The Numerical Solution of Choked and Supercritical Ideal Gas Flow through Orifices and Convergent Conical Nozzles

Alder, G M

doi:10.1243/jmes_jour_1979_021_032_02

Cited by 15 publications

(14 citation statements)

References 3 publications

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“…It is known that under the condition (P 1 /P 0 ) > (P 1 /P 0 ) * a decrease of P 1 leads to an increase of the flow rate if P 0 is fixed. However, under the condition ( Liepmann (1961) 0.0507 Ar 5/3 0.812 1.48 Barashkin et al (1977b) 0.0420 Ar 5/3 0.826 1.50 Jitschin et al (1999) 0.0162 He, Ar, Kr 5/3 0.853 1.55 Perry (1949) 0.151 air 1.4 0.843 1.45 Fujimoto & Usami (1984) 0.050 air 1.4 0.844 1.45 Liepmann (1961) 0.0478 N 2 1.4 0.824 1.41 Barashkin et al (1977b) 0.0420 H 2 1.4 0.853 1.46 Jitschin et al (1999) 0.0162 H 2 , N 2 , air 1.4 0.869 1.49 Alder (1979) 0 diatomic 1.4 0.830 1.42 Liepmann (1961) 0.0478 CO 2 1.3 0.830 1.39 Barashkin et al (1977b) 0.0420 CO 2 1.3 0.856 1.43 Jitschin et al (1999) 0.0162 CO 2 1.3 0.891 1.49 Jitschin et al (1999) 0.0162 C 3 H 8 1.13 0.876 1.41 Table 1. Discharge coefficient C and flow rate W in the hydrodynamic regime (δ → ∞) for outflow into vacuum (P 1 /P 0 = 0) for various specific heat ratios γ .…”

Section: Statement Of the Problem And Definitionsmentioning

confidence: 99%

“…Some numerical data for the outflow into vacuum in the transition regime are reported by Shakhov (1974) and Sharipov (2002b). In the hydrodynamic regime the problem was solved by Alder (1979) on the basis of the Euler equation, which is valid for high values of the Reynolds number. In the case of low Reynolds number Roscoe (1949) and Hasimoto (1958) solved the Stokes equation analytically.…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of rarefied gas flow through a thin orifice

Sharipov

2004

J. Fluid Mech.

104

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Rarefied gas flow through a thin orifice is studied on the basis of the direct simulation Monte Carlo method. The mass flow rate and the flow field are calculated over the whole range of the Knudsen number for various values of the pressure ratio. It is found that at all values of the pressure ratio a significant variation of the flow rate occurs in the transition regime between the free-molecular and hydrodynamic regimes. In the hydrodynamic regime the flow rate tends to a constant value. In the case of finite pressure ratio the flow field qualitatively differs from that for outflow into vacuum, namely vortices appear in the downflow container on approaching the hydrodynamic regime. Then, in the hydrodynamic regime the gas flow forms a strong jet. A comparison of the numerical results with experimental data available in the open literature has been performed.

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Section: Statement Of the Problem And Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical simulation of rarefied gas flow through a thin orifice

Sharipov

2004

J. Fluid Mech.

104

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“…It was attributed to the change in boundary conditions at the exit planes when the gas separated to form a free jet. Alder et al [9] described how a jet becomes supersonic with its boundaries expanding to adjust to the lower surrounding downstream chamber pressure resulting in a higher flow rate.…”

Section: Introductionmentioning

confidence: 99%

“…decreasing pressure ratio) beyond the critical value due to the changing shape and location of the multi-dimensional sonic surface around the plane of the orifice lip. In comprehensive theoretical studies by Alder et al [9] and Jobson [10], a numerical solution of choked and supercritical orifice gas flows tries to explain the increase of flow rate beyond the critical pressure ratio as the downstream jet is becoming supersonic. The pressure ratio needs to be low in order for the position of the sonic surface to stabilize in shape and position, thereby allowing the flow to "choke".…”

Section: Introductionmentioning

confidence: 99%

On the Measurement and Modeling of High-Pressure Flows in Poppet Valves Under Steady-State and Transient Conditions

Mohr

Clarke

Garner

et al. 2017

Journal of Fluids Engineering

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Flow coefficients of intake valves and port combinations were determined experimentally for a compressed nitrogen engine under steady-state and dynamic flow conditions for inlet pressures up to 3.2 MPa. Variable valve timing was combined with an indexed parked piston cylinder unit for testing valve flows at different cylinder volumes while maintaining realistic in-cylinder transient pressure profiles by simply using a fixed area outlet orifice. A one-dimensional modeling approach describing three-dimensional valve flow characteristics has been developed by the use of variable flow coefficients that take into account the propagation of flow jets and their boundaries as a function of downstream/upstream pressure ratios. The results obtained for the dynamic flow cases were compared with steady-state results for the cylinder to inlet port pressure ratios ranges from 0.18 to 0.83. The deviation of flow coefficients for both cases is discussed using pulsatile flow theory. The key findings include the followings: (1) for a given valve lift, the steady-state flow coefficients fall by up to 21% with increasing cylinder/manifold pressure ratios within the measured range given above and (2) transient flow coefficients deviated from those measured for the steady-state flow as the valve lift increases beyond a critical value of approximately 0.5 mm. The deviation can be due to the insufficient time of the development of steady-state boundary layers, which can be quantified by the instantaneous Womersley number defined by using the transient hydraulic diameter. We show that it is possible to predict deviations of the transient valve flow from the steady-state measurements alone.

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“…There are several experimental investigations regarding flow through finite (or zero) length channels [126,138,127]. Results include mass flow rates, discharge coefficients and interpolating formulas.…”

Section: Flow Through Channelsmentioning

confidence: 99%

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

Πανταζής¹

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The approval of the current dissertation by the Department of Mechanical Engineering of the University of Thessaly does not imply acceptance of the author's opinions (Law 5343/32 number 202 paragraph 2). Also, the views and opinions expressed herein do not necessarily reflect those of the European Commission. There are several other people who I feel that have contributed in the writing of this dissertation.The most important contributions, along with several helpful conversations, were made by Prof. F.Sharipov, who provided the basic concept of the channel end effect study, and Dr. Chr. Day along with the KIT personnel, who briefly introduced me in the world of experimental rarefied gas dynamics. It was also a priviledge to discuss and work for a brief period of time with Prof. A. Grecos, who tirelessly discussed with me on various subjects of statistical mechanics. Financial support for this Ph.D. has been provided by the Euratom Association -Hellenic Republic, to which I am deeply indepted. Also, partial support for conference mobility expenses has been received from the GASMEMS Marie Curie programme. In this work, non-equilibrium transport phenomena have been examined via the kinetic theory of gases. The behaviour of the gas in low pressure conditions or in low-dimensionality systems can not be captured by the usual Navier-Stokes formulation, in conjunction with the constitutive laws of Newton-Fourier-Fick. The limited number of intermolecular collisions results in departure from equilibrium and the particulate nature of the gas must be taken into account, greatly increasing the computational effort.The problem is described by the integro-differential Boltzmann equation, which is used to determine the distribution of particles in physical and molecular velocity space, as well as in time.There are difficulties associated with the seven-dimensional nature of the distribution function, as well as with the complexity of the collision term, which is usually substituted by an appropriate model.The most widely used and successful numerical methodologies, the Discrete Velocity Method (DVM) and the Direct Simulation Monte Carlo (DSMC), are applied here in the whole range of the Knudsen number. It is important to employ approaches based on kinetic theory, since these are the only ones which are valid for any rarefaction level.In this work, several problems including non-equilibrium phenomena are considered. The interaction of gases with solid surfaces is considered for several problems according to the CercignaniLampis boundary conditions. The non-linear form of this scattering kernel, which had not been pre- viously used in the literature, is applied on the problem of heat transfer between parallel plates and coaxial cylinders. Its linearized form has also been employed for both flow and heat transfer problems and a comparison with relevant experiments has lead to surface characterization with respect to argon and helium flows.Non-linear heat conduction phenomena are also studied for the parallel plates and coaxial c...

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The Numerical Solution of Choked and Supercritical Ideal Gas Flow through Orifices and Convergent Conical Nozzles

Cited by 15 publications

References 3 publications

Numerical simulation of rarefied gas flow through a thin orifice

Numerical simulation of rarefied gas flow through a thin orifice

On the Measurement and Modeling of High-Pressure Flows in Poppet Valves Under Steady-State and Transient Conditions

Simulation of transport phenomena in conditions far from thermodynamic equilibrium via kinetic theory with applications in vacuum technology and MEMS

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