Developing Region of Laminar Jets With Uniform Exit Velocity Profiles

1978 ◽  
Vol 100 (1) ◽  
pp. 55-59 ◽  
Author(s):  
G. W. Rankin ◽  
K. Sridhar
Keyword(s):  
Shear Layer ◽  
Graphical Method ◽  
Integral Form ◽  
Free Shear Layer ◽  
Potential Core ◽  
Laminar Jet ◽  
Laminar Jets ◽  
Present Solution ◽  
Developing Region ◽  
Energy Equations

The integral form of the momentum and energy equations, subject to the boundary layer simplifications, are used to obtain an approximate solution for an axisymmetric laminar jet with a uniform profile at the nozzle exit. The solution is expressed in a closed form. The jet flow field is divided into a developing and developed region. In the developing region a potential core is assumed to exist, bounded by an annular free shear layer, Schlichting’s velocity profile for an axisymmetric laminar jet is assumed in the free shear layer. The present solution is compared with existing experimental and analytical results in the developing region. Also a graphical method for determining the potential core radius and the parameters of the assumed Schlichting profile is given.

scholarly journals Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets

2010 ◽  
Vol 663 ◽  
pp. 507-538 ◽  
Author(s):  
C. BOGEY ◽  
C. BAILLY
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Nozzle Exit ◽  
Initial Conditions ◽  
Frequency Noise ◽  
Noise Component ◽  
Potential Core ◽  
Velocity Fluctuations ◽  
Laminar Jets ◽  
Exit Boundary

Round jets originating from a pipe nozzle are computed by large-eddy simulations (LES) to investigate the effects of the nozzle-exit conditions on the flow and sound fields of initially laminar jets. The jets are at Mach number 0.9 and Reynolds number 105, and exhibit exit boundary layers characterized by Blasius velocity profiles, maximum root-mean-square (r.m.s.) axial velocity fluctuations between 0.2 and 1.9% of the jet velocity, and momentum thicknesses varying from 0.003 to 0.023 times the jet radius. The far-field noise is determined from the LES data on a cylindrical surface by solving the acoustic equations. Jets with a thinner boundary layer develop earlier but at a slower rate, yielding longer potential cores and lower centreline turbulent intensities. Adding random pressure disturbances of low magnitude in the nozzle also increases the potential core length and reduces peak r.m.s. radial velocity fluctuations in the shear layer. In all the jets, the shear-layer transition is dominated by vortex rolling-ups and pairings, which generate strong additional acoustic components, but also amplify the downstream-dominant low-frequency noise component when the exit boundary layer is thick. The introduction of inlet noise however results in weaker pairings, thus spectacularly reducing their contributions to the sound field. This high sensitivity to the initial conditions is in good agreement with experimental observations.

Potential Core of a Submerged Laminar Jet

1988 ◽  
Vol 110 (4) ◽  
pp. 392-398 ◽  
Author(s):  
Shiro Akaike ◽  
Mitsumasa Nemoto
Keyword(s):  
Numerical Solution ◽  
Flow Pattern ◽  
Stokes Equations ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Potential Core ◽  
Laminar Jet ◽  
Cone Type ◽  
Developing Region

This study is intended to clarify the flow pattern in the flow developing region of an axisymmetric laminar water jet issuing into the surrounding calm water. The jet, initially having a potential core region of some extent at the nozzle exit, was studied. The numerical solution of the Navier-Stokes equations in the developing region was obtained using a finite-difference approximation. The velocity profile was measured using a miniature cone-type hot probe. Flow visualization by the hydrogen bubble method was also performed. Experiments were carried out for the jet Reynolds number ranging from 100 to 600. The flow pattern in the developing region was made clear. The experimental results were compared with the numerical solution.

Flow in the Initial Region of Axisymmetric Turbulent Jets

1980 ◽  
Vol 102 (1) ◽  
pp. 85-91 ◽  
Author(s):  
S. M. N. Islam ◽  
H. J. Tucker
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Nonlinear Function ◽  
Turbulent Jets ◽  
Integral Form ◽  
Eddy Diffusivity ◽  
Axial Distance ◽  
Free Shear Layer ◽  
Initial Region ◽  
Mean Velocity

In the initial region of axisymmetric turbulent jets a core of uniform velocity is assumed to exist, bounded by an annular free shear layer. An empirical model for axial mean velocity is found from experimental measurements using a length scale which forces self-preservation in the central part of the free shear layer. This model is applied to the integral form of the momentum and energy equations, subject to the boundary layer simplifications, to obtain an approximate solution for the development of jets where the thickness of the mixing layer at the nozzle exit is assumed negligible. The differential form of momentum and continuity equations are also solved by a finite difference technique of DuFort-Frankel type using a typical boundary layer type of velocity profile at the exit of the nozzle. The results of this method are compared with those of the empirical velocity method, and the present and existing experimental results. Prandtl’s mixing length is shown to be a slightly nonlinear function of the axial distance and is used to define the eddy diffusivity for this region.

Developing Region of Laminar Jets With Parabolic Exit Velocity Profiles

1981 ◽  
Vol 103 (2) ◽  
pp. 322-327 ◽  
Author(s):  
G. W. Rankin ◽  
K. Sridhar
Keyword(s):  
Experimental Data ◽  
Approximate Solution ◽  
Velocity Distribution ◽  
Velocity Profiles ◽  
Exit Velocity ◽  
Parabolic Profile ◽  
Laminar Jet ◽  
Laminar Jets ◽  
Developing Region

An approximate solution to the velocity distribution in a submerged axisymmetric, laminar jet which issues from a long tube is presented. The solution is a modification of that of Okabe [17] and takes into account the changes that occur in the parabolic profile downstream of the jet exit. Comparisons are made with experimental data and other approximate theories taken from the literature.

Deformable bubbles in a free shear layer

1997 ◽  
Vol 23 (5) ◽  
pp. 977-1001 ◽  
Author(s):  
E. Loth ◽  
M. Taeibi-Rahni ◽  
G. Tryggvason
Keyword(s):  
Shear Layer ◽  
Free Shear Layer

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

2021 ◽  
Vol 931 ◽  
Author(s):  
D. Li ◽  
J. Komperda ◽  
A. Peyvan ◽  
Z. Ghiasi ◽  
F. Mashayek
Keyword(s):  
Shear Layer ◽  
Compressible Flows ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Correlation Coefficients ◽  
Free Shear Layer ◽  
Smagorinsky Model ◽  
Reynolds Analogy ◽  
Velocity Fluctuations ◽  
Scale Similarity

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

CFD analysis of free shear layer approximations for a pulsed air jet

2014 ◽  
Vol 43 ◽  
pp. 49-58
Author(s):  
Nawel Khaldi ◽  
Salwa Marzouk ◽  
Hatem Mhiri ◽  
Philippe Bournot
Keyword(s):  
Shear Layer ◽  
Cfd Analysis ◽  
Free Shear Layer ◽  
Air Jet
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