NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

A Comparative Study for Compressible Turbulence Models

The incompressible models for the pressure-strain correlation are unable to correctly predict the turbulence flows evolving with significant compressibility. Huang and Fu use a damping function of the turbulent Mach number to modify two numerical coefficients of the incompressible model for the pressure strain developed by Launder, Reece and Rodi. This model predicts the spreading rate and the shear stress behavior in compressible turbulent mixing well. However, the model does not show the well-known compressibility effects on the compressible homogenous shear flow. In the present work, the model of Huang-Fu is revised, all resulting model coefficients become dependent on the turbulent Mach number, the gradient Mach number and the convective Mach number. The proposed model is tested in different compressible turbulent homogeneous shear flow and mixing layers cases. In general, the predicted results from the proposed model are in an acceptable agreement with DNS and experiment data.

Artificial neural network-based subgrid-scale models for LES of compressible turbulent channel flow

Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.

Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method

A user-defined three-dimensional （3D） discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete （AC）. The 3D discrete element method （DEM） model of AC was constructed employing a user-defined computer program developed using the ＂Fish＂ language in PFC3D. Important microstructural features of AC were modeled, including aggregate gradation, air voids and mastic. The irregular shape of aggregate particle was modeled using a clump of spheres. The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test, based on which the dynamic modulus and phase angle were calculated from the output stress- strain relationship. The effects of air void content, aggregate stiffness and volumetric fraction on AC modulus were further investigated. The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies. The user- defined 3D model also demonstrated significant improvement over the general existing two-dimensional models.

Three-Dimensional Water-Quality Simulation for River Based on VOF Method

In the present study, considering the transport and transformation processes of variables, a threedimensional water quality model for the river system was established, which coupled the volume of fluid(VOF) method with the k-ε turbulence mathematical model. Then, the water hydrodynamic characteristics and transport processes for BOD_5, NH_(3^-)N and TP were analyzed. The results showed that the water surface of convex bank was a little lower than that of concave bank due to the centrifugal force near the bend, and most concentrations were inferior to the type Ⅴ standard indexes of surface water environmental quality. The model validation indicated that the errors between the simulated and monitored values were comparatively small, satisfying the application demands and providing scientific basis and decision support for the restoration and protection of water quality.

A FULLY ELLIPTIC CALCULATING PROCEDURE FOR THREE-DIMENSIONAL THERMAL POLLUTION

The use of the mathematical models so far for three-dimensional flow has some limitations because of their simplifications. Many characteristics of the flow field can not be predicted by these models. In this paper the three dimensional elliptic governing equations are solved by finite-volume methods; the buoyancy extensions of the widely tested k-?. model is adapted. The method is first applied to calculate the field of side discharge into open channel flow. The results are in good agreement with those of ref. [7]. Then it is further used to the intake discharge problem which is of a typical layout in cooling-water projects, and the calculated results, which predict in detail the charactreistics of flow field, are reasonable.

A Three-Dimensional Prediction Method for Thermal Diffusion

A three-dimensional, first order turbulence closure, thermal diffusion model is described in this paper. The governing equations consist of an equation of continuity, three components of momentum, conservation equations for salt, temperature and subgridscale energy, and an equation of state. In the model, according to the hypothesis of Kolmogorov and Prandtl, the viscosity coefficient of turbulent flow of homogeneous fluid is related to the local turbulent energy, and the horizontal and vertical exchange coefficients of mass, heat and momentum are computed with the introduction of subgridscale turbulence energy. The governing equations are solved by finite difference techniques. This model is applied to the Jiaozhou bay to predict thermal pollution by the Huangdao power plant. An instantaneous tidal current field is computed, then the distribution of temperature increment is predicted, and finally the effect of wind stress on thermal discharge is discussed.

Research on the Correlation of the Fluctuating Density Gradient of the Compressible Flows

This work is to study a role of the fluctuating density gradient in the compressible flows tbr the computational fluid dynamics （CFD）. A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups proportional to the mean velocity, proportional to the mean strain rate, and proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vortices in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.

Deconvolutional artificial-neural-network framework for subfilter-scale models of compressible turbulence

We establish a deconvolutional artificial-neural-network(D-ANN)approach in large-eddy simulation(LES)of compressible turbulent flow.Filtered variables in the neighboring locations are taken as the inputs of D-ANN to recover original(unfiltered)variables,including density,momentum and pressure.The scale-similarity form is adopted to reconstruct subfilter-scale(SFS)terms.The proposed D-ANN models can give better a priori predictions of the sub-filter stress and heat flux than the classical approximate-deconvolution method(ADM)and the velocity-gradient model(VGM).The predicted SFS terms with the D-ANN models have correlation coefficients larger than 98.4%and relative errors smaller than 18%.In the a posteriori analysis,the D-ANN model compares against the implicit LES(ILES),the dynamic-Smagorinsky model(DSM),and the dynamic-mixed model(DMM).The D-ANN model predicts better than these classical models for velocity spectra,statistical properties of SFS kinetic energy flux and velocity increments.The turbulence statistics and transient velocity divergence are also accurately reconstructed.The type of explicit filter and the impact of compressibility do not significantly affect a posteriori accuracy of the D-ANN model.Results showthat the proposed D-ANN approach has a great potential in developing highly accurate SFS models for large-eddy simulation of complex compressible turbulent flow.

A THREE-DIMENSIONAL CLOUD-SCALE MODEL SUITABLE FOR COMPRESSIBLE ATMOSPHERE

A three-dimensional cloud-scale model has been designed.The governing equations of the model are composed of two groups of equations:one group includes compressible motion equations,continuity equation, pressure equation and thermodynamic equation,which are of Eulerian type,and the other consists of cloud- precipitation microphysics equations which are of Lagrangian type.Since the degree of influence of sound wave on the air motion is quite different from that on the temperature or hydrometeors,the time splitting procedure is used in solving governing equations.Both unstaggered and staggered meshes have been utilized.Integra- tion schemes adopted are the Eulerian backward difference method for the unstaggered mesh and semi-implicit method for staggered mesh.Several experiments of modelling have been conducted and a reasonable three- dimensional image of deep convection is obtained.With this model the horizontal and vertical vortex circula- tions are simulated.Furthermore,the effects of horizontal vortex on the formation and development of downdraft within cloud have also been studied.

Advances and challenges in developing a stochastic model for multi-scale fluid dynamic simulation:One-dimensional turbulence

The modeling of turbulence,especially the high-speed compressible turbulence encountered in aerospace engineering,has always being a significant challenge in terms of balancing efficiency and accuracy.Most traditional models typically show limitations in universality,accuracy,and reliance on past experience.The stochastic multi-scale models show great potential in addressing these issues by representing turbulence across all characteristic scales in a reduced-dimensional space,maintaining sufficient accuracy while reducing computational cost.This review systematically summarizes advances in methods related to a widely used and refined stochastic multi-scale model,the One-Dimensional Turbulence(ODT).The advancements in formulations are emphasized for stand-alone incompressible ODT models,stand-alone compressible ODT models,and coupling methods.Some diagrams are also provided to facilitate more readers to understand the ODT methods.Subsequently,the significant developments and applications of stand-alone ODT models and coupling methods are introduced and critically evaluated.Despite the extensively recognized effectiveness of ODT models in low-speed turbulent flows,it is crucial to emphasize that there is still a research gap in the field of ODT coupling methods that are capable of accurately and efficiently simulating complex,three-dimensional,high-speed compressible turbulent flows up to now.Based on an analysis of the advantages and limitations of existing ODT methods,the recent advancement in the conservative compressible ODT model is considered to have provided a promising approach to tackle the modeling challenges of high-speed compressible turbulence.Therefore,this review outlines several recommended new research subjects and challenging issues to inspire further research in simulating complex,three-dimensional,high-speed compressible turbulent flows using ODT models.

Assessment of Two Turbulence Models and Some Compressibility Corrections for Hypersonic Compression Corners by High-order Difference Schemes

The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.

Numerical study of compression corner flowfield using Gao-Yong turbulence model

A numerical simulation of shock wave turbulent boundary layer interaction induced by a 24° compression corner based on Gao-Yong compressible turbulence model was presented.The convection terms and the diffusion terms were calculated using the second-order AUSM(advection upstream splitting method) scheme and the second-order central difference scheme,respectively.The Runge-Kutta time marching method was employed to solve the governing equations for steady state solutions.Significant flow separation-region which indicates highly non-isotropic turbulence structure has been found in the present work due to intensity interaction under the 24° compression corner.Comparisons between the calculated results and experimental data have been carried out,including surface pressure distribution,boundary-layer static pressure profiles and mean velocity profiles.The numerical results agree well with the experimental values,which indicate Gao-Yong compressible turbulence model is suitable for the prediction of shock wave turbulent boundary layer interaction in two-dimensional compression corner flows.

Numerical Prediction of Laminar-to-Turbulent Transition Around the Prolate Spheroid

In this work,the laminar-to-turbulent transition phenomenon around the two-and three-dimensional ellipsoid at different Reynolds numbers is numerically investigated.In the present paper,Reynolds Averaged Navier Stokes(RANS)equations with the Spalart-Allmaras,SST k-ω,and SST-Trans models are used for numerical simulations.The possibility of laminar-toturbulent boundary layer transition is summarized in phase diagrams in terms of skin friction coefficient and Reynolds number.The numerical results show that SST-Trans method can detect different aspects of flow such as adverse pressure gradient and laminar-to-turbulent transition onset.Our numerical results indicate that the laminar-to-turbulent transition location on the 6:1 prolate spheroid is in a good agreement with the experimental data at high Reynolds numbers.

A new compressibility modification k-ε turbulence model with shock unsteadiness effect

A new compressibility modification k-ε model,including shock unsteadiness effect and the previous compressibility modification of pressure dilatation and dilatational dissipation rate,was developed with a simple formulation for numerical simulation in supersonic complex turbulent flows.The shock unsteadiness effect was modeled by inhibiting turbulent kinetic energy production in the governing equations of turbulent kinetic energy and the turbulent kinetic energy dissipation rate.Sarkar's correction models were employed accounting for the dilatational compressibility effects in the new model.Two types of flows,the free supersonic mixing layers and complex supersonic flow with transverse injection were simulated with different flow conditions.Comparisons with experimental data of the free supersonic mixing layers showed that the new compressibility modification k-ε model significantly inhibited the excessive growth of turbulent kinetic energy and improved predictions.On the supersonic mixing layer flows,prediction results with the new model were in close agreement with experimental data,accurately predicting the decreasing trend of the mixing layer spreading rate with the increase of the convective Mach number.Due to the complicated flow field with flow separation,shock unsteadiness modification inhibited excessive growth of the turbulent kinetic energy in shock regions and wider shock regions are predicted,thereby significantly improving results of the flow with a strong separation forecast.The flow separation was stronger,which was the primary modification effect of the new model.Predictions accord with experimental results even in strong separation flows.

Anisotropic characteristics and creep model for thin-layered rock under true triaxial compression

The failure phenomenon of thin-layered rock tunnels not only exhibits asymmetric spatial characteristics,but also significant time-dependent characteristics under high in-situ stress,which is attributed to the time-dependent fracture of thin-layered rocks.This paper conducted a series of true triaxial creep compression tests on typical thin-layered rock siliceous slate with acoustic emission technique to reveal its anisotropic time-dependent fracture characteristics.The anisotropic long-term strength,creep fracturing process,and fracture orientation characteristics of thin-layered rocks under different loading angles(b,u)and intermediate principal stress were summarized.A three-dimensional(3D)non-linear visco-plastic creep model for thin-layered rock was developed to simulate its anisotropic creep behavior.The time-dependent fracturing of rocks during true triaxial creep loading is reflected through the change of equivalent strain based on an improved Euler iteration method.By constructing the plastic potential function and overstress index related to loading angles and stress state,the anisotropic timedependent fracturing process and propagation of thin-layered rocks under different loading angles and intermediate principal stress are expounded.The model was validated experimentally to show it can reflect the long-term strength and creep deformation characteristics of thin-layered rocks under true triaxial compression.

A TVD SCHEME FOR INCOMPRESSIBLE FLOW COUPLED WITH DIFFERENT TURBULENCE MODLES ON A GROUND-MOUNTED SQUARE-RIB FLOW

A finite-difference Total Variation Diminishing （TVD） numerical simulation model for coupling the Reynolds Averaged Navier-Stokes （RANS） equations, pressure-relative continuity equation and various k-εturbulence models was developed to solve the incompressible flow based on the pseudo-compressibility method. The hyperbolicity of all these equations was studied and the discretization of the fully coupling equations with all the primal variables and source terms were made in this article. Numerical simulation for modeling the flow around a ground-mounted square rib was implemented and validated by comparing with the published wind tunnel experimental data. It is shown that such a numerical simulation method with a proper turbulence model has a very good accuracy to simulate the flow around a surface-mounted rib. It is concluded that the Renormalization Group （RNG） and Chen-Kim k-εturbulence models have much better ability to predict the characteristics of the vortex structure and flow separation than the standard k-εmodel.

基于时空最优低维动力系统的多尺度可压缩湍流数值模拟方法

按照周培源教授关于研究湍流数值模拟建模时必须分析和求解脉动速度场的思想,该研究基于第一性原理,系统地建立了基于时空低维最优动力系统的多尺度可压缩湍流数值模拟方法(LMS方法),并将其应用于多次冲击Richtmyer-Meshkov问题的数值模拟中,首次得到了可压缩湍流的中尺度流场和不同于DNS近似解的湍流近似解.数值结果表明,LMS方法可以用较少的网格获得更精确的湍流近似解.首先解决了研究中遇到的几个问题,为LMS方法的构建铺平了道路.这些问题是:基于湍流的物理特性,提出了湍流大、中、小尺度分解的新概念;找到了box滤波空间相关性的计算方法;指出了湍流建模理论中长期存在的逻辑错误,提出了多尺度湍流模型的概念;讨论了湍流封闭问题的本质和关键,给出了克服湍流封闭问题的数值方法.采用box滤波方法/空间网格平均方法且在大尺度网格的意义下,LMS方法的本质是一种将RANS、LES、DES和DNS等湍流数值模拟方法统一的全新湍流数值模拟方法.需要指出的是,LMS方法也可以作为湍流模型研究的辅助工具,以检验SGS尺度方程/脉动方程中各项所对应的湍流模型是否正确.

Experimental and numerical evaluation of multidirectional compressive and flexure behavior of three-dimensional printed concrete

Three-dimensional concrete printing(3DCP)can proliferate the industrialization of the construction sector,which is notoriously conservative and indolent toward changes.However,the mechanical behavior of 3DCP should be characterized and modeled considering the interfaces when its performance is thoroughly compared to that of the existing concrete construction methods.This study presents an experimental and numerical investigation of uniaxial compression and three-point bending(TPB)tests on extruded 3DCP beams in different loading directions.The orientation of translational and depositional interfaces with respect to the direction of loading influenced the strength.Both the elastic and post-damage behavior of the 3DCP specimens were compared with those of the conventionally cast specimen under quasi-static loading conditions.Despite the higher compressive strength of the casted specimen,the flexural strength of the 3DCP specimens was higher.This study employed the finite element and cohesive zone models of the appropriate calibrated traction-separation law to model fracture in the notched TPB specimens.Furthermore,the real-time acoustic emission test revealed the nature of failure phenomenon of three-dimensional-printed specimens under flexion,and accordingly,the cohesive law was chosen.The predicted load-displacement responses are in good agreement with the experimental results.Finally,the effects of cohesive thickness and notch shape on the performance under bending were explored through parametric studies.

Compressible Turbulent Boundary Layers on a Strongly Heated Wall

This paper concerns the theoretical and experimental modelling of the flat wall,highly heated,compressible turbulent boundary layer.Its final objective is to develop a numerical Navier-Stokes solver and to conclude on its capability to correctly represent complex aerothermic viscous flows near the wall.The paper presents a constructed numerical method with particular attention given to the turbulence modelling at low Reynolds number and comparisons with supersonic and transonic experimental data.For the transonic experiment,very high wall temperature(Tw=1100K)is realized.The method of this difficult experimental set up is discussed.The comparison between experimental and computational data conducts to the first conclusion and gives some indications for the future work.