Studies on Cavitation Inception Process in Separated Flows

Studies related to cavitation inception process in separated flows are reported. Experimental observations of bubble appearance in grooves with laminar or turbulent boundary layer over them have clearly shown that gaseous diffusion process is significantly enhanced in turbulent flow. This process can lead to local nuclei size modification in environment similar to that of flow over a groove, like laminar separation "bubbles." Cavitation inception modeling including this aspect is carried out for predicting inception conditions associated with "bubble-ring" cavitation commonly observed on hemispherically nosed axisymmetric body. Qualitative dependence of predicted inception numbers with velocity is found to agree very well with experimental observations of Carroll (1981).

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

Two-dimensional moist stratified turbulence and the emergence of vertically sheared horizontal flows

Moist stratified turbulence is studied in a two-dimensional Boussinesq system influenced by condensation and evaporation. The problem is set in a periodic domain and employs simple evaporation and condensation schemes, wherein both the processes push parcels towards saturation. Numerical simulations demonstrate the emergence of a moist turbulent state consisting of ordered structures with a clear power-law type spectral scaling from initially spatially uncorrelated conditions. An asymptotic analysis in the limit of rapid condensation and strong stratification shows that, for initial conditions with enough water substance to saturate the domain, the equations support a straightforward state of moist balance characterized by a hydrostatic, saturated, vertically sheared horizontal flow (VSHF). For such initial conditions, by means of long time numerical simulations, the emergence of moist balance is verified. Specifically, starting from uncorrelated data, subsequent to the development of a moist turbulent state, the system experiences a rather abrupt transition to a regime which is close to saturation and dominated by a strong VSHF. On the other hand, initial conditions which do not have enough water substance to saturate the domain, do not attain moist balance. Rather, the system is observed to remain in a turbulent state and oscillates about moist balance. Even though balance is not achieved with these general initial conditions, the time scale of oscillation about moist balance is much larger than the imposed time scale of condensation and evaporation, thus indicating a distinct dominant slow component in the moist stratified two-dimensional turbulent system. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694805]

Stochastically driven instability in rotating shear flows

The origin of hydrodynamic turbulence in rotating shear flows is investigated, with particular emphasis on the flows whose angular velocity decreases but whose specific angular momentum increases with the increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain the observed data. Such a mismatch between the linear theory and the observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. This work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow, which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disc. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities and hence large energy dissipations of perturbation, which presumably generate the instability. A range of angular velocity (Omega) profiles of the background flow, starting from that of a constant specific angular momentum (lambda = Omega r(2); r being the radial coordinate) to a constant circular velocity (v(phi) = Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of their perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand the origin of instability and turbulence in three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion discs.

Magnetohydrodynamic stability of stochastically driven accretion flows

We investigate the evolution of magnetohydrodynamic (or hydromagnetic as coined by Chandrasekhar) perturbations in the presence of stochastic noise in rotating shear flows. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows, however, are Rayleigh stable but must be turbulent in order to explain astrophysical observed data and, hence, reveal a mismatch between the linear theory and observations and experiments. The mismatch seems to have been resolved, at least in certain regimes, in the presence of a weak magnetic field, revealing magnetorotational instability. The present work explores the effects of stochastic noise on such magnetohydrodynamic flows, in order to resolve the above mismatch generically for the hot flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect, mimicking a small section of an astrophysical accretion disk around a compact object. It is found that such stochastically driven flows exhibit large temporal and spatial autocorrelations and cross-correlations of perturbation and, hence, large energy dissipations of perturbation, which generate instability. Interestingly, autocorrelations and cross-correlations appear independent of background angular velocity profiles, which are Rayleigh stable, indicating their universality. This work initiates our attempt to understand the evolution of three-dimensional hydromagnetic perturbations in rotating shear flows in the presence of stochastic noise.

On the k(1)(-1) scaling in sink-flow turbulent boundary layers

Scaling of the streamwise velocity spectrum phi(11)(k(1)) in the so-called sink-flow turbulent boundary layer is investigated in this work. The present experiments show strong evidence for the k(1)(-1) scaling i.e. phi(11)(k(1)) = Lambda(1)U(tau)(2)k(1)(-1), where k(1)(-1) is the streamwise wavenumber and U-tau is the friction velocity. Interestingly, this k(1)(-1) scaling is observed much farther from the wall and at much lower flow Reynolds number (both differing by almost an order of magnitude) than what the expectations from experiments on a zero-pressure-gradient turbulent boundary layer flow would suggest. Furthermore, the coefficient A(1) in the present sink-flow data is seen to be non-universal, i.e. A(1) varies with height from the wall; the scaling exponent -1 remains universal. Logarithmic variation of the so-called longitudinal structure function, which is the physical-space counterpart of spectral k(1)(-1) scaling, is also seen to be non-universal, consistent with the non-universality of A(1). These observations are to be contrasted with the universal value of A(1) (along with the universal scaling exponent of 1) reported in the literature on zero-pressure-gradient turbulent boundary layers. Theoretical arguments based on dimensional analysis indicate that the presence of a streamwise pressure gradient in sink-flow turbulent boundary layers makes the coefficient A(1) non-universal while leaving the scaling exponent -1 unaffected. This effect of the pressure gradient on the streamwise spectra, as discussed in the present study (experiments as well as theory), is consistent with other recent studies in the literature that are focused on the structural aspects of turbulent boundary layer flows in pressure gradients (Harun etal., J. Flui(d) Mech., vol. 715, 2013, pp. 477-498); the present paper establishes the link between these two. The variability of A(1) accommodated in the present framework serves to clarify the ideas of universality of the k(1)(-1) scaling.

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.

CMC simulations of lifted turbulent jet flame in a vitiated coflow

Lifted turbulent jet diffusion flame is simulated using Conditional Moment Closure (CMC). Specifically, the burner configuration of Cabra et al. [R. Cabra, T. Myhrvold, J.Y. Chen. R.W. Dibble, A.N. Karpetis, R.S. Barlow, Proc. Combust. Inst. 29 (2002) 1881-1887] is chosen to investigate H-2/N-2 jet flame supported by a vitiated coflow of products of lean H-2/air combustion. A 2D, axisymmetric flow-model fully coupled with the scalar fields, is employed. A detailed chemical kinetic scheme is included, and first order CIVIC is applied. Simulations are carried out for different jet velocities and coflow temperatures (T-c) The predicted liftoff generally agrees with experimental data, as well as joint-PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for T-c = 1025 and 1080 K reveal that (1) Inside the flame zone, the chemical term balances the molecular diffusion term, and hence the Structure is of a diffusion flamelet for both cases. (2) In the pre-flame zone, the structure depends on the coflow temperature: for the 1025 K case, the chemical term being small, the advective term balances the axial turbulent diffusion term. However, for the 1080 K case. the chemical term is large and balances the advective term, the axial turbulent diffusion term being small. It is concluded that, lift-off is controlled (a) by turbulent premixed flame propagation for low coflow temperature while (b) by autoignition for high coflow temperature. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Helmholtz Instability In Stratified Shear Flows With Magnetic-Fields

The stability characteristics of a Helmholtz velocity profile in a stratified Boussinesq fluid in the presence of a rigid boundary is studied, A jump in the magnetic field is introduced at a level different from the velocity discontinuity. New unstable modes in addition to the Kelvin-Helmhottz mode are found. The wavelengths of these unstable modes are close to the wavelengths of internal Alfv6n gravity waves in the atmospher.

Compressible second-order boundary layers for three-dimensional stagnation point flows with mass transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Experimental evidence of the kinematic Cosserat effect in dense granular flows

To capture shear localization in the flow of dense granular materials in a continuum description, it has earlier been proposed that granular materials be treated as Cosserat, or micropolar, continua. Here, we provide experimental verification of the kinematic Cosserat effect, or the deviation of the particle spin from the material spin induced by the velocity gradient. Contrary to earlier belief, we find this effect to be sizable even outside the shear layers. Remarkably, the particles and material elements spin in opposite directions in flow through a hopper.

The possible influence of curvature and rotation on ocean currents

Recent laboratory investigations have shown that rotation and (streamwise) curvature can have spectacular effects on momentum transport in turbulent shear flows. A simple model that takes account of these effects (based on an analogy with buoyant flows) utilises counterparts of the Richardson number Rg and the Monin-Oboukhov length. Estimates of Rg for meanders in ocean currents like the Gulf Stream show it to be of order 1 or more, while laboratory investigations reveal strong effects even at |Rg|∼0·1. These considerations lead to the conclusion that at a cyclonic bend in the Gulf Stream, a highly unstable flow in the outer half of the jet rides over a highly stable flow in the inner half. It is conjectured that the discrepancies noticed between observation and the various theories of Gulf Stream meanders, and such phenomena as the observed detachment of eddies from the Gulf Stream, may be due to the effects of curvature and rotation on turbulent transport.