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Direct numerical simulations (DNS) are performed in a triply periodic unit cell of a face-centred cubic (FCC) lattice covering the unsteady inertial, to fully turbulent, flow regimes. The DNS data are used to quantify the flow topology, integral scales, turbulent kinetic energy (TKE) transport and anisotropy distribution in the tortuous geometry. Several unique flow features are observed within this low porosity configuration, where the mean flow undergoes strong acceleration and deceleration regions with presence of three-dimensional helical motions, weak wake-like structures behind spheres, stagnation and jet-impingement-like flows together with merging and spreading jets in the main pore space. The jet-impingement and weak wake-like flow structures give rise to regions with negative total TKE production. Unlike flows in complex shaped ducts, the turbulence intensity levels in the cross-stream directions are found to be larger than those in the streamwise direction. Furthermore, due to the compact nature and confined geometry of the FCC packing, the turbulent integral length scales are estimated to be less than 10 % of the bead diameter even for the lowest Reynolds number studied, indicating the absence of macroscale turbulence structures for this configuration. This finding suggests that even for the highly anisotropic flow within the pore, the upscaled flow statistics are captured well by the representative volumes defined by the unit cell.

Large-eddy simulations (LES) of a single-phase, turbulent flow in a 90° pipe bend are performed at three Reynolds numbers (5300, 27 000, and 45 000) to investigate the correlation between secondary flow motion and wall shear stresses, which is suspected to be a potential mechanism responsible for material erosion. The isothermal flows are validated against available experimental and numerical data first. The snapshot proper orthogonal decomposition (POD) is applied for the medium and high Reynolds number flows to identify the secondary flow motions and the oscillation of the Dean vortices that are found to cause swirl-switching. Distinguished frequencies of the POD time coefficients at Strouhal numbers of 0.25 and 0.28 are identified for Reynolds numbers at 27 000 and 45 000, respectively. Moreover, shear stress on the pipe wall and the associated power spectral density are obtained and shown to have the same oscillating frequency as the swirl-switching.

Particle-resolved direct numerical simulations (DNS) are performed to investigate the behaviour of an oscillatory flow field over a rough bed, corresponding to the experimental set-up of Keiller & Sleath (J. Fluid Mech., vol. 73 (04), 1976, pp. 673–691) for transitional and turbulent flows over a range of Reynolds numbers (95–400) based on the Stokes-layer thickness. It is shown that the roughness modulates the near-bed turbulence, produces streamwise horseshoe structures which then undergo distortion and breaking, and therefore reduces the large-scale anisotropy. A fully developed equilibrium turbulence is observed in the central part of the oscillation cycle, with two-component turbulence in the near-bed region and cigar-shaped turbulence in the outer region. A double averaging of the flow field reveals spatial inhomogeneities at the roughness scale and alternate paths of energy transport in the turbulent kinetic energy (TKE) budget. Contrary to the unidirectional, steady flow over rough beds, bed-induced production terms are important and comparable to the shear production term. It is shown that the near-bed velocity and pressure fluctuations are non-Gaussian, a result of critical importance for the modelling of incipient motion of sediment grains.

International audience; Direct numerical simulation of pore-scale turbulence is performed in a unit cell of a face-centered cubic lattice at three different pore Reynolds numbers (300, 500, and 1000). The pore-geometry gives rise to very low porosity resulting in rapid acceleration and deceleration of the flow in different regions. Eulerian statistics of mean velocity and turbulent kinetic energy are first described to provide a good understanding of the overall flow topology. In addition, the spatial variances and probability density functions for the instantaneous and temporal fluctuation velocities are computed to assess the higher-order statistics. The flow field is then analyzed using angular Lagrangian multiscale statistics of fluid particles to study their directional change at different timescales. Two power laws are observed for the evolution of the mean absolute angle as a function of time lag, demarking the early time and an intermediate, inertial range. The effect of the geometric confinement on the asymptotic behavior of the angular statistics is examined in detail. An asymptotic limit different than π/2 (corresponding to equidistribution of the mean angle, observed for three-dimensional isotropic turbulence with periodic boundaries) or 2 3 π (observed for two-dimensional wall-bounded turbulence) is obtained, representing the strong effect of geometric confinement on turbulence. Besides, the probability density functions (PDFs) for the instantaneous curvature angles are computed and the normalized PDFs are fit to a Fisher distribution. Furthermore, a Monte Carlo-based stochastic model is developed to predict the asymptotic curvature angle.

Natural lateral cavities in open channels are important because their lower water velocities promote water quality and provide refugia for organisms. Little is known about the influence of natural cavity shapes and roughness on flow structure and exchange dynamics. We investigated the effects of cavity shape (semi-circular, backward conic, and forward conic) and bed roughness on the flow structure and mean residence time (MRT) of a lateral cavity in a flume. All cavity shapes have a flow field dominated by a one-gyre recirculation pattern, contrasting results of rectangular cavities at similar Reynolds number and aspect ratios. Transverse velocity energy spectra indicate the flow is dominated by large-scale quasi-2D coherent structures. Fundamental frequencies of mixing layer vortex shedding are fastest for forward conic cavities and slowest for backward conic cavities. Fluid enters cavities at shallower mixing layer depths, and fluid exits cavities at deeper mixing layer depths. MRTs are smaller for hydraulically smooth cases and forward conic cavities due to higher recirculation velocities. MRTs are larger for rough bed cases and backward conic cavities. Rough flow cases have a strong correlation to a predictive MRT relationship derived by Jackson et al. (Water Resour Res: 10.1002/wrcr.20272 , 2013) (R 2 = 0.77); however, this predictive model does not work well for smooth cavities. Two MRT relationships were derived for smooth lateral cavities and both have strong power-law correlations to normalized MRT. Understanding cavity shape and bed roughness effects will provide a guideline for designing lateral embayments in stream restoration projects.

DNS coupled with a Point-Particle based model (PP) is used to study and predict particle-turbulence interactions in an open channel flow at Reynolds number of 811 (based on the friction velocity) corresponding to the experimental observations of [Righetti & Romano, JFM 2004]. Large particles of diameter 200 microns (8.1 in wall units) with average volume loading on the order of 0.001 are simulated using four-way coupling with closure models for drag, added mass, lift, pressure, and inter-particle/particle-wall collision forces. The point-particle model is able to accurately capture the effect of particles on the fluid flow in the outer layer where particles are under resolved. However, the dynamical interaction of particle-turbulence is under predicted in the near wall region where particles size are much larger than Kolmogorov scale and grid resolution in wall-normal direction, but smaller in both stream and span wise directions. It is conjectured that due to the large size particles compared to the Kolmogorov length scale near the bed, the effect of disturbances and deflections in the flow due to presence of such large particles is not captured using Lagrangian Point-Particle approach. For this configuration, the point-particle model is not appropriate in the near wall region and a hybrid resolved particle approach may be necessary.

The relative performance of two numerical approaches involving body conforming and non-conforming grids for simulating porescale flow in complex configurations of fixed packed beds of spheres at moderate pore Reynolds numbers (12 ⩽ Re ⩽ 600) is examined. In the first approach, an unstructured solver is used with tetrahedral meshes which conform to the boundaries of the porespace. In the second approach, a fictitious domain formulation is used which employs non-body conforming Cartesian grids and enforces the no-slip conditions on the pore boundaries implicitly through a rigidity constraint force. Sphere to sphere contact points, where the fluid gap between solid boundaries becomes infinitesimal, are not resolved by either approach, but this is shown to have a negligible effect on the local flow field at the Reynolds numbers considered. Detailed grid convergence studies of both steady and unsteady flow through simple cubic packings indicate that for a fixed level of uncertainty, significantly lower grid densities may be used with the fictitious domain approach which also does not require complex grid generation techniques. This translates into large savings for simulation of flow through realistic packed beds, which is shown by both analytic estimates and actual CPU timings. The applicability of the fictitious domain approach is demonstrated by simulating unsteady flow through a randomly packed bed of 51 spheres at a pore Reynolds number of 600. The results are used to examine the dominance of helical vortices in the porescale flow field.

[2] Accurate estimates of mass-exchange parameters in transient storage zones are needed to better understand and quantify solute transport and dispersion in riverine systems. Currently, the predictive mean residence time relies on an empirical entrainment coefficient with a range in variance due to the absence of hydraulic and geomorphic quantities driving mass exchange. Two empirically derived relationships are presented for the mean residence time of lateral cavities—a prevalent and widely recognized type of transient storage—in gravel-bed rivers and streams that incorporates hydraulic and geomorphic parameters. The relationships are applicable for gravel-bed rivers and streams with a range of cavity width to length (W/L) aspect ratios (0.2–0.75), shape, and Reynolds numbers (Re, ranging from 1.0 � 10 4 to 1.0 � 10 7 ). The relationships equate normalized mean residence time to nondimensional quantities: Froude number, Re, W/L, depth ratio (ratio of cavity to shear layer depth), roughness factor (ratio of shear to channel velocity), and shape factor (representing degree of cavity equidimensionality). One relationship excludes bed roughness (equation (13)) and the other includes bed roughness (equation (14)). The empirically derived relationships have been verified for conservative tracers (R 2 of 0.83) within a range of flow and geometry conditions. Topics warranting future research are testing the empirical relationship that includes the roughness factor using parameters measured in the vicinity of the cavity to reduce the variance in the correlation, and further development of the relationship for nonconservative transport.

When a few bubbles are entrained in a travelling vortex ring, it has been shown that, even at extremely low volume loadings, their presence can significantly affect the structure of the vortex core (Sridhar & Katz, J. Fluid Mech., vol. 397, 1999, pp. 171–202). A typical Euler–Lagrange point-particle model with two-way coupling for this dilute system, wherein the bubbles are assumed subgrid and momentum point sources are used to model their effect on the flow, is shown to be unable to capture accurately the experimental trends of bubble settling location, bubble escape and vortex distortion for a range of bubble parameters and vortex strengths. The bubbles experience significant amounts of drag, lift, added mass, pressure and gravity forces. However, these forces are in balance with each other as the bubbles reach a mean settling location away from the vortex core. The reaction force on the fluid due to the net summation of these forces alone is thus very small and is unable to affect the vortex core. By accounting for fluid volume displacement due to bubble motion, experimental trends on vortex distortion and bubble settling location are captured accurately. The fluid displacement effects are studied by computing various contributions to an effective volume displacement force and are found to be important even at low volume loadings. As the bubble size and hence bubble Reynolds number increase, the bubbles settle further away from the vortex centre and have strong potential for vortex distortion. The net volume displacement force depends on the radial pressure force, the radial settling location of the bubble, as well as the vortex Reynolds number. The resultant of the volume displacement force is found to be roughly at $4{5}^{\circ } $ with the vortex travel direction, resulting in wakes directed towards the vortex centre. Finally, a simple modification to the standard point-particle two-way coupling approach is developed wherein the interphase reaction source terms are consistently altered to account for the fluid displacement effects and reactions due to bubble accelerations.

Particle-resolved direct numerical simulations are performed using fictitious domain approach [1] to investigate the effect of an oscillatory flow field over a rough wall made up of a regular hexagonal pack of fixed spherical particles, in a setup similar to the experimental configuration of [2]. Turbulent flows at Reynolds numbers, Reδ = 200 and 400 (based on the Stokes-layer thickness δ) are studied. The unsteady nature of hydrodynamic forces on particles and their cross-correlations with measurable flow variables are investigated. Temporal correlations showed drag and lift to be positively correlated with a phase difference, which is approximately equal to the Taylor micro-scale related to drag/lift correlations. Spatio-temporal correlations between the flow field and particle-related quantities showed that the lift force is well correlated with the streamwise velocity fluctuations up to distances of the same order as the particle diameter, beyond which the cross correlation decays considerably. On the other hand, the pressure fluctuations are correlated and anti-correlated with the lift force in the front and aft regions of the particle, respectively, as a result of wake effects. Further statistical analyses showed that the near-bed velocity and pressure fluctuations fit poorly with Gaussian distributions. Instead, a fourth order Gram-Charlier distribution model is proposed that may have consequences on the Gaussian descriptions of sediment pick-up functions typically used in quantification of turbulent transport of sediment particles.Copyright © 2015 by ASME

Three-dimensional Reynolds averaged Navier-Stokes modeling, validated against experimental data, is used to parameterize the flow features and time scales in idealized rectangular cavities for a wide range of width-to-length ratios, 0.4≤W/L≤1.1, and Reynolds number based on the depth, 5,000≤RD≤20,300, representative of isolated dead zones in small natural streams. The flow features for this parameter range are similar to open cavity flows and consist of a mixing layer spanning the entire length of the dead zone together with a single main recirculation region. The Langmuir time scale (ratio of dead-zone volume to discharge) based on the assumption of a well-mixed dead zone is found to be a function of the mean rotation time scale (inverse of average rotation rate) within the dead zone, the momentum thickness of the upstream boundary layer, and the dead-zone width. The entrainment coefficient, used to relate the exchange velocity to the average free- stream velocity, is shown to be directly related...

Unsteadye owevolutioninaporouschamberwithsurfacemassinjectionsimulatinganozzlelessrocketmotorhas been investigated numerically. The analysis is based on a large-eddy-simulation technique in which the spatially e ltered and Favre averaged conservation equations for large, energy-carrying turbulent structures are solved explicitly. The effect of the unresolved scales is modeled semi-empirically by considering adequate dissipation rates for the energy present in the resolved scale motions. The e owe eld is basically governed by the balance between the inertia force and pressure gradient, as opposed to viscouseffects and pressuregradient corresponding to channel e ows without transpiration. It accelerates from zero at the head end and becomes supersonic in the divergent section of the nozzle. Three successive regimes of development, laminar, transitional, and fully turbulent e ow, are observed. Transition to turbulence occurs away from the porous wall in the midsection of the motor, and the peak in the turbulence intensity moves closer to the wall farther downstream as the local Reynolds number increases. Increase in pseudoturbulence level at the injection surface causes early transition to turbulence. As the e ow develops farther downstream, the velocity proe le transits into the shape of a fully developed turbulent pipe e ow with surface transpiration. The compressibility effect also plays an important role, causing transition of the mean velocity proe les from their incompressible e ow counterparts as the local Mach number increases. The e ow evolution is characterized primarily by three nondimensional numbers: injection Reynolds number, centerline Reynolds number, and momentum e ux coefe cient.

[1] Surface transient storage (STS) has functional significance in stream ecosystems because it increases solute interaction with sediments. After volume, mean residence time is the most important metric of STS, but it is unclear how this can be measured accurately or related to other timescales and field-measureable parameters. We studied mean residence time of lateral STS in small streams over Reynolds numbers (Re) 5000–200,000 and STS width to length (W/L) aspect ratios between 0.2–0.75. Lateral STS have flow fields characterized by a shear layer spanning the length of the STS entrance, and one primary gyre and one or more secondary gyre(s) in the STS. The study's purpose was to define, measure, and compare residence timescales: volume to discharge ratio (Langmuir timescale); area under normalized concentration curve; and characteristic time of exponential decay, and to compare these timescales to field measureable parameters. The best estimate of STS mean residence time—primary gyre residence time—was determined to be the first characteristic time of exponential decay. An apparent mean residence time can arise, which is considerably larger than other timescales, if probes are placed within secondary gyre(s). The Langmuir timescale is the minimum mean residence time, and is linearly correlated to channel velocity and STS width. The lateral STS mean residence time can be predicted using a physically based hydromorphic timescale derived by Uijttewaal et al. (2001) with an entrainment coefficient of 0.031 ± 0.009 for the Re and W/L studied.

The relative performance of (i) a body-fitted unstructured grid Navier-Stokes solver [Moin and Apte, AIAA J. 2006], and (ii) a fictitious domain based finite-volume approach [Apte et al. JCP 2009] is examined for simulating flow through packed beds of spheres at moderate flow rates, 50 ≲ Re ≲ 1300. The latter employs non-body conforming Cartesian grids and enforces the no-slip conditions on the pore boundaries implicitly through a rigidity constraint force. At these flow rates, fluid inertia can result in complex steady and unsteady pore scale flow features that influence macro-scale properties. We examine the requirements on both methods to properly capture these features in both simple and complex arrangements of spheres. First, two prototypical test cases of flow through packed beds are studied thoroughly at a range of Reynolds numbers in the inertial flow regime. Next flow through a random packing of 51 spheres at Re = 1322 is simulated using both methods. The suitability of both approaches to the complex configurations observed in large randomly packed beds is discussed.Copyright © 2012 by ASME

Natural stream systems contain a variety of flow geometries which contain flow separation, turbulent shear layers, and recirculation zones. This work focuses on stream dead zones. Characterized by slower flow and recirculation, dead zones are naturally occurring cutouts in stream banks. These dead zones play an important role in stream nutrient retention and solute transport studies. Previous experimental work has focused on idealized dead zone geometries studied in laboratory flumes. This work studies the capabilities of computational fluid dynamics (CFD) to investigate the scaling relationships between flow parameters of an idealized geometry and the passive scalar exchange rate. The stream geometry can be split into two main regions, the main stream flow and the dead zone. For the base case simulation, the depth-based Reynolds number is 16,000 and the dead zone is 0.5 depths in the flow direction and 7.5 depths in the transverse direction. Dead zone lengths and the main stream velocity were varied. These flow geometries are simulated using RANS turbulence model and the standard k–ω closure. Scalar transport in dead zones is typically modeled as a continuously stirred tank with an exchange coefficient for the interface across the shear layer. This first order model produces an exponential decay of scalar in the dead zone. A two region model is also developed and applied to the RANS results. Various time scales are found to characterize the exchange process. The volumetric time scale varies linearly with the aspect ratio. The simulations showed significant spatial variation in concentration leading to many different time scales. An optimized two region model was found to model these different time scales extremely well.Copyright © 2012 by ASME

Direct numerical simulations were performed to study the effect of an elastically mounted trailing edge actuator on the unsteady flow over a plunging, thin airfoil at Reynolds number of 14700 based on the chord length. The goal is to investigate potential benefits of flow-induced passive actuation of the trailing edge to the lift and drag characteristics of flapping MAV wings. The trailing edge, of 30% the chord length, is hinged to the wing using a torsion spring. It may undergo flow induced rotation resulting in dynamic variations in the airfoil shape. This trailing-edge spring assembly is modeled by simple, linear, torsion spring dynamics. A small parameter space varying the spring flexibility is explored to investigate its effect on the airfoil performance. Firstly, the second-order fictitious domain based finite volume approach by Apte et al. (J. Comp. Phys. 2009) was extended to model this fluid-structure interaction problem on a fixed, Cartesian mesh. Verification studies were conducted on a canonical test case of a spring-mounted cylinder to show good predictive capability. Secondly, flow over a plunging thin flat airfoil, at reduced frequency of 5.7 (10 Hz) and 5◦ angle of attack was investigated with and without the actuation of the trailing edge. It was found that, spring natural frequencies higher than the plunging frequency result in the tailing edge actuation that leads to net increase in thrust. The phase difference between the leading and trailing edge motions was found to vary based on the spring flexibility and played a critical role in governing wing performance.

Use of oscillatory actuation of the leading edge of a thin, flat, rigid airfoil, as a potential mechanism for control or improved performance of a micro-air vehicle (MAV), was investigated by performing direct numerical simulations at low Reynolds numbers. The leading edge of the airfoil is hinged at one-third chord length allowing dynamic variations in the effective angle of attack through specified oscillations (flapping). This leading edge actuation results in transient variations in the effective camber and angle of attack that can be used to alleviate the strength of the leading edge vortex at high angles of attack. A fictitious-domain based finite volume approach [Apte et al., JCP 2009] was used to compute the moving boundary problem on a fixed background mesh. The flow solver is three-dimensional, parallel, secondorder accurate, capable of using structured or arbitrarily shaped unstructured meshes and has been validated for a range of canonical test cases including flow over cylinder and sphere at different Reynolds numbers, and flow-induced by inline oscillation of a cylinder. Flow over a plunging SD7003 airfoil at two Reynolds numbers (1000 and 10,000) was computed and results compared with those obtained using AFRL’s high-fidelity solver [Visbal, AIAA J. (2009)] to show good predictive capability. To assess the effect of an actuated leading edge on the flow field and aerodynamic loads, two-dimensional parametric studies were performed on a thin, flat airfoil at 20 degrees angle of attack and Reynolds number of 14,700 (based on the chord length) with sinusoidal actuation of the leading edge over a range of reduced frequencies (k=0.57-11.4) and actuation amplitudes. It was found that high-frequency, low-amplitude actuation of the leading edge significantly alters the leading edge boundary-layer and vortex shedding and increases the mean lift-to-drag ratio. This study indicates that the concept of an actuated leading-edge has potential for development of control techniques to stabilize and maneuver MAVs in response to unsteady perturbations at low Reynolds numbers. The summer research at AFRL’s computational sciences division has resulted in several opportunities for future collaborations with AFRL scientists and researchers. At Oregon State, new projects for senior students are initiated to build and modify the existing physical setup and measure lift and drag coefficients.

Numerical modeling of methane-steam reforming is performed in a microchannel with heat input through Palladium-deposited channel walls corresponding to the experimental setup of Eilers [1]. The low-Mach number, variable density Navier-Stokes equations together with multicomponent reactions are solved using a parallel numerical framework. Methane-steam reforming is modeled by three reduced-order reactions occurring on the reactor walls. The surface reactions in the presence of Palladium catalyst are modeled as Neumann boundary conditions to the governing equations. Use of microchannels with deposited layer of Palladium catalyst gives rise to a non-uniform distribution of active reaction sites. The surface reaction rates, based on Arrhenius type model and obtained from literature on packed-bed reactors, are modified by a correction factor to account for these effects. The reaction-rate correction factor is obtained by making use of the experimental data for specific flow conditions. The modified reaction rates are then used to predict hydrogen production in a microchannel configuration at different flow rates and results are validated to show good agreement. It is found that the endothermic reactions occurring on the catalyst surface dominate the exothermic water-gas-shift reaction. It is also observed that the methane-to-steam conversion occurs rapidly in the first half of the mircochannel. A simple one-dimensional model solving steady state species mass fraction, energy, and overall conservation of mass equations is developed and verified against the full DNS study to show good agreement.Copyright © 2011 by ASME

Large-eddy simulation of flow over an open cavity corresponding to the experimental setup of Liu and Katz (2008, “Cavitation Phenomena Occurring Due to Interaction of Shear Layer Vortices With the Trailing Corner of a Two-Dimensional Open Cavity,” Phys. Fluids, 20(4), p. 041702) is performed. The filtered, incompressible Navier–Stokes equations are solved using a co-located grid finite-volume solver with the dynamic Smagorinsky model for a subgrid-scale closure. The computational grid consists of around 7×106 grid points with 3×106 points clustered around the shear layer, and the boundary layer over the leading edge is resolved. The only input from the experimental data is the mean velocity profile at the inlet condition. The mean flow is superimposed with turbulent velocity fluctuations generated by solving a forced periodic duct flow at a freestream Reynolds number. The flow statistics, including mean and rms velocity fields and pressure coefficients, are compared with the experimental data to show reasonable agreement. The dynamic interactions between traveling vortices in the shear layer and the trailing edge affect the value and location of the pressure minima. Cavitation inception is investigated using two approaches: (i) a discrete bubble model wherein the bubble dynamics is computed by solving the Rayleigh–Plesset and the bubble motion equations using an adaptive time-stepping procedure and (ii) a scalar transport model for the liquid volume fraction with source and sink terms for phase change. Large-eddy simulation, together with the cavitation models, predicts that inception occurs near the trailing edge similar to that observed in the experiments. The bubble transport model captures the subgrid dynamics of the vapor better, whereas the scalar model captures the large-scale features more accurately. A hybrid approach combining the bubble model with the scalar transport is needed to capture the broad range of scales observed in cavitation.

Controlling flow in an unsteady separating flow requires accurate information about the surface forces and the effect that vortical structures in the flow field have on those surface forces. A correlation between vortex passage and surface pressure is defined to determine appropriate locations for sensors on the surface of a square cylinder for control feedback. Data are generated using a large eddy simulation of flow over a square cylinder at Reynolds number of 21; 000. The flow is decomposed using proper orthogonal decomposition (POD) based on the frequency and energy content of the velocity and pressure fields around the square cylinder. Two data sets are reconstructed from the POD: (i) the first two modes containing approximately 75% of the energy of the flow and representing the large scale wake oscillation, and (ii) higher order modes containing the remainder of the energy of the flow representing smaller scale features in the flow, such as those shed from the leading edge. Vortex detection using the G function is performed on both data sets, where the G function is an area-averaged measure of the swirl around each point in the flow. Vortices in the data set composed of the first two modes tend to be large scale features and oscillate with the same frequency as the bluff body wake oscillation. The vortices detected in the higher order modes are smaller and tend to be the vortical structures shed from the leading edge of the square cylinder and convected downstream. In both data sets, the correlation values increase from the leading edge to the trailing edge, indicating that the downstream half of the square cylinder is most affected by vortical structures in the flow. Based on the correlation values, the segments of the square cylinder surface closest to the trailing edge would be best for sensor location to provide input for flow control.

Turbulent compressible flows in a porous chamber with acoustic oscillations have been analyzed numerically. Emphasis is placed on the interactions between turbulence and periodic motions, and their effect on mean flow properties. The impetus for the current work is to investigate the velocity-coupled combustion response of the propellant grain. Specifically, interactions between chamber gas dynamics and transient combustion responses of the propellants can be further explored based on present cold-flow analysis. The formulation treats the complete conservation equations of mass, momentum, and energy for the large energy-carrying turbulent structures. The effect of small, unresolved scales is modeled in this large eddy simulation (LES) technique. A stationary turbulent flowfield is first obtained and the coupling between the acoustic oscillations and turbulence are studied by imposing traveling waves over the mean flowfield. Loss of acoustic energy in a motor due to the flow-turning phenomenon is studied using a onedimensional analytical model. Turbulence characteristics and their effects on the mean flow properties are validated against available experimental data The impact of mean velocity transition and the turbulence kinetic energy transition on the turbulence structure are elucidated using time evolution of the voiticity and scalar fields. The flow in the duct undergoes three successive regimes of development governed by the injection, the turbulence, and the compressibility effect, respectively. The acoustic fields obtained in these regimes are quite different because of the turbulence-enhanced transport and dissipation rates. The shear waves obtained from periodic motions are damped in the turbulent region and serves as an additional mechanism for energy transfer to the turbulent flow. Enhanced production of vorticity in oscillatory flows may increase turbulence intensity in various parts of the chamber. The time-averaged effect of dynamical motions associated with the turbulence production in non-stationary flowfield is quite different from the stationary turbulent flow indicating strong interactions with acoustic excitations. The present work is a major step towards a complete analysis of the transient combustion response of propellants to the imposed periodic oscillations in turbulent environmenments. G = spatial filter function Nomenclature Gk u = amplification factor per time step cs =Smagorinsky constant f = flux vector in y-direction of Naviers ° J Stokes equations D = near wall damping function h = duct half-height, m B = filtered total energy per unit volume, i— —=• p/(Y-l)+0.5p(u+v) ,J/m l = turbulence intensity, Vu'u'+W, m/s E = flux vector in x-direction of Navierj = number of time steps required for one Stokes equations . E = turbulence energy , eddy life time f = frequency, Hz k = wave number, 1/m L = duct length, m * This work was performed under ONR Grant No. NOOO14-95-1-1338 1 Ph.D. Student, Department of Mechanical Engineering. 2 Professor, Department of Mechanical Engineering. m" = mass flux per unit area, kg/ ms M = mean cross-sectional-averaged Mach number Mc = mean centerline Mach number p = pressure, N/m Q = conservation variables vector of Navier-Stokes equations q = large scale velocity, m/s Re = Reynolds number S = strain-rate tensor, jo. = dynamic viscosity, kg/ms v = kinematic viscosity, m /s vs = subgrid-scale kinematic viscosity, m /s p = density, kg/m cr = CFL number T = viscous shear stress, N/m \ = grid parameter for LES T = temperature, K t = time coordinate, s u = velocity in x direction, m/s v = velocity in y direction, m/s vw = injection velocity, m/s y = ratio of specific heats A = filter width Sjj = Kronecker delta 8 = a constant* 0.0025 & dissipation rate of turbulence kinetic energy, m/s TI = Kolmogorov length scale, m K = thermal conductivity, W/mK

The computation of Lagrangian coherent structures typically involves post-processing of experimentally or numerically obtained fluid velocity fields to obtain the largest finite-time Lyapunov exponent (FTLE) field. However, this procedure can be tedious for large-scale complex flows of general interest. In this work, an alternative approach involving computation of the FTLE on-the-fly during direct numerical simulation of the full three dimensional Navier-Stokes equations is developed. The implementation relies on Lagrangian particle tracking to compose forward time flow maps, and an Eulerian treatment of the backward time flow map [S. Leung, J. Comput. Phys. 230, 3500-3524 (2011)] coupled with a semi-Lagrangian advection scheme. The flow maps are accurately constructed from a sequence of smaller sub-steps stored on disk [S. Brunton and C. Rowley, Chaos 20, 017503 (2010)], resulting in low CPU and memory requirements to compute evolving FTLE fields. Several examples are presented to demonstrate the capability and parallel scalability of the approach for a variety of two and three dimensional flows.