Lifting Surface in Subsonic Unsteady Regime

The paper refers to the solution of the integral equation for the acceleration (or pressure) potential for the study of subsonic linearized unsteady flow in view of aeroelastic applications. The case considered is relevant to a trapezoidal wing infinitely thin surface without discontinuities. As is well known [1, 2], the kernel of the integral equation exhibits three singularities, two of which are integrable in elementary form, whereas, for the third one integration in principal part according to Hadamard's rule is necessary. The kernel is therefore reworked in such a way that all the singularities are separated from the regular part, and eventually the discretization is performed in such a way that only the regular part is to be recalculated for each new value of the reduced frequency. Convergence tests, comparison with other methods of solution, and time saving associated with the technique of separation are also shown.Sommario. II lavoro tratta la risoluzione del problema relativo alla equazione integrale nel potenziale di accelerazione (o di pressione) per lo studio di una corrente subsonica linearizzata nonstazionaria, in vista di applicazioni aeroelastiche. Il caso considerato è quello di una superficie alare a pianta trapezoidale in assenza di discontinuità di spessore infinitesimo. Come è noto [1, 2], il nucleo della equazione integrale in parola presenta tre singolarità, due sole delle quali sono integrabili in forma elementare, (o riconducibili ad essa), mentre per la terza è necessario far ricorso alla integrazione in parte principale alla Hadamard. Il nucleo stesso viene quindi rielaborato in modo da isolare tutte le singolarità dalla componente regolare del nucleo; si procede così alla discretizzazione dell' equazione integrale, e, per ogni valore della frequenza ridotta, va ricalcolata solo la parte regolare della matrice risolvente. Vengono poi effettuati tests di convergenza, confronti con altri metodi di soluzione, analisi sui tempi di calcolo e risparmio di tempo di calcolo dovuto alla tecnica di separazione.     

可变形儒可夫斯基翼型亚音速非定常气动力的研究

对于翼面变形速度远小于来流速度情况下的儒可夫斯翼型亚音速绕流问题,通过仿射变换将可压缩流动转换成不可压缩流动,将解析解和离散涡方法相结合计算变形机翼的不可压缩流动速度场,再利用逆变换得到变形机翼的亚音速流动速度场,进而分析非定常气动力特性,建立变形机翼的准定常升力系数和非定常附加升力系数在可压缩和不可压缩两种状态下的简单近似对应关系。计算结果显示变形机翼的非定常气动升力近似等于准定常计算结果叠加上虚拟质量力导致的非定常附加升力,该非定常附加升力随翼型变形速率呈线性关系,由机翼当前时刻飞行姿态、翼型及其变形速率确定,与具体变形历史过程无关。低来流马赫数时虚拟质量力导致的非定常效应显著,高亚音速流动时准定常升力起主导作用。同时还分析了不同马赫数下机翼往复变形过程中升力的变化特性,指出尽管高亚音速变形机翼的气动升力近似等于准定常气动升力,但不能忽视非定常附加升力的影响,非定常附加升力将导致完成往复变形需要外界输入正比于Ma∞/[(1-Ma2∞)]的功。     

Existence of Global Solutions for Unsteady Isentropic Gas Flow in a Laval Nozzle

In this paper, we study the motion of isentropic gas in the Laval nozzle. The Laval nozzle is the most important type of nozzle utilized in some turbines. In particular, we consider unsteady flows, including transonic gas flows, and prove the existence of global solutions for the Cauchy problem. In spite of its importance, this problem has received little attention until now. The most difficult point is to obtain bounded estimates for approximate solutions. To overcome this, we introduce a modified Godunov scheme. The corresponding approximate solutions consist of piecewise steady-state solutions of an auxiliary equation and yield a sharper bounded estimate. As a result, we find an invariant region for our solutions. Finally, in order to prove their convergence, we use the compensated compactness framework.     

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.     

On Mathematical Models of Average Flow in Heterogeneous Formations

We consider a general model of transient flow in media of random conductivity and storativity. The flow is driven by the spatially distributed source function (x, t) and the initial head distribution h ₀(x). The function models sources and wells and can be deterministic, random or a sum of both. The deterministic source function corresponds to singularities of deterministic strength, whereas the random models the head boundary condition. In the latter case, is shown to be proportional to the hydraulic conductivity. The aim of the study is to analyze the feasibility of averaging the flow equations and of developing the mathematical model of average flow (AFM) without solving problems in detail. It is shown that the problem of averaging is reduced to deriving two constitutive equations. The first equation, the effective Darcy's law (EDL) stems from averaging Darcy's law at local scale. The second one is related to the medium ability to store a fluid and expresses the correlation between the storativity and head in terms of the mean head. Both relationships are required to be completely determined by the medium structure (conductivity and storativity statistical properties) and independent of the flow configuration (functions and h ₀). We show that if one of the constitutive equations exists, the same is true respective to the second. This reduces the problem of averaging to the classic one of deriving the EDL. For steady flows the EDL is shown to exist for flows driven by sources (wells) of either deterministic flux or head boundary conditions. No EDL can be derived if both types of sources are present in the flow domain. For unsteady flows the EDL does not exist if the initial head correlates with the medium properties. For uncorrelated initial head distribution, its random residual (due to the measurement errors and scarcity of the data) has no impact on the EDL and is immaterial. For deterministic h ₀, the only case for which the EDL exists is the flow by sources of deterministic discharge. For sources of given head boundary condition the EDL can be derived only for uniform initial head distribution. For all other cases, the EDL does not exist. The results of the study are not limited by usually adopted assumptions of weak heterogeneity and of stationarity of the formation random properties.     

Transonic Shocks in Compressible Flow Passing a Duct for Three-Dimensional Euler Systems

In this paper we study the transonic shock in steady compressible flow passing a duct. The flow is a given supersonic one at the entrance of the duct and becomes subsonic across a shock front, which passes through a given point on the wall of the duct. The flow is governed by the three-dimensional steady full Euler system, which is purely hyperbolic ahead of the shock and is of elliptic–hyperbolic composed type behind the shock. The upstream flow is a uniform supersonic one with the addition of a three-dimensional perturbation, while the pressure of the downstream flow at the exit of the duct is assigned apart from a constant difference. The problem of determining the transonic shock and the flow behind the shock is reduced to a free-boundary value problem. In order to solve the free-boundary problem of the elliptic–hyperbolic system one crucial point is to decompose the whole system to a canonical form, in which the elliptic part and the hyperbolic part are separated at the level of the principal part. Due to the complexity of the characteristic varieties for the three-dimensional Euler system the calculus of symbols is employed to complete the decomposition. The new ingredient of our analysis also contains the process of determining the shock front governed by a pair of partial differential equations, which are coupled with the three-dimensional Euler system. The paper is partially supported by National Natural Science Foundation of China 10531020, the National Basic Research Program of China 2006CB805902, and the Doctorial Foundation of National Educational Ministry 20050246001.     

Unsteady Boundary Layer on a Blunt Body in a Hypersonic Flow of Non-Uniform Dusty Gas

The unsteady heat transfer at the stagnation point on a blunt body traveling at hypersonic velocity through a layer of nonuniform dusty gas with low-inertia particles (not deposited on the body surface) is investigated. Using the matched asymptotic expansion method, the equations of the two-phase unsteady boundary layer near the symmetry axis of the body are derived with account for the polydispersity of the particles. The structure of the unsteady boundary layer and the variation of the friction and heat transfer coefficients at the stagnation point are studied numerically. Layered nonuniformities of the particle concentration and size are considered, the limits of variation of the thermal and mechanicals loads are found, and the effect of the dust polydispersity on the heat transfer is investigated.     

Mathematical Simulation of Dust Lifting from the Surface

Results of numerical simulation of the shock wave passing along a dusty layer are presented; the simulation was performed under the onetemperature, onevelocity assumption. It is shown that a system of compression and expansion waves is formed inside the layer, and these waves are successively reflected from the external boundary and solid wall. Regular and irregular reflections of the leading shock wave from the solid wall with different scenarios of instability evolution on the layer edge are described. Possible mechanisms of particle lifting from the surface are described.     

A Parallel 3D Unsteady Flow Analysis in an Asymmetrically Constricted Vessel

In this study, parallel computation of unsteady incompressible flow in an asymmetrically constricted 3D vessel has been presented. A time accurate cell centered finite volume method (FVM) in conjunction with pseudo-compressibility technique and Roe's flux difference splitting of nonlinear terms has been employed for solving the Navier-Stokes (NS) equations on the multiple instruction multiple data (MIMD) machine VPP700. The influence of Reynolds' number ( Re ) and the Strouhal number ( St ) on flow dynamic factors like wall pressure (WP), wall shear stress (WSS), central axis velocity (CAV), etc., have been analyzed. Three-dimensional (3D) features in the formation and detachment of separation zones, which are sensitive to both Re and St have been noticed on the diverging wall of the constriction.     

蒸汽发生器干燥器三维流场数值模拟计算

针对压水堆核电厂蒸汽发生器波形板干燥器的结构特点,采用通用计算流体力学软件ANSYS-Fluent中的多孔介质模型对蒸汽发生器用波形板干燥器进行三维流场的数值模拟计算,得到干燥器区域的流场情况以及干燥器孔板入口处蒸汽的流速分布情况,确定在极限工况下干燥器孔板入口处蒸汽的最高流速．在设计蒸汽发生器干燥器时,应确保极限工况下干燥器入口蒸汽的最高流速低于通过试验确定的特定波形板片的临界速度,以确保干燥器的所有区域均工作在其允许的分离能力以内．     

A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems

Various attempts have been made to model flow in shale gas systems. However, there is currently little consensus regarding the impact of molecular and Knudsen diffusion on flow behavior over time in such systems. Direct measurement or model-based estimation of matrix permeability for these “ultra-tight” reservoirs has proven unreliable. The composition of gas produced from tight gas and shale gas reservoirs varies with time for a variety of reasons. The cause of flowing gas compositional change typically cited is selective desorption of gases from the surface of the kerogen in the case of shale. However, other drivers for gas fractionation are important when pore throat dimensions are small enough. Pore throat diameters on the order of molecular mean free path lengths will create non-Darcy flow conditions, where permeability becomes a strong function of pressure. At the low permeabilities found in shale gas systems, the dusty-gas model for flow should be used, which couples diffusion to advective flow. In this study we implement the dusty-gas model into a fluid flow modeling tool based on the TOUGH+ family of codes. We examine the effects of Knudsen diffusion on gas composition in ultra-tight rock. We show that for very small average pore throat diameters, lighter gases are preferentially produced at concentrations significantly higher than in situ conditions. Furthermore, we illustrate a methodology which uses measurements of gas composition to more uniquely determine the permeability of tight reservoirs. We also describe how gas composition measurement could be used to identify flow boundaries in these reservoir systems. We discuss how new measurement techniques and data collection practices should be implemented in order to take advantage of this method. Our contributions include a new, fit-for-purpose numerical model based on the TOUGH+ code capable of characterizing transport effects including permeability adjustment and diffusion in micro- and nano-scale porous media.     

跨音速压气机级的三维周期性非定常流动计算

对跨音速压气机级动静叶排相干形成的三维非定常流场进行了数值研究，利用时间推进ＬＵ－ＳＧＳ稳式迭代法求解三维非定常欧拉方程，对流项采用高分辨率ＮＮＤ格式离散。对某压气机第一级动静叶排相干非定常流场的计算结果表明，本文方法不仅在收敛速度上明显地优于一般显式方法，而且保持了流场中激波的高分辨率，适于推广到计算量巨大的的多级轴流压气机三维非定常流场的数值分析问题     

Forces Exerted on a Body in an Unsteady Vortex Separation Flow of an Ideal Incompressible Fluid

A formula relating the forces exerted on a three-dimensional body to the motion of a vortex and source system simulating that body is derived for an unsteady vortex separation flow of an ideal incompressible fluid. The shape of the body can vary with time. In the case of steady-state homogeneous flow past an airfoil the formula obtained coincides with the Joukovski formula.     

Unsteady Flow of an Oscillating Porous Disk and a Fluid at Infinity

An exact analytic solution of the unsteady Navier–Stokes equations is obtained for the flow caused by the non-coaxial rotations of a porous disk and a fluid at infinity. The porous disk is executing oscillations in its own plane with superimposed injection or suction. An increasing or decreasing velocity amplitude of the oscillating porous disk is also discussed. Further, it is shown that a combination of suction/injection and decreasing/increasing velocity amplitude is possible as well. In addition, the flow due to porous oscillating disk and a fluid at infinity rotating about an axis parallel to the z-axis is attempted as a second problem. Sommario. Si studia il flusso non stazionario prodotto dall'oscillazione di un disco poroso in un fluido e si fornisce una soluzione analitica delle equazioni di Navier–Stokes. Si discute l'effetto di una suzione/iniezione e di una variazione sull'ampiezza della velocità' di oscillazione. Infine si studia il flusso dovuto alle oscillazioni non coassiali di un disco poroso e di un fluido all'infinito.     

Equivalent Cylinder Systems Representing the Soil Matrix in Diffusion-Reaction Models for an Aggregated Soil

The structure of an aggregated soil or a dual-porosity medium is characterized by a function called the generalized surface-area-to-volume ratio, which can be measured as a distance distribution. For an isotropic structure the distance measurements may be done in the digitized image of a cross-section. A diffusion-reaction process in the soil matrix can be described by means of an equivalent cylinder system which preserves the generalized surface-area-to-volume ratio of the structure. The contribution of each cylinder radius is described by a weight function, which is obtained by transforming the measured cross-sectional distance distribution. In order to test the method, a diffusion-reaction model from the literature has been applied to spheres with a lognormal radius distribution and to an irregular, generated structure. Both geometries can be represented by just a few cylinder radii and cylinder weights. The method works best for dual-porosity structures with a convex shape. Deviations occur if parts of the matrix structure have a concave shape.     

Effect of the Chemical Reaction and Injection on Flow Characteristics in an Unsteady Upward Motion of an Isothermal Plate

The transient incompressible viscous fluid flow regime past a semiinfinite isothermal plate under conditions of natural convection is studied numerically. The solution obtained takes into account the firstorder homogeneous chemical reaction and the mass flux through the plate. The calculated velocity profile is in good agreement with the known exact solution. Velocity, temperature, and concentration profiles are presented. It is shown that the fluid velocity decreases with increasing chemical reaction parameter. The distributions of local and averaged values of skin friction and Nusselt and Sherwood numbers are analyzed.     

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.     

Unsteady Motion of a Gas in a Strip

An exact solution is constructed, which describes a gas glow in a strip between a rectilinear source and sink. With time, the strip turns and expands. In the case of consistent boundary conditions, the flow in the strip is continuous. If the consistency constraints are violated, a shock wave is formed inside the strip.     

Stability of Vibroconvective Flow in an Inclined Layer with Respect to Three-Dimensional Perturbations

The stability of the average flow in a laterally heated fluid layer is investigated. The flow is driven by the joint action of the gravity force and vertical high-frequency vibrations. Three-dimensional longwave perturbations are analytically considered. A comparison with the numerical results obtained earlier shows that this instability mode is the most dangerous over a wide parameter range.