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IN THIS ISSUE

### TECHNICAL PAPERS

J. Fluids Eng. 2007;129(7):813-824. doi:10.1115/1.2742724.

This work is focused on the development of a reduced-order model based on experimental data for the design of feedback control for subsonic cavity flows. The model is derived by applying the proper orthogonal decomposition (POD) in conjunction with the Galerkin projection of the Navier-Stokes equations onto the resulting spatial eigenfunctions. The experimental data consist of sets of 1000 simultaneous particle image velocimetry (PIV) images and surface pressure measurements taken in the Gas Dynamics and Turbulent Laboratory (GDTL) subsonic cavity flow facility at the Ohio State University. Models are derived for various individual flow conditions as well as for their combinations. The POD modes of the combined cases show some of the characteristics of the sets used. Flow reconstructions with 30 modes show good agreement with experimental PIV data. For control design, four modes capture the main features of the flow. The reduced-order model consists of a system of nonlinear ordinary differential equations for the modal amplitudes where the control input appears explicitly. Linear and quadratic stochastic estimation methods are used for real-time estimation of the modal amplitudes from real-time surface pressure measurements.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):825-833. doi:10.1115/1.2742729.

This study deals with the optimization of the location of a synthetic jet on the suction side of an airfoil to control stall. The optimal location is found by coupling a time-accurate flow solver with adaptive mesh refinement/coarsening techniques and an automatic optimization algorithm. The flow and jet are modeled by the unsteady Reynolds-averaged Navier-Stokes equations (URANSE) with a near-wall low-Reynolds number turbulence closure. An unstructured grid refinement/coarsening method is used to automatically generate meshes adapted to the presence of the synthetic jet at a prescribed location. An optimization algorithm modifies the location of the synthetic jet to determine the best actuator location to increase the time-averaged lift for high angles of attack. The proposed methodology is applied to optimize the location of a synthetic jet on the suction side of the NACA 0012 airfoil at a Reynolds number $Re=2×106$ and incidences of $18deg$ and $20deg$. Finally, a physical analysis of the influence of the synthetic jet location on the control efficiency is proposed to provide some guidelines for practical jet positioning.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):834-841. doi:10.1115/1.2742723.

In this study, particle image velocimetry (PIV) is used to investigate the physical process of separated flow in a square channel roughened with periodically transverse ribs on one wall. The ribs obstruct the channel by 15% of its height and are arranged 12 rib heights apart. The Reynolds number, based on the bulk-mean velocity and the corresponding hydraulic diameter of the channel, is fixed at 22,000. Assuming flow periodicity in the streamwise direction, the investigated domain is between two consecutive ribs. The emphasis of this study is to give some insight into the turbulence mechanism associated with separation, reattachment, and subsequent redevelopment. Results are included for mean velocity, friction coefficient, vorticity thickness, Reynolds shear stress, anisotropy parameter, and production of turbulent kinetic energy and shear stress. Based on the two-point correlation profiles, Taylor microscales are derived to reveal the sizes of the turbulence structure in the longitudinal and lateral directions. Moreover, Galilean decomposition is applied to the instantaneous velocity fields. The result shows that the separated shear layer is dominated by the large-scale, unsteady vortical structures.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):842-851. doi:10.1115/1.2745840.

A new self-excited jet methodology was developed for the mixing enhancement of jet fluid with its surrounding, quiescent, stagnant, or coflowing fluid. The nozzles, of a square or rectangular cross section, featured two flexible side walls that could go into aerodynamically-induced vibration. The mixing of nozzle fluid was measured using planar laser-induced fluorescence (PLIF) from acetone seeded into the nozzle fluid. Overall, the self-excited jet showed enhanced mixing with the ambient fluid; for example, at $390Hz$ excitation a mixing rate enhancement of 400% at $x∕D=4$ and 200% at $x∕D=20$ over the unexcited jet. The mixing rate was sensitive to the excitation frequency, increasing by 60% with the frequency changing from 200 to $390Hz$ (corresponding to a Strouhal number from 0.052 to 0.1). It was also observed that the mixing rate increased with the coflow velocity. To explain the observed mixing enhancement, the flow field was studied in detail using four-element hot wire probes. This led to the observation of two pairs of counter rotating large-scale streamwise vortices as the dominant structures in the excited flow. Shedding right from the nozzle exit, these inviscid vortices provided a rapid transport of the momentum and mass between the jet and the surrounding fluid at a length scale comparable to half-nozzle diameter. Moreover, the excited jet gained as much as six times the turbulent kinetic energy at the nozzle exit over the unexcited jet. Most of the turbulent kinetic energy is concentrated within five diameters from the nozzle exit, distributed across the entire jet width, explaining the increased mixing in the near field.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):852-870. doi:10.1115/1.2742736.

The wake of a square cylinder at zero angle of incidence oscillating inline with the incoming stream has been experimentally studied. Measurement data are reported for Reynolds numbers of 170 and 355. The cylinder aspect ratio is set equal to 28 and a limited study at an aspect ratio of 16 has been carried out. The frequency of oscillation is varied around the Strouhal frequency of a stationary cylinder, and the amplitude of oscillation is 10–30% of the cylinder size. Spatial and temporal flow fields in the cylinder wake have been studied using particle image velocimetry and hot-wire anemometry, the former providing flow visualization images as well. A strong effect of forcing frequency is clearly seen in the near wake. With an increase in frequency, the recirculation length substantially reduces and diminishes the time-averaged drag coefficient. The time-averaged vorticity contours show that the large-scale vortices move closer to the cylinder. The rms values of velocity fluctuations increase in magnitude and cluster around the cylinder as well. The production of turbulent kinetic energy shows a similar trend as that of spanwise vorticity with the former showing greater asymmetry at both sides of the cylinder centerline. The instantaneous vorticity contours show that the length of the shear layer at separation decreases with increasing frequency. The effect of amplitude of oscillation on the flow details has been studied when the forcing frequency is kept equal to the vortex-shedding frequency of the stationary cylinder. An increase in amplitude diminishes the time-averaged drag coefficient. The peak value of rms velocity increases, and its location moves upstream. The length of the recirculation bubble decreases with amplitude. The reduction in drag coefficient with frequency and amplitude is broadly reproduced in experiments with the cylinder of lower aspect ratio.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):871-876. doi:10.1115/1.2745838.

Synchronous rotating cavitation is known as one type of cavitation instability, which causes synchronous shaft vibration or head loss. On the other hand, cavitation in cryogenic fluids has a thermodynamic effect on cavitating inducers because of thermal imbalance around the cavity. It improves cavitation performances due to delay of cavity growth. However, relationships between the thermodynamic effect and cavitation instabilities are still unknown. To investigate the influence of the thermodynamic effect on synchronous rotating cavitation, we conducted experiments in which liquid nitrogen was set at different temperatures ($74K$, $78K$, and $83K$). We clarified the thermodynamic effect on synchronous rotating cavitation in terms of cavity length, fluid force, and liquid temperature. Synchronous rotating cavitation occurs at the critical cavity length of $Lc∕h≅0.8$, and the onset cavitation number shifts to a lower level due to the lag of cavity growth by the thermodynamic effect, which appears significantly with rising liquid temperature. Furthermore, we confirmed that the fluid force acting on the inducer notably increases under conditions of synchronous rotating cavitation.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):877-885. doi:10.1115/1.2742738.

The present paper illustrates the setup and the preliminary results of an experimental investigation of cavitation flow instabilities carried out by means of a high-speed camera on a three-bladed inducer in the cavitating pump rotordynamic test facility (CPRTF) at Alta S.p.A. The brightness thresholding technique adopted for cavitation recognition is described and implemented in a semi-automatic algorithm. In order to test the capabilities of the algorithm, the mean frontal cavitating area has been computed under different operating conditions. The tip cavity length has also been evaluated as a function of time. Inlet pressure signal and video acquisitions have been synchronized in order to analyze possible cavitation fluid-dynamic instabilities both optically and by means of pressure fluctuation analysis. Fourier analysis showed the occurrence of a cavity length oscillation at a frequency of $14.7Hz$, which corresponds to the frequency of the rotating stall instability detected by means of pressure oscillation analysis.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):886-893. doi:10.1115/1.2742748.

An experimental work has been carried out to investigate the dynamic behavior and the intensity of erosive partial cavitation on a 2-D hydrofoil. Both sheet (stable) and cloud (unstable) cavitation have been tested in a cavitation tunnel for various free stream velocities. Special attention has been given to validate the use of acceleration transducers for studying the physical process. In particular, the modulation in amplitude of the cavitation induced vibrations in a high frequency band has allowed us to determine the shedding frequency and the relative intensity of the collapse process for each testing condition. Regarding the cavity dynamics, a typical Strouhal value based on its length of about 0.28 has been found for cloud cavitation; meanwhile, for sheet cavitation, it presents a value of about 0.16. Furthermore, the level of the vibration modulation in the band from $45kHz$ to $50kHz$ for cloud cavitation shows a power law dependency on the free stream velocity as well as a good correlation with the pitting rate measured on stainless steel samples mounted on the hydrofoil.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(7):894-901. doi:10.1115/1.2742730.

A nonlocal pressure equation is derived from mean-field free energy theory for calculating liquid-vapor systems. The proposed equation is validated analytically by showing that it reduces to van der Waals’ square-gradient approximation under the assumption of slow density variations. The proposed nonlocal pressure is implemented in the mean-field free energy lattice Boltzmann method (LBM). The LBM is applied to simulate equilibrium liquid-vapor interface properties and interface dynamics of capillary waves and oscillating droplets in vapor. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, Laplace’s law of capillarity, dispersion relationship between frequency and wave number of capillary waves, and the relationship between radius and the oscillating frequency of droplets in vapor. It is shown that the nonlocal pressure formulation gives excellent agreement with theory.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):902-907. doi:10.1115/1.2742732.

A new particle sorting technique called aerodynamic vectoring particle sorting (AVPS) has recently been shown to be effective at sorting particles without particles contacting surfaces. The technique relies on turning a free jet sharply without extended control surfaces. The flow turning results in a balance of particle inertia and several forces (pressure, drag, added mass, and body forces) that depend on particle size and density. The present paper describes a theoretical study of particle sorting in a turning flow. The purpose of this study is to extend AVPS to parameter spaces other than those that are currently under investigation. Spherical particles are introduced into a turning flow in which the velocity magnitude increases like $r$. The trajectory of each particle is calculated using the particle equation of motion with drag laws that are appropriate for various Knudsen number regimes. Large data sets can be collected rapidly for various particle sizes, densities, turning radii, flow speeds, and fluid properties. Ranges of particle sizes that can be sorted are determined by finding an upper bound (where particles move in a straight line) and a lower bound (where particles follow flow streamlines). It is found that the size range of particles that can be sorted is larger for smaller turning radii, and that the range moves toward smaller particles as the flow speed and the particle-to-fluid density ratio are increased. Since this flow is laminar and 2-D, and particle loading effects are ignored, the results represent a “best case” scenario.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(7):908-912. doi:10.1115/1.2742725.

We present a coarse-grained steady-state solution framework for the Boltzmann kinetic equation based on a Newton-Broyden iteration. This approach is an extension of the equation-free framework proposed by Kevrekidis and coworkers, whose objective is the use of fine-scale simulation tools to directly extract coarse-grained, macroscopic information. Our current objective is the development of efficient simulation tools for modeling complex micro- and nanoscale flows. The iterative method proposed and used here consists of a short Boltzmann transient evolution step and a Newton-Broyden contraction mapping step based on the Boltzmann solution; the latter step only solves for the macroscopic field of interest (e.g., flow velocity). The predicted macroscopic field is then used as an initial condition for the Boltzmann solver for the next iteration. We have validated this approach for isothermal, one-dimensional flows in the low Knudsen number regime. We find that the Newton-Broyden iteration converges in $O(10)$ iterations, starting from arbitrary guess solutions and a Navier-Stokes based initial Jacobian. This results in computational savings compared to time-explicit integration to steady states when the time to steady state is longer than $O(40)$ mean collision times.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):913-920. doi:10.1115/1.2742737.

This paper deals with the temporal stability of a Carreau fluid flow down an inclined plane. As a first step, a weakly non-Newtonian behavior is considered in the limit of very long waves. It is found that the critical Reynolds number is lower for shear-thinning fluids than for Newtonian fluids, while the celerity is larger. In a second step, the general case is studied numerically. Particular attention is paid to small angles of inclination for which either surface or shear modes can arise. It is shown that shear dependency can change the nature of instability.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):921-928. doi:10.1115/1.2743666.

This work assesses the performance of two single-equation eddy viscosity transport models that are based on Menter’s transformation of the $k$-$ε$ and the $k$-$ω$ closures. The coefficients of both models are set exactly the same and follow directly from the constants of the standard $k$-$ε$ closure. This in turn allows a cross-comparison of the effect of two different destruction terms on the performance of single-equation closures. Furthermore, some wall-free modifications to production and destruction terms are proposed and applied to both models. An assessment of the baseline models with and without the proposed modifications against experiments, and the Spalart-Allmaras turbulence model is provided via several boundary-layer computations. Better performance is indicated with the proposed modifications in wall-bounded nonequilibrium flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):929-941. doi:10.1115/1.2742721.

The development of the large-scale structures in three-dimensional wall jets formed using long rectangular channels with aspect ratios of 1 and 4 was investigated using measurements of the fluctuating wall pressure and point measurements of the turbulent velocity throughout the near and intermediate field. The instantaneous pressure fluctuations in both jets were laterally asymmetric causing the fluctuating wall pressure to be poorly correlated across the jet centerline. A frequency-dependent proper orthogonal decomposition (POD) of the fluctuating pressure measurements indicated that the first two mode shapes were opposite and each mode made similar contributions to the mean square fluctuations at all frequencies in order to capture the instantaneous asymmetry of the pressure field. The mode shapes in the intermediate field of both jets were strongly frequency dependent, and a subsequent wavelet analysis indicated that there are both large-scale horseshoe structures that span one-half of the jet and separate, smaller, near-wall structures located near the jet centerline. The initial development of the large-scale structures in the two jets differed, with the most energetic fluctuations being more antisymmetric in the square jet.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(7):942-953. doi:10.1115/1.2743665.

Planar velocity measurements under cold-flow conditions in a swirl-stabilized dump combustor typical of land-based gas turbine combustors were carried out using two-dimensional particle image velocimetry (PIV). Axial, radial, and tangential velocity components were measured sequentially using two experimental configurations. Mean and root-mean-squared velocity components are presented along with instantaneous realizations of the flowfield. A numerical study of the flowfield using large-eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) techniques was conducted in an effort to help understand the complex hydrodynamics observed in the experiments. The agreement between the experimental data and LES simulation was good with both showing evidence of a precessing vortex core. The results of the RANS simulation were not as encouraging. The results provide a fundamental understanding of the complex flowfield associated with the relatively simple geometry and also serve as a baseline validation dataset for further numerical simulations of the current geometry. Validation of LES models in a highly swirled, nonreacting flowfield such as the work presented here is an essential step towards more accurate prediction in a reacting environment.

Commentary by Dr. Valentin Fuster