Shock wave interaction with porous plates

Previous detailed studies of the interaction of a shock wave with a perforated sheet considered the impact of a shock wave on a plate with regularly spaced slits giving area blockages of 60 and 67%, at various angles of incidence, and resulting in both regular and Mach reflection. The current work extends this study to a much wider variety of plate geometries. Blockage ratios of 20, 25, 33, 50, and 67 and inclinations of 45, 60, 75, and 90° to the shock wave were tested. Four different thicknesses of plate were tested at the same frontal blockage in order to assess the effects of gap guidance. Tests were conducted at two shock Mach numbers of 1.36 and 1.51 (inverse pressure ratios of 0.4 and 0.5). It is found that secondary reflected and transmitted waves appear due to the complex interactions within the grid gaps, and that the vortex pattern which is generated under the plate is also complex due to these interactions. The angle of the reflected shock, measured relative to the plate, decreases with plate blockage and the angle of inflow to the plate reduces with increasing blockage. By analysing the flow on the underside of the plate the pseudo-steady flow assumption is found to be a reasonable approximation. Both the pressure difference and the stagnation pressure loss across the plate are evaluated. It is found that over the range tested the plate thickness has a minimal effect.     

The dynamics of disordered systems and the motion of vortices in disordered type-II superconductors

We develop a field theoretical method which permits us to study the dynamics of interacting particles in disordered systems. In particular, making use of a Hartree-type approximation, we obtain a self-consistent system of equations for disorder averaged quantities. The method is first applied to a single particle on a rough surface. Then, we calculate the current-voltage (I-V) characteristics of a type-II superconductor in the flux flow regime. Finally, the structure of the steps is discussed which arise in the I-V-characteristics when a small ac field is superimposed on the constant voltage. These may serve as a probe for incipient melting of the vortex lattice.     

Computational study of shock wave focusing in a log-spiral duct

The mechanism of shock wave focusing in a two-dimensional log-spiral duct has been investigated here numerically using a finite volume method. This approach is based on a MUSCL TVD scheme with flux-vector splitting applied to the Euler equations. The isopycnics determined from the calculations are compared with the experimental results obtained by use of holographic interferometric photography and are found to be in excellent qualitative agreement with the experiments. The computational results clarify the details of the wave interactions very near to the focus. In particular, phenomena such as the formation of secondary shock waves prior to the implosion, their interaction with the reflected shock and the formation of vortices after the implosion have been examined.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

Breakup régimes and self-sustained pulsations in coaxial jets

We report on a new flow pattern transition observed in a coaxial jet configuration. Above a critical momentum ratio between the outer and the inner stream, it is found experimentally that the inner potential core breaks down into an unsteady recirculation bubble. The origin of the transition is explained and an expression for the critical velocity ratio is derived. The nature and the features of the pulsation of the bubble are discussed using an original evolution equation which relies on the interplay between the linear growth rate of the jet mixing layer disturbances and the recirculating flow induced delay of the non-linear saturation.

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Sommario In questo articolo si discute di un nuovo tipo di transizione di flusso osservata in una configurazione di getto coassiale. Si stabilisce sperimentalmente che il potenziale interno disgrega la parte interna del flusso in una ricircolazione instabile a bolla oltre un valore critico nel rapporto tra la corrente interna e quella esterna. Viene spiegata l'origine della transizione e viene derivata l'espressione della velocità critica. Sono discusse, inoltre, la natura e le caratteristiche della pulsazione della bolla, avendo a disposizione una equazione di evoluzione originale che evidenzia l'influenza reciproca tra la crescita lineare dei disturbi dello strato di mescolamento del getto ed il flusso ricircolante, che induce il ritardo della saturazione non-lineare.

     

Vortex‐assisted liquid–liquid microextraction using a low‐toxicity solvent for the determination of five organophosphorus pesticides in water samples by high‐performance liquid chromatography

Vortex‐assisted liquid–liquid microextraction followed by high‐performance liquid chromatography with UV detection was applied to determine Isocarbophos, Parathion‐methyl, Triazophos, Phoxim and Chlorpyrifos‐methyl in water samples. 1‐Bromobutane was used as the extraction solvent, which has a higher density than water and low toxicity. Centrifugation and disperser solvent were not required in this microextraction procedure. The optimum extraction conditions for 15 mL water sample were: pH of the sample solution, 5; volume of the extraction solvent, 80 μL; vortex time, 2 min; salt addition, 0.5 g. Under the optimum conditions, enrichment factors ranging from 196 to 237 and limits of detection below 0.38 μg/L were obtained for the determination of target pesticides in water. Good linearities (r > 0.9992) were obtained within the range of 1–500 μg/L for all the compounds. The relative standard deviations were in the range of 1.62–2.86% and the recoveries of spiked samples ranged from 89.80 to 104.20%. The whole proposed methodology is simple, rapid, sensitive and environmentally friendly for determining traces of organophosphorus pesticides in the water samples.     

Compact finite difference-Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported. The project supported by the National Natural Science Foundation of China     

Flow produced in a conical container by a rotating endwall

Numerical calculations have been carried out for flow in a truncated cone generated by rotation of one endwall. For both convergent (radius increasing with approach to the rotating endwall) and divergent geometries, vortex breakdown is suppressed beyond a certain angle of inclination of the sidewall. At the same time Moffat eddies of increasing strength and extent appear in the corner between the sidewall and the non-rotating endwall. For the divergent geometry, a zone of recirculation appears on the sidewall and eventually merges with the Moffat eddies. The flow phenomena identified from streamline patterns are consistent with the calculated variation of pressure around the periphery of the computational domain.     

Columnar vortices in isotropic turbulence

The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the rangeRe =35–170, and is found to be organized in coherent, cylindrical or ribbon-like, vortices (worms). At the Reynolds numbers studied, they are responsible for much of the extreme intermittent tails observed in the statistics of the velocity gradients, but their importance seems to decrease at higherRe . Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow, while their circulation increases monotonically withRe . An explanation is offered for this latter scaling, based in the assumed presence of axial inertial waves along their cores, excited by a random background strain of the order of the root mean square vorticity. This explanation is consistent with the presence of comparable amounts of stretching and compression along the vortex cores.

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Sommario La struttura di regioni ad intensa vorticità in campi di flusso turbolento omogenei, isotropi ed in equilibrio, simulati numericamente, viene studiata per quattro differenti numeri di Reynolds nell'intervalloRe =35÷170, e si trova che tali regioni si organizzano in vortici coerenti, cilindrici o a forma di nastro (vermi). Con rifermento ai numeri di Reynolds studiati, si vede che tali vortici sono responsabili per gran parte delle code estreme ed intermittenti, osservate nelle statistiche dei gradienti di velocità, ma la loro importanza sembra decrescere a più altiRe . I loro raggi scalano con la microscala di Kolmogorov e le loro lunghezze con la scala integrale del flusso, mentre la loro circolazione cresce monotonicamente conRe . Per quest'ultimo riscalamento viene offerta una spiegazione basata sull'assunzione della presenza di onde inerziali assiali lungo i loro nuclei, eccitate da una deformazione di fondo casuale dell'ordine della radice quadrata della velocità media. Questa spiegazione è consistente con la presenza di incrementi paragonabili di allungamenti e compressioni lungo i nuclei dei vortici.

     

On drag, Strouhal number and vortex-street structure

A phenomenological model for the vortex-shedding process behind bluff cylindrical bodies is proposed. Relationships between Strouhal frequency St, drag coefficient c_D, Reynolds number Re and geometric wake parameters are obtained from mass conservation, momentum conservation in the transverse direction and energy considerations. For the first time, Roshko's (Technical Report TN 3169, NACA, US Government Printing Office, Washington DC, 1954) experimental discovery of vortex-street similarity behind different cylinders is analytically derived. In addition, the empirically obtained Strouhal-frequency laws of Roshko (Technical Report TN1191, NACA, US Government Printing Office, Washington DC, 1954) and Fey (Phys. fluids A 10 (1998) 1547) are also reproduced. Measurements of St and c_D including their Re dependency for flows around cylinders with circular, square, triangular, semi-circular and other cross sections agree favorably with the proposed model.