Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Passive pressure coefficients, critical failure surface and its kinematic admissibility

Using a combination of a logarithmic spiral and a straight line as a failure surface, comprehensive charts have been developed to determine the passive earth pressure coefficients and the positions of the critical failure surface for positive as well as negative wall friction angles. Translational movement of the wall has been examined in detail, considering the soil as either an associated flow dilatant material or a non-dilatant material, to determine the kinematic admissibility of the limit equilibrium solutions.

Seismic passive earth pressure coefficients using the method of characteristics

The method of characteristics was used to generate passive earth pressure coefficients for an inclined wall retaining cohesionless backfill material in the presence of pseudostatic horizontal earthquake body forces. The variation of the passive earth pressure coefficients K-pq and K-pgamma with changes in horizontal earthquake acceleration coefficient due to the components of soil unit weight and surcharge pressure, respectively, has been obtained; a closed-form solution for K-pq is also provided. The passive earth resistance has been found to decrease sharply with an increase in the magnitude of horizontal earthquake acceleration. The computed passive earth pressure coefficients were found to be the lowest when compared to all of the previous solutions available in the literature.

Elerctron Transport Coefficients in N2 in Crossed Fields at Low E/p

The numerical solutions of Boltzmann transpott equation for the energy distribution of electrons moving in crossed fields in nitrogen have been obtained for 100 ÿ E/p ÿ 1000 V M-1 Torr-1 and for 0ÿ B/p ÿ 0.02 Tesla Torr-1 using the concept of energy dependent effective field intensity. From the derived distribution functions the electron mean energy, the tranaverse and perpendicular drift velocities and the averaged effective field intensity (Eavef) which signifies the average field intensity experienced by electron swarms in E àB field have been derived. The maximum difference between the electron mean energy for a given E ÃÂB field and that corresponding to Eavef/p (p is the gas pressure) is found to be within ñ3.5%.

Sparking potentials and ionisation coefficients in SF6

Steady-state ionisation currents under uniform field conditions have been measured in SF6 over the range 110 ÿE/pÿ1000V cmÿ1torrÿ1 with gas pressures varying from 1 to 10 torr, at 20ðC. Sparking potentials Vs were also measured for a range 1ÿpdÿ20 torr-cm. Townsend's primary ionisation (ÿ/p) and electron-attachment (ÿ/p) coefficients were found to depend on E/p only. The values of secondary-ionisation coefficient (ÿ) were also determined over the range 140ÿE/pÿ600 V cmÿ1 torrÿ1. Measurements of Vs of SF6 have shown that the deviations from Paschen's law rise up to ñ3.5% at values of pd near the Paschen minimum.

Hypersonic wave drag reduction in re-entry capsules using concentrated energy deposition

Experiments are carried out in a shock tunnel at a nominal Mach number of 5.75 in order to study the effect of concentrated energy deposition on the drag force experienced by a 120° blunt cone. Electrical energy was deposited along the stagnation streamline of the model using a high voltage DC discharge circuit (1.5 – 3.5KW) and the drag force was measured by a single component accelerometer balance. Numerical simulations were also carried complimenting the experiments. These simulations showed a substantial drag reduction (20% ~ 65%) whereas the experiments show no appreciable reduction in drag

Effect of gas injection on drag and surface heat transfer rates for a 30 degrees semi-apex angle blunt body flying at Mach 5.75

Effect of coolant gas injection in the stagnation region on the surface heat transfer rates and aerodynamic drag for a large angle blunt body flying at hypersonic Mach number is reported for two stagnation enthalpies. A 60° apex-angle blunt cone model is employed for this purpose with air injection at the nose through a hole of 2mm diameter. The convective surface heating rates and aerodynamic drag are measured simultaneously using surface mounted platinum thin film sensors and internally mounted accelerometer balance system, respectively. About 35–40% reduction in surface heating rates is observed in the vicinity of stagnation region whereas 15–25% reduction in surface heating rates is felt beyond the stagnation region at stagnation enthalpy of 1.6MJ/kg. The aerodynamic drag expressed in terms of drag coefficient is found to increase by 20% due to the air injection.

Force measurements on hypersonic waveriders in the IISc hypersonic shock tunnel HST2

The drag and lift coefficients for a viscous optimized Mach 6 conical waverider has been measured using an accelerometer force balance system in the IISc hypersonic shock tunnel. A rubber bush placed in between the waverider model and the steel sting ensures unrestrained motion to the model during shock tunnel testing (500 mu s). Two accelerometers mounted on the model are used to measure the model accelerations in the axial and normal directions. The measured value of lift to drag ratio at zero angle of incidence for the IISc conical waverider with viscous optimized leading edge is 2.149, which compares well with the value reported in the open literature (Anderson et al 1991) for similar class of waveriders designed for a flight Mach number of 6. The details of the experimental study along with illustrative numerical results are discussed in this paper.

Minimum power consumption for drag reduction on a circular cylinder by tangential surface motion

We investigate the effect of a prescribed tangential velocity on the drag force on a circular cylinder in a spanwise uniform cross flow. Using a combination of theoretical and numerical techniques we make an attempt at determining the optimal tangential velocity profiles which will reduce the drag force acting on the cylindrical body while minimizing the net power consumption characterized through a non-dimensional power loss coefficient (C-PL). A striking conclusion of our analysis is that the tangential velocity associated with the potential flow, which completely suppresses the drag force, is not optimal for both small and large, but finite Reynolds number. When inertial effects are negligible (R e << 1), theoretical analysis based on two-dimensional Oseen equations gives us the optimal tangential velocity profile which leads to energetically efficient drag reduction. Furthermore, in the limit of zero Reynolds number (Re -> 0), minimum power loss is achieved for a tangential velocity profile corresponding to a shear-free perfect slip boundary. At finite Re, results from numerical simulations indicate that perfect slip is not optimum and a further reduction in drag can be achieved for reduced power consumption. A gradual increase in the strength of a tangential velocity which involves only the first reflectionally symmetric mode leads to a monotonic reduction in drag and eventual thrust production. Simulations reveal the existence of an optimal strength for which the power consumption attains a minima. At a Reynolds number of 100, minimum value of the power loss coefficient (C-PL = 0.37) is obtained when the maximum in tangential surface velocity is about one and a half times the free stream uniform velocity corresponding to a percentage drag reduction of approximately 77 %; C-PL = 0.42 and 0.50 for perfect slip and potential flow cases, respectively. Our results suggest that potential flow tangential velocity enables energetically efficient propulsion at all Reynolds numbers but optimal drag reduction only for Re -> infinity. The two-dimensional strategy of reducing drag while minimizing net power consumption is shown to be effective in three dimensions via numerical simulation of flow past an infinite circular cylinder at a Reynolds number of 300. Finally a strategy of reducing drag, suitable for practical implementation and amenable to experimental testing, through piecewise constant tangential velocities distributed along the cylinder periphery is proposed and analysed.

Time dependent superhydrophobicity of drag reducing surfaces

Air can be trapped on the crevices of specially textured hydrophobic surfaces immersed in water. This heterogenous state of wetting in which the water is in contact with both the solid surface and the entrapped air is not stable. Diffusion of air into the surrounding water leads to gradual reduction in the size and numbers of the air bubbles. The sustainability of the entrapped air on such surfaces is important for many underwater applications in which the surfaces have to remain submersed for longer time periods. In this paper we explore the suitability of different classes of surface textures towards the drag reduction application by evaluating the time required for the disappearance of the air bubbles under hydrostatic conditions. Different repetitive textures consisting of holes, pillars and ridges of different sizes have been generated in silicon, aluminium and brass by isotropic etching, wire EDM and chemical etching respectively. These surfaces were rendered hydrophobic with self-assembled layer of fluorooctyl trichlorosilane for silicon and aluminium surfaces and 1-dodecanethiol for brass surfaces. Using total internal reflection the air bubbles are visualized with the help of a microscope and time lapse photography. Irrespective of the texture, both the size and the number of air pockets were found to decrease with time gradually and eventually disappear. In an attempt to reverse the diffusion we explore the possibility of using electrolysis to generate gases at the textured surfaces. The gas bubbles are nucleated everywhere on the surface and as they grow they coalesce with each other and get pinned at the texture edges.

Experiments and zero D modeling studies using specific Wiebe coefficients for producer gas as fuel in spark-ignited engines

The paper addresses experiments and modeling studies on the use of producer gas, a bio-derived low energy content fuel in a spark-ignited engine. Producer gas, generated in situ, has thermo-physical properties different from those of fossil fuel(s). Experiments on naturally aspirated and turbo-charged engine operation and subsequent analysis of the cylinder pressure traces reveal significant differences in the heat release pattern within the cylinder compared with a typical fossil fuel. The heat release patterns for gasoline and producer gas compare well in the initial 50% but beyond this, producer gas combustion tends to be sluggish leading to an overall increase in the combustion duration. This is rather unexpected considering that producer gas with nearly 20% hydrogen has higher flame speeds than gasoline. The influence of hydrogen on the initial flame kernel development period and the combustion duration and hence on the overall heat release pattern is addressed. The significant deviations in the heat release profiles between conventional fuels and producer gas necessitates the estimation of producer gas-specific Wiebe coefficients. The experimental heat release profiles are used for estimating the Wiebe coefficients. Experimental evidence of lower fuel conversion efficiency based on the chemical and thermal analysis of the engine exhaust gas is used to arrive at the Wiebe coefficients. The efficiency factor a is found to be 2.4 while the shape factor m is estimated at 0.7 for 2% to 90% burn duration. The standard Wiebe coefficients for conventional fuels and fuel-specific coefficients for producer gas are used in a zero D model to predict the performance of a 6-cylinder gas engine under naturally aspirated and turbo-charged conditions. While simulation results with standard Wiebe coefficients result in excessive deviations from the experimental results, excellent match is observed when producer gas-specific coefficients are used. Predictions using the same coefficients on a 3-cylinder gas engine having different geometry and compression ratio(s) indicate close match with the experimental traces highlighting the versatility of the coefficients.

A unified view of energetic efficiency in active drag reduction, thrust generation and self-propulsion through a loss coefficient with some applications

An analysis of the energy budget for the general case of a body translating in a stationary fluid under the action of an external force is used to define a power loss coefficient. This universal definition of power loss coefficient gives a measure of the energy lost in the wake of the translating body and, in general, is applicable to a variety of flow configurations including active drag reduction, self-propulsion and thrust generation. The utility of the power loss coefficient is demonstrated on a model bluff body flow problem concerning a two-dimensional elliptical cylinder in a uniform cross-flow. The upper and lower boundaries of the elliptic cylinder undergo continuous motion due to a prescribed reflectionally symmetric constant tangential surface velocity. It is shown that a decrease in drag resulting from an increase in the strength of tangential surface velocity leads to an initial reduction and eventual rise in the power loss coefficient. A maximum in energetic efficiency is attained for a drag reducing tangential surface velocity which minimizes the power loss coefficient. The effect of the tangential surface velocity on drag reduction and self-propulsion of both bluff and streamlined bodies is explored through a variation in the thickness ratio (ratio of the minor and major axes) of the elliptical cylinders.