Showing papers on "Fluid parcel published in 1971"

Some simple flows of a para-magnetic fluid

Abstract: Using a simple continuum model for a paramagnetic fluid we analyze a simple shearing flow and parallel flow through a pipe. We also examine the possibility of maintaining a steady circular flow in a circular cylinder by rotating a homogeneous magnetic field.

Phenomenon of separation in second-order fluids

Abstract: It has been proved that the separation from a curved wall for a second-order fluid occurs earlier than that for a Newtonian fluid. This fact is confirmed by determining the flow of a second-order fluid past a circular cylinder and finding the location of the point of separation for various values of a non-dimensional parameter formed from the material constants of the fluid, the velocity at infinity and the radius of the cylinder. The dependence of the point of separation on the material constants of the fluid and the flow parameters is a peculiarity of a second-order fluid since the location of the point of separation for a Newtonian fluid is independent of these quantities.

Stability of the Flow of an Elastico-Viscous Fluid

Abstract: The eigenvalues of the generalized Orr-Sommerfeld equation for an elasticoviscous fluid are found for a constant velocity profile. The result shows that the effect of elasticity is to stabilize the flow.

Equations of averaged axisymmetric vortex flow of an ideal incompressible fluid

Abstract: The mathematical difficulties involved in the direct solution of unsteady three-dimensional problems of hydrodynamics lead to the need to resort to idealized oneor two-dimensional models. In this case, in the complete problem equations, if they can be written, the derivatives with respect to the Coordinates being eliminated cannot always be set equal to zero, if the flow along these coordinates ( i .e . , across the duet, layer, or basic flow) is not uniform. In this connection, it is useful in constructing these models to subject the complete initial system of equations to averaging with respect to the corresponding coordinateS. This approach is the usual one for hydraulics [1] and is used in mrbcmachine theory [2], problems of motion in a thin layer [3], etc. The present article describes an averaging method which is more general than those of [1-,'3]. Thus, the flow is not considered slowly varying, and those cases in which the assumption of layer thinuess is required are noted. A justification is given also for the introduction of the central impervious surface S 2' in three-dimensional ducts (by analogy with the hydraulic axis in two-dimensional duets). The averaging method was first used in problems of mrbomaehine hydrodynamics in [2]. Further development of this method is given in [4, .5]; however, those studies do not consider the averaging scheme, and the quadratic pulsation terms are not written out. This gap is filled by the present paper. For simplicity of exposition the averaging method is applied to an example of axisymmetric flow in the theory of turbomachines for an incompressible fluid, although this method is also suitable for deriving the averaged equations of a broad class of flows in ducts, three-dimensional channels, and layers of varied geometric form, including the equations of motion of an ideal compressible fluid and magnemhydrodynamics. Lorentz [6] first introduced the mass forces F of the blade action on the stream in writing the equations for the axisymmetric problem of turbomachine t~eory within the framework of the hypothesis of an infinitely large number of infinitely thin blades. In the present paper it is shown that these forces, and also the restriction coefficient X accounting for the finite thickness of the impeller blade, appear in the equations of the probtem as a result of introducing the impervious wails of the interblade passages and performing the averaging operation across the nozzle pitch between these walls. Here we also consider the questions of determining the surface S~ and closing the system of averaged equations with the presence of pulsation terms in the equations. In conclusion, the effect of the puIsation terms on the averaged axisymmetric flow stream is evaluated using as an example a stationary annular nozzle assembiy of an axiaI turbomachine.

The penetration of a jet into a channel

Abstract: The method of S. A. Chaplygin [1], as generalized by S. V. Fal'kovich [2] to the case of a few characteristic velocities, is used to solve the two-dimensional problem of the penetration of a subsonic jet of compressible fluid flowing at an angle from a slit into a stream of the same fluid bounded by parallel walls. The problem is solved for the case of an incompressible fluid by passing to the asymptotic limit. Using the tables of [3] the compression coefficient is calculated for a stream of gas merged with an incompressible fluid.