Computer simulation of turbulence in internal combustion engines

The paper presents two- and three-dimensional computations of the in-cylinder turbulent flow in a diesel engine. The mathematical formulation is presented first, with emphasis on the modifications made to the standard k-ε model of turbulence, to account for rapid compression/expansion, and on the k-w model also used in the computations. Then, the results of two-and three-dimensional transient calculations are presented and compared with experimental data. It is realized that two-dimensional computations may be of little value to real engines, which would probably require three-dimensional analyses. However, two-dimensional studies are still useful in allowing the testing of new ideas easily and economically. It is concluded that the standard k-ε model may lead to poor predictions when used for internal combustion (IC) engine simulations, and that the modified model leads to more reasonable length-scale distributions, and it improves significantly the overall agreement of velocity predictions with experiment. The effect of the k-ε modification is apparent in both the two- and three-dimensional simulations. It is also demonstrated that the k-w model provides better turbulence predictions than the unmodified k-ε model, for the cases considered, and that a similar modification of the k-w model, to account for rapid compression/expansion, might improve its predictions even further.     

Large eddy simulation and direct simulation of compressible turbulence and combusting flows in engines based on the BI-SCALES method

Physical features of turbulence and vortex-flame interaction in engines are investigated by performing large eddy simulation and direct numerical simulation of compressible flows. A BI-SCALES (Boundary-Inner Smoothly Coupled, Alternating multi-Level Equations System) is proposed, which is a mathematical formulation of the system of governing equations suitable for computations of compressible flows. A numerical method based on the proposed formulation is developed. Using the method, the transition to turbulence in the compression process and the cyclic variations are examined. Then, the vortex-flame interaction is studied, mainly on the relation between the flame structure and the Kalvoritz- and turbulent Reynolds number effect. Finally, the large wrinkle simulation (LWS) of engine combusting flow is performed.     

可压缩多介质粘性流体和湍流的大涡模拟

在可压缩多介质粘性流体动力学高精度计算方法MVPPM(multi-viscous-fluid piecewise parabolicmethod)基础上,引入Smagorinsky和Vreman亚格子湍流模型,采用大涡数值模拟方法求解可压缩粘性流体NS(Navier-Stokes)方程,给出适用于可压缩多介质流体界面不稳定性发展演化至湍流阶段的计算方法和二维计算程序MVFT(multi-viscosity-fluid and turbulence)。在2种亚格子湍流模型下计算了LANL(Los Ala-mos National Laboratory)激波管单气柱RM不稳定性实验,分析了气柱的形状、流场速度以及涡的特征,通过与LANL实验和计算结果的比较可知,Vreman模型略优于Smagorinsky模型,MVFT方法和计算程序可用于对界面不稳定性发展演化至湍流阶段的数值模拟。     

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.     

Subgrid length-scales for large-eddy simulation of stratified turbulence

The influence of buoyancy on the length-scales for the dissipation rate of kinetic energy, and for momentum, heat, and other scalar transport has to be known for subgrid-scale (SGS) models in a large-eddy simulation (LES). For the inertial subrange, Lilly (1967) has shown that grid spacing is the relevant length-scale for SGS effects. Deardorff (1980) proposed to reduce all the length-scales for stable stratification. Numerical and experimental data show, however, that the dissipation length-scale may strongly increase in stable layers with little shear. Lumley's (1964) theory for the energy spectrum in a stratified fluid also suggests such an increase. In this paper we apply the analysis of previous algebraic second-order closure SGS models, parameter studies with different length-scale models in LES, and the analysis of direct simulations of sheared and unsheared stably stratified homogeneous turbulence. These analyses show advantages of first-order closures for LES and suggest that the limiting effect of stratification should only be applied to the length-scales of vertical eddy-diffusivities of heat and scalars but not to those of momentum and dissipation.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This work was supported by the Deutsche Forschungsgemeinschaft.     

Kinematic simulation for stably stratified and rotating turbulence

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory (RDT) to a kinematic simulation (KS) of the Boussinesq equation with a Coriolis term.Scalings for one- and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.     

All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence

As a type of shock-capturing scheme, the traditional Roe scheme fails in large eddy simulation (LES) because it cannot reproduce important turbulent characteristics, such as the famous k^?5/3 spectral law, as a consequence of the large numerical dissipation. In this work, the Roe scheme is divided into five parts, namely, ξ, δU_p, δp_p, δU_u, and δp_u, which denote basic upwind dissipation, pressure difference-driven modification of interface fluxes, pressure difference-driven modification of pressure, velocity difference-driven modification of interface fluxes, and velocity difference-driven modification of pressure, respectively. Then, the role of each part in the LES of homogeneous decaying turbulence with a low Mach number is investigated. Results show that the parts δU_u, δp_p, and δU_p have little effect on LES. Such minimal effect is integral to computational stability, especially for δU_p. The large numerical dissipation is due to ξ and δp_u, each of which features a larger dissipation than the sub-grid scale model. On the basis of these conditions, an improved all-speed Roe scheme for LES is proposed. This scheme can provide satisfactory LES results even for coarse grid resolutions with usually adopted second-order reconstructions for the finite volume method.     

An improved parallel compact scheme for domain-decoupled simulation of turbulence

An improved domain-decoupled compact scheme for first and second spatial derivatives is proposed for domain-decomposition-based parallel computational fluid dynamics. The method improves the accuracy of previously developed decoupled schemes and preserves the accuracy and bandwidth properties of fully coupled compact schemes, even for a very large degree of parallelism, and enables the Navier-Stokes equations to be solved independently on each processor. The scheme is analysed using Fourier analysis and error analysis, and tested on one-dimensional wave-packet propagation, a two-dimensional vortex convection problem, and in the direct numerical simulation of the three-dimensional Taylor-Green vortex problem and turbulent channel flow. Our results demonstrate the scheme's effectiveness in performing direct numerical simulation of turbulence in terms of accuracy and scalability.     

Desingularization of Vortices for the Euler Equation

We study the existence of stationary classical solutions of the incompressible Euler equation in the planes that approximate singular stationary solutions of this equation. The construction is performed by studying the asymptotics of equation ${-\varepsilon^2 \Delta u^\varepsilon=(u^\varepsilon-q-\frac{\kappa}{2\pi} \log \frac{1}{\varepsilon})_+^p}$ with Dirichlet boundary conditions and q a given function. We also study the desingularization of pairs of vortices by minimal energy nodal solutions and the desingularization of rotating vortices.     

Numerical simulation of a developed shear turbulence

Results of two-dimensional numerical studies of turbulence that arises at the interface of two flows of poorly compressible gases are described. The results were obtained using a MAKh software system. The interrelation between spatial and time problems on the development of a turbulent zone induced by shear instability is analyzed. A constant that characterizes the degree of turbulent shear mixing is calculated. The effect of the density difference of the mixing fluids on the growth rate of the turbulence zone is studied. For all density differences considered, the coefficient of heterogeneity of the resultant mixture is evaluated. Institute for Technical Physics, Snezhinsk 456770. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 77–83, January–February, 2000.     

NUMERICAL SIMULATION OF WING-BODY JUNCTION TURBULENCE FLOW

Wing-body junction turbulence flow is simulated by using RANS equation and boundary fitted coordinate technique.Three order differential scheme is used in the computation of convection term and two layers turbulence model are employed in the calculation.     

Injection characteristics simulation and analysis in diesel engines

By means of a purposely developed numerical code an investigation of injection systems in diesel engines has been carried out. Cavitation at low pressure was simulated. The experimental results obtained were compared with the numerical ones. Data on cavitation waves, in the pipe between pump and injector, were obtained during that simulation. In particular, the influence of the relief volume on cavitation volume and injected fuel rate were computed. Unstable working conditions, characterized by a large variation of the injected fuel, at the same operating point, have been experimentally investigated and simulated. Lecture delivered at the Workshop on Fluiddynamics, Combustion and Exposition in Reciprocating Engines, held at Capri in 1990.     

Chaos and direct numerical simulation in turbulence

We show that direct numerical simulation will yield turbulent flowfields which are strongly dependent upon computer hardware and software. A computed flow trajectory is apparently uncorrelated to the true solution of a flowfield if it is allowed to evolve over a long time, and hence is called a pseudo-orbit. This is due to the trajectory instability of chaotic turbulent flows. All is not lost, however; a long-time average of flow quantities can now be computed using a pseudo-orbit by invoking the shadowing lemma. For the inviscid flow, this time average tends to approach asymptotically the phase average as predicted by the classical ergodic theorem. Although the inviscid two-dimensional flow has no real physical importance, the existence of canonical (equilibrium) distribution permits us to examine the accuracy of time averaging based on the pseudo-orbit and its inherent limitations.This work was supported by AFOSR task 2304N1.     

Evaluation of bubble-induced turbulence using direct numerical simulation

The presented research evaluates the interaction between a single bubble and homogeneous turbulent flow using direct numerical simulation (DNS) approach. The homogeneous single-phase turbulence is numerically generated by passing a uniform flow through grid planes. The turbulence decay rate is compared with experiment-based correlation. The single phase turbulence is then used as an inflow boundary condition for a set of single bubble studies. By estimating the turbulent field around the fully resolved bubble, the effects of bubble deformability, turbulent intensity and relative velocity on the bubble-induced turbulence are investigated. The existence of bubble creates new vortices in the wake region and the enhancement of turbulence is observed in the region behind the bubble. The results show that the magnitude of the turbulence enhancement would increase as the bubble encounters larger liquid turbulent intensity or higher relative velocity. Set of bubble Weber numbers from 0.34 to 3.39 are used to investigate the effect of bubble deformability. The more deformable bubble is the higher the increase in the magnitude of the turbulence enhancement behind the bubble. This research provides systematic insight on the bubble-induced turbulence (BIT) mechanism and is important for multiphase computational fluid dynamics (M-CFD) closure model development.     

Direct and large eddy simulation of stratified turbulence

Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing. In these simulations we found that energy dissipation is concentrated within thin layers of horizontal tagliatelle-like vortex sheets between large pancake-like structures. We propose a new implicit subgrid-scale model for stratified fluids, based on the Adaptive Local Deconvolution Method (ALDM). Our analysis proves that the implicit turbulence model ALDM correctly predicts the turbulence energy budget and the energy spectra of stratified turbulence, even though dissipative structures are not resolved on the computational grid.     

Large eddy simulation of turbulence in engineering applications

Flows of engineering interest which have been investigated with the large eddy simulation (LES) technique are discussed. Using this technique the filtered Navier-Stokes equations are solved to simulate the three-dimensional unsteady motion. Not only the statistically-averaged fields, but in addition, the spatial and temporal variations in the flow fields can be examined. Grids are equidistant in the three coordinate directions and typically consist of 150,000 to 200,000 mesh cells. Examples of flows include the turbulent boundary layer with a sudden change in the freestream pressure gradient and the separating and reattaching flow behind a rearward-facing step. Results which illustrate the large-scale structure of these two high Reynolds number turbulent flows are discussed in the present paper.     

Direct numerical simulation of homogeneous stratified rotating turbulence

The effects of the Prandtl number on stratified rotating turbulence have been studied in homogeneous turbulence by using direct numerical simulations and a rapid distortion theory. Fluctuations under strong stable-density stratification can be theoretically divided into the WAVE and the potential vorticity (PV) modes. In low-Prandtl-number fluids, the WAVE mode deteriorates, while the PV mode remains. Imposing rotation on a low-Prandtl-number fluid makes turbulence two-dimensional as well as geostrophic; it is found from the instantaneous turbulent structure that the vortices merge to form a few vertically-elongated vortex columns. During the period toward two-dimensionalization, the vertical vortices become asymmetric in the sense of rotation. Communicated by S. Obi PACS 47.55.Hd     

Three‐dimensional remeshed smoothed particle hydrodynamics for the simulation of isotropic turbulence

We present a remeshed particle‐mesh method for the simulation of three‐dimensional compressible turbulent flow. The method is related to the meshfree smoothed particle hydrodynamics method, but the present method introduces a mesh for efficient calculation of the pressure gradient, and laminar and turbulent diffusion. In addition, the mesh is used to remesh (reorganise uniformly) the particles to ensure a regular particle distribution and convergence of the method. The accuracy of the presented methodology is tested for a number of benchmark problems involving two‐ and three‐dimensional Taylor‐Green flow, thin double shear layer, and three‐dimensional isotropic turbulence. Two models were implemented, direct numerical simulations, and Smagorinsky model. Taking advantage of the Lagrangian advection, and the finite difference efficiency, the method is capable of providing quality simulations while maintaining its robustness and versatility.