scholarly journals Turbulent theory of velocity-profile-induced jet breakup

2019 ◽  
Author(s):  
Ben Trettel
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Turbulent Jets ◽  
Velocity Profiles ◽  
Common Belief ◽  
Integral Scale ◽  
Nozzle Length ◽  
Jet Breakup

Velocity profile relaxation is commonly believed to be a cause of jet breakup. This claim is critically reevaluated in this work. Contrary to common belief, laminar liquid jets with parabolic velocity profiles are actually more stable than laminar jets with flatter velocity profiles. This is shown using prior theory and experiments. For turbulent jets, the influence of the velocity profile is more difficult to determine. Previous experimentalists claimed to show that the velocity profile has an effect by varying the nozzle length. The claim is that the boundary layer thickness grows with nozzle length, and that the larger the boundary layer, the less stable the jet. In this work, nozzle length is shown to be a poor proxy for velocity profile effects because the turbulence intensity also increases as the nozzle length increases. Studies with this confounding were ignored in this work. Thinner boundary layers have greater shear, yet experiments have shown that if the boundary layer were made thinner (all else constant), the jet often is more stable. This is termed the "shear paradox". A potential resolution to the shear paradox is developed by considering that the area with shear also decreases as the boundary layer thickness is decreased, and by non-dimensionalizing the turbulent production rate by the dissipation. This theory shows an interaction between the integral scale and velocity profile relaxation which has not been previously discussed. The theoretical prediction that a smaller integral scale leads to more stable jets (due to increased turbulent dissipation) is shown to be somewhat consistent with the limited experimental and DNS data available.

Magnetohydrodynamics Williamson Fluid Comprising Gyrotactic Microorganisms Flows Through a Permeable Stretching Layer with Variable Fluid Properties

2020 ◽  
Vol 9 (4) ◽  
pp. 375-387
Author(s):  
Amit Parmar ◽  
Rakesh Choudhary ◽  
Krishna Agarwal
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Schmidt Number ◽  
Gyrotactic Microorganisms ◽  
Williamson Fluid ◽  
Non Linear ◽  
Fluid Properties ◽  
Variable Prandtl Number

The present study shows the impacts of Williamson fluid with magnetohydrodynamics flow containing gyrotactic microorganisms under the variable fluid property past permeable stretching sheet. Variable Prandtl number, mass Schmidt number, and gyrotactic microorganisms Schmidt number were all considered. The momentum, energy, mass, and microorganism equations’ governing PDEs are converted into nonlinear coupled ODEs and numerically solved with the bvp4c solver using suitable transformations. The main outcome of this study is that Williamson fluid parameter constantly decreases in velocity profile, however reverse effects can be shown in temperature profile. Also, M parameter and Kp parameter enhance the heat transfer rate, concentration rate and microorganisms boundary layer thickness but declines in momentum boundary layer thickness and velocity profile. The aim of this research is to see how velocity slide, temperature jump, concentration slip, and microorganism slip affect MHD Williamson fluid flow with gyrotactic microorganisms over a leaky surface embedded in spongy medium, with non-linear radiation and non-linear chemical reaction.

scholarly journals Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Swirling Flow ◽  
Velocity Profiles ◽  
Partial Slip ◽  
Injection Velocity ◽  
Slip Boundary Conditions ◽  
Slip Boundary

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

Melting heat transfer in the stagnation-point flow of Maxwell fluid with double-diffusive convection

2014 ◽  
Vol 24 (3) ◽  
pp. 760-774 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Stagnation Point ◽  
Boundary Layer Thickness ◽  
Double Diffusive Convection ◽  
Content Type ◽  
Diffusive Convection ◽  
Double Diffusive

Purpose – The purpose of this paper is to analyze the melting heat transfer in the stagnation-point flow with double-diffusive convection. Design/methodology/approach – Series solutions for velocity, temperature and concentration are constructed via homotopy analysis method. Findings – The authors observed that the behaviors of N, ?2 and M on the velocity and boundary layer thickness are qualitatively similar. Further, for A<1 the velocity profile and boundary layer thickness increase with the increase of A. However, when A>1 then the velocity profile increases but the boundary layer thickness decreases when A is increased. Originality/value – This analysis has not been discussed in the literature previously.

Effect of velocity profile on instability of the viscoelastic liquid sheet

2014 ◽  
Vol 229 (11) ◽  
pp. 2031-2044 ◽  
Author(s):  
Runze Duan ◽  
Zhiying Chen ◽  
Liansheng Liu
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Liquid Sheet ◽  
Viscoelastic Liquid ◽  
Rheological Parameters ◽  
Liquid Sheets ◽  
Elasticity Number

A linear analysis method has been used to investigate the instability behavior of the viscoelastic liquid sheets moving in the surrounding ambient gas. The gas boundary layer thickness and the liquid sheet velocity profile were taken into account. The effects of gas and liquid viscosity on the growth rate were revealed. The governing equations were obtained through analysis of the liquid and gas domain and solved using the spectral method. The viscoelastic rheological parameters and some flow parameters have been tested to investigate their influences on the instability of the viscoelastic liquid sheets. The results reveal that the disturbances grow faster for the viscoelastic liquid sheet than Newtonian one with identical viscosity. Moreover, the increases of Weber number, elasticity number, gas Reynolds number, and momentum flux ratio can accelerate the breakup of the viscoelastic liquid sheet. However, the increases of time constant ratio, boundary layer thickness, and liquid Reynolds number have the opposite effects.

Generation Mechanism of Streaky Structure in Natural Transition

2003 ◽  
Author(s):  
Ayumu Inasawa ◽  
Fredrik Lundell ◽  
Masaharu Matsubara ◽  
P. H. Alfredsson ◽  
Yasuaki Kohama
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Streamwise Velocity ◽  
Mean Flow ◽  
Integral Scale ◽  
Free Stream Turbulence ◽  
Local Boundary ◽  
Streaky Structure ◽  
Streaky Structures

In a transitional boundary layer subjected to free-stream turbulence, streaky structures develop and eventually break down to turbulence after wavy motions. The purpose of the present study is to reveal the dominant scales of the streaky structures using a novel stereo PTV system measuring the streamwise and wall-normal velocities. The correlation of the streamwise velocity exhibit a negative peak at a certain spanwise separation. If normalized with the local boundary layer thickness, the spanwise separation minimizing the correlation decreases downstream and reaches the boundary layer thickness at the most downstream position. The streamwise correlation coefficient is asymptotically decreasing to zero and the streamwise integral scales are increasing downstream, indicating the large streamwise elongation of the streaky structure. The normalized spanwise scale of the wall-normal disturbance velocity also decreases downstream and it is always narrower than the width of the disturbances of the streamwise velocity. In contrast to the elongating streamwise velocity disturbance, the integral scale in the streamwise direction of the wall-normal disturbance is constant with downstream position. The length scales of the wall-normal disturbance are more less constant with the streamwise position and this result concludes that the wall-normal disturbance is simply convected by the mean flow after the receptivity process.

A Second Turbulent Regime When a Fully Developed Axial Turbulent Flow Enters a Rotating Pipe

2016 ◽  
Author(s):  
Ferdinand-J. Cloos ◽  
Anna-L. Zimmermann ◽  
Peter F. Pelz
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Circumferential Velocity ◽  
Turbulent Regime ◽  
Self Similarity ◽  
Flow Number

When a fluid enters a rotating circular pipe a swirl boundary layer with thickness of δ̃s appears at the wall and interacts with the axial momentum boundary layer with thickness of δ̃. We investigate a turbulent flow applying Laser-Doppler-Anemometry to measure the circumferential velocity profile at the inlet of the rotating pipe. The measured swirl boundary layer thickness follows a power law taking Reynolds number and flow number into account. A combination of high Reynolds number, high flow number and axial position causes a transition of the swirl boundary layer development in the turbulent regime. At this combination, the swirl boundary layer thickness as well as the turbulence intensity increase and the latter yields a self-similarity. The circumferential velocity profile changes to a new presented self-similarity as well. We define the transition inlet length, where the transition appears and a stability map for the two regimes is given for the case of a fully developed axial turbulent flow enters the rotating pipe.

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