil was investigated. These flows were calculated with a code of SIMPLE-type finite volume scheme, associated with a barotropic vapor/liquid state law which strongly links density and pressure variation. To simulate turbulent flows, modified RNG k − ɛ model was used. Numerical results obtained in the Venturi-type flow simulated periodic shedding of sheet cavity and was compared with experiment data, and the results of the NACA0012 foil show quasi-periodic vortex cavitation phenomenon. Results obtained concerning cavity shape and unsteady behavior, void ratio, and velocity field were found in good agreement with experiment ones.

원추 유동 해와 최적화 기법을 이용한 축대칭 초음속 흡입구의 예비 설계

초음속 축대칭 흡입구의 형상 설계를 위하여 원추 유동 해법과 충격파 근사 기법을 기반으로 하고 구배 기반의 최적화 기법을 이용한 설계 프로그램을 개발하였다. 압력 회복률과 항력을 고려한 두 가지 목적 함수에 대하여 충격파 위치와 카울의 형상, 흡입관 목 면적 등에 대한 제한 조건 등을 고려하여 여러 운용 조건에 대해 흡입구 설계를 수행하였다. 최적 설계를 위하여 압력 회복률과 항력을 동시에 고려한 목적 함수를 제안하고 압력 회복률만을 고려하여 설계된 흡입구 형상과 비교하였다. 설계된 결과는 전산 유체 역학을 이용한 비점성/점성 유동 해석으로부터 산출된 흡입구 성능 결과와 비교하여 검증하였으며 예측된 성능이 계산된 결과와 잘 일치하였다. Design program was developed to determine the external shape of the supersonic axisymmetric inlet by combining conical flow solver and approximation technique of conical shock with gradient-based optimization algorithm. Inlet designs were carried out under various operation conditions through optimization with respectively two object functions which consist of pressure recovery and cowl drag and with constraints about shock position, cowl shape, and minimum throat area. New object function consisting of pressure recovery and drag of the external cowl was proposed and the optimized shapes from new object function were compared to the ones from the old object function which maximize only the pressure recovery. Through computations of inviscid and turbulent flow, was tested performance of the design program and performance estimated in design program agreed well with computation results for inlets designed under various flight conditions.

Finite element computation of turbulent flow past a multi-element airfoil

Flow past multi-element airfoil is studied via two-dimensional numerical simulations. The incompressible Reynolds averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite element formulation. The Spalart–Allmaras and Baldwin–Lomax models are employed for turbulence closure. The implementation of the Spalart–Allmaras model is verified by computing flow over a flat plate with a specified trip location. Good agreement is seen between the results obtained with the two models for flow past a NACA 0012 airfoil at 5° angle of attack. Results for the multi-element airfoil, with the two turbulence models, are compared with experiments for various angles of attack. In general, the pressure distribution, from both the models matches quite well with the experimental results. However, at larger angles of attack, the computational results overpredict the suction peak on the slat. The velocity profiles from the Baldwin–Lomax model are, in general, more diffused compared to those from the Spalart–Allmaras model. The agreement between the computed and experimental results is not too good in the flap region for large angles of attack. Both the models are unable to predict the stall; the flow remains attached even for relatively large angles of attack. Consequently, the lift coefficient is over predicted at large α by the computations. Overall, compared to the Baldwin–Lomax model, the predictions from the Spalart–Allmaras model are closer to experimental measurements.

A multiblock joint PDF finite-volume hybrid algorithm for the computation of turbulent flows in complex geometries

A new hybrid joint probability density function (JPDF) solution algorithm for turbulent flows in complex 3D geometries is presented. The main focus is to demonstrate the applicability of JPDF methods for complex flows as observed in industrial applications. All elements of the algorithm are explained in detail and extensive validation studies are presented. A multiblock finite-volume solver, capable of handling globally unstructured, locally structured grids, was implemented together with a Lagrangian particle method. Efficient and robust particle management and accurate schemes for estimation and interpolation of particle statistics have been developed. For numerical efficiency particle sub-time stepping and an implicit finite-volume solver are applied. A fast coupling strategy was developed together with a multigrid method that allows very fast convergence on refined grids. Comparison with an established JPDF code for a bluff-body stabilized flow shows very good agreement. Furthermore, robustness and consistency of the algorithm for turbulent flow simulations with complex geometry is demonstrated.

Impact of Subgrid-Scale Models on Jet Turbulence and Noise

Introduction V ISBAL and Rizzetta1 and Visbal et al.2 have recently performed large-eddy simulation (LES) calculations of turbulent channel flow and compressible isotropic turbulence decay without using any explicit subgrid-scale (SGS) model. In those simulations, spatial filtering was treated as an implicit SGS model. They also showed that use of an SGS model in those simulations did not produce results superior to those obtained without employing an SGS model. Bogey and Bailly3 also performed LES calculations for jet flows by using spatial filtering only. Moreover, they brought up the issue of the effects of the eddy–viscosity-based Smagorinsky SGS model on jet noise in yet another recent study.4,5 They showed that the high-frequency portion of the noise spectra was significantly suppressed by the eddy–viscosity. It is well understood that in turbulent flows the energy cascade is associated with a mean flux of energy that is directed from large scales toward small scales. The large scales contain the major part of the turbulent kinetic energy, and they continuously feed the turbulent kinetic energy via the cascade to the smallest eddies where it is dissipated. Because the grid resolution is too coarse to resolve all of the relevant length scales in an LES, the pile-up of energy at high wave numbers can be eliminated through the use of a spatial filter. Hence, the spatial filter can be thought of as an effective SGS model in an LES. In this study, we perform two jet simulations to study the impact of the SGS model on jet turbulence and far-field noise. The first simulation does not employ any explicit SGS model, but treats the spatial filter as an implicit SGS model. In the second simulation, we employ a localized version of the dynamic Smagorinsky model (DSM) (see Ref. 6) and keep all test case parameters the same as those in the first simulation. We examine the differences between the two simulations to quantify the effect of the SGS model on the near-field jet turbulence and the far-field noise. Although this study is similar to those done by Bogey and Bailly,4,5 our work additionally does a comparison of the two LES results with experimental jet noise spectra with the hope

Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles

The main purpose of this article is to investigate the effects of the subgrid fluid turbulence on the motion of nonsettling colliding particles suspended in steady homogeneous isotropic turbulent flow. An additional goal is to characterize the statistical properties of the subgrid fluid turbulence “viewed” by inertial particles to support the development of large eddy simulation (LES) approach for particle-laden turbulent flows. Two types of numerical experiments have been carried out: first, the discrete particle trajectories were computed using the fluid velocity field given by direct numerical simulation (DNS) in order to characterize the small-scale fluid velocity fluctuations “seen” by the particles. In a second stage, the particle trajectory simulations were performed using several filtered velocity fields computed from the DNS data to evaluate the effect of the subgrid fluid turbulence on the particle statistics (turbulent dispersion, kinetic energy, accumulation efficiency, particle-particle relative velocity and collision frequency). The first part of this study shows that particle inertia has a limited effect on the subgrid fluid turbulent statistics: subgrid kinetic energy and Lagrangian integral time scale measured along the particle trajectories. In addition, the subgrid fluid Lagrangian integral time scale is found to be nearly equal to the subgrid Eulerian integral time scale and proportional to the ratio of the filter width to the whole fluid turbulent velocity. The second part shows that the particle turbulent dispersion and kinetic energy are affected by the filtering only when a significant percentage of the turbulent kinetic energy was removed from the velocity field seen by the particles. In contrast, accumulation and collision phenomena are found to be significantly influenced by the subgrid fluid velocity fluctuations when the particle response time is of the same order or smaller than the subgrid Lagrangian integral time scale measured along particle paths. Finally, these results are used to characterize, in terms of particle response time to subgrid time scale ratio, the validity range of LES for the computation of gas-solid turbulent flow.

Runge‐Kutta based calculation of turbulent forced convection flows of metallic liquids through tubes

PurposeTo provide a suitable linkage of a computational fluid dynamics code and a shape optimization code for the augmentation of local heat transfer coefficients in forced convection channels normally used in the cooling of electronic equipment.Design/methodology/approachA parallel‐plate channel with a discrete array of heat sources embedded in one wall, while the other wall is insulated, constitutes the starting model. Using water as coolant, the objective is to optimize the shape of the channel employing a computerized design loop. The two‐part optimization problem is constrained to allow only the unheated wall to deform, while keeping the same inlet shape and observing a maximum pressure drop constraint.FindingsFirst, the results for the linearly deformed unheated wall show significant decrease compared with the wall temperatures of the heated wall, with the maximum wall temperature occurring slightly upstream of the outlet. Second, when the unheated wall is allowed to deform nonlinearly, a parabolic‐like shaped wall is achieved where the maximum wall temperature is further reduced, with a corresponding intensification in the local heat transfer coefficient. The effectiveness of the computerized design loop is demonstrated in complete detail.Originality/valueThis paper offers a simple technique for optimizing the shapes of forced convection channels subjected to pre‐set design constraints.

받음각을 갖는 축대칭 물체의 후류 유동 계산

The turbulent wake flow of an axisymmetric body at incidence of <TEX>$10.1^{\circ}$</TEX> is investigated by commericial CFD code, Fluent 6.2. Reynolds stress turbulence model with wall function is applied for the turbulent flow computation. For the grid generation, the Gridgen V15 is used. Numerical predictions are compared with experimental data for the validation. The computed results show goof agreements with the experimental measurements, implying that the CFD analysis is a useful and efficient tool for predicting turbulent flow characteristics of wake field of an axisymmetric body at incidence.

Investigation on RANS Computation for Unsteady Turbulent Flow (In Case of Backward-Facing Step Flow with Periodic Perturbation)

With improving a computer hardware and CFD software, the problems treated in industries tend to be more complex, physically and geometrically. The turbulent flow with strong unsteadiness is one of physically complex examples. Since Large Eddy Simulation (LES) is still too time-consuming, a great number of unsteady Reynolds-Averaged Navier-Stokes (RANS) computations have been employed in such engineering applications. However, the applicability of RANS to unsteady flows has not been clear. In the present study, RANS computations for two-dimensional turbulent flow with periodic perturbation over a backward-facing step are performed to verify the performance of a low-Reynolds-number type k-ε turbulence model. Visualizing and investigating the temporal change of the flow pattern and the instantaneous term-by-term budget of the governing equations, it is clarified that the RANS computation can reproduce the unsteady nature satisfactorily, and why the RANS model captures the unsteady turbulent flow reasonably.

LARGE EDDY SIMULATION OF TURBULENT INCOMPRESSIBLE FLUID FLOWS BY A NINE-NODES CONTROL VOLUME-FINITE ELEMENT METHOD

The main purpose of this work is the numerical computation of turbulent incompressible fluid flows by a nine-node control volume finite element method (CVFEM) using the methodology of large-eddy simulation.. The domain is discretized using nine nodes finite elements and the equations are integrated into control volumes around the nodes of the finite elements. The Navier?Stokes equations are filtered for simulation of the large scales variables and the sub-grid scales stress appearing due to the filtering process are modeled through the eddy viscosity model of Smagorinsky. The two-dimensional benchmark problem of the lid-driven cavity flow is solved to validate the numerical code and preliminary results for the horizontal and vertical velocity profiles at the centerlines of the cavity and the stream functions are presented and compared with available results from the literature.

LARGE EDDY SIMULATION OF TURBULENT INCOMPRESSIBLE FLUID FLOWS BY A NINE-NODES CONTROL VOLUME-FINITE ELEMENT METHOD

The main purpose of this work is the numerical computation of turbulent incompressible fluid flows by a nine-node control volume finite element method (CVFEM) using the methodology of large-eddy simulation.. The domain is discretized using nine nodes finite elements and the equations are integrated into control volumes around the nodes of the finite elements. The Navier?Stokes equations are filtered for simulation of the large scales variables and the sub-grid scales stress appearing due to the filtering process are modeled through the eddy viscosity model of Smagorinsky. The two-dimensional benchmark problem of the lid-driven cavity flow is solved to validate the numerical code and preliminary results for the horizontal and vertical velocity profiles at the centerlines of the cavity and the stream functions are presented and compared with available results from the literature.

Turbulent compressible fluid flow computation in a male rotor‐housinggap of screw compressors

AbstractThis contribution is devoted to a turbulent compressible fluid flow computation through a 2‐D model of the male rotor‐housing gap in screw compressors. For the numerical solution of the nonlinear conservative system of the Favre‐averaged Navier‐Stokes equations the cell‐centred finite volume formulation of the explicit two‐step TVD MacCormack scheme proposed by Causon on a structured quadrilateral grid is used. The turbulent viscosity is calculated by using the algebraic Baldwin‐Lomax turbulence model which is implemented into the own developed numerical code. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD)

The streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) methods are among the most popular stabilized formulations in finite element computation of flow problems. The discontinuity-capturing directional dissipation (DCDD) was first introduced as a complement to the SUPG and PSPG stabilizations for the computation of incompressible flows in the presence of sharp solution gradients. The DCDD stabilization takes effect where there is a sharp gradient in the velocity field and introduces dissipation in the direction of that gradient. The length scale used in defining the DCDD stabilization is based on the solution gradient. Here we describe how the DCDD stabilization, in combination with the SUPG and PSPG stabilizations, can be applied to computation of turbulent flows. We examine the similarity between the DCDD stabilization and a purely dissipative energy cascade model. To evaluate the performance of the DCDD stabilization, we compute as test problem a plane channel flow at friction Reynolds number Re τ = 180.

On steady state computation of turbulent flows using k–ε models approximated by the time splitting method

AbstractThe time splitting method is frequently used in numerical integration of flow equations with source terms since it allows almost independent programming for the source part. In this paper we will consider the question of convergence to steady state of the time splitting method applied to k–ε turbulence models. This analysis is derived from a properly defined scalar study and is carried out with success for the coupled k–ε equations. It is found that the time splitting method does not allow convergence to steady state for any choice of finite values of the time step. Numerical experiments for some typical turbulent compressible flow problems support the fact that the time splitting method is always nonconvergent, while its nonsplitting counterpart is convergent. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Robust and efficient computation of turbulent flows around civil transport aircraft at flight Reynolds numbers

This work aims at providing numerical methods that enable the robust and efficient simulation of turbulent flows around civil transport aircraft configurations at flight Reynolds numbers. Robustness problems related to the multigrid treatment of advanced transport equation turbulence models have been identified preventing convergence of simulations at high or flight Reynolds numbers. Therefore the application of multigrid to the turbulence equations is omitted while the multigrid treatment of the mean flow equations stays unchanged. Moreover, a fully implicit time integration scheme – a DDADI approach – is applied to the turbulence equations. The new approach raised robustness to a sufficient level to converge viscous computations at flight Reynolds numbers. Furthermore, the convergence speed of aerodynamic coefficients for three dimensional applications has also been improved significantly.

Will RANS Survive LES? A View of Perspectives

The paper provides a view of some developments and a perspective on the future role of the Reynolds-averaged Navier-Stokes (RANS) approach in the computation of turbulent flows and heat transfer in competition with large-eddy simulations (LES). It is argued that RANS will further play an important role, especially in industrial and environmental computations, and that the further increase in the computing power will be used more to utilize advanced RANS models to shorten the design and marketing cycle rather than to yield the way to LES. We also discuss some current and future developments in RANS aimed at improving their performance and range of applicability, as well as their potential in hybrid approaches in combination with the LES strategy. Limitations in LES at high Reynolds (Re) and Rayleigh (Ra) number flows and heat transfer are revisited and some hybrid RANS/LES routes are discussed. The potential of very large eddy simulations (VLES) of flows dominated by (pseudo)-deterministic eddy structures, based on transient RANS (T-RANS) and similar approaches, is discussed and illustrated in an example of “ultra-hard” (very high Ra) thermal convection.

Simulations of incompressible fluid flows by a least squares finite element method

In this work simulations of incompressible fluid flows have been done by a Least Squares Finite Element Method (LSFEM) using velocity-pressure-vorticity and velocity-pressure-stress formulations, named u-p-omega and u-p-tau formulations respectively. These formulations are preferred because the resulting equations are partial differential equations of first order, which is convenient for implementation by LSFEM. The main purposes of this work are the numerical computation of laminar, transitional and turbulent fluid flows through the application of large eddy simulation (LES) methodology using the LSFEM. The Navier-Stokes equations in u-p-omega and u-p-tau formulations are filtered and the eddy viscosity model of Smagorinsky is used for modeling the sub-grid-scale stresses. Some benchmark problems are solved for validate the numerical code and the preliminary results are presented and compared with available results from the literature.

An artificial compressibility based characteristic based split (CBS) scheme for steady and unsteady turbulent incompressible flows

An artificial compressibility method is presented for the solution of incompressible turbulent flow problems at moderate Reynolds numbers. The presented approach has been used to solve both steady and unsteady state turbulent flow problems. Three different RANS models have been employed to investigate the application of present matrix solution free approach. They are one-equation model of Wolfstein, Spalart–Allmaras model and standard κ– ε model. In addition to the results of standard steady two-dimensional flow problems, solutions to transient two-dimensional flow past a circular cylinder and steady state three-dimensional turbulent flow in a model “upper human airway” are also presented. The results presented demonstrate that the artificial compressibility based CBS scheme is suitable for both steady and unsteady state incompressible turbulent flow calculations at moderate Reynolds numbers.

Assessment of numerical uncertainty for the calculations of turbulent flow over a backward‐facing step

AbstractNumerical uncertainty analysis has been performed for the turbulent flow past a backward‐facing step. The analysis is based on calculations on seven non‐rectangular, but structured, grid sets that were provided by the organizers of the 2004 Lisbon Workshop (Proceedings of the Workshop on CFD Uncertainty Analysis, Lisbon, 21–22 October 2004). The calculations were performed by using a commercial code, namely, FLUENT with the Spalart–Allmaras one‐equation turbulence model. The present study constitutes a calculation verification process: a set of partial differential equations are solved on gradually refined grid sets, the selected quantities are extrapolated, and then the overall numerical uncertainty in selected quantities is estimated by various methods. Some new ideas are presented for estimating the coefficient of variation, which is related to standard deviation (or standard error of estimate in case of the least squares method).The major problem that stands out in extrapolation is the cases of non‐monotonic convergence. For such cases some alternative methods are proposed, and the results are compared to assess these methods. Copyright © 2005 John Wiley &amp; Sons, Ltd.