Turbulent Boundary Layer Wall Research Articles

A numerical study of drag reduction by mini-belts in a smooth wall turbulent boundary layer

A numerical study of drag reduction by mini-belts in a smooth wall turbulent boundary layer is carried using a second-moment closure turbulence model. The main objective of this exploratory work is to investigate the possibility of using mini-belts, driven by frictional drag only, to reduce the drag of a smooth wall. The results clearly show that such technique can be an effective and cheap means for achieving drag reduction. Furthermore, it is observed that, in contrast to riblets, the use of mini-belts does not suffer from geometrical or size constraints in the context of drag reduction. Also mini-belts will always reduce the skin friction regardless of the flow regime (laminar, transitional and turbulent). These advantages may quite well balance the major difficulty related to their mounting in practical situations

Power laws for rough wall turbulent boundary layers

An assessment of the ability of power laws to describe the mean velocity profile in the overlap region of a zero pressure gradient turbulent boundary layer is reported. The experiments were performed in a wind tunnel on smooth and four different types of rough surfaces at moderate Reynolds numbers. A novel modification to the power law velocity profile is proposed to account for the effect of surface roughness in the overlap region. This modification is analogous to the use of a roughness function to produce a downward shift in the logarithmic velocity profile. The roughness parameters in the proposed equation more accurately follow the effect of roughness on skin friction than does the roughness shift ΔU+. The present study shows that power laws can be used to effectively describe the mean velocity profile over a wider range than a log law for both smooth and rough surfaces.

Unit-cell finite element analysis of the response of complex structures to flow excitation

Analytic estimation of the vibration response of rib-reinforced structures excited by turbulent boundary layer (TBL) wall pressure fluctuations is a subject of ongoing interest for numerous applications in airborne and underwater acoustics. Previous investigators have developed a variety of closed form and approximate analytic methods for estimating the response of structures of interest. Fluid-loading and rib-reinforcement effects make problems involving the response of sea-going vessels particularly challenging. Recent advances in finite element based methods and the enhanced capabilities of modern computer hardware now permit the application of the FEA method to such flow-induced vibration problems. This paper describes the application of the unit-cell capability in BBN’s SARA-2D finite element code to evaluate the response of fluid-loaded, rib-reinforced cylinders to TBL excitation. An overview of the unit-cell modeling method is presented, and example results are provided to illustrate the effects of variations in rib and shell dimensions.

Vibrations of infinite plates and the mean value vibrations of finite plates excited by turbulent boundary layer flows

The vibration response of a turbulent boundary layer (TBL) excited flat plate is analyzed using a finite-element model and infinite plate theory. For the finite-element models, discretization sufficient to resolve the convective fluctuations in the flow excitation field is used for the study. Clamped boundary conditions are assumed for the finite-element models and analyses are conducted at a variety of flow speeds and structural loss factors. Two equivalent TBL wall pressure excitation models are applied to the plates: (1) a modified Corcos cross-spectrum model for the finite-element models, and (2) a wave-vector-frequency spectrum model (the Fourier transform of the modified Corcos cross spectra) for the infinite plate theory. The TBL wall pressure autospectrum is approximated using the model derived by Smolyakov and Tkachenko. The infinite plate predicts the mean value response of the finite plate very well for all speeds and loss factors considered, showing consistency with Skudrzyks mean value theory and its usefulness for generating sound and vibration estimates.

Skin Friction Correlation in Open Channel Boundary Layers

Skin Friction Correlation in Open Channel Boundary Layers

Turbulence structure in boundary layers over different types of surface roughness

The classical treatment of rough wall turbulent boundary layers consists in determining the effect the roughness has on the mean velocity profile. This effect is usually described in terms of the roughness function ΔU+. The general implication is that different roughness geometries with the same ΔU+ will have similar turbulence characteristics, at least at a sufficient distance from the roughness elements. Measurements over two different surface geometries (a mesh roughness and spanwise circular rods regularly spaced in the streamwise direction) with nominally the same ΔU+ indicate significant differences in the Reynolds stresses, especially those involving the wall-normal velocity fluctuation, over the outer region. The differences are such that the Reynolds stress anisotropy is smaller over the mesh roughness than the rod roughness. The Reynolds stress anisotropy is largest for a smooth wall. The small-scale anisotropy and intermittency exhibit much smaller differences when the Taylor microscale Reynolds number and the Kolmogorov-normalized mean shear are nominally the same. There is nonetheless evidence that the small-scale structure over the three-dimensional mesh roughness conforms more closely with isotropy than that over the rod-roughened and smooth walls.

The Similarity of the Velocity Defect Profile for the Outer Layer in Smooth Wall and Rough Wall Turbulent Boundary Layers.

The Similarity of the velocity defect profile has been investigated for the turbulent boundary layer over smooth wall, d-type rough wall and k-type rough wall. The velocity defect profiles normalized with the friction velocity uτ and boundary layer thickness δ are not similar, depending systematically on the wake parameter II. Therefore, a new velocity scale uo is defined based on the similarity of the wake velocity component for the outer region. The velocity defect profiles normalized with uo and δ are similar much better with each flow fields, except for the results of a low Reynods number Rθ=960 for the smooth wall flow. These results show that the velocity scale uo is a proper scale in the outer region for three flow fileds. Then the wake function for each flow fields is succesfully represented by a single curve. In addition, investigating the contorted shape of turbulent bulge, the interval of up and down in the streamwise direction is narrower as II increases, but the width in the transverse direction is almost constant.

Investigation of the upstream end effect on the flow characteristics of yawed circular cylinders

The flow over a yawed circular cylinders is a research area of current interest in aerodynamics due to the inherent similarities with that of the swept wing configuration. These models however, must be carefully mounted in order to suppress a phenomenon known as attachment line contamination. This contamination occurs when models span the entire test section width, exposing the flow to the highly disruptive test section wall turbulent boundary layers. One way of suppressing this phenomenon is to mount the upstream end of the model off the test section wall, whereby eliminating the interaction between the boundary layer and the model. Mounting the model with the upstream end free of the wall however, introduces end effects which are transported inboard from the downwash over the free end.

Rough Wall Turbulent Boundary Layers in Shallow Open Channel Flow

An experimental study was undertaken to investigate the effects of roughness on the structure of turbulent boundary layers in open channels. The study was carried out using a laser Doppler anemometer in shallow flows for three different types of rough surface, as well as a hydraulically smooth surface. The flow Reynolds number based on the boundary layer momentum thickness ranged from 1400 to 4000. The boundary layer thickness was comparable with the depth of flow and the turbulence intensity in the channel flow varied from 2 to 4 percent. The defect profile was correlated using an approach which allowed both the skin friction and wake strength to vary. The wake parameter was observed to vary significantly with the type of surface roughness in contradiction to the “wall similarity” hypothesis. Wall roughness also led to higher turbulence levels in the outer region of the boundary layer. The profound effect of surface roughness on the outer region as well as the effect of channel turbulence on the main flow indicates a strong interaction, which must be accounted for in turbulence models. [S0098-2202(00)00803-8]

Visualization and Detection of Wall Shear Stress using Micro Shear Stress Sensor and Discrete Wavelet Analysis

Shear stress stripe structure on the wall in turbulent boundary layer has been clearly visualized by a combination of a shear stress sensor using MEMS (Micro-Electro-Mechanical-Systems) and discrete wavelets transform. The MEMS shear stress micro chip is designed and fabricated by surface micro-machining technology, contributing to obtaining the time-space two dimensional shear stress data. One array of 25 micro shear stress sensors in the chip that covers a length of 7.5mm is used to measure the instantaneous spanwise distribution of the surface shear stress. The discrete wavelets transform is a software technique to decompose the frequency level with the time and space information of the wave form. In details, the structure in lower Reynolds number is shown clearly on lower frequency wavelets level, the structure in high Reynolds number is done clearly on higher frequency wavelets level. To visualize and detect the high shear stress area more clearly, the frequency levels are recomposed using the multiresolution filtering effect of wavelets transform. The experiments for the shear stress distribution were carried out on Re=8700 and 17400.

Effect of different surface roughnesses on a turbulent boundary layer

The classical treatment of rough wall turbulent boundary layers consists in determining the effect the roughness has on the mean velocity profile. This effect is usually described in terms of the roughness function D U+. The general implication is that different roughness geometries with the same D U+ will have similar turbulence characteristics, at least at a sufficient distance from the roughness elements. Measurements over two different surface geometries (a mesh roughness and spanwise circular rods regularly spaced in the streamwise direction) with nominally the same D U+ indicate significant differences in the Reynolds stresses, especially those involving the wall-normal velocity fluctuation, over the outer region. The differences are such that the Reynolds stress anisotropy is smaller over the mesh roughness than the rod roughness. The Reynolds stress anisotropy is largest for a smooth wall. The small-scale anisotropy and interniittency exhibit much smaller differences when the Taylor microscale Reynolds number and the Kolmogorov-normalized mean shear are nominally the same. There is nonetheless evidence that the small-scale structure over the three-dimensional mesh roughness conforms more closely with isotropy than that over the rod-roughened and smooth walls.

Approach to isotropy in a smooth wall turbulent boundary layer

The approach to local isotropy in a smooth wall turbulent boundary layer is examined using measurements of velocity spectra and moments, up to order 4, of velocity increments. The ratio of the measured spectrum of the wall normal velocity fluctuation v to that calculated using isotropy from the measured spectrum of the longitudinal velocity fluctuation u, depends mainly on the Kolmogorov-normalized local mean strain rate and the Taylor microscale Reynolds number. These parameters also affect in a systematic way the departure from isotropy of the u− v spectral correlation coefficient and of the v increment moments.

Three-Dimensional Large Eddy Simulation of Breaking Waves

A three-dimensional large eddy simulation (LES) of wave breaking was carried out. A numerical method for LES is proposed in this paper. The following characteristics of vorticity and velocity field after wave breaking are discussed on the basis of results of the LES: (1) generation and evolution of the widthwise (shore direction) velocity component; (2) transition from a two-dimensional velocity field to a three-dimensional one after wave breaking; (3) evolution process of large-scale eddies comprised by horizontal, vertical and helical eddies; and (4) a coherent eddy structure involving a turbulent bottom and wall boundary layer.

Effects of Low Reynolds Number on the Outer Layer Structure in a Smooth Wall Turbulent Boundary Layer. Re-examination of Statistical Quantities.

Re-examination of the low-Reynolds-number effect on the outer layer structure has been made in a zero pressure gradient, smooth wall turbulent boundary layer where the two-dimensionality of a flow field was corroborated using the momentum integral equation. The measurements associated with the higher-order moments and the conditional averages were made over a momentum thickness Reynolds number range 840&InE;Rθ&InE;6120. The magnitude of the triple products normalized with friction velocity and relative typical eddy scale Cx/δ are affected with a achievement level of the two-dimensionality of a flow field. For Rθ<2130, the absolute values of the triple products and the turbulent diffusion terms normalized with outer variables increase with Rθ. Intermittency factor is approximately independent of Rθ when Rθ is greater than 4410. Therefore, average turbulent and non-turbulent zone lengths are constant independent of Rθ.

Re-examination of the Reynolds-Number-Effect on the Mean Flow Quantities in a Smooth Wall Turbulent Boundary Layer.

Measurement of the local skin friction coefficient and re-examination of the Reynolds-number-effect on the mean flow quantities were made in a zero-pressure gradient, smooth wall, turbulent boundary layer. In order to do this fairly, the two-dimensionality of the flow field was carefully adjusted. And, the wall shear stress τω was determined by direct measurement using a floating element device. The Reynolds number based on the momentum thickness Rθ=U1θ / ν ranges from 840 to 6 220. The present experimental results of cf propose a new empirical formula which well represents the present experimental data and confirms that the Karman constant χ=0.41, which implies a slope of the logarithmic linear layer, is independent of Rθ down to Rθ=860, whereas the additive constant varies with Rθ. The magnitude of the wake parameter takes an asymptotic value of 0.62 if the Reynolds number is sufficiently high. The effect of Rθ on all the turbulent intensities is evident even within the viscous sublayer. The constant stress layer does exist in the Reynolds shear stress profiles despite that the constant value varies with Rθ.

Compressibility and pressure-gradient correction assessment for turbulent hypersonic flows

NOWLEDGE of the flow development in hypersonic windtunnel nozzles is of primary importance to the design of such nozzles as well as to the characterization of the flowfield in the test section. In the perfect-gas regime, reliable numerical methods have been developed for both of the design work and the flow analysis, but there still exist some deficiencies in predicting the turbulent hypersonic nozzle wall boundary layers. This problem is believed to be a consequence of the deficiencies in the compressible eddy-viscosity turbulence models currently adopted in engineering applications. Specifically, to improve the accuracy of such calculations, the importance of compressibility and pressure-gradient effects should be investigated, since the hypersonic wind-tunnel nozzle flow is characterized by the existence of an increasing main flow Mach number and a varying pressure gradient in the streamwise direction. A numerical study of that nature is presented in this work. Several explicit compressibility and pressure-gradient corrections are introduced to two widely used eddy-viscosity turbulence models for the calculations of hypersonic wind-tunnel nozzle flows. The results are compared with those obtained with the standard models to evaluate the effects of the corrections, and are compared with measurements to verify the accuracy of the calculations and to see the improvements gained. Numerical Modeling The study was carried out by solving three-dimensional Reynolds-averaged Navier-Stokes equations. They are the transport equations to describe the conservation of mass, momentum, and energy with the assumption of a perfect gas. When two-equation turbulence models are employed, the system has two more equations for the turbulent kinetic energy k and its dissipation rate €. In the present work the turbulence is closed by four alternative eddy-viscosity models, among which the Baldwin-Lomax algebraic model1 and the k-€ model of Chien 2 are chosen as the baseline models for the purpose of evaluating the compressibility and pressure-gradient corrections. The other two are their modified versions, respectively, with the modifications outlined below.

An integrated pressure—flow sensor for correlation measurements in turbulent gas flows

A new integrated pressure—flow sensor has been specially designed for measurements in turbulent gas flows. The pressure sensor is based on polysilicon diaphragm technology and the flow sensor on the gas cooling of a polyimide-insulated heated mass. With a pressure-sensor diaphragm area of 100 μm × 100 μm, a flow-sensor hot-chip area of 300 μm × 60 μm and an edge-to-edge distance of 100 μm between the different sensor areas, the smallest eddies in technically interesting turbulent flows can be resolved and measured. The pressure-sensor design shows a flat frequency response curve within ±2 dB between 10 Hz and 10 kHz with an acoustic sensitivity of 0.9 μV Pa −1 for a supply voltage of 10 V. The flow sensor has a thermal response with a time constant of 7 ms and a response time of 25 μs when the sensor is operated at constant temperature using feedback electronics. The measured steady-state flow-sensor power dissipation in a turbulent wall boundary layer at an overtemperature of 100 °C was P = 34 + 0.4 τ 0 0.47 mW where τ 0 is the time-average flow-dependent wall shear stress. The integrated sensor has been used for simultaneous measurement of fluctuating pressure and wall shear stress in a turbulent boundary layer yielding pressure—wall shear stress correlation coefficients never previously presented.

Anisotropy of the Reynolds stresses in a turbulent boundary layer on a rough wall

The measured anisotropy invariants of the Reynolds stress tensor in a self-preserving rough wall turbulent boundary layer indicate that the anisotropy is significantly smaller than in a smooth wall layer.

The use of orthogonal X-wire arrays for structure investigation in a turbulent boundary layer

This note focuses on details of the experimental technique used to obtain simultaneous velocity measurements from two orthogonal arrays of X-wires and its potential for extracting information on various aspects of the organized motion. The experiments were carried out in a rough wall turbulent boundary layer in an attempt to obtain some insight into the 3-D nature of the large scale motion. Although information is only obtained in two orthogonal planes, it is shown that the technique can provide useful information about the 3-D nature of the large structures. Relative to large scale structure detections in the (x, y) plane, the most probable pattern in the (x, z) plane consists of counter-rotating vortical motions of approximately equal strength. Co-rotating patterns are strongly asymmetrical.

Scaling of the bursting period in turbulent rough wall boundary layers

Measurements in laboratory rough wall turbulent boundary layers have been made over a sufficient Reynolds number range for independence on the Reynolds number to be established adequately. The data have been analyzed with respect to the average period between ejections and sweeps, using methods previously applied to smooth wall flows. The results clearly show that the period is independent of Reynolds number when it is scaled on outer variables.