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Showing papers in "Journal of Fluids Engineering-transactions of The Asme in 2011"


Journal ArticleDOI
TL;DR: In this article, the authors investigated the mechanisms leading to vortex formation and rotating stall in a pump-turbine model by means of numerical simulations and test rig measurements and found that stationary vortex formation is associated with a total pressure rise over the machine and leads to the slope change of the characteristic.
Abstract: Reversible pump-turbines are versatile in the electricity market since they can be switched between pump and turbine operation within a few minutes. The emphasis on the design of the more sensitive pump flow however often leads to stability problems in no load or turbine brake operation. Unstable characteristics can be responsible for hydraulic system oscillations in these operating points. The cause of the unstable characteristics can be found in the blocking effect of either stationary vortex formation or rotating stall. The so-called unstable characteristic in turbine brake operation is defined by the change of sign of the slope of the head curve. This change of sign or “S-shape” can be traced back to flow recirculation and vortex formation within the runner and the vaneless space between runner and guide vanes. When approaching part load from sound turbine flow the vortices initially develop and collapse again. This unsteady vortex formation induces periodical pressure fluctuations. In the turbine brake operation at small guide vane openings the vortices increase in intensity, stabilize and circumferentially block the flow passages. This stationary vortex formation is associated with a total pressure rise over the machine and leads to the slope change of the characteristic. Rotating stall is a flow instability which extends from the runner, the vaneless space to the guide and the stay vane channels at large guide vane openings. A certain number of channels is blocked (rotating stall cell) while the other channels comprise sound flow. Due to a momentum exchange between rotor and stator at the front and the rear cell boundary, the cell is rotating with subsynchronous frequency of about 60 percent of the rotational speed for the investigated pump-turbine (nq=45). The enforced rotating pressure distributions in the vaneless space lead to large dynamic radial forces on the runner. The mechanisms leading to stationary vortex formation and rotating stall were analyzed with a pump-turbine model by the means of numerical simulations and test rig measurements. It was found that stationary vortex formation and rotating stall have initially the same physical cause, but it depends on the mean convective acceleration within the guide vane channels, whether the vortex formations will rotate or not. Both phenomena lead to an unstable characteristic. [DOI: 10.1115/1.4003874]

196 citations


Journal ArticleDOI
TL;DR: A review of the current status of X-ray flow visualization can be found in this paper, where the authors provide qualitative and quantitative information about the characteristics of complex multiphase flows, as well as their applications in the field of complex fluid analysis.
Abstract: Flow visualization and characterization of multiphase flows have been the quest of many fluid mechanicians. The process is fairly straight forward only when there is good optical access (i.e., the vessel is not opaque or there are appropriate viewing ports) and the flow is transparent, implying a very low volume fraction of the dispersed phase; however, when optical access is not good or the fluid is opaque, alternative methods must be developed. Several different noninvasive visualization tools have been developed to provide high-quality qualitative and quantitative data of various multiphase flow characteristics, and overviews of these methods have appeared in the literature. X-ray imaging is one family of noninvasive measurement techniques used extensively for product testing and evaluation of static objects with complex structures. X-rays can also be used to visualize and characterize multiphase flows. This paper provides a review of the current status of X-ray flow visualization and details various X-ray flow visualization methods that can provide qualitative and quantitative information about the characteristics of complex multiphase flows. Disciplines Complex Fluids | Engineering | Mechanical Engineering | Thermodynamics Comments This article is from Journal of Fluids Engineering 133 (2011): 074001, doi:10.1115/1.4004367. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/me_pubs/20 A Review of X-Ray Flow Visualization With Applications to Multiphase Flows

178 citations


Journal ArticleDOI
TL;DR: In this article, a new generation CFD tool for pump cavitation simulation, using an axial flow water pump as a demonstration case, is presented and discussed using a novel CFD methodology and advanced cavitation model.
Abstract: Due to complexities in geometry and physics, computational fluid dynamics (CFD) pump simulation has historically been very challenging and time consuming, especially for cases with cavitation. However, with the evolution and innovation of CFD technologies, pump cavitation simulation has improved significantly in recent years. In view of these developments, this paper will discuss a new generation CFD tool for pump cavitation simulation, using an axial flow water pump as a demonstration case. A novel CFD methodology and advanced cavitation model will be presented and discussed. Key components that are relevant to the improvement of accuracy and CFD simulation speed will be discussed in detail. An axial flow water pump is chosen as the test case to demonstrate and validate the capability and accuracy of the code discussed. Simulation results include pump head, hydraulic efficiency, and cavitation characteristic in terms of incipient net positive suction head for the whole pump flow passages using both multiple reference frame and transient approaches. Multiple operation conditions, from 70% to 120% of duty flow rate, have been evaluated and will be projected against experimental data. Furthermore, simulated cavitation patterns will be compared with video images recorded during the experiments.

174 citations


Journal ArticleDOI
TL;DR: In this paper, an experimental investigation of the rotating stall in reduced scale model of a low specific speed radial pump-turbine at runaway and turbine brake conditions in generating mode is achieved.
Abstract: An experimental investigation of the rotating stall in reduced scale model of a low specific speed radial pump-turbine at runaway and turbine brake conditions in generating mode is achieved. Measurements of wall pressure in the stator are performed along with high-speed flow visualizations in the vaneless gap with the help of air bubbles injection. When starting from the best efficiency point (BEP) and increasing the impeller speed, a significant increase of the pressure fluctuations is observed mainly in the wicket gates channels. The spectral analysis shows a rise of a low frequency component (about 70% of the impeller rotational frequency) at runaway, which further increases as the zero discharge condition is approached. Analysis of the instantaneous pressure peripheral distribution in the vaneless gap reveals one stall cell rotating with the impeller at sub-synchronous speed. High-speed movies reveal a quite uniform flow pattern in the guide vanes channels at the normal operating range, whereas at runaway the flow is highly disturbed by the rotating stall passage. The situation is even more critical at very low positive discharge, where backflow and vortices in the guide vanes channels develop during the stall cell passage. A specific image processing technique is applied to reconstruct the rotating stall evolution in the entire guide vanes circumference for a low positive discharge operating point. The findings of this study suggest that one stall cell rotates with the impeller at sub-synchronous velocity in the vaneless gap between the impeller and the guide vanes. It is the result of rotating flow separations developed in several consecutive impeller channels which lead to their blockage.

150 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated various aspects of the flow physics of a supercavitating vehicle, including shape, closure, and ventilation requirements versus Froude number, and effects related to flow choking.
Abstract: A study has been carried out at the Saint Anthony Falls Laboratory (SAFL) to investigate various aspects of the flow physics of a supercavitating vehicle. For the experimental work presented here, artificial supercavitation behind a sharp-edged disk was investigated for various model configurations. Results regarding supercavity shape, closure, and ventilation requirements versus Froude number are presented. Conducting experiments in water tunnels introduces blockage effects that are not present in nature. As a result, effects related to flow choking are also discussed. Various methods for computing ventilated cavitation number, including direct measurement of pressure, Laser Doppler Velocimetry, and use of previous numerical results, were compared. Results obtained are similar in character to previous results from various authors, but differ significantly in measured values. Supercavitation parameters, especially the minimum obtainable cavitation number are strongly affected by tunnel blockage.Copyright © 2010 by ASME

117 citations


Journal ArticleDOI
TL;DR: In this paper, the amplitude of pressure fluctuation at the impeller rotating frequency and some lower frequencies dominated in the semispiral suction chamber and the volute casing of a double-suction pump.
Abstract: Pressure fluctuation is the primary reason for unstable operations of double-suction centrifugal pumps. By using flush mounted pressure transducers in the semispiral suction chamber and the volute casing of a double-suction pump, the pressure fluctuation signals were obtained and recorded at various operating conditions. Spectral analyses were performed on the pressure fluctuation signals in both frequency domain and time-frequency domain based on fast Fourier transform (FFT) and an adaptive optimal-kernel time-frequency representation (AOK TFR). The results show that pressure fluctuations at the impeller rotating frequency and some lower frequencies dominated in the semispiral suction chamber. Pressure fluctuations at the blade passing frequency, the impeller rotating frequency, and their harmonic frequencies were identified in the volute casing. The amplitude of pressure fluctuation at the blade passing frequency significantly increased when the flow rate deviated from the design flow rate. At 107% of the design flow rate, the amplitude increased more than 254% than that at the design flow rate. The time-frequency characteristics of these pressure fluctuations were affected greatly by both operating conditions and measurement locations. At partial flow rates the pulsation had a great irregularity and the amplitudes at the investigated frequencies were much larger than ones at the design flow rate. An asymmetrical pressure fluctuation structure in the volute casing was observed at all flow rates. The pulsation behavior at the blade passing frequency was the most prominent near the volute tongue zone, and the pressure waves propagated in both the radial and circumferential directions.

83 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe the development and description of the aerodynamic models used to estimate aerodynamic loads on wind turbine constructions, including a status of the capabilities of computation fluid dynamics and the need for reliable airfoil data for the simpler engineering models.
Abstract: The paper describes the development and description of the aerodynamic models used to estimate the aerodynamic loads on wind turbine constructions. This includes a status of the capabilities of computation fluid dynamics and the need for reliable airfoil data for the simpler engineering models. Also a discussion of the use of passive and active aerodynamic devices is included such as, e.g., Vortex Generators and distributed active flaps. Finally the problem of wakes in wind farms is addressed and a section of the likely future development of aerodynamic models for wind turbines is included.

83 citations


Journal ArticleDOI
TL;DR: In this article, the authors used modal analysis to determine the eigenfrequencies and eigenmodes of the rotor of a centrifugal pump to evaluate the risk of resonance vibration excited from fluctuating fluid forces.
Abstract: Flow instabilities like rotating stall can lead to severe vibrations in turbomachines if the eigenfrequency of the rotor is equal to the stall frequency. The goal of the present work is to shed some light on the origin of the rotating stall phenomenon in a centrifugal pump. The resulting fluctuating loads are quantified using numerical computations. For the chosen configuration transient PIV data are available for validation. In addition to measuring the stall frequency in the stationary frame, the CFD data is analyzed in the rotating frame. A Fourier analysis is done for a large number of sample points. This enables us to determine the local variation of amplitudes for a given frequency. Together with eigenfrequencies and eigenmodes of the rotor determined from modal analysis, it is possible to evaluate the risk of resonance vibration excited from fluctuating fluid forces.

82 citations


Journal ArticleDOI
TL;DR: In this paper, a power-law based effective mean free path (MFP) model was proposed for the transition-regime flows typical of gas micro/nanodevices.
Abstract: We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime.

72 citations


Journal ArticleDOI
TL;DR: In this article, the impact load measurements were carried out in a high-speed cavitation loop by means of a conventional pressure sensor flush-mounted in the region of closure of the cavity where maximum damage was observed.
Abstract: Impact load measurements were carried out in a high-speed cavitation loop by means of a conventional pressure sensor flush-mounted in the region of closure of the cavity where maximum damage was observed. The sensor was dynamically calibrated by the ball drop test technique. Pressure pulse amplitudes were measured at different velocities and constant cavitation number and cavity length. It was found that pressure pulse height spectra follow a simple exponential law, which depends upon two parameters interpreted as a reference peak rate and a reference load. By exploring the dependence of both parameters on flow velocity, it was possible to show that the various histograms measured at different velocities can be reduced to a unique non-dimensional one and derive scaling laws, which enable to transpose results from one velocity to another. The measured values of impact loads are compared to similar data in the literature, and the impact load spectra are discussed with respect to pitting test results available from a previous investigation. It is concluded that an uncertainty remains on the measured values of impact loads and that a special effort should be made to compare quantitatively pitting test results and impact load measurements. To evaluate the coherence of both sets of data with each other, it is suggested to introduce two-dimensional histograms of impact loads by considering the size of the impacted area in addition to the measured impact load amplitude. It is conjectured that the combination of impact load measurements and pitting test measurements should allow the determination of such two-dimensional histograms, which are an essential input for analyzing the material response and computing the progression of erosion with exposure time. [DOI: 10.1115/1.4005342]

70 citations




Journal ArticleDOI
Hitoshi Soyama1
TL;DR: In this article, the effect of the geometry of the nozzle through which the jet is driven on the aggressive intensity of a cavitating jet for practical applications was investigated, in which the parameters varied were the bore diameter, D, and length, L, the standoff distance, the nozzle throat diameter, d, and the upstream and downstream pressures of the jet.
Abstract: In order to enhance the aggressive intensity of a cavitating jet for practical applications, the effect of the geometry of the nozzle through which the jet is driven on the aggressive intensity was investigated. The nozzle under test was cylindrical and consisted of a plate and a cap with a hole bored through it. The aggressive intensity of the jet was estimated by the erosion suffered by pure aluminum test specimens. The parameters varied were the bore diameter, D, and length, L, the standoff distance, the nozzle throat diameter, d, and the upstream and downstream pressures of the nozzle. The mass loss at the optimum standoff distance, where the mass loss was at a relative maximum, was found for each bore diameter and length, and then the optimum bore diameter and length were obtained. The optimum ratio of d : D : L was shown to be 1 : 8 : 8, and this was the optimum for both d =1 mm and d =2 mm. It was also the optimum ratio for upstream pressures of 15 MPa and 30 MPa, and downstream pressures of 0.1 MPa and 0.42 MPa.

Journal ArticleDOI
Bin Ji1, X W Luo1, Xin Wang1, Xiaoxing Peng, Yulin L. Wu1, H Y Xu1 
TL;DR: In this paper, the cavitating flows around a highly skewed model marine propeller in both uniform flow and wake flow have been simulated by applying a mass transfer cavitation model based on Rayleigh-Plesset equation and k- shear stress transport (SST) turbulence model.
Abstract: The cavitating flows around a highly skewed model marine propeller in both uniform flow and wake flow have been simulated by applying a mass transfer cavitation model based on Rayleigh‐Plesset equation and k- shear stress transport (SST) turbulence model From comparison of numerical results with the experiment, it is seen that the thrust and torque coefficients of the propeller are predicted satisfactory It is also clarified from unsteady simulation of cavitating flow around the propeller in wake flow that the whole process of cavitating-flow evolution can be reasonably reproduced including sheet cavitation and tip vortex cavitation observed in the experiments Furthermore, to study the effect of pressure fluctuation on the surrounding, pressure fluctuations induced by the cavitation as well as the propeller rotation are predicted at three reference positions above the propeller for comparison with the experimental data: The amplitudes of the dominant components corresponding to the first, second, and third blade passing frequencies were satisfactorily predicted It is noted that the maximum difference of pressure fluctuation between the calculation and experiment reached 20%, which might be acceptable by usual engineering applications DOI: 101115/14003355

Journal ArticleDOI
TL;DR: The parametric shroud configuration studies carried out in the Glenn experiments and the CFD analyses elucidate the physical mechanisms of windage losses as well as mitigation strategies due to shrouding and newly proposed tooth contour modifications.
Abstract: A computational fluid dynamics (CFD) method has been applied to gear configurations with and without shrouding. The goals of this work have been to validate the numerical and modeling approaches used for these applications and to develop physical understanding of the aerodynamics of gear windage loss. Several spur gear geometries are considered, for which experimental data are available. Various canonical shrouding configurations and free spinning (no shroud) cases are studied. Comparisons are made with experimental data from open literature, and data recently obtained in the NASA Glenn Research Center Gear Windage Test Facility, Cleveland, OH. The results show good agreement with the experiment. The parametric shroud configuration studies carried out in the Glenn experiments and the CFD analyses elucidate the physical mechanisms of windage losses as well as mitigation strategies due to shrouding and newly proposed tooth contour modifications.

Journal ArticleDOI
TL;DR: In this article, the flow downstream of a three-dimensional double backward facing step (3D DBWFS) is investigated for Reynolds number Re h ranging from 5 x 10 3 to 8 × 10 4 (based on the first step height h).
Abstract: The flow downstream of a three-dimensional double backward facing step (3D DBWFS) is investigated for Reynolds number Re h ranging from 5 x 10 3 to 8 × 10 4 (based on the first step height h). The flow is studied both qualitatively by means of laser tomoscopy and oil-flow visualizations and quantitatively by means of particle image velocimetry (PIV) measurements. In particular, the results show a mean flow asymmetry. A sensitivity study around zero degree sideslip has shown that the flow is bistable for this geometry. This bistability has been observed in two different wind tunnels for very different upstream conditions. As a main consequence, the zero degree drift angle could be a relevant validation case of unstable flow computation. More tests are carried out to understand and control this particular flow feature.

Journal ArticleDOI
TL;DR: In this article, a theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed, which uses a one-dimensional solution of flow conditions through the turbine along the mean streamline.
Abstract: A study has been conducted to determine the off-design performance of cryogenic turboexpander. A theoretical model to predict the losses in the components of the turboexpander along the fluid flow path has been developed. The model uses a one-dimensional solution of flow conditions through the turbine along the mean streamline. In this analysis, the changes of fluid and flow properties between different components of turboexpander have been considered. Overall, turbine geometry, pressure ratio, and mass flow rate are input information. The output includes performance and velocity diagram parameters for any number of given speeds over a range of turbine pressure ratio. The procedure allows any arbitrary combination of fluid species, inlet conditions, and expansion ratio since the fluid properties are properly taken care of in the relevant equations. The computational process is illustrated with an example.


Journal ArticleDOI
TL;DR: In this paper, a hybrid multiobjective evolutionary algorithm (MOEA) coupled with a response surface approximation (RSA) surrogate model is proposed for axial-flow ventilation fan design.
Abstract: This paper presents an optimization procedure for axial-flow ventilation fan design through a hybrid multiobjective evolutionary algorithm (MOEA) coupled with a response surface approximation (RSA) surrogate model. Numerical analysis of a preliminary fan design is conducted by solving three-dimensional (3-D) Reynolds-averaged Navier-Stokes (RANS) equations with the shear stress transport (SST) turbulence model. The multiobjective optimization processes are performed twice to understand the coupled effects of diverse variables. The first multiobjective optimization process is conducted with three design variables defining stagger angles at the hub, mid-span, and tip, and the second is conducted with five design variables defining hub-to-tip ratio, hub cap installation distance, hub cap ratio, and the stagger angles at the mid-span and tip. Two aerodynamic performance parameters, the total efficiency and total pressure rise, are selected as the objective functions for optimization. These objective functions are numerically assessed through 3-D RANS analysis at design points sampled by Latin hypercube sampling in the design space. The optimization yields a maximum increase in efficiency of 1.8% and a 31.4% improvement in the pressure rise. The off-design performance is also improved in most of the optimum designs except in the region of low flow rate.



Journal ArticleDOI
TL;DR: In this paper, the second law of thermodynamics is linked to the local entropy generation in the flow field, and it is shown that most of the flow losses occur downstream of the components.
Abstract: Losses in a flow field due to single conduit components often are characterized by experimentally determined head loss coefficients K. These coefficients are defined and determined with the pressure as the critical quantity. A thermodynamic definition, given here as an alternative, is closer to the physics of flow losses, however. This definition is based upon the dissipation of mechanical energy as main quantity. With the second law of thermodynamics this dissipation can be linked to the local entropy generation in the flow field. For various conduit components K values are determined and physically interpreted by determining the entropy generation in the component as well as upstream and downstream of it. It turns out that most of the losses occur downstream of the components what carefully has to be taken into account when several components are combined in a flow network.

Journal ArticleDOI
TL;DR: In this paper, the performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data.
Abstract: The performance of some commonly used eddy-viscosity turbulence models has been evaluated using direct numerical simulation (DNS) and large-eddy simulation (LES) data. Two configurations have been tested, a two-dimensional boundary layer undergoing pressure-driven separation, and a square duct. The DNS and LES were used to assess the k ― e, ζ ― f, k — ω, and Spalart―Allmaras models. For the two-dimensional separated boundary layer, anisotropic effects are not significant and the eddy-viscosity assumption works well. However, the near-wall treatment used in k ― e models was found to have a critical effect on the predictive accuracy of the model (and, in particular, of separation and reattachment points). None of the wall treatments tested resulted in accurate prediction of the flow field. Better results were obtained with models that do not require special treatment in the inner layer (ζ ― f, k ― ω, and Spalart―Allmaras models). For the square duct calculation, only a nonlinear constitutive relation was found to be able to capture the secondary flow, giving results in agreement with the data. Linear models had significant error.

Journal ArticleDOI
TL;DR: In this paper, a 3D simulation of a radial flow pump during the rapid stopping period was numerically studied by CFD, where the dynamic mesh (DM) method combined with non-conformal grid boundaries was applied to simulate the transient stopping process.
Abstract: Three-dimensional (3-D) unsteady incompressible and non-cavitating flow in a radial flow pump during the rapid stopping period was numerically studied by CFD. The dynamic mesh (DM) method combined with non-conformal grid boundaries was applied to simulate the transient stopping process. In order to exclude the uncertainty of the unsteady inlet and outlet boundaries, a loop pumping system was established, which was composed of pipes, a reservoir with an air part on the top, and a driving pump. Simulations were performed based on the standard k-e turbulence model and volume of fluid (VOF) model. Results showed that the air part in the reservoir approximated real conditions when using the VOF model. Pressure fluctuations were reduced and a sharp increase of pressure at the inlet of the pump was observed at the beginning of the stopping period. Specific transient characteristics, such as the flow-rate, head and efficiency, were analyzed during the deceleration period and compared with corresponding quasi-steady results. The deviation of the quasi-steady hypothesis in predicting the transient stopping process of radial flow pumps is thought to be caused by differences in the predicted vortex in the impeller. The transient curve showing the relationship between the instantaneous flow coefficient and total pressure rise coefficient was analyzed and compared with the quasi-steady curve. The two curves had a crossover point when the stall just occurs in the impeller during the transient process. Simulation results were also compared and validated using published data.

Journal ArticleDOI
TL;DR: In this article, the authors considered the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows and determined from experiments performed on elementary flows and they are subject to uncertainty.
Abstract: This paper is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are determined from experiments performed on elementary flows and they are subject to uncertainty. The widely used k–e turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for the flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte-Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise velocity component in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly affected.Copyright © 2010 by ASME

Journal ArticleDOI
TL;DR: In this article, a three-dimensional turbulent wall jet was investigated using a particle image velocimetry technique and three Reynolds numbers based on the jet exit velocity and diameter of 5000, 10,000, and 20,000 were studied.
Abstract: Three-dimensional turbulent wall jet was investigated using a particle image velocimetry technique. Three Reynolds numbers based on the jet exit velocity and diameter of 5000, 10,000, and 20,000 were studied. Profiles of the mean velocities, turbulence intensities, and Reynolds shear stresses as well as two-point velocity correlations and proper orthogonal decomposition analyses were used to document the salient features of the wall jets. The decay and spread rates are independent of Reynolds numbers in the self-similar region. The estimated values of 1.15, 0.054, and 0.255 for the decay rate, wall-normal spread rate, and lateral spread rate, respectively, are within the range of values reported in the literature. The two-point correlation analysis showed that the inclination of the streamwise velocity correlation contours in the inner layer is 11 ± 3 deg in the wall region, which is similar to those of canonical turbulent boundary layers. The results from the proper orthogonal decomposition indicate that low-order modes contribute more to the turbulence statistics in the self-similar region than in the developing region. The Reynolds shear stresses are the biggest benefactors of the low-order mode contribution while the wall-normal turbulence intensities are the least.

Journal ArticleDOI
TL;DR: In this paper, the Richardson Extrapolation (RE) method was used to evaluate two new variants of the GCI method and one new variant of the FS method for solution verification.
Abstract: The Technical Brief by Roache [1] presents ten items of discussion of our factor of safety (FS) method for solution verification [2]. Our responses are listed below item-by-item using the same numbering as Roache. The nomenclature mostly follows our own and not Roache’s such as pRE for the order of accuracy calculated using the Richardson Extrapolation as opposed to the observed order of convergence and the GCI and GCI2 methods as opposed to the GCI0 and the real GCI methods. However, we agree with Roache to use FS for the factor of safety used in all the verification methods. In response to item (10), we have used our approach to evaluate two new variants of the GCI method and one new variant of the FS method.

Journal ArticleDOI
TL;DR: In this paper, the effects of momentum flux ratio and recess length on the spray characteristics of gas-centered swirl coaxial injectors have been investigated by cold flow tests with a photographic technique.
Abstract: Gas-centered swirl coaxial injectors have become an important subject of study for staged combustion rocket engines with hydrocarbon fuels. While these injectors are employed successfully in rocket engines, it is very rare to find the related research results as applicable to design data. An experimental study on spray characteristics of gas-centered swirl coaxial injectors has been performed. The effects of momentum flux ratio and recess length on the spray characteristics have been investigated by cold flow tests with a photographic technique. The liquid intact length L, which profoundly affects the global spray characteristics, decreases as the momentum flux ratio M increases. The critical momentum flux ratio Mc is introduced to identify the flow patterns as internal or external mixing in the injectors. Concerning the effect of the recess length lR, it is shown that the spray cone angle and the drop size decrease as lR increases.

Journal ArticleDOI
TL;DR: In this article, closed form solutions are presented for fully developed pressure driven slip-flow in straight microchannels of uniform noncircular cross-sections to achieve this goal, starting from the general solution of the Poisson's equation in the cylindrical coordinate, a least-squares-matching of boundary values is employed for applying the slip boundary condition at the wall.
Abstract: Closed form solutions are presented for fully developed pressure driven slip-flow in straight microchannels of uniform noncircular cross-sections To achieve this goal, starting from the general solution of the Poisson's equation in the cylindrical coordinate, a least-squares-matching of boundary values is employed for applying the slip boundary condition at the wall Then the application of boundary conditions for three different types of cross sections is examined While the model is general enough to be extended to almost any arbitrary cross section, microchannels of polygonal (with circular as a limiting case), rectangular, and rhombic cross sections are analyzed in this study The results are then successfully compared to the existing data in the literature

Journal ArticleDOI
TL;DR: In this article, a new variant of the SST k-ω model sensitized to system rotation and streamline curvature is presented, which is based on a direct simplification of the Reynolds stress model under weak equilibrium assumptions.
Abstract: A new variant of the SST k-ω model sensitized to system rotation and streamline curvature is presented. The new model is based on a direct simplification of the Reynolds stress model under weak equilibrium assumptions [York et al., 2009, "A Simple and Robust Linear Eddy-Viscosity Formulation for Curved and Rotating Flows," International Journal for Numerical Methods in Heat and Fluid Flow, 19(6), pp. 745-776]. An additional transport equation for a transverse turbulent velocity scale is added to enhance stability and incorporate history effects. The added scalar transport equation introduces the physical effects of curvature and rotation on turbulence structure via a modified rotation rate vector. The modified rotation rate is based on the material rotation rate of the mean strain-rate based coordinate system proposed by Wallin and Johansson (2002, "Modeling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models," International Journal of Heat and Fluid Flow, 23, pp. 721-730). The eddy viscosity is redefined based on the new turbulent velocity scale, similar to previously documented k-e-v 2 model formulations (Durbin, 1991, "Near-Wall Turbulence Closure Modeling without Damping Functions," Theoretical and Computational Fluid Dynamics, 3, pp. 1-13). The new model is calibrated based on rotating homogeneous turbulent shear flow and is assessed on a number of generic test cases involving rotation and/or curvature effects. Results are compared to both the standard SST k-ω model and a recently proposed curvature-corrected version (Smirnov and Menter, 2009, "Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart-Shur Correction Term," ASME Journal of Turbomachinery, 131, pp. 1-8). For the test cases presented here, the new model provides reasonable engineering accuracy without compromising stability and efficiency, and with only a small increase in computational cost.