Project 1373

Analytical and Numerical Methods of the Fluid Mechanics

Leader: Academician Vladan Šorševię


Subject of research

Research subject on the Project can be divided into three categories:

The work on the first theme will be the most voluminous and will comprise the wide spectrum of laminar and turbulent, incompressible and compressible, forced and convective flows. Research subject within the second theme will include the effect of the form of the body and of other relevant parameters, concerned with fluid flow, on the form of cavities. The work on the third theme will consist in the investigation of the strong interaction between the fluid flow over a porous contour and the fluid flow inside the body.

Description of the work

Theme 1: Boundary layer theory

The work on this theme will comprise laminar and turbulent flows of incompressible and compressible fluids. In compressible flow case there will be treated, as equally important, both flows of thermally perfect gases and very complex flows that take place with the presence of chemical reactions, as for example dissociated and ionized gas flows. Since an ionized gas is electronically conducted medium, there will be considered its flow in the presence of an applied magnetic field. The effect of the magnetic field upon the position of the separation point of the boundary layer and the WR!| shear stress will be given particular attention. Particular attention will be given also to the methods of calculation of turbulent compressible boundary layers. At that an attempt will be made to generalize the methods used for incompressible flows to compressible ones. For turbulent channel flows direct, large eddy numerical simulation of full Navier-Stokes equations will be performed.

Theme 2: Theory of cavitational fluid flows

Within this theme the influence of various governing parameters on the formation of cavities in the fluid flow over a body will be investigated. These parameters are: body form, free stream velocity, gravitation, free stream turbulence intensity, etc. At that, both flow with the prescribed position of separation of the cavity, and flow in .which the position of the cavity separation is not known in advance, will be treated. Steady and unsteady flows will ,be encountered, and the methods used will be the method of singularities and the method of finite differences.

Theme 3: Fluid flow over porous surfaces

Problems of fluid flow over porous surfaces belong to the very important class of problems of strong interaction between mechanical systems with different dynamical behavior. As a rule, for solving such problems the empirical formula by Beavers and Joseph is used, by means of which the slip velocity on the contour is simply related to the v/all shear stress. Within the work on this theme the Beavers-Joseph formula will be checked by simultaneously solving the problem of fluid flow in the channel above the; porous body and the problem of fluid flow inside the body. Flow of a liquid and isothermal flow of a gas will both be treated. Also, a possibility of flow control of the boundary layer over a porous contour will be explored.

Originality of research

In planning the contents of the project we have taken a good care to provide the obtained results be original and worthwhile publication in our and international journals.

Research Goal

Simply speaking, the goal of research on this project consists in solving the most number of problems described in the Research contents, in agreement with the foreseen plan, and in publishing the obtained results in well known acknowledged domestic and foreign journals.

State of the Art in Scientific Field

World-wide Situation

As emphasized already there have been several results in the literature concerned with the subject of Theme 1. Problems pertinent to this theme are of immense importance in low speed and high speed aerodynamics, and in flow control by the blowing/ suction of the fluid into/from the boundary layer, by the applied magnetic field, etc. Without having paid much attention to the wide spectrum of problems from the field of boundary layer theory, great progress in aerodynamics attained during last few decades obviously would not be feasible.

We have similar situation with cavitational fluid flows (Theme 2) which are very important for studying flow of liquids (mostly water!) in hydraulic turbomachinery, like pumps, turbines and propellers, in liquid flow through nozzles and diffusers, and in cases of motion of a body with relatively high speeds, as for example torpedoes and underwater projectiles.

As for the contents of work on Theme 3, there is a lack of literature in analytical methods concerned with the investigation of fluid flow over porous surfaces and through porous bodies. Mostly, some empirical formulas obtained experimentally are used for treating these problems, to which the aforementioned Beavers-Joseph condition belongs also.

Domestic Situation

Author of the method of generalized similarity is the well known Russian scientist L. Loicianski. Our scientist, V. Saljnikov contributed much to the improvement of this method and established the whole school of the boundary layer theory in our country. The most of researchers which will be dealt with the problems of Theme 1, already have considerable experience in various applications of this method in solving some other problems of the boundary layer theory. They have also mastered the numerical method for solving the type of universal equations appearing in the method of generalized similarity. Until now they have already published several papers from this field of fluid mechanics. Same experience in treating the problems of Theme 2 exists also, but it cannot be considered as important. As far as we know, none of our scientists have until now dealt with the problems of flow over porous surfaces and through porous bodies from the theoretical point of view (Theme 3).

Planned Project Results

It has been planned that all results obtained in the work on the Project be applicable, because all three Themes are intrinsically applicable in their character. About that we have written in the sections: The state of research in the field - in the world, and with us!

Direct applicability does not depend on the form of the obtained results only, but also it depends on the state of the development of the country as a whole! In principle, the results which are expected from the subject of Theme 1 could be directly applied in aerospace engineering (low speed and high speed aerodynamics) and in thermoenergetics, the results from Theme 2 - in hydroenergetics and in marine engineering, and the results from Theme 3 - in chemical engineering and processing techniques.