Numerical simulation of turbulent flow in the inlet region of a smooth pipe

An algebraic-Q4 turbulent eddy viscosity model expresses the eddy viscosity as a solution of a quartic (Q4) equation. The model is applied to numerical simulation of developing turbulent flow in the inlet region of a smooth pipe. Predictions of the flow characteristics, such as velocity profiles accross and along a pipe, pressure drop along a pipe are found in good agreement with experimental data.     

Numerical simulation of a compressible turbulent boundary layer over a conductive wall with line heat source

A conjugated problem of supersonic turbulent flow over a conductive solid wall with an embedded line heat source has been investigated as a model of a separation detector and skin friction gage. The 2-D Navier-Stokes equations for compressible fluid, including a two layer eddy viscosity model, are solved simultaneously with the heat transfer equation for the solid, written in general coordinates. The effect of the interface boundary condition on the stability of the implicit scheme of the flow field has been checked. A careful investigation of the effect of heat source strength, solid and fluid conductivity and Mach and Reynolds numbers on flow and temperature fields has been performed. The results of this investigation may be used to design an optimal gage with a minimum influence on the flow field.     

Numerical simulation of three-dimensional turbulent separated and reattaching flows using a modified turbulence model

A modified version of k-ε model is proposed through modification of the damping function of eddy viscosity that incorporates the effect of wall proximity in the near the wall region and the effect of non-equilibrium away from the wall together with the simple model functions in the ε equation. The proposed turbulence model is validated with the available experimental data of reattachment length, mean streamwise velocity distribution, turbulence intensity profile, and wall static pressure coefficient in the turbulent backward-facing step flows. The predicted results with the present model are in good agreement with the experiments. Computed results reveal that the reattachment length (recirculation zone) and the wall static pressure are decreased with increasing inlet velocity. And the asymmetric distributions of the reattachment point, cross-section view of velocity vector, streamwise skin friction coefficient, and turbulent kinetic energy demonstrate the important three-dimensional side-wall effect in an insufficient aspect ratio channel flow.     

An algebraic-Q 4 turbulence model for attached and separated airfoil flows

An algebraic eddy viscosity model, based on a new length scale has been developed. The model proposes the eddy viscosity as a solution of a quartic (Q ₄) equation. The turbulent length scale for attached and separated flows is defined by employing a vorticity functionF =yD introduced in the Baldwin-Lomax model. The algebraic-Q ₄ eddy viscosity model was incorporated into Navier-Stokes code and tested for complex transonic airfoil flows with separation. The results are compared with the experimental data.     

Numerical solution of incompressible flow through branched channels

The work deals with numerical solution of 3D turbulent flow in straight channel and branched channels with two outlets. The mathematical model of the flow is based on Reynolds-averaged Navier–Stokes equations for incompressible flow in 3D with explicit algebraic Reynolds stress turbulence model (EARSM). The mathematical model is solved by artificial compressibility method with implicit finite volume discretization. The channels have constant square or circular cross-section, where the hydraulic diameter is same in order to enable comparison between these numerical simulations. First, developed flow in a straight channel of square cross-section is presented in order to show the ability of the used EARSM turbulence model to capture secondary corner vortices, which are not predicted by eddy viscosity models. Next the flow through channels with perpendicular branch is simulated. Methods of setting the flow rate are discussed. The numerical results are presented for two flow rates in the branch.     

Capturing of transition by the RNG based algebraic turbulence model

This paper concerns the RNG based algebraic turbulence model. This model has characteristics to capture transitional process from laminar to turbulent flow. This is determined by the argument of the Heaviside function, which becomes a threshold for the occurrence of turbulence. It is supposed that proper modeling of this argument will lead to correctly capture transition location. In the present paper, this argument is modeled in such a way that the form of cubic equation for the turbulent kinematic viscosity be maintained. Moreover, the length scale which is required to calculate the turbulent kinematic viscosity is newly proposed, taking into account the freestream pressure gradient. The validation is performed by comparing the calculated results with the empirical expressions as well as the experimental data. This model can simulate the streamwise intermittency effect, by which a sudden increase of skin friction is prevented. Moreover, the transition location can be predicted within reasonable accuracy compared with the experimental data.     

Turbulent boundary layer structure of flow over a smooth-curved ramp

The effects of a convex-curved wall followed by a recovery over a flat surface on a turbulent boundary layer structure are addressed via large-eddy simulation (LES). The curved wall constitutes a smooth ramp formed by a portion of circular arc. The statistically two-dimensional upstream boundary layer flow is realistically fed by an injected inflow boundary condition. The inflow is extracted from a simultaneously simulated flat-plate boundary layer which is computed based on a compressible rescaling method. After flowing over the curved surface the flow is allowed to recover its realistic condition by passing over a downstream flat surface. The Reynolds number introduced at the inlet section of the computational domain which starts 4 times the ramp length (L_r) upstream of the curved surface is Re_δo=U_∞δ_o/ν=9907. The Reynolds number is based on the inflow boundary layer thickness δ_o, the free-stream velocity U_∞ and the kinematic viscosity ν.Mean flow predictions obtained using the present LES with the rescaling–recycling inflow condition agree well with the available experimental data from literature. The Reynolds stress components match the experimental one. However, small deviation occurs due to the smaller-domain height used in the present simulation. The experiments showed that there is a generated pressure gradient on the upper wall and this in return affects the turbulence energy on the other wall. The numerical data as well as the experiments show an enhancement of the turbulent stresses in the adverse pressure gradient region. The increased level of turbulent stresses is accompanied with large peaks aligned with the inflection point of the velocity profiles. The high stress levels are nearly unchanged by reattachment process, decaying only after the mean velocity recovered and the high production of turbulence near the outer layer drops. The recovery of the outer layer is due to the turbulent eddies generated by the separation region. Numerical visualizations show strong elongation and lifting of eddies in the region of the adverse pressure gradient generated by the curved wall. Computations of two-point correlations are also performed to represent the formation and deformation of the turbulent eddies before, over and after the curved wall. Different effects on the eddy size and its structure angle are presented.     

An investigation of pulsating turbulent open channel flow by large eddy simulation

Pulsating turbulent open channel flow is investigated by use of large eddy simulation (LES) technique coupled with a dynamic subgrid-scale (SGS) model for turbulent SGS stress. The three-dimensional filtered Navier-Stokes equation is numerically solved by a fractional-step method. The objective of this study is to deal with the behaviors of pulsating turbulent open channel flow, in particular turbulence characteristics in the free surface-influenced layer, and to examine the reliability of the LES approach for predicting the pulsating turbulent flow with a free surface. In this study, the frequency of driving pressure gradient ranges low, medium and high value. The mean and phase-averaged statistical turbulence quantities, the resolved turbulent kinetic energy and Reynolds stresses budgets, and the flow structures are obtained and analyzed. With the increase of the driving frequency, the depth of the surface-influenced layer increases and the turbulent Stokes length near the bottom wall decreases. Different turbulence characteristics between the accelerating and decelerating phases are interpreted comprehensively. Turbulence intensities reveal that turbulent flow has a strong anisotropy in the free surface-influenced layer, in particular in the decelerating phases during the pulsating cycle. The budget terms of the resolved turbulent kinetic energy, the vertical and spanwise Reynolds stresses in the free surface region are analyzed. The flow structures clearly exhibit that bursting processes near the bottom wall are ejected toward the surface and the most surface renewal events are closely correlated with the bursting processes. These processes are strengthened during the decelerating period since strong turbulence intensities are generated.     

A new second-order closure model for rough-wall turbulent flows using the Brinkman equation

A second-order turbulence closure is developed for the new rough-wall layer modeling approach using the Brinkman equation for turbulent flows over rough walls. In the proposed approach, we model the fluid dynamics of the volume averaged flow in the near-wall rough layer by using the Brinkman equation. The porosity can be calculated based on the volumetric characteristics of the roughness and the permeability is modeled. Interface stress jump conditions including the Reynolds stress components are also considered. The Reynolds-averaged Navier-Stokes equations are solved numerically above the near-wall rough layer, while a second-order turbulence closure is employed in all regions. The rough-wall second-order closure is developed by adopting an existing smooth-wall model. The computational results, including the skin friction coefficient, the log-law mean velocity, the roughness function, the Reynolds stresses, and the turbulent kinetic energy, are presented and compared with those obtained by using a previously developed two-equation turbulence closure. The results show that the new rough-wall layer modeling approach with the second-order turbulence closure model satisfactorily predicted the skin friction coefficient, the log-law mean velocity, the roughness function, and the Reynolds shear stress. However, the results for the Reynolds normal stresses are different from the measured data in the inner 20-60% of the boundary layer due to the interface stress jump conditions employed in the present rough-wall layer modeling approach.     

Prediction of complex flow fields using higher-order turbulent closures

The tool of choice in computing turbulent flows of engineering interest is the Reynolds averaged Navier-Stokes equations for the mean motion, coupled with a closure scheme for the unknown higher-order turbulent correlations. The focus of this paper is to discuss some recent advances in turbulent closure schemes and their application to a weakly compressible flow. Specifically highlighted are the development and utilization of formulations for obtaining explicit algebraic stress and dissipation rate models. Results are presented for the flow over a two-dimensional single element airfoil as well as the downstream wake flow using the explicit algebraic stress model with a comparison to both experiment and a standard isotropic eddy viscosity model.     

An investigation of turbulent open channel flow with heat transfer by large eddy simulation

Large eddy simulation of fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. Two typical temperature boundary conditions, i.e., constant temperature and constant heat flux being maintained at the free surface, respectively, are used. The objective of this study is to explore the behavior of heat transfer in the turbulent open channel flow for different temperature boundary conditions and to examine the reliability of the LES technique for predicting turbulent heat transfer at the free surface, in particular, for high Prandtl number. Calculated parameters are chosen as the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel depth. Some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures based on the velocity, vorticity and temperature fluctuations, are analyzed.     

Numerical simulation of turbulent combustion of subsonic gas jet flows

A physical and mathematical model of turbulent combustion of subsonic gas fuel jet flows flowing into an air space is proposed. The processes are described by averaged equations of the boundary layer with a turbulent viscosity model and a combustion diffusion model. As turbulent viscosity models, the well-known two-parameter k-? standard and k-?? models are taken. The results of the averaged and pulsating flow characteristics?? comparison of numerical calculations with the experimental data are presented.     

An algebraic stress model for stratified turbulent shear flows

Utilizing a simple time dependent one dimensional example as a test case this paper discusses a solution which represents the important characteristics of a bouyancy dominated shear flow by solving four partial differential equations in addition to the mean equations of motion. This suggested model solves equations for total turbulent kinetic energy, $\text{k}$, total turbulent temperature fluctuations, $\text{k}{}_{\mathrm{t}}$, eddy dissipation, ?, and thermal eddy dissipation, ?_$\text{t}$. Three separate versions of this model are discussed—an algebraic length scale version, a Prandtl-Kolmogorov eddy viscosity version, and an algebraic stress and heat flux model. The final version (requiring six partial differential equations) manages to replicate results for a much more complicated version (requiring ten partial differential equations). The advantages for two and three dimensional problems are even greater.     

Large eddy simulation of complex flow fields

The large eddy simulation (LES) technique can provide detailed information about time-dependent and three-dimensional turbulent flow fields at high Reynolds number. The application of LES to practical problems and in the basic study of turbulence require investigation. More studies are needed on the boundary conditions and on the subgrid-scale (SGS) model in order to make LES practical. In this paper, the laws of the wall (two-layer model or Spalding's law) are applied as a special approach to the solid boundary in LES. This wall boundary condition is adapted to plane channel flow and the suitability of this method is tested. Further, improvements of the SGS model in which the Smagorinsky model coefficient C_S is not constant are attempted. Recently, Yoshizawa [Phys. Fluids A1(7), 1293 (1989)] derived the form of the variable C_S from a statistical analysis. Here, we optimize this new model in both the decay of isotropic turbulence and plane channel flow simultaneously.     

基于等离子流动控制的翼型减阻技术

为研究基于等离子流动控制的减阻技术,基于Langtry-Menter转捩模型提出边界层转捩数值模拟技术.该技术可有效结合转捩模型与湍流模型,用标准模型验证其精确性,为采用等离子流动控制抑制边界层分离和转捩研究提供数值模拟平台.采用基于现象学模型的等离子流动控制数值模拟技术,对流动分离以及边界层转捩抑制进行数值模拟,为基于等离子流动控制的翼型减阻技术提供参考.     

Multiscale modelling strategy using the lattice Boltzmann method for polymer dynamics in a turbulent flow

Polymer dynamics in a turbulent flow is a problem spanning several orders of magnitude in length and time scales. A microscopic simulation covering all those scales from the polymer segment to the inertial scale of turbulence remains improbable within the foreseeable future. We propose a multiscale simulation strategy to enhance the spatio-temporal resolution of the local Lagrangian turbulent flow by matching two different simulation techniques, i.e. direct numerical simulation for the flow as a whole, and the lattice Boltzmann method coupled to polymer dynamics at the Kolmogorov dissipation scale. Local turbulent flows sampled by Lagrangian tracer particles in the direct numerical simulation are reproduced in the lattice Boltzmann model with a finer resolution, by supplying the latter with both the correct initial condition as well as the correct time-dependent boundary condition, sampled from the former. When combined with a Molecular Dynamics simulation of a polymer chain in the lattice Boltzmann model, it provides a strategy to simulate the passive dynamics of a polymer chain in a turbulent flow covering all these scales. Although this approach allows for a fairly realistic model of the macromolecule, the back-coupling to the flow on the large scales is missing.     

直方槽道中重力对颗粒相二次流的影响

采用Eulerian／Lagrangian方法模拟直方槽道中气粒两相流动过程。气相采用大涡模拟方法,直接求解大尺度涡运动,小尺度涡采用标准的Smagorinsky亚格子模式模拟,壁面采用幂次率应力模型代替无滑移边界条件。颗粒相采用轨道模型求解。大涡模拟预报的气相平均速度与DNS结果相吻合。结果表明,在直方槽道流向截面,气相存在二次流现象。受气相二次流的作用,颗粒相也存在类似于气相的二次流现象,并考察了重力对颗粒相二次流的影响。     

Direct numerical simulation of flow separation around a NACA 0012 airfoil

Direct numerical simulation (DNS) for the flow separation and transition around a NACA 0012 airfoil with an attack angle of 4° and Reynolds number of 10⁵ based on free-stream velocity and chord length is presented. The details of the flow separation, detached shear layer, vortex shedding, breakdown to turbulence, and re-attachment of the boundary layer are captured in the simulation. Though no external disturbances are introduced, the self-excited vortex shedding and self-sustained turbulent flow may be related to the backward effect of the disturbed flow on the separation region. The vortex shedding from the separated free shear layer is attributed to the Kelvin-Helmholtz instability.     

The Reynolds stress vector and tensor

The problem of the asymmetry of the stress tensor is considered. The mechanism of the origination of turbulence in a flow is shown. On the basis of a vector form of the Newton’s law for the viscous liquid, a tensor of the generalized viscosity coefficient whose components take into account both the molecular and turbulent viscosity is introduced. It is shown that the Reynolds turbulent stresses can be represented as a Reynolds stress vector. An expression is found for the Reynolds stresses in the boundary layer approximation.     

Large eddy simulation of turbulent open duct flow using a lattice Boltzmann approach

Large eddy simulations of turbulent open duct flow are performed using the lattice Boltzmann method (LBM) in conjunction with the Smagorinsky sub-grid scale (SGS) model. A smaller value of the Smagorinsky constant than the usually used one in plain channel flow simulations is used. Results for the mean flow and turbulent fluctuations are compared to experimental data obtained in an open duct of similar dimensions. It is found that the LBM simulation results are in good qualitative agreement with the experiments.