Effect of external turbulence on the evolution of a wake in stratified and unstratified environments

2015 ◽  
Vol 772 ◽  
pp. 361-385 ◽  
Author(s):  
Anikesh Pal ◽  
Sutanu Sarkar
Keyword(s):  
Reynolds Number ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Free Stream ◽  
Vertical Direction ◽  
Integral Length Scale ◽  
Moderate Intensity ◽  
Length Scale ◽  
Wake Turbulence ◽  
External Turbulence

Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10 000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds.

scholarly journals The scaling of straining motions in homogeneous isotropic turbulence

2017 ◽  
Vol 829 ◽  
pp. 31-64 ◽  
Author(s):  
G. E. Elsinga ◽  
T. Ishihara ◽  
M. V. Goudar ◽  
C. B. da Silva ◽  
J. C. R. Hunt
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Local Strain ◽  
Scale Structure ◽  
Small Scale ◽  
Length Scale ◽  
Local Flow ◽  
Small Scale Structure

The scaling of turbulent motions is investigated by considering the flow in the eigenframe of the local strain-rate tensor. The flow patterns in this frame of reference are evaluated using existing direct numerical simulations of homogeneous isotropic turbulence over a Reynolds number range from $Re_{\unicode[STIX]{x1D706}}=34.6$ up to 1131, and also with reference to data for inhomogeneous, anisotropic wall turbulence. The average flow in the eigenframe reveals a shear layer structure containing tube-like vortices and a dissipation sheet, whose dimensions scale with the Kolmogorov length scale, $\unicode[STIX]{x1D702}$. The vorticity stretching motions scale with the Taylor length scale, $\unicode[STIX]{x1D706}_{T}$, while the flow outside the shear layer scales with the integral length scale, $L$. Furthermore, the spatial organization of the vortices and the dissipation sheet defines a characteristic small-scale structure. The overall size of this characteristic small-scale structure is $120\unicode[STIX]{x1D702}$ in all directions based on the coherence length of the vorticity. This is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Comparing the overall size of the characteristic small-scale structure with the largest flow scales and the vorticity stretching motions on the scale of $4\unicode[STIX]{x1D706}_{T}$ shows that transitions in flow structure occur where $Re_{\unicode[STIX]{x1D706}}\approx 45$ and 250. Below these respective transitional Reynolds numbers, the small-scale motions and the vorticity stretching motions are progressively less well developed. Scale interactions are examined by decomposing the average shear layer into a local flow, which is induced by the shear layer vorticity, and a non-local flow, which represents the environment of the characteristic small-scale structure. The non-local strain is $4\unicode[STIX]{x1D706}_{T}$ in width and height, which is consistent with observations in high Reynolds number flow of a $4\unicode[STIX]{x1D706}_{T}$ wide instantaneous shear layer with many $\unicode[STIX]{x1D702}$-scale vortical structures inside (Ishihara et al., Flow Turbul. Combust., vol. 91, 2013, pp. 895–929). In the average shear layer, vorticity aligns with the intermediate principal strain at small scales, while it aligns with the most stretching principal strain at larger scales, consistent with instantaneous turbulence. The length scale at which the alignment changes depends on the Reynolds number. When conditioning the flow in the eigenframe on extreme dissipation, the velocity is strongly affected over large distances. Moreover, the associated peak velocity remains Reynolds number dependent when normalized by the Kolmogorov velocity scale. It signifies that extreme dissipation is not simply a small-scale property, but is associated with large scales at the same time.

Normalized dissipation rate in a moderate Taylor Reynolds number flow

2017 ◽  
Vol 818 ◽  
pp. 184-204 ◽  
Author(s):  
Alejandro J. Puga ◽  
John C. LaRue
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Integral Length Scale ◽  
Length Scale ◽  
Velocity Correlation ◽  
Time Resolved ◽  
Reynolds Number Flow ◽  
Active Grid

Time-resolved velocity measurements are obtained using a hot-wire in a nearly homogeneous and isotropic flow downstream of an active grid for a range of Taylor Reynolds numbers from$191$to$659$. It is found that the dimensionless dissipation rate,$C_{\unicode[STIX]{x1D716}}$, is nearly a constant for sufficiently high values of Taylor Reynolds number,$R_{\unicode[STIX]{x1D706},u_{q}}$, and is approximately equal to$0.87$. This value is approximately$5\,\%$less than the value reported by Boset al.(Phys. Fluids, vol. 19 (4), 2007, 045101), which is obtained using DNS/LES (direct numerical simulation combined with large eddy simulation) for decaying homogeneous and isotropic turbulence, and is in excellent agreement with the active grid experiment of Thormann & Meneveau (Phys. Fluids, vol. 26 (2), 2014, 025112.). The results presented herein show that deviation from isotropy may cause inconsistencies in the computation of$C_{\unicode[STIX]{x1D716}}$. As a result, it is suggested that the velocity scale be the square root of the turbulence kinetic energy. The integral length scale measurements obtained from the longitudinal velocity correlation are in close agreement with the integral length scale measured from the peak of the energy spectrum,$\unicode[STIX]{x1D705}E_{11}(\unicode[STIX]{x1D705})$, where$\unicode[STIX]{x1D705}$is the wavenumber and$E_{11}(\unicode[STIX]{x1D705})$is the one-dimensional power spectrum of the downstream velocity.

scholarly journals Influence of Turbulence Parameters, Reynolds Number, and Body Shape on Stagnation-Region Heat Transfer

1995 ◽  
Vol 117 (3) ◽  
pp. 597-603 ◽  
Author(s):  
G. J. Van Fossen ◽  
R. J. Simoneau ◽  
C. Y. Ching
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Velocity Gradient ◽  
Isotropic Turbulence ◽  
Leading Edge ◽  
Length Scale ◽  
Stagnation Region ◽  
Free Stream Turbulence ◽  
Heat Transfer Augmentation ◽  
Optimum Scale

This experiment investigated the effects of free-stream turbulence intensity, length scale, Reynolds number, and leading-edge velocity gradient on stagnation-region heat transfer. Heat transfer was measured in the stagnation region of four models with elliptical leading edges downstream of five turbulence-generating grids. Stagnation-region heat transfer augmentation increased with decreasing length scale but ann optimum scale was not found. A correlation was developed that fit heat transfer data for isotropic turbulence to within ±4 percent but did not predict data for anisotropic turbulence. Stagnation heat transfer augmentation caused by turbulence was unaffected by the velocity gradient. The data of other researchers compared well with the correlation. A method of predicting heat transfer downstream of the stagnation point was developed.

Free-Stream Turbulence Effects on Film Cooling With Shaped Holes

2003 ◽  
Vol 125 (1) ◽  
pp. 65-73 ◽  
Author(s):  
Christian Saumweber ◽  
Achmed Schulz ◽  
Sigmar Wittig
Keyword(s):  
Turbulence Intensity ◽  
Film Cooling ◽  
Free Stream ◽  
Operating Conditions ◽  
Integral Length Scale ◽  
Length Scale ◽  
Free Stream Turbulence ◽  
Blowing Ratio ◽  
Cylindrical Holes ◽  
The Impact

A comprehensive set of generic experiments has been conducted to investigate the effect of elevated free-stream turbulence on film cooling performance of shaped holes. A row of three cylindrical holes as a reference case, and two rows of holes with expanded exits, a fanshaped (expanded in lateral direction), and a laidback fanshaped hole (expanded in lateral and streamwise direction) have been employed. With an external (hot gas) Mach number of Mam=0.3 operating conditions are varied in terms of free-stream turbulence intensity (up to 11%), integral length scale at constant turbulence intensity (up to 3.5 hole inlet diameters), and blowing ratio. The temperature ratio is fixed at 0.59 leading to an enginelike density ratio of 1.7. The results indicate that shaped and cylindrical holes exhibit very different reactions to elevated free-stream turbulence levels. For cylindrical holes film cooling effectiveness is reduced with increased turbulence level at low blowing ratios whereas a small gain in effectiveness can be observed at high blowing ratios. For shaped holes, increased turbulence intensity is detrimental even for the largest blowing ratio M=2.5. In comparison to the impact of turbulence intensity the effect of varying the integral length scale is found to be of minor importance. Finally, the effect of elevated free-stream turbulence in terms of heat transfer coefficients was found to be much more pronounced for the shaped holes.

scholarly journals Characteristics of Low Reynolds Number Shear-Free Turbulence at an Impermeable Base

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
W. H. M. Wan Mohtar ◽  
A. ElShafie
Keyword(s):  
Reynolds Number ◽  
Horizontal Velocity ◽  
Energy Spectra ◽  
Integral Length Scale ◽  
Length Scale ◽  
Turbulence Structure ◽  
Viscous Damping ◽  
Water Tank ◽  
Velocity Data ◽  
Standard Profile

Shear-free turbulence generated from an oscillating grid in a water tank impinging on an impermeable surface at varying Reynolds number74≤Rel≤570was studied experimentally, where the Reynolds number is defined based on the root-mean-square (r.m.s) horizontal velocity and the integral length scale. A particular focus was paid to the turbulence characteristics for lowRel<150to investigate the minimum limit ofRelobeying the profiles of rapid distortion theory. The measurements taken at near base included the r.m.s turbulent velocities, evolution of isotropy, integral length scales, and energy spectra. Statistical analysis of the velocity data showed that the anisotropic turbulence structure follows the theory for flows withRel≥117. At lowRel<117, however, the turbulence profile deviated from the prediction where no amplification of horizontal velocity components was observed and the vertical velocity components were seen to be constant towards the tank base. Both velocity components sharply decreased towards zero at a distance of≈1/3of the integral length scale above the base due to viscous damping. The lower limit whereRelobeys the standard profile was found to be within the range114≤Rel≤116.

scholarly journals The Turbulence That Matters

1997 ◽  
Author(s):  
R. E. Mayle ◽  
K. Dullenkopf ◽  
A. Schulz
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Gas Turbines ◽  
Free Stream ◽  
Transitional Flow ◽  
Stream Velocity ◽  
Length Scale ◽  
Effective Frequency ◽  
Large Wave ◽  
Free Stream Turbulence

A unified expression for the spectrum of turbulence is developed by asymptotically matching known expressions for small and large wave numbers, and a formula for the one-dimensional spectral function which depends on the turbulence Reynolds number Reλ is provided. In addition, formulas relating all the length scales of turbulence are provided. These relations also depend on Reynolds number. The effects of free-stream turbulence on laminar heat transfer and pre-transitional flow in gas turbines are re-examined in light of these new expressions using our recent thoughts on an ‘effective’ frequency of turbulence and an ‘effective’ turbulence level. The results of this are that the frequency most effective for laminar heat transfer is about 1.3U/Le, where U is the free-stream velocity and Le is the length scale of the eddies containing the most turbulent energy, and the most effective frequency for producing pre-transitional boundary layer fluctuations is about 0.3U/η where η is Kolmogorov’s length scale. In addition, the role of turbulence Reynolds number on stagnation heat transfer and transition is discussed, and new expressions to account for its effect are provided.

scholarly journals A new linear forcing method for isotropic turbulence with controlled integral length scale

2021 ◽  
Vol 33 (4) ◽  
pp. 045127
Author(s):  
Jérémie Janin ◽  
Fabien Duval ◽  
Christophe Friess ◽  
Pierre Sagaut
Keyword(s):  
Isotropic Turbulence ◽  
Integral Length Scale ◽  
Length Scale
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