Instability of the attachment line boundary layer in a supersonic swept flow

Theoretical analysis of attachment-line instabilities is performed for supersonic swept flows using the compressible Hiemenz approximation for the mean flow and the successive approximation procedures for disturbances. The theoretical model captures the dominant attachment-line modes in wide ranges of the sweep Mach number ${M_e}$ and the wall temperature ratio. It is shown that these modes behave similar to the first and second Mack modes in the boundary layer flow. This similarity allows us to extrapolate the knowledge gained for Mack modes to the attachment-line instabilities. In particular, we find that at sufficiently large ${M_e}$ , the dominant attachment-line instability is associated with the synchronisation of slow and fast modes of acoustic nature. Point-by-point comparisons of the theoretical predictions with the experiments of Gaillard et al. (Exp. Fluids, vol. 26, 1999, pp. 169–176) demonstrate that at ${M_e} > 4$ , the theory captures a significant drop of the transition onset Reynolds number, which is below the contamination criterion of Poll $({R_\mathrm{\ast }} = 250)$ at ${M_e} > 6$ . This contradicts the generally accepted assumption that the attachment-line flow is stable for ${R_\mathrm{\ast }} \le 250$ . The theoretical critical Reynolds numbers lie well below the experimental transition-onset Reynolds numbers. Stability computations using the Navier–Stokes mean flow and accounting for the leading-edge curvature effect do not eliminate this discrepancy. Most likely, in the experiments of Gaillard et al., we face with an unknown effect that does not fit to the concept of transition arising from linear instability.

Linear instability of lid- and pressure-driven flows in channels textured with longitudinal superhydrophobic grooves

It is known that an increased flow rate can be achieved in channel flows when smooth walls are replaced by superhydrophobic surfaces. This reduces friction and increases the flux for a given driving force. Applications include thermal management in microelectronics, where a competition between convective and conductive resistance must be accounted for in order to evaluate any advantages of these surfaces. Of particular interest is the hydrodynamic stability of the underlying basic flows, something that has been largely overlooked in the literature, but is of key relevance to applications that typically base design on steady states or apparent-slip models that approximate them. We consider the global stability problem in the case where the longitudinal grooves are periodic in the spanwise direction. The flow is driven along the grooves by either the motion of a smooth upper lid or a constant pressure gradient. In the case of smooth walls, the former problem (plane Couette flow) is linearly stable at all Reynolds numbers whereas the latter (plane Poiseuille flow) becomes unstable above a relatively large Reynolds number. When grooves are present our work shows that additional instabilities arise in both cases, with critical Reynolds numbers small enough to be achievable in applications. Generally, for lid-driven flows one unstable mode is found that becomes neutral as the Reynolds number increases, indicating that the flows are inviscidly stable. For pressure-driven flows, two modes can coexist and exchange stability depending on the channel height and slip fraction. The first mode remains unstable as the Reynolds number increases and corresponds to an unstable mode of the two-dimensional Rayleigh equation, while the second mode becomes neutrally stable at infinite Reynolds numbers. Comparisons of critical Reynolds numbers with the experimental observations for pressure-driven flows of Daniello et al. (Phys. Fluids, vol. 21, issue 8, 2009, p. 085103) are encouraging.

Wake Flow Measurements Behind Rotating Smooth Spheres and Baseballs Near Critical Reynolds Numbers

The flow field behind spinning baseballs at two different seam orientations was investigated, and compared with a smooth sphere, to isolate effects of seams on the Magnus effect at Reynolds numbers of 5×104 and 1×105. The rotational speed of the three spheres varied from 0-2400 rpm, which are typical of spin rates imparted to a thrown baseball. These spin rates are represented non-dimensionally as a relative spin rate relating the surface tangential velocity to the freestream velocity, and varied between 0-0.94. Mean velocity profiles, streamline patterns, and power spectral density of the velocity signals were taken using hot-wire anemometry and/or stereoscopic particle image velocimetry in the wake region. The sphere wake orientation changed over a range of relative spin rates, indicating an inverse Magnus effect. Vortex shedding at a Strouhal number of 0.25 was present on the sphere at low relative spin rates. However, the seams on the baseball prevented any consequential change in wake orientation and, at most spin rates, suppressed the shedding frequency exhibited by the sphere. Instead, frequencies corresponding to the seam rotation rates were observed in the wake flow. It was concluded that the so-called inverse Magnus effect recorded by previous investigators at specific combinations of Reynolds number and relative spin rate on a sphere exists for a smooth sphere or an axisymmetrically dimpled sphere but not for a baseball near critical Reynolds numbers, where the wake flow pattern is strongly influenced by the raised seams.

Large Eddy Simulation of the Flow Past a Circular Cylinder at Super-Critical Reynolds Numbers

Turbulent flow past a circular cylinder at super-critical Reynolds numbers is simulated using large eddy simulation in this study. A novel combination of O- and H-grid structures is used to reduce mesh cells and, in turn, the computational cost. To investigate the influence of sub-grid scale (SGS) models on the accuracy of simulations, four different SGS models are applied to simulate the flow. In this study, the effect of mesh resolution near the wall on the accuracy of results is also evaluated by applying different y+ values at the wall. The results show that due to the complexity of the flow around the cylinder particularly at high Reynolds numbers, using very high resolution mesh near the cylinder wall, can not guarantee the accuracy of results and other parameters such as mesh resolutions at the top and bottom shear layers and the wake shortly behind the cylinder should be considered appropriately.

Direct Numerical Simulations on the Flow Normal to a Plate With Transit Shape From Circular Disk to Triangle

This paper presents a numerical study of the flow normal to a triangular plate. A total of four plates with the same frontal area Ar and different curved edges are used. The curvature of edges is determined by the compression ratio k (k = 0.3, 0.4, 0.5, 0.8; the large value of k corresponds to the large curvature of the edges). A disk of χ = 50 (χ is the diameter-thickness aspect ratio) is used as the reference disk. The Reynolds number Re based on the characteristic length is up to 250. Four states are observed and denoted as: (I) steady and geometric symmetry state (SG); (II) steady and reflectional symmetry state (SR); (III) reflectional symmetry breaking with periodic flow (RSB); (IV) chaotic state (CS). The critical Reynolds numbers at the first two stages (Rec1, Rec2) decrease with the increasing k, indicating that flow of the plates with a larger curvature is more unstable. Therefore, we believe that the flow around a triangular plate is more stable than that around a circular disk.

Determining critical flow parameters for the Poiseuille, Couette and Taylor – Couette flows

Based on a detailed analysis of the known Dou method for determining the critical parameters of a Newtonian fluid flow during the transition of a laminar flow regime to a turbulent one, an alternative to determining the critical Reynolds number for the Poiseuille and Couette flows in cylindrical, coaxial and flat channels, the article proposes a new mathematical justification of the Dou method leading to simpler calculation relations, while preserving the initial ideas about the physical conditions of the transition. New computing expressions for determining the critical Dou number for the generalized Poiseuille – Couette flow in a flat channel not considered by Dou are obtained. Analytical expressions for calculating critical parameters for the Taylor – Couette flow approximating experimental results for critical Reynolds numbers are given, as well as calcula-ted values of critical Dou numbers.

Two dimensional simulation of laminar flow by three- jet in a semi-confined space

Equipment performance improvement in a wide range of working conditions is one of the major goals of aerodynamics. This goal can be achieved by the deformation of the object being examined or by using flow control techniques in active or inactive modes. In different researches, how to change the development ratio on the semi-confined space with input jet system is surveyed. In this study, two-dimensional simulation of the flow has been investigated in three-jet laminar flow in a semi-confined space. To determine the effective and optimal mixing in a laminar flow, critical Reynolds numbers were determined to distinguish when the flow in the channel from a steady-state symmetric flowformed downstream recirculation and ultimately transient flow. To better understand the flow characteristics, the simulations were changed at a fixed jet spacing (input jets distance to height of space ratio). Also, in this paper, for comparison, four jets were considered. Based on the results, it was observed that in all cases, mixing occurred in the space between three jets. Placing the jet along the walls of the semi-confined space allows the best combination, and increase in the distance between the first and third jets and reduction of the particle coefficient caused to reach the critical Reynolds number faster and, as a result, mixing in a laminar flow with geometric changes of the semi-confined space.