Simulation Analysis of New Energy Vehicle Engine Cooling System Based on K-E Turbulent Flow Mathematical Model

New energy vehicles have better clean and environmental protection characteristics than traditional fuel vehicles.The new energy engine cooling technology is critical in the design of new energy vehicles.This paper used oneand three-way joint simulation methods to simulate the refrigeration system of new energy vehicles.Firstly,a k-εturbulent flow model for the cooling pump flow field is established based on the principle of computational fluid dynamics.Then,the CFD commercial fluid analysis software FLUENT is used to simulate the flow field of the cooling pump under different inlet flow conditions.This paper proposes an optimization scheme for new energy vehicle engines’“boiling”phenomenon under high temperatures and long-time climbing conditions.The simulation results show that changing the radiator’s structure and adjusting the thermostat’s parameters can solve the problem of a“boiling pot.”The optimized new energy vehicle engine can maintain a better operating temperature range.The algorithm model can reference each cryogenic system component hardware selection and control strategy in the new energy vehicle’s engine.

Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.

Heat Transfer and Flow Characteristics Predictions with a Refined k-ε-f_u Turbulent Model in Impinging Jet

Local heat transfer and flow characteristics in a round turbulent impinging jet for Re≈23 000 is predicted numerically with the RANS approach and a k-ε-fu turbulence model. The heat transfer predictions and turbulence parameters are verified against the axis-symmetric free jet impingement measurements and compared with previous other turbulence models, and results show the k-ε-fu model has a good performance in predictions of the local wall heat transfer coefficient, and in agreement with measurements in mean velocity profiles at different radial positions as well. The numerical model is further used to examine the effect of the fully confined impingement jet on the local Nusselt number. Local Nusselt profiles in x and y-centerlines for the target plate over three separation distances are predicted. Compared with the experimental data, the numerical results are accurate in the central domain around the stagnation region and present a consistent structure distribution.

Solution of Self-similar Equations of the k-ε Model in the Shear Turbulent Mixing Problem and Its Numerical Simulation

The paper presents the k-ε model equations of turbulence with a single set of constants chosen by the authors, which is appropriate to simulate a wide range of turbulent flows. The model validation has been performed for a number of flows and its main results are given in the paper. The turbulent mixing of flow with shear in the tangential velocity component is discussed in details. An analytical solution to the system of ordinary differential equations of the k-ε model of turbulent mixing has been found for the self-similar regime of flow. The model coefficients were chosen using simulation results for some simplest turbulent flows. The solution can be used for the verification of codes. The numerical simulation of the problem has been performed by the 2D code EGAK using this model. A good agreement of the numerical simulation results with the self-similar solution, 3D DNS results and known experimental data has been achieved. This allows stating that the k-ε model constants chosen by the authors are acceptable for the considered flow.

Mathematical Model of Combustion in Blunt Annular Ceramic Burner

The computer simulation of the combustion process in blast furnace(BF) stove has been studied by using the k-ε-g turbulent diffusion flame model.The combustion process in blunt annular ceramic burner was calculated by using the software.The profiles of gas and air velocity,temperature of the combustion products,concentration of the components,and the shape and length of the flame during combustion have been researched.Compared with the original annular ceramic burner,the new design of the blunt one improves the mixing of the gas and the air significantly,and shortened the length of the flame.

Multi-layer analytic solution for k-ωmodel equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.

Assessment of k–ε models using tetrahedral grids to describe the turbulent flow field of a PBT impeller and validation through the PIV technique

In turbulence modeling, the RNG and Realizable models have important improvements in the turbulent production and dissipation terms in comparison to the Standard. The selection of the appropriate turbulence model has an impact on the convergence and solution in STRs, and they are used in mixing, multiphase modeling or as starting solution of transient models as DES and LES. Although there are several studies with the pitched blade turbine(PBT) impeller, most of them used the Standard model as representative of all k–ε models, using structured hexahedral grids composed of low number of cells, and in some cases under axial symmetry assumptions.Accordingly, in this work the assessment of the Standard, RNG and Realizable models to describe the turbulent flow field of this impeller, using the Multiple Reference Frame(MRF) and Sliding Mesh(SM) approaches with tetrahedral domains in dense grids, is presented. This kind of cell elements is especially suitable to reproduce complex geometries. Flow velocities and turbulent parameters were verified experimentally by PIV and torque measurements. The three models were capable of predicting fairly the pumping number, the power number based on torque, and velocities. Although the RNG improved the predictions of the turbulent kinetic energy and dissipation rate, the Realizable model presented better performance for both approaches. All models failed in the prediction of the total dissipation rate, and a dependence of its value on the number of cells for the MRF was found.

MATHEMATICAL MODELLING OF BUBBLE DRIVENFLOWS IN A NOVEL ALUMINUM ELECTROLYSIS CELL

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REVISED k-ε TURBULENCE MODEL IN ELECTROMAGNETIC CONTINUOUS CASTING OF MELT

The research is motivated by the ongoing the electromagnetic continuous casting of molten metal. The revised k-ε model considering the effect of magnetic field application was derived. The specific model equations for the electromagnetic braking were used to calculate the velocity distribution in the continuous casting mold of steel. The results show that the revised k-ε model considering the effect of magnetic field application tends to suppress the production of turbulence and difference between the conventional and revised k-e model is small.

Three-dimensional turbulent model of heat transfer and fluid flow in GTAW process

A two-equation K-ε turbulent fluid flow model is built to model the heat transfer and fluid flow in gas tungsten arc welding （GTAW） process of stainless steel S US310 and S US316. This model combines the buoyancy force, lorentz force and marangni force as the driving forces of thefluidflow in the weld pool. The material properties are functions of temperature in this model. The simulated results show that the molten metal flowing outward is mainly caused by the marangoni convection, which makes the weld pool become wider and shallower. The comparison of the weld pool shape of SUS310 and SUS316 shows that the slight differences of the value of thermal conductivity mainly attributes to the difference of the weld pool shape and the distinction of heat transport in laminar and turbulent model makes large diversity in the simulated results.

A K-εTWO-EQUATION TURBULENCE MODEL FOR THE SOLID-LIQUID TWO-PHASE FLOWS

A two-equation turbulence model has been dereloped for predicting two-phase flow the two equations describe the conserration of turbulence kinetic energy and dissipation rate of that energy for the incompressible carrier fluid in a two-phase flow The continuity, the momentum, K and εequations are modeled. In this model,the solid-liquid slip veloeites, the particle-particte interactions and the interactions between two phases are considered,The sandy water pipe turbulent flows are sueeessfuly predicted by this turbulince model.

A New Mathematical Justification for the Hypothesis of the Longevity of Jupiter’s Great Red Spot

As is known, the Great Red Spot (GRS) is one of the most mysterious sights in the solar system and is a strong storm that is quite large. According to the laws of hydrodynamics and gas dynamics, it should have disappeared several centuries ago, but scientists still observe it and cannot accurately explain this phenomenon. Since turbulence and atmospheric waves in the GRS region absorb the energy of its winds, the vortex loses energy by radiating heat. In the work, it is proved with a mathematical and non-classical approach that the GRS and anticyclones will live for a long time;otherwise, we had to first of all prove that the vortex threads (loops) and ovals could not exist. Based on these supports, mathematical methods prove their existence forever by observing a large vortex (GRS);moreover, they are sources of heat. When proofs are obtained, the results are consistent with the previous hypotheses of the researcher. The introduction of the work gives a comparison of various hypotheses;for example, one of them states that the decrease in the size of the GRS is only an illusory observation. Next, we first consider the applicability conditions for the mathematical justification of the hypothesis of the longevity of the Great Red Spot. The wind equation and the GRS are energized by absorbing smaller eddies and ovals, and this total energy is constant. With the help of the KH mechanism in the case of Brunt Vaisala, the frequencies (which can be calculated by a program with given formulas) are determined using very strictly mathematical evidence to substantiate the validity of the hypothesis about the longevity of Jupiter’s Great Red Spot.

Mathematical Modeling of Crown Forest Fire Spread

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. In this paper the assignment and theoretical investigations of the problems of crown forest fire spread in windy condition were carried out. In this context, a study—mathematical modeling—of the conditions of forest fire spreading that would make it possible to obtain a detailed picture of the change in the temperature and component concentration fields with time, and determine as well as the limiting condition of fire propagation in forest with fire break.

THE EQUATIONS OF COMPLETE DEPTH-AVERAGED TURBULENCE MODEL IN GENERAL ORTHOGONAL COORDINATES

For shallow water flow, the depth-averaged governing equations are derived by depth-averaging of the mean equations for three-dimensional turbulent flows. The influences of free water surface and of topography of river bed are taken into account.The depth-averaged equations of k-εturbulence model are also obtained. Because it Accounts for the three-dimensional effect, this model is named as the complete Depth-averaged model.The boundaries of natural water bodies are usually curved.In this work, the derived equations in Cartesian coordinates are transformed into orthogonal coordinates. The obtained equations can be applied directly to numerical computation of practical problems.

CURVAURE SENSITIVE NONLINEAR TURBULENCE MODEL

By modifying the Rodi assumption to take account of the influence of flow curvature, a new curvature modified algebraic stress model(CMASM) is de- veloped from the second moment closure in the generalized curvilinear coordinate system. And the explicit form of this ASM, a new curvature modified nonlinear k-ε model (CMNKE), is derived in the orthogonal curvilinear coordinate system. This new nonlinear k-ε model is further validated by a numerical simulation of a two- dimensional U-type turnaround duct flow. The results show that the CMNKE can effectively capture the main characteristic of this curvature flow and simulate the damping effect of the shear stress by a convex curvature and the enhancing effect by a concave curvature. So, this model is a rational and effective simplification to the second moment closure.

Optimal convergence rates for three-dimensional turbulent flow equations

In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6）.

3D mathematical model for suspended load transport by turbulent flows and its applications

This paper presents a 3D mathematical model for suspended load transport in turbulent flows. Based on Dous stochastic theory of turbulent flow, numerical schemes of Reynolds stresses for anisotropic turbulent flows were obtained. A refined wall function was employed to treat solid wall boundaries. The equations for 2D suspended load motion and sorting of bed material have been expanded into 3D cases. Numerical results are validated by the measured data of the Gezhouba Project, and proved to be in good agreement with the experimental. The present method has been employed to simulate sediment erosion and deposition in the dam area of Three Gorges Project, and for the operation of the project, siltation process and deposition pattern in the near-dam area of the reservoir, size distribution of the deposits and bed material, and flow fields and sediment concentration fields at different time and elevations are predicted. The predicted results are close to the experimental observations in physical model studies. Thus, a new method is established for 3D simulation of sediment motion in dam areas of multi-purpose water projects.

对 k-ω 湍流模型的改进

为了更适合于较复杂几何外形的数值计算，本文提出仅引入１个参数来改进ｋ－ω湍流模型并采用了一种双网格系统的有限体积格式来求解Ｎ－Ｓ方程与改进的的ｋ－ω模型方程。通过平板附面层的计算结果表明了用本文提出的对ｋ－ω湍流模型的改进对控制转捩是有效的。

用k-ε-Re模型预测高聚物稀溶液射流的湍流场

根据理论分析和某些实验结果,提出了适用于高聚物稀溶液湍流射流K-ε-Re模型,并用差分方法进行了数值计算。结果表明:与清水射流相比,在相同的初始状态下,高聚物添加剂能改变湍动能及其耗散率的分布特性,使雷诺应力减小,离散减弱,中心线速度增加,密集性提高。这些结果与实验数据和理论分析相吻合。

TWO MODIFICATORY K-ε TURBULENCE MODELS FOR TURBULENT SWIRLING FLOWS

Since the standard K-ε model used to predict the strongly swirling flowleads to a large deviation from experimental results, it is necessary to introduce modification tothe standard K-ε model. Based on the algebraic Reynolds stress model and Bradshaw's turbulentlength scale modification conception, we present two modified K-ε models. To investigate thebehaviour of the modified turbulence models, they are used to predict two representative turbulentswirling flows. The computational results, after compared with the experimental data, show that themodified K-ε models substantially improve the prediction of the standard K-ε model for theturbulent swirling flows.