Disturbance of a free fluid surface by a hydrofoil profile

The data of a laboratory experiment to observe the small perturbations of a free surface by a thin hydrofoil profile moving horizontally in water are presented and compared with the calculation results obtained for a hydrofoil modeled by a system of distributed sources and sinks within the framework of the small-wave approximation.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 145–152.Original Russian Text Copyright – 2004 by Boyarintsev, Lednev, Prudnikov, Savin, and Savina.     

Numerical solution of a nonlinear problem of the motion of a plane hydrofoil beneath the free surface of an ideal incompressible fluid

A nonlinear problem of the motion of a hydrofoil of infinite span beneath the free surface of an ideal incompressible fluid with gravity is studied. The stream function is used as the dependent variable. Iterative algorithms for small and large Froude numbers based upon solving a linear boundary value problem in each step with subsequent updating of the shape of the free boundary are proposed. Typical predictions are given for a symmetric profile at different values of the submersion depth, the Froude number and the angle of attack. The free surface and streamlines shapes are shown. The dependence of the lift on the submersion depth for motion through fluid layers of different thickness is presented.Dnepropetrovsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 100–107, July–August, 1995.     

Postcritical regimes in the nonlinear problem of vortex motion under the free surface of a weighable fluid

An improved Levi-Civita method in which the singularities of the desired function are taken into account by introducing terms containing power singularities is proposed. Results of numerical analysis of the nonlinear problem of a vortex in a bounded flow of an ideal weighable fluid (Fr>1) are given. The following limiting flow regimes are studied: the Stokes waves with one and two crests, emergence of a critical point on the surface, and the detachment of a vortex from a soliton and a uniform flow. It is shown that nonperiodic waves can form in a local zone in the vicinity of the critical point. Ufa State Technical Aviation University, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 70–76, January–February, 2000.     

Parameters of spatial flow past a hydrofoil near the free surface of a ponderable liquid

An approach is presented to the investigation of spatial flow past an submerged hydrofoil in the presence of a ponderable liquid. The approach uses the method of singularities, which represents the influence of the free surface of the water by the influence of an unbounded layer of sources. The linear solution is completely found for the problem of determining the wave production and downwash behind an submerged hydrofoil with given parameters of the eddy system. An estimate is made of the influence on the flow characteristics of nonlinear factors associated with the change produced by the wave production in the form of the free eddies leaving the hydrofoil. The distribution of the downwash in the flow behind the hydrofoil is found and recommendations given for the arrangement of a hydrofoil system with positive interaction of the elements. The results of the calculation are compared with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 2, pp. 54–62, March–April, 1979.     

Flow and heat transfer in a moving fluid over a moving flat surface

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E _c (E _ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.      

Separating impact on an elliptic cylinder floating on the surface of an ideal incompressible finite-depth fluid

The method of nonlinear integral equations of the Hammerstein type is applied to numerically analyze the problem of the separating impact on an elliptic cylinder floating on the surface of an ideal incompressible finite-depth fluid. The bottom effect and the influence of the kinematic and geometric parameters on the zone of fluid particle separation from the cylinder surface are studied.     

求解带自由面渗流问题移动网格法的改进及其工程应用

采用有限元固定网格和移动网格相结合的方法,求解带自由面的坝体稳定渗流问题。本方法是针对一般坝体的结构,在有限元网格生成之后,又自动生成了网格移动所需的信息,实现了网格在迭代计算中随自由面的变化自动均匀移动;讨论了网格奇异的不同类型,提出了避免单元形状怪异的移动网格方法;在欧拉空间中分区记录坝体不同的渗透性能,在网格移动到新位置后,自动识别网格所在的物性空间,从而确定单元在新位置上的渗流系数。本文将该方法应用到吉林丰满混凝土重力坝防渗加固的实际工程当中,在考虑大坝原有防渗措施的前提下,利用数值分析,研究了防渗芯墙对大坝渗流性能的影响。计算结果表明,加芯墙后坝体自由面位置明显下移,湿水部分大为减少,坝基扬压力没有明显提升,下游出水点位置没有明显下降。计算过程表明,本文方法及措施具有很好的收敛性与稳定性,且收敛性与自由面初始位置的选择无关。     

Asymptotic solution to the problem of drag of a fluid by a moving plate

An analogy is established between the formulations of the problem of the drag of a fluid by a moving plate [1–3] and the problem of propagation of a stationary flame [4, 5]. The theory of singular perturbations is used to a find a two-term asymptotic expression for the film thickness h₀. The expansion parameter is the Bond number Bo 1. The limited applicability of the well-known formula of [1, 2] is estimated quantitatively. Such an estimate has been obtained earlier experimentally [3]. The approach used in the present paper should also be fruitful for the solution of other problems in capillary hydrodynamics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–56, November–December, 1980.     

Mixing layer under a free surface

In the long-wave approximation, the flow of a homogeneous fluid with a free surface in the gravity field is considered. Mathematical models of the surface turbulent layer in shear flows are derived. Steady solutions of the problem of evolution of the mixing layer under the free surface and formation of a surface turbulent jet are constructed. In particular, the problem of the structure of a turbulent bore in a supercritical flow is solved, and the conditions for the formation of a local subcritical zone ahead of the obstacle are studied.     

Translational motion of a cylinder below the free surface of a fluid

A method of solving the problem of the translational motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is developed. As distinct from existing techniques, the method permits the obtaining of a solution which becomes exact as the Froude number increases without bound. The solution of the problem of the motion of a circular cylinder is considered in detail. Suggestions are made concerning the characteristic properties of an exact solution of the general problem.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 9–22, November–December, 1996.     

Simulation of nonlinear waves on the surface of a thin fluid film moving under the action of turbulent gas flow

This paper derives a new system of equations for the simulation of the long-wave perturbation dynamics on the surface of a thin horizontal layer of heavy viscous fluid moving under the action of turbulent gas flow. In the case of small Reynolds numbers of the fluid, this system of equations is used to derive an evolution equation for the value of deviation of the film thickness from the unperturbed level. Some solutions of this equation are given.     

Displacement of the free surface of a fluid during flow over a cylinder

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 48–51, July–August, 1988.