An ISPH simulation of coupled structure interaction with free surface flows

An incompressible smoothed particle hydrodynamics (ISPH) model is developed for the simulation of fluid–structure coupling problems, especially for moving structures. The mirror particle method is employed in the model for a moving boundary. The surface force integration and force-motion algorithms are presented to solve the body translation and rotation. An additional free surface criterion is introduced with the consideration of both the particle number density and the local particle symmetry. A series of numerical experiments are conducted to verify the applicability of the model for simulations of fluid interaction with various types of moving structures. These problems include the fluid motion by a moving body with a prescribed trajectory, such as liquid sloshing in a moving tank. Water entry problems in which the body motions are coupled with the fluid forces are also studied. In all of the cases, there is good agreement when the numerical results are compared with the available analytical, experimental and other numerical data found in the literature.     

Influences of surface on the interaction between holes or edge

The effects of surface energy on the interaction between holes or edge are investigated. Three typical problems are discussed: (1) an infinite plate containing two holes of unequal size subjected to an all-round tension, (2) a circle disc containing an eccentric hole subjected to uniform pressure on either external or internal surface, (3) a semi-infinite plate containing an unstressed circular hole subjected to a uniform tension parallel to its straight edge. The problems are solved by series expansion in bipolar coordinates. The results show that the surface energy significantly affects the stress concentrations around the holes as the size of the holes shrinks to nanometers. Meanwhile, the interaction between the holes or edge influences the stress distribution around the holes or edge, which becomes evident as the holes or edge close to each other and is affected by the surface effect significantly.     

Diffuse surface reflection in free-molecular flow at a speed of 10 km/sec

An experimental investigation has been made of a diffuse-reflection scheme for conditions where the velocity of the particles bombarding a surface is 10 km/sec, and the surface is covered with an adsorbing layer. It is shown that the use of diffuse reflection is valid over a range of incident angles from θ=0 to θ?40?. For θ>40? the diffuse reflection is a crude approximation, since it does not take into account the contribution of scattered particles which are reflected in a quasispecular manner and have speed approximately equal to the incident speed.     

Aerodynamic characteristics of an element of surface washed by a high-speed free-molecular flow

An analysis is presented of the dependence of local aerodynamic coefficients on the angle of attack for surfaces covered by an adsorbed layer, for a flow velocity of ≈10 km/sec. The analysis is based on comparison of coefficients calculated for diffuse reflection and experimental data on momentum transfer between the flow and the surface, and with the assumed quasispecular reflection in which the velocity of the reflected particles depends on the angle of attack. It is shown that the quasispecular case is a more accurate approximation in comparison with the diffuse case.     

On the surface equations in two-phase flows and reacting single-phase flows

This paper summarizes the mathematical surface equations which are useful in two-phase flows and single-phase reacting flows. The connection between the interfacial area concentration transport equation for two-phase flows and the flame surface density transport equation for turbulent reacting flows is established. Several analytical examples are given to clarify the physical significance of the different quantities involved in the different transport equations. An introduction to the mathematical treatment of anisotropic interfaces is also given. This theory is illustrated on two different numerical examples: a single inclusion in a simple shear and a single inclusion in an uni-axial elongation.     

Boundary layer interaction in three-dimensional flows

An approach known from the theory of matched asymptotic expansions involving the isolation of subregions with different scales is used to study flows which are assumed to be described by the boundary layer equations almost everywhere near the surface except for a fairly narrow zone in which the inflowing boundary layers interact. Two characteristic types of interaction are identified. An approximate theory describing the flow in the interaction zone, which makes it possible to locate the position of the interaction zone on the surface, is proposed. The interaction flow on the end wall of a vane channel is calculated subject to certain simplifications. The results of an experimental investigation of this flow are presented and it is shown that the theoretical model proposed describes the three-dimensional corner separation which occurs in the neighborhood of the line of intersection of the end wall and the convex edge of the vane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 116–123, May–June, 1988.     

Basic flows of a micropolar liquid

Steady plane shear flow, rotation flow, plane wave disturbances, oscillatory boundary layers, and free surface waves in a micropolar liquid are investigated.     

Experimental determination of the speed ratio in free-molecular flow of nitrogen

The results are given for measurements of the speed ratio carried out in free-molecular flow of nitrogen. It is shown that hypersonic flow is achieved; the values of the speed ratio are close to theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 184–186, July–August, 1973.     

Instantaneous visualization of surface flows

An experimental system is described for visualizing the surface flow of a wing, using an oil smoke tracer technique. The method leads to the determination of the instantaneous velocity direction at the output of surface injectors. A preliminary investigation is made on a flat plate to optimize the conditions of oil smoke injection. Then, the visualization is performed on the upperside of a sweptback wing in the vicinity of the reattachment of the vortex flow. This visualization technique can be applied to other types of wall flows — separated or not — around various bodies.List of symbols b wing span - c _n normal (to leading edge) chord - c _r streamwise (or root) chord - d diameter of the injectors - distance from the apex along the leading edge - relative distance from the apex along the leading edge ( = /C _d) - sweep angle - e injector geometric parameter (e = d/l) - angle of attack - K injection parameter - l length of the injectors - v kinematic viscosity - P _t, P_s total and static pressure of the flow - P _inj injection pressure - P _r reduced pressure (P _r = (P_inj – P_t)/(P_t – P_s)) - Re flow Reynolds number (Re = V ·c _n/v) - Re _i injector Reynolds number (Re = V ·d/v) - s curvilinear distance along c _d - s relative curvilinear distance along c _d(s = s/c _d) - V infinite upstream flow velocity     

Unsteady interaction of uniformly vortex flows

The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows. An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998.     

Basic principles and concepts of model analysis

The techniques and the problems associated with the design and use of models are covered. Particular emphasis is placed on the development of modeling laws by means of dimensional analysis. Special problems associated with the use of true and distorted models are illustrated by means of selected examples.     

Kinetics of charge-exchange interaction of dense flows

The nonlinear problem of charge exchange between an ion flow and neutral particles is considered. An exact solution of the equations of charge-exchange interaction in plane geometry is found. Parameters determining the effectiveness of interpenetration of dense flows and the structure of the layer of intense interaction are obtained. Institute of Laser Physics, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 11–19, March–April, 2000.     

Summation of Gaussian beams in a surface waveguide

The Gaussian beams summation method is applied to a surface waveguide problem in the parabolic approximation. It is shown by means of numerical comparison with an exact solution that the method is effective for computations. Its accuracy does not depend on the complication of the ray field, but the method fails for long distances from the source because of the beam's spreading if a large parameter of the problem is fixed.     

Constitutive relations for the interaction force in multicomponent particulate flows

In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.     

Method of calculation of interaction of wall flows

A flow of viscous compressible fluid in the neighborhood of the line of interaction of wall flows is considered. A method of calculating the line of interaction and the direction of the self-induced secondary flow is developed. Papers [1–3] are devoted to the simulation of a separation flow with singularities in the neighborhood of singular lines and points, where boundary-layer equations are invalid. However, the theories of local separation used at present have mainly been developed only for two-dimensional problems, while the models of viscous-inviscid interaction have restrictions in application for turbulent flows with developed separation. The interaction of three-dimensional wall turbulent flows is considered below. It is assumed that the thickness of the boundary layers and the scales of the interaction zones are small in comparison with the characteristic dimension of the system, while the line of discontinuity of the solutions of the three-dimensional boundary layer equations is the same as the line of interaction of the wall flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–59, March–April, 1987.The author is grateful to G. Yu. Stepanov and V. N. Ershov for their interest in my work and their valuable remarks.     

Laser diagnostics of molecular states in nonequilibrium gas flows

Laser diagnostics techniques are developed, and some typical results are presented on the vibrational CO₂ molecule level population measurements under highly nonequilibrium conditions for two types of flows: (i) in a conventional gasdynamic lasers and (ii) in a flow mixing gasdynamic laser. The measuring procedure is based on recording spectral gain coefficient distributions at several resolved rotational transitions of different vibrational bands. The laser optical system with spatial selection of single lines is described. The system allows fast (about 10^–5–10^–4 s) line tuning, thus providing a variable and arbitrary choice of the selected line sequences. The optimum choice of the laser generation spectrum is discussed, and the sources of measuring uncertainties are analyzed. Typical illustrations and results are given and discussed.