Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.     

Hybrid LES-RANS using synthesized turbulent fluctuations for forcing in the interface region

The main bottleneck in using Large Eddy Simulations at high Reynolds number is the requirement of very fine meshes near walls. One of the main reasons why hybrid LES-RANS was invented was to eliminate this limitation. In this method unsteady RANS (URANS) is used near walls and LES is used away from walls. The present paper evaluates a method for improving standard LES-RANS. The improvement consists of adding instantaneous turbulent fluctuations (forcing conditions) at the matching plane between the LES and URANS regions in order to trigger the equations to resolve turbulence. The turbulent fluctuations are taken from synthesized homogeneous turbulence assuming a modified von Kármán spectrum. Both isotropic and non-isotropic fluctuations are evaluated. The new approach is applied to fully developed channel flow and it is shown that the imposed fluctuations considerably improve the predictions. It is found that increasing the prescribed turbulent length scale of the synthesized turbulence provides excellent agreement with the classical log-law.     

Introduction of turbulent model in a mixed finite volume/finite element method

The aim of this work is to present a new numerical method to compute turbulent flows in complex configurations. With this in view, a k-? model with wall functions has been introduced in a mixed finite volume/finite element method. The numerical method has been developed to deal with compressible flows but is also able to compute nearly incompressible flows. The physical model and the numerical method are first described, then validation results for an incompressible flow over a backward-facing step and for a supersonic flow over a compression ramp are presented. Comparisons are performed with experimental data and with other numerical results. These simulations show the ability of the present method to predict turbulent flows, and this method will be applied to simulate complex industrial flows (flow inside the combustion chamber of gas turbine engines). The main goal of this paper is not to test turbulence models, but to show that this numerical method is a solid base to introduce more sophisticated turbulence model.     

无壁面参数低雷诺数非线性涡黏性模式研究

建立了一个低雷诺数的非线性涡黏性湍流模式,该模式的一个显著特性是它不包含壁面参数（如y^ ,n等）,因而特别适用于复杂几何流场的计算,本模式在几种包括回流、分离、激波等典型流动中进行了验证,结果令人满意。     

Parallel large eddy simulation of turbulent flow around MIRA model using linear equal‐order finite element method

A parallel large eddy simulation code that adopts domain decomposition method has been developed for large‐scale computation of turbulent flows around an arbitrarily shaped body. For the temporal integration of the unsteady incompressible Navier–Stokes equation, fractional 4‐step splitting algorithm is adopted, and for the modelling of small eddies in turbulent flows, the Smagorinsky model is used. For the parallelization of the code, METIS and Message Passing Interface Libraries are used, respectively, to partition the computational domain and to communicate data between processors. To validate the parallel architecture and to estimate its performance, a three‐dimensional laminar driven cavity flow inside a cubical enclosure has been solved. To validate the turbulence calculation, the turbulent channel flows at Re_τ = 180 and 1050 are simulated and compared with previous results. Then, a backward facing step flow is solved and compared with a DNS result for overall code validation. Finally, the turbulent flow around MIRA model at Re = 2.6 × 10⁶ is simulated by using approximately 6.7 million nodes. Scalability curve obtained from this simulation shows that scalable results are obtained. The calculated drag coefficient agrees better with the experimental result than those previously obtained by using two‐equation turbulence models. Copyright © 2007 John Wiley & Sons, Ltd.     

PANS模型在空化湍流数值计算中的应用

采用一种基于标准k-ε模型改进的局部时均化模型（Partially-Averaged Navier-Stokes Model,PANS）,并应用于空化流动计算。控制不同的模型参数,分别对绕平头轴对称回转体和Clark-Y型水翼的空化流动进行模拟,并与实验结果进行对比。结果表明：PANS模型中未分解湍动能比率fk的取值对预测空化流动的数值计算精度有重要影响,改变fk的取值可实现对不同滤波尺度范围内的求解;随着fk值的减小PANS的预测精度逐步提高,能在相对较大范围内求解较小尺度的湍流运动过程中,预测到湍流运动中强烈的非定常特性;同时可以比较准确地预测空化流场结构和动力特性。     

Analysis of unsteady gas–liquid flows in a rectangular tank: Comparison of Euler–Eulerian and Euler–Lagrangian simulations

We study the dynamics of gas–liquid flows experimentally and computationally in a rectangular bubble column where the gas source is introduced at the corner. The flow in this reactor is complex and inherently unsteady in nature. The two-dimensional liquid phase velocity field is calculated by an Eulerian approach solving the unsteady Reynolds Averaged Navier Stokes equations. The conservation equations are closed using a two parameter turbulence model. The two-way coupling was accounted for by adding source terms in the conservation equations of the continuous phase to take into account the interaction with the dispersed phase. Bubble tracking is achieved through a Lagrangian approach. Here the equations of motion are solved taking into account the drag, pressure, buoyancy and gravity forces. The time-averaged flows along with the variables which characterize turbulence are analyzed for a wide range of gas flow-rates using Euler–Lagrangian simulations. These simulation predictions are validated with Euler–Eulerian simulations where the gas-phase distribution is captured as a void fraction and PIV experiments. The motion of bubbles induces turbulence in the flow. The applicability of two parameter models for turbulence like the standard k–ε model on time-averaged flow properties is addressed. From the results of the time averaged velocity field, turbulence intensity, turbulent viscosity and gas hold-up profiles, it is concluded that the Euler–Lagrangian model is applicable at lower gas flow-rates. The Euler–Eulerian approach was found to be valid at lower as well as higher gas flow-rates.     

The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 2: Application to Complex Flows

The paper summarises the validation activity performed with the Scale-Adaptive Simulation turbulence model (SAS model) using the two commercial CFD solvers, ANSYS-FLUENT and ANSYS-CFX. Both the KSKL-SAS and the SST-SAS model variants have been tested, although most cases have been computed with the second. The turbulence-resolving capability of the SAS method has been validated with a representative set of test cases, covering both underlying generic flows as well as practical engineering applications. In addition to the purely aerodynamic flows with massive separation and heat transfer they include also such physical phenomena as turbulent combustion and aeroacoustics. The illustrating results show the potentials of the SAS approach for industrial flow simulations. Most of the test case simulations were conducted during the recent EU project “DESider”.     

Interactions of particles and microbubbles with turbulence

Dilute, dispersed two-phase flows arise in many contexts ranging from solid particles or droplets in gas flows to bubbles in liquids. Many of the flows of interest are turbulent, which presents a complex problem to analyze or to determine the dominant physical processes contributing to the observed phenomena. Advances in experimental techniques have made it possible to measure directly turbulent and particle velocity fluctuations in dilute systems. This has provided a counterpart to advances in computational and analytical models and a basis on which to test these models. Three specific areas are considered: the fluctuating forces on an individual particle in an unsteady flow, the response of a solid particle to a turbulent air flow, and the corresponding response of a small bubble in turbulent liquid flows. Results from direct numerical simulations are presented for each of these, including the nonuniform distribution of particles generated by local instantaneous features of the flow. The issue of turbulence modulation at low to moderate void fractions is discussed.     

A two-scale second-moment turbulence closure based on weighted spectrum integration

A two-scale second-moment turbulence closure has been derived based on the weighted integration of the dynamic equation for the covariance spectrum. The goal is to close the Reynolds stress equations with two additional scalar equations that provide separately the scales of the spectral energy transfer and of the turbulence energy dissipation rate. Such a model should provide better prediction of nonequilibrium turbulent flows. The derivation consists of analytical integration of the wave-number-weighted covariance spectrum using a model of the spectral equations with an assumed simple representation of the shape of the energy spectrum. The resulting closure consists of a set of three tensorial equations, one for the Reynolds stress and two for length scale tensors, the latter representing the energy containing- and dissipative eddies respectively. The trace of the two tensor-scale equations leads to a set of two scalar scale parameters. In the equilibrium limit, the model reduces to the standard second-moment single-scale closure. The approach makes it also possible to derive the scale equations in a more systematic manner as compared with the common single-scale and other multi-scale models. The performance of the model in capturing the scale dynamics is illustrated by predictions of several generic homogeneous and inhomogeneous unsteady flows, demonstrating the expected response of the two scale equations. PACS 03.50.De, 04.20-q, 42.65-k     

Numerical simulation of turbulence suppression: Comparisons of the performance of four k-? turbulence models

The standard k-ε model and three low-Reynolds number k-ε models were used to simulate pipe flow with a ring device installed in the near-wall region. Both developing and fully developed turbulent pipe flows have been investigated. Turbulence suppression for fully developed pipe flows revealed by hot-wire measurements has been predicted with all three low-Reynolds number models, and turbulence enhancement has been predicted by the standard k-ε model. All three low-Reynolds number models have predicted similar distributions of velocities, turbulence kinetic energy, and dissipation rate. For developing pipe flows, the region of turbulence suppression predicted by the three low-Reynolds number models is much more extensive (up to 30 pipe diameters downstream of the device) than for full developed flow; whereas the standard k-ε model has only predicted turbulence enhancement.     

Adaptive resolution refinement for pseudospectral simulations of isotropic homogeneous turbulence

Pseudospectral simulations of homogeneous turbulence provide an important class of benchmark flow problems used for fundamental studies of turbulence and for numerical validation purposes. Depending on the numerical resolution, fully resolved computations of homogeneous turbulence can consume large amounts of central processing unit (CPU) time. Here, we present an approach analogous to adaptive mesh refinement for computations performed in physical space to adaptively refine the spectral resolution for pseudospectral computations of isotropic homogeneous turbulent flows. The method is applied to simulations of two-dimensional and three-dimensional isotropic homogeneous turbulence, and the results are compared with direct numerical simulations (DNS) performed using a fixed fine mesh. Significant savings in computational time are found in each case, with little to no compromise in the accuracy of the solutions.     

Large Eddy simulation for engineering applications

In the field of fluid engineering, controlling turbulent flows remains a crucial problem. This paper presents a basis of numerical methods and turbulence models for the large Eddy simulation. Simulation results include the unsteady analyses of complex flows, such as the vortex dynamics of turbulent jets subject to inlet perturbations and the reacting flow with flame propagation in a gas–turbine combustor flow. Applications employing large Eddy simulation are emerging as one of the most important aspects of the “Frontier Simulation Software for Industrial Science” project for the next generation of fluid dynamic design and development.     

Development of projection and artificial compressibility methodologies using the approximate factorization technique

Predictions for two-dimensional, steady, incompressible flows under both laminar and turbulent conditions are presented. The standard k-? turbulence model is used for the turbulent flows. The computational method is based on the approximate factorization technique. The coupled approach is used to link the equations of motion and the turbulence model equations. Mass conservation is enforced by either the pseudocompressibility method or the pressure correction method. Comparison of the two methods shows a superiority of the pressure correction method. Second- and fourth-order artifical dissipation terms are used in order to achieve good convergence and to handle the turbulence model equations efficiently. Several internal and external test cases are investigated, including attached and separated flows.     

Hybrid simulations of the near field of a split-vane spacer grid in a rod bundle

Three-dimensional, unsteady simulations of isothermal turbulent flows in a rod bundle with a split-vane spacer grid have been performed using a segregated turbulence model, which is a combination of scale adaptive simulations and large eddy simulations. These simulations have been conducted within the framework of an international blind CFD benchmark exercise. A finer mesh than that submitted to the benchmark exercise was used for the present study, which improved the agreement of the turbulence predictions with the measurements. For the first time, several vortices were identified in the vicinity of the vanes. The strongest among these vortices, which was a central vortex in the core of each subchannel, was generated by the vane pair in each subchannel. Each vane also created a strong stream across the gap between two rods and towards an adjacent subchannel. Axial profiles of turbulent kinetic energy in each subchannel core exhibited two peaks, a low peak in the near-vane zone and a larger peak one hydraulic diameter downstream of the vanes.     

An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows

An unsteady incompressible Navier–Stokes solver that uses a dual time stepping method combined with spatially high‐order‐accurate finite differences, is developed for large eddy simulation (LES) of turbulent flows. The present solver uses a primitive variable formulation that is based on the artificial compressibility method and various convergence–acceleration techniques are incorporated to efficiently simulate unsteady flows. A localized dynamic subgrid model, which is formulated using the subgrid kinetic energy, is employed for subgrid turbulence modeling. To evaluate the accuracy and the efficiency of the new solver, a posteriori tests for various turbulent flows are carried out and the resulting turbulence statistics are compared with existing experimental and direct numerical simulation (DNS) data. Copyright © 1999 John Wiley & Sons, Ltd.     

Continuation methods applied to the 2D Navier–Stokes equations at high Reynolds numbers

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two‐dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two‐dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

The influence of phase-averaging window size on the determination of turbulence quantities in unsteady turbulent flows

 The phase-averaging window size is shown to affect the measurement of phase-averaged turbulence quantities in unsteady turbulent flows. The flow turbulence is usually estimated on the assumption of quasi-constant flow velocity during the duration of the phase-averaging window. The calculated turbulence level then consists of two parts: one due to the turbulent velocity fluctuations and the other due to the changes in the mean flow velocity. This second part is shown to be directly proportional to the averaging window size. In order to determine the true turbulence the averaging window size has to be made as small as possible, especially if the unsteady flow exhibits large temporal gradients and the flow turbulence itself is small. Received: 9 April 1996/Acceped: 17 August 1996