A Receptivity Based Transition Model

2003 ◽  
Author(s):  
Mark W. Johnson
Keyword(s):  
Boundary Layers ◽  
Reasonable Agreement ◽  
Narrow Band ◽  
Numerical Procedure ◽  
Separated Flow ◽  
Pressure Gradients ◽  
Laminar Boundary Layers ◽  
Wide Range ◽  
Improve Accuracy ◽  
Near Wall

A numerical procedure for predicting the receptivity of laminar boundary layers to freestream turbulence, consisting of vortex arrays with arbitrary orientation, has been developed previously. In the current paper this method is refined to improve accuracy using an unstructured computational grid. Results show that boundary layers only have high receptivity to a narrow band of normal and spanwise frequencies. The computed near wall gains have similar values to those obtained by experiment for zero pressure gradient boundary layers. Near wall gains are also obtained for a wide range of favourable and adverse pressure gradients for both attached and separated boundary layers. The gain values are used to predict start of transition values which are in reasonable agreement with Reθ values which are in reasonable agreement with the Abu-Ghannam and Shaw correlations. The current results extend transition inception prediction into the separated flow regime.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

A Reference Temperature Method for Compressible Laminar Boundary Layers

1973 ◽  
Vol 2 (4) ◽  
pp. 201-204
Author(s):  
R. Camarero
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Reference Temperature ◽  
Integral Approach ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Temperature Method ◽  
Compressibility Effects

A calculation procedure for the solution of two-dimensional and axi-symmetric laminar boundary layers in compressible flow has been developed. The method is an extension of the integral approach of Tani to include compressibility effects by means of a reference temperature. Arbitrary pressure gradients and wall temperature can be specified. Comparisons with experiments obtained for supersonic flows over a flat plate indicate that the method yields adequate results. The method is then applied to the solution of the boundary layer on a Basemann inlet.

A Method for the Calculation of 3D Boundary Layers on Practical Wing Configurations

1981 ◽  
Vol 103 (1) ◽  
pp. 104-111 ◽  
Author(s):  
J. P. F. Lindhout ◽  
G. Moek ◽  
E. De Boer ◽  
B. Van Den Berg
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Flow ◽  
Eddy Viscosity ◽  
Separated Flow ◽  
Laminar Boundary Layers ◽  
Eddy Viscosity Model ◽  
Airplane Wing ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

This paper gives a description of a calculation method for 3D turbulent and laminar boundary layers on nondevelopable surfaces. A simple eddy viscosity model is incorporated in the method. Special attention is given to the organization of the computations to circumvent as much as possible stepsize limitations. The method is also able to proceed the computation around separated flow regions. The method has been applied to the laminar boundary layer flow over a flat plate with attached cylinder, and to a turbulent boundary layer flow over an airplane wing.

Hot-wire spatial resolution issues in wall-bounded turbulence

2009 ◽  
Vol 635 ◽  
pp. 103-136 ◽  
Author(s):  
N. HUTCHINS ◽  
T. B. NICKELS ◽  
I. MARUSIC ◽  
M. S. CHONG
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Spatial Resolution ◽  
Reynolds Numbers ◽  
Energy Spectra ◽  
Small Scale ◽  
Wire Length ◽  
Hot Wire ◽  
Wide Range ◽  
Near Wall

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

The Origin of Turbulent Spots

1999 ◽  
Vol 122 (1) ◽  
pp. 88-92 ◽  
Author(s):  
M. W. Johnson ◽  
A. Dris
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Linear Perturbation ◽  
Bypass Transition ◽  
Turbulent Spot ◽  
Turbulent Spots ◽  
Free Stream Turbulence ◽  
Wide Range ◽  
Asme Paper ◽  
Near Wall

It has been suggested that a turbulent spot is formed when a transient separation occurs in the laminar boundary layer and this criterion has been successfully used by Johnson and Ercan (1996, ASME Paper No. 96-GT-44; 1997, ASME Paper No. 97-GT-475) to predict bypass transition for boundary layers subjected to a wide range of free-stream turbulence levels and streamwise pressure gradients. In the current paper experimental results are presented that support the premise that the formation of turbulent spots is associated with transient separation. Near-wall hot-wire signals in laminar and transitional boundary layers are analyzed statistically to produce probability distributions for signal level and trough frequency. In the laminar period the signal level is normally distributed, but during the inter-turbulent periods in the transitional boundary layer, the distribution is truncated at the lower end, i.e., the lowest velocity periods in the signal disappear, suggesting that these are replaced during transition by the turbulent periods. The number of these events (troughs) also correlates with the number of turbulent spots during early transition. A linear perturbation theory is also used in the paper to compute the streamlines through a turbulent spot and its associated calmed region. The results indicate that a hairpin vortex dominates the flow and entrains a low-momentum fluid stream from upstream with a high-momentum stream from downstream and then ejects the combined stream into the turbulent spot. The hairpin can only exist if a local separation occurs beneath its nose and the current results suggest that this separation is induced when the instantaneous velocity in the near-wall signal drops below 50 percent of the mean. [S0889-504X(00)01001-1]

scholarly journals A Bypass Transition Model for Boundary Layers

1993 ◽  
Author(s):  
Mark W. Johnson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Transition Model ◽  
Wall Region ◽  
Bypass Transition ◽  
Pressure Gradients ◽  
Turbulence Level ◽  
Velocity Fluctuations ◽  
Laminar Boundary Layers

Experimental data for laminar boundary layers developing below a turbulent free stream shows that the fluctuation velocities within the boundary layer increase in amplitude until some critical level is reached which initiates transition. In the near wall region, a simple model, containing a single empirical parameter which depends only on the turbulence level and length scale, is derived to predict the development of the velocity fluctuations in laminar boundary layers with favourable, zero or adverse pressure gradients. A simple bypass transition model which considers the streamline distortion in the near wall region brought about by the velocity fluctuations suggests that transition will commence when the local turbulence level reaches approximately 23%. This value is consistent with experimental findings. This critical local turbulence level is used to derive a bypass transition prediction formula which compares reasonably with start of transition experimental data for a range of pressure gradients (λθ = −0.01 to 0.01) and turbulence levels (Tu = 0.2% to 5%). Further improvement to the model is proposed through prediction of the boundary layer distortion, which occurs due to Reynolds stresses generated within the boundary layer at high free stream turbulence levels and also through inclusion of the effect of turbulent length scale as well as turbulence level.

scholarly journals The Origin of Turbulent Spots

1999 ◽  
Author(s):  
Mark W. Johnson ◽  
Antonis Dris
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Probability Distributions ◽  
Linear Perturbation ◽  
Bypass Transition ◽  
Turbulent Spot ◽  
Turbulent Spots ◽  
Wide Range ◽  
Linear Perturbation Theory ◽  
Near Wall

It has been suggested that a turbulent spot is formed when a transient separation occurs in the laminar boundary layer and this criterion has been successfully used by Johnson and Ercan [1996,1997] to predict bypass transition for boundary layers subjected to a wide range of freestream turbulence levels and streamwise pressure gradients. In the current paper experimental results are presented which support the premise that the formation of turbulent spots is associated with transient separation. Near wall hot wire signals in laminar and transitional boundary layers are analysed statistically to produce probability distributions for signal level and trough frequency. In the laminar period the signal level is normally distributed, but during the inter-turbulent periods in the transitional boundary layer the distribution is truncated at the tower end, i.e. the lowest velocity periods in the signal disappear, suggesting that these are replaced during transition by the turbulent periods. The number of these events (troughs) also correlates with the number of turbulent spots during early transition. A linear perturbation theory is also used in the paper to compute the streamlines through a turbulent spot and its associated calmed region. The results indicate that a hairpin vortex dominates the flow and entrains a low momentum fluid stream from upstream with a high momentum stream from downstream and then ejects the combined stream into the turbulent spot. The hairpin can only exist if a local separation occurs beneath its nose and the current results suggest that this separation is induced when the instantaneous velocity in the near wall signal drops below 50% of the mean.

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