A Conservative Difference Scheme for Conservative Differential Equation with Periodic Boundary

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Nonlinear Disturbances and Weak Discontinuities in a Supersonic Boundary Layer

The processes of wave disturbance propagation in a supersonic boundary layer with self-induced pressure [1–4] are analyzed. The application of a new mathematical apparatus, namely, the theory of characteristics for systems of differential equations with operator coefficients [5–8], makes it possible to obtain generalized characteristics of the discrete and continuous spectra of the governing system of equations. It is shown that the discontinuities in the derivatives of the solution of the boundary layer equations are concentrated on the generalized characteristics. It is established that in the process of flow evolution the amplitude of the weak discontinuity in the derivatives may increase without bound, which indicates the possibility of breaking of nonlinear waves traveling in the boundary layer.     

Three-Wave Interactions of Disturbances in a Supersonic Boundary Layer

Within the framework of the weakly nonlinear stability theory, group interaction of disturbances in a supersonic boundary layer is considered. The disturbances are represented by two spatial packets of traveling instability waves (wave trains) with multiple frequencies. The possibility of energy redistribution in such wave systems in the case of three-wave resonant interactions of packet constituents is considered. The model is used to test the dynamics of unstable waves arising due to introduction of controlled high-intensity disturbances into a supersonic boundary layer. It is found that this mechanism is not the main one for the features of streamwise dynamics of such nonlinear waves being observed.     

Decay theorems for the Broadwell equations

Communicated by R. Muncaster     

Self-similar fluid-dynamic limits for the Broadwell system

This report discusses a new approach for the resolution of the fluid-dynamic limit for the Broadwell system of the kinetic theory of gases, appropriate in the case of Riemann, Maxwellian data. Since the formal limiting system is expected to have self-similar solutions, we are motivated to replace the Knudsen number in the Broadwell model so that the resulting model admits self-similar solutions =x/t and then let go to zero. The limiting procedure is justified and the resulting limit is a solution of the Riemann problem for the fluid-dynamic limit equations. A class of Riemann data for which this program can be carried out is exhibited. Furthermore, it is shown that for the Carleman model the complete program can be done successfully for arbitrary Riemann data.     

Energy Addition to a Gas in a Turbulent Supersonic Boundary Layer

The effect of the thermal action on a turbulent supersonic boundary–layer flow is studied numerically. It is shown that the friction force on an isothermal surface decreases significantly. The effectiveness of using a thermal source for decreasing friction is evaluated.     

Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is attached to a point on the left and there is a force (tension) τ acting on the right. In order to provide good ergodic properties to the system, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distributions of the elongation, momentum and energy converge to the solution of the Euler system of equations in the smooth regime.     

Numerical Simulation of Disturbance Evolution in the Supersonic Boundary Layer over an Expansion Corner

Fluid Dynamics - The linear and nonlinear stages of disturbance development in the supersonic boundary layer over a 10° expansion corner is investigated numerically within the framework of...     

Statistical Characteristics of an Isothermal, Supersonic Developing Boundary Layer Flow from DNS Data

Direct numerical simulation results for a developing, supersonic boundary layer flow with either an adiabatic wall temperature condition or a cold wall (relative to adiabatic) temperature condition are evaluated to assess the comparative effect on the mean and turbulent fields. Included in the analysis are two-point turbulent spanwise spatial correlations and the corresponding one-dimensional energy spectra distributions as well as higher-order statistics including skewness and flatness factors. In addition to the mean field velocity and temperature behavior, the turbulent Reynolds stress, temperature variance, and heat and mass flux distributions are discussed. An overall focus of the analysis is to both contrast the velocity and thermal field behavior and to provide some additional insight into the dynamic balance of the various statistical correlations and their impact on model development.     

Effect of Heat Supply on the Stability of the Supersonic Swept Atiachment-Line Boundary Layer

The stability of a boundary layer with volume heat supply on the attachment line of a swept wing is investigated within the framework of the linear theory at supersonic inviscid-free-stream Mach numbers. The results of numerical calculations of the flow stability and neutral curves are presented for the flow on the leading edge of a swept wing with a swept angle χ=60° at various free-stream Mach numbers. The effect of volume heat supply on the characteristics of boundary layer stability on the attachment line is studied at a surface temperature equal to the temperature of the external inviscid flow. It is shown that in the case of a supersonic external inviscid flow volume heat supply may result in an increase in the critical Reynolds number and stabilization of disturbances corresponding to large wave numbers. For certain energy supply parameters the situation is reversed, the unstable disturbances corresponding to the main flow-instability zone are stabilized but another zone of flow-instability with small wave numbers and a significantly lower critical Reynolds number appears.     

Non-stationary two-dimensional potential flows by the Broadwell model equations

The two-dimensional Broadwell model of discrete kinetic theory is studied in order to clarify the physical relevance of its solutions in comparison to the solutions of the continuous Boltzmann equation. This is achieved by determining completely, in closed form, all non-stationary potential flows with steady limiting conditions and isotropic pressure tensor at infinity. Several classes of exact solutions are also constructed when some of the above hypotheses are dropped. Most results are made possible by suitable transformations, which reduce essentially a complicated overdetermined system of partial differential equations to solving explicitly a Liouville equation. The structure of the obtained solutions, and especially the unphysical features that they exhibit, are finally commented on. It is remarkable that, for the problem considered here, there is no solution showing the typical qualitative features which characterize the continuous Boltzmann equation.     

Wave structure induced by fluid-dynamic limits in the Broadwell model

Consider the fluid-dynamic limit problem for the Broadwell system of the kinetic theory of gases, for Maxwellian Riemann initial data. The formal limit is the Riemann problem for a pair of conservation laws and is invariant under dilations of coordinates. The approach of self-similar fluid-dynamic limits consists in replacing the mean free path in the Broadwell model so that the resulting problem preserves the invariance under dilations. The limiting procedure was justified in [ST]. Here, we study the structure of the emerging solutions. We show that they consist of two wave fans separated by a constant state. Each wave fan is associated with one of the characteristic fields and is either a rarefaction wave or a shock wave. The shocks satisfy the Lax shock conditions and have the internal structure of a Broadwell shock profile.     

Two dimensional half-space problems for the Broadwell discrete velocity model

Stationary boundary value problems for the Broadwell model in a half-space and in a half-infinite channel are considered. By means of the analogy between the stationary boundary value problems for the Broadwell equations and the initial-boundary value problem of Carleman's system, solutions are found for various situations. Uniqueness and non-uniqueness of solutions is discussed as well. The non-uniqueness problem in the channel leads to the investigation of the initial value problem for Carleman's equation with partly negative initial densities. Some new results for this problem are given. Received January 20, 1996     

Problem of Optimal Control of the Turbulent Boundary Layer on a Permeable Surface in Supersonic Gas Flow

The problem of constructing the law of distribution of the normal component of the velocity of blowing to the turbulent boundary layer at supersonic flow velocities which ensure the minimum convective heat flow transmitted from the boundary layer to the surface is considered. The power of the control system calculated with regard to Darcy’s law of flow through a porous medium acts as the isoperimetric condition. The problemis solved using the Dorodnitsyn generalized integral relations. The numerical experiments carried out in the case of flow past a sphere showed the effectiveness of the optimal blowing laws as compared with the uniform law, namely, the gain in the minimized functional reaches 31.82%.     

Evolution of Artificial Perturbations in the Boundary Layer on a Plate and in Its Wake at Supersonic Free-Stream Velocity

The evolution of artificial perturbations in the boundary layer on the flat section of a plate, on the backward-facing wedge behind the rarefaction wave fan, and in the wake is studied experimentally at the Mach number M=2.     

Development of an Intermittency Equation for the Modeling of the Supersonic/Hypersonic Boundary Layer Flow Transition

An intermittency transport equation is developed in this study to model the laminar-turbulence boundary layer transition at supersonic and hypersonic conditions. The model takes into account the effects of different instability modes associated with the variations in Mach numbers. The model equation is based on the intermittency factor γ concept and couples with the well-known SST k–ω eddy-viscosity model in the solution procedures. The particular features of the present model approach are that: (1) the fluctuating kinetic energy k includes the non-turbulent, as well as turbulent fluctuations; (2) the proposed transport equation for the intermittency factor γ triggers the transition onset through a source term; (3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ, which are often cost-ineffective with the modern CFD methods; (4) in the fully turbulent region, the model retreats to SST model. This model is validated with a number of available experiments on boundary layer transition including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition with a reasonably wide range of Mach numbers.     

小肠的结构及边界润滑模型建立

为了实现内窥镜的无损诊治,提高肠道机器人的行走能力,需构建肠道的结构模型和边界润滑模型.本文以小肠为研究对象,表征了其内部结构,测定了肠道内表面摩擦系数与径向应变、载荷和滑动速度之间关系.结果表明:小肠内表面结构由皱襞、绒毛和微绒毛组成;直径变化是影响其摩擦的首要因素,其次是滑动速度和载荷.运用薄膜理论,根据小肠内部结构特征和摩擦系数的变化规律,构建其结构模型及边界润滑模型,并推断出小肠收缩状态润滑形式为流体动压润滑,摩擦阻力主要由肠黏液表面剪切力决定,膨胀时,润滑形式为薄膜润滑,摩擦阻力由肠黏液表面剪切力、绒毛产生的约束力和吸附力决定.     

Supersonic combustion and hypersonic propulsion

50 多年的努力和曲折经历证明了超声速燃烧冲压发动机概念的可行性. 本文对影响超燃冲压发动机技术成熟的主要因素作了扼要的分析. 高超声速推进的首要问题是净推力, 利用超声速燃烧获得推力遇到各种实际问题的制约, 它们往往互相牵制. 几次飞行试验表明高超声速飞行需要的发动机净推力仍差强人意, 液体碳氢燃料(煤油) 超燃冲压发动机在飞行马赫数5 上下的加速和模态转换过程, 成为高超声速吸气式推进继续发展的瓶颈. 研究表明, 利用吸热碳氢燃料不仅是发动机冷却的需要也是提高发动机推力和性能的关键举措, 燃料吸热后物性改变对燃烧性能的附加贡献对超燃冲压发动机的净推力至关重要.当前, 实验模拟技术和测量技术相对地落后, 无法对环境、尺寸和试验时间做到完全的模拟. 计算流体动力学(Computational Fluid Dynamics, CFD) 逐渐成为除实验以外唯一可用的工具, 然而, 超声速燃烧的数值模拟遇到湍流和化学反应动力学的双重困难. 影响对发动机的性能作正确可靠的评估.提出双模态超燃冲压发动机模态转换、吸热碳氢燃料主动冷却燃料催化裂解与超声速燃烧耦合、燃烧稳定性、实验模拟技术与装置、内流场特性和发动机性能测量、数值模拟中的湍流模型、煤油替代燃料及简化机理等研究前沿课题, 和未来5~10 年重点发展方向的建议.     

Supersonic annular jet

The flow in supersonic annular jets has been investigated experimentally. Schemes for shock interaction during reconstruction from an open to a closed base region are determined. The fundamental parameters characterizing the structure of the separation flow are extracted.