Experiments on rarefied gas flows through tubes

Experiments were carried out in order to evaluate the conductance of tubes of circular cross section as a function of the Knudsen number. The range of the rarefaction level spans from the free molecular flow to the continuum regime. A different experimental approach was followed with respect to previous researches in that the mass flow rate was assigned and the corresponding pressure drop was measured. Single tubes and a bundle of capillaries were adopted. The results are compared with the existing experimental data and analytical models. An analysis of the sensitivity of the conductance to the error in measurements, in free molecular flow, was also dealt with.     

A mathematical model of laminar axisymmetrical natural gas flames

A computational procedure for determining the velocities, temperatures and species concentrations in a laminar Bunsen type flame is presented. The boundary layer form of the Navier-Stokes equations with coupled chemistry are solved for a compressible, viscous and axisymmetric flow. An implicit finite difference method is used in the solutions. Velocities, temperatures and stable species concentrations are compared with experimental data.     

Similarity solutions for axisymmetric plane radial power law fluid flows through a porous medium

This paper investigates the unsteady flow of non-Newtonian fluids of power low behavior through a porous medium in a plane radial geometry. The equation governing the flow is a nonlinear parabolic partial differential equation with a source term whose solution satisfies certain fixed and moving boundary conditions. The attention is focused on the finding of similarity solution when the fixed boundary condition and the source term satisfy certain restrictions. In this case similarity transformations are determined and the resulting ordinary differential equations are deduced. For shear thinning fluids the existence of a pressure disturbance front moving with finite velocity is shown and expression for its location as a function of time is determined. The solutions in closed form have been given for certain particular cases where the resulting differential equations can be analytically solved. A numerical procedure has also been presented.     

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

A comparative study between computational and experimental results for pressure-driven binary gas flows through long microchannels is performed. The theoretical formulation is based on the McCormack kinetic model and the computational results are valid in the whole range of the Knudsen number. Diffusion effects are taken into consideration. The experimental work is based on the Constant Volume Method, and the results are in the slip and transition regime. Using both approaches, the molar flow rates of the He–Ar gas mixture flowing through a rectangular microchannel are estimated for a wide range of pressure drops between the upstream and downstream reservoirs and several mixture concentrations varying from pure He to pure Ar. In all cases, a very good agreement is found, within the margins of the introduced modeling and measurement uncertainties. In addition, computational results for the pressure and concentration distributions along the channel are provided. As far as the authors are aware of, this is the first detailed and complete comparative study between theory and experiment for gaseous flows through long microchannels in the case of binary mixtures.     

Time-dependent reliability analysis through projection outline-based adaptive Kriging

Structural and Multidisciplinary Optimization - Time-dependent reliability analysis (TRA) has drawn much attention due to its ability in measuring the probability that a system or component keeps...     

Numerical study of interference between simple-shape bodies in hypersonic flows

Hypersonic rarefied-gas flows near two side-by-side plates and cylinders, toroidal balloon, plate and cylinder over a plane surface, and plate behind a cylinder in argon, nitrogen, oxygen, and carbon dioxide have been studied numerically using the direct simulation Monte-Carlo technique under the transition flow conditions at Knudsen numbers from 0.004 to 10. Strong influences of the geometrical factor (the ratio of a distance between bodies to a body length) and the Knudsen number on the flow structure about the bodies (shock-wave shapes, the configuration of subsonic flow zones), skin friction, pressure distribution, lift, and drag have been found.     

Construction of harmonic map flows through the method of discrete Morse flows

By the method of discrete Morse flows, we construct the Morse flow of harmonic map from a Riemannian manifold with measurable and bounded metric into that with Alexander non-positive curvature. The construction is directly derived without isometrically embedding of the target manifold into Euclidean space. Our method will be in force in the case, as treated in [11], where a target manifold has the bounded positive curvature.     

The method of fundamental solutions for oscillatory and porous buoyant flows

Accurate solutions of oscillatory Stokes flows in convection and convective flows in porous media are studied using the method of fundamental solutions (MFS). In the solution procedure, the flows are represented by a series of fundamental solutions where the intensities of these sources are determined by the collocation on the boundary data. The fundamental solutions are derived by transforming the governing equation into the product of harmonic and Helmholtz-type operators, which can be classified into three types depending on the oscillatory frequencies of temperature field. All the velocities, the pressure, and the stresses corresponding to the fundamental solutions are expressed explicitly in tensor forms for all the three cases. Three numerical examples were carried out to validate the proposed fundamental solutions and numerical schemes. Then, the method was also applied to study exterior flows around a sphere. In these studies, we derived the MFS formulas of drag forces. Numerical results were compared accurately with the analytical solutions, indicating the ability of the MFS for obtaining accurate solutions for problems with smooth boundary data. This study can also be treated as a preliminary research for nonlinear convective thermal flows if the particular solutions of the operators can be supplied, which are currently under investigations.     

Behaviour of an immersed boundary method in unsteady flows over sharp-edged bodies

The behaviour of the immersed boundary method proposed by Goldstein et al. [Goldstein D, Handler R, Sirovich L. Modelling a no-slip boundary condition with an external force field. J Comput Phys 1993;105:354-66] as a second-order damped control system is investigated. The natural frequency and the damping coefficient are introduced as driving parameters of the method. The comparison between the velocity response at forced points in the startup flow over a square cylinder with the theoretical response of a second-order damped oscillator is performed. The role of each parameter appears clearly. At the beginning of the startup flow, the response time depends directly on the natural frequency, and this parameter determines the level of residual velocities achieved in an unsteady flow. The damping coefficient drives the oscillation of the velocity response at the beginning of the startup flow, but has negligible influence during the establishment and in the unsteady flow. At forced points facing no unsteady perturbation from the flow, the zero-velocity set point is reached asymptotically, as usual in second-order damped-systems. Through the simulation of the flow over a blunt flat plat at Re=1000, it is observed that the initial thickness of the mixing layer due to the separation at the edge may vary during the simulation because the sharpness of the edge increases as the residual velocities decrease. This insight gained on the behaviour of the response allows a time-step optimisation, which, completed with comparisons to reference literature results, confirms the feedback forcing method a competitive tool for accessing near-wall unsteady flow over sharp-edged bodies.     

Mathematical simulation of turbulent separated transonic flows around the bodies of revolution

The properties of the turbulent separated flows around boat-tailed objects, especially in transonic regimes, are very complex and have still not been fully understood. With a variation of the free-stream Mach number, the flow structure, the size and location of separation areas, internal supersonic regions, and the position and intensity of internal shocks vary significantly. These flow properties determine the complexity of the numerical modeling problem and high demands on the algorithms used. The paper presents a comparison of the numerical results obtained on the basis of different mathematical models with the experimental data. The investigations into fundamental properties of transonic flow transformation are presented as well.     

Drying-induced stresses in porous bodies —an elastoviscoplastic model

The paper describes the application of the finite element method to the calculation of drying-induced stresses in capillary porous bodies, using an elastoviscoplastic stress-strain relationship. The method is illustrated by its application to the problem of drying of a clay brick. Stress distributions are shown at three distinct stages of the drying process, and at each stage the relaxation of the stresses due to plastic flow is indicated. Zones of potential failure are clearly seen, and hence geometry or rate of drying can be modified to avoid such failure.     

A contribution to the computation of transonic supersonic flows over blunt bodies

Stationary inviscid transonic supersonic flowfield around sphrese, ellipsoids and hemisphere-cylinders are calculated. The freestream Mach numbers considered are between $\text{M}{}_{\mathrm{\infty }}\text{= 1.02}$ and $\text{M}{}_{\mathrm{\infty }}\text{= 1.1}$. A special coordinate system is created which is adjusted to the subsonic stagnation point region for transonic freestream Mach numbers. The integration of the governing equations is carried out by means of a time-dependent finite-difference procedure. All the calculations discussed were stable and converged uniquely to the asymptotic stationary state. The influence of an artificial dissipation term added to the finite-difference scheme is studied. It is further shown, that in all cases the limiting characteristics come from the front part of the bodies. The results include bow shocks, sonic lines, characteristics, lines of constant pressure, density and Mach numbers. A comparison is made between such flow quantities which are calculable by analytical functions and the predicted ones. The quality of the results is checked by considering the conservation of the total enthalpy. For some examples the present solutions are compared with other theories and experimental data.     

Molecular dynamics simulations of shear-driven gas flows in nano-channels

Using the recently developed smart wall molecular dynamics algorithm, shear-driven gas flows in nano-scale channels are investigated to reveal the surface–gas interaction effects for flows in the transition and free molecular flow regimes. For the specified surface properties and gas–surface pair interactions, density and stress profiles exhibit a universal behavior inside the wall force penetration region at different flow conditions. Shear stress results are utilized to calculate the tangential momentum accommodation coefficient (TMAC) between argon gas and FCC walls. The TMAC value is shown to be independent of the flow properties and Knudsen number in all simulations. Velocity profiles show distinct deviations from the kinetic theory based solutions inside the wall force penetration depth, while they match the linearized Boltzmann equation solution outside these zones. Results indicate emergence of the wall force field penetration depth as an additional length scale for gas flows in nano-channels, breaking the dynamic similarity between rarefied and nano-scale gas flows solely based on the Knudsen and Mach numbers.     

A method for computing selfgravitating gas flows with radiation

We present a numerical method which is suitable for calculating selfgravitating gas flows including thermodynamic processes and radiation. Such problems arise for example in connection with the formation of new stars by gravitational collapse of interstellar clouds. A particularly difficult problem which must be numerically solved in a consistent way is the settling of matter from a supersonic flow into a hydrostatic equilibrium after passing through a strong shock front. Because this must be done without continuously exciting spurious oscillations with extremely small time scales, very stringent constraints are imposed upon the method of solution. Technically, the method here described incorporates a freely moving coordinate system with a generalized form of Richtmyer's artificial viscosity for smoothing shock fronts (tensor viscosity), the two most important improvements to earlier attempts to solve this problem. The method has been extensively tested for spherically and axially symmetric flows. How to proceed in the full 3D case is briefly outlined. Accuracy problems are discussed in connection with numerical stability. We give examples for collapse, accretion and explosion in spherical symmetry and for collapse and ring formation in an axially symmetric rotating cloud.     

A Newton-like finite element scheme for compressible gas flows

Semi-implicit and Newton-like finite element methods are developed for the stationary compressible Euler equations. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers, which is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. Special emphasis is laid on the numerical treatment of weakly imposed characteristic boundary conditions. Numerical evidence for unconditional stability is presented. It is shown that the proposed approach offers higher accuracy and better convergence behavior than algorithms in which the boundary conditions are implemented in a strong sense.     

Pressure-sensitive molecular film for investigation of micro gas flows

For the development of micro- and nano-technology, it has been strongly desired to understand thermo-fluid phenomena inside or around micro- and nano-devices. An optical measurement technique based on the absorption and the emission of photons by molecules is useful for experimental analyses of thermo-fluid phenomena of micro and nanoflows. The pressure-sensitive paint (PSP) technique is a potential diagnostic tool for pressure measurements of micro/nano gas flows because it works as a so-called “molecular sensor”. However, the micro-scale measurement of PSP has been limited by the aggregation of the luminescent molecules and their thick film due to the use of a polymer binder. In our previous work, we adopted the Langmuir–Blodgett (LB) technique to fabricate pressure-sensitive molecular film (PSMF) with ordered molecular assemblies, and investigated properties of PSMF. In this study, a novel approach to enhance the luminescent intensity of PSMF is proposed, and the pressure distribution in a micro-nozzle is successfully measured by using PSMF. Moreover, we compared the pressure distribution measured by PSMF with that numerically analyzed by the direct simulation monte carlo (DSMC) method, showing good agreement with each other.