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### Research Papers: Flows in Complex Systems

J. Fluids Eng. 2015;137(5):051101-051101-15. doi:10.1115/1.4028996.

This paper describes the design of a nonaxisymmetric hub contouring in a shroudless axial flow compressor cascade operating at near stall condition. Although an optimum tip clearance (TC) reduces the total pressure loss, further reduction in the loss was achieved using hub contouring. The design methodology presented here combines an evolutionary principle with a three-dimensional (3D) computational fluid dynamics (CFD) flow solver to generate different geometric profiles of the hub systematically. The resulting configurations were preprocessed by GAMBIT© and subsequently analyzed computationally using ANSYSFluent©. The total pressure loss coefficient was used as a single objective function to guide the search process for the optimum hub geometry. The resulting three dimensionally complex hub promises considerable benefits discussed in detail in this paper. A reduction of 15.2% and 16.23% in the total pressure loss and secondary kinetic energy (SKE), respectively, is achieved in the wake region. An improvement of 4.53% in the blade loading is observed. Other complimentary benefits are also listed in the paper. The majority of the benefits are obtained away from the hub region. The contoured hub not only alters the pitchwise static pressure gradient but also acts as a vortex generator in an effort to alleviate the total pressure loss. The results confirm that nonaxisymmetric contouring is an effective method for reducing the losses and thereby improving the performance of the cascade.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051102-051102-12. doi:10.1115/1.4029442.

This paper presents a simulation model of an oil-lubrication gerotor pump for internal combustion engines. The model was constructed by using a monodimensional commercial code that accounted for all phenomena that occur during the revolution of the pump shaft. Several geometric considerations and theoretical observations are presented. An experiment was also performed to validate the simulation model. In these experimental tests, particular attention was paid to the behavior of the pressure oscillations during the pump shaft revolutions. The final aim of this activity is to obtain an instrument that allows the in-depth analysis of the functioning of the pump and lubrication circuit. Additionally, this instrument can be coupled with other models (e.g., variable valve actuation (VVA) and variable valve timing (VVT)) to account for different problems experienced by the hydraulic components of engines.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051103-051103-10. doi:10.1115/1.4029412.

Analytical and experimental investigations have been conducted to characterize the performance of “short” ejectors. In short ejectors, the core of primary (motive) flow still exists at the mixing duct exit, and nonuniform mixed flow is discharged from the mixing duct. Due to incomplete mixing, short ejector pumping performance is degraded and cannot be predicted by the existing “long” ejector models. The new analytical short ejector model presented in this paper is based on the control volume analysis and jet expansion model. The secondary (entrained) flow velocity and the corresponding shear layer (between the primary and the secondary flows) growth rate variations along the mixing duct are taken into account. In addition, measurements have been made in ejectors with length ratios (LRs) of two and three for an area ratio (AR) of 1.95; and a LR of two for an AR of 3.08. Velocity profiles at the mixing duct inlet and exit, and static pressure distribution along the mixing duct have been measured with pitot probes and pressure taps. All of the tests have been carried out at a Reynolds number of 420,000. Comparison shows that the new ejector model can accurately predict flow characteristics and performance of short ejectors. For all of the test cases, the velocity profiles at the mixing duct inlet and exit are well predicted. Also, both predictions and measurements show pumping enhancement with increasing mixing duct length. The pumping enhancement is due to the increase in the static pressure difference between the mixing duct inlet and atmosphere as the mixing duct is lengthened. Furthermore, both measured and predicted static pressure distributions along the mixing duct show a kink. According to the analysis, the kink occurs when the outer shear layer reaches the mixing duct wall, and the secondary flow velocity decreases along the mixing duct upstream of the kink and increases downstream of the kink. Thus, the new ejector model can accurately predict not only the integral performance but also different mixing regimes in short ejectors.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051104-051104-9. doi:10.1115/1.4029396.

An existing computer code for solving the quasi-one-dimensional (Q1D) flow equations governing unsteady compressible flow in tubes with smoothly varying cross section areas has been adapted to the simulation of the oscillatory flow in Stirling engines for engine design purposes. By utilizing an efficient smoothing algorithm for the area function that preserves the total volume of the tube, it has been possible to achieve a highly accurate and fully conservative numerical scheme. Submodels for wall friction and heat transfer have been added, enabling the simulation of gas heaters, gas coolers, and regenerators. The code has been used for the modeling of an α-type Stirling engine and validated for a range of operating conditions with good results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051105-051105-11. doi:10.1115/1.4029443.

The surface pressure distributions and flow patterns developed on and around a NACA 0012 airfoil undergoing heaving and pitching were investigated at Re = 3.6 × 104. Despite extensive investigations conducted by researchers elsewhere, the surface pressure measurements are, however, not readily available in the open archives, which are of importance not only in understanding the unsteady-airfoil boundary-layer flow but also for computational fluid dynamics (CFD) validation. Nevertheless, the results show that the behavior of the surface pressure distribution and the flow pattern of pure heaving closely resembled those of pure pitching. For combined heaving and pitching, the critical aerodynamic values (such as dynamic Cl,max, peak negative Cm, Cl-hysteresis and torsional damping) always exhibited a maximum value at phase shift ϕ = 0 deg. More interestingly, the ϕ = 180 deg phase shift produced a virtually unchanged surface pressure distribution over an entire combined motion cycle.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051106-051106-9. doi:10.1115/1.4029397.

A generalized model for mapping the trend of the performance characteristics of a double-discharge centrifugal fan is developed based on the work by Casey and Robinson (C&R), which formulated compressor performance maps for tip-speed Mach numbers ranging from 0.4 to 2 using test data obtained from turbochargers with vaneless diffusers. The current paper focuses on low-speed applications for Mach number below 0.4. The C&R model uses four nondimensional parameters at the design condition including the flow coefficient, the work input coefficient, the tip-speed Mach number, and the polytropic efficiency, in developing a prediction model that requires limited geometrical knowledge of the centrifugal turbomachine. For the low-speed fan case, the C&R formulas are further extended to a low-speed, incompressible analysis. The effort described in this paper begins by comparing generalized results using efficiency data obtained from a series of fan measurements to that using the C&R model. For the efficiency map, the C&R model is found to heavily depend on the ratio of the flow coefficient at peak efficiency to that at the choke flow condition. Since choke flow is generally not applicable in the low-speed centrifugal fan operational environment, an alternate, but accurate estimation method based on fan free delivery derived from the fan test data is presented. Using this new estimation procedure, the modified C&R model predicts reasonably well using the double-discharge centrifugal fan data for high-flow coefficients, but fails to correlate with the data for low-flow coefficients. To address this undesirable characteristic, additional modifications to the C&R model are also presented for the fan application at low flow conditions. A Reynolds number correction is implemented in the work input prediction of the C&R model to account for low-speed test conditions. The new model provides reasonable prediction with the current fan data in both work input and pressure rise coefficients. Along with the developments for the efficiency and work input coefficient maps, the use of fan shut-off and free delivery conditions are also discussed for low-speed applications.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051107-051107-12. doi:10.1115/1.4029534.

Passive, heat actuated ejector pumps offer simple and energy-efficient options for a variety of end uses with no electrical input or moving parts. In an effort to obtain insights into ejector flow phenomena and to evaluate the effectiveness of commonly used computational and analytical tools in predicting these conditions, this study presents a set of shadowgraph images of flow inside a large-scale air ejector and compares them to both computational and first-principles-based analytical models of the same flow. The computational simulations used for comparison apply k-ε renormalization group (RNG) and k-ω shear stress transport (SST) turbulence models to two-dimensional (2D), locally refined rectangular meshes for ideal gas air flow. A complementary analytical model is constructed from first principles to approximate the ejector flow field. Results show that on-design ejector operation is predicted with reasonable accuracy, but accuracy with the same models is not adequate at off-design conditions. Exploration of local flow features shows that the k-ω SST model predicts the location of flow features, as well as global inlet mass flow rates, with greater accuracy. The first-principles model demonstrates a method for resolving the ejector flow field from relatively little visual data and shows the evolving importance of mixing, momentum, and heat exchange with the suction flow with distance from the motive nozzle exit. Such detailed global and local exploration of ejector flow helps guide the selection of appropriate turbulence models for future ejector design purposes, predicts locations of important flow phenomena, and allows for more efficient ejector design and operation.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051108-051108-8. doi:10.1115/1.4029535.

Transportation of goods and people involves moving objects through air, which leads to a force opposing motion. This drag force can account for more than 60% of power consumed by a ground vehicle, such as a car or truck, at highway speeds. This paper studies drag reduction on the 25-deg Ahmed generic vehicle model with quasi-steady blowing at the roof–slant interface using a spanwise array of fluidic oscillators. A fluidic oscillator is a simple device that converts a steady pressure input into a spatially oscillating jet. Drag reduction near 7% was attributed to separation control on the rear slant surface. Particle image velocimetry (PIV) and pressure taps were used to characterize the flow structure changes behind the model. Oil flow visualization was used to understand the mechanism behind oscillator effectiveness. An energy analysis suggests that this method may be viable from a flow energy perspective.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051109-051109-11. doi:10.1115/1.4029572.

The unsteady phenomena of a low specific speed pump–turbine operating in pump mode were characterized by dynamic pressure measurements and high-speed flow visualization of injected air bubbles. Analyses were carried out on the pressure signals both in frequency and time–frequency domains and by bispectral protocol. The results obtained by high-speed camera were used to reveal the flow pattern in the diffuser and return vanes channels The unsteady structure identified in the return vane channel appeared both at full and part load condition. Furthermore, a rotating stall structure was found and characterized in the diffuser when the pump operated at part load. The characteristics of these two unsteady structures are described in the paper.

Commentary by Dr. Valentin Fuster

### Research Papers: Fundamental Issues and Canonical Flows

J. Fluids Eng. 2015;137(5):051201-051201-12. doi:10.1115/1.4029386.

Considered is a cylinder channel with a single row of ten aligned impinging jets, with exit flow in the axial direction at one end of the channel. For the present predictions, an unsteady Reynolds-Averaged Navier–Stokes (RANS) solver is employed for predictions of flow characteristics within and nearby the ten impingement jets, where the jet Reynolds number is 15,000. Spectrum analysis of different flow quantities is also utilized to provide data on associated frequency content. Visualizations of three-dimensional, unsteady flow structural characteristics are also included, including instantaneous distributions of Y-component vorticity, three-dimensional streamlines, shear layer parameter $ψ$, and local static pressure. Kelvin–Helmholtz vortex development is then related to local, instantaneous variations of these quantities. Of particular importance are the cumulative influences of cross flows, which result in locally increased shear stress magnitudes, enhanced Kelvin–Helmholtz vortex generation instabilities, and increased magnitudes and frequencies of local flow unsteadiness, as subsequent jets are encountered with streamwise development.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051202-051202-9. doi:10.1115/1.4029630.

The gas flow characteristics in rectangular cross section converging–diverging micronozzles incorporating the effect of three-dimensional (3D) rough surface topography are investigated. The fractal geometry is utilized to describe the multiscale self-affine roughness. A first-order slip model suitable for rough walls is adopted to characterize the slip velocities. The flow field in micronozzles is analyzed by solving 3D Navier–Stokes (N–S) equation. The results show that the dependence of mass flow rate on the pressure difference has a good agreement with the reported results. The presence of surface topography obviously perturbs the gas flow near the wall. Moreover, as the surface roughness height increases, this perturbation induces the supersonic “multiwaves” phenomenon in the divergent region, in which the Mach number fluctuates. In addition, the effect of 3D surface topography on performance is also investigated.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051203-051203-22. doi:10.1115/1.4029631.

This study focuses on interactions of vortices generated by a family of eddy-promoting upstream rectangular cylinders (of different heights a* and widths b*) with the shear layers of a downstream square cylinder (of height A*) placed near a plane in an in-line tandem arrangement under the incidence of Couette–Poiseuille flow based nonuniform linear/nonlinear velocity profile. The dimensionless operational parameters are cylinders spacing distance S, ratio of heights $r2=a*/A*$ (≤1), aspect ratio $r1=b*/a*$ (≤1), Reynolds number Re (based on the velocity at height A* for Couette flow), $ReU2$ (based on the velocity at height 10A* for Couette–Poiseuille flow), and nondimensional pressure gradient P at the inlet. The governing equations are solved numerically through a pressure-correction-based iterative algorithm (SIMPLE) with the quadratic upwind interpolation for convective kinematics (QUICK) scheme for convective terms. The major issue of appearing multiple peaks in the spectrum of the fluctuating lift coefficient of the downstream cylinder is addressed and justified exhibiting the flow patterns. While considering the rectangular shape (for the upstream cylinder) and nonlinear velocity (at the inlet), the possibility of generating the unsteadiness in the steady wake flow of the downstream cylinder at a Re (based on height a*) less than the critical Re for the downstream cylinder is documented here. The dependence of flow characteristics of the downstream cylinder on the angle of incident linear velocity at specific S and r1 is also demonstrated here. It is observed that the discontinuous jump in the aerodynamic characteristics (due to a sudden change from one distinct flow pattern to the other in the critical spacing distance regime) is directly proportional to the height of the vortex generator. Increasing P under the same characteristic velocity causes the steady flow of cylinder(s) to convert to a periodic flow and reduces the critical spacing distance for the vortex generator.

Commentary by Dr. Valentin Fuster

### Research Papers: Multiphase Flows

J. Fluids Eng. 2015;137(5):051301-051301-7. doi:10.1115/1.4029080.

A mathematical method was conducted to investigate the mechanism of formation of cavitation cloud, while the inlet stream contains a fluctuating flow. Based on the Rayleigh–Plesset equation and the static pressure distribution in a cone flow channel, parameters related to cavitation cloud are estimated, and the collapse pressure of the cavitation cloud is obtained by solving the equation of Mørch’s model. Moreover, the effect of the amplitude and frequency of inlet fluctuation on cavitation is studied. Results revealed that the smaller the amplitude, the smaller the cloud and the lower the collapse pressure. And frequency of fluctuating stream was found to have a relative great effect on frequency of peak pressure but not so significant on peak collapse pressure and size of cloud. It is concluded that limiting the inlet fluctuation reduces the erosion and noise generated by cavitation collapse.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2015;137(5):051302-051302-9. doi:10.1115/1.4029533.

We are comparing results of numerical simulations against high-speed simultaneous observations of cavitation and cavitation erosion. We performed fully compressible, cavitating flow simulations to resolve the formation of the shock waves at cloud collapse—these are believed to be directly related to the formation of the damage. Good agreements were noticed between calculations and tests. Two high pressure peaks were found during one cavitation cycle. One relates to the cavitation collapse and the other one corresponds to the cavitation shed off, both contributing to a distinctive stepwise erosion damage growth pattern. Additional, more precise, simulations with much shorter time step were performed to investigate the processes of cavitation collapse and shedding off in more detail. There the importance of small cavitation structures which collapse independently of the main cloud was found. The present work shows a great potential for future development of techniques for accurate predictions of cavitation erosion by numerical means only.

Commentary by Dr. Valentin Fuster

### Research Papers: Techniques and Procedures

J. Fluids Eng. 2015;137(5):051401-051401-9. doi:10.1115/1.4029313.

Pump-turbine characteristics greatly affect the operational stability of pumped-storage plants. In particular, the S-shaped region of the characteristic curves leads to severe instability during runaway conditions with servomotor failure. Thus, this paper aims to investigate the runaway stability criterion by considering all of the important effects in the hydromechanical system. The criterion also helps to judge the S-characteristics of pump-turbines and can provide a guide for plant design and turbine optimization. First, the pump-turbine characteristic curves are locally linearized to obtain formulae for the relative changes of discharge and torque, which depend on the relative changes of rotational speed and water head. Control theory is then applied to analyze the high-order system, by importing the transfer function of the conduits in the elastic mode. Two different kinds of oscillation are found, associated with water inertia and elasticity, based on the established theoretical mathematical model. New stability criteria for the inertia wave in both rigid and elastic modes are developed and compared. The comparison reveals the effect of the water elasticity on runaway instability, which has often been neglected in the previous work. Other effects, such as friction loss and the timescales of water flow and machinery, are also discussed. Furthermore, the elastic wave, which often has a higher frequency than the inertia wave, is also studied. The stability criterion is deduced with analyses of its effects. Based on the stability criteria for the inertia wave and elastic wave, the unstable regions for two waves of the S-shaped curves are plotted. The results are applied to explain the development from inertia wave to elastic wave during transient behavior at runaway conditions. Model tests of runaway conditions were conducted on a model pumped storage station and the experimental data show good agreement with the theoretical analyses regarding the instability of the inertia wave. Further analyses and validations are made based on transient simulations. The simulation software topsys, which uses the method of characteristics (MOC) and a unit boundary represented by a spatial pump-turbine characteristic surface, was applied to analyze the elastic wave. This also supports the conclusions of the theoretical research.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Fluids Eng. 2015;137(5):054501-054501-9. doi:10.1115/1.4029573.

In the paper, the selected aspects concerning description of viscoelastic behavior of pipe walls during unsteady flow are analyzed. The alternative convolution expression of the viscoelastic term is presented and compared with the corresponding term referring to unsteady friction. Both approaches indicate similarities in the forms of impulse response functions and the parameter properties. The flow memory was introduced into convolution and its impact on the solution was analyzed. To reduce the influence of the numerical errors, implicit Preissmann scheme was applied. The calculation results were verified based on laboratory tests. The study indicated that the flow memory is related to pipe material properties and significantly influences the calculation results. It also showed the role of retardation time in calculations and its relation to flow memory. The proposed approach enabled more detailed analysis of viscoelasticity impact on the pressure characteristics.

Commentary by Dr. Valentin Fuster