Two-Dimensional Jet Mixing With a Pressure Gradient

1975 ◽  
Vol 42 (1) ◽  
pp. 55-60 ◽  
Author(s):  
D. F. Brink ◽  
W. L. Chow
Keyword(s):  
Pressure Gradient ◽  
Analytical Study ◽  
Constant Pressure ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Governing Equations ◽  
Jet Mixing ◽  
Laminar Mixing ◽  
Parallel Streams ◽  
Boundary Layer Problems

An analytical study of nonsimilar jet mixing is made for compressible, nonisoenergetic flows. The conservation equations are solved for each of the streams above and below the dividing streamline by using Meksyn’s asymptotic method of integration for solving boundary-layer problems. The problem of laminar mixing between two parallel streams is investigated for the case of a constant pressure gradient. It is found that the velocity and temperature profiles from the exact solution to the nonsimilar governing equations can be well approximated by the locally similar solution.

Near-similarity approximation for compressible, laminar boundary layers on adiabatic walls

1997 ◽  
Vol 211 (5) ◽  
pp. 285-294 ◽  
Author(s):  
H P Horton
Keyword(s):  
Differential Equations ◽  
Boundary Layers ◽  
Constant Pressure ◽  
Boundary Layer Stability ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Careful Choice ◽  
Laminar Boundary Layers ◽  
Gradient Parameter ◽  
Prandtl Numbers

Two-dimensional, compressible, laminar boundary layers with zero heat transfer and a constant pressure gradient parameter are considered. Although it is well known that exact similarity is, in general, only possible when the Prandtl number is equal to unity, it is shown here that, at least for Prandtl numbers in the range from 0.5 to 2.0, a careful choice of transformation gives partial differential equations in which the streamwise derivatives are practically negligible, irrespective of Mach number. The set of ordinary differential equations which results from setting the streamwise derivatives to zero is proposed as a useful approximation for generating families of velocity and temperature profiles, for use in database methods for analysing boundary layer stability, for example.

Displacement Effects on the Laminar Mixing of Two Parallel Streams

1968 ◽  
Vol 19 (4) ◽  
pp. 388-402 ◽  
Author(s):  
M. J. Casarella ◽  
Y. Choo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Analytical Study ◽  
General Procedure ◽  
Perturbation Technique ◽  
Mixing Layer ◽  
Compressible Fluids ◽  
Laminar Mixing ◽  
Parallel Streams ◽  
Displacement Effects

SummaryAn analytical study is made of the laminar mixing of two semi-infinite streams that are initially parallel. The equations governing the mixing process and the boundary conditions are derived by application of the perturbation technique. The “missing” correct third boundary condition is shown to be the condition that the pressures of the inviscid upper and lower streams due to the displacement thicknesses be balanced across the mixing layer. A general procedure for solution of the mixing problems is established by means of a transformation of the mixing-layer equations and two boundary conditions.As an example, the laminar mixing of two parallel uniform streams of both incompressible and compressible fluids is solved. It is shown that the profiles of v are entirely different from those based on the approximate third boundary condition. The improved profiles are in excellent agreement with the experimental data.

On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow

1974 ◽  
Vol 63 (3) ◽  
pp. 529-536 ◽  
Author(s):  
A. Davey ◽  
L. M. Hocking ◽  
K. Stewartson
Keyword(s):  
Pressure Gradient ◽  
Poiseuille Flow ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Governing Equations ◽  
Amplitude Function ◽  
Coupled Partial Differential Equations

The equations governing the nonlinear development of a centred three-dimensional disturbance to plane parallel flow at slightly supercritical Reynolds numbers are obtained, In contrast to the corresponding equation for two-dimensional disturbances, two slowly varying functions are needed to describe the development: the amplitude function and a function related to the secular pressure gradient produced by the disturbance. These two functions satisfy a pair of coupled partial differential equations. The equations derived in Hocking, Stewartson & Stuart (1972) are shown to be incorrect, Some of the properties of the governing equations are discussed briefly.

A simplified numerical and analytical study for assessing the seismic response of a gravity concrete lock

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Neander Berto Mendes ◽  
Lineu José Pedroso ◽  
Paulo Marcelo Vieira Ribeiro
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Study ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Fluid Structure ◽  
Analytical Formulation ◽  
Acoustic Cavity ◽  
Water Chamber ◽  
Structure Problem

ABSTRACT: This work presents the dynamic response of a lock subjected to the horizontal S0E component of the El Centro earthquake for empty and completely filled water chamber cases, by coupled fluid-structure analysis. Initially, the lock was studied by approximation, considering it similar to the case of a double piston coupled to a two-dimensional acoustic cavity (tank), representing a simplified analytical model of the fluid-structure problem. This analytical formulation can be compared with numerical results, in order to qualify the responses of the ultimate problem to be investigated. In all the analyses performed, modeling and numerical simulations were done using the finite element method (FEM), supported by the commercial software ANSYS.

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

Mixing of an Acoustically Excited Air Jet With a Confined Hot Crossflow

1992 ◽  
Vol 114 (1) ◽  
pp. 46-54 ◽  
Author(s):  
P. J. Vermeulen ◽  
P. Grabinski ◽  
V. Ramesh
Keyword(s):  
Strouhal Number ◽  
Temperature Profiles ◽  
Measured Temperature ◽  
Mixing Zone ◽  
Wake Region ◽  
Mixing Processes ◽  
Jet Mixing ◽  
Air Jet ◽  
Percent Increase ◽  
Jet Structure

The mixing of an acoustically pulsed air jet with a confined hot crossflow has been assessed by temperature profile measurements. These novel experiments were designed to examine the effects of acoustic driver power and Strouhal number on jet structure, penetration, and mixing. The results showed that excitation produced strong changes in the measured temperature profiles. This resulted in significant increases in mixing zone size, penetration (at least 100 percent increase), and mixing, and the length to achieve a given mixed state was shortened by at least 70 percent. There was strong modification to the jet-wake region. The increase in jet penetration and mixing was saturating near 90 W, the largest driving power tested. The jet response as determined by penetration and mixing was optimum at a Strouhal number of 0.27. Overall, pulsating the jet flow significantly improved the jet mixing processes in a controllable manner.

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