Mean and fluctuating pressure in boat-tail separated flows at transonic speeds

Experiments were carried out investigating the features of mean and unsteady surface pressure fluctuations in boat-tail separated flows relevant to launch vehicle configurations at transonic speeds. The tests were performed on a generic axisymmetric body in the Mach-number range of 0.7-1.2, and the important geometrical parameters, namely, the boat-tail angle and diameter ratio, were varied systematically. The measurements made included primarily the mean and unsteady surface-pressure fluctuations on nine different model configurations. Flow-visualization studies employing a surface oil flow, and schlieren techniques were carried out to infer features like boundary-layer separation, reattachment, and shock waves in the flow. The features of mean and fluctuating surface pressures are discussed in detail including aspects of similarity. It has been observed that, on a generic configuration employed in the present study, the maximum levels of surface-pressure fluctuations in the reattachment zone are appreciably lower than those found on launch vehicle configurations having a bulbous or hammerhead nose shape. A simple correlation is suggested for the maximum value of rms pressure fluctuations in the reattachment zone at different freestream Mach numbers.

Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

Stability of fluid flow past a membrane

The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and H R*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (alpha --> 0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Lambda(t), and this critical value increases proportional to alpha(2) in this limit. Here, alpha is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*(-1), and the dimensionless strain rate is given by Lambda(t) = ((gamma) over dot* R*eta*/Gamma*), where eta* is the fluid viscosity, Gamma* is the tension of the membrane and (gamma) over dot* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the alpha --> 0 limit.

Studies on a new high-intensity low-emission burner

This paper presents computational and experimental results on a new burner configuration with a mild combustion concept with heat release rates up to 10 MW/m(3). The burner configuration is shown to achieve mild combustion by using air at ambient temperature at high recirculation rates (similar to250%-290%) both experimentally and computationally. The principal features of the configuration are: (1) a burner with forward exit for exhaust gases; (2) injection of gaseous fuel and air as multiple, alternate, peripheral highspeed jets at the bottom at ambient temperature, thus creating high enough recirculation rates of the hot combustion products into fresh incoming reactants; and (3) use of a suitable geometric artifice-a frustum of a cone to help recirculation. The computational studies have been used to reveal the details of the flow and to optimize the combustor geometry based on recirculation rates. Measures, involving root mean square temperature fluctuations, distribution of temperature and oxidizer concentration inside the proposed burner, and a classical turbulent diffusion jet flame, are used to distinguish between them quantitatively. The system, operated at heat release rates of 2 to 10 MW/m(3) (compared to 0.02 to 0.32 MW/m(3) in the earlier studies), shows a 10-15 dB reduction in noise in the mild combustion mode compared to a simple open-top burner and exhaust NOx emission below 10 ppm for a 3 kW burner with 10% excess air. The peak temperature is measured around 1750 K, approximately 300 K lower than the peak temperature in a conventional burner.

The physics of active membranes

We review recent work on the physical properties of model fluid membranes in nonequilibrium situations resembling those encountered in the living cell and contrast their properties with those of the more familiar membranes at thermal equilibrium. We survey models for the effect of (i) active pumps and (ii) active fission–fusion processes encountered in intracellular trafficking on the stability and fluctuations of fluid membranes. Our purpose is twofold: to highlight the exciting nonequilibrium phenomena that arise in biological systems, and to show how some crucial features of living systems, namely dissipative energy uptake and directed motion, can fruitfully be incorporated into physical models of biological interest.

Vertical thermal structure of the atmosphere during active and weak phases of convection over the north Bay of Bengal: Observation and model results

Owing to the lack of atmospheric vertical profile data with sufficient accuracy and vertical resolution, the response of the deep atmosphere to passage of monsoon systems over the Bay of Bengal. had not been satisfactorily elucidated. Under the Indian Climate Research Programme, a special observational programme called 'Bay of Bengal Monsoon Experiment' (BOBMEX), was conducted during July-August 1999. The present study is based on the high-resolution radiosondes launched during BOBMEX in the north Bay. Clear changes in the vertical thermal structure of the atmosphere between active and weak phases of convection have been observed. The atmosphere cooled below 6 km height and became warmer between 6 and 13 km height. The warmest layer was located between 8 and 10 km height, and the coldest layer was found just below 5 km height. The largest fluctuations in the humidity field occurred in the mid-troposphere. The observed changes between active and weak phases of convection are compared with the results from an atmospheric general circulation model, which is similar to that used at the National Centre for Medium Range Weather Forecasting, New Delhi. The model is not able to capture realistically some important features of the temperature and humidity profiles in the lower troposphere and in the boundary layer during the active and weak spells.

An experimental study of reverse transition in two-dimensional channel flow

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$ and $\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but $\overline{u^{\prime}v^{\prime}} $ tends to become zero at a reasonably well-defined point. During reverse transition $\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$ also decreases as the flow moves downstream and Lissajous figures taken with u’ and v’ signals confirm this trend. There is approximate similarly between $\overline{u^{\prime 2}} $ profiles if the value of $\overline{u^{\prime 2}_{\max}} $ and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of $\overline{u^{\prime 2}} $ is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

Turbulence measurements in an ‘equilibrium’ axisymmetric wall jet Journal

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale of u fluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for the u, v and w components at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of $\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the $\overline{q^2}$ spectra, using a slightly modified version of a previously suggested method.

Turbulent free convection above a heated plate inclined at a small angle to the horizontal Journal

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion. Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments. The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating-force model

A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

On the criteria for reverse transition in a two-dimensional boundary layer flow

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations $\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$ and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter \[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \] where U* is the friction velocity. Downstream of this region the decay of $\tilde{u}^{\prime}$ fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

Biaxial strain induced electrical inhomogenities and phase separation in the ferromagnetic metallic phase in thin films of La0.7Ca0.3MnO3: A scanning tunneling potentiometry/spectroscopy study

We have investigated the effect of biaxial strain on local electrical/electronic properties in thin films of La0.7Ca0.3MnO3 with varying degrees of biaxial strain in them. The local electrical properties were investigated as a function of temperature by scanning tunneling spectroscopy (STS) and scanning tunneling potentiometry (STP), along with the bulk probe like conductance fluctuations.The results indicate a positive correlation between the lattice mismatch biaxial strain and the local electrical/electronic inhomogenities observed in the strained sample. This is plausible since the crystal structure of the manganites interfere rather strongly with the magnetic/electronic degrees of freedom. Thus even a small imbalance (biaxial strain) can induce significant changes in the electrical properties of the system.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.