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IN THIS ISSUE

### TECHNICAL PAPERS

J. Fluids Eng. 2007;129(10):1245-1254. doi:10.1115/1.2776960.

A general procedure to extend turbulence models to account for wall roughness, in the framework of the equivalent sand grain approach, is proposed. It is based on the prescription of the turbulent quantities at the wall to reproduce the shift of the logarithmic profile and hence provide the right increase in wall friction. This approach was previously applied to Spalart and Allmaras one equation (1992, “A One-Equation Turbulence Model for Aerodynamic. Flows  ,” 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA paper No. 92-0439;1994, ibid, Rech. Aerosp.1, pp. 5–21). Here, the strategy is detailed and applied to Smith’s two-equation $k-L$ model (1995, “Prediction of Hypersonic Shock Wave Turbulent Boundary Layer Interactions With The k-l Two Equaton Turbulence Model  ,” 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. 95-0232). The final model form is given. The so-modified Spalart and Allmaras and Smith models were tested on a large variety of test cases, covering a wide range of roughness and boundary layer Reynolds numbers and compared with other models. These tests confirm the validity of the approach to extend any turbulence model to account for wall roughness. They also point out the deficiency of some models to cope with small roughness levels as well as the drawbacks of present correlations to estimate the equivalent sand grain roughness.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1255-1267. doi:10.1115/1.2776961.

The friction factor data from transitional rough test pipes, from the measurements of Sletfjerding and Gudmundsson (2003, “Friction Factor Directly From Roughness Measurements  ,” J. Energy Resour. Technol.125, pp. 126–130), have been analyzed in terms of directly measurable roughness parameters, $Ra$ the arithmetic mean roughness, $RZ$ the mean peak to valley heights roughness, $Rq$ the root mean square (rms) roughness, and $Rq∕H$ rms textured roughness ($H$, the Hurst exponent is a texture parameter), in addition to $h$ the equivalent sand grain roughness. The proposed friction factor $λ$, in terms of new scaling parameter, viz., the roughness Reynolds number $Reϕ=Re∕ϕ$ (where $ϕ$ is a nondimensional roughness scale), is a universal relation for all kinds of surface roughness. This means that Prandtl’s smooth pipe friction factor relation would suffice provided that the traditional Reynolds number Re is replaced by the roughness Reynolds number $Reϕ$. This universality is very well supported by the extensive rough pipe data of Sletfjerding and Gudmundsson, Shockling’s (2005, “Turbulence Flow in Rough Pipe  ,” MS thesis, Princeton University) machined honed pipe surface roughness data, and Nikuradse’s (1933, Laws of Flow in Rough Pipe, VDI, Forchungsheft No. 361) sand grain roughness data. The predictions for the roughness function $ΔU+$, and the roughness scale $ϕ$ for inflectional roughness compare very well with the data of the above mentioned researchers. When surface roughness is present, there is no universality of scaling of the friction factor $λ$ with respect to the traditional Reynolds number Re, and different expressions are needed for various types of roughnesses, as suggested, for example, with inflectional roughness, monotonic roughness, etc. In traditional variables, the proposed friction factor prediction for inflectional roughness in the pipes, is supported very well by the experimental data of Sletfjerding and Gudmundsson, Shockling, and Nikuradse. In the present work, the predictions of friction factor as implicit relations, as well as approximate explicit relations, have also been proposed for various roughness scales.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1268-1276. doi:10.1115/1.2776966.

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure $pstg$ is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on $fRe$. The correlation for $fRe$ for the slip flow is obtained from that of $fRe$ of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that $fRe$ is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1277-1280. doi:10.1115/1.2776965.

We show that flow in the entry region of a circular pipe is linearly unstable at a Reynolds number of 1000, a factor of 10 smaller than assumed hitherto. The implication that dynamics in this region could greatly hasten the transition to turbulence assumes relevance because in spite of major recent progress, the issue of how pipe flow becomes turbulent is far from settled. Being axisymmetric and close to the centerline, the present instability would be easily distinguishable in an experiment from other generators of turbulence.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1281-1287. doi:10.1115/1.2776969.

In the current study, we report the results of a detailed and systematic numerical investigation of developing pipe flow of inelastic non-Newtonian fluids obeying the power-law model. We are able to demonstrate that a judicious choice of the Reynolds number allows the development length at high Reynolds number to collapse onto a single curve (i.e., independent of the power-law index $n$). Moreover, at low Reynolds numbers, we show that the development length is, in contrast to existing results in the literature, a function of power-law index. Using a simple modification to the recently proposed correlation for Newtonian fluid flows (Durst, F., 2005, “The Development Lengths of Laminar Pipe and Channel Flows  ,” J. Fluids Eng., 127, pp. 1154–1160) to account for this low Re behavior, we propose a unified correlation for $XD∕D$, which is valid in the range $0.4 and $0.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1288-1296. doi:10.1115/1.2776959.

Jet flows are encountered in a variety of industrial applications. Although from the points of view of manufacturing with ease and small spatial requirement it is convenient to use short slit nozzles, most of the available studies deal with turbulent jets issuing from contoured nozzles. In the present work, experiments have been conducted in the moderate Reynolds number range of 250–6250 for a slit jet. Mixing characteristics of slit jets seem to be quite different from those of jets emerging out of contoured nozzles. This is primarily due to the differences in the decay characteristics and the large scale eddy structures generated in the near field, which are functions of the initial momentum thickness. It is evident that, in the range of $250⩽Re⩽6250$, the overall spreading characteristics of the slit jet flow have stronger Reynolds number dependence than those of contoured nozzle jets. In particular, the slit jets exhibit slower mean velocity decay rates and slower half-width growth rates. Normalized power spectra and probability distribution functions are used to assess the spatial evolution and the Reynolds number dependence of jet turbulence. It is seen that the fluctuating components of velocity attain isotropic conditions at a smaller axial distance from the nozzle exit than that required for mean velocity components to become self-similar.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1297-1305. doi:10.1115/1.2776964.

In this paper, vortex-shedding patterns and lock-in characteristics that vortex-shedding frequency synchronizes with the natural frequency of a thin cambered blade were numerically investigated. The numerical simulation was based on solving the vorticity-stream function equations with the fourth-order Runge–Kutta scheme in time and the Chakravaythy–Oscher total variation diminishing (TVD) scheme was used to discretize the convective term. The vortex-shedding patterns for different blade attack angles were simulated. In order to confirm whether the vortex shedding would induce blade self-oscillation, numerical simulation was also carried out for blade in a forced oscillation. By changing the pitching frequency and amplitude, the occurrence of lock-in at certain attack angles was determined. Inside the lock-in zone, phase differences between the blade’s pitching displacement and the torque acting on the blade were used to infer the probability of the blade self-oscillation.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1306-1313. doi:10.1115/1.2776958.

This paper focuses on the interaction between the flow unsteadiness and disk vibration of shrouded corotating disk system to identify the nature of the flow-induced vibration of disks in the wide range of rotation speed below critical. Special attention is paid to the role of the vortical flow structure on the disk vibration and vice versa. The water test rig for optical measurement and the air test rig for hot-wire and vibration measurements are employed, both being axisymmetric models of $3.5in.$ hard disk drive. Before investigating fluid-solid interaction, the velocity and vorticity fields between disks are examined by employing a particle image velocimetry, in order to check the flow within our own apparatus to have the same characteristics as those commonly accepted. In the course of this preliminary experiment, it is found that “vortical structures” reported in the previous papers based on the flow visualization are actually “vortices” in the sense that it exhibits closed streamlines with concentrated vorticity at its center when seen from an observer rotating with the structure itself. The measurements of out-of-plane displacement of the disk employing different disk materials reveal that disk vibration begins to occur even in low subcritical speed range, and amplitude of nonrepeatable run out (NRRO) can be uniquely correlated by using the ratio between the rotating speed and the critical speed. The power spectral densities of disk vibration showed that the disk vibrates as a free vibration triggered by, but not forced by, the flow unsteadiness even in the high subcritical speed range. The disk vibration has negligible effect on the vortical flow structure suggesting the soundness of the rigid disk assumption employed in the existing CFD . However, RRO has significant influence on the flow unsteadiness even if the disks are carefully manufactured and assembled. Since the RRO is unavoidable in the real disk system, the flat disk assumption should be considered more carefully.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1314-1327. doi:10.1115/1.2776970.

The results of flow experiments performed in a row of confined cylinders designed to mimic a model of a prismatic gas-cooled reactor lower plenum design are presented. Pressure measurements between the cylinders were made. Additionally, the flow field was measured using particle image velocimetry at two different resolutions (one at high resolution and a second with wide angle that includes three cylinders). Based on these measurements, five regimes of flow behavior are identified that are found to depend on Reynolds number. It is found that the recirculation region behind the cylinders is shorter than that of half-cylinders placed on the wall representing the symmetry plane. Unlike a single cylinder, the separation point is always found to be on the rear of the cylinders, even at very low Reynolds number.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1328-1338. doi:10.1115/1.2776962.

High-order accurate solutions of parabolized Navier–Stokes (PNS) schemes are used as basic flow models for stability analysis of hypersonic axisymmetric flows over blunt and sharp cones at Mach 8. Both the PNS and the globally iterated PNS (IPNS) schemes are utilized. The IPNS scheme can provide the basic flow field and stability results comparable with those of the thin-layer Navier–Stokes (TLNS) scheme. As a result, using the fourth-order compact IPNS scheme, a high-order accurate basic flow model suitable for stability analysis and transition prediction can be efficiently provided. The numerical solution of the PNS equations is based on an implicit algorithm with a shock fitting procedure in which the basic flow variables and their first and second derivatives required for the stability calculations are automatically obtained with the fourth-order accuracy. In addition, consistent with the solution of the basic flow, a fourth-order compact finite-difference scheme, which does not need higher derivatives of the basic flow, is efficiently implemented to solve the parallel-flow linear stability equations in intrinsic orthogonal coordinates. A sensitivity analysis is also conducted to evaluate the effects of numerical dissipation and grid size and also accuracy of computing the basic flow derivatives on the stability results. The present results demonstrate the efficiency and accuracy of using high-order compact solutions of the PNS schemes as basic flow models for stability and transition prediction in hypersonic flows. Moreover, indications are that high-order compact methods used for basic-flow computations are sensitive to the grid size and especially the numerical dissipation terms, and therefore, more careful attention must be kept to obtain an accurate solution of the stability and transition results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1339-1345. doi:10.1115/1.2776968.

A microelectromechanical system (MEMS) vapor-jet pump for vacuum generation in miniaturized analytical systems, e.g., micro-mass-spectrometers (Wapelhorst, E., Hauschild, J., and Mueller, J., 2005, “A Fully Integrated Micro Mass Spectrometer  ,” in Fifth Workshop on Harsh-Environment Mass Spectrometry;Hauschild, J., Wapelhorst, E., and Mueller, J., 2005, “A Fully Integrated Plasma Electron Source for Micro Mass Spectrometers  ,” in Ninth International Conference on Miniaturized Systems for Chemistry and Life Sciences $(μTAS)$, pp. 476–478), is presented. A high velocity nitrogen or water vapor jet is used for vacuum generation. Starting from atmospheric pressure, a high throughput of more than $23ml∕min$ and an ultimate pressure of $495mbars$ were obtained with this new type of micropump. An approach for the full integration of all components of the pump is presented and validated by experimental results. The pump is fabricated from silicon and glass substrates using standard MEMS fabrication techniques including deep reactive ion etching, trichlorosilane molecular vapor deposition, and metal-assisted chemical etching for porous silicon fabrication. Micromachined pressure sensors based on the Pirani principle have been developed and integrated into the pump for monitoring.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(10):1346-1357. doi:10.1115/1.2776967.

Electrical power generation employing pressure-driven flows is a fundamental problem in microfluidics. In the present work, analytical and numerical analyses are performed to study the interplaying effects of electrolyte motion with the associated electrical current in a flat microchannel with and without fluid reservoirs. The modified Navier–Stokes equations as well as a Poisson equation for the distribution of electric potential and the Nernst–Planck equations for the distribution of charge densities are solved for the steady flow of a Newtonian liquid. The results show that for a pressure-driven flow, an electric potential is induced due to the motion of charged particles, which increases linearly along the microchannel. This streaming potential generates an opposing conduction current in the core region of the channel as well as in the immediate vicinity of the walls, where the streaming current is negligible. The streaming potential varies in a nonlinear manner with the zeta potential at the walls such that a maximum potential exists at a certain zeta potential. The maximum potential is also observed to increase with both the applied pressure difference and the electric double layer thickness in the range studied. The presence of reservoirs adds significant complexity to this electrokinetic flow.

Commentary by Dr. Valentin Fuster