Showing papers in "Journal of Fluids Engineering-transactions of The Asme in 2009"

Factors of Safety for Richardson Extrapolation

Abstract: A factor of safety method for quantitative estimates of grid-spacing and time-step uncertainties fbr solution verification is developed. It removes the two deficiencies of the grid convergence index and correction factor methods, namely, unreasonably small uncertainty when the estimated order of accuracy using the Richardson extrapolation method is greater than the theoretical order of accuracy and lack of statistical evidence that the interval of uncertainty at the 95% confidence level bounds the comparison error. Different error estimates are evaluated using the effectivity index. The uncertainty estimate builds on the correction factor method, but with significant improvements. The ratio of the estimated order of accuracy and theoretical order of accuracy P instead of the correction factor is used as the distance metric to the asymptotic range. The best error estimate is used to construct the uncertainty estimate. The assumption that the factor of safety is symmetric with respect to the asymptotic range was removed through the use of three instead of two factor of safety coefficients. The factor of safety method is validated using statistical analysis of 25 samples with different sizes based on 17 studies covering fluids, thermal, and structure disciplines. Only the factor of safety method, compared with the grid convergence index and correction factor methods, provides a reliability larger than 95% and a lower confidence limit greater than or equal to 1.2 at the 95% confidence level for the true mean of the parent population of the actual factor of safety. This conclusion is true for different studies, variables, ranges of P values, and single P values where multiple actual factors of safety are available. The number of samples is large and the range of P values is wide such that the factor of safety method is also valid for other applications including results not in the asymptotic range, which is typical in industrial and fluid engineering applications. An example for ship hydrodynamics is provided.

Experimental Investigation of Vortex-Induced Vibration in One and Two Dimensions With Variable Mass, Damping, and Reynolds Number

Abstract: Measurements are made of vortex-induced vibration of an elastically supported circular cylinder in water with reduced velocity (U/f n D) from 2 to 12, damping factors (ξ) from 0.2% to 40% of critical damping, mass ratios (m/ρD 2 ) from π/2 to π/17, and transverse, inline, and combined inline and transverse motions at Reynolds numbers up to 150,000. Effects of mass, damping, Reynolds number, and strakes on vortex-induced vibration amplitude, frequency, entrainment, and drag are reported.

Assessment Measures for Engineering LES Applications

Abstract: Anticipating that large eddy simulations will increasingly become the future engineering tool for research, development, and design, it is deemed necessary to formulate some quality assessment measures that can be used to judge the resolution of turbulent scales and the accuracy of predictions. In this context some new and refined measures are proposed and compared with those already published by the authors in the common literature. These measures involve (a) fraction of the total turbulent kinetic energy, (b) relative grid size with respect to Kolmogorov or Taylor scales, and (c) relative effective subgrid/numerical viscosity with respect to molecular viscosity. In addition, an attempt is made to segregate the contributions from numerical and modeling errors. Proposed measures are applied to various test cases and validated against fully resolved large eddy simulation and/or direct numerical simulation whenever possible.

Pressure Drop in Laminar Developing Flow in Noncircular Ducts: A Scaling and Modeling Approach

Abstract: A detailed review and analysis of the hydrodynamic characteristics of laminar developing and fully developed flows in noncircular ducts is presented. New models are proposed, which simplify the prediction of the friction factor―Reynolds product f Re for developing and fully developed flows in most noncircular duct geometries found in heat exchanger applications. By means of scaling analysis it is shown that complete problem may be easily analyzed by combining the asymptotic results for the short and long ducts. Through the introduction of a new characteristic length scale, the square root of cross-sectional area, the effect of duct shape has been minimized. The new model has an accuracy of ±10% or better for most common duct shapes when nominal aspect ratios are used, and ±3% or better when effective aspect ratios are used. Both singly and doubly connected ducts are considered.

2D Numerical Simulations of Blade-Vortex Interaction in a Darrieus Turbine

Abstract: The aim of this work is to provide a detailed two-dimensional numerical analysis of the physical phenomena occurring during dynamic stall of a Darrieus wind turbine. The flow is particularly complex because as the turbine rotates, the incidence angle and the blade Reynolds number vary, causing unsteady effects in the flow field. At low tip speed ratio, a deep dynamic stall occurs on blades, leading to large hysteresis lift and drag loops (primary effects). On the other hand, high tip speed ratio corresponds to attached boundary layers on blades (secondary effects). The optimal efficiency occurs in the middle range of the tip speed ratio where primary and secondary effects cohabit. To prove the capacity of the modeling to handle the physics in the whole range of operating condition, it is chosen to consider two tip speed ratios (λ=2 and λ=7), the first in the primary effect region and the second in the secondary effect region. The numerical analysis is performed with an explicit, compressible RANS k-ω code TURBFLOW , in a multiblock structured mesh configuration. The time step and grid refinement sensitivities are examined. Results are compared qualitatively with the visualization of the vortex shedding of Brochier (1986, "Water channel experiments of dynamic stall on Darrieus wind turbine blades," J. Propul. Power, 2(5), pp. 445-449). Hysteresis lift and drag curves are compared with the data of Laneville and Vitecoq (1986, "Dynamic stall: the case of the vertical axis wind turbine," Prog. Aerosp. Sci., 32, pp. 523-573).

Efficiency Improvement of Centrifugal Reverse Pumps

Abstract: Pumps as turbines have been successfully applied in a wide range of small hydrosites in the world. Since the overall efficiency of these machines is lower than the overall efficiency of conventional turbines, their application in larger hydrosites is not economical. Therefore, the efficiency improvement of reverse pumps is essential. In this study, by focusing on a pump impeller, the shape of blades was redesigned to reach a higher efficiency in turbine mode using a gradient based optimization algorithm coupled by a 3D Navier-Stokes flow solver. Also, another modification was done by rounding the blades' leading edges and hub/shroud interface in turbine mode. After each modification, a new impeller was manufactured and tested in the test rig. The efficiency was improved in all measured points by the optimal design of the blade and additional modification as the rounding of the blade's profile in the impeller inlet and hub/shroud inlet edges in turbine mode. Experimental results confirmed the numerical efficiency improvement in all measured points. This study illustrated that the efficiency of the pump in reverse operation can be improved just by impeller modification.

Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials

Abstract: A phenomenological analysis of the cavitation erosion process of ductile materials is proposed. On the material side, the main parameters are the thickness of the hardened layer together with the conventional yield strength and ultimate strength. On the fluid side, the erosive potential of the cavitating flow is described in a simplified way using three integral parameters: rate, mean amplitude, and mean size of hydrodynamic impact loads. Explicit equations are derived for the computation of the incubation time and the steady-state erosion rate. They point out two characteristic scales. The time scale, which is relevant to the erosion phenomenon, is the covering time-the time necessary for the impacts to cover the material surface-whereas the pertinent length scale for ductile materials is the thickness of the hardened layer. The incubation time is proportional to the covering time with a multiplicative factor, which strongly depends on flow aggressiveness in terms of the mean amplitude of impact loads. As for the erosion rate under steady-state conditions, it is scaled by the ratio of the thickness of hardened layers to the covering time with an additional dependence on flow aggressiveness, too. The approach is supported by erosion tests conducted in a cavitation tunnel at a velocity of 65 m/s on stainless steel 316 L. Flow aggressiveness is inferred from pitting tests. The same model of material response that was used for mass loss prediction is applied to derive the original hydrodynamic impact loads due to bubble collapses from the geometric features of the pits. Long duration tests are performed in order to determine experimentally the incubation time and the mean depth of penetration rate and to validate the theoretical approach.

Improvements of Particle Near-Wall Velocity and Erosion Predictions Using a Commercial CFD Code

Abstract: The determination of a representative particle impacting velocity is an important component in calculating solid particle erosion inside pipe geometry. Currently, most commercial computational fluid dynamics (CFD) codes allow the user to calculate particle trajectories using a Lagrangian approach. Additionally, the CFD codes calculate particle impact velocities with the pipe walls. However, these commercial CFD codes normally use a wall function to simulate the turbulent velocity field in the near-wall region. This wall-function velocity field near the wall can affect the small particle motion in the near-wall region. Furthermore, the CFD codes assume that particles have zero volume when particle impact information is being calculated. In this investigation, particle motions that are simulated using a commercially available CFD code are examined in the near-wall region. Calculated solid particle erosion patterns are compared with experimental data to investigate the accuracy of the models that are being used to calculate particle impacting velocities. While not considered in particle tracking routines in most CFD codes, the turbulent velocity profile in the near-wall region is taken into account in this investigation, and the effect on particle impact velocity is investigated. The simulation results show that the particle impact velocity is affected significantly when near-wall velocity profile is implemented. In addition, the effects of particle size are investigated in the near-wall region of a turbulent flow in a 90 deg sharp bend. A CFD code is modified to account for particle size effects in the near-wall region before and after the particle impact. It is found from the simulations that accounting for the rebound at the particle radius helps avoid nonphysical impacts and reduces the number of impacts by more than one order-of-magnitude for small particles (25 μm) due to turbulent velocity fluctuations. For large particles (256 μm), however, nonphysical impacts are not observed in the simulations. Solid particle erosion is predicted before and after introducing these modifications, and the results are compared with experimental data. It is shown that the near-wall modification and turbulent particle interactions significantly affect the simulation results. Modifications can significantly improve the current CFD-based solid particle erosion modeling.

Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine

Abstract: Under part-load conditions, a Francis turbine often suffers from very severe low-frequency and large-amplitude pressure fluctuation, which is caused by the unsteady motion of vortices (known as "vortex ropes") in the draft tube This paper first reports our numerical investigation of relevant complex flow phenomena in the entire draft tube, based on the Reynolds-averaged Navier-Stokes (RANS) equations We then focus on the physical mechanisms underlying these complex and somewhat chaotic flow phenomena of the draft-tube flow under a part-load condition The flow stability and robustness are our special concern, since they determine what kind of control methodology will be effective for eliminating or alleviating those adverse phenomena Our main findings about the flow behavior in the three segments of the draft tube, ie, the cone inlet, the elbow segment, and the outlet segment with three exits, are as follows (1) In the cone segment, we reconfirmed a previous finding of our research group based on the turbine's whole-flow RANS computation that the harmful vortex rope is an inevitable consequence of the global instability of the swirling flow We further identified that this instability is caused crucially by the reversed axial flow at the inlet of the draft tube (2) In the elbow segment, we found a reversed flow continued from the inlet cone, which evolves to slow and chaotic motion There is also a fast forward stream driven by a localized favorable axial pressure gradient, which carries the whole mass flux downstream The forward stream and reversed flow coexist side-by-side in the elbow, with a complex and unstable shear layer in between (3) In the outlet segment with three exits, the forward stream always goes through a fixed exit, leaving the other two exits with a chaotic and low-speed fluid motion Based on these findings, we propose a few control principles to suppress the reversed flow and to eliminate the harmful helical vortex ropes Of the methods we tested numerically, a simple jet injection in the inlet is proven successful

Pressure Drop in Rectangular Microchannels as Compared With Theory Based on Arbitrary Cross Section

Abstract: Pressure driven liquid flow through rectangular cross-section microchannels is investigated experimentally. Polydimethylsiloxane microchannels are fabricated using soft lithography. Pressure drop data are used to characterize the friction factor over a range of aspect ratios from 0.13 to 0.76 and Reynolds number from 1 to 35 with distilled water as working fluid. Results are compared with the general model developed to predict the fully developed pressure drop in arbitrary cross-section microchannels. Using available theories, effects of different losses, such as developing region, minor flow contraction and expansion, and streaming potential on the measured pressure drop, are investigated. Experimental results compare well with the theory based on the presure drop in channels of arbitrary cross section.

Experimental Evidence of Hydroacoustic Pressure Waves in a Francis Turbine Elbow Draft Tube for Low Discharge Conditions

Abstract: The complex three-dimensional unsteady flow developing in the draft tube of a Francis turbine is responsible for pressure fluctuations, which could prevent the whole hydropower plant from operating safely. Indeed, the Francis draft tube is subjected to inlet swirling flow, divergent cross section, and the change of flow direction. As a result, in low discharge off-design operating conditions, a cavitation helical vortex, so-called the vortex rope develops in the draft tube and induces pressure fluctuations in the range of 0.2–0.4 times the runner frequency. This paper presents the extensive unsteady wall pressure measurements performed in the elbow draft tube of a high specific speed Francis turbine scale model at low discharge and at usual plant value of the Thoma cavitation number. The investigation is undertaken for operating conditions corresponding to low discharge, i.e., 0.65–0.85 times the design discharge, which exhibits pressure fluctuations at surprisingly high frequency value, between 2 and 4 times the runner rotation frequency. The pressure fluctuation measurements performed with 104 pressure transducers distributed on the draft tube wall, make apparent in the whole draft tube a fundamental frequency value at 2.5 times the runner frequency. Moreover, the modulations between this frequency with the vortex rope precession frequency are pointed out. The phase shift analysis performed for 2.5 times the runner frequency enables the identification of a pressure wave propagation phenomenon and indicates the location of the corresponding pressure fluctuation excitation source in the elbow; hydroacoustic waves propagate from this source both upstream and downstream the draft tube.

Perspective: Validation—What Does It Mean?

Abstract: Ambiguities, inconsistencies, and recommended interpretations of the commonly cited definition of validation for computational fluid dynamics codes/models are examined. It is shown that the definition-deduction approach is prone to misinterpretation, and that bottom-up descriptions rather than top-down legalistic definitions are to be preferred for science-based engineering and journal policies, though legalistic definitions are necessary for contracts.

A Novel Explicit Equation for Friction Factor in Smooth and Rough Pipes

Abstract: 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.

Creation and Maintenance of Cavities Under Horizontal Surfaces in Steady and Gust Flows

Abstract: An experimental study of air supply to bottom cavities stabilized within a recess under a horizontal surface has been carried out in a specially designed water tunnel. The air supply necessary for creating and maintaining an air cavity in steady and gust flows has been determined over a wide range of speed. Flux-free ventilated cavitation at low flow speeds has been observed. Stable multiwave cavity forms at subcritical values of Froude number were also observed. It was found that the cross-sectional area of the air supply ducting has a substantial effect on the air demand. Air supply scaling laws were deduced and verified with the experimental data obtained.

Simulation of turbine blade trailing edge cooling

Abstract: The cause of overprediction of cooling efficiency by unsteady Reynolds averaged simulations of turbine blade trailing edge cooling flow is investigated. This is due to the deficiency in the level of unsteady coherent energy very near to the wall. Farther from the wall, the Reynolds averaged simulation produces the correct level of mixing. Eddy simulations of the instantaneous turbulent eddying produce a close agreement to data on film effectiveness. In particular, they reproduce the reduction in cooling effectiveness toward the trailing edge that has been seen in experiments. The scale adaptive simulation model of Menter and Egorov (2005, “A Scale-Adaptive Simulation Modeling Using Two-Equation Models ,” AIAA Paper No. 2005-1095) is invoked for the eddy simulations.

Detailed CFD Analysis of the Steady Flow in a Wells Turbine Under Incipient and Deep Stall Conditions

Abstract: This paper presents the results of the numerical simulations carried out to evaluate the performance of a high solidity Wells turbine designed for an oscillating water column wave energy conversion device. The Wells turbine has several favorable features (e.g., simplicity and high rotational speed) but is characterized by a relatively narrow operating range with high efficiency. The aim of this work is to investigate the flow-field through the turbine blades in order to offer a description of the complex flow mechanism that originates separation and, consequently, low efficiency at high flow-rates. Simulations have been performed by solving the Reynolds-averaged Navier―Stokes equations together with three turbulence models, namely, the Spalart―Allmaras, k-ω, and Reynolds-stress models. The capability of the three models to provide an accurate prediction of the complex flow through the Wells turbine has been assessed in two ways: the comparison of the computed results with the available experimental data and the analysis of the flow by means of the anisotropy invariant maps. Then, a detailed description of the flow at different flow-rates is provided, focusing on the interaction of the tip-leakage flow with the main stream and enlightening its role on the turbine performance.

Numerical and Experimental Investigations of Steam Condensation in LP Part of a Large Power Turbine

Abstract: This paper presents the experimental investigations of steam flow with condensation in the blading system of the low-pressure (LP) part of a 360 MW turbine. To this end, special probes were used, which provided flow visualization opportunities including localization of the front of condensation, determining distributions of pressure, temperature, velocity, and flow angle in the inter-row gaps, measurements of water droplet concentration and sizes. The measurements have proved that the condensation process in the LP turbine might be of heterogeneous nature, depending on the concentration of chemical impurities in steam. The measurement results constituted the basis for computational fluid dynamics (CFD) flow calculations, which were performed using the time-dependent 3D Reynolds averaged Navier-Stokes equations coupled with two-equation turbulence model (k-ω SST) and additional conservation equations for the liquid phase. The set of governing equations has been closed by a "local" real gas equation of state. The condensation phenomena were modeled on the basis of the classical nucleation theory. The heterogeneous condensation model on the insoluble and soluble impurities was implemented into presented CFD code. The system of governing equations was solved by means of a finite volume method on a multiblock structured grid. The obtained numerical results and experimental data were compared and discussed.

Performance and Radial Loading of a Mixed-Flow Pump Under Non-Uniform Suction Flow

Abstract: Many centrifugal pumps have a suction velocity profile, which is nonuniform, either by design like in double-suction pumps, sump pumps, and in-line pumps, or as a result of an installation close to an upstream disturbance like a pipe bend. This paper presents an experimental study on the effect of a nonuniform suction velocity profile on performance of a mixed-flow pump and hydrodynamic forces on the impeller. In the experiments, a newly designed dynamometer is used, equipped with six full Wheatstone bridges of strain gauges to measure the six generalized force components. It is placed in between the shaft of the pump and the impeller and corotates with the rotor system. A high accuracy is obtained due to the orthogonality of bridge positioning and the signal conditioning electronics embedded within the dynamometer. The suction flow distribution to the pump is adapted using a pipe bundle situated in the suction pipe. Results of measurements show the influence of the suction flow profile and blade interaction on pump performance and forces. Among the most important observations are a backward whirling motion of the rotor system and a considerable steady radial force.

Slip-flow pressure drop in microchannels of general cross section

Abstract: In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson's equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, "Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section," ASME J. Fluids Eng., 128, pp. 1036-1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

Transient Simulation of the Aerodynamic Response of a Double-Deck Bus in Gusty Winds

Abstract: The purpose of the research reported in this paper was to investigate the aerod ynamic response of a double-deck bus in gusty winds using a Detached-Eddy Simula tion (DES). The bus was subjected to three different scenarios of wind gusts: g ust in a wind tunnel, gust in a natural wind and gust behind the exit of a tunne l. The proposed scenarios of gusts are in the time domain and take into account the dynamic behavior of natural winds. The Reynolds number of the flow, based on the time-averaged speed of the side wind and a reference length of squre root of 0.1 [m], was 1300000. Detailed transient responses of the aerodynamic coe fficients and flow structures were investigated. Good agreement was found betwe en the DES results and the available experimental data. A comparison between the influence of the different gust scenarios on the aerodynamic coefficients shows that the gust behind the exit from a tunnel has a stronger influence on the aer odynamics than the other gust scenarios. Moreover, the influence of the gusts o n the time history of aerodynamics coefficients is found to be limited to the pe riod of the gust.

An Experimental and Analytical Investigation of Rectangular Synthetic Jets

Abstract: In this paper the flow field of a rectangular synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied. The similarities exhibited by synthetic and continuous turbulent jets lead to the hypothesis that a rectangular synthetic jet within a limited region downstream of the orifice be modeled using similarity analysis just as a continuous planar jet. Accordingly, the jet is modeled using the classic twodimensional solution to a continuous jet, where the virtual viscosity coefficient of the continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet at a particular axial location is related to the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flow field of rectangular synthetic jets is thought to consist of four regions as distinguished by the centerline velocity decay. The regions are the developing, the quasi-two-dimensional, the transitional, and the axisymmetric regions. It is in the quasi-two-dimensional region that the planar model applies, and where indeed the jet exhibits self-similar behavior as distinguished by the collapse of the lateral time average velocity profiles when scaled. Furthermore, within this region the spanwise velocity profiles display a saddleback profile that is attributed to the secondary flow generated at the smaller edges of the rectangular orifice. The scaled spreading and decay rates are seen to increase with stroke ratio and be independent of Reynolds number. However, the geometry of the actuator is seen to additionally affect the external characteristics of the jet. The eddy viscosities of the synthetic jets under consideration are shown to be larger than equivalent continuous turbulent jets. This enhanced eddy viscosity is attributed to the additional mixing brought about by the introduction of the periodic vortical structures in synthetic jets and their ensuing break down and transition to turbulence. Further, a semi-empirical modeling approach is proposed, the final objective of which is to obtain a functional relationship between the parameters that describe the external flow field of the synthetic jet and the input operational parameters to the system. DOI: 10.1115/1.4000422

Pressure Fluctuation Prediction of a Model Kaplan Turbine by Unsteady Turbulent Flow Simulation

Abstract: While larger and larger turbines are being developed, hydraulic stability has become one of the key issues for their performance assessments. An accurate prediction of their pressure fluctuations is vital to the success of new model development. In this paper, we briefly introduced the method, i.e., the three-dimensional unsteady turbulent flow simulation of the complete flow passage, which we used for predicting the pressure fluctuations of a model Kaplan turbine. In order to verify the prediction, the model turbine was tested on the test rig at the Harbin Electric Machinery Co., Ltd. (HEC), China, which meets all the international standards. Our main findings from this numerical prediction of pressure fluctuations for a model Kaplan turbine are as follows. (1) The approach by using 3D unsteady turbulent flow including rotor-stator interaction for the whole flow passage is a feasible way for predicting model turbine hydraulic instability. The predicted values at different points along its flow passage all agree well with the test data in terms of their frequencies and amplitudes. (2) The low-frequency pressure fluctuation originating from the draft tube is maximal and influences the stability of the turbine operation mostly. The whole flow passage analysis shows that the swirling vortex rope in the draft tube is the major source generating the pressure fluctuations in this model turbine. (3) The second harmonic of the rotational frequency 2f(n) is more dominant than the blade passing frequency Zf(n) in the draft tube. This prediction, including the turbulence model, computational methods, and the boundary conditions, is valid either for performance prediction at design stage and/or for operation optimization after commissioning.

Tip Vortex Cavitation Inception Scaling for High Reynolds Number Applications

Abstract: Tip vortices generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and antiroll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise distributions of the section lift coefficients are the same between the model-scale and the full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick's assumption about the dependence of the vortex core size on the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the scaling of the cavitation inception index as the ratio of Reynolds numbers to an exponent m, the values of m are not constant and are dependent on the values of the model- and full-scale Reynolds numbers themselves. This contrasts traditional scaling for which m is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of m to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples of the values of m are given for different model- to full-scale sizes and Reynolds numbers.

CFD Modeling and X-Ray Imaging of Biomass in a Fluidized Bed

Abstract: Computational modeling of fluidized beds can be used to predict the operation of biomass gasifiers after extensive validation with experimental data. The present work focused on validating computational simulations of a fluidized bed using a multifluid Eulerian― Eulerian model to represent the gas and solid phases as interpenetrating continua. Simulations of a cold-flow glass bead fluidized bed, using two different drag models, were compared with experimental results for model validation. The validated numerical model was then used to complete a parametric study for the coefficient of restitution and particle sphericity, which are unknown properties of biomass. Biomass is not well characterized, and so this study attempts to demonstrate how particle properties affect the hydrodynamics of a fluidized bed. Hydrodynamic results from the simulations were compared with X-ray flow visualization computed tomography studies of a similar bed. It was found that the Gidaspow (blending) model can accurately predict the hydrodynamics of a biomass fluidized bed. The coefficient of restitution of biomass did not affect the hydrodynamics of the bed for the conditions of this study; however, the bed hydrodynamics were more sensitive to particle sphericity variation.

Effect of Side Wind on a Simplified Car Model: Experimental and Numerical Analysis

Abstract: A prior analysis of the effect of steady cross wind on full size cars or models must be conducted when dealing with transient cross wind gust effects on automobiles. The experimental and numerical tests presented in this paper are performed on the Willy square-back test model. This model is realistic compared with a van-type vehicle; its plane underbody surface is parallel to the ground, and separations are limited to the base for moderated yaw angles. Experiments were carried out in the semi-open test section at the Conservatoire National des Arts et Metiers, and computations were performed at the Ecole Centrale de Nantes (ECN). The ISIS-CFD flow solver, developed by the CFD Department of the Fluid Mechanics Laboratory of ECN, used the incompressible unsteady Reynolds-averaged Navier-Stokes equations. In this paper, the results of experiments obtained at a Reynolds number of 0.9×10 6 are compared with numerical data at the same Reynolds number for steady flows. In both the experiments and numerical results, the yaw angle varies from 0 deg to 30 deg. The comparison between experimental and numerical results obtained for aerodynamic forces, wall pressures, and total pressure maps shows that the unsteady ISIS-CFD solver correctly reflects the physics of steady three-dimensional separated flows around bluff bodies. This encouraging result allows us to move to a second step dealing with the analysis of unsteady separated flows around the Willy model.

Cavitating Turbulent Flow Simulation in a Francis Turbine Based on Mixture Model

Abstract: As a numerical method to study the cavitation performance of a Francis turbine, the mixture model for the cavity/liquid two-phase flow is adopted in the cavitating turbulent flow analysis together with the re-normalization group (RNG) k-e turbulence model in the present paper. The direct coupling numerical technique is used to solve the governing equations of the mixture model for the two-phase flow. Unsteady cavitating flow simulation around a hydrofoil of ALE15 is conducted as preliminary evaluation. Then, the cavitating flow in a Francis turbine is treated from the steady flow simulation since the feasibility of the cavitation model to the performance prediction of the turbine is the present major concern. Comparisons of the computational results with the model test data, i.e., the cavitation characteristics of hydraulic efficiency and the overload vortex rope at the draft tube inlet being reproduced reasonably, indicate that the present method has sufficient potential to simulate the cavitating flow in hydraulic turbines. Further, the unsteady cavitating flow simulation through the Francis turbine is conducted as well to study the pressure fluctuation characters caused by the vortex rope in the draft tube at partial load operation.

Large-Eddy Simulation of Wake and Boundary Layer Interactions Behind a Circular Cylinder

Abstract: Large-eddy simulations (LESs) of flow past a circular cylinder in the vicinity of a flat plate have been carried out for three different gap-to-diameter (G/D) ratios of 0.25, 0.5, and 1.0 (where G signifies the gap between the flat plate and the cylinder, and D signifies the cylinder diameter) following the experiment of Price et al. (2002, "Flow Visualization Around a Circular Cylinder Near to a Plane Wall, " J. Fluids Struct., 16, pp. 175―191). The flow visualization along with turbulent statistics are presented for a Reynolds number of Re = 1440 (based on D and the inlet free-stream velocity U ∞ ). The three-dimensional time-dependent, incompressible Navier―Stokes equations are solved using a symmetry-preserving finite-difference scheme of second-order spatial and temporal accuracy. The immersed-boundary method is employed to impose the no-slip boundary condition at the cylinder surface. An attempt is made to understand the physics of flow involving interactions of shear layers shed from the cylinder and the wall boundary layer. Present LES reveals the shear layer instability and formation of small-scale eddies apart from their mutual interactions with the boundary layer. It has been observed that G/D ratio has a large influence on the modification of wake dynamics and evolution of the wall boundary layer. For a low gap ratio, it is difficult to identify the boundary layer because of its strong interactions with the shear layers; however, a rapid transition to turbulence of the boundary layer, which is similar to bypass transition, is observed for a large gap ratio.

Modeling of Pressure Drop During Condensation in Circular and Noncircular Microchannels

Abstract: This paper presents a multiple flow-regime model for pressure drop during condensation of refrigerant R134a in horizontal microchannels. Condensation pressure drops measured in two circular and six noncircular channels ranging in hydraulic diameter from 0.42 mm to 0.8 mm are considered here. For each tube under consideration, pressure drop measurements were taken over the entire range of qualities from 100% vapor to 100% liquid for five different refrigerant mass fluxes between 150 kg/m 2 s and 750 kg/m 2 s. Results from previous work by the authors on condensation flow mechanisms in microchannel geometries were used to assign the applicable flow regime to the data points. Garimella et al. (2005, "Condensation Pressure Drop in Circular Microchannels," Heat Transfer Eng., 26(3) pp. 1-8) reported a comprehensive model for circular tubes that addresses the progression of the condensation process from the vapor phase to the liquid phase by modifying and combining the pressure drop models for intermittent (Garimella et al., 2002, "An Experimentally Validated Model for Two-Phase Pressure Drop in the Intermittent Flow Regime for Circular Microchannels," ASME J. Fluids Eng., 124(1), pp. 205-214) and annular (Garimella et al., 2003, "Two-Phase Pressure Drops in the Annular Flow Regime in Circular Microchannels," 21st IIR International Congress of Refrigeration, International Institute of Refrigeration, p. ICR0360) flows reported earlier by them. This paper presents new condensation pressure drop data on six noncircular channels over the same flow conditions as the previous work on circular channels. In addition, a multiple flow-regime model similar to that developed earlier by Garimella et al. for circular microchannels is developed here for these new cross sections. This combined model accurately predicts condensation pressure drops in the annular, disperse-wave, mist, discrete-wave, and intermittent flow regimes for both circular and noncircular microchannels of similar hydraulic diameters. Overlap and transition regions between the respective regimes are also addressed to yield relatively smooth transitions between the predicted pressure drops. The resulting model predicts 80% of the data within ±25%. The effect of tube shape on pressure drop is also demonstrated.

Equation-Free/Galerkin-Free Reduced-Order Modeling of the Shallow Water Equations Based on Proper Orthogonal Decomposition

Abstract: In this paper, two categories of reduced-order modeling (ROM) of the shallow water equations (SWEs) based on the proper orthogonal decomposition (POD) are presented. First, the traditional Galerkin-projection POD/ROM is applied to the one-dimensional (1D) SWEs. The result indicates that although the Galerkin-projection POD/ROM is suitable for describing the physical properties of flows (during the POD basis functions' construction time), it cannot predict that the dynamics of the shallow water flows properly as it was expected, especially with complex initial conditions. Then, the study is extended to applying the equation-free/Galerkin-free POD/ROM to both 1D and 2D SWEs. In the equation-free/Galerkin-free framework, the numerical simulation switches between a fine-scale model, which provides data for construction of the POD basis functions, and a coarse-scale model, which is designed for the coarse-grained computational study of complex, multiscale problems like SWEs. In the present work, the Beam & Warming and semi-implicit time integration schemes are applied to the 1D and 2D SWEs, respectively, as fine-scale models and the coefficients of a few POD basis functions (reduced-order model) are considered as a coarse-scale model. Projective integration is applied to the coarse-scale model in an equation-free framework with a time step grater than the one used for a fine-scale model. It is demonstrated that equation-free/Galerkin-free POD/ROM can resolve the dynamics of the complex shallow water flows. Moreover, the computational cost of the approach is less than the one for a fine-scale model.