Non-Isotropic Length Scales During the Compression Stroke of a Motored Piston Engine

For the case of axial compression the two-point velocity correlation equations of axisymmetric homogeneous turbulence are derived. Appropriate integrations then lead to equations for the components of the Reynolds stress tensor as well as to those for the two independent integral length-scales characterizing axisymmetric homogeneous turbulence. These equations contain a certain number of empirical constants. Values for these constants are taken from the literature, or were adjusted from the present data.The resulting model is validated using data from a motored piston engine. The flow field, which has negligible swirl and tumble, has been measured using particle image velocimetry (PIV). Since turbulence is axisymmetric and homogeneous in the counter region, two-dimensional PIV provides the time history of the axial and radial length-scales. The experimental data are compared with the mathematical model.     

Effect of particles suspended in a fluid flow on the decay of isotropic turbulence

Dynamic equations have been obtained for the two-point double correlations of the fluctuation velocities of a fluid and the particles suspended in it at low volume concentrations of the solid phase. In the case of uniform isotropic turbulence these equations can be considerably simplified. The final period of decay of isotropic turbulence has been studied in detail. At this stage in the case of high-inertia particles the inhomogeneous-fluid turbulence is similar to the turbulence of a homogeneous fluid (without particles) in the sense that the presence of the particles affects only the fluctuation energy but leaves unchanged the spatial scales of turbulence and the spatial energy spectrum function. The suspended particles lead to exponential damping of the turbulent pulsations.Little theoretical information is available on the hydrodynamics of a suspension of fine particles in a turbulent liquid or gas. Research has been mainly confined to the behavior of the individual particles in a given turbulence field [1]. The problem of the turbulent motion of the mixture as a whole has been examined by Barenblatt [2], who derived the equations of motion of the mixture, using Kolmogorov's hypothesis to close them. Hinze [3] has also attempted to derive equations for turbulent pulsations of the mixture. However, as Murray showed [4], Hinze' s equations contradict Newton' s third law.The effect of suspended particles on the turbulence of a two-phase flow is governed by the noncorrespondence of the local velocities of the particles and the medium. The forces of resistance to the motion of the particles relative to the fluid lead to additional dissipation of fluctuation energy and decay of turbulence [2]. On the other hand, if the averaged velocities of particles and medium do not correspond, the suspended particles may also have a destabilizing effect [5, 6], causing energy transfer from the averaged to the pulsating motion. Below we shall consider the case where the averaged velocities of the two phases coincide, i.e., we shall deal only with the first of the two above-mentioned effects.The authors thank G.I. Barenblatt for his useful advice.     

The decay of weak,homogeneous turbulence in the presence of a vertical body force and concentration gradient with a first-order reaction

The effects of buoyancy, produced by a uniform vertical concentration gradient and body force, on a homogeneous turbulent field accompanied by a first-order chemical reaction, are analysed by considering a simplified model. A system of two-point correlation equations, which contains mean concentration gradient and body force terms, is constructed from the Navier-Stokes, convective diffusion and continuity equations. By well-known methods, these equations are converted into equations for the spectrum functions in the wave-number space and solutions for different spectral tensors are obtained by neglecting the contributions of the triple correlation terms. For carrying out the numerical calculations, it is assumed that the turbulence is initially isotropic and the concentration fluctuations initially zero. It turns out that the turbulence decays with time, although the buoyancy forces do alter the rate of decay. The buoyancy forces can either extract energy from the turbulent field or feed energy into it, depending upon the direction of the body force and the concentration gradient. Spectra are displayed graphically for several values of the reaction rate parameter for stabilizing, as well as destabilizing, buoyancy forces.     

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M _t ² ), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

On the spectrum of magnetic field and scalar impurity fluctuations in acoustic turbulence

The fluctuations of a magnetic field in acoustic turbulence are examined. An equation is derived for the spectral tensor of homogeneous magnetic field fluctuations. In a certain limit case the spectrum of steady-state pulsations is obtained in the presence of an external source. It is shown that three kinds of spectra exist in an inertial subdomain, each of which corresponds to a definite domain in wave space. Analogous results have been obtained for the fluctuations of a homogeneous scalar impurity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 26–31, March–April 1971.In conclusion, the author grateful to R. Z. Sagdeev for discussing the results obtains at a seminar.     

One class of exact analytical solutions of three-dimensional thermoelastic-equilibrium equations for orthotropic plates

A structural method is proposed to construct one class of analytical solutions of three-dimensional thermoelastic-equilibrium equations for rectilinearly orthotropic plates. This method allows us to establish the analytical structure of a partial solution of the inhomogeneous equations of thermoelastic equilibrium for orthtropic plates based on the known analytical structure of a temeprature field (found by solving the corresponding boundary-value problem of the stationary theory of thermoelasticity). The well-known solution of inhomogeneous equations of thermoelastic equilibrium for transversely isotropic plates follows from the obtained exact solution as a partial case. The exact general solutions of the three-dimensional homogeneous equations of elastic equilibrium are also presented. Their analytical structure is similar to the constructed partial solution corresponding to the known temperature field. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 1, pp. 78–87, January, 2000.     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Systematic tuning of dispersion models for simulation of evaporating sprays

In this study, via an Eulerian–Lagrangian framework, the performance of two recent dispersion models, i.e. a first-order autoregressive process and the PDF model, is compared. The appropriate relations for the turbulence scales and the drift correction term are suggested and the tuned values for the constants of the models are proposed in a systematic approach by starting with the simplest case, i.e. particle-laden stationary isotropic turbulence and adding more complexities in the subsequent cases, including the homogeneous anisotropic shear flow, decaying grid turbulence, and inhomogeneous gas–solid spray. Also, the isotropic relation for the effect of inertia in the Lagrangian turbulence time scale seen by particles is extended to the anisotropic case while it remains consistent in the isotropic limit. Finally, the performance of the tuned models is evaluated for the simulation of an evaporating spray. It is observed that, the tuned constants for the evaporating spray are close to the ones obtained for the homogeneous shear flow.     

磁流体湍流及数值模拟研究综述

自从20世纪90年代初,AJAX计划的提出掀起了磁流体技术的研究热潮.本文总结了国内外关于磁流体湍流研究的成果,包括两方面:磁流体湍流的特点和数值模型.相比于普通湍流,磁流体湍流表现出电磁诱导的各向异性、线性焦耳耗散、湍流重层流化等特性,本文同时对磁流体湍流的结构和脉动抑制现象进行了描述:数值模型研究从雷诺平均方程和大涡模拟两方面作了介绍.当前研究集中在不可压缩磁流体湍流,距离能够应用于航空航天问题还有很长的路要走.     

Investigation of turbulence effects on forced convection in a composite porous/fluid duct: Constant wall flux and constant wall temperature cases

Forced convection heat transfer in composite porous/fluid domains is of great practical and theoretical significance. However, research in this area traditionally addressed only the laminar flow case in both homogeneous fluid and porous regions of the domain. This paper investigates the interaction between turbulent flow in the center of a circular tube filled with a homogeneous fluid and laminar flow in the porous layer adjacent to the tube wall. A two-layer algebraic turbulence model suggested by Cebeci and Smith is utilized for the flow in the central region of the tube. The effects of turbulence in the central region on velocity and temperature distributions as well as on the Nusselt number are analyzed.     

Adaptive resolution refinement for pseudospectral simulations of isotropic homogeneous turbulence

Pseudospectral simulations of homogeneous turbulence provide an important class of benchmark flow problems used for fundamental studies of turbulence and for numerical validation purposes. Depending on the numerical resolution, fully resolved computations of homogeneous turbulence can consume large amounts of central processing unit (CPU) time. Here, we present an approach analogous to adaptive mesh refinement for computations performed in physical space to adaptively refine the spectral resolution for pseudospectral computations of isotropic homogeneous turbulent flows. The method is applied to simulations of two-dimensional and three-dimensional isotropic homogeneous turbulence, and the results are compared with direct numerical simulations (DNS) performed using a fixed fine mesh. Significant savings in computational time are found in each case, with little to no compromise in the accuracy of the solutions.     

Dispersion of Gas Bubbles in Large-Scale Homogeneous Isotropic Turbulence

An approximate analysis is given of the dispersion of gas bubbles that rise at large Reynolds number through large-scale homogeneous, isotropic turbulence, characterized by the Kraichnan energy-spectrum function. A fairly well-established equation of motion of the bubbles, originally proposed by Thomas et al. [16], is used to derive a closed set of equations for the components of the dispersion tensor of the bubbles in a manner analogous to that used by Saffman [12] for fluid particles and by Pismen and Nir [10, 11] for solid particles. The equations are then solved to obtain the diffusivities and the intensities of bubble velocity fluctuations. Analytical solutions are compared with results from simulations of the bubble motion in a Gaussian random velocity field.     

Compressibility effects due to turbulent fluctuations

This paper deals with intrinsic effects of compressibility, i.e. with dilatation fluctuations in response to pressure fluctuations. Three different types of turbulent flows are considered in more detail: homogeneous turbulent shear flow, wall-bounded turbulent shear flow and shock/turbulence interaction. A survey of the present knowledge in this field, mainly based on DNS data, is given. Using the linear inviscid perturbation equations a direct link between fluctuations of dilatation and of velocity in the direction of mean shear is presented for homogeneous shear flow. This relation might form the basis for a more universal pressure-dilatation model. It is conjectured that the insignificance of intrinsic compressibility effects in wall-bounded supersonic shear flow is mainly due to the impermeability constraint of the wall. To this end, a linear stability analysis of supersonic channel flow along cooled, but permeable walls has been performed based on Coleman et al.'s [5] mean flow data. It shows an increase in the moduli of eigenfunctions related to compressibility, like pressure, and in moduli of quantities derived from eigenfunctions such as ‘pressure dilatation’ and squared dilatation. Although these results do not prove our hypothesis they provide hints in this direction. Shock/turbulence interaction is viewed as a source of compressibility. Former DNS data of Hannappel and Friedrich [10] for shock/isotropic turbulence interaction showing the effect of compressibility on the amplification of fluctuations are interpreted based on linear perturbation equations.     

Whitham—Broer—Kaup浅水波方程新的多孤子解

Whitham-Broer-Kaup（简记WBK）方程具有重要的意义,至今人们只给出了它的单孤子解,本利用齐次平衡法并借助数学给出它新的多孤子解,并作为特例得到一类变式Boussinesq方程的多孤子解。     

On thermoelastostatics of composites with nonlocal properties of constituents II. Estimation of effective material and field parameters

One considers a linear thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated heterogeneities. It is assumed that the stress–strain constitutive relations of constituents are described by the nonlocal integral operators, whereas the equilibrium and compatibility equations remain unaltered as in classical local elasticity. The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained. The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. In a simplified case of using of the effective field hypothesis for analyzing composites with one sort of heterogeneities, one proves that the effective moduli explicitly depend on both the strain and stress concentrator factor for one heterogeneity inside the infinite matrix and does not directly depend on the elastic properties (local or nonlocal) of heterogeneities. In such a case, the Levin’s (1967) formula in micromechanics of composites with locally elastic constituents is generalized to their nonlocal counterpart. A solution of a volume integral equation for one heterogeneity subjected to inhomogeneous remote loading inside an infinite matrix is proposed by the iteration method. The operator representation of this solution is incorporated into the new general integral equation of micromechanics without exploiting of basic hypotheses of classical micromechanics such as both the effective field hypothesis and “ellipsoidal symmetry” assumption. Quantitative estimations of results obtained by the abandonment of the effective field hypothesis are presented.     

涡度拟能传输惯性区二维湍流标量场方差谱

本文应用非平衡统计力学封闭方法,给出涡度拟能传输惯性区二维湍流标量场方差谱的完整表达式,数值计算该表达式中的比例系数B。由于传输过程的非局部性,B依赖于表征波数变化范围的局部化因子,不再是普适常数。     

Influence of buoyancy in a mixed convection liquid metal flow for a horizontal channel configuration

This article presents the direct numerical simulation (DNS) of mixed convection turbulent heat transfer in a horizontal channel case for liquid lead. Cartesian mesh is used and the incompressible Navier-Stokes equations are discretized with highly accurate finite difference sixth-order compact schemes to perform the DNS. The influence of mixed convection in liquid metal with Prandtl number equal to 0.025 and Reynolds number equal to 4667 has been studied by varying the Richardson number (Ri = 0, 0.25, 0.50, 1.00). The obtained results are extensively analyzed and discussed in this article. In particular, large-scale circulation is observed under the influence of buoyancy. Compared to the forced convection case (Ri = 0), stronger velocity fluctuations are noticed that highlight the fact that turbulence is strongly enhanced with the increasing buoyancy. It also proves that the thermal plumes rising up from the hot wall of the channel activate the cross-stream eddies. Moreover, temperature fluctuations are found to be more homogeneously distributed with increasing buoyancy effects and mixing is more effective in the center of the channel. In addition, compared with forced convection, mixed convection has shown enlargement of the large-scale structures that only appear in the temperature field for low Prandtl number fluids. Extensive results of flow and temperature fields are analyzed and presented.     

Buoyancy effects on turbulent swirling flows

A three-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T ′². Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl. The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.