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### Research Papers: Flows in Complex Systems

J. Fluids Eng. 2014;136(7):071101-071101-10. doi:10.1115/1.4026477.

The unsteady flow inside a large centrifugal pump with stay vanes was analyzed in this study. The static performance and pressure fluctuations in the pump were numerically predicted and were compared with experimental data. Considering the relative positions of the impeller to the volute tongue and stay vanes, the static performance which was obtained using a full unsteady calculation was compared with traditional steady calculation results. A comparison of the results with the experimental data showed that the operation condition farther from the design condition resulted in larger differences between the steady simulation and experimental results, with errors beyond reasonable limits, while the performance curves obtained by the unsteady calculations were closer to the experimental data. A comparison of the pressure fluctuations at four monitoring points with the experimental data showed that the amplitudes at HVS1 and HVS2 are much larger than at HD1 and HD2. The main frequency for these four monitoring points, which agreed well with the experimental data, was the blade passing frequency. The relative obvious errors in pressure fluctuations for HD1and HD2 were due to the inlet flow rate variation of the simulation. Thus, unsteady numerical simulations can be used to predict the pressure fluctuations when designing a pump.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071102-071102-13. doi:10.1115/1.4026880.

Tandem blades can be superior to single blades, particularly when large turning angles are required. This is well documented in the open literature and many investigations have been performed on the 2D-flow of tandem cascades to date. However, much less information on the flow near the sidewalls is available. Thus, the question arises as to how the geometry of a tandem cascade should be chosen near the sidewall in order to minimize the flow losses for large turning angles. The present work examines the 3D-flow field in the region of the sidewall of two high turning tandem cascades. A large spacing ratio was chosen for the forward blade of the first tandem cascade ($(t/l)1=1.92$). The second tandem cascade possessed a smaller spacing ratio for the forward blades ($(t/l)1=1.0$). Both cascades had the same total spacing ratio of $t/l=0.6$. Flow phenomena, such as the corner stall of the 3D boundary layer near the sidewall, are examined using both numerical and experimental methods. The empirical correlations of Lieblein and Lei are applied. The flow topology of both tandem cascades is explained and the locations of loss onset are identified. In addition, oil pictures from experiments and streamline pictures of the numerical simulations are shown and discussed for the flow close to the sidewalls. Finally, design rules such as the aerodynamic load splitting and the spacing ratio of the forward- and aft-blades, etc. are taken into account. The examinations are performed for tandem cascades designed for flow turning of approximately $50 deg$ at a Reynolds number of $8×105$. The tandem cascades consist of NACA65 blades with circular camber lines and an aspect ratio of $b/l=1.0$.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071103-071103-7. doi:10.1115/1.4026665.

In this paper, the flow and mass transfer of a two-dimensional unsteady stagnation-point flow over a moving wall, considering the coupled blowing effect from mass transfer, is studied. Similarity equations are derived and solved in a closed form. The flow solution is an exact solution to the two-dimensional unsteady Navier–Stokes equations. An analytical solution of the boundary layer mass transfer equation is obtained together with the momentum solution. The examples demonstrate the significant impacts of the blowing effects on the flow and mass transfer characteristics. A higher blowing parameter results in a lower wall stress and thicker boundary layers with less mass transfer flux at the wall. The higher wall moving parameters produce higher mass transfer flux and blowing velocity. The Schmidt parameters generate a local maximum for the mass transfer flux and blowing velocity under given wall moving and blowing parameters.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071104-071104-9. doi:10.1115/1.4026859.

The wandering motion of tip vortices trailed from a hovering helicopter rotor is described. This aperiodicity is known to cause errors in the determination of vortex properties that are crucial inputs for refined aerodynamic analyses of helicopter rotors. Measurements of blade tip vortices up to 260 deg vortex age using stereo particle-image velocimetry (PIV) indicate that this aperiodicity is anisotropic. We describe an analytical model that captures this anisotropic behavior. The analysis approximates the helical wake as a series of vortex rings that are allowed to interact with each other. The vorticity in the rings is a function of the blade loading. Vortex core growth is modeled by accounting for vortex filament strain and by using an empirical model for viscous diffusion. The sensitivity of the analysis to the choice of initial vortex core radius, viscosity parameter, time step, and number of rings shed is explored. Analytical predictions of the orientation of anisotropy correlated with experimental measurements within 10%. The analysis can be used as a computationally inexpensive method to generate probability distribution functions for vortex core positions that can then be used to correct for aperiodicity in measurements.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071105-071105-9. doi:10.1115/1.4026584.

A series of numerical simulations for a Francis turbine were carried out to estimate the unsteady motion of the cavity in the draft tube of the turbine under a much larger flow rate condition than the swirl-free flow rate. The evaporation and condensation process was described by using a simplified Rayleigh–Plesset equation. A two-phase homogeneous model was adopted to calculate the mixture of gas and liquid phases. Instantaneous pressure monitored at a point on the draft tube formed long-period pulsations. Detailed analysis of the simulation results clarified the occurrence of a uniquely shaped cavity and the corresponding flow pattern in every period of the pressure pulsations. The existence of a uniquely shaped cavity was verified with an experimental approach. A simulation without rotor-stator interaction also obtained long-period pulsations after an extremely long computational time. This result shows that the rotor-stator interaction does not contribute to the excitation of long-period pulsations.

Commentary by Dr. Valentin Fuster

### Research Papers: Fundamental Issues and Canonical Flows

J. Fluids Eng. 2014;136(7):071201-071201-9. doi:10.1115/1.4026663.

The paper presents an analytical solution of velocity, mass flow rate, and pressure distribution for fully developed gaseous slip flow in nonsymmetric and symmetric parabolic microchannels. The flow is considered to be steady, laminar, and incompressible with constant fluid properties. Fully developed gaseous slip flow in microchannels of parabolic cross section is solved analytically for various aspect ratios using a parabolic cylindrical coordinate system on applying the method of separation of variables. Prior to apply separation of variables, Arfken transform [Arfken, 1970, Mathematical Methods for Physicists, Academic Press, Orlando, FL, Ch. 2] was used on momentum equations and first-order slip boundary conditions at each channel wall were imposed. A simple model is proposed to predict the friction factor and Reynolds number product $fRe$ for slip flow in parabolic microchannels. Through the selection of a characteristic length scale, the square root of cross-sectional area and the effect of duct shape have been minimized. The results of a normalized Poiseuille number for symmetric parabolic microchannels ($ɛ=1$) shows good agreement with the previous results [Morini et al., 2004, “The Rarefaction Effect on the Friction Factor of Gas Flow in Micro/Nano-Channels,” Superlattices Microstruct., 35(3–6), pp. 587–599; Khan and Yovanovich, 2008, “Analytical Modeling of Fluid Flow and Heat Transfer in Microchannel/Nanochannel Heat Sinks,” J. Thermophys. Heat Transf., 22(3), pp. 352–359] for rectangular microchannels. The developed model can be used to predict mass flow rate and pressure distribution of slip flow in parabolic microchannels.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071202-071202-8. doi:10.1115/1.4026857.

Several examples illustrating the energy balance associated with a mixing process at the interface of a planar dynamical model describing two-phase perfect fluid circulating around a circle with a sufficiently large radius within a central gravitational field are presented. The model is associated with the spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around the Earth. The fluid is supposed to be irrotational and pressure on a outer layer is constant. It is postulated that the total fluid depth is small compared to the radius of the circle and the gravity vector is directed to the center of the circle. Under these assumptions, this problem can be associated with a spatial and temporal structure of the zonally averaged global-scale atmospheric longitudinal circulation around equatorial plane. The model is the subject to the rigid lid approximation to the external boundary conditions for the outer fluid layer. One of the novelties in this work is the derivation of the nonlinear shallow water model by means of the average velocity. This introduction simplifies essentially further potential studies of mixing criteria associated with nonlinear mathematical models representing shallow water equations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071203-071203-11. doi:10.1115/1.4026858.

A computational study of the Richtmyer–Meshkov instability (RMI) is presented for an inclined interface perturbation in support of experiments being performed at the Texas A&M shock tube facility. The study is comprised of 2D, viscous, diffusive, compressible simulations performed using the arbitrary Lagrange Eulerian code, ARES, developed at Lawrence Livermore National Laboratory. These simulations were performed to late times after reshock with two initial interface perturbations, in the linear and nonlinear regimes each, prescribed by the interface inclination angle. The interaction of the interface with the reshock wave produced a complex 2D set of compressible wave interactions including expansion waves, which also interacted with the interface. Distinct differences in the interface growth rates prior to reshock were found in previous work. The current work provides in-depth analysis of the vorticity and enstrophy fields to elucidate the physics of reshock for the inclined interface RMI. After reshock, the two cases exhibit some similarities in integral measurements despite their disparate initial conditions but also show different vorticity decay trends, power law decay for the nonlinear and linear decay for the linear perturbation case.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071204-071204-14. doi:10.1115/1.4026881.

This paper presents experimental investigations of the flow-field characteristics downstream a Scaled-Up Micro-Tangential-Jet (SUMTJ) film-cooling scheme using the particle image velocimetry (PIV) technique over a flat plate. The SUMTJ scheme is a shaped scheme designed so that the secondary jet is supplied tangentially to the surface. The scheme combines the thermal benefits of tangential injection and the enhanced material strength of discrete holes’ schemes compared with continuous slot schemes. The flow-field characteristics downstream one row of holes were investigated at three blowing ratios, 0.5, 1.0, and 1.5, and were calculated based on the scheme exit area. A density ratio of unity, a Reynolds number of 1.16 × 105, and an average turbulence intensity of 8% were used throughout the investigations. The performance of the SUMTJ scheme was compared to that of the circular hole scheme, base line case case, at the same test conditions and blowing ratios. From the investigations, it was noticeable that the SUMTJ scheme jet stays attached to the surface for long downstream distances at all investigated blowing ratios. Moreover, the lateral expansion angles of the scheme help perform a continuous film from adjacent jets close to the schemes’ exits; however, they have a negative impact on the uniformity of the film thickness in the lateral direction. The vorticity strength downstream the SUMTJ scheme in the y-z plane was much less than the vorticity strength downstream the circular scheme at all blowing ratios. However, the vorticity behavior in the shear layer between the secondary SUMTJ scheme jet and the main stream was changing dramatically with the blowing ratio. The latter is expected to have a significant impact on the film-cooling performance as the blowing ratio increases.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071205-071205-9. doi:10.1115/1.4026666.

This article describes the development of a reduced order model (ROM) based on residual minimization for a generic power-law fluid. The objective of the work is to generate a methodology that allows for the fast and accurate computation of polymeric flow fields in a multiparameter space. It is shown that the ROM allows for the computation of the flow field in a few seconds, as compared with the use of computational fluid dynamics (CFD) methods in which the central processing unit (CPU) time is on the order of hours. The model fluid used in the study is a polymeric fluid characterized by both its power-law consistency index m and its power-law index n. Regarding the ROM development, the main difference between this case and the case of a Newtonian fluid is the order of the nonlinear terms in the viscous stress tensor: In the case of the polymeric fluid these terms are highly nonlinear while they are linear when a Newtonian fluid is considered. After the method is validated and its robustness studied with regard to several parameters, an application case is presented that could be representative of some industrial situations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071206-071206-7. doi:10.1115/1.4026667.

Harmonic oscillations from cantileverlike structures have found use in applications ranging from thermal management to atomic force microscopy and propulsion, due to their simplicity in design and ease of implementation. In addition, making use of resonance conditions, a very energy efficient solution is achievable. This paper focuses on the application of providing thrust through cantilever oscillations at or near the first mode of resonance. This method of actuation provides a balance between full biomimicry and ease of fabrication. Previous studies have shown promise in predicting the propulsion performance based on the operating parameters, however, they have only considered a single cantilever geometry. Here, additional cantilever sizes and materials are included, yielding a much larger design space to characterize the thrust trends. The thrust data is experimentally captured and is assembled into two sets of predictive correlations. The first is based on Reynolds and Strouhal numbers, while the second only employs the Keulegan–Carpenter number. Both correlations are proven to predict the experimental data and can be shown to yield nearly identical proportional relationships after accounting for the cantilever frequency response. The findings presented in this research will aid in further understanding and assessing the capabilities of thrust generation for oscillating cantilevers, but also provides a foundation for other applications such as convection heat transfer and fluid transport.

Commentary by Dr. Valentin Fuster

### Research Papers: Multiphase Flows

J. Fluids Eng. 2014;136(7):071301-071301-7. doi:10.1115/1.4026855.

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle with a throat. The presence of a throat in an expanding-contracting nozzle can result in flow transition from the subsonic regime to the supersonic regime (choked conditions) for a bubbly mixture flow, which may result in a substantial increase in jet thrust. This increase would primarily arise from the fact that the injected gas bubbles expand drastically in the supersonic region of the flow. In the current work, an analytical 1D model is developed to capture choked bubbly flow in an expanding-contracting nozzle with a throat. The study provides analytical and numerical support to analytical observations and serves as a design tool for nozzle geometries that can achieve efficient choked bubbly flows through nozzles. Starting from the 1D mixture continuity and momentum equations, along with an equation of state for the bubbly mixture, expressions for mixture velocity and gas volume fraction were derived. Starting with a fixed geometry and an imposed upstream pressure for a choked flow in the nozzle, the derived expressions were iteratively solved to obtain the exit pressures and velocities for different injected gas volume fractions. The variation of thrust enhancement with the injected gas volume fraction was also studied. Additionally, the geometric parameters were varied (area of the exit, area of the throat) to understand the influence of the nozzle geometry on the thrust enhancement and on the flow conditions at the inlet. This parametric study provides a performance map that can be used to design a bubble augmented waterjet propulsor, which can achieve and exploit supersonic flow. It was found that the optimum geometry for choked flows, unlike the optimum geometry under purely subsonic flows, had a dependence on the injected gas volume fraction. Furthermore, for the same injected gas volume fraction the optimum geometry for choked flows resulted in greater thrust enhancement compared to the optimum geometry for purely subsonic flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(7):071302-071302-12. doi:10.1115/1.4026582.

We report a detailed investigation on the measurement and prediction of pressure gradient characteristics of moderately viscous lubricating oil-water flow through a horizontal pipe of 0.025 m internal diameter. Experiments are carried out over a wide range of phase velocities of both oil (USO = 0.015–1.25 m/s) and water (USW  =  0.1–1.1 m/s). Experimental pressure gradients yield significant errors when fitted to the existing correlations, which are largely used for gas-liquid flow. To predict pressure gradient characteristics for liquid-liquid flow, the existing correlations need to be modified. We propose two correlations, based on the Lockhart–Martinelli's approach (by modifying the correlation between the Lockhart–Martinelli parameter and a two-phase multiplier suitable for the present system) and dimensionless analysis, following the Buckingham's Pi-theorem. We observe significant improvement in the prediction of pressure gradient. The correlation based on the dimensionless analysis predicts better with an average absolute error of 17.9%, in comparison with the modified Lockhart–Martinelli correlation, which yields an average error of 22%, covering all the flow patterns. The present analysis shows better prediction as compared to two-fluid model Zhang et al. (2012, “Modeling High-Viscosity Oil/Water Concurrent Flow in Horizontal and Vertical Pipes,” SPE J., 17(1), pp. 243–250) and Al-Wahaibi (2012, “Pressure Gradient Correlation for Oil-Water Separated Flow in Horizontal Pipes,” Exp. Therm. Fluid Sci., 42, pp. 196–203) work.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Fluids Eng. 2014;136(7):074501-074501-10. doi:10.1115/1.4026882.

The “sudden-rising head effect” may be prevalent in the head curve when a centrifugal pump transports highly viscous liquids, but it is not well understood presently. To clarify this effect the hydraulic performance of centrifugal pump when handling water and viscous oils was evaluated numerically by using a CFD code. The “sudden-rising head effect” is confirmed to exist at a higher viscosity and a certain large surface roughness. The viscosity and roughness, which make a transition of boundary layer flow pattern in both the impeller and volute to the hydraulically smooth regime from the fully rough one, are responsible for the effect.

Commentary by Dr. Valentin Fuster