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.

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.

Measurement of Heat Transfer Rate on Backward-Facing Steps at Hypersonic Mach Number

Two backward-facing models with step heights of 2 and 3 mm are used to measure the convective surface heat transfer rates by using platinum thin-film gauges, deposited on Macor inserts. Heat transfer rates have been theoretically calculated along the flat plate portion of a model using the Eckert reference temperature method. The experimentally determined surface heat transfer rate distributions are compared with theoretical and numerical estimations. Experimental heat flux distribution over a flat plate model showed good agreement with the reference temperature method at stagnation enthalpy range of 0.8-2 MJ/kg. Theoretical analysis has been used for downstream of a backward-facing step using Gai's nondimensional analysis. It has been found from the present study that approximately 10 and 8 step heights are required for the flow to reattach for 2 and 3 mm step height backward-facing step models, respectively, at a nominal Mach number of 7.6.

Plume structure in high-Rayleigh-number convection

Near-wall structures in turbulent natural convection at Rayleigh numbers of $10^{10}$ to $10^{11}$ at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log–normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.

Defining the ‘modified Griffin plot’ in vortex-induced vibration: revealing the effect of Reynolds number using controlled damping

In the present work, we study the transverse vortex-induced vibrations of an elastically mounted rigid cylinder in a fluid flow. We employ a technique to accurately control the structural damping, enabling the system to take on both negative and positive damping. This permits a systematic study of the effects of system mass and damping on the peak vibration response. Previous experiments over the last 30 years indicate a large scatter in peak-amplitude data ($A^*$) versus the product of mass–damping ($\alpha$), in the so-called ‘Griffin plot’. A principal result in the present work is the discovery that the data collapse very well if one takes into account the effect of Reynolds number ($\mbox{\textit{Re}}$), as an extra parameter in a modified Griffin plot. Peak amplitudes corresponding to zero damping ($A^*_{{\alpha}{=}0}$), for a compilation of experiments over a wide range of $\mbox{\textit{Re}}\,{=}\,500-33000$, are very well represented by the functional form $A^*_{\alpha{=}0} \,{=}\, f(\mbox{\textit{Re}}) \,{=}\, \log(0.41\,\mbox{\textit{Re}}^{0.36}$). For a given $\mbox{\textit{Re}}$, the amplitude $A^*$ appears to be proportional to a function of mass–damping, $A^*\propto g(\alpha)$, which is a similar function over all $\mbox{\textit{Re}}$. A good best-fit for a wide range of mass–damping and Reynolds number is thus given by the following simple expression, where $A^*\,{=}\, g(\alpha)\,f(\mbox{\textit{Re}})$: \[ A^* \,{=}\,(1 - 1.12\,\alpha + 0.30\,\alpha^2)\,\log (0.41\,\mbox{\textit{Re}}^{0.36}). \] In essence, by using a renormalized parameter, which we define as the ‘modified amplitude’, $A^*_M\,{=}\,A^*/A^*_{\alpha{=}0}$, the previously scattered data collapse very well onto a single curve, $g(\alpha)$, on what we refer to as the ‘modified Griffin plot’. There has also been much debate over the last three decades concerning the validity of using the product of mass and damping (such as $\alpha$) in these problems. Our results indicate that the combined mass–damping parameter ($\alpha$) does indeed collapse peak-amplitude data well, at a given $\mbox{\textit{Re}}$, independent of the precise mass and damping values, for mass ratios down to $m^*\,{=}\,1$.

Rainbow Connection Number and Radius

Rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this note we show that for every bridgeless graph G with radius r, rc(G) <= r(r+2). We demonstrate that this bound is the best possible for rc(G) as a function of r, not just for bridgeless graphs, but also for graphs of any stronger connectivity. It may be noted that, for a general 1-connected graph G, rc(G) can be arbitrarily larger than its radius (K_{1,n} for instance). We further show that for every bridgeless graph G with radius r and chordality (size of a largest induced cycle) k, rc(G) <= rk. Hitherto, the only reported upper bound on the rainbow connection number of bridgeless graphs is 4n/5 - 1, where n is order of the graph [Caro et al., 2008]

Landslide Susceptible Locations in Western Ghats: Prediction through openModeller

Many shallow landslides are triggered by heavy rainfall on hill slopes resulting in enormous casualties and huge economic losses in mountainous regions. Hill slope failure usually occurs as soil resistance deteriorates in the presence of the acting stress developed due to a number of reasons such as increased soil moisture content, change in land use causing slope instability, etc. Landslides triggered by rainfall can possibly be foreseen in real time by jointly using rainfall intensity-duration and information related to land surface susceptibility. Terrain analysis applications using spatial data such as aspect, slope, flow direction, compound topographic index, etc. along with information derived from remotely sensed data such as land cover / land use maps permit us to quantify and characterise the physical processes governing the landslide occurrence phenomenon. In this work, the probable landslide prone areas are predicted using two different algorithms – GARP (Genetic Algorithm for Rule-set Prediction) and Support Vector Machine (SVM) in a free and open source software package - openModeller. Several environmental layers such as aspect, digital elevation data, flow accumulation, flow direction, slope, land cover, compound topographic index, and precipitation data were used in modelling. A comparison of the simulated outputs, validated by overlaying the actual landslide occurrence points showed 92% accuracy with GARP and 96% accuracy with SVM in predicting landslide prone areas considering precipitation in the wettest month whereas 91% and 94% accuracy were obtained from GARP and SVM considering precipitation in the wettest quarter of the year.

HLA-B*57 and Gender Influence the Occurrence of Tuberculosis in HIV Infected People of South India

Background. Substantial evidence exists for HLA and other host genetic factors being determinants of susceptibility or resistance to infectious diseases. However, very little information is available on the role of host genetic factors in HIV-TB coinfection. Hence, a longitudinal study was undertaken to investigate HLA associations in a cohort of HIV seropositive individuals with and without TB in Bangalore, South India. Methods. A cohort of 238 HIV seropositive subjects were typed for HLA-A, B, and DR by PCR-SSP and followed up for 5 years or till manifestation of Tuberculosis. HLA data of 682 HIV Negative healthy renal donors was used as control. Results. The ratio of males and females in HIV cohort was comparable (50.4% and 49.6%). But the incidence of TB was markedly lower in females (12.6%,) than males (25.6%). Further, HLA-B* 57 frequency in HIV cohort was significantly higher among females without TB (21.6%, 19/88) than males (1.7%, 1/59); P = 0.0046; OR = 38. CD4 counts also were higher among females in this cohort. Conclusion. This study suggests that HIV positive women with HLA-B* 57 have less occurrence of TB as compared to males.

Predictive distribution modeling for rare Himalayan medicinal plant Berberis aristata DC

Predictive distribution modelling of Berberis aristata DC, a rare threatened plant with high medicinal values has been done with an aim to understand its potential distribution zones in Indian Himalayan region. Bioclimatic and topographic variables were used to develop the distribution model with the help of three different algorithms viz. GeneticAlgorithm for Rule-set Production (GARP), Bioclim and Maximum entroys(MaxEnt). Maximum entropy has predicted wider potential distribution (10.36%) compared to GARP (4.63%) and Bioclim (2.44%). Validation confirms that these outputs are comparable to the present distribution pattern of the B. atistata. This exercise highlights that this species favours Western Himalaya. However, GARP and MaxEnt's prediction of Eastern Himalayan states (i.e. Arunachal Pradesh, Nagaland and Manipur) are also identified as potential occurrence places require further exploration.