Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2002;124(1):2-3. doi:10.1115/1.1447925.

 Stochastic simulation of flow past a vibrating cylinder with a noisy inflow. Shown is the instantaneous pressure distribution on the cylinder. The error band is shown by gray and the deterministic and mean stochastic solutions are superimposed on this polar plot. (Courtesy of Didier Lucor and Dongbin Xiu, Brown University).

Commentary by Dr. Valentin Fuster


J. Fluids Eng. 2001;124(1):4-10. doi:10.1115/1.1436090.

Verification of Calculations involves error estimation, whereas Verification of Codes involves error evaluation, from known benchmark solutions. The best benchmarks are exact analytical solutions with sufficiently complex solution structure; they need not be realistic since Verification is a purely mathematical exercise. The Method of Manufactured Solutions (MMS) provides a straightforward and quite general procedure for generating such solutions. For complex codes, the method utilizes Symbolic Manipulation, but here it is illustrated with simple examples. When used with systematic grid refinement studies, which are remarkably sensitive, MMS produces strong Code Verifications with a theorem-like quality and a clearly defined completion point.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):11-21. doi:10.1115/1.1436092.

This work presents a post-processing tool for the verification of steady-state fluid flow and heat transfer finite volume computations. It is based both on the generalized Richardson extrapolation and the Grid Convergence Index (GCI). The observed order of accuracy and a error band where the grid independent solution is expected to be contained are estimated. The results corresponding to the following two and three-dimensional steady-state simulations are post-processed: a flow inside a cavity with moving top wall, an axisymmetric turbulent flow through a compressor valve, a premixed methane/air laminar flat flame on a perforated burner, and the heat transfer from an isothermal cylinder enclosed by a square duct. Discussion is carried out about the certainty of the estimators obtained with the post-processing procedure. They have been shown to be useful parameters in order to assess credibility and quality to the reported numerical solutions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):22-28. doi:10.1115/1.1436091.

The accuracy of boundary-element methods for computing Stokes flow past boundaries with sharp corners where singularities occur is discussed. To resolve the singular behavior, a graded mesh of boundary elements whose length increases in a geometrical fashion with respect to distance from the corners according to a prescribed stretch ratio is used. Numerical results for two-dimensional Stokes flow past bodies with polygonal shapes reveal the existence of an optimal value of the stretch ratio for best accuracy in the computation of the force and torque. When the optimal value is used, fast convergence is achieved with respect to the number of boundary elements.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):29-41. doi:10.1115/1.1445139.

A general discussion of the quantification of uncertainty in numerical simulations is presented. A principal conclusion is that the distribution of solution errors is the leading term in the assessment of the validity of a simulation and its associated uncertainty in the Bayesian framework. Key issues that arise in uncertainty quantification are discussed for two examples drawn from shock wave physics and modeling of petroleum reservoirs. Solution error models, confidence intervals and Gaussian error statistics based on simulation studies are presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):42-50. doi:10.1115/1.1445138.

This paper presents a method for the propagation of uncertainty, modeled in a probabilistic framework, through a model-based simulation of rainflow on a rough terrain. The adopted model involves a system of conservation equations with associated nonlinear state equations. The topography, surface runoff coefficient, and precipitation data are all modeled as spatially varying random processes. The Karhunen-Loeve expansion is used to represent these processes in terms of a denumerable set of random variables. The predicted state variables in the model are identified with their coordinates with respect to the basis formed by the Polynomial Chaos random variables. A system of linear algebraic deterministic equations are derived for estimating these coordinates.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):51-59. doi:10.1115/1.1436089.

We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expansion, which was first introduced by N. Wiener (1938) and employs the Hermite polynomials (a subset of the Askey scheme) as the basis in random space. The algorithm is first applied to second-order oscillators to demonstrate convergence, and subsequently is coupled to incompressible Navier-Stokes equations. Error bars are obtained, similar to laboratory experiments, for the pressure distribution on the surface of a cylinder subject to vortex-induced vibrations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):60-69. doi:10.1115/1.1446068.

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 1-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first-and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):70-80. doi:10.1115/1.1448332.

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations—Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation—relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):81-90. doi:10.1115/1.1445797.

Computations of the time-averaged and phase-averaged fluid flow and heat transfer based on large eddy simulation (LES) are presented for turbulent flows past a square cylinder with and without a nearby wall at a fixed Reynolds number of 2.2×104. The finite-volume technique was used to solve the time-dependent filtered compressible Navier-Stokes equations with a dynamic subgrid-scale turbulence model, and the numerical fluxes were computed using alternating in time the second-order, explicit MacCormack’s and the modified Godunov’s scheme. Results show some improvements in predicting the streamwise evolutions of the long-time-averaged streamwise mean velocity and total fluctuation intensity along the centerline over those predicted by using Reynolds stress models. A better overall centerline streamwise mean velocity distribution is also predicted by the present LES than by other LES. The wall proximity effect is studied through the comparison of turbulent wake flow past one free standing cylinder and one with a nearby wall, and is illustrated by the phase-averaged spanwise vorticity components and the vortex celerity of spanwise vortices. Moreover, documentation is given on the mechanisms responsible for the augmentation of heat transfer through the spanwise and longitudinal vortices as well as periodic and random fluctuations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):91-101. doi:10.1115/1.1431545.

Interactions between surface waves and underlying viscous wake are investigated for a turbulent flow past a free surface piercing circular cylinder at Reynolds number Re=2.7×104 using large eddy simulation (LES). The computations have been performed for three Froude numbers Fr=0.2, 0.5 and 0.8 in order to examine the influence of the Froude number. A second-order finite volume method coupled with a fractional step method is used for solving the grid-filtered incompressible Navier-Stokes equations. The computational results are found to be in good agreement with the available experimental data. At low Froude numbers Fr=0.2 and 0.5, the amplitude of generated surface wave is small and the influence on the wake is not evident. On the other hand, strong wave-wake interactions are present at Fr=0.8, when the generated free surface wave is very steep. It is shown that structures of the underlying vortical flow correlate closely with the configuration of the free surface. Computational results show presence of a recirculation zone starting at the point where the surface slope changes discontinuously. Above this zone the surface elevation fluctuates intensively. The computed intensity of the surface fluctuation is in good agreement with the measurements. It is also shown that the periodic vortex shedding is attenuated near the free surface at a high Froude number. The region in which the periodic vortex shedding is hampered extends to about one diameter from the mean water level. It is qualitatively shown that the separated shear layers are inclined outward near the free surface due to the generation of the surface waves. This change in the relation between two shear layers is suggested to be responsible for the attenuation of the periodic vortex shedding.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):102-107. doi:10.1115/1.1431546.

The recently proposed multi-environment model, R. O. Fox, 1998, “On the Relationship between Lagrangian Micromixing Models and Computational Fluid Dynamics,” Chem. Eng. Proc., Vol. 37, pp. 521–535. J. Villermaux and J. C. Devillon, 1994, “A Generalized Mixing Model for Initial Contacting of Reactive Fluids,” Chem. Eng. Sci., Vol. 49, p. 5127, provides a new category of modeling techniques that can be employed to resolve the turbulence-chemistry interactions found in reactive flows. By solving the Eulerian transport equations for volume fractions and chemical species simultaneously, the local concentrations of chemical species in each environment can be obtained. Assuming micromixing occurs only in phase space, the well-known IEM (interaction by exchange with the mean) model can be applied to close the micromixing term. This simplification allows the model to use micromixing timescales obtained from more sophisticated models and can be applied to any number of environments. Although the PDF shape doesn’t change under this assumption, the interaction between turbulence and chemistry can be resolved up to the second moments without any ad-hoc assumptions for the mean reaction rates. Furthermore, the PDF shape is found to have minimal effect on mean reaction rates for incompressible turbulent reacting flows. In this formulation, a spurious dissipation term arises in the transport equation of the scalar variances due to the use of Eulerian transport equations. A procedure is proposed to eliminate this spurious term. The model is applied to simulate the experiment of S. Komori, et al., 1993, “Measurements of Mass Flux in a Turbulent Liquid Flow With a Chemical Reaction,” AIChE J., Vol. 39, pp. 1611–1620, for a reactive mixing layer and the experiment of K. Li and H. Toor, 1986, “Turbulent Reactive Mixing With a Series Parallel reaction: Effect of Mixing on Yield,” AIChE J., Vol. 32, pp. 1312–1320, with a two-step parallel/consecutive reaction. The results are found to be in good agreement with the experimental data of Komori et al. and the PDF simulation of K. Tsai and R. Fox, 1994, “PDF Simulation of a Turbulent Series-Parallel Reaction in an Axisymmetric Reactor,” Chem. Eng. Sci., Vol. 49, pp. 5141–5158, for the experiment of Li and Toor. The resulting model is implemented in the commercial CFD code, FLUENT,1 and can be applied with any number of species and reactions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):108-117. doi:10.1115/1.1446067.

New fundamental measurements are presented for the transition process in flat plate boundary layers downstream of two-dimensional square ribs. By use of laser Doppler anemometry (LDA) and a large Matched-Index-of-Refraction (MIR) flow system, data for wall-normal fluctuations and Reynolds stresses were obtained in the near wall region to y+<0.1 in addition to the usual mean streamwise velocity component and its fluctuation. By varying velocity and rib height, the experiment investigated the following range of conditions: k+=5.5 to 21, 0.3<k/δ1<1,180<Rek<740,6×104<Rex,k<1.5×105,ReΘ660,−125<(x−xk)/k<580. Consequently, results covered boundary layers which retained their laminar characteristics through those where a turbulent boundary layer was established shortly after reattachment beyond the forcing rib. For “large” elements, evolution of turbulent statistics of the viscous layer for a turbulent boundary layer (y+<∼30) was rapid even in flows where the mean velocity profile still showed laminar behavior.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):118-126. doi:10.1115/1.1431269.

The near-wall physics of a planar, shear-driven, 3-D turbulent boundary layer with varying strengths of crossflow are examined. Flow visualization data reveals a reduction of mean streak length by as much as 50% with increasing spanwise shear. Power spectra of velocity confirm this shift towards higher temporal frequencies, corresponding to decreased streamwise length scales. PIV measurements indicate a significant modification of the inner region of the boundary layer with increasing spanwise shear. Streamwise velocity profiles exhibit an increasing velocity deficit with increased crossflow. Increased levels of the normal Reynolds stresses u′2 and v′2 and an increase in the uv Reynolds shear stress are also observed. Modifications in the spanwise and transverse vorticity were also observed at higher shear rates.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):127-135. doi:10.1115/1.1445141.

A turbulent boundary layer structure which develop over a k-type rough wall displays several differences with those found on a smooth surface. The magnitude of the wake strength depends on the wall roughness. In the near-wall region, the contribution to the Reynolds shear stress fraction, corresponding to each event, strongly depends on the wall roughness. In the wall region, the diffusion factors are influenced by the wall roughness where the sweep events largely dominate the ejection events. This trend is reversed for the smooth-wall. Particle Image Velocimetry technique (PIV) is used to obtain the fluctuating flow field in the turbulent boundary layer in order to confirm this behavior. The energy budget analysis shows that the main difference between rough- and smooth-walls appears near the wall where the transport terms are larger for smooth-wall. Vertical and longitudinal turbulent flux of the shear stress on both smooth and rough surfaces is compared to those predicted by a turbulence model. The present results confirm that any turbulence model must take into account the effects of the surface roughness.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):136-142. doi:10.1115/1.1436096.

An experimental investigation was undertaken to study the effect of various fences and vortex generator configurations in reducing the exit flow distortion and improving total pressure recovery in two-dimensional S-duct diffusers of different radius ratios. Detailed measurements including total pressure and velocity distribution, surface static pressure, skin friction, and boundary layer measurements were taken in a uniform inlet flow at a Reynolds number of 7.8×105. These measurements are presented here along with static pressure rise, distortion coefficient, and the transverse velocity vectors at the duct exit determined from the measured data. The results indicate that substantial improvement in static pressure rise and flow quality is possible with judicious deployment of fences and vortex generators.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):143-153. doi:10.1115/1.1428330.

All first-order spatial derivatives of the turbulent velocity fluctuations were measured using a pair of X hot-wire probes. Measurements were performed in the self-preserving region of a turbulent plane wake downstream of a cylinder and in an axisymmetric wake behind the sphere. Good spatial resolution of the measurements was ensured by choosing small values for the cylinder/sphere diameter and a low flow speed. Errors due to the finite hot-wire length and the wire and probe separation were analyzed using Wyngaard’s correction method. The derived corrections were verified experimentally. The measuring technique and the experimental results were systematically checked and compared with the results available in the literature. The assumptions of local isotropy and local axisymmetry were examined. Both investigated flows deviate only moderately from local isotropy and local axisymmetry. Support for the measured results is provided by plotting the data on an anisotropy invariant map. The budgets of the turbulent kinetic energy were computed from the measured data. In contrast to the results obtained in the plane wake, where the pressure transport is nearly negligible, in the axisymmetric wake it was found to play an important role and closely follows the estimate made by Lumley, uip/ρ≈−0.2q2ui.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):154-165. doi:10.1115/1.1431267.

This paper presents results obtained from a combined experimental and computational study of the flow field over a multi-element aerofoil with and without an advanced slat. Detailed measurements of the mean flow and turbulent quantities over a multi-element aerofoil model in a wind tunnel have been carried out using stationary and flying hot-wire (FHW) probes. The model configuration which spans the test section (600 mm×600 mm), is made of three parts: 1) an advanced (heel-less) slat, 2) a NACA 4412 main aerofoil and 3) a NACA 4415 flap. The chord lengths of the elements were 38, 250 and 83 mm, respectively. The results were obtained at a chord Reynolds number of 3×105 and a free Mach number of less than 0.1. The variations in the flow field are explained with reference to three distinct flow field regimes: attached flow, intermittent separated flow, and separated flow. Initial comparative results are presented for the single main aerofoil and the main aerofoil with a nondeflected flap at angles of attacks of 5, 10, and 15 deg. This is followed by the results for the three-element aerofoil with emphasis on the slat performance at angles of attack α=10, 15, 20, and 25 deg. Results are discussed both for a nondeflected flap f=0 deg) and a deflected flap f=25 deg). The measurements presented are combined with other related aerofoil measurements to explain the main interaction of the slat/main aerofoil and main aerofoil/flap both for nondeflected and deflected flap conditions. These results are linked to numerically calculated variations in lift and drag coefficients with angle of attack and flap deflection angle.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):166-175. doi:10.1115/1.1429638.

Flow-field interactions are studied in a high-through-flow, axial-flow transonic compressor using Digital Particle Image Velocimetry (DPIV). Measurement of instantaneous velocities in two-dimensional (2D) planes in the main flow direction allows characterization of the unsteadiness of spatial structures from an upstream blade row and their interaction with the downstream rotor. The measurement system is specially designed for a large transonic environment, which introduces conditions that differ from those generally encountered by traditional DPIV systems. Viewing windows on the compressor housing are used to allow optical access, and the design of a special optical probe permits laser-sheet delivery through one of the wake generators (WG). The system is synchronized with the blade passage and is remotely monitored and controlled. Through flow visualization and instantaneous and ensemble-averaged quantities, it clearly captures the interactions of the wake with the potential field of the rotor leading edge (LE) and its bow shock, vortex shedding, vortex-blade synchronization, wake chopping, and boundary-layer flow at the housing for several configurations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):176-181. doi:10.1115/1.1436093.

Fluid-induced rotordynamic forces produced by the fluid in an annular seal or in the leakage passage surrounding the shroud of a pump or turbine, are known to contribute substantially to the potential excitation forces acting on the rotor. The present research explores some of the important features of the equations governing bulk-flow models of these flows. This in turn suggests methods which might be used to solve these bulk-flow equations in circumstances where the linearized solutions may not be accurate. This paper presents a numerical method for these equations and discusses comparison of the computed results with experimental measurements for annular seals and pump leakage paths.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):182-185. doi:10.1115/1.1445140.

Droplet size distribution function and mean diameter formulas are derived using information theory. The effects of fuel droplet evaporation and coalescence within combustion chamber on the droplet size are emphasized in nonreactive diesel sprays. The size distribution function expressions at various spray axial cross sections are also formulated. The computations are compared with experimental data and KIVA-II code. A good agreement is obtained between numerical and experimental results. Droplet size distribution and mean diameter at various locations from injector exit and at various temperature conditions are predicted. The decreases of droplet number and variations of mean diameter are computed at downstream and higher temperature.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):186-193. doi:10.1115/1.1427689.

Cavitation inception on an E817 hydrofoil issued from an inverse calculus for ideal fluid has been numerically analyzed for speeds and scales inherent to both model test and full-scale marine conditions. The computations have been carried out with account to the Reynolds number effect on hydrofoil lift and combined effect of the Reynolds number and Weber number on the equilibrium of sheet cavities in the hydrofoil boundary layer. Different levels of scale effects for cavitation inception on suction and pressure sides of E817 hydrofoil are shown. Comparison with the scale effect of cavitation inception on conventional NACA-0012 hydrofoil has helped to explain this difference. Issues in blade design with sections similar to E817 are discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):194-204. doi:10.1115/1.1430668.

Water hammer transients in a pipe line with an entrapped air pocket are analyzed with three one-dimensional models of varying complexity. The most simple model neglects the influence of gas-liquid interface movement on wave propagation through the liquid region and assumes uniform compression of the entrapped noncondensable gas. In the most complex model, the full two-region wave propagation problem is solved for adjoining gas and liquid regions with time varying domains. An intermediate model which allows for time variation of the liquid domain, but assumes uniform gas compression, is also considered. Calculations are carried out for a wide range of initial system pressure ranging from 0.101 MPa (14.7 psia) to 6.89 MPa (1000 psia). A step increase in pressure equal to 5 times the initial system pressure is imposed at the pipe inlet and the pressure response of the system is investigated. Results show that time variation of the liquid domain and nonuniform gas compression can be neglected for initial air volumes comprising 5% or less of the initial pipe volume. The uniform compression model with time-varying liquid domain captures all of the essential features predicted by the full two-region model for the entire range of pressure and initial gas volume considered in the study, and it is the recommended model for analysis of waterhammer in pipe lines with entrapped air.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):205-214. doi:10.1115/1.1428327.

This paper reports the development of an experimentally validated model for pressure drop during intermittent flow of condensing refrigerant R134a in horizontal microchannels. Two-phase pressure drops were measured in five circular channels ranging in hydraulic diameter from 0.5 mm to 4.91 mm. For each tube under consideration, pressure drop measurements were first taken over the entire range of qualities from 100% vapor to 100% liquid. In addition, the tests for each tube were conducted for five different refrigerant mass fluxes between 150 kg/m2 -s and 750 kg/m2 -s. Results from previous work by the authors on condensation flow mechanisms in microchannel geometries were then used to identify data that corresponded to the intermittent flow regime. A pressure drop model was developed for a unit cell in the channel based on the observed slug/bubble flow pattern for these conditions. The unit cell comprises a liquid slug followed by a vapor bubble that is surrounded by a thin, annular liquid film. Contributions of the liquid slug, the vapor bubble, and the flow of liquid between the film and slug to the pressure drop were included. Empirical data from the literature for the relative length and velocity of the slugs and bubbles, and relationships from the literature for the pressure loss associated with the mixing that occurs between the slug and film were used with assumptions about individual phase friction factors, to estimate the total pressure drop in each unit cell. A simple correlation for non-dimensional unit-cell length based on slug Reynolds number was then used to estimate the total pressure drop. The results from this model were on average within ±13.4% of the measured data, with 88% of the predicted results within ±25% of the 77 measured data points.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):215-226. doi:10.1115/1.1436097.

A numerical investigation on Glimm’s method as applied to water sloshing and impacting is carried out. Emphasis is given to the handling and predicting hydraulic jumps. The effects of the spatial and temporal discretizations are examined. Three shallow water problems, 1) dam-breaking problem, 2) water sloshing in a rolling tank, and 3) impact of breaking of a water reservoir, are studied. It is shown numerically that Glimm’s method is stable and converged solutions can be obtained. The characteristics of the hydraulic jumps are well captured by the numerical calculations. The numerical results are in good agreement with either analytical solutions or experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):227-234. doi:10.1115/1.1427927.

A detailed computational investigation into the periodic two-dimensional performance of a NACA 0012 section fitted with 2 and 4 percent h/c Gurney flaps operating at a Reynolds number of 0.85×106 is presented. The aim of the work was to determine the suitability of the incompressible Reynolds-averaged Navier-Stokes (RANS) formulation in modeling the vortex shedding experienced by lifting sections with blunt, sharp edged features. In particular, whether under-converged steady state calculations could be used for section design performance evaluation in place of the computationally intensive time accurate flow simulations. Steady, periodic, and time-averaged two-dimensional lift and drag coefficients, as well as vortex shedding frequency, were predicted and compared with the available experimental data. Reasonable agreement was found, once sufficiently fine grids had been generated, and the correct time step determined for the time accurate simulations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):235-240. doi:10.1115/1.1445137.

The aim of this study was to investigate first departures from laminar conditions in both impulsively started and steady pipe entrance flows. Wall shear stress measurements were conducted of transition in impulsively started pipe flows with large disturbances. These results were reconciled in a framework of displacement thickness Reynolds number and a velocity profile shape parameter, with existing measurements of pipe entrance flow instability, pipe-Poiseuille and boundary layer flow responses to large disturbances, and linear stability predictions. Limiting critical Reynolds number variations for each type of flow were thus inferred, corresponding to the small and gross disturbance limits respectively. Consequently, insights have been provided regarding the effect of disturbance levels on the stability of both steady and unsteady pipe flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):241-250. doi:10.1115/1.1429636.

A thorough numerical investigation was performed for the two-dimensional convective heat transfer of a circular cylinder in a Couette flow close to a wall in order to study the hot-wire near-wall correction. A finite-volume Navier-Stokes solver enhanced by local block refinement and multigrid acceleration guaranteed highly accurate and efficient computational results. Unlike all previous numerical simulations, a more realistic model was used in the present study by taking the heat transfer in the solid wall into account to bridge the discrepancy between the previous theoretical models and the real situation. The computed results from the present investigation show good agreement with experimental data in the literature. Reference correction curves for hot-wire anemometers with respect to different wall materials (e.g., aluminum, glass, Perspex, air, etc.) were obtained.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):251-262. doi:10.1115/1.1445796.

In this paper, new finite-difference based detailed general methodologies are presented for numerical simulation of injection mold-filling during the production of a long cylindrical object. The polymer considered is low density polyethylene (LDPE) following power-law viscosity model for nonzero shear rate zone. However, where shear rate becomes zero, “zero-shear viscosity” value has been used. Three cases have been considered, namely; (i) isothermal filling at constant injection pressure; (ii) isothermal filling at constant flow rate and; (iii) nonisothermal filling at constant flow rate. For (iii), the viscosity of LDPE is also a function of temperature. The material of the mold is steel. For the nonisothermal filling, the concept of melt-mold thermal contact resistance coefficient has been incorporated into the model. The length and diameter of the body in all three cases have been taken as 0.254 m and 0.00508 m, respectively. The results show excellent agreement with the corresponding analytical solutions for the first two cases showing the correctness of the numerical method. The simulation results for nonisothermal filling are reported for the first time for this particular geometry and lend insight into various important aspects of mold-filling including injection pressure versus time, and effects of flow rates on melt temperature fields at various axial locations as well as on frozen skin layer.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):263-272. doi:10.1115/1.1429637.

Open-cell aluminum foams were investigated using water to determine their hydraulic characteristics. Maximum fluid flow velocities achieved were 1.042 m/s. The permeability and form coefficient varied from 2.46×10−10 m2 and 8701 m−1 to 3529×10−10 m2 and 120 m−1, respectively. It was determined that the flowrate range influenced these calculated parameters, especially in the transitional regime where the permeability based Reynolds number varied between unity and 26.5. Beyond the transition regime where ReK≳30, the permeability and form coefficient monotonically approached values which were reported as being calculated at the maximum flow velocities attained. The results obtained in this study are relevant to engineering applications employing metal foams ranging from convection heat sinks to filters and flow straightening devices.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):273-278. doi:10.1115/1.1430669.

Creeping flow through a sudden contraction/expansion in an axisymmetric pipe is studied. Sampson’s solution for flow through a circular orifice in an infinite wall is used to derive an approximation for the excess pressure drop due to a sudden contraction/expansion in a pipe with a finite expansion ratio. The accuracy of this approximation obtained is verified by comparing its results to finite-element simulations and other previous numerical studies. The result can also be extended to a thin annular obstacle in a circular pipe. The “equivalent length” corresponding to the excess pressure drop is found to be barely half the radius of the smaller tube.

Commentary by Dr. Valentin Fuster


J. Fluids Eng. 2001;124(1):279-280. doi:10.1115/1.1436095.

In this note we present a proof showing that the contribution from the extra stress tensor to the normal component of the stress on the surface of a moving rigid body in an incompressible Oldroyd-B fluid is zero.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2001;124(1):280-283. doi:10.1115/1.1427926.

Variable pitch axial flow fans are widely used in industrial applications to satisfy variable operating conditions. The change of the blade pitch leads to a different rotor geometry and has a major influence on the unsteady operation of the machine. In this work, an experimental research on an axial flow fan with variable pitch blades has been carried out. First of all, the fan performance curves has been obtained. Then the flow field has been measured at ten radial locations both at the inlet and exit rotor plane using hot wire anemometry. Velocity components and total unsteadiness were determined and analyzed in order to characterize the influence of pitch blade and operating conditions on the flow structure.

J. Fluids Eng. 2001;124(1):284-286. doi:10.1115/1.1436094.

The findings of a numerical solution of the flowfield downstream of a six-plate array are compared to a previous experimental study. In both studies, the chord-to-thickness ratio, c/t, is 6.67, the Reynolds number, Re, is 500, and the spacing-to-thickness ratio, H/t, is 3.67. Consistent with experimental results, the numerical simulation shows that the recirculation zones formed at the trailing edges of the surfaces that form channels in the plate array are in-phase. Also consistent, they are nearly 180 deg out-of-phase with the recirculation zones formed at the trailing edges of the surfaces of adjacent channels. Comparison of the locations of recirculation zones and peaks in the downstream variation in axial velocity confirms that “vortex pumping” is described by 1) the axial velocity increase on the midplane of the channel in the region where the separation between pairs of recirculation zones is a minimum and 2) the axial velocity decrease in the region where the separation between pairs of recirculation zones is a maximum.

J. Fluids Eng. 2001;124(1):287-290. doi:10.1115/1.1431268.

A computational method is used to analyze the viscous flow in the spiral grooves of the molecular drag pump of Holweck type. The flow is assumed in the slip flow regime and, thus, the slip boundary condition is imposed at walls. Tests are conducted to examine the effects of clearance gap, spiral angle, channel height, number of channels, and rotating speed. The appearance of clearance brings about lower pressure gradient between side walls of the channel and, thus, reduces the pressure rise in the channel. Testing on spiral angle and channel height indicates that these parameters need to be optimized to achieve better performance. Results also reveal that increase of rotating speed is an effective way to promote compression ratio. In calculations, pressure rise is enhanced when the number of channel is decreased. However, it should be understood that by reducing channel number the cross-sectional area of the channel is decreased, which has the effects of reducing the pressure rise.

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