Flow Of Ideal Incompressible Fluid Research Articles

Simulation of the aerodynamics of buildings and structures by means of the closed vortex loop method

Problems of the numerical simulation of the air flow past buildings and structures are considered using the closed vortex loop method. A mathematical model, based on the vortex approach, of the time-dependent ideal incompressible fluid flow past a system of bodies is proposed. A numerical scheme for solving the problem and an algorithm for calculating the distributed wind loads over the body surface are outlined. An example of calculating the aerodynamic loads is given for a real building and the results are compared with the known results of testing a model of the building in a wind tunnel. An example of the calculation and analysis of the wind distribution over a system of several buildings is also presented.

Stagnation zones of ideal flows in long and narrow bands

We investigate stagnation zones of flows of ideal incompressible fluid in narrow and long bands. With the bandwidth being much less than its length, these flows are almost stationary over large subdomains, where their potential functions are almost constant. These subdomains are called s‐zones. We estimate the size and the location of these s‐zones.

Numerical modelling of three-dimensional steady fluid flows on adaptive grids

- This paper deals with the development of the iterative finite difference method of the numerical solution to three-dimensional stationary problems of an ideal incompressible fluid flow through channels of complex geometry. We use curvilinear adaptive grids and introduce new dependent variables, viz. the vector potential ψ⃗ and the vorticity vector ω⃗.

An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral.

On the existence of three solutions for a supercritical steady flow of a heavy fluid over obstructions

The paper is devoted to the solution of the steady problem of ideal incompressible fluid flow over a semi-circular cylinder located at the bottom. Calculations showed that the problem has at least three solutions for the Froude number. In the absence of an obstruction at the bottom, the proposed algorithm allows one to construct solitary waves up to limiting waves. The paper reports the most important wave characteristics: circulation, mass, and potential and kinetic energy. Analysis of the calculation results leads to the conclusion that all maximum values of the solitary-wave characteristics are attained before the maximum amplitude and the maximum of the mass does not coincide with the maxima of the total energy and the Froude number.

Vortex Flow in the Outlet Duct of An Axial Compressor in the Rotating Stall Regime

An ideal incompressible fluid flow in the right half-plane periodic in the transverse direction is considered. This flow models that in the outlet duct of an axial compressor in the rotating stall regime. It is a feature of the problem that in the inlet cross-section two velocity components are prescribed while the vorticity distribution is unknown. An explicit solution is found in the form of a series in a small parameter characterizing the deviation of the velocity from a constant value. Numerical results are obtained.

On finite amplitude waves at the boundary of separation of two flows of a heavy ideal incompressible fluid

A planar Cauchy-Poisson problem of the waves at the interface of two flows of a heavy ideal incompressible fluid which move at different velocities when there is a small homogeneity in the density is investigated. A method is proposed which enables one to investigate not only travelling and standing waves but also the general Cauchy-Poisson problem taking account of the difference in the velocities of the flows. The basis of this method is a linear integral relationship which associates the value of a harmonic function on the boundary of its derivative. A system of integrodifferential equations is obtained for the function which determines the profile of the wave and the discontinuity in the potential at the interface of the flows. The equations of the internal waves which have been found are convenient for analytical and numerical investigations. It is shown that there is an analogy between the linear Cauchy-Poisson problem for the internal waves under consideration and waves on the surface of a heavy fluid. Solutions of the travelling-wave and standing-wave types are found by expansion in series up to the third order of smallness with respect to the wave amplitude.

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.

Aerodynamic characteristics of permeable disks at subsonic free-stream flow velocities

A large number of investigations have been carried out to study the aerodynamic characteristics of grids and permeable plates completely covering a pipe section [1]. The theoretical bases of the external aerodynamics of permeable bodies are established in [2], where the concept of a uniformly permeable surface is introduced and the problem of flow past a permeable plate at a small angle of attack is solved. Papers [3, 4] are devoted to the solution of problems of a jet flow of ideal incompressible fluid past a permeable wedge and a plate. The flow past a wedge with a high degree of permeability at low subsonic velocities was investigated theoretically and experimentally in [5]. Papers [6, 7] are devoted to the experimental investigation of the aerodynamic characteristics of plates and disks at low subsonic velocities. The results of the experimental investigations of permeable bodies are given in [8]. In the present paper the aerodynamic characteristics of permeable disks positioned perpendicular to the direction of the oncoming flow are investigated experimentally in a wide range of variation of the perforation parameters and the subsonic free-stream flow velocities.

Classical free-streamline flow over a polygonal obstacle

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to use except for very simple obstacles, because the conformal mapping problem has been too difficult. This paper presents a practical method for computing flows over arbitrary polygonal obstacles to high accuracy in a few seconds of computer time. We achieve this high speed and flexibility by working with a modified Schwarz-Christoffel integral that maps onto the flow region directly rather than onto the log-hodograph polygon. This integral and its associated parameter problem are treated numerically by methods developed earlier by Trefethen for standard Schwarz-Christoffel maps.

The construction of discrete vortex models of ideal incompressible fluid flows

A variational method is given for constructing discrete vortex models which describe two-dimensional ideal incompressible fluid flows. The connection of these models with those used previously is found. The working of the method is illustrated by solving test problems on Rankin and Kirchhoff vortices, which have analytic solutions.

On the asymptotic behavior of localized perturbations in the presence of Kelvin-Helmholtz instability

The asymptotic behavior of localized two-dimensional perturbations of the surface of a shear discontinuity separating two homogeneous steady flows of ideal incompressible fluid is studied in the linear approximation. The effect of surface tension and gravity forces is taken into account. Mathematically the problem reduces to the investigation by the method of steepest descent of the asymptotic behavior of a double integral for various values of parameters which are the components of the group velocity vector. In this problem the principal difficulty is to find the two-dimensional steepest descent contour in the space of two complex variables that determines which of the various saddle points gives the asymptotic form. First, for the Fourier component with respect to one of the variables with allowance for all the saddle points we find an asymptotic form which parametrically depends on the second variable. The choice of the second variable makes it possible to prove analytically that in the absence of gravity the asymptotic behavior of the growing perturbations is determined by a single saddle point in the plane of that variable. In this way it is possible to justify the authors' previous conclusions [1] concerning the shape of the boundary L of the region D in the group velocity plane occupied by growing perturbations. In the presence of gravity the growth rates of perturbations corresponding to different group velocities are found numerically and the region D occupied by the growing perturbations is indicated.

Flow of a multilayer ideal incompressible and heavy fluid past a body

The two-dimensional steady flow of a layered fluid past a body with discontinuous stratification is disucssed. The number of layers in finite, and the channel which has a horizontal floor is open. To study the flow behind the body, a hypothesis on the possibility of approximating the velocity profile at the body boundary by that which arises in weightless flow (see /1,2/) is postulated. A boundary value problem for a second-order elliptic equation in combined Euler-Lagrange variables is formulated. The problem is formulated in a rectilinear band with a separation, and under the conditions of consistency, on a finite number of parallel straight lines which correspond to the separation boundary. The introduction of a measure which gives rise to a monotonic density distribution in a non-perturbed flow, makes it possible to reduce the boundary value problem to the symmetrization of Fredholm-type kernels. The linearized equation is solved by Fourier methods. The results obtained in /3/ are amplified : it is shown that for any specified Froude number, the corresponding homogeneous integral equation has only a finite number of positive eigenvalues to which the oscillation modes correspond. It is also shown that if the flow velocity is close to one of a denumerable set of propagation velocities of long-wave modes, the corresponding harmonic becomes stronger because of the resonance.

Simulation by a source of a thin jet from a body

An exact analytic solution is found to the following plane hydrodynamic problem. An unbounded flow of an ideal incompressible fluid flows around a plate BB' placed at right angles to the velocity vector of the flow at infinity. The pressure on the free boundary P∞ is equal to the pressure in the flow. From an opening in the center of the plate, a jet with flow rate Q from a cavity with pressure P0 encounters the flow head-on. As a result of the solution, it is found that for fixed width of the opening the values of Q allowed by the scheme are limited. In the limiting case Q = 0 Chaplygin's flow is obtained with stagnation region at the front [1], and in the limiting case Q = Qmax a jet out of a cavity with pressure P0 into a cavity with pressure P∞. As Q varies in this interval, the total drag, regarded as the drag of the plate and the chamber from which the jet emerges, takes a minimal value at a certain point. If the width of the opening tends to the length of the slab, the problem of the collision of two jets is obtained; if the width of the opening tends to zero (Q ≠ o), the problem of jet flow past a slab with a source is obtained. It is shown that the replacement of the jet by the source gives a good approximation in both the sense of the force characteristics and in the sense of the behavior of the free streamlines.

Vortical momentum of bounded ideal incompressible fluid flows

Vortical momentum of bounded ideal incompressible fluid flows

Motion of a cylinder in arbitrary planar ideal incompressible fluid flow

Motion of a cylinder in arbitrary planar ideal incompressible fluid flow

Formulation of the inverse axisymmetric problem of steady rotational flow of an ideal incompressible fluid in turbomachinery

The problem of the design of rotor blades within the framework of the hypothesis of an infinitely large number of blades reduces to the solution of an inverse axisymmetric problem. In the Bauersfeld-Voznesenskii formulation [1–3] this problem may be stated as follows: for given meridional flow and angular rotor velocity, construct the blade surface S 2 ′ (Fig. 1) passing through a given inlet ab (or exit cd) edge and a given line of intersection ad of the blade with one axisymmetric stream surface of the given meridional flow. Henceforth, S 2 ′ will be used to designate the median (or concave) surface of the blade, which, under certain conditions, coincides with the median interblade stream surface abcd.