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A numerical study of three-dimensional equilibria and transition to turbulence in flow over a backward-facing step is performed using direct numerical solution of the incompressible Navier-Stokes equations. The numerical method is a high-order-accurate mixed spectral/spectral-element method with efficient viscous outflow boundary conditions. The appearance of three-dimensionality in nominally two-dimensional geometries is investigated at representative Reynolds numbers ranging from the onset of three-dimensional bifurcation to later transitional stages. Strongly three-dimensional regions are identified through standard correlation coefficients and new three-dimensionality indices, as well as through instantaneous and time-average streamline patterns and vorticity contours. Our results indicate that onset of three-dimensionality occurs at the boundaries between the primary and secondary recirculating zones with the main channel flow, the latter being the most stable flow component. There is. therefore, strong secondary instability in the shear layers, mainly due to the one emanating from the step corner.The flow further downstream is excited through the action of the upstream shear layers acquiring a wavy form closely resembling Tollmien–Schlichting waves both spatially and temporally with a characteristic frequency f1; upstream, at the shear layer another incommensurate frequency, f2, is present. The two-frequency flow locks-in to a single frequency if external excitations are imposed at the inflow at a frequency close to f1 or f2; the smaller amplitude excitations, however, may cause a strong quasi-periodic response. Such excitations may significantly increase or decrease (by more than 20%) the length of the primary separation zone XR at lock-in or quasi-periodic states. The equilibrium states resulting from the secondary instability at supercritical Reynolds numbers produce a flow modulated in the spanwise direction, with corresponding variations in the reattachment location XR. While three-dimensionality explains partially the discrepancy between numerical predictions and experimental results on XR at higher Reynolds number Re, the main source of discrepancy is attributed to the inflow conditions, and in particular to external disturbances superimposed on the mean flow, the latter being the main reason also for the somewhat earlier transition found in laboratory experiments.

A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds numberRe= 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability analysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalues of a base flow state. The distinction is made between convectively and absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up toRe= 2500 are time-independent in the absence of any external excitation, whereas the flow is convectively unstable, in a large portion of the flow domain, for Reynolds numbers in the range 700 [les ]Re[les ] 2500. Consequently, upstream generated small disturbances propagate downstream at exponentially amplified amplitude with a space-dependent speed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, selective sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two different types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from the shear layer frequency; and (ii) random noise. It is found that for small-amplitude monochromatic excitation the flow acquires a time-periodic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequency. On the other hand, for the random noise as input, an unsteady behaviour is obtained with a fundamental frequency close to the shear layer frequency.

This paper presents an optimization study of the geometry of three-dimensional microthrust bearings in a wide range of convergence ratios. The optimization goal is the maximization of the bearing load carrying capacity. The bearings are modeled as microchannels, consisting of a smooth moving wall (rotor), and a stationary wall (stator) with partial periodic rectangular texturing. The flow field is calculated from the numerical solution of the Navier-Stokes equations for incompressible isothermal flow; processing of the results yields the bearing load capacity and friction coefficient. The geometry of the textured channel is defined parametrically for several width-to-length ratios. Optimal texturing geometries are obtained by utilizing an optimization tool based on genetic algorithms, which is coupled to the CFD code. Here, the design variables define the bearing geometry and convergence ratio. To minimize the computational cost, a multi-objective approach is proposed, consisting in the simultaneous maximization of the load carrying capacity and minimization of the bearing convergence ratio. The optimal solutions, identified based on the concept of Pareto dominance, are equivalent to those of singleobjective optimization problems for different convergence ratio values. The present results demonstrate that the characteristics of the optimal texturing patterns depend strongly on both the convergence ratio and the width-to-length ratio. Further, the optimal load carrying capacity increases at increasing convergence ratio, up to an optimal value, identified by the optimization procedure. Finally, proper surface texturing provides substantial load carrying capacity even for parallel or slightly diverging bearings. Based on the present results, we propose simple formulas for the design of textured micro-thrust bearings.

The paper presents a detailed computational study of flow patterns and performance indices in a dimpled parallel thrust bearing. The bearing consists of eight pads; the stator surface of each pad is partially textured with rectangular dimples, aiming at maximizing the load carrying capacity. The bearing tribological performance is characterized by means of computational fluid dynamics (CFD) simulations, based on the numerical solution of the Navier–Stokes and energy equations for incompressible flow. Realistic boundary conditions are implemented. The effects of operating conditions and texture design are studied for the case of isothermal flow. First, for a reference texture pattern, the effects of varying operating conditions, in particular minimum film thickness (thrust load), rotational speed and feeding oil pressure are investigated. Next, the effects of varying texture geometry characteristics, in particular texture zone circumferential/radial extent, dimple depth, and texture density on the bearing performance indices (load carrying capacity, friction torque, and friction coefficient) are studied, for a representative operating point. For the reference texture design, the effects of varying operating conditions are further investigated, by also taking into account thermal effects. In particular, adiabatic conditions and conjugate heat transfer at the bearing pad are considered. The results of the present study indicate that parallel thrust bearings textured by proper rectangular dimples are characterized by substantial load carrying capacity levels. Thermal effects may significantly reduce load capacity, especially in the range of high speeds and high loads. Based on the present results, favorable texture designs can be assessed.

We present detailed experimental and numerical results of three-dimensional laminar flow over a backward-facing step with an expansion ratio of 2 and a downstream aspect ratio of 20. Experimental results for transitional and turbulent flow are also reported. We focus on the effects of sidewalls on flow structure. Experiments were based on both digital and stereoscopic particle image velocimetry; a spectral element method was used for the simulations. For laminar flow, both experimental and computational results illustrate the presence of a wall-jet at the channel lower wall, directed toward the channel midplane, in agreement with previous observations. The development of self-similar wall-jet profiles with increasing distance from the sidewalls is demonstrated. The intensity of this secondary flow increases with Reynolds number in the laminar regime, and decreases in the transitional and turbulent regimes. The effect of sidewalls on the primary and upper wall recirculation zones is demonstrated, and explains the literature discrepancies between experiments and two-dimensional simulations.

The effect of steady base suction and blowing on the stability and dynamics of the cylinder wake is investigated at low Reynolds numbers, using numerical simulation and stability analysis. Simulation results show that, in the supercritical Reynolds number regime (Re>47), slight blowing or high enough suction stabilizes the wake; in the subcritical regime, suction destabilizes the wake and results in vortex shedding, whereas blowing has no detectable effect on the flow stability. At supercritical Reynolds numbers, the transition from unsteady to steady flow at a critical suction flow rate is accompanied by simultaneous symmetry breaking, resulting in strongly asymmetric steady flow. For finite flow domain, the flow undergoes another transition from steady asymmetric to steady symmetric flow at even higher suction flow rates. The dynamics of vortex shedding in the controlled flow can be strongly modified, in comparison to the uncontrolled flow. Global stability analysis confirms the results of numerical simulation, and yields detailed information on the dynamics of linear global modes. Computational domain size can significantly affect the flow transitions, in particular, at high suction flow rates.

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