可压缩多介质粘性流体的数值计算

将考虑热传导和粘性情况下的Navier Stokes方程描述的物理过程分解成3个子过程进行数值计算,即把整个流量计算分解成无粘性流量、粘性流量和热流量3部分,采用多介质流体高精度parabolic piecewise method（PPM）方法、二阶空间中心差方法和两步Rung-Kutta时间推进方法相结合进行数值计算。给出了激波管中Riemann问题和二维、三维Richtmyer-Meshkov界面不稳定性的Navier Stokes方程和Euler方程对比计算结果,显示了粘性对界面不稳定性的影响。     

One-dimensional transonic gas flow in a wind tunnel with perforated walls

Near-sonic inviscid gas flow in the working section of a wind tunnel with perforated walls is investigated in the context of the one-dimensional theory with Darcy's boundary condition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 143–148, November–December, 1988.     

On the size of cavities in tunnels with continuous and perforated walls

A one-dimensional theory is developed to describe the hydrodynamic interaction of cavities with walls of continuous and perforated working sections, allowance being made for the influence of hydraulic losses and the boundary layers on the walls, and also the ponderability and surface-tension forces. It is shown that if some of the fluid is sucked through the perforated boundaries of the working section one can not only strongly reduce the influence of the walls of the tunnel on the size of a cavity but also appreciably increase the useful loading of the flow by the cavity. The available experiments and some made specially by the authors are compared with the calculations, and this reveals satisfactory agreement in the complete range of cavitation numbers and relative blocking of the flow by the body and cavity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 163–167, March–April, 1979.     

Turbulence statistics in rotating channel flows with rough walls

We performed direct simulations of channel flow subjected to rotation about a spanwise axis, comparing cases with smooth and rough walls. The destabilizing effect of roughness counteracts the stabilizing effect of rotation on the cyclonic (stable) side. When the surface is rough the Reynolds stresses remain significant at all rotation rates considered, even those that results in a quasi-laminar state when the wall is smooth. The wake fluctuations result in significant dispersive stresses, which give an important contribution to the generation of turbulence on the stable side, mainly through added production of shear stresses. The dispersive stresses are mostly associated with the channeling of the flow between roughness elements.     

Computation of two-dimensional dam-break flood flows

Sudden total collapse of a dam holding back a reservoir of water, whenever it occurs, becomes formidably impressive in the extent of destruction with which it is associated. The movement on a dry bed of a two-dimensional flood wave resulting from the break of a dam has been one of the most important and challenging subjects in rapidly varied unsteady flows from the computational point of view. An implicit time-marching finite volume numerical scheme was developed and subsequently applied for the solution of the two-dimensional unsteady open channel flow equations written in conservation form. In order to avoid the problems associated with a conventional grid system, a body-fitted non-orthogonal local co-ordinate system was utilized. The proposed numerical technique was applied to determine the stage hydrographs, water surface profiles and velocities of flood flows resulting from suddenly breached storage dams. Predictions were compared with an analytical solution, with available numerical solutions using MacCormack's two-step explicit scheme and with experimental measurements. Agreement between predictions and measurements regarding the wave front advancement and stage hydrographs is considered to be satisfactory.     

Wall-resolved large-eddy simulation of turbulent channel flows with rough walls

Turbulent flows over rough surfaces widely exist in nature and industry. Investigating its mechanism is of theoretical and practical significance. In this work we simulate the turbulent channel flow with rough walls using large-eddy simulation with rough elements resolved using the curvilinear immersed boundary method and compare the results obtained in this work with those in the paper by Yuan and Piomelli( J. Fluid Mech., vol. 760, pp. R1, 2014), where the volume of fluid method was employed for modeling rough elements. The mean streamwise velocity profiles predicted by the two methods agree well with each other. Differences in Reynolds stresses and dispersive stresses are observed, which are attributed to the different approaches in dealing with the complex geometry of the rough surface.     

Computation of viscoelastic cable coating flows

A viscoelastic analysis is presented for model tube tooling, draw-down and combined geometry flows encountered in the cable coating industries. The work investigates the development of stress fields and studies the effect of varying entry flow stress boundary conditions. The analysis takes into account tube tooling and draw-down flow sections individually, and in combination. The flow behaviour of cable-coating grade low density polyethylene is studied assuming a viscoelastic, isothermal flow, and employing a Taylor–Petrov–Galerkin finite element scheme with an exponential Phan-Thien–Tanner constitutive model. © 1998 John Wiley & Sons, Ltd.     

Mathematical modeling of viscous gas flow in a doubly connected volume with perforated walls

A numerical method is proposed for computing viscous gas flow in an initial doubly connected domain which is a volume having perforated walls and enclosing a sphere. The types of subdomains (finite volumes) into which the initial domain can be divided are considered. For each type of finite volume, there is a curvilinear coordinate system. Results of flow computation for Re = 100 and 500, and M = 0.6 are given.     

Computation of free‐surface flows with local mesh adaptation

This paper describes a modern free‐surface capturing strategy implemented in an unstructured finite‐volume viscous flow solver that can handle moving grids composed of arbitrary‐shaped control volumes. An adaptive mesh strategy is fully integrated in the code making it a single tool for dynamically maintaining a prescribed density of grid points around the steady or unsteady interface between air and water. The whole adaptive procedure is described in detail. The efficiency of the overall approach is examined on two‐ and three‐dimensional hydrodynamic applications. The adaptive strategy achieves interesting gains in terms of computational and human efforts compared to single‐mesh computations. Copyright © 2005 John Wiley & Sons, Ltd.     

Computation of compressible flows with high density ratio and pressure ratio

The WENO method, RKDG method, RKDG method with original ghost fluid method, and RKDG method with modified ghost fluid method are applied to singlemedium and two-medium air-air, air-liquid compressible flows with high density and pressure ratios： We also provide a numerical comparison and analysis for the above methods. Numerical results show that, compared with the other methods, the RKDG method with modified ghost fluid method can obtain high resolution results and the correct position of the shock, and the computed solutions are converged to the physical solutions as themesh is refined.     

Transonic flows around an airfoil in wind tunnels with porous walls

A study is made of two-dimensional transonic flows of gas around an airfoil in the working part of a wind tunnel with porous walls. The values of the flow parameters are determined by the numerical solution of a boundary-value problem for the equation of the velocity potential; this problem simulates the gas flow around the profile in the tunnel with porous walls. The obtained results are then used to construct an asymptotic theory of the influence of the wind-tunnel height and the Mach number M of the flow in it on the characteristics of the flow around the airfoil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1980.     

Stability of flows of the Hamel type in channels with permeable walls

The stability of nonparallel flows of a viscous incompressible fluid in an expanding channel with permeable walls is studied. The fluid is supplied to the channel through the walls with a constant velocity v₀ and through the entrance cross section, where a Hamel velocity profile is assigned. The resulting flow in the channel depends on the ratio of flow rates of the mixing streams. This flow was studied through the solution of the Navier—Stokes equations by the finite-difference method. It is shown that for strong enough injection of fluid through the permeable walls and at a distance from the initial cross section of the channel the flow approaches the vortical flow of an ideal fluid studied in [1]. The steady-state solutions obtained were studied for stability in a linear approximation using a modified Orr—Sommerfeld equation in which the nonparallel nature of the flow and of the channel walls were taken into account. Such an approach to the study of the stability of nonparallel flows was used in [2] for self-similar Berman flow in a channel and in [3] for non-self-similar flows obtained through a numerical solution of the Navier—Stokes equations. The critical parameters *, R*, and Cr* at the point of loss of stability are presented as functions of the Reynolds number R₀, characterizing the injection of fluid through the walls, and the parameter , characterizing the type of Hamel flow. A comparison is made with the results of [4] on the stability of Hamel flows with R₀ = 0.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 125–129, November–December, 1977.The author thanks G.I. Petrov for a discussion of the results of the work at a seminar at the Institute of Mechanics of Moscow State University.     

Development of self-aeration process for supercritical chute flows

When a high-velocity flow discharges into a chute, air is entrained through the free surface. This is relevant to the development of self-aeration for mixture flow. In this study, the air concentration was measured in the self-aerated developing region for various initial flow velocities, depths, and chute slopes. The effect of hydraulic conditions on the bottom self-aeration process was analyzed. Increasing the initial flow velocity and depth was found to increase the rate of air diffusion into the water flow. This positive correlation indicates that flow turbulence is a key factor for the self-aeration development process. The Reynolds number of the flow was found to be an appropriate hydraulic condition for describing self-aeration development. In addition, the constraint of buoyancy on air bubble diffusion into the chute bottom decreased as the chute slope was increased, which made the development process for bottom self-aeration more pronounced. A new empirical equation is presented for predicting the development process of bottom self-aeration in open channel flows.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.     

On stress distribution in flows of viscoelastic fluids through ducts with porous walls

Summary In continuation of an earlier investigation, the present paper discusses the stress distribution in the inertialess flow of a viscoelastic fluid confined between two plane parallel walls, in which the upper wall moves with a constant velocity while the lower is held at rest with a uniform constant suction applied on its surface. However, the stress field is discussed in detail for the case when the upper wall is also held at rest and the effects arising due to application of suction are pointed out. The most important difference in the behaviour of viscoelastic fluid, compared with that ofNewtonian fluid, lies in the fact that the gradient of the normal stress component in the horizontal direction depends on the distance from the walls.A short discussion has also been provided for the flow in a cylindrical tube with uniform constant suction applied on its surface. Though not evident from general considerations, it is seen that the situation here also is quite similar to that of plane flow.

---

Zusammenfassung In Fortsetzung einer früheren Untersuchung wird in der vorliegenden Arbeit die Spannungsverteilung in einer viskoelastischen Flüssigkeit diskutiert, die trägheitslos zwischen zwei parallelen Wänden strömt, wenn die obere Wand mit konstanter Geschwindigkeit bewegt wird und an der unteren, in Ruhe befindlichen eine gleichförmige konstante Absaugung erfolgt. Das Spannungsfeld wird indessen im einzelnen nur für den Spezialfall diskutiert, daß auch die obere Wand ruht, und die infolge der Absaugung entstehenden Effekte werden aufgezeigt. Der wichtigste Unterschied im Verhalten einer viskoelastischen Flüssigkeit, verglichen mit einerNewtonschen Flüssigkeit, besteht darin, daß der Gradient der Normalspannungskomponente in horizontaler Richtung vom Wandabstand abhängt.Abschließend wird noch die Strömung durch ein zylindrisches Rohr mit gleichmäßiger konstanter Absaugung kurz diskutiert. Man findet, daß die Situation hier ganz ähnlich ist wie bei der ebenen Strömung, wenngleich dies nicht aus allgemeinen Betrachtungen gefolgert werden kann.

---

---

Paper presented at the annual meeting of German Rheologists held in Berlin, May 11–13, 1970.     

气液两相流动与固壁相互作用耦合求解的研究

气液两相流动与固壁相互作用的研究是液滴撞击壁面运动研究的重要基础.以结合了VOF和Level Set两种方法优点的用于气液相界面追踪的复合Level Set-VOF方法和利用唯象分析方法建立的能够反映接触角滞后性及壁面性质对润湿过程影响的壁面润湿模型为基础,提出了气液两相流动与固壁相互作用耦合求解流程,给出了气液两相流动与固壁相互作用耦合求解过程中接触线速度的计算方法及边界条件的确定方法.通过与已有实验结果的对比,对提出的气液两相流动与固壁相互作用耦合求解方法的有效性进行了验证.     

Computation of incompressible flows with immersed bodies by a simple ghost cell method

The incompressible Navier–Stokes equations are solved by an implicit pressure correction method on Cartesian meshes with local refinement. A simple and stable ghost cell method is developed to treat the boundary condition for the immersed bodies in the flow field. Multigrid methods are developed for both velocity and pressure correction to enhance the stability and convergence of the solution process. It is shown that the spatial accuracy of the method is second order in L₂ norm for both velocity and pressure. Various steady and unsteady flows over a 2D circular cylinder and a 3D sphere are computed to validate the present method. The capability of the present method to treat a moving body is also demonstrated. Copyright © 2008 John Wiley & Sons, Ltd.     

Subcritical and supercritical shear flows above an uneven bottom

The concepts of subcritical and supercritical flows are introduced for the long-wave approximation model describing stationary free-boundary rotational flows of an ideal incompressible fluid. Shear flows of a fluid layer above an uneven bottom are analyzed. Exact solutions describing different flow regimes are constructed, and the flow properties are studied as a function of the flow regime. Flows with backward streamlines are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 26–38, July–August, 2006. An erratum to this article is available at .