Showing papers by "Mohamed Gad-el-Hak published in 2003"

Debate Concerning the Mean-Velocity Profile of a Turbulent Boundary Layer

Abstract: 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£ 10 2 ‐2:732£ 10 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 § §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. I. The Opening Arguments T HE Reynolds numbers encountered in many practical situations are typically several orders of magnitude higher than those studied computationally or even experimentally. High-Reynoldsnumber research facilities are expensive to build and operate, and the few existing are heavily scheduled with mostly developmental work. For traditional wind tunnels, additional complications are introduced at high speeds due to compressibility effects and probe-resolution limitations near walls. Likewise, full computational simulation of high-Reynolds-number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will, therefore, continue to play a vital role in the computation of high Reynolds number practical flows using the Reynolds averaged Navier‐Stokes equations. Because the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed toward the low Reynolds numbers, the key question in modeling high-Reynolds-number flows is what the Reynolds number effects are on the mean and statistical turbulence quantities. One of the fundamental tenets of boundary-layer research is the idea that, for a given geometry, any statistical turbulence quantity (mean, rms, Reynolds stress, etc.) measured at different facilities and at different Reynolds numbers will collapse to a single universal profile when nondimensionalized using the proper length and velocity scales. (Different scales are used near the wall and away from it.) This is termed self-similarity or self-preservation and allows convenient extrapolation from the low-Reynolds-number laboratory experiments to the much higher-Reynolds-number situations encountered in typical field applications. The universal log profile

Generalized Logarithmic Law and Its Consequences

Abstract: 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

Drag Reduction Using Compliant Walls

Abstract: 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 chapter, 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 the 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 coatings 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.

Micropumps, microturbines, and flow physics in microdevices

Abstract: Manufacturing processes that can create extremely small machines have been developed in recent years. Microelectromechanical systems (MEMS) refer to devices that have characteristic length of less than 1 mm but more than 1 micron, that combine electrical and mechanical components and that are fabricated using integrated circuit batch-processing techniques. Electrostatic, magnetic, pneumatic and thermal actuators, motors, valves, gears and tweezers of less than 100 mm size have been fabricated. These have been used as sensors for pressure, temperature, mass flow, velocity and sound, as actuators for linear and angular motions, and as simple components for complex systems such as micro-heat-engines and micro-heat-pumps. The technology is progressing at a rate that far exceeds that of our understanding of the unconventional physics involved in the operation as well as the manufacturing of those minute devices. The primary objective of this paper is to critically review the status of our understanding of fluid flow phenomena particular to microdevices. Continuum as well as molecular approaches to the problem will be surveyed. A second objective is to discuss a novel pump/turbine suited for MEMS applications.

Challenges in the understanding of microscale phenomena

Abstract: Manufacturing processes that can create extremely small machines have been developed in recent years. Microelectromechanical systems (MEMS) refer to devices that have characteristic length of less than 1 mm but more than 1 micron, that combine electrical and mechanical components and that are fabricated using integrated circuit batch-processing techniques. Electrostatic, magnetic, pneumatic and thermal actuators, motors, valves, gears and tweezers of less than 100 μm size have been fabricated. These have been used as sensors for pressure, temperature, mass flow, velocity and sound, as actuators for linear and angular motions, and as simple components for complex systems such as micro-heat-engines and micro-heat-pumps. The technology is progressing at a rate that far exceeds that of our understanding of the unconventional physics involved in the operation as well as the manufacturing of those minute devices. The primary objective of this paper is to critically review the status of our understanding of fluid flow phenomena particular to microdevices. The emphasis here will be on liquid flows and surface phenomena.