Compressible gas flow between closely spaced plates

A theoretical analysis is presented to solve numerically the steady state Navier–Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non-choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.     

Choked flow mechanism of HFC-134a flowing through short-tube orifices

This paper is a continuation of the author’s previous work. New experimental data on the occurrence of choked flow phenomenon and mass flow rate of HFC-134a inside short-tube orifices under choked flow condition are presented. Short-tube orifices diameters ranging from 0.406 mm to 0.686 mm with lengths ranging from 1 mm to 3 mm which can be applied to a miniature vapour-compression refrigeration system are examined. The experimental results indicated that the occurrence of choked flow phenomena inside short-tube orifices is different from that obtained from short-tube orifice diameters of greater than 1 mm, which are typically used in air-conditioner. The beginning of choked flow is dependent on the downstream pressure, degree of subcooling, and length-to-diameter ratio. Under choked flow condition, the mass flow rate is greatly varied with the short-tube orifice dimension, but it is slightly affected by the operating conditions. A correlation of mass flow rate through short-tube orifices is proposed in terms of the dimensionless parameters. The predicted results show good agreement with experimental data with a mean deviation of 4.69%.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

Inertial,viscous and yield stress effects in Bingham fluid filling of a 2-D cavity

The present study concentrates on Bingham fluid filling of a 2-D cavity and examines the relative importance of inertial, viscous and yield stress effects on the filling profile. The results presented are obtained using PAM-CAST/SIMULOR, which was modified by introducing a regularized Bingham fluid constitutive relation. The results identify five different flow patterns: “mound,” “disk,” “shell,” “bubble,” and a “transition flow” between that of mound and bubble patterns. A complete map of the flow patterns as a function of the Reynolds and Bingham numbers is also presented and discussed using dimensional and physical arguments within a simplified theoretical framework.     

Magma flow through elastic-walled dikes

A convection–diffusion model for the averaged flow of a viscous, incompressible magma through an elastic medium is considered. The magma flows through a dike from a magma reservoir to the Earth’s surface; only changes in dike width and velocity over large vertical length scales relative to the characteristic dike width are considered. The model emerges when nonlinear inertia terms in the momentum equation are neglected in a viscous, low-speed approximation of a magma flow model coupled to the elastic response of the rock.Stationary- and traveling-wave solutions are presented in which a Dirichlet condition is used at the magma chamber; and either a (i) free-boundary condition, (ii) Dirichlet condition, or (iii) choked-flow condition is used at the moving free or fixed-top boundary. A choked-flow boundary condition, generally used in the coupled elastic wave and magma flow model, is also used in the convection–diffusion model. The validity of this choked-flow condition is illustrated by comparing stationary flow solutions of the convection–diffusion and coupled elastic wave and magma flow model for parameter values estimated for the Tolbachik volcano region in Kamchatka, Russia. These free- and fixed-boundary solutions are subsequently explored in a conservative, local discontinuous Galerkin finite-element discretization. This method is advantageous for the accurate implementation of the choked flow and free-boundary conditions. It uses a mixed Eulerian–Lagrangian finite element with special infinite curvature basis function near the free boundary and ensures positivity of the mean aperture subject to a time-step restriction. We illustrate the model further by simulating magma flow through host rock of variable density, and magma flow that is quasi-periodic due to the growth and collapse of a lava dome.     

Transonic swirling flow in axisymmetric nozzles

Summary The transonic flow in axisymmetric choked nozzles is computed in the case of a radial distribution of tangential velocity. The flow configuration is obtained by means of a time-dependent technique. The swirling flow is achieved through a particular surface located at the inlet of the nozzle. The pressure distribution and the sonic line are presented for choked flows without or with swirling.

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Sommario Viene calcolato il flusso transonico in ugelli assialsimmetrici in condizione critica, nel caso di distribuzione radiale di velocità tangenziale.La soluzione è ottenuta numericamente tramite una tecnica instazionaria. Il flusso vorticoso viene creato attraverso una opportuna superficie all'ingresso dell'ugello. Vengono presentati i campi di pressione e la posizione della linea sonica per flussi critici, con e senza vortice.

     

Aerodynamic thermal environment around transonic tube train in choked/unchoked flow

The aerodynamic thermal environment in an evacuated tube transport (ETT) system is an important factor in ensuring the operational safety of tube trains, where choking can further worsen air flow and aerodynamic heating. A compressible flow solver based on total variation diminishing (TVD) schemes was used to calculate the transonic aerodynamic behaviour of a capsule train in a confined space under low pressure conditions, and the flow fields and aerodynamic heating effect on the train were obtained. The results showed that the flow state around the train could be classified into choked and unchoked flow according to the blockage ratio (BR) and train speed based on the Kantrowitz limit. The wall viscosity caused a difference in the boundary-layer flow and potential flow in the annular space between the train and the tube with an increase in the BR. The choked flow was driven forward by the train, passing through its throat at the speed of sound. Owing to the complicated compressible flow in the tube, the thermal environment around the train gave rise to extreme temperature changes on its surface. In transonic choked flow, the temperature rise of the train head reached a maximum of 525 K, whereas local cooling could occur in the afterbody, causing the surface temperature to fall below the ambient temperature under certain conditions. The findings can be used to guide the design of ETT systems.     

Supersonic flow past a wedge on a flat plate. Laminar boundary layer separation and reattachment

Supersonic laminar flow past a two-dimensional “flat-plate/wedge“ configuration is numerically investigated. The pressures at the boundary layer separation and reattachment points are calculated over wide Mach and Reynolds number ranges. The minimum angles of the wedge surface inclination at which a return flow occurs are determined. The results are presented in the form of generalized Mach-number-dependences of the theoretical pressure on the wedge surface initiating boundary layer separation and the pressure at the boundary layer reattachment point.     

Stretching flow instabilities at the exits of extrusion dies

As liquid leaves an extrusion die, the surface layers are rapidly stretched. Stretching flows may become unstable in two ways: by breaking, or in a ductile manner producing an uneven “necked” sample which, in continuous extrusion and drawing, is sometimes called “draw resonance”. There is a quantitative correlation between the extrusion defect known as “sharkskin” and the cohesive failure of polymer melts. By extruding under closely defined conditions, it is possible to introduce a transitory “structure” into the surface layer of the extrudate greatly enhancing its cohesive strength and eliminating this defect. A similar quantitative correlation is established between the uneven coating thickness sometimes obtained during coextrusion of a high viscosity melt on the surface of a low viscosity melt and the tensile drawing instability known as “draw resonance”. Simple criteria are established to avoid this problem in practical flow engineering.     

Compressible gas-liquid mixture flow at abrupt pipe enlargements

A detailed investigation was made of the flow of compressible gas-liquid mixtures through sudden enlargements in diameter of circular pipes. One-dimensional analysis shows that the dimensionless pressure rise varies with mixture void fraction and mixture momentum, while the establishment of choking conditions at the enlargement is controlled by the length of pipe downstream in which frictional pipe flow occurs. The flows were found to exhibit two characteristic modes, jet flow and submerged flow, with intermediate flows displaying unsteady oscillation between these modes. The distance to the downstream position of maximum pressure increased steadily with mixture void fraction when the upstream pipe outlet was choked, varying from 5 to 50 times the downstream pipe diameter. If the flow was not choked, this distance was much smaller and showed discrete fixed values associated with the mode of flow.

One-dimensional analysis accurately predicted maximum pressure, but when flow was choked at the enlargement the calculation was sensitive to the pressure in the region of separated flow surrounding the central jet in the enlargement. Although analysis of maximum pressure in terms of flow expansion and normal shock gave a general indication of the maximum pressure (which was thus concluded to depend on the general flow processes expected in the enlargement), accurate prediction of maximum pressures will depend on empirical knowledge of the separated flow region pressures. The maximum pressure rise was found to be in the range extending down to 0.3 of the upstream pipe outlet pressure and reduced with void fraction; it was also influenced by the enlargement area ratio. Flows in the approach and outlet pipes were found to be compressible, frictional pipe flows of the Fanno type, with somewhat reduced friction factors occurring in the outlet pipe.     

The Blasius and Sakiadis flow with variable fluid properties

A theoretical study of the effect of variable fluid properties on the classical Blasius and Sakiadis flow is presented in this paper. The investigation concerns engine oil, water and air taking into account the variation of their physical properties with temperature. The results are obtained with the numerical simulation of the governing equations and cover large temperature differences. Velocity and temperature profiles are presented, as well as values of wall shear stress and wall heat transfer, for a variety of temperatures between the plate and the ambient fluid. It is found that the variation of fluid properties and especially viscosity have a strong influence on the results. The results of oil and water are, in general, similar and are generalized to liquids whereas air results are different and are generalized to gases. Except of the new results found in the present work some inaccurate results existing in the literature have been identified.     

A method for determining valve coefficient and resistance coefficient for predicting gas flowrate

A method is introduced to determine the valve flow coefficient and resistance coefficient with the experiment of air discharging from a reservoir, and with the least squares method to fit the cumulative molar quantities discharged. The test valve is an angle-seat valve (Type 2632, Bürkert) with different apertures. At pressure difference of about 6 bar, the choked flow occurs when the valve aperture over 60%. Both the valve coefficient and resistance coefficient model can exactly predict the flowrate for the non-choked flow, while there are larger deviations for the choked flow. The modified equation for the choked flow can improve the prediction. In the resistance coefficient model, the value of resistance coefficient and the discharged cumulative molar quantities obtained with both the compressible and incompressible assumption are very close. The compressibility of air is negligible within the experimental pressure difference of about 6 bar. The additivity of the resistance coefficient makes the model more convenient to use.     

Inducing 3D vortical flow patterns with 2D asymmetric actuation of artificial cilia for high-performance active micromixing

Driven by the advancement of the “lab-chip” concept, a new beating behavior of artificial cilia was identified to meet the demands on rapid and complete fluid mixing in miniaturized devices. This beating behavior is characterized by an in-plane asymmetric motion along a modified figure-of-eight trajectory. A typically symmetric figure-of-eight motion was also tested for comparison. Results showed that with this new beating behavior, the mixing efficiency for complete mixing is 1.34 times faster than that with the typical figure-of-eight motion. More importantly, the required beating area was only approximately two-thirds of that in the typical figure-of-eight motion, which is beneficial for more compact designs of various “lab-chip” applications. The unique planar asymmetric motion of the artificial cilia, which enhanced the magnitudes of the induced three-dimensional (3D) flow, was identified by micro-particle image velocimetry (µPIV) measurement and numerical modeling as a major contributor in enhancing microscale mixing efficiency. Quantitatively, 3D vortical flow structures induced by the artificial cilia were presented to elucidate the underlying interaction between the artificial cilia and the surrounding flow fields. With the presented quantification methods and mixing performance results, a new insight is provided by the hydrodynamic advantage of the presented micromixing concept on efficiently mixing highly viscous flow streams at microscale, to leverage the attributes of artificial cilia in the aspect of microscale flow manipulation.     

Supersonic flow past a system of two swept wedges mounted on a preliminary compression surface

The results of a numerical modeling of flow past a configuration consisting of two wedges with swept leading edges, so mounted on a preliminary compression surface that the beveled wedge surfaces deflect the wedge-compressed flows counter to each other, are presented. The calculations are performed on the basis of the averaged Navier-Stokes equations, together with the SST k-ω turbulence model, at the freestream Mach number M = 6. For the configuration geometry chosen the flow pattern is characterized by an irregular interaction between the wedge-induced shocks in the plane of symmetry. These shocks also induce three-dimensional, quasi-conical separations of a turbulent boundary layer on the preliminary compression wedge. In the separation zones the flows are directed toward the plane of symmetry of the configuration and interact with one another with the formation of a typical central “bulged” separation flow zone.     

Capillary flow of linear polyethylene melt: sudden increase of flow rate

During the oscillatory flow of linear polyethylene (HDPE) melt through a capillary, the shape of the extrudate varies periodically with time: sharkskin, plug and rough. This paper deals with the transition between increasing and decreasing pressure. At that transition, the flow rate through the tube is suddenly and intensively increased. We present a theoretical analysis which is in good agreement with experiment. The “slip” at the wall is held to be a consequence of and not the cause of phenomenon. The radial profile of the shear rate is described by means of Dirac's delta function.     

Compressible and confined vortex flow

The internal compressible flow of a thin vortex chamber was investigated experimentally by measuring the radial distribution of temperature and pressure, from which the velocity field was calculated. The bulk of the internal vortex was found to be described by u_θr^0.69 = constant. The total resistance of the vortex chamber to the flow was also investigated in the context of fluidic vortex diode behavior under conditions of compressible and choked flow. It was found that the vortex chamber choked at an upstream-to-downstream pressure ratio of about 6 and in doing so passed a mass flow rate of 28% of the equivalent one-dimensional ideal nozzle. The resistance of vortex chambers is known to be strongly influenced by the presence of reversed flow in the exit due to vortex breakdown. Schlieren photography of the swirling exhaust flow was used to show that, while vortex breakdown does occur, it can only do so after the flow has become subsonic downstream of the exit and cannot therefore influence the vortex chamber resistance.     

Euler flow solutions for transonic shock wave–boundary layer interaction

Steady 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave–boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss–Seidel relaxation, accelerated by non-linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non-choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.     

Choking and shock phenomena in a single component two-phase flow including vibrational effects

An analytical and experimental investigation including vibratory effects of flashing flow in a tube with a sharp edged entrance is presented. A free streamline flow model is applied to predict choking in single-component two-phase flow. By identifying three separate regimes (i.e. jet flow, two-phase homogeneous flow, and single-phase liquid flow) in the flashing flow system, an expression is obtained for the prediction of the minimum stagnation pressure loss under choked flow conditions. A normal shock located between the flashing two-phase mixture and the single-phase liquid was experimentally observed. The location of the shock is predicted as a function of the stagnation pressure drop across the tube. The analytical predictions are verified by experimental data.     

Choking of ideal-gas flow in convergent nozzles and integral nozzle characteristics

The results of a numerical and theoretical investigation of the local and integral characteristics of convergent nozzles are presented. It is shown that self-similar (choked) nozzle flow, when the gas flow rate does not depend on the external pressure, may occur at subcritical values of the pressure ratio _c . If the nozzle contour consists of the contour of the conical nozzle and the convergent part corresponds to the boundary of the emerging jet, then on a certain interval of _c this nozzle will have a higher thrust coefficient than the initial conical nozzle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–157, November–December, 1994.