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Author(s): Mohamed Gad-el-Hak [sup.1] Author Affiliations: (Aff1) 0000 0004 0458 8737, grid.224260.0, Mechanical & Nuclear Engineering, Virginia Commonwealth University, , Richmond, VA, USA [Displayed Quote]'Happiness is not the absence of [...]

Employing data of peak position and peak values of Reynolds shear stress provided by canonical channel flow direct numerical simulations and pipe and channel flow experiments, three recent theories predicting the mean-velocity profile of wall-bounded turbulent flows are compared. Based on that analysis it is verified that the mean-velocity profile of such internal flows is logarithmic only to leading order and that the higher-order terms are proportional to reciprocal powers of the Karman number. This finding clearly indicates that higher-order effects with respect to the Karman number and the wall-normal coordinate must be considered. Furthermore, our results show that even the statistics of the flow region closest to the wall are affected by flow phenomena that scale with outer variables.

A new law of the wall accounting for curvature effects in swirling axial flows is derived. The influence of the curvature on the turbulence mixing lengths in both axial and tangential directions is examined theoretically using the Reynolds stress transport equations. For equilibrium flows with weak curvature, identical mixing lengths are derived for the axial and tangential directions. Additionally, the effect of finite local curvature and shear stress ratio on the near-wall velocities is systematically explored. It is found that the curvature effect in swirling axial flows is suppressed by a factor of 1/(1 + [[sigma].sup.2.sub.w]) compared to that in curved channel flows, where [[sigma].sub.w] is the ratio of the axial to swirl shear stress. For a given curvature radius, the maximum velocity deviation occurs when the axial-to-swirl shear stress ratio is zero. Finally, the performance of the new curvature law is evaluated by implementing it as a wall function in a well-established CFD code. The new wall function provides improved agreement for swirl velocity distributions inside labyrinth cavities in comparison with existing experimental laser Doppler anemometry measurements. [DOI: 10.1115/1.2409360] Keywords: dynamic modeling, curvature, law of the wail swirling axial flow

Turbulent boundary layers approaching separation are a common flow situation in many technical applications. Numerous theoretical, experimental, and numerical attempts have been made to find the proper scaling for the mean-velocity profile of this type of wall-bounded flow. However, none of these approaches seems to be completely satisfactory. New water-tunnel experiments of adverse-pressure-gradient turbulent boundary layers are presented that clearly show the breakdown of the logarithmic law. With these data and experimental results from several independent research groups, the classical scaling for zero-pressure-gradient turbulent boundary layers, the scaling by Castillo and George (Castillo, L., and George, W. K., 'Similarity Analysis for Turbulent Boundary Layer with Pressure Gradient: Outer Flow,' AIAA Journal, Vol. 39, No. 1, 2001, pp. 41-47), and the scaling by Zagarola and Smits (Zagarola, M. V., and Smits, A. J., 'Mean-Flow Scaling of Turbulent Pipe Flow,' Journal of Fluid Mechanics, Vol. 373, 1998, pp. 33-79) are analyzed. Only the latter can be applied successfully for the outer region of the mean-velocity profile close to separation. It is shown that Zagarola and Smits's scaling is consistent with the classical two-layer approach and can be applied to collapse the different data. When the Reynolds shear stress is analyzed, George and Castillo's scaling shows a reasonably good collapse of the data in the outer region.

Proper scaling of a fluid flow permits convenient, dimensionless representation of experimental data, prediction of one flow based on a similar one, and extrapolation of low-Reynolds-number, laboratory-scale experiments to field conditions. This is a particularly powerful technique for turbulent flows where analytical solutions derived from first principles are not possible. We review in the present paper the topical development in scaling the canonical turbulent boundary layer and pipe and channel flows. Additional to utilizing some of the most comprehensive and high-quality databases available to date, the article focuses on contemporary advances in analytical and asymptotic approaches to determine the meanvelocity profile as well as to scale higher-order statistics. The current debate concerning the mean-velocity profile of turbulent wall-bounded flows has ruled out neither a logarithmic nor power law behavior. Furthermore, a Reynolds number dependence of the mean-velocity profile has not been excluded either. Clearly, a more complex functional form is needed to describe the profile. The present results can be utilized to extrapolate the available low-Reynolds-number physical and numerical data to the more practically important high-Reynolds-number field conditions. Knowledge of the proper scaling of the canonical cases can also be useful to non-canonical wall-bounded flows as well as to calibrate turbulence models and flow sensors in the vicinity of walls. Keywords: Turbulent wall-bounded flows; Turbulent boundary layers: Pipe flows: Channel flows; Similarity laws: Self-similarity: Scaling; Asymptotic methods

There has been considerable controversy during the past few years concerning the validity of the classical log law that describes the overlap region of the mean-velocity profile in the canonical turbulent boundary layer. Alternative power laws have been proposed by Barenblatt, Chorin, George, and Castillo, to name just a few. Advocates of either law typically have used selected data sets to foster their claims. The experimental and direct numerical simulation data sets from six independent groups are analyzed. For the range of momentum-thickness Reynolds numbers of 5 X [10.sup.2]-2.732 x [10.sup.4], the best-fit values are determined for the 'constants' appearing in either law. Our strategy involves calculating the fractional difference between the measured/computed mean velocity and that calculated using either of the two respective laws. This fractional difference is bracketed in the region [+ or -] 0.5%, so that an accurate, objective measure of the boundary and extent of either law is determined. It is found that, although the extent of the power-law region in outer variables is nearly constant over a wide range of Reynolds numbers, the log-region extent increases monotonically with Reynolds number. The log law and the power law do not cover the same portion of the velocity profile. A very small zone directly above the buffer layer is not represented by the power law. On the other hand, the inner region of the wake zone is covered by it. In the region where both laws show comparable fractional differences, the mean and variance were calculated. From both measures, it is concluded that the examined data do not indicate any statistically significant preference toward either law.

There has been considerable controversy during the past few years concerning the validity of the universal logarithmic law that describes the mean velocity profile in the overlap region of a turbulent wall-bounded flow. Alternative Reynolds-number-dependent power laws have been advanced. We propose herein an extension of the classical two-layer approach to higher-order terms involving the Karman number and the dimensionless wall-normal coordinate. The inner and outer regions of the boundary layer are described using Poincare expansions, and asymptotic matching is applied in the overlap zone. Because of the specific sequence of gauge functions chosen, the resulting profile depends explicitly on powers of the reciprocal of the Karman number. The generalized law does not exhibit a pure logarithmic region for large but finite Reynolds numbers. On the other hand, the limiting function of all individual Reynolds-number-dependent profiles described by the generalized law shows a logarithmic behavior. As compared to either the simple log or power law, the proposed generalized law provides a superior fit to existing high-fidelity data.

Compliant coating research is one of those areas which experienced its fair share of triumphs and debacles. For over forty years, the subject has fascinated, frustrated and occasionally gratified scientists and engineers searching for methods to delay laminar-to-turbulence transition, to reduce skin-friction drag in turbulent wall-bounded flows, to quell vibrations, and to suppress flow-induced noise. In its simplest form, the technique is passive, relatively easy to apply to an existing vehicle or device, and perhaps not too expensive. Through the years, however, claims for substantial drag and noise reductions were made, only to be later refuted when the results were more critically examined. There are several important issues with regard to the reliability of available analytical, numerical and experimental results. In this article, some of these issues, particularly as they relate to the search for drag-reducing compliant coatings, will be addressed with the objective of elucidating the potential pitfalls to newcomers to the field. Problem formulation with proper boundary conditions, impossibility of obtaining first-principles analytical solutions when the wall-bounded flow is turbulent, and limitations of existing numerical simulations will be elaborated. The effects of background turbulence in a wind or water tunnel, accurate drag measurements, compliant wall motion, and the geometry and properties of the coating used will be among the outstanding experimental issues discussed. Attempts will be made to explain some of the seemingly contradictory results available in the open literature.

A study was conducted on a robust genetic algorithm for constrained functional optimization. The findings indicate that the performance of the piecewise-linear-representation method deteriorates as the number of degrees of freedom increases, provided the population size of the chromosome pool is constant. Moreover, the Fourier series representation and the CRA were more efficient methods for functional optimization.

A numerical study of flow in a novel viscous-based pumping device appropriate for microscale applications is described. The device, essentially consisting of a rotating cylinder eccentrically placed in a channel, is shown to be capable of generating a net flow against an externally imposed pressure gradient. Navier-Stokes simulations at low Reynolds numbers are carried out using a finite-volume approach to study the influence of various geometric parameters. Slip effects for gas flows are also briefly investigated. The numerical results indicate that the generated flow rate is a maximum when the cylinder is in contact with a channel wall and that an optimum plate spacing exists. These observations are in excellent agreement, both qualitatively and quantitatively, with a previous experimental study. Furthermore, it is shown that effective pumping is obtained even for considerably higher Reynolds numbers, thereby extending the performance envelope of the proposed device to non-microscale applications as well. Finally, slip-flow effects appear to be significant only for Knudsen numbers greater than 0.1, which is important from the point of view of microscale applications.

A unique method for pumping fluids in micro-electro-mechanical systems at very low Reynolds numbers is shown. It is based on the rotation of a cylinder which is asymmetrically located in a narrow duct where the differential viscous resistance between the small and large gaps induces a net flow along the channel. Experiments employing glycerin and various cm-scale prisms of different shapes, indicate that a two-dimensional, rotating cylinder eccentrically located within a channel can drive a viscous fluid.

Assessment of the present stature of boundary-layer research reveals the need for high-resolution, precise estimates of average and statistical turbulence movements at high Reynolds numbers in flat-plate turbulent boundary layers. This is a vital initiative to provide for efficient resolution of Reynolds-averaged Navier-Stokes equations in computing practical flows.