Momentum analysis of complex time-periodic flows

Several methods have been proposed to characterize the complex interactions in turbulent wakes, especially for flows with strong cyclic dynamics. This paper introduces the concept of Fourier-Averaged Navier-Stokes (FANS) equations as a framework to obtain direct insights into the dynamics of complex coherent wake interactions. The method simplifies the interpretations of flow physics by identifying terms contributing to momentum transport at different timescales. The method also allows for direct interpretation of non-linear interactions of the terms in the Navier-Stokes equations. By analysing well-known cases, the characteristics of FANS are evaluated. Particularly, we focus on physical interpretation of the terms as they relate to the interactions between modes at different timescales. Through comparison with established physics and other methods, FANS is shown to provide insight into the transfer of momentum between modes by extracting information about the contributing pressure, convective, and diffusive forces. FANS provides a simply calculated and easily interpreted set of equations to analyse flow physics by leveraging momentum conservation principles and Fourier analysis. The method is applicable to flows with complex cyclic waveforms, including broadband spectral energy distributions.Comment: 28 pages, 23 figures. Submitted to the Journal of Fluid Mechanic

Granular circulation in a cylindrical pan: simulations of reversing radial and tangential flows

Granular flows due to simultaneous vertical and horizontal excitations of a flat-bottomed cylindrical pan are investigated using event-driven molecular dynamics simulations. In agreement with recent experimental results, we observe a transition from a solid-like state, to a fluidized state in which circulatory flow occurs simultaneously in the radial and tangential directions. By going beyond the range of conditions explored experimentally, we find that each of these circulations reverse their direction as a function of the control parameters of the motion. We numerically evaluate the dynamical phase diagram for this system and show, using a simple model, that the solid-fluid transition can be understood in terms of a critical value of the radial acceleration of the pan bottom; and that the circulation reversals are controlled by the phase shift relating the horizontal and vertical components of the vibrations. We also discuss the crucial role played by the geometry of the boundary conditions, and point out a relationship of the circulation observed here and the flows generated in vibratory conveyors.Comment: 10 pages, 8 figure

FEDSM2002-31431 THE MEASUREMENT OF MEAN FLOW ANGLES BETWEEN AN AUTOMOTIVE FAN AND STATOR

ABSTRACT Measurements of the mean velocity vector were conducted to determine the exit angle from an automotive engine cooling fan module. The measurements were made at 15 locations along a radius between the hub and the band. The radius investigated was located in a plane roughly half-way between the blade trailing edge and stator leading edge. A two-component laser Doppler velocimeter and a four-wire hot-wire probe were used to measure the flow fields. It was found that the results obtained from hot-wire anemometry will have significant bias errors when used to measure the velocity vectors between the fan and the stator unless phase-averaged data are obtained with the probe re-oriented by phase. The differences between the techniques occur because the distribution of instantaneous swirl angles is bi-modal. Further, the mean flow angle is close to a local minimum in the probability density function of the swirl angle. This will act to increase errors in measurement devices whose accuracy depends on flow direction (the quantity being measured) such as five-hole probes which are used in industry. INTRODUCTION Knowing the exit velocity directions from automotive fans are key to designing the downstream stators. Since the flow field is elliptic, the stators will influence the flow coming through the fan. In industry, the velocity fields pertaining to the radiator-fan-stator assemblies are typically measured with fivehole probes due to their ease of use and robustness. However, due to the high turbulence levels and large velocity gradients, the reliability of these five-hole measurements is uncertain. Measurements to determine the mean swirl velocity projection and mean swirl angle from the fan blades upstream of the stator stage were conducted. Estimates of the average swirl angle, defined as that subtended by the swirl velocity projection relative to the fan axis, were obtained based on full three component resolution of the mean velocity vector. To thi

The use of microscopy and three-dimensional visualization to evaluate the structure of microbial biofilms cultivated in the Calgary Biofilm Device

Microbes frequently live within multicellular, solid surface-attached assemblages termed biofilms. These microbial communities have architectural features that contribute to population heterogeneity and consequently to emergent cell functions. Therefore, three-dimensional (3D) features of biofilm structure are important for understanding the physiology and ecology of these microbial systems. This paper details several protocols for scanning electron microscopy and confocal laser scanning microscopy (CLSM) of biofilms grown on polystyrene pegs in the Calgary Biofilm Device (CBD). Furthermore, a procedure is described for image processing of CLSM data stacks using amira(™), a virtual reality tool, to create surface and/or volume rendered 3D visualizations of biofilm microorganisms. The combination of microscopy with microbial cultivation in the CBD – an apparatus that was designed for high-throughput susceptibility testing – allows for structure-function analysis of biofilms under multivariate growth and exposure conditions

Effects of Pulsation to the Mean Field and Vortex Development in a Backward-Facing Step Flow

This work is concerned with the behavior of pulsatile flows over a backward-facing step geometry. The paper mainly focuses on the effects of the pulsation frequency on the vortex development of a 2:1 backward-facing step for mean Reynolds number of 100 and for 0.035 St 2.19. The dependence of the flow field on the Reynolds number (Re ¼ 100 and 200) was also examined for a constant Strouhal number, St of 1. A literature survey was carried out and it was found that the pulsation modifies the behavior of the flow pattern compared to the steady flow. It was shown in the present work that the inlet pulsation generally leads to differences in the mean flow compared to the steady field although the inlet bulk velocity is the same due to energy redistribution of the large-scale vortices, which result in nonlinear effects. The particle-image velocimetry results show that the formation of coherent structures, dynamical shedding, and transport procedure are very sensitive to the level of pulsation frequencies. For low and moderate inlet frequencies, 0.4 St 1, strong vortices are formed and these vortices are periodically advected downstream in an alternate pattern. For very low inlet frequency, St ¼ 0.035, stronger vortices are generated due to an extended formation time, however, the slow formation process causes the forming vortices to decay before shedding can happen. For high inlet frequencies, St ! 2.19, primary vortex is weak while no secondary vortex is formed. Flow downstream of the expansion recovers quickly. For Re ¼ 200, the pattern of vortex formation is similar to Re ¼ 100. However, the primary and secondary vortices decay more slowly and the vortices remain stronger for Re ¼ 200. The strength and structure of the vortical regions depends highly on St, but Re effects are not negligible

Wake dynamics and surface pressure variations on two-dimensional normal flat plates

The relationship between vortex dynamics and surface pressure fluctuations on the leeward face of a two-dimensional normal thin flat plate was studied using Direct Numerical Simulations for incompressible flow at a Reynolds number of 1200. The vortex shedding frequency was observed in the spectra of pressure fluctuations on both faces of the plate, while a lower frequency spectral peak was only evident on the leeward pressure fluctuations. Local sharp peaks of low pressure in the separated shear layers coincide with increases in the leeward face pressure fluctuations. These observations are tied to the vortex dynamics using the invariant Q, commonly used for vortex identification. Q is also proportional to the source term for the Poisson equation for the instantaneous pressure. The pressure, which is the only contributor to the plate drag, varies significantly in response to alterations to the vortex shedding, which can be observed in differences of vortex trajectories. At minimum drag, the pressure fluctuations are small, which is attributed to lower values of Q associated with weaker vortices

Modal energy flow analysis of a highly modulated wake behind a wall-mounted pyramid

International audienceWe experimentally investigate the highly modulated turbulent wake behind a wall-mounted square-base pyramid protruding through the boundary layer. We present the first modal energy flow analysis of a time-resolved three-dimensional velocity field from experimental particle image velocimetry data. The underlying low-order representation is optimized for resolving the base-flow variation as well as the first and second harmonics associated with vortex shedding – generalizing the triple decomposition of Reynolds & Hussain (J. Fluid Mech., vol. 54, 1972, pp. 263–288). This analysis comprises not only a detailed modal balance of turbulent kinetic energy as pioneered by Rempfer & Fasel (J. Fluid Mech., vol. 275, 1994, pp. 257–283) for proper orthogonal decomposition (POD) models, but also the companion energy balance of the mean flow. The experimental results vividly demonstrate how constitutive elements of mean-field theory (Stuart, J. Fluid Mech., vol. 4, 1958, pp. 1–21) near laminar Hopf bifurcations remain strongly pronounced in a turbulent wake characterized by highly modulated, quasi-periodic shedding. The study emphasizes, for instance, the stabilizing role of mean-field manifolds, as explored in the pioneering POD model of Aubry et al. (J. Fluid Mech., vol. 192, 1988, pp. 115–173). The presented low-order representation of the flow and modal energy flow analyses may provide important insights and reference data for computational turbulence modelling, e.g. unsteady Reynolds-averaged Navier–Stokes simulations