Modified Spalart-Allmaras one-equation turbulence model for rough wall boundary layers

1996 ◽  
Vol 12 (4) ◽  
pp. 809-812 ◽  
Author(s):  
Jaesoo Lee ◽  
Gerald C. Paynter
Keyword(s):  
Boundary Layers ◽  
Turbulence Model ◽  
Rough Wall ◽  
Wall Boundary

Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer: Part I—Model Formulations

2008 ◽  
Author(s):  
M. Stripf ◽  
A. Schulz ◽  
H.-J. Bauer ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulence Intensity ◽  
Discrete Element ◽  
Rough Wall ◽  
Test Cases ◽  
Wall Boundary ◽  
Turbine Vane

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent state. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from Durbin et al., which builds upon a two-layer k-ε-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer k-ε-turbulence model by the present authors. The discrete element model will be formulated in a new way suitable for randomly rough topographies. Part I of the paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both, the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high-pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors as well as new experimental data from a low-pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer: Part II—Model Validation and Benchmarking

2008 ◽  
Author(s):  
M. Stripf ◽  
A. Schulz ◽  
H.-J. Bauer ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulence Intensity ◽  
Discrete Element ◽  
Rough Wall ◽  
Test Cases ◽  
Wall Boundary ◽  
Turbine Vane

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent state. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from Durbin et al., which builds upon a two-layer k-ε-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer k-ε-turbulence model by the present authors. The discrete element model will be formulated in a new way suitable for randomly rough topographies. Part I of the paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both, the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high-pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors as well as new experimental data from a low-pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer—Part II: Model Validation and Benchmarking

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Stripf ◽  
A. Schulz ◽  
H.-J. Bauer ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulence Intensity ◽  
Discrete Element ◽  
Rough Wall ◽  
Test Cases ◽  
Wall Boundary ◽  
Turbine Vane

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity, and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent states. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from (Durbin, et al., 2001, “Rough Wall Modification of Two-Layer k-ε ,” ASME J. Fluids Eng., 123, pp. 16–21), which builds on a two-layer k-ε-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer k-ε-turbulence model by the present authors. The discrete-element model will be formulated in a new way suitable for randomly rough topographies. Part I of this paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors, as well as new experimental data from a low pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

Extended Models for Transitional Rough Wall Boundary Layers With Heat Transfer—Part I: Model Formulations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Stripf ◽  
A. Schulz ◽  
H.-J. Bauer ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layers ◽  
Turbulence Model ◽  
Turbulence Intensity ◽  
Discrete Element ◽  
Rough Wall ◽  
Test Cases ◽  
Wall Boundary ◽  
Turbine Vane

Two extended models for the calculation of rough wall transitional boundary layers with heat transfer are presented. Both models comprise a new transition onset correlation, which accounts for the effects of roughness height and density, turbulence intensity, and wall curvature. In the transition region, an intermittency equation suitable for rough wall boundary layers is used to blend between the laminar and fully turbulent states. Finally, two different submodels for the fully turbulent boundary layer complete the two models. In the first model, termed KS-TLK-T in this paper, a sand roughness approach from Durbin et al. (2001, “Rough Wall Modification of Two Layer k-ε ,” ASME J. Fluids Eng., 123, pp. 16–21), which builds upon a two-layer k-ε-turbulence model, is used for this purpose. The second model, the so-called DEM-TLV-T model, makes use of the discrete-element roughness approach, which was recently combined with a two-layer k-ε-turbulence model by the present authors. The discrete-element model will be formulated in a new way, suitable for randomly rough topographies. Part I of the paper will provide detailed model formulations as well as a description of the database used for developing the new transition onset correlation. Part II contains a comprehensive validation of the two models, using a variety of test cases with transitional and fully turbulent boundary layers. The validation focuses on heat transfer calculations on both the suction and the pressure side of modern turbine airfoils. Test cases include extensive experimental investigations on a high-pressure turbine vane with varying surface roughness and turbulence intensity, recently published by the current authors as well as new experimental data from a low-pressure turbine vane. In the majority of cases, the predictions from both models are in good agreement with the experimental data.

Applicability of Taylor’s hypothesis in rough- and smooth-wall boundary layers

2016 ◽  
Vol 812 ◽  
pp. 398-417 ◽  
Author(s):  
D. T. Squire ◽  
N. Hutchins ◽  
C. Morrill-Winter ◽  
M. P. Schultz ◽  
J. C. Klewicki ◽  
...  
Keyword(s):  
Boundary Layers ◽  
Outer Region ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Normal Velocity ◽  
Turbulent Shear Flow ◽  
Smooth Wall ◽  
Wall Boundary ◽  
Taylor’S Hypothesis ◽  
Velocity Spectra

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number ($\unicode[STIX]{x1D6FF}^{+}\approx 12\,000$). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor’s frozen turbulence hypothesis (Proc. R. Soc. Lond. A, vol. 164, 1938, pp. 476–490). The same applies for the streamwise velocity spectra on rough walls. For the wall-normal velocity spectra, however, clear differences are observed between the true spatial and temporally convected spectra. For the rough-wall spectra, a correction is derived to enable accurate prediction of wall-normal velocity length scales from measurements of their time scales, and the implications of this correction are considered. Potential violations to Taylor’s hypothesis in flows above perturbed walls may help to explain conflicting conclusions in the literature regarding the effect of near-wall modifications on outer-region flow. In this regard, all true spatial and corrected spectra presented here indicate structural similarity in the outer region of smooth- and rough-wall flows, providing evidence for Townsend’s wall-similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956).

scholarly journals Assessment of inner–outer interactions in the urban boundary layer using a predictive model

2019 ◽  
Vol 875 ◽  
pp. 44-70 ◽  
Author(s):  
Karin Blackman ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Predictive Model ◽  
Boundary Layers ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rough Wall ◽  
Wall Boundary ◽  
Layer Flow

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

scholarly journals On the decay of dispersive motions in the outer region of rough-wall boundary layers

2019 ◽  
Vol 862 ◽  
Author(s):  
Johan Meyers ◽  
Bharathram Ganapathisubramani ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Layer ◽  
Stokes Equations ◽  
Outer Region ◽  
Rough Wall ◽  
Rough Boundary ◽  
Mean Flow ◽  
Wall Boundary

In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier–Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of $\exp (-kz)$ and $\exp (-Kz)$, with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $\boldsymbol{k}$, and where $K(\boldsymbol{k},Re)$ is a function of $\boldsymbol{k}$ and the Reynolds number $Re$. Moreover, for $k\rightarrow \infty$ or $k_{1}\rightarrow 0$ (with $k_{1}$ the stream-wise wavenumber), $K\rightarrow k$ is found, in which case solutions consist of a linear combination of $\exp (-kz)$ and $z\exp (-kz)$, and are independent of the Reynolds number. These analytical relations are compared in the limit of $k_{1}=0$ to the rough boundary layer experiments by Vanderwel & Ganapathisubramani (J. Fluid Mech., vol. 774, 2015, R2) and are in reasonable agreement for $\ell _{k}/\unicode[STIX]{x1D6FF}\leqslant 0.5$, with $\unicode[STIX]{x1D6FF}$ the boundary-layer thickness and $\ell _{k}=2\unicode[STIX]{x03C0}/k$.

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