Inclusion Of Viscous Effects Research Articles

Simulating volume-controlled invasion of a non-wetting fluid in volumetric images using basic image processing tools

A new algorithm is presented for simulating volume-controlled invasion of a non-wetting phase into voxel images. This method is complementary to the traditional morphological image opening method which mimics pressure-based invasion. A key advantage of the volume-based approach is that fluid configuration at any saturation between 0 and 1 can obtained rather than the irregularly and widely spaced saturation steps obtained by pressure-based methods. Because of the incremental increases in saturation, it becomes possible to correctly predict defending phase trapping, which is not the case when pressure-based steps are applied. The algorithm is verified by comparing to morphological image opening and obtains near perfect agreement at equal saturations as expected from theory. It is also demonstrated that a volume-controlled capillary pressure curve can be obtained that displays the characteristic jumps in capillary pressure. Moreover, the envelop of peak pressures yields the pressure-based capillary pressure obtained by morphological opening, so in fact the results of the proposed algorithm are a superset of the morphological approach. Finally, results are compared to multiphase lattice Boltzmann and qualitatively similar results were achieved in substantially less time. The lattice Boltzmann method is more flexible in terms of variable contact angle and inclusion of viscous effects, but for quasi-static volume-based injection of a non-wetting fluid, the proposed method is viable alternative.

Modeling of a continuous physical vapor deposition process: Mass transfer limitations by evaporation rate and sonic choking

• Novel evaporation boundary condition is proposed to consider Hertz-Knudsen limitation. • A comprehensive numerical model for continuous PVD processes in OpenFoam is presented. • Non-isentropic losses reduce discharge; this effect decreases with melt temperature. • The isentropic overestimate is 110%–150%, that of the new CFD model only 30%. • Numerical model predictions are relatively insensitive to unknown process parameters. In recent years, Physical Vapor Deposition has been advanced to a continuous process which makes it amenable for in-line, high-quality and energy-efficient galvanization. To achieve the high and uniform mass flow required for in-line production, a Vapor Distribution Box is used, in which the zinc is evaporated. The zinc fills the Vapor Distribution Box at a relatively high pressure and leaves into the coating chamber via nozzles. A reliable modeling approach that can be used in the design and optimization of Vapor Distribution Boxes is as yet not available in the literature. The present paper analyses which phenomena play a major role and therefore have to be included in a simulation model of continuous Physical Vapor Deposition processes, and identifies process parameters which have a significant impact on deposition rate and uniformity. To this end, a model for the flow and heat transfer is developed based on the numerical solution of the compressible Navier–Stokes-Fourier equations in combination with the Launder and Sharma low-Reynolds k- ∊ turbulence model, using the open-source CFD-library OpenFOAM. To account for the vapor mass flow to be limited by both evaporation and sonic choking, a novel inlet boundary condition is proposed based on the Hertz-Knudsen condition. Results from the CFD model are compared to those of analytical models based on isentropic flow, the influence of various modeling parameters is evaluated against experiments, and sensitivity of the process to various process parameters studied. The proposed numerical model predicts mass flow rates with a much better accuracy than analytical models previously proposed in the literature. The latter overpredict the mass flow rate by a factor of 2.1–2.5, whereas the proposed numerical model overpredicts only by a factor of 1.3. Next to the novel Hertz-Knudsen boundary condition, the inclusion of viscous effects is found to be crucial to achieve this improvement, since viscous effects – especially in the boundary layer inside the nozzles – severely reduce the mass flow. The numerical model is shown to be only weakly sensitive to uncertainties in the evaporation coefficients and metal vapor viscosity. For the device studied, the mass flow discharge efficiency was found to be relatively low ( ≈ 40 % ). To increase this efficiency, viscous losses in the nozzle boundary layers have to be reduced, for instance by employing shorter or a bigger radius nozzles (possibly impairing nozzle-to-nozzle uniformity) or by employing a higher melt temperature and vapor pressure.

New Solutions of Viscous Relativistic Hydrodynamics

Relativistic hydrodynamics represents a powerful tool to investigate the time evolution of the strongly interacting quark gluon plasma created in ultrarelativistic heavy ion collisions. The equations are solved often numerically, and numerous analytic solutions also exist. However, the inclusion of viscous effects in exact, analytic solutions has received less attention. Here we utilize Hubble flow to investigate the role of bulk viscosity, and present different classes of exact, analytic solutions valid also in the presence of dissipative effects.

Shape Effects on Viscous Damping and Motion of Heaving Cylinders1

Fluid viscosity is known to influence hydrodynamic forces on a floating body in motion, particularly when the motion amplitude is large and the body is of bluff shape. While traditionally these hydrodynamic force or force coefficients have been predicted by inviscid-fluid theory, much recent advances had taken place in the inclusion of viscous effects. Sophisticated Reynolds-Averaged Navier–Stokes (RANS) software are increasingly popular. However, they are often too elaborate for a systematic study of various parameters, geometry or frequency, where many runs with extensive data grid generation are needed. The Free-Surface Random-Vortex Method (FSRVM) developed at UC Berkeley in the early 2000 offers a middle-ground alternative, by which the viscous-fluid motion can be modeled by allowing vorticity generation be either turned on or turned off. The heavily validated FSRVM methodology is applied in this paper to examine how the draft-to-beam ratio and the shaping details of two-dimensional cylinders can alter the added inertia and viscous damping properties. A collection of four shapes is studied, varying from rectangles with sharp bilge corners to a reversed-curvature wedge shape. For these shapes, basic hydrodynamic properties are examined, with the effects of viscosity considered. With the use of these hydrodynamic coefficients, the motion response of the cylinders in waves is also investigated. The sources of viscous damping are clarified.

Two dimensional pore network modelling and simulation of non-isothermal drying by the inclusion of viscous effects

Drying as an immiscible displacement process has a great importance in chemical industries. The efficiency of the process is highly affected by the pore space structure of the solids. In this study non-isothermal drying behaviour of capillary porous media is studied in two dimensional (2D) mono-modal and bi-modal pore network models. Non-isothermal drying in the absence of viscous force has been studied previously. The presented model includes viscous flow in liquid phase while capillary pumping in liquid phase and diffusion in gas phase are the other mass transfer mechanisms at the pore scale. Conduction is considered as the heat transfer mechanism. The effect of viscous flow and temperature of drying air are studied. The simulation results are compared with a non-viscous model. The results indicate that the effect of viscous force is more significant in low temperatures. During the first falling drying rate period viscous forces dominate capillary pumping and decrease drying rate. The first drying rate period is not affected by viscous forces; however, the morphology of the pore space is an important parameter in forming this period. In bi-modal pore network, drying rate is higher due to the suitable arrangement of macro and microthroats in its structure.

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

Inclusion of viscous effects in the description of instability waves in supersonic jets

Tam’s theory of supersonic jet noise based on the asymptotic linear theory of instability waves is considered. It is shown that the theory needs additional validation (experimental, theoretical, and numerical), since it possesses a singularity near the nozzle lip as the shear layer thickness vanishes. A possible approach to removing the singularity by introducing turbulent viscosity is considered. It is shown that in this case the instability wave itself disappears: its amplitude remains small and does not stand out against the other disturbances. In this case, the totality of the different turbulent disturbances having a supersonic phase velocity would be the main noise source rather than the instability wave; the numerical description of these disturbances is very sensitive to the closure method adopted.

A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: Formulation and comparison with experimental data

Experiments in articular cartilage have shown highly nonlinear stress–strain curves under finite deformations, nonlinear tension–compression response as well as intrinsic viscous effects of the proteoglycan matrix and the collagen fibers. A biphasic viscohyperelastic fibril-reinforced model is proposed here, which is able to describe the intrinsic viscoelasticity of the fibrillar and nonfibrillar components of the solid phase, the nonlinear tension-compression response and the nonlinear stress–strain curves under tension and compression. A viscohyperelastic constitutive equation was used for the matrix and the fibers encompassing, respectively, a hyperelastic function used previously for the matrix and a hyperelastic law used before to represent biological connective tissues. This model, implemented in an updated Lagrangian finite element code, displayed good ability to follow experimental stress–strain equilibrium curves under tension and compression for human humeral cartilage. In addition, curve fitting of experimental reaction force and lateral displacement unconfined compression curves showed that the inclusion of viscous effects in the matrix allows the description of experimental data with material properties for the fibers consistent with experimental tensile tests, suggesting that intrinsic viscous effects in the matrix of articular cartilage plays an important role in the mechanical response of the tissue.

Viscous and Inertial Pressure Effects at the Inlet to a Bearing Film

A numerical solution of the flow equations in an inlet groove and parallel land is used to evaluate and examine the leading edge ram pressure in parallel surface thrust bearings. The separate viscous and inertial effects on the ram pressure are considered and a correlation with the film Reynolds number developed. A comparison of the computed results with Lewicki's model and with available experimental data shows good agreement. Most treatments of inlet flow consider only inertial effects. It is shown that the inclusion of viscous effects can give inlet ram pressures substantially higher than the component due to inertial effects. Presented at the 42nd Annual Meeting in Anaheim, California May 11–14, 1987

Compressibility corrections for multifoil sections

HE calculation of compressible flow about multifoil sections has not developed at the same rate as that for single foils. Flap configurations are generally used at low Mach numbers where the inclusion of viscous effects is somewhat more important than the inclusion of compressibili ty effects, with the result that the latter is often neglected. The evolution at de Havilland of the transonic multifoil (Fig. 1) from the proven STOL capable augmentor wing1 has necessitated the parallel development of multifoil compressible methods. To date this has centered around the use of a standard surface singularity potential flow technique that incorporates compressibility by using the Goethert transformation and corrections similar to those developed by Wilby 2 and Labrujere.3 However, the application of these compressibility corrections to the geometry of Fig. 1 is fraught with difficulty. First, the foils are very thick, typically in the range 18-30%, while the compressibility corrections have been developed for thinner sections. Second, the combination of internal and external flow regions has not been addressed by these methods. For a number of years, the accepted method for obtaining the compressible flow within a duct has been that due to Lieblein and Stockman (LS).4 This has been shown to be reliable.5 However, until recently, it suffered from the absence of a counterpart for external flow and, therefore, could not be applied to general configurations. This deficiency has been remedied by Dietrich, Oehler, and Stockman (DOS),6 who have modified the internal flow method to produce a compressible flow correction for external flow. Apart from the attraction of now having consistent corrections for all regions of the flow about a general flap configuration, there is also the advantage of them being based on incompressible calculations and, therefore, allowing the combination of solutions. It is the application of the LS and DOS methods in concert to the geometry of Fig. 1 that is the subject of this paper. Basic Formulation

Instability of a viscous, incompressible and electrically conducting fluid cylinder due to axial current

The stability of an incompressible, viscous and electrically conducting fluid cylinder in the presence of an axial current is investigated. The effect of surface tension is taken into account while the effect of gravity is neglected. It is shown that the inclusion of viscous effects reduces the growth rate of instabilities. In the case of mercury the amount of reduction in the growth rates is negligibly small.