Brian Brzek

Influence of external conditions on transitionally rough favorable pressure gradient turbulent boundary layers

Laser Doppler anemometry measurements are carried out in order to investigate the influences of the external conditions on a transitionally rough favorable pressure gradient turbulent boundary layer. The acquired data is normalized using the scalings obtained by the means of equilibrium similarity of the outer flow. The point at hand is to not only understand the interaction between the rough surface and the outer flow but also to include the external pressure gradient as the flow evolves in the streamwise direction. It is found that the velocity profiles show the effects of the upstream conditions imposed on the flow when normalized with the free-stream velocity. However, the profiles do collapse when normalized with U ∞ δ*/δ, demonstrating that this scaling absorbs the roughness effects and upstream conditions. An augmentation in the Reynolds stresses occurs with an increase in the roughness parameter and a decrease due to the external favorable pressure gradient. However, close to the wall, there is an increase due to the favorable pressure gradient while on the outer part of the boundary layer there is a decrease in magnitude due to this imposed effect. The near-wall peak of the ⟨ u 2 ⟩ component is dampened by the surface roughness condition due to the destruction of the viscous sublayer. In addition, the shape of the profile in the inner region tends to flatten due to the surface roughness. The upstream wind-tunnel speed also plays an important role thus creating a Reynolds number dependence on the outer flow of the Reynolds stress components. Furthermore, through 11 consecutive downstream locations, the skin friction coefficient is obtained for smooth and rough favorable pressure gradient data. The skin friction shows dependencies on the Reynolds number, the roughness parameter, and the favorable pressure gradient condition in the transitionally rough regime; while for the fully rough regime, it becomes form drag and the dependencies are on the favorable pressure gradient and the Reynolds shear stress. The external condition effects are isolated with a fixed parameter comparison. Favorable pressure gradient effects slow down the growth of the boundary layer while the surface roughness promotes its growth.

Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers

A new set of experiments have been performed in order to study the effects of surface roughness and Reynolds number on a zero pressure gradient turbulent boundary layer. In order to properly capture the x dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed which enabled the use of the full boundary layer equations to calculate the skin friction. This quantity was obtained within 3% and 5% accuracy for smooth and rough surfaces, respectively. For the sand grain type roughnesses used, only the Zagarola and Smits scaling, U∞δ*∕δ, was able to remove the effects of roughness and Reynolds number from the velocity profiles in outer variables. However, each scaling used for the velocity deficit profiles resulted in self-similar solutions for fixed experimental conditions. When examining the Reynolds stresses in the inner region [i.e., 0<(y+ϵ)+<0.1δ+], the ⟨u2⟩ component showed the largest influence of roughness, where the high peak near the wall was decrea...

Theoretical evaluation of the Reynolds shear stress and flow parameters in transitionally rough turbulent boundary Layers

The theory by W.K. George and L. Castillo (Zero-pressure gradient turbulent boundary layers, Appl. Mech. Rev. 50 (1997), pp. 689–729) is extended for rough surfaces and numerically implemented on zero pressure gradient turbulent boundary layers. The method is based on the similarity transformations of the Navier–Stokes equations. From these equations, a composite profile for the Reynolds shear stress-⟨ uv⟩ is obtained over the entire boundary layer. The solution is in good agreement with the experiments in the inner and outer regions, for hydraulically smooth (k+ < 5) and transitionally rough surfaces up to roughness parameter of k+ ≈ 55. Beyond this limit, the accuracy of the solutions decreases with k+, especially in the inner region of the mean velocity. However, the accuracy always increases with the Reynolds number, Re_θ. In addition, the eddy viscosity ⟨ ν_T⟩/ν and flow parameters, including the x-dependence, have also been computed and tested with experimental data. Furthermore, the friction power law for smooth/rough surfaces has been used for all calculations and comparisons with direct methods and velocity-based methods are shown to be in good agreement with the theory.

Effects of free-stream turbulence on rough surface turbulent boundary layers

Several effects of nearly isotropic free-stream turbulence in transitionally rough turbulent boundary layers are studied using data obtained from laser Doppler anemometry measurements. The free-stream turbulence is generated with the use of an active grid, resulting in free-stream turbulence levels of up to 6.2 %. The rough surface is characterized by a roughness parameter k + ≈ 53, and measurements are performed at Reynolds numbers of up to Re θ = 11 300. It is confirmed that the free-stream turbulence significantly alters the mean velocity deficit profiles in the outer region of the boundary layer. Consequently, the previously observed ability of the Zagarola & Smits (J. Fluid Mech., vol. 373, 1998, p. 33) velocity scale U ∞ δ*/δ to collapse results from both smooth and rough surface boundary layers, no longer applies in this boundary layer subjected to high free-stream turbulence. In inner variables, the wake region is significantly reduced with increasing free-stream turbulence, leading to decreased mean velocity gradient and production of Reynolds stress components. The effects of free-stream turbulence are clearly identifiable and significant augmentation of the streamwise Reynolds stress profiles throughout the entire boundary layer are observed, all the way down to the inner region. In contrast, the Reynolds wall-normal and shear stress profiles increase due to free-stream turbulence only in the outer part of the boundary layer due to the blocking effect of the wall. As a consequence, there is a significant portion of the boundary layer in which the addition of nearly isotropic turbulence in the free-stream, results in significant increases in anisotropy of the turbulence. To quantify which turbulence length scales contribute to this trend, second-order structure functions are examined at various distances from the wall. Results show that the anisotropy created by adding nearly isotropic turbulence in the free-stream resides mostly in the larger scales of the flow. Furthermore, by analysing the streamwise Reynolds stress equation, it can be predicted that it is the wall-normal gradient of (u 2 v) term that is responsible for the increase in (u 2 ) profiles throughout the boundary layer (i.e. an efficient turbulent transport of turbulence away from the wall). Furthermore, a noticeable difference between the triple correlations for smooth and rough surfaces exists in the inner region, but no significant differences are seen due to free-stream turbulence. In addition, the boundary layer parameters δ*/δ 95 , H and c f are also evaluated from the experimental data. The flow parameters δ*/δ 95 and H are found to increase due to roughness, but decrease due to free-stream turbulence, which has significance for flow control, particularly in delaying separation. Increases in c f due to high free-stream turbulence are also observed, associated with increased momentum flux towards the wall.

Inner and Outer Scalings in Rough Surface Turbulent Boundary Layers

The incompressible, zero-pressure-gradient turbulent boundary layer is investigated in light of the effect of the Reynolds number and surface roughness. The experimental data from various researchers has been collected and analyzed in order to study the effect of the roughness on the inner and outer flow. The scalings of George and Castillo (GC) (1997) for the mean velocity profiles and Reynolds stresses are used for the analysis and compared with the results of the classical scalings. Moreover, the true asymptotic profile (self-preserving) solution for the velocity deficit profiles is found when the profiles are normalized by the Zagarola/Smits (1998) scaling, U∞δ /δ. This scaling successfully removes the effects of the Reynolds number, the upstream conditions, and the roughness from the outer flow. Similarly, the classical scaling, uτ , tends to remove the effects from the outer flow but not in the inner region. However, it will be shown that as the roughness parameter, k, increases beyond k ≈ 28 or less, the Reynolds stresses and velocity profiles are influenced in the outer flow by roughness. This limit corresponds to the lower limit of the outer region of a boundary layer, thus the outer flow is affected by roughness beyond this limit. However, for the inner layer, the Reynolds stresses are sensitive to values of the roughness parameter, k ≈ 0.4 while the velocity profiles are affected for values of about k ≈ 17.

LDA Measurements in Rough Surface ZPG Turbulent Boundary layers

A new set of experiments have been performed in order to study the effects of the upstream conditions and the surface roughness on a zero pressure gradient turbulent boundary layer. In order to properly capture the x-dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed. These 2-D Laser Doppler Anemometry (LDA) measurements enable us to use the full boundary layer equations in order to calculate the skin friction and determine the boundary layer development which is not possible in the majority of experiments on rough surfaces. It will be shown that for fixed experimental conditions (i.e., fixed upstream wind tunnel speed, trip wire, etc), the velocity deficit profiles collapse for each of the scalings investigated but only the Zagarola/Smits scaling (1998) could collapse all the different experimental conditions into a single curve. In addition, the Reynolds stresses were increasingly affected by the surface roughness as the roughness parameter, k+ , increased. Moreover, it was found that the shape of the Reynolds stress profiles was very different throughout the entire boundary layer, particularly the component. This is likely the result of the flow becoming more isotropic for increased k+ , and will be seen in the anisotropy coefficients. Moreover, increased production of and due to roughness is also seen throughout the entire boundary layer although its overall role in the changing shape of the profiles still needs to be determined. The effect of roughness on the boundary layer parameters is also evident and their x-dependence is also shown.Copyright

Isotropic Free-stream Turbulence Promotes Anisotropy in a Turbulent Boundary Layer

The study of how external conditions affect turbulent boundary layers is important since such effects are often present in common engineering applications. Earlier investigations on surface roughness have shown its effect on the mean velocity and Reynolds stress profiles. Similarly, the effects of free-stream turbulence have been well documented [1, 2, 3]. However, the results available until now are limited to low Reynolds numbers. Hence, the aim of this investigation is to study the effects of high free-stream turbulence on rough surface turbulent boundary layers, at relatively high Reynolds numbers. This investigation focused on the penetration mechanisms of free-stream turbulence into the boundary layer, identifying the length scales that dominate these mechanisms and studying the effects on the resulting turbulence anisotropy [4]. These effects will also be studied in turbulent boundary layers subject to favorable pressure gradients.

Skin Friction and the Inner Flow in Pressure Gradient Turbulent Boundary Layers

This investigation will look at multiple methods to determine the wall shear stress for several pressure gradient turbulent boundary layer flows, particularly favorable pressure gradient and zero pressure gradient. These methods include using the slope at the wall, the integrated bounary layer equation, momentum integral equation and the Clauser method. In order to perform this study, 2D Laser Doppler Anemometry, (LDA), measurements of the velocity field near the wall for various streamwise positions have been carried out at the Chalmers L2 wind-tunnel. With the resulting wall shear stress calculations, the effects of pressure gradient and upstream conditions will be investigated on the inner region of the velocity profiles and Reynolds stresses. As will be seen, the integrated boundary layer equation is the most accurate technique to determine the wall shear stress when direct measurements are not available. In addition, the velocity profiles show a mild effect of the pressure gradient. The Reynolds stresses show a large effect of the pressure gradient in inner variables, but not below, y and components changes significantly due to the external pressure gradient, damping them as much as 40%, though the streamwise component exhibits an insignificant amount of change. Introduction The effects of Reynolds number and pressure gradient on the skin friction coefficient, Cf , and the velocity field have long been debated as well as the accuracy ∗MS, Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical and Nuclear Engineering, Troy, NY 12180 †PhD, Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical and Nuclear Engineering, Troy, NY 12180 ‡Post-doctoral fellow, The Johns Hopkins University, Department of Mechanical Engineering, Baltimore, MD §Associate Professor, Chalmers Institute of Technology, Gothenburg, Sweden ¶Associate Professor, Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical and Nuclear Engineering, Troy, NY 12180, also Research Professor at University of Puerto Rico-, Mayaguez, Mayaguez, P.R., Department of Mechanical Eng. Copyright c

Effect of Isotropic Free-stream Turbulence in Favorable Pressure Gradient Turbulent Boundary Layers over a Rough Surface

Laser Doppler and Hotwire anemometry measurements were performed to study the effect of various conditions, namely free-stream turbulence (FST), favorable pressure gradient, and surface roughness, on turbulent boundary layers. Measurements were carried out at Re θ ≤ 4,300 and free-stream turbulence levels of up to 7%, generated using an active grid. Results show that with the addition of FST, classical scaling laws are not able to collapse the profiles of mean velocity. Moreover, boundary layer parameters, including skin friction coefficient, confirm a complex interaction between the external conditions and the inner/outer flow. The discrepancy in the behavior of the stream-wise and wall-normal variances due to the presence of free-stream turbulence suggests that the addition of nearly isotropic free-stream turbulence promotes anisotropy in the body of the boundary layer. Second-order structure functions are examined to identify and quantify which turbulence length-scales contribute mostly to creating this discrepancy. The analysis demonstrates that the effect of FST resides in a wide range of length scales, and is not limited to the largest scales of the flow as in the case of ZPG flows.

Effect of Isotropic Free-stream Turbulence on the Anisotropy of Favorable Pressure Gradient Turbulent Boundary Layers

up to 76. The free-stream turbulence was generated by means of an active grid. Results show that classical scaling laws are not able to collapse the mean velocity profiles when additional levels of free-stream turbulence are present. The differences in the influence of free-stream turbulence on the streamwise and wall-normal components of the Reynolds normal stresses show that there is a portion of the boundary layer where the presence of free-stream turbulence results in a significant increase in anisotropy. This was also observed for zero pressure gradient (ZPG) boundary layers in a prior paper. Second order structure functions are examined, at various distances from the wall, to identify and quantify the length scales that dominate this process. It is shown that for favorable pressure gradient flows the effect of free-stream turbulence resides in a much wider range of turbulent length scales as compared to the ZPG case.