On the power laws for turbulent jets, wakes and shearing layers and their relationship to the principle of marginal instability

1978 ◽  
Vol 88 (3) ◽  
pp. 535-540 ◽  
Author(s):  
Martin Lessen
Keyword(s):  
Reynolds Number ◽  
Turbulent Jets ◽  
Power Laws ◽  
Similarity Solutions ◽  
Turbulent Reynolds Number

The classical power laws describing the similarity solutions for turbulent jets, wakes and shearing layers are found to determine a fixed turbulent Reynolds number for each flow. The power laws are then derived from the principle of marginal instability without the usual assumptions.

scholarly journals Turbulence, entrainment and low-order description of a transitional variable-density jet

2017 ◽  
Vol 836 ◽  
pp. 1009-1049 ◽  
Author(s):  
B. Viggiano ◽  
T. Dib ◽  
N. Ali ◽  
L. G. Mastin ◽  
R. B. Cal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Jets ◽  
Reynolds Numbers ◽  
Variable Density ◽  
Quadrant Analysis ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Buoyant Jet ◽  
Entrainment Ratio ◽  
Turbulent Reynolds Number

Geophysical flows occur over a large range of scales, with Reynolds numbers and Richardson numbers varying over several orders of magnitude. For this study, jets of different densities were ejected vertically into a large ambient region, considering conditions relevant to some geophysical phenomena. Using particle image velocimetry, the velocity fields were measured for three different gases exhausting into air – specifically helium, air and argon. Measurements focused on both the jet core and the entrained ambient. Experiments considered relatively low Reynolds numbers from approximately 1500 to 10 000 with Richardson numbers near 0.001 in magnitude. These included a variety of flow responses, notably a nearly laminar jet, turbulent jets and a transitioning jet in between. Several features were studied, including the jet development, the local entrainment ratio, the turbulent Reynolds stresses and the eddy strength. Compared to a fully turbulent jet, the transitioning jet showed up to 50 % higher local entrainment and more significant turbulent fluctuations. For this condition, the eddies were non-axisymmetric and larger than the exit radius. For turbulent jets, the eddies were initially smaller and axisymmetric while growing with the shear layer. At lower turbulent Reynolds number, the turbulent stresses were more than 50 % higher than at higher turbulent Reynolds number. In either case, the low-density jet developed faster than a comparable non-buoyant jet. Quadrant analysis and proper orthogonal decomposition were also utilized for insight into the entrainment of the jet, as well as to assess the energy distribution with respect to the number of eigenmodes. Reynolds shear stresses were dominant in Q1 and Q3 and exhibited negligible contributions from the remaining two quadrants. Both analysis techniques showed that the development of stresses downstream was dependent on the Reynolds number while the spanwise location of the stresses depended on the Richardson number.

scholarly journals Effects of Turbulent Reynolds Number on the Performance of Algebraic Flame Surface Density Models for Large Eddy Simulation in the Thin Reaction Zones Regime: A Direct Numerical Simulation Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Mohit Katragadda ◽  
Nilanjan Chakraborty ◽  
R. S. Cant
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Fractal Dimension ◽  
Direct Numerical Simulation ◽  
Surface Density ◽  
Flame Surface ◽  
Algebraic Models ◽  
Flame Surface Density ◽  
Turbulent Reynolds Number ◽  
Reaction Zones

A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models based on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Rethas been varied by modifying the Karlovitz number Ka and the Damköhler number Da independently of each other in such a way that the flames remain within the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both have a significant influence on the fractal dimension, which is found to increase with increasing Retand Ka before reaching an asymptotic value for large values of Retand Ka. A parameterisation of the fractal dimension is presented in which the effects of the Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the Zel’dovich flame thicknessηi/δzdoes not exhibit any significant dependence on Retfor the cases considered here. The performance of several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in performance with increasing the LES filter width.

scholarly journals Feasibility study of power generation using a turbine mounted in aircraft wing

2018 ◽  
Vol 7 (2-1) ◽  
pp. 433
Author(s):  
K. Sri Vamsi Krishna ◽  
Shiva Prasad ◽  
R. Sabari Vihar ◽  
K. Babitha ◽  
K Veeranjaneyulu ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Power Systems ◽  
Free Stream ◽  
Mechanical Energy ◽  
Electrical Energy ◽  
Aircraft Wing ◽  
Aerodynamic Efficiency ◽  
Turbulent Reynolds Number ◽  
Main Motive ◽  
Emergency Power

The main objective of this study is to increase the aerodynamic efficiency of turbine mounted novel wing. The main motive behind this work is to reduce the drag by attaining the positive velocity gradient and generate power by converting the stagnation pressure which also acts as emergency power source. By using the energy source of free stream air, Mechanical energy is converted into electrical energy. The obtained power is presented in terms of voltage generated at various angles of attack with different Reynolds number. Experimental analysis is carried out for NACA4415 airfoil at various angles with respect to free stream ranging from 0deg to 30deg from laminar to turbulent Reynolds number. The results were obtained using the research tunnel at IARE aerodynamic facility center. The aerodynamic advantage of this design in terms of voltage is 9.5 V at 35m/s which can be utilized for the aircraft on board power systems.

Reynolds Number Effect on the Flow Demeanorin a Vertical Circular Free Turbulent Jet with Cross Flow

2021 ◽  
Vol 409 ◽  
pp. 158-178
Author(s):  
Abdelkader Feddal ◽  
Abbes Azzi ◽  
Ahmed Zineddine Dellil
Keyword(s):  
Reynolds Number ◽  
Cross Flow ◽  
Turbulence Models ◽  
Turbulent Jets ◽  
Turbulent Jet ◽  
Low Velocity ◽  
Transverse Current ◽  
Ansys Cfx ◽  
The Cross ◽  
Two Jets

This paper deals with studying numerically two circular turbulent jets impinging on a flat surface with a low velocity cross flow by using ANSYS CFX 16.2, with the aim of proving the effect ofReynolds number on the flow demeanor in a vertical circular free turbulent jet with cross flow. Five turbulence models of the RANS (Reynolds Averaged Navier–Stokes) approach were tested and the k -ω SST model was chosen to validate CFD results with the experimental data. Average velocity profiles, velocity and turbulent kinetic energy contours and streamlines are presented for four case configurations. In the first three cases, the following parameters have been varied: Reynolds number at the level of the two jets ( ), wind velocity at the level of the cross-flow ( ), and the distance between the two jets (S = 45mm, 90mm and 135mm). In the last case, a new configuration of the phenomenon not yet studied so far was treated, where horizontal cross-flows were introduced from both sides in order to simulate gusts of wind disrupting a VSTOL aircraft which tries to operate close to the ground. This case was carried out for Reynolds number based on the crossflow of 4 104, 10 104 and 20 104 .The numerical results obtained show that the deflection of the jets is minimal when the Reynolds number at the level of the jets is greater than that of the cross-flow. The increase of Reynolds number at the level of the cross-flow reveals a significant deviation of the two jets with an intensity which always remains less for the second jet. As for the space parameter between the two jets, it turns out that the fact of further spacing the two jets makes the first jet even more vulnerable and leads to a greater deflection. Finally, the simulation of the wind gusts from the front and the back caused a zone of turbulence which resulted from a form of "interlacing" of the two jets under the effect of the transverse current imposed by the two sides.

scholarly journals Effects of Turbulent Reynolds Number on the Displacement Speed Statistics in the Thin Reaction Zones Regime of Turbulent Premixed Combustion

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Nilanjan Chakraborty ◽  
Markus Klein ◽  
R. S. Cant
Keyword(s):  
Reynolds Number ◽  
Strain Rate ◽  
Surface Density ◽  
Three Dimensional ◽  
Flame Surface ◽  
Tangential Strain ◽  
Turbulent Reynolds Number ◽  
Qualitative Nature ◽  
Displacement Speed ◽  
Turbulent Premixed

The effects of turbulent Reynolds number on the statistical behaviour of the displacement speed have been studied using three-dimensional Direct Numerical Simulation of statistically planar turbulent premixed flames. The probability of finding negative values of the displacement speed is found to increase with increasing turbulent Reynolds number when the Damköhler number is held constant. It has been shown that the statistical behaviour of the Surface Density Function, and its strain rate and curvature dependence, plays a key role in determining the response of the different components of displacement speed. Increasing the turbulent Reynolds number is shown to reduce the strength of the correlations between tangential strain rate and dilatation rate with curvature, although the qualitative nature of the correlations remains unaffected. The dependence of displacement speed on strain rate and curvature is found to weaken with increasing turbulent Reynolds number when either Damköhler or Karlovitz number is held constant, but the qualitative nature of the correlation remains unaltered. The implications of turbulent Reynolds number effects in the context of Flame Surface Density (FSD) modelling have also been addressed, with emphasis on the influence of displacement speed on the curvature and propagation terms in the FSD balance equation.

Local similarity solutions and their limitations

1980 ◽  
Vol 96 (2) ◽  
pp. 299-313 ◽  
Author(s):  
H. K. Moffatt ◽  
B. R. Duffy
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Similarity Solution ◽  
Similarity Solutions ◽  
Normal Velocity ◽  
Local Similarity ◽  
Reynolds Number Flow ◽  
Interesting Conclusion ◽  
Number Flow ◽  
Pressure Driven Flow

Two problems exhibiting breakdown in local similarity solutions are discussed, and the appropriate asymptotic form of the exact solution is determined in each case. The first problem is the very elementary problem of pressure driven flow along a duct whose cross-section has a sharp corner of angle 2α. When 2α < ½π, a local similarity solution is valid, whereas, when 2α > ½π, the solution near the corner depends on the global geometry of the cross-section. The transitional behaviour when 2α = ½π is determined.The second problem concerns low-Reynolds-number flow in the wedge-shaped region |θ| < α when either a normal velocity proportional to distance from the vertex is imposed on both boundaries, or a finite flux 2Q is introduced or extracted at the vertex (the Jeffery–Hamel problem). It is shown that the similarity solution in either case is valid only when 2α < 2αc ≈ 257·5°; a modified problem is solved exactly revealing the behaviour when α > αc, and the transitional behaviour when α = αc (when the similarity solutions become infinite everywhere). An interesting conclusion for the Jeffery–Hamel problem is that when α > αc, inertia forces are of dominant importance throughout the flow field no matter how small the source Reynolds number 2Q/ν may be.

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