Choked Flow Conditions Research Articles

Numerical Modelling of Cavitation: Validation and Parametric Studies

The objective of the present work is to investigate numerically the 3D flow within diesel injector-like geometries using a cavitation model implemented in a commercial CFD code. A comprehensive study of various numerical parameters is performed which can subsequently be used to simulate cavitation under realistic diesel engine conditions. Numerical predictions were performed on a throttle channel at different operating conditions, with and without cavitation, and compared to available experimental measurements. Overall, it was found that the cavitation model was able to predict the onset of cavitation. Satisfactory agreement was found in both the injection rate and the occurrence of choked flow conditions when compared with experiments.

Effects of choking on flow and heat transfer in micro-channels

The gas flows through micro-channels are encountered in many engineering applications such as the cooling devices of electronic chips, semiconductors, micro-electro-mechanical systems ( MEMS), etc. Many works have been performed to investigate the flow and heat transfer characteristics generally occurring in the micro channels. According to these investigations, the majority of heat was transferred in the entrance region of the channel, due to high strain rate of the developing flow. These findings are valid only for unchoked micro channel flows. Once the gas flow is choked, the major flow features may be changed but no detailed works have been carried out to date. In these regards, the choked flow characteristics should be known to investigate the heat transfer phenomena in the micro channel flows. In the present study, numerical simulations have been used to provide detailed flow and heat transfer characteristics of micro-channel gas flows. The main objectives of the present effort are to understand the evolution of choking inside micro-channels with isothermally-heated-walls and to elucidate the regions of high heat transfer. The results obtained show that for choked flow conditions, high heat transfer is generated at both the entrance and the exit of the micro-channel. The exit effects like increased strain rate, high temperature gradient and the thinning of the boundary layer cause a rapid increase in heat transfer at the exit of the micro-channel. The location where the flow is choked is practically important in determining the heat transfer phenomena at the vicinity of the channel exit.

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 0.406mm to 0.686mm with lengths ranging from 1mm to 3mm 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 1mm, 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%.

Choked flow and importance of Mach I in freeze-drying process design

Occasionally the freeze drying cycle conditions are developed on a small scale dryer that result in a water vapor flux during primary drying that the full-scale equipment cannot handle, resulting in loss of the ability to control chamber pressure. A primary cause of loss of pressure control is a phenomenon commonly described as “choked flow”, where the required mass transfer through the duct connecting the drying and condenser chamber cannot be maintained at the control pressure. Water vapor flow rate increases as the condenser pressure decreases, but it can continue to do so only until the velocity of water vapor reaches speed of sound (i.e., Mach I) at the duct exit. The flow is then said to be choked, and any further increase in water vapor flow rate results in an increase in chamber pressure (i.e., loss in chamber pressure control). Sublimation tests were carried out in Lyostar II freeze-dryer (SP Industries, NY) to predict the occurrence of choked flow. A capacitance manometer was installed in the “condenser chamber” and differential pressure ( P c − P cd ) was measured as a function of sublimation rate ( P c =chamber pressure and P cd =condenser pressure). Water vapor flow rate was measured by Tunable Diode Laser Absorption Spectroscopy (TDLAS) methodology, with a check by gravimetric data. Flow of water vapor in the duct connecting chamber and the condenser was modeled using computational fluid dynamics software (Fluent 6.3). The critical pressure ratio ( K⁎= P c / P cd ) has been identified as an important variable that determines the onset of choked flow during primary drying. This ratio can be calculated given the mass flux. For our freeze-dryer, K* greater than 2.5 (for P c <150 mTorr) resulted in choked flow. The gas velocity indeed reaches Mach I limit at the duct exit under the choked flow conditions, as modeled by Fluent. Using the differential pressure measurements, the throat connecting the chamber and the condenser can be used as an “in process” mass flow meter to measure sublimation rate under non-choked flow conditions during primary drying without interrupting the process. Also, TDLAS is a useful tool for determination of sublimation rate even at very high mass flux.

The Parameters Influencing High-Pressure Mechanical Gas Face Seal Behavior in Static Operation

The increase in the operating pressure of gas compressors makes it necessary to develop numerical tools for designing optimal high-performance mechanical seals. The authors developed a numerical model of the TEHD behavior of an axisymetric mechanical face seal, working with a high-pressure real gas. The model includes thermal and inertia effects and a choked flow condition. Heat transfer between the fluid and the solids as well as elastic and thermal distortions are computed. This article presents a dimensional analysis that allows the influence of inertia effects to be evaluated and a small number of nondimensional parameters determining seal behavior to be identified. A parametric study was carried out to calculate the mechanical face seal performance under various operating conditions. The results are presented as curves for nondimensional load, mass flow, and exit pressure. Temperature versus characteristic nondimensional parameters is also shown.

Direct Simulation Monte Carlo Solution of Subsonic Flow Through Micro/Nanoscale Channels

We use a direct simulation Monte Carlo (DSMC) method to simulate gas heating/cooling and choked subsonic flows in micro/nanoscale channels subject to either constant wall temperature or constant/variable heat flux boundary conditions. We show the effects of applying various boundary conditions on the mass flow rate and the flow parameters. We also show that it is necessary to add a buffer zone at the end of the channel if we wish to simulate more realistic conditions at the channel outlet. We also discuss why applying equilibrium-based Maxwellian distribution on molecules coming from the channel outlet, where the flow is nonequilibrium, will not disturb the DSMC solution. The current velocity, pressure, and mass flow rate results are compared with different analytical solutions of the Navier–Stokes equations. Although there are good agreements between the DSMC results and the analytical solutions in low compressible flow, the analytical solutions yield incorrect velocity and mass flow rate values in short micro/nanochannel flows with high compressibility and/or choked flow conditions.

Deflector Ski Jump Hydraulics

Ski jumps are a standard element of dam spillways for an efficient energy dissipation if takeoff velocities are large, and stilling basins cannot be applied. This laboratory study investigates the hydraulic performance of a triangular-shaped, rather than the conventional circular-shaped, bucket placed at the takeoff of ski jumps. The following items were addressed: (1) pressure head maximum and pressure distribution along the triangular-shaped bucket; (2) takeoff characteristics as a function of the bucket deflector angle and the relative bucket height including the lower and the upper jet trajectories; (3) jet impact characteristics in a prismatic tailwater channel including the shock wave formation and the height of recirculation depth below the jet cavity; (4) energy dissipation across the ski jump, from the approach flow channel to downstream of jet impact; and (5) choking flow conditions of the flip bucket. A significant effect of the approach flow Froude number, the relative bucket height, and the deflector angle is found. A comparison with previous results for the circular-shaped bucket geometry indicates a favorable behavior of the novel bucket design.

Thermoelastohydrodynamic Behavior of Mechanical Gas Face Seals Operating at High Pressure

A numerical modeling of thermoelastohydrodynamic mechanical face seal behavior is presented. The model is an axisymmetric one and it is confined to high pressure compressible flow. It takes into account the behavior of a real gas and includes thermal and inertia effects, as well as a choked flow condition. In addition, heat transfer between the fluid film and the seal faces is computed, as are the elastic and thermal distortions of the rings. In the first part of this paper, the influence of the coning angle on mechanical face seal characteristics is studied. In the second part, the influence of the solid distortions is analyzed. It is shown that face distortions strongly modify both the gap geometry and the mechanical face seal’s performance. The mechanical distortions lead to a converging gap, while the gas expansion, by cooling the fluid, creates a diverging gap.

Closure to “Discussion of ‘The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions’ ” (2007, ASME J. Eng. Gas Turbines Power, 129, p. 1143)

Closure to “Discussion of ‘The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions’ ” (2007, ASME J. Eng. Gas Turbines Power, 129, p. 1143)

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

Abstract The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal, choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons to the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section, the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section, the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint, this behavior is explained by the modification of the Lomakin effect, which changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

Dynamical constraints on kimberlite volcanism

Kimberlite volcanism involves the ascent of low viscosity (0.1 to 1 Pa s) and volatile-rich (CO 2 and H 2O) ultrabasic magmas from depths of 150 km or greater. Theoretical models and empirical evidence suggest ascent along narrow (∼1 m) dykes at speeds in the range > 4 to 20 m/s. With typical dyke breadths of 1 to 10 km, magma supply rates are estimated in the range 10 2 to 10 5 m 3/s with eruption durations of many hours to months. Based on observations, theory and experiments we propose a four-stage model for kimberlite eruptions to explain the main geological relationships of kimberlites. In stage I magma reaches the Earth's surface along fissures and erupts explosively due to their high volatile content. The early flow exit conditions are overpressured with choked flow conditions; an exit velocity of ∼200 m/s is estimated as representative. Explosive expansion and near surface overpressures initiate crater and pipe formation from the top downwards. In stage II under-pressures (the difference between the lithostatic pressure and pressure of the erupting mixture) develop within the evolving pipe causing rock bursting at depth, undermining overlying rocks and causing down-faulting and crater rim slumping. Rocks falling into the pipe interior are ejected by the strong explosive flows. Stage II is the erosive stage of pipe formation. As the pipe widens and deepens larger under-pressures develop enhancing pipe wall instability. A critical threshold is reached when the exit pressure falls to one atmosphere. As the pipe widens and deepens further the gas exit velocity declines and ejecta becomes trapped within the pipe, initiating stage III. A fluidised bed of pyroclasts develops within the pipe as the eruption wanes to form typical massive volcaniclastic kimberlite. Marginal breccias represent the transition between stages II and III. After the eruption stage IV is a period of hydrothermal metamorphism (principally serpentinisation) and alteration as the pipe cools and meteoric waters infiltrate the hot pipe fill. Following an eruption an open crater can be filled by kimberlite- and country-rock derived sediments, forming the crater-facies.

Real gas choked flow conditions at low reduced-temperatures

Real gas choked mass flux is calculated for a frictionless stream expanding isentropically until it reaches the speed of sound and without phase changes. The other parameters associated with the choked state are the pressure, density, temperature ratios, and the speed of sound. Departure of the choked mass flux from the ideal gas model is discussed first in absolute terms and then in relative terms, using the Principle of Corresponding States, for gases with boiling points in the low temperature range. Reduced-stagnation pressures are examined up to values of 30 for hydrogen, neon, nitrogen, argon, methane, krypton, xenon, and R-14 and up to 100 for 4He. The corresponding reduced-stagnation temperatures go down to 1.4 and in some cases down to 1.2 for nitrogen and argon. Also discussed are the limiting values of stagnation parameters for which no phase change occurs in the choked state. Compared to the ideal gas, the mass flux may almost double and the critical pressure ratio may decrease by an order of magnitude. The relevance of results is discussed qualitatively and quantitatively for Joule–Thomson cryocooling.

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.

Ski Jump Hydraulics

Ski jumps are a major element of each dam spillway because these are the only structures able to accomplish satisfactory energy dissipation for takeoff velocities in excess of some 20 m / s. This research aims to add to several hydraulic problems with ski jumps that have not yet been systematically solved so far. Based on an experimental campaign, the following problems were addressed: ~1! pressure head maximum and pressure distribution along a circular-shaped flip bucket; ~2! takeoff characteristics for a certain bucket deflection and a relative bucket curvature including the jet trajectories of both the lower and the upper nappes; ~3! impact characteristics in a prismatic tailwater channel with details of shock wave formation and height of recirculation depth; ~4! energy dissipation across the ski jump, from the upstream channel to downstream of jet impact; and ~5! choking flow conditions by the flip bucket. These results demonstrated the significant effect of the approach Froude number, the relative bucket curvature and the bucket angle. The results allow immediate application to the design of ski jumps in hydraulic engineering.

Temporal evolution of flow conditions in sustained magmatic explosive eruptions

The temporal evolution of fundamental flow conditions in the magma chamber plus conduit system–such as pressure, velocity, mass flow-rate, erupted mass, etc.–during sustained magmatic explosive eruptions was investigated. To this aim, simplified one-dimensional and isothermal models of magma chamber emptying and conduit flow were developed and coupled together. The chamber model assumed an homogeneous composition of magma and a vertical profile of water content. The chamber could have a cylindrical, elliptical or spherical rigid geometry. Inside the chamber, magma was assumed to be in hydrostatic equilibrium both before and during the eruption. Since the time-scale of pressure variations at the conduit inlet–of the order of hours–is much longer than the travel time of magma in the conduit–of the order of a few minutes–the flow in the conduit was assumed as at steady-state. The one-dimensional mass and momentum balance equations were solved along a circular conduit with constant diameter assuming choked-flow conditions at the exit. Bubble nucleation was considered when the homogeneous flow pressure dropped below the nucleation pressure given the total water content and the solubility law. Above the nucleation level, bubbles and liquid magma were considered in mechanical equilibrium. The same equilibrium assumption was made above the fragmentation level between gas and pyroclasts. Due to the hydrostatic hypothesis, the integration of the density distribution in the chamber allowed to obtain the total mass in the chamber as a function of pressure at the chamber top and, through the conduit model, as a function of time. Simulation results pertaining to rhyolitic and basaltic magmas defined at the Volcanic Eruption Mechanism Modeling Workshops (Durham, NH, 2002; Nice, France, 2003) are presented. Important flow variables, such as pressure, density, velocity, shear stress in the chamber and conduit, are discussed as a function of time and magma chamber and conduit properties. Results indicate that vent variables react in different ways to the pressure variation of the chamber. Pressure, density and mass flow-rate show relative variations of the same order of magnitude as the conduit inlet pressure, whereas velocity is more constant in time. Sill-like chambers produce also significantly longer and more voluminous eruptions than dike-like chambers. Water content stratification in the chamber and the increase of chamber depth significantly reduce the eruption duration and volume. Maximum erupted mass fractions of about 0.2 are computed for small water-saturated and shallow chambers.

Study of the effects of unsteady downstream conditions on the gas flow through a critical nozzle

The present study addresses a computational result of unsteady gas flow through a critical nozzle. The axisymmetric unsteady compressible Navier-Stokes equations are solved using a finite volume method that makes use of the second-order upwind scheme for spatial derivatives and the multi-stage Runge-Kutta integral scheme for time derivatives. The steady solutions of the governing equation system are validated with the previous experimental data to ensure that the present computational method is valid to predict the critical nozzle flows. In order to simulate the effects of back-pressure fluctuations on the critical nozzle flows, an excited pressure oscillation with an amplitude and frequency is assumed downstream of the exit of the critical nozzle. The results obtained show that, for low Reynolds numbers, the unsteady effects of the pressure fluctuations can propagate upstream of the throat of the critical nozzle, thus giving rise to the applicable fluctuations in mass flow rate through the critical nozzle, while, for high Reynolds numbers, the pressure signals occurring at the exit of the critical nozzle do not propagate upstream beyond the nozzle throat. For a low Reynolds number, it is found that the sonic line near the throat of the critical nozzle markedly fluctuates with time, providing an important mechanism for pressure signals to propagate upstream of the nozzle throat, even in choked flow conditions. The present study is the first investigation to clarify the unsteady effects on the critical nozzle flows.

Effervescent atomization under sub-sonic and choked conditions—a theoretical approach

Spray formation of a bi-component mixture under sub- and choked-flow conditions has been studied. Special attention has been drawn to the processes inside the atomizer, i.e., the expansion chamber and two orifices. The relevant processes, which include the pressure drop at the inlet orifice, nuclei formation, bubble growth inside the expansion chamber, pressure drop at the discharge orifice, the velocity slip between the bubbles and the liquid bulk, and the flow regime (sub- and choked-flow) at the discharge orifice, have been analyzed by using a one-dimensional model approach. Three different operating regions have been identified. In the 1st, when the inlet to discharge orifices' diameter ratio is small, subsonic flow is anticipated, and no noticeable slip between the bubbles and the bulk liquid is expected. As the orifices' diameter ratio increases, the slip becomes more and more significant (2nd region). When the pressure at the expansion chamber exceeds the critical pressure, the flow chokes, and the slip maximizes. Further increase results in maximum slip (3rd region). The two main roles of the expansion chamber were described: (a) to provide the required time for the bubbles to grow till one bubble touches the other, and (b) to provide the discharge orifice with a well-mixed mixture to allow dominant flashing enhanced by shear stress disintegration. Optimized operation conditions for best atomization, optimized expansion chamber volume, and optimized orifices' diameter ratio are proposed in terms of the thermodynamic properties of the mixture.

Numerical analysis of choked refrigerant flow in adiabatic capillary tubes

This paper presents a homogeneous simulation model for choked flow conditions for pure refrigerants (R134a, R600a) in adiabatic capillary tubes. The model is based on the first principles of thermodynamics and fluid mechanics and some empirical relations. This study presents a fresh-look at the classical fluid flow problem, known as ‘Fanno flow’ for refrigerant flow in capillary tubes. A new diagram called the full range simulation diagram has been developed that presents a better way to understand the choked flow phenomenon graphically. The diagram is useful for design and analysis of refrigerant flow in capillary tubes. The model has been validated with published experimental data for R22, R134a and R600a and is found to agree to within ±7%.

Approximate analytic solutions of adiabatic capillary tube

Approximate analytic solution of capillary tube is valuable for theoretical analysis and engineering calculation. In this work, two kinds of approximate analytic solutions of adiabatic capillary tube have been developed. One is the explicit function of capillary tube length. Another is the explicit function of refrigerant mass flow rate. In these solutions, the choked flow condition is taken into account without iterative calculations. The approximate predictions are found to agree reasonably well with experimental data in open literatures.

Critical heat flux under choking flow conditions: Part II – Maximum values of flow parameters attained under choking flow conditions

Under conditions of forced convective boiling at low pressures and high mass fluxes, beyond a certain quality, choking flow may occur at the exit of a heated channel. An experimental investigation carried out by Olekhnovitch et al. (Olekhnovitch, A., Teyssedou, A., Tye, P., Champagne, P., 2000. Critical heat flux under choking flow conditions. Part I — Outlet pressure fluctuations. Nucl. Eng. Des., this issue) has shown that the occurrence of choking flow does not radically influence the values of the critical heat flux (CHF). However, once the choking flow conditions have occurred, for a given mass flux and quality, the outlet pressure cannot be lowered below a certain value that is fixed by the flow itself. A model that allows this pressure to be determined and which must be used in conjuction with correlations for the prediction of the CHF is presented.