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### Research Papers: Flows in Complex Systems

J. Fluids Eng. 2014;136(5):051101-051101-15. doi:10.1115/1.4026441.

S-shaped blade profiles with double camber find use in fully reversible turbomachines that can extract power from tides. Though noncavitating characteristics of S-blades were determined in the past, yet characterizing cavitating flow was not carried out. This work, which is the first step in this direction, uses a two-pronged approach of experimental and numerical characterization of cavitating flow past these hydrofoils. Experimental results indicate that as the angle of attack increases in either positive or negative directions, cavitation inception number increases. Minimum cavitation effect is observed at 2 deg, which is zero lift angle of attack. For higher angles of attack ($±6deg$, $±4deg$) and moderate or low cavitation number ($σ/σi≤0.3$), unsteady cloud cavitation was characterized through visual observation and from pressure fluctuation data. It was observed that for unsteady cavity shedding to take place is the length and thickness of the cavity should be more than 50% and 10% of the chord length, respectively. Predicting flow past this geometry is difficult and the problem may be compounded in many applications because of laminar-to-turbulence transition as well as due to the presence of cavitation. Present simulations indicate that the $k-kL-ω$ transition model may be useful in predicting hydrodynamic performance of this type of geometry and for the range of Reynolds number considered in this paper. Hydrodynamic performance under cavitation indicates that pumping mode is more adversely affected by cavitation and, hence, a fully reversible turbomachine may not perform equally well in turbine and pump modes as expected from noncavitating results.

Commentary by Dr. Valentin Fuster

### Research Papers: Fundamental Issues and Canonical Flows

J. Fluids Eng. 2014;136(5):051201-051201-9. doi:10.1115/1.4026199.

We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051202-051202-11. doi:10.1115/1.4026419.

Even after several decades of experimental and numerical testing, our present-day knowledge of the axisymmetric turbulent boundary layer (TBL) along long thin circular cylinders still lacks a clear picture of many fundamental characteristics. The main issues causing this reside in the experimental testing complexities and the numerical simplifications. An important characteristic that is crucial for routine scaling is the boundary layer length scales, but the downstream growth of these scales (boundary layer, displacement, and momentum thicknesses) is largely unknown from the leading to trailing edges. Herein, we combine pertinent datasets with many complementary numerical computations (large-eddy simulations) to address this shortfall. We are particularly interested in expressing the length scales in terms of the radius-based and axial-based Reynolds numbers (Rea and Rex). Although the composite dataset gave an averaged shape factor H = 1.09 that is substantially lower than the planar value (H = 1.27), the shape factor distribution along the cylinder axis actually begins at the flat plate value then decays logarithmically to near unity. The integral length scales displayed power-law evolutions with variable exponents until high Rea (Rea > 35,000) where both scales then mimic streamwise consistency. Beneath this threshold, their streamwise growth is much slower than the flat plate (especially at low-Rea). The boundary layer thickness grew according to an empirical expression that is dependent on both Rea and Rex where its streamwise growth can far exceed the planar turbulent flow. These unique characteristics rank the thin cylinder axisymmetric TBL as a separate canonical flow, which was well documented by the previous investigations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051203-051203-11. doi:10.1115/1.4026136.

Fully developed turbulent flow of water through a horizontal flow loop with concentric annular geometry was investigated using high resolution particle image velocimetry (PIV). Reynolds number range varied from 17,700 to 66,900. Axial mean velocity profile was found to be following the universal wall law (u+= y+) in the viscous sublayer (y+ < 10) and log law away from the wall (y+> 30). Radial position of zero shear stress and maximum velocity were found to be slightly different (2%). Root mean square values of velocity fluctuations velocity, Reynolds stresses, vorticity, and turbulent kinetic energy budget were also analyzed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051204-051204-10. doi:10.1115/1.4026512.

Smooth and rough wall turbulent boundary layer profiles are frequently scaled using the wall shear velocity u*, thus it is important that u* is accurately known. This paper reviews and assesses several wall similarity techniques to determine u* and compares results with data from the total stress, Preston tube, and direct force methods. The performance of each method was investigated using experimental repeatability data of smooth and rough wall turbulent boundary layer profiles at Reθ of 3330 and 4840, respectively, obtained using laser Doppler velocimetry (LDV) in a recirculating water tunnel. To validate the results, an analysis was also performed on the direct numerical simulation (DNS) data of Jimenez et al. (2010, “Turbulent Boundary Layers and Channels at Moderate Reynolds Numbers,” J. Fluid Mech., 657, pp. 335–360) at Reθ = 1968. The inner layer similarity methods of Bradshaw had low experimental uncertainty and accurately determined u* and ε for the DNS data and are the recommended wall similarity methods for turbulent boundary layer profile analysis. The outer layer similarity methods did not perform well, due to the need to simultaneously solve for three parameters: u*, ε, and Π. It is strongly recommended that the u* values determined using wall similarity techniques are independently verified using another method such as the total stress or direct force methods.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051205-051205-14. doi:10.1115/1.4026563.

A large eddy simulation (LES) of an incompressible spatially developing circular jet at a Reynolds number of 10,000 is performed. The shear-improved Smagorinsky model (Lévêque et al., 2007, “A Shear-Improved Smagorinsky Model for the Large-Eddy Simulation of Wall-Bounded Turbulent Flows,” J. Fluid Mech., 570, pp. 491–502) is used for the resolution of the subgrid stress tensor within the filtered three-dimensional unsteady Navier–Stokes equations. Higher-order spatial and temporal discretization schemes are used for capturing the details of the turbulent flow field. With the help of instantaneous and time-averaged flow data, the spatial transition from the laminar state to the turbulent is analyzed. Flow structures are visualized using isosurfaces of the Q-criterion. Instantaneous flow patterns show single tearing and multiple pairing processes. Tracing individual vortex rings over a longer time period, a detailed understanding of the vortex interaction is revealed. The observed trends and the length of the potential core are in conformity with the findings of earlier experiments. The time-averaged axial velocity profile shows that the jet attains self-similarity and the computed profile matches well with the experimental results of Hussein et al. (1994, “Velocity Measurements in a High-Reynolds-Number, Momentum-Conserving, Axisymmetric, Turbulent Jet,” J. Fluid Mech., 258, pp. 31–75). The centerline decay of the velocity and entrainment rate are in agreement with published experiments. The Reynolds stress components $u'u'¯$, $v'v'¯$, and $u'v'¯$ and the third-order velocity moment are in good agreement with thr experimental results, thus confirming the validity of the present simulation.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051206-051206-11. doi:10.1115/1.4026618.

Wing configuration is a parameter that affects the performance of wing-in-ground effect (WIG) craft. In this study, the aerodynamic characteristics of a new compound wing were investigated during ground effect. The compound wing was divided into three parts with a rectangular wing in the middle and two reverse taper wings with anhedral angle at the sides. The sectional profile of the wing model is NACA6409. The experiments on the compound wing and the rectangular wing were carried to examine different ground clearances, angles of attack, and Reynolds numbers. The aerodynamic coefficients of the compound wing were compared with those of the rectangular wing, which had an acceptable increase in its lift coefficient at small ground clearances, and its drag coefficient decreased compared to rectangular wing at a wide range of ground clearances, angles of attack, and Reynolds numbers. Furthermore, the lift to drag ratio of the compound wing improved considerably at small ground clearances. However, this improvement decreased at higher ground clearance. The drag polar of the compound wing showed the increment of lift coefficient versus drag coefficient was higher especially at small ground clearances. The Reynolds number had a gradual effect on lift and drag coefficients and also lift to drag of both wings. Generally, the nose down pitching moment of the compound wing was found smaller, but it was greater at high angle of attack and Reynolds number for all ground clearance. The center of pressure was closer to the leading edge of the wing in contrast to the rectangular wing. However, the center of pressure of the compound wing was later to the leading edge at high ground clearance, angle of attack, and Reynolds number.

Commentary by Dr. Valentin Fuster

### Research Papers: Multiphase Flows

J. Fluids Eng. 2014;136(5):051301-051301-11. doi:10.1115/1.4026476.

An experimental investigation has been made to detect cavitation in a pump–storage hydropower plant prototype suffering from leading edge cavitation in pump mode. Vibrations and acoustic emission on the housing of the turbine bearing and pressure fluctuations in the draft tube were measured and the corresponding signals were recorded and analyzed. The analysis was based on the analysis of high-frequency content of measured variables. The pump–storage hydropower plant prototype has been operated at various input loads and Thoma numbers. Several estimators of cavitation were evaluated according to a coefficient of determination between the Thoma number and cavitation estimators. The best results were achieved with a compound discharge coefficient cavitation estimator that is based on the discharge coefficient and several rms estimators: vibrations, acoustic emission, and pressure fluctuations. The compound discharge estimator was set as a product of the rms estimator and the squared discharge coefficient. Cavitation estimators were evaluated in several intervals of frequencies; the best frequency interval for the vibration sensor on the turbine cover was from 24 to 26 kHz, for the vibration sensor on the guide vane 36–40 kHz, for the acoustic emission sensor on the turbine cover 140–145 kHz, and for the pressure fluctuation sensor in the draft tube wall 130–150 kHz.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051302-051302-10. doi:10.1115/1.4026565.

This study was undertaken to look at the effect of a slight inclination of pipe on upward flow characteristics especially at 10 deg from vertical position. Air-silicone oil flows in a 67 mm diameter pipe have been investigated using a capacitance wire mesh sensor (WMS) and electrical capacitance tomography (ECT). They provide time and cross-sectionally resolved data on void fraction. Superficial gas and liquid velocities of 0.05–1.9 and 0.05–0.5 were studied. Statistical methods and visual observation methods were used to characterize the fluid flows obtained into different flow patterns. From the output results from the tomography instruments, flow patterns were identified using both the reconstructed images as well as the characteristic signatures of Probability density function (PDF) plots of the time series of cross-sectionally averaged void fraction. Bubbly, cap bubble, slug, and churn flows were observed when the pipe was deviated by 10 deg from vertical pipe for the range of superficial gas velocities considered.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2014;136(5):051303-051303-8. doi:10.1115/1.4026583.

Cavitation generally occurs where the pressure is lower than the saturated vapor pressure. Based on large eddy simulation (LES) methodology, an approach is developed to simulate dynamic behaviors of cavitation, using $k-μ$ transport equation for subgrid terms combined with volume of fluid (VOF) description of cavitation and the Kunz model for mass transfer. The computation model is applied in a 3D field with an axisymmetric projectile at cavitation number σ = 0.58. Evolution of cavitation in simulation is consistent with the experiment. Clear understanding about cavitation can be obtained from the simulation in which many details and mechanisms are present. The phenomenon of boundary separation and re-entry jet are observed. Re-entry jet plays an important role in the bubble shedding.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Fluids Eng. 2014;136(5):054501-054501-8. doi:10.1115/1.4026544.