Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

A Simplified Version of Bradshaw’s Method for Calculating Two-dimensional Turbulent Boundary Layers

1970 ◽  
Vol 21 (3) ◽  
pp. 243-262 ◽  
Author(s):  
V. C. Patel ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Computing Time ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Simplified Approach ◽  
Appreciable Increase ◽  
Momentum Integral

SummaryBradshaw’s method of calculating the development of two-dimensional turbulent boundary layers involves the simultaneous solution of partial differential equations of mean motion and turbulent kinetic energy. The present approach avoids the computational complexities of this procedure.The use of Thompson’s two-parameter family of velocity profiles and associated skin-friction law enables the momentum integral equation to be satisfied, along with Bradshaw’s version of the turbulent kinetic-energy equation at a specified fraction of the boundary layer thickness. This fraction (y/δ = 0·5) is chosen as representing the position in the boundary layer where Bradshaw’s equation, which contains several empirical functions, is shown by comparisons with experiment to hold with greatest accuracy. Thus the present simplified approach leads not only to a reduction in computing time but also to an appreciable increase in the general accuracy of prediction.

The Effect of Surface Roughness and Favorable Pressure Gradient on Turbulent Boundary Layers

2011 ◽  
Author(s):  
Ju Hyun Shin ◽  
Seung Jin Song
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Layer Growth ◽  
Rough Wall ◽  
Favorable Pressure Gradient

Rough wall turbulent boundary layers subjected to pressure gradient have engineering interest for many fluid machinery applications. A number of investigations have been made to understand surface roughness and pressure gradient effects on turbulent boundary layer characteristics, but separately. In this paper, turbulent boundary layers over a flat plate with surface roughness and favorable pressure gradient (FPG) are experimentally investigated. Boundary layers in different streamwise locations were measured using boundary layer type hot-wire anemometry. Rough wall zero pressure gradient (ZPG) turbulent boundary layers were also measured to compare the result from the investigation. The surface roughness was applied by attaching sandpapers on the flat plate. The magnitude of surface roughness is representative of land-based gas turbine compressor blade. Pressure gradient was adjusted using movable endwall of the test section. Results from the measurement show characteristics of the turbulent boundary layer growth affected by both surface roughness and favorable pressure gradient.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Prediction of Turbulent Boundary Layer Development in Conical Diffusers

1966 ◽  
Vol 8 (4) ◽  
pp. 426-436 ◽  
Author(s):  
A. D. Carmichael ◽  
G. N. Pustintsev
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Energy Deficit ◽  
Momentum Thickness ◽  
Boundary Layer Development ◽  
Layer Development

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

2018 ◽  
Author(s):  
Yvan Maciel ◽  
Tie Wei ◽  
Ayse G. Gungor ◽  
Mark P. Simens
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Inertial Parameter ◽  
Velocity Scale ◽  
Gradient Parameter

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows — not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow — in a global sense — the streamwise evolution of the stream-wise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

Two-equation turbulence modeling of an oscillatory boundary layer under steep pressure gradient

2010 ◽  
Vol 37 (4) ◽  
pp. 648-656 ◽  
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Reynolds Stress ◽  
Turbulence Modeling ◽  
Turbulence Models ◽  
Detailed Comparison ◽  
Stream Velocity ◽  
Oscillatory Boundary Layer

A total of seven versions of two-equation turbulence models (four versions of low Reynolds number k–ε model, one k–ω model and two versions of k–ε / k–ω blended models) are tested against the direct numerical simulation (DNS) data of a one-dimensional oscillatory boundary layer with flat crested free-stream velocity that results from a steep pressure gradient. A detailed comparison has been made for cross-stream velocity, turbulent kinetic energy (TKE), Reynolds stress, and ratio of Reynolds stress and turbulent kinetic energy. It is observed that the newer versions of k–ε model perform very well in predicting the velocity, turbulent kinetic energy, and Reynolds stress. The k–ω model and blended models underestimate the peak value of turbulent kinetic energy that may be explained by the Reynolds stress to TKE ratio in the logarithmic zone. The maximum bottom shear stress is well predicted by the k–ε model proposed by Sana et al. and the original k–ω model.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

Comparison of Two Analyses of Boundary-Layer Data on a Flat Plate

1958 ◽  
Vol 2 (01) ◽  
pp. 21-33
Author(s):  
L. Landweber ◽  
T. T. Siao
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Logarithmic Law

In a recent paper (1) it was indicated that there appeared to be a need for generalizing the well-known logarithmic law of turbulent boundary layers and such a generalization was derived on the basis of a suggestion due to Townsend (2). It was found that the logarithmic formulas constitute only one member of a family of possible formulas, among which that one which best fits the boundary-layer data should be selected.

On the scaling in sink-flow turbulent boundary layers

2013 ◽  
Vol 737 ◽  
pp. 329-348 ◽  
Author(s):  
Shivsai Ajit Dixit ◽  
O. N. Ramesh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Physical Space ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Velocity Spectrum ◽  
Scaling Exponent ◽  
Order Of Magnitude

AbstractScaling of the streamwise velocity spectrum ${\phi }_{11} ({k}_{1} )$ in the so-called sink-flow turbulent boundary layer is investigated in this work. The present experiments show strong evidence for the ${ k}_{1}^{- 1} $ scaling i.e. ${\phi }_{11} ({k}_{1} )= {A}_{1} { U}_{\tau }^{2} { k}_{1}^{- 1} $, where ${k}_{1} $ is the streamwise wavenumber and ${U}_{\tau } $ is the friction velocity. Interestingly, this ${ k}_{1}^{- 1} $ scaling is observed much farther from the wall and at much lower flow Reynolds number (both differing by almost an order of magnitude) than what the expectations from experiments on a zero-pressure-gradient turbulent boundary layer flow would suggest. Furthermore, the coefficient ${A}_{1} $ in the present sink-flow data is seen to be non-universal, i.e. ${A}_{1} $ varies with height from the wall; the scaling exponent −1 remains universal. Logarithmic variation of the so-called longitudinal structure function, which is the physical-space counterpart of spectral ${ k}_{1}^{- 1} $ scaling, is also seen to be non-universal, consistent with the non-universality of ${A}_{1} $. These observations are to be contrasted with the universal value of ${A}_{1} $ (along with the universal scaling exponent of −1) reported in the literature on zero-pressure-gradient turbulent boundary layers. Theoretical arguments based on dimensional analysis indicate that the presence of a streamwise pressure gradient in sink-flow turbulent boundary layers makes the coefficient ${A}_{1} $ non-universal while leaving the scaling exponent −1 unaffected. This effect of the pressure gradient on the streamwise spectra, as discussed in the present study (experiments as well as theory), is consistent with other recent studies in the literature that are focused on the structural aspects of turbulent boundary layer flows in pressure gradients (Harun et al., J. Fluid Mech., vol. 715, 2013, pp. 477–498); the present paper establishes the link between these two. The variability of ${A}_{1} $ accommodated in the present framework serves to clarify the ideas of universality of the ${ k}_{1}^{- 1} $ scaling.

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