Similarity Analysis for Chemical Reactors and the Scaling of Liquid-Fuel Rocket Engines

Penner, S.S.

doi:10.21236/ad0046523

Cited by 9 publications

(23 citation statements)

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“…It is presumed that the problem to be solved when h is nonzero is truly a perturbation of the exactly solvable problem for h = 0 in the sense that it is possible to proceed continuously from one to the other by appropriately varying h. The solutions 1' / in both the perturbed and unperturbed problems satisfy the same boundary conditions (13) and' (15). Useful information therefore may be gained by separating off the mode tf N to which 1' / tends when h tends to zero; tfN may, of course, be anyone of the "natural" modes.…”

Section: Approximate Solution For Mode Shapes and Eigenvaluesmentioning

confidence: 99%

Stability of High-Frequency Pressure Oscillations in Rocket Combustion Chambers

Culick

1963

AIAA Journal

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Section: Approximate Solution For Mode Shapes and Eigenvaluesmentioning

confidence: 99%

Stability of High-Frequency Pressure Oscillations in Rocket Combustion Chambers

Culick

1963

AIAA Journal

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“…Scaling criteria for homogeneous and heterogeneous chemical reactors may be obtained from the conservation equations for reacting gas mixtures. The complete set of similarity parameters has been shown to include the following dimensionless groups (5) Froude number = Fr = v0 2 /gL . ........... [5] Damkohler's first similarity group = Dr = (L/vo)/t •.…”

Section: Outline Of Theoretical Studiesmentioning

confidence: 99%

“…The complete set of similarity parameters has been shown to include the following dimensionless groups (5) Froude number = Fr = v0 2 /gL . ........... [5] Damkohler's first similarity group = Dr = (L/vo)/t •. .. [6] Damkohler's third similarity group = Dm = (6) five similarity criteria are obtained (viz., only [1,2,3,6, and 7] must remain invariant in order to maintain thermal, dynamic, and reaction kinetic similarity).…”

Section: Outline Of Theoretical Studiesmentioning

confidence: 99%

“…Thus the important similarity parameters have been obtained (5) and shown to include the same dimensionless groups which are required for flow systems without chemical reactions, as well as two of the five similarity groups considered by Damkohler (6) in a classical paper on the scaling of chemical reactors. The dimensionless groups which must be maintained invariant in the scaling of chemical reactors (of which liquid-fuel rocket engines constitute a special class) are summarized in Section IIA.…”

Section: Introductionmentioning

confidence: 99%

“…The dimensionless groups which must be maintained invariant in the scaling of chemical reactors (of which liquid-fuel rocket engines constitute a special class) are summarized in Section IIA. Following Damkohler's procedure for chemical reactors, the problem of scaling for the steady internal aerothermochemistry of liquid-fuel rocket engines has been formulated (5). The method was then developed into an exact prescription for engine scaling on the assumption that the rocket combustion chamber may be considered to be a stirred reactor (7).…”

Section: Introductionmentioning

confidence: 99%

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On the Development of Rational Scaling Procedures for Liquid-Fuel Rocket Engines

Penner

1957

Journal of Jet Propulsion

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A critical surnrnary is presented of recent theoretical studies concerning sirnilarity analysis and the scaling of liquid-fuel rocket engines. On the hasis of this work, some suggestions are offered for an experimental program which has as its ohjective the development of rational scaling procedures. I IntroductionT HE construction of large liquid-fuel rocket engines has been hampered by the necessity of full-scale engine development programs. The experimental difficulties encountered with engines of different sizes are perhaps best illustrated by the occurrence of uncontrolled combustion oscillations, which are sometimes minimized or eliminated by artistic variations in injector design based on previous encounters with similar problems (1).a In a survey paper concerned with experimental aspects of the rocket engine development program, Ross (2) has recently summarized the sort of concepts current among designers. Crocco ,(3) and Penner (4), commenting on this work, conclude that the science of engine scaling is still in an early phase of development.During the last two years a concerted effort has been made to define the problem of engine scaling in scientific terms. Thus the important similarity parameters have been obtained (5) and shown to include the same dimensionless groups which are required for flow systems without chemical reactions, as well as two of the five similarity groups considered by Damkohler (6) in a classical paper on the scaling of chemical reactors. The dimensionless groups which must be maintained invariant in the scaling of chemical reactors (of which liquid-fuel rocket engines constitute a special class) are summarized in Section IIA. Following Damkohler's procedure for chemical reactors, the problem of scaling for the steady internal aerothermochemistry of liquid-fuel rocket engines has been formulated (5). The method was then developed into an exact prescription for engine scaling on the assumption that the rocket combustion chamber may be considered to be a stirred reactor (7). The resulting scaling procedure maybe shown to be consistent with a microscopic analysis of the combustion reactions, based on the assumption that the mass burning rate of the droplets is a linear function of the effective droplet diameter. Control over chemical conversion rate, which is essential for engine scaling with maintenance of exact similarity, is supposed to be obtained by control of droplet size, for example, through variation of the surface tension by 156 the addition of suitable surface-active agents. Following Crocco's terminology (3), we shall refer to this scaling procedure as the P-T (Penner-Tsien) method. It is evident from the preceding remarks, relating to the physical model on which the P-T technique is based, that successful scaling of engines by this method can be accomplished only for bipropellant systems with greatly different volatilities (e.g., LOX -JP4 or HNOa -NHa).The next important theoretical development is due to Crocco (3), who has succeeded in developing a rational scaling pr...

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The Optimum Size of a Rocket Engine

Dunning¹

1960

J. R. Aeronaut. Soc.

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Summary:The paper gives a précis account of studies made at the Rocket Propulsion Establishment of the Ministry of Aviation to determine the relationship between the specific weight and thrust of a liquid bi-propellent rocket engine.Although the need for a better understanding of basic phenomena is established, the conclusion is reached that, within the selected premises, the minimum specific weight is achieved at a thrust level near 50,000 lb. The difference in specific weight between engines of 200,000 lb. thrust and 50,000 lb. thrust is only about 10 per cent and this is shown to be equivalent to only one per cent in propellent specific impulse. Although small, it is considered significant that a minimum has been established and this fact is used as an argument to justify the use of clusters of engines (generally four) to provide levels of thrust greater than 100,000 lb.

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Similarity Analysis for Chemical Reactors and the Scaling of Liquid-Fuel Rocket Engines

Cited by 9 publications

References 0 publications

Stability of High-Frequency Pressure Oscillations in Rocket Combustion Chambers

Stability of High-Frequency Pressure Oscillations in Rocket Combustion Chambers

On the Development of Rational Scaling Procedures for Liquid-Fuel Rocket Engines

The Optimum Size of a Rocket Engine

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