Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle

In the present study, the turbulent gas flow dynamics in a two-dimensional convergent–divergent rocket nozzle is numerically predicted and the associated physical phenomena are investigated for various operating conditions. The nozzle is assumed to have impermeable and adiabatic walls with a flow straightener in the upstream side and is connected to a plenum surrounding the nozzle geometry and extended in the downstream direction. In this integrated component model, the inlet flow is assumed a two-dimensional, steady, compressible, turbulent and subsonic. The physics based mathematical model of the considered flow consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The system of the governing equations with turbulent effects is solved numerically using different turbulence models to demonstrate their numerical accuracy in predicting the characteristics of turbulent gas flow in such complex geometry. The performance of the different turbulence models adopted has been assessed by comparing the obtained results of the static wall pressure and the shock position with the available experimental and numerical data. The dimensionless shear stress at the nozzle wall and the separation point are also computed and the flow field is illustrated. The various implemented turbulence models have shown different behavior of the turbulent characteristics. However, the shear-stress transport (SST) k–ω model exhibits the best overall agreement with the experimental measurements. In general, the proposed numerical procedure applied in the present paper shows good capability in predicting the physical phenomena and the flow characteristics encountered in such kinds of complex turbulent flow.     

CFD of turbulent transport of particles behind a backward-facing step using a new model—k-ε-Sp

The k-ε-S_p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models (k-ε-A_p, k-ε-k_p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.     

A model for two coupled turbulent fluids Part III: Numerical approximation by finite elements

Summary. This paper introduces a scheme for the numerical solution of a model for two turbulent flows with coupling at an interface. We consider a variational formulation of the coupled model, where the turbulent kinetic energy equation is formulated by transposition. We prove the convergence of the approximation to this formulation for 2D flows by piecewise affine triangular elements. Our main contribution is to prove that the standard Galerkin - finite element approximation of the Laplace equation approximates in L² norm its solution by transposition, for data with low smoothness. We include some numerical tests for simple geometries that exhibit the behaviour predicted by our analysis.Mathematics Subject Classification (2000): 65 N30, 76M10Revised version received March 24, 2003This research was partially supported by Spanish Government REN2000-1162-C02-01 and REN2000-1168-C02-01 grants     

Turbulent diffusion of mass in circular pipe flow

An implicit finite difference scheme was used to solve the convective-diffusion equation to predict the steady-state transport of a conservative, neutrally bouyant tracer injected along the centreline into a fully developed turbulent pipe flow. Three different distributions for the radial mass diffusivity have been compared with two independent sets of experimental data. The results indicate that the distribution based on the turbulent kinematic eddy viscosity predicted by a k?l model produces the closest agreement between the numerical model predictions and the experimentally observed tracer distribution.     

弯曲扩压管道中三维不可压粘性流的数值计算及湍流模型的研究

为了便于复杂形状管道中粘性流动的数值计算,本文在任意曲线坐标系下导出了控制方程的Favre质量加权平均形式,导出了一种考虑曲率影响的湍流模型.采用抛物化方法对弯曲扩压管道内的层流和湍流流动进行了数值计算.根据计算结果对压气机静叶流道内的气动性能进行了初步的分析.     

High order upwind scheme for modelling turbulent shallow water flow in hydraulic structures

An unstructured finite volume model for quasi-2D free surface flow with wet-dry fronts and turbulence modelling is presented. The convective flux is discretised with either a an hybrid second-order/first-order scheme, or a fully second order scheme, both of them upwind Godunov's schemes based on Roe's average. The hybrid scheme uses a second order discretisation for the two unit discharge components, whilst keeping a first order discretisation for the water depth [2]. In such a way the numerical diffusion is much reduced, without a significant reduction on the numerical stability of the scheme, obtaining in such a way accurate and stable results. It is important to keep the numerical diffusion to a minimum level without loss of numerical stability, specially when modelling turbulent flows, because the numerical diffusion may interfere with the real turbulent diffusion. In order to avoid spurious oscillations of the free surface when the bathymetry is irregular, an upwind discretisation of the bed slope source term [4] with second order corrections is used [2]. In this way a fully second order scheme which gives an exact balance between convective flux and bed slope in the hydrostatic case is obtained. The k – ε equations are solved with either an hybrid or a second order scheme. In all the numerical simulations the importance of using a second order upwind spatial discretisation has been checked [1]. A first order scheme may give rather good predictions for the water depth, but it introduces too much numerical diffusion and therefore, it excessively smooths the velocity profiles. This is specially important when comparing different turbulence models, since the numerical diffusion introduced by a first order upwind scheme may be of the same order of magnitude as the turbulent diffusion. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A large-eddy-based lattice Boltzmann model for turbulent flow simulation

In this paper a novel and simple large-eddy-based lattice Boltzmann model is proposed to simulate two-dimensional turbulence. Unlike existing lattice Boltzmann models for turbulent flow simulation, which were based on primitive-variables Navier–Stokes equations, the target macroscopic equations of the present model are vorticity-streamfunction equations. Thanks to the intrinsic features of vorticity-streamfunction equations, the present model is efficient, stable and simple for two-dimensional turbulence simulation. The advantages of the present model are validated by numerical experiments.     

Space Mapping Approach for Particle Control in Turbulent Flows

Controlling the motion of particles in turbulent flows, the paper at hand presents an efficient space–mapping approach that is based on a hierarchy of models. The approach reduces the highly complex optimization of the k-ε turbulence model for high Reynolds–number flows (fine model) to the cheaper one of the Navier–Stokes equations for smaller Reynolds–number (laminar) flows in direct numerical simulations on coarser grids (coarse model) by help of a space–map function that maps the respective coarse model control onto the desired fine model control. The numerical results are very convincing in terms of accuracy and computational effort. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian Joint PDF Approach for Turbulent Premixed Combustion

A model for premixed turbulent combustion based on a joint velocity probability density function (PDF) method and a progress variable is presented. Compared with other methods employing progress variables, the advantage here is that turbulent mixing of the progress variable requires no modeling. Moreover, by applying scale separation, the Lagrangian framework allows to account for the embedded, quasi laminar flame structure in a very natural way. The numerical results presented here are based on a simple closure of the progress variable source term and it is demonstrated that the new modeling approach is robust and shows the correct qualitative behavior. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

An efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cross-relaxation dynamics on anomalous saturation processes in low pressure supersonic cw HF chemical laser amplifier

It is assumed that both translational and rotational nonequilibrium cross-relaxations play a role simultaneoulsy in low pressure supersonic cw HF chemical laser amplifier. For two-type models of gas flow medium with laminar and turbulent flow diffusion mixing, the expressions of saturated gain spectrum are derived respectively, and the numerical calculations are performed as well. The numerical results show that turbulent flow diffusion mixing model is in the best agreement with the experimental result. Project supported by the National Natural Science Foundation of China (Grant No. 19474036) and by the Laboratory of Hih-temperature Gas Dynamics. Insititute of Mechanics, Chinese Academy of Sciences (Grant No. KJ951-E-202).     

Multiphase Jet Flow in Abrasive Water Jet Cutting

A numerical model for ultra-high velocity abrasive water jets (AWJ) is developed and jet dynamic characteristics are calculated under steady-state, turbulent, compressible, multi-phase flow conditions. The model is tested by comparison with analytical solutions for related theoretical problems, generally with very good agreement. Simulations of more realistic flows produce the expected values and behavior. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Φ—伪压缩型映象的具误差的lshikawa和Mann迭代程序的收敛性问题

引入Φ－伪压缩型映象的概论,并研究了此类映象的具误差的Ｉｓｈｉｋａｗａ和Ｍａｎｎ迭代程序的收敛性问题。本文结果改进和发展了许多人的最新结果。     

各向异性湍浮力模型的研究

通过对隐式代数应力模型应力结构的分析,认为湍浮力流动的应力由应变和浮力作用引起,从而利用应力输运的线性近似和平衡近似提出了非线性各向异性湍浮力模型·　该模型避免了数值奇异,其可靠性通过计算和实验的对比得到了验证·     

Numerical modelling of turbulent flow over rough walls

The numerical simulation of turbulent flow over rough walls was carried out for various types of roughness. The mathematical model was based on the Reynolds averaged Navier-Stokes equations for incompressible flow. The two-equation SST and oneequation Spalart-Allmaras turbulence models were used. Boundary conditions on rough walls were prescribed directly on the wall using the SST model modified to account for wall roughness by Hellsten and Laine (1997) and the SA model modified by Aupoix and Spalart (2003). Turbulence models were tested for the constant pressure turbulent boundary layer on the rough wall formed by commercial abrasive paper and by tightly packed spheres. The effect of wall roughness on the decelerated flow over a smoothly contoured ramp with flow separation was investigated. Obtained results were compared with experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A self-similar premixed turbulent flame model

This paper is devoted to premixed combustion modelling in turbulent flow. First, we derive a model for the turbulent flame velocity based on the observed self-similarity of the turbulent flame. The model uses the local flame brush width as a fundamental parameter and, therefore, we show how it can be retrieved for numerical implementation. The diffusive property of the brush width is treated in such a way as to theoretically let the brush have a clearly defined boundary propagating at finite velocity. The model, implemented in Star-CD CFD software through user programming, is then numerically tested on three configurations for which another model, the Turbulent Flame Closure model, is known to give very good agreement. Some effects of numerics are commented and results for both models are compared. While based on very different approaches the two models lead to substantially similar results. In this way, we have shown that the local brush width can effectively be used, giving an additional degree of freedom for premixed turbulent combustion modelling.     

Fast spectral solutions of the double-gyre problem in a turbulent flow regime

Several semi-analytical models are considered for a double-gyre problem in a turbulent flow regime for which a reference fully numerical eddy-resolving solution is obtained. The semi-analytical models correspond to solving the depth-averaged Navier–Stokes equations using the spectral Galerkin approach. The robustness of the linear and Smagorinsky eddy-viscosity models for turbulent diffusion approximation is investigated. To capture essential properties of the double-gyre configuration, such as the integral kinetic energy, the integral angular momentum, and the jet mean-flow distribution, an improved semi-analytical model is suggested that is inspired by the idea of scale decomposition between the jet and the surrounding flow.     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．     

Drag reduction via wall-normal oscillations in turbulent flat plate boundary layer flow at very high Reynolds number

The effects of wall-normal single point oscillations in turbulent boundary layers at very high Reynolds number are investigated by numerical simulation. The impact on the friction drag and on the turbulent structures is analyzed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)