Convergent-divergent nozzle flows.

Kliegel, J. R.; Quan, Victor

doi:10.2514/3.4851

Cited by 18 publications

(5 citation statements)

References 2 publications

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“…6 Such solutions are extremely complex for nonequilibrium flows however, and it is doubtful if more than one term of the expansion can be determined.…”

Section: Methods Of Solution Initial Line Constructionmentioning

confidence: 99%

“…5) An axisymmetric two-zone transonic flowfield is constructed using the average expansion coefficients obtained in steps 2 and 4 and employing the second-order analysis of Kliegel and Quan. 6 The throat wall pressure and the location and flow angle variation along the constant pressure line originating at the throat wall are determined.…”

Section: Methods Of Solution Initial Line Constructionmentioning

confidence: 99%

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Kinetic performance of barrier-cooled rocket nozzles.

Frey¹,

Kliegel²,

Melde³

et al. 1968

Journal of Spacecraft and Rockets

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The analysis and the computer solution for the flow of a chemically reacting propellant exhaust mixture in a barrier-cooled axisymmetric rocket nozzle are described. The flowfield is represented by two nonmixing gas streams, one for the cool barrier zone near the nozzle wall and the other for the hot core zone. The two streams have the same pressure and flow angle at the streamline dividing the two zones, and each stream is characterized by a given oxidizer/fuel mixture ratio at the combustion chamber. This study allows simultaneous consideration of the nozzle performance losses due to chemical kinetics, nozzle divergence, and barrier cooling. Results of differences in temperature, density, velocity, and chemical composition across the two zones are illustrated, and are compared to the one-dimensional solution having the same over-all mixture ratio. Values of specific impulse are compared to those obtained by simpler and less rigorous methods. Nomenclature A, B= see Eqs. (26) and (27), respectively a = nozzle cross-sectional area a kj, bj = reaction-rate parameters C p = specific heat at constant pressure Ci = mass fraction of ith species F, G = see Eqs. (40) and (41), respectively H = see Eq. (42) h = enthalpy /s P = specific impulse KJ = equilibrium constant kRjj kRkj = reaction-rate parameters M = Mach number Mi = third body reaction term Mi = ith species in reaction equation m,ji= reaction-rate ratio mi = molecular weight of ith species HJ = reaction-rate parameter P, Pi = pressure and partial pressure of ith species, respectively R = gas constant r = radial distance perpendicular to nozzle axis; also, r = 0/F = oxidizer/fuel mixture ratio r* = nozzle throat radius T = temperature V = flow velocity Uj v = velocities in x and r directions, respectively X = max flow fraction in outer zone Xj -species production-rate term x = axial distance a = angle between streamline and Mach line . 7 = ratio of specific heats •y = see Eq. (43) e = expansion area ratio 0 = angle between streamline and axis va, v'a = stoichiometric coefficients

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“…6 Such solutions are extremely complex for nonequilibrium flows however, and it is doubtful if more than one term of the expansion can be determined.…”

Section: Methods Of Solution Initial Line Constructionmentioning

confidence: 99%

Section: Methods Of Solution Initial Line Constructionmentioning

confidence: 99%

Kinetic performance of barrier-cooled rocket nozzles.

Frey¹,

Kliegel²,

Melde³

et al. 1968

Journal of Spacecraft and Rockets

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the present work, 2-mm-thick nozzles are adopted to obtain a suitable thrust range. For the experimental and computational work, the nozzle profile is designed with an algorithm based on the method of characteristics (Shapiro 1953;Anderson 2003) initialized with a flow field from a power-series expansion, centered in the nozzle throat, given by Kliegel and Quan (1966) targeted for Mach 4.41 at the exit section. The estimated Reynolds number ranges between 2 10 3 and 4 10 4 under test conditions.…”

Section: Mass Flow and Thrust Controlmentioning

confidence: 99%

Planar Nozzles for Controllable Microthrusters

2017

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Orbital maneuvering of microsatellite and nanosatellite requirements can be efficiently addressed by planar nozzles, in which realtime thrust control is gained actuating on the nozzle throat area. In the present work, the method of characteristics is used to design a hypersonic contour; then, the resulting profile is laser cut, assembled, and built into a propulsion system to finally perform tests in a vacuum chamber under several working conditions. Results are used to validate the profile and modeling assumptions and investigate overall behavior. Tests showed that thrust-inlet pressure ratio is a linear function of separation between nozzle contours and that no additional losses are introduced in the system. The corresponding design/manufacture/assembly tools can be used to a provide low-cost/low-weight controllable propulsion systems to the small-satellite industry with no efficiency loss.

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“…Equations (9, 10, 13, and 14) constitute a system of partial differential equations for x, y, K, and 6 with respect to a and /3. The boundary conditions which must be satisfied by the system are where L is a reference nozzle length, and p, K, p, and d are the density, velocity, pressure, and speed of sound of the gas, respectively, of which the last is defined by a 2 =y(p/p) (4) where 7 is the ratio of the specific heats. The asterisk denotes the critical (sonic) conditions and the quantities p*, /?…”

Section: Basic Equationsmentioning

confidence: 99%

A new method of nozzle design

Ishii

1978

AIAA Journal

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Convergent-divergent nozzle flows.

Cited by 18 publications

References 2 publications

Kinetic performance of barrier-cooled rocket nozzles.

Kinetic performance of barrier-cooled rocket nozzles.

Planar Nozzles for Controllable Microthrusters

A new method of nozzle design

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