Axisymmetric Fluid Research Articles

Stability Analysis of a Thin Pseudoplastic Fluid with Condensation Effects Flowing on a Rotating Circular Disk

This paper investigates the linear stability of a thin axisymmetric pseudoplastic fluid with condensation effects flowing on a rotating circular disk. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The method of normal mode is applied to study the linear stability. The neutral stability curve and the linear growth rate are obtained subsequently as the by-products of linear solution. The study reveals that the rotation number generates a destabilizing effect in pseudoplastic fluid. The degree of the flow index n plays a vital role in stabilizing the film flow.

Analysis of Transient Dynamic Behaviour of Spherical Cavity in Viscoelastic Soil Medium

Stress, displacement, and pore pressure of a partially sealed spherical cavity in viscoelastic soil condition have been obtained in Laplace transform domain. Solutions of axisymmetric surface load and fluid pressure are derived.

Stress-based mathematical model for graded proppant injection in coal bed methane reservoirs

A technology called graded proppant (propping agent) injection that consists of the injection of proppant particles, with increasing sizes and decreasing concentrations, into a naturally fractured reservoir results in deeper percolation of the particles into the natural fracture system, and thus expansion of the stimulated reservoir area. The placement of graded proppant particles keeps the fractures open, even after pressure decline due to production. There is, therefore, an enhancement in the well productivity. This proposed technology could be used to improve the productivity of CSG wells and other unconventional resources; for example, in shales, tight gas, and geothermal reservoirs. In this peer-reviewed paper, a mathematical model for well injectivity/productivity was developed for graded particle injection in a vertical well, lying at the centre of a circular drainage area. The model is based on an analytical solution of the quasi 1D problem of coupled axisymmetric fluid flow and geomechanics. Explicit analytical equations were derived for stress, and pressure and permeability distributions, as well as for the well index during injection and production. Results of previous computational fluid dynamic studies were used to determine the hydraulic resistance resulting from proppant plugging in the fractured system. An optimal stimulation radius was identified, which resulted in the highest increment in the productivity index due to the application of graded proppant injection technology. The model was subsequently used for a sensitivity analysis using field data. The results showed that the productivity index increased more than four times by the application of this technology.

Inviscid and viscous models of axisymmetric fluid jets or plumes

The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear free- boundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume. doi:10.1017/S1446181112000156

Study of thin Film Formation From Silicon‐Containing Precursors Produced by an RF Non‐Thermal Plasma Jet at Atmospheric Pressure

AbstractThe deposition of thin silicon‐organic films by atmospheric pressure PECVD using an RF‐excited plasma jet has been investigated experimentally and theoretically. Static deposition experiments have been performed on flat polymer and glass samples using the silicon containing molecules HMDSO, OMCTS and silane. The experiments are classified with respect to power, flow rate, operating conditions and deposition rate. The deposited films have been analysed using profilometry and Fourier transform infrared spectroscopy. It is found that electric power and gas flow stability determine distinctive areas in the operating diagram characterized by the deposition rate, profile shape and the chemical properties of the film depending on introduced precursors. The highest O/Si ratio (close to two) is found for laminar flow regimes. Here, the films are characterized by a low carbon content, too. The experimental findings for different flow conditions are discussed in relation to results of a two‐dimensional axisymmetric fluid model. The model predicts the interaction of gas heating and flow, the plasma generation in the active volume, the transport of active plasma particles into the effluent and the generation and transport of precursor fragments towards the substrate surface. A remarkable influence of the gas flow on the plasma kinetics is observed only with respect to the density of molecular argon ions, which are transported together with electrons into the effluent. The calculated flux of precursor fragments onto the substrate surface agrees qualitatively with measured profiles of the film thickness (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical investigations on coupled heat transfer and synthetical performance of a pressurized volumetric receiver with MCRT–FVM method

This paper presents an axisymmetric steady-state computational fluid dynamics model and further studies on the complex coupled heat transfer combined radiation–convection–conduction in the pressurized volumetric receiver (PVR), by combining the Finite Volume Method (FVM) and the Monte Carlo Ray-Trace (MCRT) method. Based on this, effects of geometric parameters of the compound parabolic concentrator (CPC) and properties of the porous absorber on synthetical characteristics and performance of the photo-thermal conversion process in the PVR are further analyzed and discussed detailedly. It is found that the solar flux density distributions are always very heterogeneous with large nonuniformities, and the variation trends of the corresponding temperature distributions are very similar to these but with much lower order of magnitude. The CPC shape determined by the CPC exit aperture has much larger effects on synthetical characteristics and performance of the PVR than that of the CPC entry aperture with a constant acceptance angle. And a suitable or optimal thickness of the porous absorber could be determined by examining where the drastic decreasing trends occur at the curves of variations of synthetical characteristics and performance with the porosity.

Rayleigh–Taylor instabilities in axi-symmetric fluid outflow from a point source

This paper studies outflow of a light fluid from a point source, starting from an initially spherical bubble. This region of light fluid is embedded in a heavy fluid, from which it is separated by a thin interface. A gravitational force directed radially inward toward the mass source is permitted. Because the light inner fluid is pushing the heavy outer fluid, the interface between them may be unstable to small perturbations, in the Rayleigh– Taylor sense. An inviscid model of this two-layer flow is presented, and a linearized solution is developed for early times. It is argued that the inviscid solution develops a point of infinite curvature at the interface within finite time, after which the solution fails to exist. A Boussinesq viscous model is then presented as a means of quantifying the precise effects of viscosity. The interface is represented as a narrow region of large density gradient. The viscous results agree well with the inviscid theory at early times, but the curvature singularity of the inviscid theory is instead replaced by jet formation in the viscous case. This may be of relevance to underwater explosions and stellar evolution. doi:10.1017/S1446181112000090

Experimental and numerical investigations of an orifice type cryogenic pulse tube refrigerator

A helium filled orifice type pulse tube refrigerator (OPTR) was designed, built and operated to provide cryogenic cooling. The OTPR is a traveling wave thermoacoustic refrigerator that operates on a modified reverse Stirling cycle. The experimental studies are carried out to characterize the performance of the OPTR at various values of the mean pressure of helium (0.35 MPa–2.2 MPa), amplitudes of pressure oscillations, frequencies of operation and sizes of orifice opening. A detailed time-dependent axisymmetric computational fluid dynamic (CFD) model of the OPTR is also developed to predict its performance. In the CFD model, the continuity, momentum and energy equations are solved for both the refrigerant gas (helium) and the porous media regions (the regenerator and the three heat-exchangers) in the OPTR. An improved representation of heat transfer in the porous media is achieved by employing a thermal non-equilibrium model to couple the gas and solid (porous media) energy equations. The computational results are compared with specific experimental results to validate the numerical model. The model predictions show better temporal comparisons with the experimental results when the effects of wall thicknesses and natural convective losses of the various components of the OPTR to the surroundings are included in the model.

Numerical study on fast filling of 70 MPa type III cylinder for hydrogen vehicle

Abstract There will be significant temperature rise within hydrogen vehicle cylinder during the fast filling process. The temperature rise should be controlled under the temperature limit (85 °C) of the structure material (set by ISO/TS 15869), because it may lead to the failure of the structure. In this paper, a 2-dimensional axisymmetric computational fluid dynamics (CFD) model for fast filling of 70 MPa hydrogen vehicle cylinder is presented. The numerical simulations are based on the modified standard k − ɛ turbulence model. In addition, both the equation of state for hydrogen gas and the thermodynamic properties are calculated by National Institute of Standards and Technology (NIST) database: REFPROP 7.0. The thermodynamic responses of fast filling with different pressure-rise patterns and filling times within type III cylinder have been analyzed in detail.

Simulations of normal and inverse laminar diffusion flames under oxygen enhancement and gravity variation

Steady-state global chemistry calculations for 20 different flames were carried out using an axisymmetric Computational Fluid Dynamics (CFD) code. Computational results for 16 flames were compared with flame images obtained at the NASA Glenn Research Center. The experimental flame data for these 16 flames were taken from Sunderland et al. [4] which included normal and inverse diffusion flames of ethane with varying oxidiser compositions (21, 30, 50, 100% O2 mole fraction in N2) stabilised on a 5.5 mm diameter burner. The test conditions of this reference resulted in highly convective inverse diffusion flames (Froude numbers of the order of 10) and buoyant normal diffusion flames (Froude numbers ∼0.1). Additionally, six flames were simulated to study the effect of oxygen enhancement on normal diffusion flames. The enhancement in oxygen resulted in increased flame temperatures and the presence of gravity led to increased gas velocities. The effect of gravity-variation and oxygen enhancement on flame shape and size of normal diffusion flames was far more pronounced than for inverse diffusion flames. For normal-diffusion flames, their flame-lengths decreased (1 to 2 times) and flames-widths increased (2 to 3 times) when going from earth-gravity to microgravity, and flame height decreased by five times when going from air to a pure oxygen environment.

Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions

We investigate squeezing flow between two large parallel plates by transforming the basic governing equations of the first grade fluid to an ordinary nonlinear differential equation using the stream functions ur(r, z, t) = (1/r)(∂ψ/∂z) and uz(r, z, t) = −(1/r)(∂ψ/∂r) and a transformation ψ(r, z) = r2F(z). The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.

Instabilities of conducting fluid layers in cylindrical cells under the external forcing of weak magnetic fields

In this work, we analyze recent results concerning the instabilities created in a layer of liquid metal by the action of time-dependent magnetic fields. The experimental setup allows the characterization of different patterns very close to the threshold. For very low frequencies of the forcing field, the axisymmetric fluid layer destabilizes with different azimuthal wavenumbers. An improved analysis allows the characterization of different patterns for interaction parameter values as low as 5 · 10 �3 .

Determination of averaged axisymmetric flow surfaces according to results obtained by numerical simulation of flow in turbomachinery

In the increasing need for energy saving worldwide, the designing process of turbomachinery, as an essential part of thermal and hydroenergy systems, goes in the direction of enlarging efficiency. Therefore, the optimization of turbomachinery designing strongly affects the energy efficiency of the entire system. In the designing process of turbomachinery blade profiling, the model of axisymmetric fluid flows is commonly used in technical practice, even though this model suits only the profile cascades with infinite number of infinitely thin blades. The actual flow in turbomachinery profile cascades is not axisymmetric, and it can be fictively derived into the axisymmetric flow by averaging flow parameters in the blade passages according to the circular coordinate. Using numerical simulations of flow in turbomachinery runners, its operating parameters can be preliminarily determined. Furthermore, using the numerically obtained flow parameters in the blade passages, averaged axisymmetric flow surfaces in blade profile cascades can also be determined. The method of determination of averaged flow parameters and averaged meridian streamlines is presented in this paper, using the integral continuity equation for averaged flow parameters. With thus obtained results, every designer can be able to compare the obtained averaged flow surfaces with axisymmetric flow surfaces, as well as the specific work of elementary stages, which are used in the procedure of blade designing. Numerical simulations of flow in an exemplary axial flow pump, used as a part of the thermal power plant cooling system, were performed using Ansys CFX.

Numerical investigation for pressure mitigation effects of dike on blast wave

The three-dimensional and two-dimensional axisymmetric fluid dynamics simulations were carried out to clarify the blast pressure mitigating effects of dike’s configuration in hemispherical explosion. The simulated peak overpressure on the ground under the hemispherical explosion was compared with the empirical formula by Kingery, and the simulated data were validated. In the analysis, the simplification techniques for the numerical simulation were employed under the following two assumptions. The pressure distribution behind the wide dike was estimated using the axisymmetric flowfield, and the back step model was applied under the small condition for θ, the angle formed by the ground and the line between the explosion core and the dike front corner. From the simulated results, it is clarified that the large θ provided the great reduction of the blast wave pressure at faraway position. In the small θ condition, the conditions of the dike end position and the dike height were significant parameters determining the magnitude of pressure reduction and mitigated area. The pressure reduction at the dike end and mitigated area were predicted numerically, and related to the dike conditions.

Frequency Response of a Fractional Derivative Viscoelastic Type Lined Tunnel with Partial Sealing

Based on Biot saturated soil theory, steady state dynamic response of the system is studied in the frequency domain when the inner boundary of a fractional derivative viscoelastic type circular lined tunnel is under the axisymmetric load and fluid pressure respectively. On the basis of introducing a partial permeable boundary condition, the solutions of stress, displacement and pore pressure of the lining and saturated soil are obtained by the inner boundary of the lining and continuity conditions of the interface, besides, the stress-displacement constitutive behavior of the lining is described by fractional derivative viscoelastic constitutive model. The influence of physical parameter on the system response is investigated. It is shown that the order of fractional derivative model has a great influence on the system dynamic response, and it depends on material parameter of the lining when the inner boundary of lining is subjected to axisymmetric load. The permeability parameter of lining has significant effects on system response induced by fluid pressure.

Computational fluid dynamics modeling of mass transfer behavior in a bioreactor for hairy root culture. I. Model development and experimental validation

A two-dimensional axisymmetric computational fluid dynamics (CFD) model based on a porous media model and a discrete population balance model was established to investigate the hydrodynamics and mass transfer behavior in an airlift bioreactor for hairy root culture.During the hairy root culture of Echinacea purpurea, liquid and gas velocity, gas holdup, mass transfer rate, as well as oxygen concentration distribution in the airlift bioreactor were simulated by this CFD model. Simulative results indicated that liquid flow and turbulence played a dominant role in oxygen mass transfer in the growth domain of the hairy root culture. The dissolved oxygen concentration in the hairy root clump increased from the bottom to the top of the bioreactor cultured with the hairy roots, which was verified by the experimental detection of dissolved oxygen concentration in the hairy root clump. This methodology provided insight understanding on the complex system of hairy root culture and will help to eventually guide the bioreactor design and process intensification of large-scale hairy root culture.

2D Axisymmetric Coupled Computational Fluid Dynamics–Kinetics Modeling of a Nonthermal Arc Plasma Torch for Diesel Fuel Reforming

The present study is dedicated to the 2D axisymmetric coupled computational fluid dynamics–kinetics modeling of a plasma-assisted diesel fuel reformer developed for two different applications: (i) onboard H2 production for fuel-cell feeding and (ii) NOx trap regeneration. These cases correspond to very different reaction conditions. In the first case, diesel fuel reacts with air, while in the second case, it reacts with diesel engine exhaust gas. The plasma is modeled with a simple power source domain. n-Heptane has been chosen as a surrogate molecule for diesel fuel. A reduced kinetic mechanism is used for the study. Both cases have been studied under adiabatic and nonadiabatic postreactor conditions. We can distinguish four zones in the torch: a reactant heating zone, a plasma zone, a mixing zone, and a postdischarge zone. The main precursors of the reforming reactions are H, O, and OH radicals. The oxygen rate is a key point of the application. The thermal losses make the reforming reaction difficult to ignite and beget a lower syngas production and a lower postdischarge temperature. For the nonadiabatic reactor, the results have been compared to experimental data. The model predicts relevant gas fractions.

General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code

We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This is aimed at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as for the evolution of magnetized neutron stars or for the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code is based on the extension of the Eulerian conservative high-order (ECHO) scheme [Del Zanna et al., A&A 473, 11 (2007)] for GRMHD, here coupled to a novel solver for the Einstein equations in the extended conformally flat condition (XCFC). We fully exploit the 3+1 Eulerian formalism, so that all the equations are written in terms of familiar 3D vectors and tensors alone, we adopt spherical coordinates for the conformal background metric, and we consider axisymmetric spacetimes and fluid configurations. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and solved, for each harmonic, by inverting band diagonal matrices. As a side product, we build and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.

Flowfield Uncertainty Analysis for Hypersonic Computational Fluid Dynamics Simulations

Uncertainty quantification in the hypersonic flow regime offers valuable information to determine physical models in need of improvement and to assist in design of vehicles and flight experiments. Here we present results of uncertainty quantification analysis based on polynomial chaos method to determine flowfield and surface heat flux uncertainty under typical blunt-body reentry conditions. The NASA Langley Aerothermodynamic Upwind Relaxation Algorithm code [Cheatwood, F., and Gnoffo, P., Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), NASA TM 4674, 1996.], was used for axisymmetric computational fluid dynamics calculations of chemically-reacting, hypersonic flow over FIRE 2 configuration. A third-order polynomial chaos method using the Gauss―Hermite quadrature was applied for determining probability density functions and moments of output quantities. Input parameters such as freestream density, velocity, and temperature were varied, and the propagation of their corresponding uncertainties on output properties of interest through the flowfield were studied. The flowfield regions where the uncertainties are amplified due to nonlinear effects have been determined. An order of magnitude increase in surface heat flux uncertainties was observed for an input freestream velocity uncertainty of ±30 m/s, or 0.29%. This parameter thus has the greatest sensitivity to variations, and conversely the freestream temperature has the least sensitivity. The utility of analyzing higher moments, such as skewness, in addition to mean and deviation of the uncertain output parameters has also been demonstrated.

An Axisymmetric Squeezing Fluid Flow between the Two Infinite Parallel Plates in a Porous Medium Channel

The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier‐Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformation ψ(r, z) = r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.