0

### Research Papers: Flows in Complex Systems

J. Fluids Eng. 2009;131(6):061101-061101-9. doi:10.1115/1.3111256.

Two geometric modalities were investigated to determine their effects on the degree of uniformity of the flow issuing from a manifold through a discrete set of exit ports. The goal of the investigation was to demonstrate how these geometric parameters can be used to achieve a high degree of exit-flow uniformity. The first investigated modality is the area ratio, which compares the total outflow area of all the exit ports with the cross-sectional area of the manifold. The second modality is the extent of pressure loading downstream of the exit ports of the manifold. The investigation was facilitated by numerical simulation for which an appropriate turbulence model was used. Three parameters were varied during the course of the research: (a) the area ratio, (b) the downstream pressure loading characterized by the length-to-diameter ratio of the outflow tubes that are attached to the exit ports, and (c) the Reynolds number. It was found that the area ratio parameter had a marked effect on the uniformity of the outflow from the manifold. Quantitative values of the area ratio corresponding to specified degrees of uniformity (i.e., 2%, 5%, and 10%) were identified. This information can be used as a guideline for manifold design. The imposition of the downstream pressure loading was also demonstrated to have a significant effect on the degree of uniformity, but that effect was not as strong as the effect of the area ratio. The manifold pressure was found to increase from the inlet of the manifold to the downstream end of the manifold. The direction of the jetlike discharge from the exit ports of the manifold into a large collection domain was found to vary along the length of the manifold, with inclined jets emanating from the upstream end and perpendicular jets at the downstream end. Over the range of investigated Reynolds numbers, from 40,000 to 200,000, the degree of uniformity of the mass effusion from the exit ports was found to be unaffected. The results of the numerical simulations were confirmed by experiments.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061102-061102-12. doi:10.1115/1.3129122.

The case investigated is the flow past a generic side mirror mounted on a flat plate at the Reynolds number of $ReD=5.2×105$ based on the mirror diameter. The present work studies both flow and acoustic sources by evaluating two second-order advection schemes, different levels of turbulence modeling, and three different grids. The advection schemes discussed in the present study are a second-order upwind scheme and a monotonic central scheme. The turbulence models investigated cover three levels of modeling. These are the original formulation of the detached eddy simulation (DES) model, the Smagorinsky–Lilly sub-grid scale (SGS) model with near-wall damping, and a dynamic Smagorinsky model. The different grids are as follows: a primary grid where all parameter studies are conducted and a second grid with significantly higher wake resolution and to some extent also increased plate resolution, while maintaining the resolution at the front side of the mirror. The final grid uses a significantly higher plate resolution and a wake resolution similar to that of grid two, but a comparably lower mirror front side resolution as compared with the two other grids. The general outcome of this work is that the estimation of the grid cutoff frequency through a relation of the velocity fluctuation and the grid size matches both the experimental results and trend lines perfectly. Findings from the flow field show that the horseshoe vortex in front of the mirror causes pressure fluctuations with a magnitude exceeding the maximum levels at the rear side of the mirror. Its location and unsteady properties are perfectly captured in the final simulation as compared with the experiments conducted by Daimler–Chrysler. A laminar separation at the front side of the mirror is more or less found for all wall resolved cases except the DES simulation. The third grid fails to predict this flow feature, but it is shown that this effect has no significant effect on either the static pressure sensors at the mirror surface or at the dynamic sensors located downstream of the mirror. The simulation also supports the fundamental frequency based on the eddy convection in the mirror shear layer, which is shown to be twice as high as the frequency peak found in the lateral force spectra.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061103-061103-7. doi:10.1115/1.3130246.

The exit flow patterns of an axial flow fan widely used in electronics cooling are experimentally characterized both in free exit and in the presence of a flat impingement plate. The axial fan is rotated with 12.0 V input from a dc power supply, leading to a nominal Reynolds number of $Re=9.0×103$ based on fan diameter. One shear layer each is found to form between the exit flow from the axial fan and the surrounding fluid at rest, and between the exit flow and the flow along the fan axis. In addition to creating a highest wall pressure region (the primary stagnation region), the presence of the flat plate induces a flow recirculation zone (the secondary stagnation region) at the plate center. When the fan exit-to-plate spacing normalized by fan diameter $(H/D)$ equals to about 0.6, the wall pressure is minimized in the secondary stagnation region due to the maximized “recirculation” as a result of intensified flow interaction. Within the range considered $(0.2≤H/D≤2.0)$ and with the case of $H/D∼0.6$ serving as a reference, the flow interaction tends to be suppressed by the proximity of the plate at $H/D=0.2$ and weakened due to the momentum dissipation at $H/D∼2.0$.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061104-061104-10. doi:10.1115/1.3026629.

This paper studies the effect of the Reynolds number on the performance characteristics of a small regenerative pump. Since regenerative pumps have low specific speeds, they are usually applicable to small devices such as micropumps. As the operating Reynolds number decreases, nondimensional similarity parameters such as flow and head coefficients and efficiency become dependent on the Reynolds number. In this study, the Reynolds number based on the impeller diameter and rotating speed varied between $5.52×103$ and $1.33×106$. Complex three-dimensional flow structures of internal flow vary with the Reynolds numbers. The coefficients of the loss models are obtained by using the calculated through flows in the impeller. The estimated performances obtained by using one-dimensional modeling agreed reasonably well with the numerically calculated performances. The maximum values of flow and head coefficients depended on the Reynolds number when it is smaller than $2.65×105$. The critical value of the Reynolds number for loss coefficient and maximum efficiency variations with Reynolds number was $1.0×105$.

Commentary by Dr. Valentin Fuster

### Research Papers: Fundamental Issues and Canonical Flows

J. Fluids Eng. 2009;131(6):061201-061201-15. doi:10.1115/1.3130244.

This paper describes a modeling method for closed-loop unsteady fluid transport systems based on 1D unsteady Euler equations with nonlinear forced periodic boundary conditions. A significant feature of this model is the incorporation of dynamic constraints on the variables that control the transport process at the system boundaries as they often exist in many transport systems. These constraints result in a coupling of the Euler equations with a system of ordinary differential equations that model the dynamics of auxiliary processes connected to the transport system. Another important feature of the transport model is the use of a quasilinear form instead of the flux-conserved form. This form lends itself to modeling with measurable conserved fluid transport variables and represents an intermediate model between the primitive variable approach and the conserved variable approach. A wave-splitting finite-difference upwind method is presented as a numerical solution of the model. An iterative procedure is implemented to solve the nonlinear forced periodic boundary conditions prior to the time-marching procedure for the upwind method. A shock fitting method to handle transonic flow for the quasilinear form of the Euler equations is presented. A closed-loop wind tunnel is used for demonstration of the accuracy of this modeling method.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061202-061202-12. doi:10.1115/1.3129130.

A two-dimensional numerical simulation of flow in patterned microchannel with alternate layers of different sizes of hydrophilic and hydrophobic surfaces at the bottom wall is conducted here. The effect of specified contact angle and working fluid (de-ionized (DI) water and ethanol) on capillary phenomena is observed here. The volume of fluid method is used for simulating the free surface flow in the microchannel. Meniscus profiles with varying amplitude and shapes are obtained under the different specified surface conditions. Nonsymmetric meniscus profiles are obtained by changing the contact angles of the hydrophilic and hydrophobic surfaces. A meniscus stretching parameter is defined here and its relation to the capillary phenomena in the microchannel is discussed. Flow variation increases as the fluid traverses alternately between the hydrophilic and hydrophobic regions. The pattern size and the surface tension of the fluid are found to have significant influence on the capillary phenomena in the patterned microchannel. Smaller pattern size produces enhanced capillary effect with DI water, whereas no appreciable gain is observed for ethanol. The magnitude of maximum velocity along the channel height varies considerably with the pattern size and the contact angle. Also, the rms velocity is found to be higher for smaller alternate patterned microchannel. The meniscus average velocity difference at the top and bottom walls increases for a dimensionless pattern size of 0.6 and thereafter it decreases with the increase in pattern size in the case of DI water with hydrophilic-hydrophobic pattern. Using such patterned microchannel, it is possible to manipulate and optimize fluid flow in microfluidic devices, which require enhanced mixing for performing biological reactions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061203-061203-4. doi:10.1115/1.3129132.

In this paper, we propose a novel explicit equation for friction factor, which is valid for both smooth and rough wall turbulent flows in pipes and channels. The form of the proposed equation is based on a new logarithmic velocity profile and the model constants are obtained by using the experimental data available in the literature. The proposed equation gives the friction factor explicitly as a function of Reynolds number and relative roughness. The results indicate that the present model gives a very good prediction of the friction factor and can reproduce the Colebrook equation and its Moody plot. Therefore, the new approximation for the friction factor provides a rational, accurate, and practically useful method over the entire range of the Moody chart in terms of Reynolds number and relative roughness.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061204-061204-10. doi:10.1115/1.3112384.

The present paper reports observations on some aspects regarding the dependence of the transition Reynolds number and flow development on the inlet flow conditions and the entrance length in circular and rectangular ducts for $Rem≤106×103$, where $Rem$ is the Reynolds number based on the bulk flow velocity $(U¯b)$ and the duct integral length scale $(D)$. The hot-wire anemometer was used to carry out measurements close to the circular duct exit; however, the laser-Doppler anemometry was utilized for the rectangular duct measurements. Particular considerations were given to the bulk flow velocity, the mean-velocity profile, the centerline-average-velocity, and the centerline turbulence statistics to the fourth order. Transition criteria in both ducts were discussed, reflecting effects of flow geometry, entrance flow conditions, and entrance length on the transition Reynolds number. A laminar behavior was maintained up to $Rem≈15.4×103$ and $Rem≈2×103$ in the circular and rectangular ducts, respectively, and the transition was observed to take place at different downstream positions as the inlet flow velocity varied.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2009;131(6):061205-061205-12. doi:10.1115/1.3112389.

This paper reports an experimental investigation of the effects of wall roughness and favorable pressure gradient on low Reynolds number turbulent flow in a two-dimensional asymmetric converging channel. Flow convergence was produced by means of ramps (of angles 2 deg and 3 deg) installed on the bottom wall of a plane channel. The experiments were conducted over a smooth surface and over transitionally rough and fully rough surfaces produced from sand grains and gravel of nominal mean diameters 1.55 mm and 4.22 mm, respectively. The dimensionless acceleration parameter was varied from $0.38×10−6$ to $3.93×10−6$ while the Reynolds number based on the boundary layer momentum thickness was varied from 290 to 2250. The velocity measurements were made using a particle image velocimetry technique. From these measurements, the distributions of the mean velocity and Reynolds stresses were obtained to document the salient features of transitionally and fully rough low Reynolds number turbulent boundary layers subjected to favorable pressure gradient.

Commentary by Dr. Valentin Fuster

### Research Papers: Multiphase Flows

J. Fluids Eng. 2009;131(6):061301-061301-8. doi:10.1115/1.3129134.

Compressive residual stresses that improve fatigue strength of material are obtained by peening the surface. Unlike traditional processes, a novel process of oil cavitation jet peening was developed. The process is based on implosion generated by the oil cavitation jet that plastically deforms the surface, imparting compressive residual stresses. The process developed involves injection of a high-speed oil jet $(∼230 m/s)$ through a suitably designed nozzle, into an oil-filled chamber containing the specimen to be peened. The region of cavitation generation, growth, and collapse, at the various cavitation numbers, was recorded using high-speed photography. To optimize the process parameters, a simple erosion test was performed in aluminum alloy, AA 6063-T6, specimens. The impact pressure generated during the implosion of cavitation bubbles causes plastic deformation and erosion of the surface. The surface deformation and cavitation jet erosion in the exposed specimens were characterized using optical and scanning electron microscopies. The standoff distance, which measures jet impact zone of the specimen from nozzle, was optimized at 15 mm in a cavitation number (which is a measure of pressure ratio across the nozzle) of 0.0017. The surface deformation produced by collapse of the oil bubble was similar to impact of oil droplet on the surface. The material removal mechanism during implosion of the bubble is predominately by ductile shear deformation.

Commentary by Dr. Valentin Fuster

### Research Papers: Techniques and Procedures

J. Fluids Eng. 2009;131(6):061401-061401-14. doi:10.1115/1.3077141.

For the aim of computing compressible turbulent flowfield involving shock waves, an implicit large eddy simulation (LES) code has been developed based on the idea of monotonically integrated LES. We employ the weighted compact nonlinear scheme (WCNS) not only for capturing possible shock waves but also for attaining highly accurate resolution required for implicit LES. In order to show that WCNS is a proper choice for implicit LES, a two-dimensional homogeneous turbulence is first obtained by solving the Navier–Stokes equations for incompressible flow. We compare the inertial range in the computed energy spectrum with that obtained by the direct numerical simulation (DNS) and also those given by the different LES approaches. We then obtain the same homogeneous turbulence by solving the equations for compressible flow. It is shown that the present implicit LES can reproduce the inertial range in the energy spectrum given by DNS fairly well. A truncation of energy spectrum occurs naturally at high wavenumber limit indicating that dissipative effect is included properly in the present approach. A linear stability analysis for WCNS indicates that the third order interpolation determined in the upwind stencil introduces a large amount of numerical viscosity to stabilize the scheme, but the same interpolation makes the scheme weakly unstable for waves satisfying $kΔx≈1$. This weak instability results in a slight increase in the energy spectrum at high wavenumber limit. In the computed result of homogeneous turbulence, a fair correlation is shown to exist between the locations where the magnitude of $∇×ω$ becomes large and where the weighted combination of the third order interpolations in WCNS deviates from the optimum ratio to increase the amount of numerical viscosity. Therefore, the numerical viscosity involved in WCNS becomes large only at the locations where the subgrid-scale viscosity can arise in ordinary LES. This suggests the reason why the present implicit LES code using WCNS can resolve turbulent flowfield reasonably well.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Fluids Eng. 2009;131(6):064501-064501-5. doi:10.1115/1.3129123.

The flow past a rectangular cylinder with small cut-corners at the front-edge is investigated to discuss a relation between drag reduction and the cutout dimension. The rectangular shape is selected in eleven kinds of the length-to-breadth ratio from 2/6 to 6/6 (square prism) with the small rectangular-shaped cut-corners at the front-edge. The wind tunnel experiment is carried out to obtain time-averaged hydrodynamic forces measured by the force transducer at $Re≈50,000$. The contour map of the hydrodynamic coefficients with respect to the cutout dimension are shown to investigate the relation between the drag reduction and the cutout shape. In the contour map for the zero angle of attack, the region of the effective drag reduction achieved, in which the value of the drag coefficient is less than that of a circular cylinder at the same Reynolds number, is observed to become wide with the increase in the length-to-breadth ratio and it is independent of the angle of attack, $α$, within $α$ being small. Furthermore, it is shown that there is a condition in which the drag reduction of $CD⪅1.5$ can be achieved even when the Strouhal number is less than 0.2.

Commentary by Dr. Valentin Fuster

### Errata

J. Fluids Eng. 2009;131(6):067001-067001-1. doi:10.1115/1.3129157.
FREE TO VIEW
Three errors have been detected in a further analysis of the data.
• The first error is that the reported frame rate of the camera is incorrect. This means that the velocities of the fibers should be divided by two. Another consequence is that the wall normal distance from the wall $y$ will be roughly (velocity gradient not constant) half of the previously reported values.
• The second error is that the computed theoretical concentration profile is incorrect.
• The third error is that the reported fiber diameter is incorrect.
Topics: Fluids , Fibers , Papermaking
Commentary by Dr. Valentin Fuster