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.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Shear Layer Development, Separation, and Stability Over a Low-Reynolds Number Airfoil

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Paul Ziadé ◽  
Mark A. Feero ◽  
Philippe Lavoie ◽  
Pierre E. Sullivan
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Layer ◽  
Separation Bubble ◽  
Low Reynolds Number ◽  
Base Flow ◽  
Mean Velocity ◽  
Laminar Separation ◽  
Low Reynolds ◽  
Layer Development

The shear layer development for a NACA 0025 airfoil at a low Reynolds number was investigated experimentally and numerically using large eddy simulation (LES). Two angles of attack (AOAs) were considered: 5 deg and 12 deg. Experiments and numerics confirm that two flow regimes are present. The first regime, present for an angle-of-attack of 5 deg, exhibits boundary layer reattachment with formation of a laminar separation bubble. The second regime consists of boundary layer separation without reattachment. Linear stability analysis (LSA) of mean velocity profiles is shown to provide adequate agreement between measured and computed growth rates. The stability equations exhibit significant sensitivity to variations in the base flow. This highlights that caution must be applied when experimental or computational uncertainties are present, particularly when performing comparisons. LSA suggests that the first regime is characterized by high frequency instabilities with low spatial growth, whereas the second regime experiences low frequency instabilities with more rapid growth. Spectral analysis confirms the dominance of a central frequency in the laminar separation region of the shear layer, and the importance of nonlinear interactions with harmonics in the transition process.

The effects of surface topography on momentum and mass transfer in a turbulent boundary layer

1981 ◽  
Vol 108 ◽  
pp. 423-442 ◽  
Author(s):  
R. A. Dawkins ◽  
D. R. Davies
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Turbulent Boundary Layer ◽  
Theoretical Calculations ◽  
Eddy Diffusivity ◽  
Open Circuit ◽  
Applied Theory ◽  
Mean Velocity ◽  
Method Of Calculation ◽  
Good Agreement

An approximate, conveniently applied theory with corresponding experimental data is presented concerning the changes in momentum and mass transfer produced by a ridge of small slopes in a flat-surface quasi-stationary turbulent boundary layer. A first-order mean velocity perturbation solution is found to be in good agreement with measured velocities on the up-slope side of a two-dimensional ridge, of length 20 cm and height 1 cm, fixed on the floor of the working section of an open-circuit wind tunnel. A vapour-transfer eddy-diffusivity distribution is then calculated for the inner boundary-layer region and solutions of the consequent vapour-transfer equation give the variation of rate of evaporation from surfaces of varying lengths placed at different positions on the up-slope region of the ridge. Corresponding measurements are found to be in good agreement with the theoretical calculations, and show that, even over small slopes (of 1 in 10), the evaporation rate varied with position by 25% from maximum to minimum. This method of calculation is extended to examine the effect of surface curvature on diffusion of gas from an upstream line source in a turbulent boundary layer over the ridge; experimental and theoretical concentration profiles compare extremely well over the leading slope.

Flow structure of the free round turbulent jet in the initial region

1979 ◽  
Vol 90 (3) ◽  
pp. 531-539 ◽  
Author(s):  
L. Bogusławski ◽  
Cz. O. Popiel
Keyword(s):  
Kinetic Energy ◽  
Turbulent Shear ◽  
Axial Distance ◽  
Initial Region ◽  
Mean Velocity ◽  
The Core ◽  
Turbulent Shear Stress ◽  
Air Jet ◽  
The Mean ◽  
Good Agreement

This note presents measurements of radial and axial distributions of mean velocity, turbulent intensities and kinetic energy as well as radial distributions of the turbulent shear stress in the initial region of a turbulent air jet issuing from a long round pipe into still air. The pipe flow is transformed relatively smoothly into a jet flow. In the core subregion the mean centre-line velocity decreases slightly. The highest turbulence occurs at an axial distance of about 6d and radius of (0·7 to 0·8)d. On the axis the highest turbulent kinetic energy appears at a distance of (7·5 to 8·5)d. Normalized distributions of the turbulent quantities are in good agreement with known data on the developed region of jets issuing from short nozzles.

Experimental Study on the Receptivity of Shear Layer Separating at a Rear-Edge of Boundary-Layer Plate

2007 ◽  
Author(s):  
Masahito Asai ◽  
Takeshi Imai
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Shear Instability ◽  
Instability Mode ◽  
Free Shear Layer ◽  
Frequency Range ◽  
Acoustic Disturbances ◽  
Rear Edge ◽  
Separated Shear Layer ◽  
Vorticity Fluctuation

Receptivity of the free shear layer developing from a 90-degrees rear-edge of boundary-layer plate to acoustic disturbances is examined experimentally to clarify the dependency of the receptivity coefficient on the rear-edge curvature. The results show that for finite rear-edge curvatures, the receptivity coefficient decreases with increasing the disturbance frequency while it is almost independent of the frequency for the sharp rear-edge over the frequency range examined. The decrease in the receptivity coefficient for the rounded rear-edge is attributed to the fact that the sound-induced Stokes layer which is the vorticity fluctuation developing into the free-shear instability mode is shed into the off-centerline of the separated shear layer.

Theoretical and Numerical Study of Vortex-Wake Flow Generated From Stack of Rectangular Bodies

2007 ◽  
Author(s):  
Khaled Alhussan
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Vortex Shedding ◽  
Numerical Study ◽  
The Body ◽  
Fluid Particle ◽  
Wake Flow ◽  
Free Shear Layer ◽  
Complex Flow ◽  
Discrete Vortex

Flow over external bodies has been studied extensively because of their many practical applications. For example, flow past a rectangular bodies, usually experiences strong flow oscillations and boundary layer separation in the wake region behind the body. As a fluid particle flows toward the leading edge of a rectangular body, the pressure of the fluid particle increases from the free stream pressure to the stagnation pressure. The boundary layer separates from the surface forms a free shear layer and is highly unstable. This shear layer will eventually roll into a discrete vortex and detach from the surface. A periodic flow motion will develop in the wake as a result of boundary layer vortices being shed alternatively from either side of the rectangular shapes. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations, especially when the shedding frequency matches one of the resonant frequencies of the structure. The work to be presented herein is a theoretical and numerical analysis of the complex fluid mechanism that occurs over stack of rectangular bodies for different number of rectangular bodies, specifically with regard to the vortex shedding and generation of wake. A number of important conclusions follow from the current research. First, study of the actual flow configuration over rectangular bodies offers some insight into the complex flow phenomena. Second, the characteristics of the vortex and wakes change considerably with the number of bodies.

Investigation of Unsteady Wake-Separated Boundary Layer Interaction Using Particle-Image-Velocimetry

2007 ◽  
Author(s):  
Og˘uz Uzol ◽  
Xue Feng Zhang ◽  
Alex Cranstone ◽  
Howard Hodson
Keyword(s):  
Boundary Layer ◽  
Particle Image Velocimetry ◽  
Shear Layer ◽  
Particle Image ◽  
Separation Bubble ◽  
Free Shear Layer ◽  
Unsteady Boundary Layer ◽  
Layer Interaction ◽  
Image Velocimetry ◽  
Boundary Layer Interaction

The current paper presents an experimental investigation of the interaction between unsteady wakes and the separated boundary layer on the suction side of an ultra-high-lift low-pressure turbine airfoil. Two-dimensional Particle Image Velocimetry (PIV) measurements of the unsteady boundary layer over the T106C LP turbine profile were performed in a low speed linear cascade facility, at selected phases of passing wakes. The wakes are created by moving cylindrical bars across the inlet of the test section. Various phenomena were investigated such as separation and transition characteristics, vortex structures within the unsteady boundary layer, their interaction and effects on the transition process, the corresponding vortex shedding mechanisms and the unsteady behaviour of the separation bubble due to the wake- boundary layer interaction. The current measurements suggest that rollup vortices are generated as the wake approaches the separated shear layer on the suction surface before the wake centerline starts impinging on the blade. At this instant, the bubble is sufficiently high for the free shear layer to roll up into a vortex and the incoming wake is highly distorted (strained) due to the velocity field within the blade passage, and the turbulence distribution within the wake is not symmetrical. Vortices within the boundary layer, identified using the swirl strength distributions calculated from the eigenvalues of the velocity gradient tensor, seem to be coalescing and forming bigger scale structures, which in turn break up into smaller but higher swirl strength eddies. In between the passing wakes, the separation bubble grows in both in height and length, trying to return to its steady state shape.

PIV Study of Separated and Reattached Open Channel Flow Over Surface Mounted Blocks

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Martin Agelinchaab ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
High Background ◽  
The Mean

A particle image velocimetry is used to study the mean and turbulent fields of separated and redeveloping flow over square, rectangular, and semicircular blocks fixed to the bottom wall of an open channel. The open channel flow is characterized by high background turbulence level, and the ratio of the upstream boundary layer thickness to block height is considerably higher than in prior experiments. The variation of the Reynolds stresses along the dividing streamlines is discussed within the context of vortex stretching, longitudinal strain rate, and wall damping. It appears that wall damping is a more dominant mechanism in the vicinity of reattachment. In the recirculation and reattachment regions, profiles of the mean velocity, turbulent quantities, and transport terms are used to document the salient features of block geometry on the flow. The flow characteristics in these regions strongly depend on block geometry. Downstream of reattachment, a new shear layer is formed, and the redevelopment of the shear layer toward the upstream open channel boundary layer is studied using the boundary layer parameters and Reynolds stresses. The results show that the mean flow rapidly redeveloped so that the Clauser parameter recovered to its upstream value at 90 step heights downstream of reattachment. However, the rate of development close to reattachment strongly depends on block geometry.

Turbulent flow over large-amplitude wavy surfaces

1984 ◽  
Vol 140 ◽  
pp. 27-44 ◽  
Author(s):  
Jeffrey Buckles ◽  
Thomas J. Hanratty ◽  
Ronald J. Adrian
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Velocity Fields ◽  
Laser Doppler Velocimeter ◽  
Free Shear Layer ◽  
Wave Surface ◽  
Velocity Measurements ◽  
Mean Velocity ◽  
Wavy Surfaces ◽  
The Mean

The laser-Doppler velocimeter is used to measure the mean and the fluctuating velocity for turbulent flow over a solid sinusoidal wave surface having a wavelength λ of 50.8 mm and a wave amplitude of 5.08 mm. For this flow, a large separated region exists, extending from x/λ = 0.14 to 0.69. From the mean velocity measurements, the time-averaged streamlines and therefore the extent of the separated region are calculated. Three flow elements are identified: the separated region, an attached boundary layer, and a free shear layer formed by the detachment of the boundary layer from the wave surface. The characteristics of these flow elements are discussed in terms of the properties of the mean and fluctuating velocity fields.

Blunt Trailing Edge Shear Wake Development With Turbulent In-Flow Boundary Layers

2005 ◽  
Author(s):  
Dhanalakshmi Challa ◽  
Joe Klewicki
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Boundary Layers ◽  
High Speed ◽  
Velocity Ratio ◽  
Free Shear Layer ◽  
Low Speed ◽  
Axial Pressure Gradient ◽  
Layer Flow ◽  
Good Agreement

Experiments are conducted to explore the structural mechanisms involved in the post-separation evolution of a wall-bounded to a free-shear turbulent flow. At the upstream, both the boundary layers are turbulent. Experiments were conducted in a two-stream shear-layer tunnel, under a zero axial pressure gradient shear-wake configuration. A velocity ratio near 2 was explored. Profile data were collected with a single wire probe at various locations downstream of the blunt separation lip. With this set of measurements, mean profile, axial intensity and measures of profile evolution indicate that the predominant shift from turbulent boundary layer to free shear-layer like behavior occurs between the downstream locations x/θ = 13.7 & 27.4, where θ is the upstream momentum deficit thickness on the low-speed stream. The shear wake width is observed to be nominally constant with the downstream position. Axial velocity spectra show that the transition from boundary layer flow to shear flow occurs earlier in high-speed stream when compared to low speed stream. Strouhal number, Sto, of initial vortex rollup based on initial momentum thickness was found to be 0.034, which is in very good agreement with the existing literature. Other measures are in good agreement with linear stability considerations found in the literature.

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