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### EDITORIAL

J. Fluids Eng. 2006;128(1):1-5. doi:10.1115/1.2163070.
FREE TO VIEW

Micrographs showing glycerin (a) and water (b)–(d) inside carbon nanotubes. The tubes shown in (a) and (b) were fabricated with chemical vapor deposition in alumina templates. The tubes in (c) and (d) were hydrothermally produced. (a) Optical micrograph of glycerin inside an open CVD-grown nanotube. (b) Environmental SEM image of water inside a nanotube similar to the one shown in (a). (c) TEM image of water inside a hydrothermally-produced, sealed carbon nanotube. (d) TEM micrographs of a fluid inside a multi-wall, hydorthermally-produced, sealed carbon nanotube.

Commentary by Dr. Valentin Fuster

### SPECIAL SECTION ON THE FLUID MECHANICS AND RHEOLOGY OF NONLINEAR MATERIALS AT THE MACRO, MICRO AND NANO SCALE

J. Fluids Eng. 2005;128(1):6-13. doi:10.1115/1.2136932.

This paper describes the combined use of controlled nanoassembly and microfabrication (photolithography) to construct multi-walled, carbon, nanotube-based fluidic devices. The nanoassembly technique utilizes dielectrophoresis to position individual nanotubes across the gap between two electrodes patterned on a wafer. The dielectrophoretic migration process was studied theoretically and experimentally. Once a tube had been trapped between a pair of electrodes, photoresist was spun over the wafer and developed to form microfluidic interfaces. Liquid condensation in and evaporation from the nanotubes were observed with optical microscopy. The nanotube-based fluidic devices can be used for studies of fluid transport under extreme confinement and as sensitive sensors.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):14-19. doi:10.1115/1.2136924.

We present a novel separation device for the front-end of a biodetection system to discriminate between biological and non-biological analytes captured in air samples. By combining AC dielectrophoresis along the flow streamlines and a field-induced phase-separation, the device utilizes “dielectrophoretic gating”to separate analytes suspended in a flowing fluid based on their intrinsic polarizability properties. The gates are integrated into batch fabricated self-sealed surface-micromachined fluid channels. We demonstrate that setting the gate to a moderate voltage in the radio frequency range removed bacteria cells from a mixture containing non-biological particles without the need for fluorescent labeling or antibody-antigen hybridization, and also validate experimentally basic relations for estimating the gate performance.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):20-26. doi:10.1115/1.2140802.

Conformal (or freeform) and steep concave optics are important classes of optics that are difficult to finish using conventional techniques due to mechanical interferences and steep local slopes. One suitable way to polish these classes of optics is by using a jet of abrasive/fluid mixture. The energy required for polishing may be supplied by the radial spread of a liquid jet, which impinges a surface to be polished. Such fluid flow may generate sufficient surface shear stress to provide material removal in the regime of chemical mechanical polishing. Once translated into a polishing technique, this unique tool may resolve a challenging problem of finishing steep concave surfaces and cavities. A fundamental property of a fluid jet is that it begins to lose its coherence as the jet exits a nozzle. This is due to a combination of abruptly imposed longitudinal and lateral pressure gradients, surface tension forces, and aerodynamic disturbance. This results in instability of the flow over the impact zone and consequently polishing spot instability. To be utilized in deterministic high precision finishing of remote objects, a stable, relatively high-speed, low viscosity fluid jet, which remains collimated and coherent before it impinges the surface to be polished, is required. A method of jet stabilization has been proposed, developed, and demonstrated whereby the round jet of magnetorheological fluid is magnetized by an axial magnetic field when it flows out of the nozzle. It has been experimentally shown that a magnetically stabilized round jet of magnetorheological (MR) polishing fluid generates a reproducible material removal function (polishing spot) at a distance of several tens of centimeters from the nozzle. The interferometrically derived distribution of material removal for an axisymmetric MR Jet™ , which impinges normal to a plane glass surface, coincides well with the radial distribution of rate of work calculated using computational fluid dynamics (CFD) modeling. Polishing results support the assertion that the MR Jet finishing process may produce high precision surfaces on glass and single crystals. The technology is most attractive for the finishing of complex shapes like freeform optics, steep concaves, and cavities.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):27-33. doi:10.1115/1.2136931.

This paper deals with coextrusion flows of two compatible polymers which are known to be generally more stable than the same flows of incompatible systems. We show that the weak response to disturbance of such flows can be predicted by considering an interphase of nonzero thickness (corresponding to an interdiffusion zone) instead of a purely geometrical interface between the two layers. As a first step we try to explain the weak sensibility to disturbance of compatible systems by the sole presence of this intermediate layer. For that purpose we study the linear stability response to very long waves of a three-layer phase Poiseuille flow with an inner thin layer which represents the interphase. Although this fact is an approximation, it nevertheless takes into account the diffusion phenomena which are generated in the interphase. This first approach (corresponding to a reduction in the effective viscosity ratio) is shown to explain the diminished growth rates but not the reduction in the size of the unstable region. As a second step, we formulate an energetic approach of the problem. We evaluate the energy dissipated during the interdiffusion process and the variation of kinetic energy of the global system. A modified growth rate is then determined by taking into account the energy dissipated by the interdiffusion process. This lower growth rate enables us to explain the increase of the stable domain in the case of compatible polymeric systems.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):34-41. doi:10.1115/1.2136926.

We present a numerical study of Dean instability for non-Newtonian fluids in a laminar $180deg$ curved-channel flow of rectangular cross section. A methodology based on the Papanastasiou model (Papanastasiou, T. C., 1987, J. Rheol., 31(5), pp. 385–404) was developed to take into account the Bingham-type rheological behavior. After validation of the numerical methodology, simulations were carried out (using FLUENT CFD code) for Newtonian and non-Newtonian fluids in curved channels of square or rectangular cross section and for a large aspect and curvature ratios. A criterion based on the axial velocity gradient was defined to detect the instability threshold. This criterion was used to optimize the grid geometry. The effects of curvature and aspect ratio on the Dean instability are studied for all fluids, Newtonian and non-Newtonian. In particular, we show that the critical value of the Dean number decreases with increasing curvature ratio. The variation of the critical Dean number with aspect ratio is less regular. The results are compared to those for Newtonian fluids to emphasize the effect of the power-law index and the Bingham number. The onset of Dean instability is delayed with increasing power-law index. The same delay is observed in Bingham fluids when the Bingham number is increased.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):42-54. doi:10.1115/1.2136930.

The flow inside a horizontal annulus due to the inner cylinder rotation is studied. The bottom of the annular space is partially blocked by a plate parallel to the axis of rotation, thereby destroying the circumferential symmetry of the annular space geometry. This flow configuration is encountered in the drilling process of horizontal petroleum wells, where a bed of cuttings is deposited at the bottom part of the annulus. The velocity field for this flow was obtained both numerically and experimentally. In the numerical work, the equations which govern the three-dimensional, laminar flow of both Newtonian and power-law liquids were solved via a finite-volume technique. In the experimental research, the instantaneous and time-averaged flow fields over two-dimensional meridional sections of the annular space were measured employing the particle image velocimetry (PIV) technique, also both for Newtonian and power-law liquids. Attention was focused on the determination of the onset of secondary flow in the form of distorted Taylor vortices. The results showed that the critical rotational Reynolds number is directly influenced by the degree of obstruction of the flow. The influence of the obstruction is more perceptible for Newtonian than for non-Newtonian liquids. The more severe is the obstruction, the larger is the critical Taylor number. The height of the obstruction also controls the width of the vortices. The calculated steady-state axial velocity profiles agreed well with the corresponding measurements. Transition values of the rotational Reynolds number are also well predicted by the computations. However, the measured and predicted values for the vortex size do not agree as well. Transverse flow maps revealed a complex interaction between the Taylor vortices and the zones of recirculating flow, for moderate to high degrees of flow obstruction.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):55-61. doi:10.1115/1.2136922.

A micro-macro simulation algorithm for the calculation of polymeric flow is developed and implemented. The algorithm couples standard finite element techniques to compute velocity and pressure fields with stochastic simulation techniques to compute polymer stress from simulated polymer dynamics. The polymer stress is computed using a microscopic-based rheological model that combines aspects of network and reptation theory with aspects of continuum mechanics. The model dynamics include two Gaussian stochastic processes, each of which is destroyed and regenerated according to a survival time randomly generated from the material’s relaxation spectrum. The Eulerian form of the evolution equations for the polymer configurations is spatially discretized using the discontinuous Galerkin method. The algorithm is tested on benchmark contraction domains for a polyisobutylene solution. In particular, the flow in the abrupt die entry domain is simulated and the simulation results are compared to experimental data. The results exhibit the correct qualitative behavior of the polymer and agree well with the experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):62-68. doi:10.1115/1.2140803.

We perform molecular dynamics (MD) simulations (based on the soft-sphere model) of a model dry granular system consisting of two types of spherical particles differing in size and/or density to characterize particle-particle momentum transfer (solid drag). The velocity difference between two types of particles is specified in the initial conditions, and the evolution of relative mean velocity and the velocity fluctuations in terms of granular temperature are quantified. The dependence of the momentum transfer is studied as a function of volume fraction, size and density ratio of the two types of particles, inelasticity, and friction coefficient. An existing continuum model of particle-particle momentum transfer is compared to the MD simulations. A modified continuum solid drag model is suggested for a limited range of parameters.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):69-76. doi:10.1115/1.2136928.

The swirling flows of water and CTAC (cetyltrimethyl ammonium chloride) surfactant solutions $(50–1000ppm)$ in an open cylindrical container with a rotating disc at the bottom were experimentally investigated by use of a double-pulsed PIV (particle image velocimetry) system. The flow pattern in the meridional plane for water at the present high Reynolds number of $4.3×104$ differed greatly from that at low Reynolds numbers, and an inertia-driven vortex was pushed to the corner between the free surface and the cylindrical wall by a counter-rotating vortex caused by vortex breakdown. For the $1000ppm$ surfactant solution flow, the inertia-driven vortex located at the corner between the bottom and the cylindrical wall whereas an elasticity-driven reverse vortex governed the majority of the flow field. The rotation of the fluid caused a deformation of the free surface with a dip at the center. The dip was largest for the water case and decreased with increasing surfactant concentration. The value of the dip was related to determining the solution viscoelasticity for the onset of drag reduction.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):77-87. doi:10.1115/1.2136929.

In Part I [Wei, 2004, 2004 ASME Int. Mech. Eng. Conference], we presented the experimental results for swirling flows of water and cetyltrimethyl ammonium chloride (CTAC) surfactant solution in a cylindrical vessel with a rotating disk located at the bottom for a Reynolds number of around $4.3×104$ based on the viscosity of solvent. For the large Reynolds number, violent irregular instantaneous secondary flows at the meridional plane were observed by use of a particle image velocimetry system. Because of the limitations of our computer resources, we did not carry out direct numerical simulation for such a large Reynolds number. The LES and turbulence model are alternative methods, but a viscoelastic LES/turbulence model has not yet been developed for the surfactant solution. In this study, therefore, we limited our simulations to a laminar flow. The marker-and-cell method proposed for Newtonian flow was extended to the viscoelastic flow to track the free surface, and the effects of Weissenberg number and Froude number on the flow pattern and surface shape were studied. Although the Reynolds number is much smaller than that of the experiment, the major experimental observations, such as the inhibition of primary and secondary flows and the decrease of the dip of the free surface by the elasticity of the solution, were qualitatively reproduced in the numerical simulations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):88-94. doi:10.1115/1.2136925.

The swirling flow of a viscoelastic fluid in a cylindrical casing is investigated experimentally, using aqueous solutions of 0.05–$1.0wt.%$ polyacrylamide as the working fluid. The velocity measurements are made using laser Doppler anemometer. The aspect ratios $H∕R$ ($H$: axial length of cylindrical casing; $R$: radius of rotating disk) investigated are 2.0, 1.0, and 0.3. The Reynolds numbers $Re0$ based on the zero shear viscosity and the disk-tip velocity are between 0.36 and 50. The velocity measurements are mainly conducted for the circumferential velocity component. The experimental velocity data are compared to the velocity profiles obtained by numerical simulations using Giesekus model and power-law model. It is revealed that at any aspect ratios tested the dimensionless circumferential velocity component $Vθ′$ decreases with increasing Weissenberg number We. Both the Giesekus and power-law models could predict the retardation of circumferential velocity fairly well at small We. The extent of the inverse flow region, where the fluid rotates in the direction opposite to the rotating disk, is clarified in detail.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):95-100. doi:10.1115/1.2137350.

Laser-induced fluorescence (LIF) was applied for the flow visualization of the formation of a Taylor vortex, which occurred in the gap between two coaxial cylinders. The test fluids were tap water and glycerin 60 %wt solution as Newtonian fluids; polyacrilamide (SeparanAP-30) solutions in the concentration range of $10$ to $1000ppm$ and polyethylene-oxide (PEO15) solutions in the range of $20$ to $1000ppm$ were tested as non-Newtonian fluids. The Reynolds number range in the experiment was $80. The rotating inner cylinder was accelerated under the slow condition $(dRe*∕dt⩽1min−1)$ in order to obtain a Taylor vortex flow in stable primary mode. Flow visualization results showed that the Görtler vortices of half the number of the Taylor cells occurred in the gap when the Taylor vortex flow was formed in the primary mode. In addition, the critical Reynolds number of the polymer solutions increased, where Taylor vortices occur, because the generation of the Görtler vortices was retarded. In high concentration polymer solutions, this effect became remarkable. Measurements of steady-state Taylor cells showed that the upper and lower cells of polymer solutions became larger in wavelength than those of the Newtonian fluids. The Taylor vortex flow of non-Newtonian fluids was analyzed and the result obtained using the Giesekus model agreed with the experimental result.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):101-106. doi:10.1115/1.2136927.

Surfactants are well known as additives which induce drag reduction in the straight (nonswirling) pipe flow. However, in industrial applications of the drag-reducing effect, many flow fields besides the straight pipe flow need to be considered. The purpose of this study is to investigate the flow characteristics of the surfactant solution in swirling pipe flow. The drag-reducing effect is estimated from the measurement of wall pressure drop and velocity profiles on various pipe sections by two-dimensional LDV (Laser Doppler Velocimeter). Since the surfactant solution has viscoelasticity, interesting flow characteristics are obtained. The decay of swirl, the vortex type and the turbulence intensity are discussed, compared with the swirling flow of the water. As the results, it is concluded that the change from Rankin’s combined vortex to the forced vortex at a more upstream section by suppressing progress of free vortex and stretch of forced vortex introduces considerable drag reduction. Oscillation of the vortex core is also investigated, and it is found that the oscillation is independent of swirl number.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):107-112. doi:10.1115/1.2137342.

The present study is related to the rimming flow of non-Newtonian fluid on the inner surface of a horizontal rotating cylinder. Using a scale analysis, the main characteristic scales and nondimensional parameters, which describe the principal features of the process, are found. Exploiting the fact that one of the parameters is very small, an approximate asymptotic mathematical model of the process is developed and justified. For a wide range of fluids, a general constitutive law can be presented by a single function relating shear stress and shear rate that corresponds to a generalized Newtonian model. For this case, the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a steady-state solution is proved. Within the bounds stipulated by this condition, film thickness admits a continuous solution, which corresponds to subcritical and critical flow regimes. It is proved that for the critical regime the solution has a corner on the rising wall of the cylinder. In the supercritical flow regime, a discontinuous solution is possible and a hydraulic jump may occur. It is shown that straightforward leading order steady-state theory can work well to study the shock location and height. For the particular case of a power-law model, the analytical solution of a steady-state equation for the fluid film thickness is found in explicit form. More complex rheological models, which show linear Newtonian behavior at low shear rates with transition to power law at moderate shear rates, are also considered. In particular, numerical computations were carried out for the Ellis model. For this model, some analytical asymptotic solutions have also been obtained in explicit form and compared with the results of numerical computations. Based on these solutions, the optimal values of parameters, which should be used in the Ellis equation for the correct simulation of the coating flows, are determined; the criteria that guarantee the steady-state continuous solutions are defined; and the size and location of the stationary hydraulic jumps, which form when the flow is in the supercritical state, are obtained for the different flow parameters.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):113-117. doi:10.1115/1.2136923.

This experimental study concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder is stationary and inner one is rotating. Pressure losses and skin friction coefficients have been measured for fully developed laminar flows of water and of 0.4% aqueous solution of sodium carboxymethyl cellulose, respectively, when the inner cylinder rotates at the speed of $0–600rpm$. The results of the present study show the effect of the bulk flow Reynolds number Re and Rossby number Ro on the skin friction coefficients. They also point to the existence of a flow instability mechanism. The effect of rotation on the skin friction coefficient depends significantly on the flow regime. In all flow regimes, the skin friction coefficient is increased by the inner cylinder rotation. The change in skin friction coefficient, which corresponds to a variation of the rotational speed, is large for the laminar flow regime, whereas it becomes smaller as Re increases for transitional flow regime and, then, it gradually approaches to zero for turbulent flow regime. Consequently, the critical bulk flow Reynolds number $Rec$ decreases as the rotational speed increases. The rotation of the inner cylinder promotes the onset of transition due to the excitation of Taylor vortices.

Commentary by Dr. Valentin Fuster

### TECHNICAL PAPERS

J. Fluids Eng. 2005;128(1):118-130. doi:10.1115/1.2073227.

Turbulent drag reduction by dilute addition of high polymers is studied by considering local stretching of the molecular structure of a polymer by small-scale turbulent motions in the region very close to the wall. The stretching process is assumed to restructure turbulence at small scales by forcing these to satisfy local axisymmetry with invariance under rotation about the axis aligned with the main flow. It can be shown analytically that kinematic constraints imposed by local axisymmetry force turbulence near the wall to tend towards the one-component state and when turbulence reaches this limiting state it must be entirely suppressed across the viscous sublayer. For the limiting state of wall turbulence, the statistical dynamics of the turbulent stresses, constructed by combining the two-point correlation technique and invariant theory, suggest that turbulent drag reduction by homogeneously distributed high polymers, cast into the functional space which emphasizes the anisotropy of turbulence, resembles the process of reverse transition from the turbulent state towards the laminar flow state. These findings are supported by results of direct numerical simulations of wall-bounded turbulent flows of Newtonian and non-Newtonian fluids and by experiments carried out, under well-controlled laboratory conditions, in a refractive index-matched pipe flow facility using state-of-the art laser-Doppler anemometry. Theoretical considerations based on the elastic behavior of a polymer and spatial intermittency of turbulence at small scales enabled quantitative estimates to be made for the relaxation time of a polymer and its concentration that ensure maximum drag reduction in turbulent pipe flows, and it is shown that predictions based on these are in very good agreement with available experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):131-141. doi:10.1115/1.2140804.

A theoretical analysis has been developed to predict the critical height and the location of the onset of gas entrainment during discharge from a stratified two-phase region through two oriented-side branches mounted on a vertical wall. In this analysis, a point sink model was first developed, followed by a more accurate three-dimensional finite branch model. The models are based on a new modified criterion for the onset of gas entrainment. The theoretically predicted critical height and the location of the onset of gas entrainment are found to be a function of the mass rate of each branch ($Fr1$ and $Fr2$), the distance between the centerlines of the two branches $(L∕d)$, and the inclination angle $(θ)$. The effects of these variables on the predicted critical height and the onset location were investigated. Furthermore, comparison between the theoretically predicted results and the available experimental data was carried out to verify the developed models. The comparison shows that the predicted results are very close to the measured data within a deviation percentage of 12% at $Fr1>10$. This small deviation percentage reflects a good agreement between the measured and predicted results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):142-150. doi:10.1115/1.2137343.

A new and generalized lattice Boltzmann model for simulating thermal two-phase flow is described. In this model, the single component multi-phase lattice Boltzmann model proposed by Shan and Chen is used to simulate the fluid dynamics. The temperature field is simulated using the passive-scalar approach, i.e., through modeling the density field of an extra component, which evolves according to the advection-diffusion equation. By coupling the fluid dynamics and temperature field through a suitably defined body force term, the thermal two-phase lattice Boltzmann model is obtained. In this paper, the theoretical foundations of the model and the validity of the thermal lattice Boltzmann equation method are laid out, illustrated by analytical and numerical examples. In a companion paper (P. Yuan and L. Schaefer, 2006, ASME J. Fluids Eng., 128, pp. 151–156), the numerical results of the new model are reported.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):151-156. doi:10.1115/1.2137344.

In the previous paper (Part 1) (P. Yuan and L. Schaefer, 2006, ASME J. Fluids Eng., 128, pp. 142–150), the multiphase isothermal lattice Boltzmann equation (LBE) model and single phase thermal LBE (TLBE) model were described. In this work, by combining these two models, the thermal two-phase LBE model is proposed. The coupling of the two models is through a suitably defined body force term. Due to the external nature of this coupling, the new model will have the same stability as the isothermal two-phase model. The applicability of the model is shown by the numerical simulation results of a thermal two-phase flow system in a rectangular channel. Our preliminary studies show that different equations of state, variable wettability, gravity and buoyancy effects, and relatively high Rayleigh numbers can be readily simulated by this new model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):157-163. doi:10.1115/1.2137345.

Laboratory experiments and numerical simulations are performed to determine the accuracy and reproducibility of the falling-ball test for viscosity determination in Newtonian fluids. The results explore the wall and end effects of the containing cylinder and other possible sources that affect the accuracy and reproducibility of the falling ball tests. A formal error analysis of the falling-ball method, an evaluation of the relative merits of calibration and individual measurements, and an analysis of reproducibility in the falling-ball test are performed. Recommendations based on this study for improving both the accuracy and reproducibility of the falling-ball test are presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):164-169. doi:10.1115/1.2062747.

A set of experiments was performed to study flow pattern suppression in horizontal air-water pipe flow by means of surfactant additive. Results suggest that addition of the surfactant to the gas-liquid flow significantly reduces the occurrence of slug flow. In addition, previously unreported flow patterns were observed to exist between slug and dispersed bubble flows. It is concluded that new mechanisms for slug flow transition need to be considered.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):170-176. doi:10.1115/1.2137346.

We computed the flow of four gases (He, $N2$, $CO2$, and $SF6$) through a critical flow venturi (CFV) by augmenting traditional computational fluid dynamics (CFD) with a rate equation that accounts for $τrelax$, a species-dependent relaxation time that characterizes the equilibration of the vibrational degrees of freedom with the translational and rotational degrees of freedom. Conventional CFD $(τrelax=0)$ underpredicts the flow through small CFVs (throat diameter $d=0.593mm$) by up to 2.3% for $CO2$ and by up to 1.2% for $SF6$. When we used values of $τrelax$ from the acoustics literature, the augmented CFD underpredicted the flow for $SF6$ by only 0.3%, in the worst case. The augmented predictions for $CO2$ were within the scatter of previously published experimental data $(±0.1%)$. As expected, both conventional and augmented CFD agree with experiments for He and $N2$. Thus, augmented CFD enables one to calibrate a small CFV with one gas (e.g., $N2$) and to use these results as a flow standard with other gases (e.g., $CO2$) for which reliable values of $τrelax$ and the relaxing heat capacity are available.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):177-189. doi:10.1115/1.2137341.

An experimental and theoretical investigation of the flow at the outlet of a Francis turbine runner is carried out in order to elucidate the causes of a sudden drop in the draft tube pressure recovery coefficient at a discharge near the best efficiency operating point. Laser Doppler anemometry velocity measurements were performed for both axial and circumferential velocity components at the runner outlet. A suitable analytical representation of the swirling flow has been developed taking the discharge coefficient as independent variable. It is found that the investigated mean swirling flow can be accurately represented as a superposition of three distinct vortices. An eigenvalue analysis of the linearized equation for steady, axisymmetric, and inviscid swirling flow reveals that the swirl reaches a critical state precisely (within 1.3%) at the discharge where the sudden variation in draft tube pressure recovery is observed. This is very useful for turbine design and optimization, where a suitable runner geometry should avoid such critical swirl configuration within the normal operating range.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Fluids Eng. 2005;128(1):190-195. doi:10.1115/1.2137348.

Since knowledge on hydrodynamic torque of a butterfly valve is very important for butterfly valve design, its hydrodynamic torque is investigated theoretically. For this, a recently developed two-dimensional butterfly valve model is solved through the free-streamline theory with a newly devised iterative scheme and the resulting two-and three-dimensional torque coefficients are compared with previous theoretical results based on the conventional butterfly valve model and experiments. Comparison shows that the improvement due to the new butterfly valve model is marginal. That is, the three-dimensional torque coefficient is well represented by the new model. Otherwise, the two-dimensional torque coefficient is well predicted by the conventional model. In spite this fact, the present results can be used in further researches on butterfly valves because the improved butterfly valve model is mathematically correct and reflects physical reality more correctly than the conventional valve model.

Topics: Torque , Valves
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):196-198. doi:10.1115/1.2137347.
Shah, R. K., and London, A. L., 1978, Supplement 1: “ Laminar Flow Forced Convection in Ducts,” Advances in Heat Transfer, Academic Press, New York, pp. 41–42, 168–169, 287–289.Guide to the Expression of Uncertainty in Measurements, 1993, ISO/IEC/OIML/BIPM, Int. Organization for Standardization (ISO), Switzerland (1st ed.).Beavers, G. S., Sparrow, E. M., and Magnuson, R. A., 1970, “ Experiments on the Breakdown of Laminar Flow in a Parallel-Plate Channel,” Int. J. Heat Mass TransferIJHMAK 0017-9310, 13, pp. 809–815.Sparrow, E. M., and Lin, S. H., 1964, “ The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts,” J. Basic Eng.JBAEAI 0021-9223, 86, pp. 827–834.Chen, R.-Y., 1973, “ Flow in the Entrance Region at Low Reynolds Number,” ASME Trans. J. Fluids Eng.JFEGA4 0098-2202, 95, pp. 153–158.Shah, R. K., 1978, “ A Correlation for Laminar Hydrodynamic Entry Length Solutions for Circular and Noncircular Ducts,” ASME Trans. J. Fluids Eng.JFEGA4 0098-2202, 100, pp. 177–179.Atkinson, B., Brockleband, M. P., Card, C. H., and Smith, J. M., 1969, “ Low Reynolds Number Developing Flows,” AIChE J.AICEAC 0001-1541[[XSLOpenURL/10.1002/aic.690150414]], 15, pp. 548–553.Heaton, H. S., Reynolds, W. C., and Kays, W. M., 1961, “ Heat Transfer in Annular Passages. Simultaneous Development of Velocity and Temperature Fields in Laminar Flow,” Int. J. Heat Mass TransferIJHMAK 0017-9310[[XSLOpenURL/10.1016/0017-9310(64)90006-7]], 7, pp. 763–781.Coney, J. E. R., and El-Shaarawi, M. A. I., 1975, “ Developing Laminar Radial Velocity Profiles and Pressure Drop in the Entrance Region of Concentric Annuli,” Nucl. Sci. Eng.NSENAO 0029-5639, 57, pp. 169–174.
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2005;128(1):199-201. doi:10.1115/1.2137349.

With the goal of intensifying turbulent free convection from heated vertical plates to cold gases, five binary gas mixtures are examined in this technical note. Helium (He) is chosen as the principal gas while xenon (Xe), nitrogen $(N2)$, oxygen $(O2)$, carbon dioxide $(CO2)$, and methane $(CH4)$ are the companion gases. From thermal physics, the thermophysical properties affecting turbulent free convection of binary gas mixtures are the viscosity $μmix$, the thermal conductivity $λmix$, the density $ρmix$, and the heat capacity at constant pressure $Cp,mix$. Invoking the similarity variable transformation, the system of two nonlinear differential equations is solved numerically by the shooting method and a fourth-order Runge-Kutta-Fehlberg algorithm. From the numerical temperature fields, the allied mean convection coefficients $h¯mix∕B$ changing with the molar gas composition $w$ in the $w$ domain [0, 1] are plotted in congruous diagrams for the five binary gas mixtures under study.

Commentary by Dr. Valentin Fuster

### MEMORIAM

J. Fluids Eng. 2006;128(1):202. doi:10.1115/1.2163048.
FREE TO VIEW

This special section of JFE is dedicated to Dr. Sankaraiyer Gopalakrishnan who unexpectedly passed away recently. Gopal, as we affectionately called him, served the Fluids Engineering Division and ASME with great distinction over many years in various capacities. We appreciate his commitment and service even more considering Gopal's responsibilities as Vice President of Flowserve Corporation in California. He was an uplifting force in moving the Division forward. His wise counsel and guidance will be missed by all who grew accustomed to his presence at the meetings of the Division. He was a dignified gentleman, a deeply caring human being, and a dear friend. Our deepest sympathies are with his family. We miss him and we wish him well in his journey beyond.

Commentary by Dr. Valentin Fuster

### ERRATA

J. Fluids Eng. 2006;128(1):203. doi:10.1115/1.2160104.
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Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;128(1):204. doi:10.1115/1.2162007.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster