Linearized Theory of Three-Dimensional Jet Mixing With and Without Walls

1970 ◽  
Vol 92 (1) ◽  
pp. 93-99 ◽  
Author(s):  
S. I. Pai ◽  
T. Y. Hsieh
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Finite Domain ◽  
Axial Pressure ◽  
Jet Mixing ◽  
Axial Pressure Gradient ◽  
Jet Velocity ◽  
Uniform Stream

The laminar jet mixing of an incompressible and viscous fluid issuing from a nozzle of rectangular cross section into a uniform stream has been studied theoretically. When the jet velocity deviates slightly from that of free stream, exact solutions have been obtained. Three different cases have been discussed. First is the three-dimensional jet in an infinite domain of uniform stream. Second is the three-dimensional jet in a finite domain of uniform flow bounded by parallel walls, and third is the three-dimensional jet with adjoining parallel walls and axial pressure gradient. The following main results are obtained: (a) The rate of decrease of maximum velocity in the jet decreases as the aspect ratio of the nozzle increases for a given jet velocity. (b) The spread of the jet is different along different directions and the cross section of the jet tends to be circular far downstream from the nozzle. (c) The adjoining walls would increase the velocity in the jet, and (d) favorable axial pressure gradient increases the velocity in the jet. Numerical results for various cases are presented.

An Experimental Study of Three-Dimensional Turbulent Boundary Layer and Turbulence Characteristics Inside a Turbomachinery Rotor Passage

1978 ◽  
Vol 100 (4) ◽  
pp. 676-687 ◽  
Author(s):  
A. K. Anand ◽  
B. Lakshminarayana
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Turbulence Intensity ◽  
Three Dimensional ◽  
Stream Line ◽  
Shear Stresses ◽  
Axial Pressure ◽  
Mean Velocity ◽  
Large Defect ◽  
Axial Pressure Gradient

Three-dimensional boundary layer and turbulence measurements of flow inside a rotating helical channel of a turbomachinery rotor are described. The rotor is a four-bladed axial flow inducer operated at large axial pressure gradient. The mean velocity profiles, turbulence intensities and shear stresses, and limiting stream-line angles are measured at various radial and chordwise locations, using rotating triaxial hot-wire and conventional probes. The radial flows in the rotor channel are found to be higher compared to those at zero or small axial pressure gradient. The radial component of turbulence intensity is found to be higher than the streamwise component due to the effect of rotation. Flow near the annulus wall is found to be highly complex due to the interaction of the blade boundary layers and the annulus wall resulting in an appreciable radial inward flow, and a large defect in the mainstream velocity. Increased level of turbulence intensity and shear stresses near the midpassage are also observed near this radial location.

Torque reduction in Taylor–Couette flows subject to an axial pressure gradient

2009 ◽  
Vol 639 ◽  
pp. 373-401 ◽  
Author(s):  
MARCELLO MANNA ◽  
ANDREA VACCA
Keyword(s):  
Pressure Gradient ◽  
Couette Flow ◽  
Large Scale ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Axial Pressure ◽  
Flow Solver ◽  
Axial Pressure Gradient ◽  
Taylor Couette ◽  
Taylor Couette Flow

The paper investigates the phenomena occurring in a Taylor–Couette flow system subject to a steady axial pressure gradient in a small envelope of the Taylor–Reynolds state space under transitional regimes. A remarkable net power reduction necessary to simultaneously drive the two flows compared to that required to drive the Taylor–Couette flow alone is documented under non-trivial conditions. The energy transfer process characterizing the large-scale coherent structures is investigated by processing a set of statistically independent realizations obtained from direct numerical simulation. The analysis is conducted with an incompressible three-dimensional Navier–Stokes flow solver employing a spectral representation of the unknowns.

Slip Flow with Axial Pressure Gradient

1962 ◽  
Vol 29 (11) ◽  
pp. 1393-1394 ◽  
Author(s):  
A. Pozzi ◽  
P. Renno
Keyword(s):  
Pressure Gradient ◽  
Slip Flow ◽  
Axial Pressure ◽  
Axial Pressure Gradient

Axial flow in trailing line vortices

1964 ◽  
Vol 20 (4) ◽  
pp. 645-658 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Pressure Gradient ◽  
Similarity Solution ◽  
Axial Velocity ◽  
Axial Flow ◽  
Radial Pressure ◽  
Axial Pressure ◽  
Line Vortex ◽  
General Terms ◽  
Axial Acceleration ◽  
Axial Pressure Gradient

A characteristic feature of a steady trailing line vortex from one side of a wing, and of other types of line vortex, is the existence of strong axial currents near the axis of symmetry. The purpose of this paper is to account in general terms for this axial flow in trailing line vortices. the link between the azimuthal and axial components of motion in a steady line vortex is provided by the pressure; the radial pressure gradient balances the centrifugal force, and any change in the azimuthal motion with distance x downstream produces an axial pressure gradient and consequently axial acceleration.It is suggested, in a discussion of the evolution of an axisymmetric line vortex out of the vortex sheet shed from one side of a wing, that the two processes of rolling-up of the sheet and of concentration of the vorticity into a smaller cross-section should be distinguished; the former always occurs, whereas the latter seems not to be inevitable.In § 4 there is given a similarity solution for the flow in a trailing vortex far downstream where the departure of the axial velocity from the free stream speed is small. The continual slowing-down of the azimuthal motion by viscosity leads to a positive axial pressure gradient and consequently to continual loss of axial momentum, the asymptotic variation of the axial velocity defect at the centre being as x−1 log x.The concept of the drag associated with the core of a trailing vortex is introduced, and the drag is expressed as an integral over a transverse plane which is independent of x. This drag is related to the arbitrary constant appearing in the above similarity solution.

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