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Space Engineering pp 219–238Cite as

Analytical and Experimental Investigations of Aerothermochemical Processes in Liquid Propellant Rocket Motors

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Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 15))

Abstract

Rapid increase in rocket performance level in the last 20 years was plagued by combustion instability. Investigators devoted considerable effort to solving this problem but no valid analysis exists for predicting stable operation of a new design. To fill this need, a non-linear approach was developed of liquid rocket design which is also useful for the investigation of oscillatory (unstable) combustion.

First, a brief history is given of the linear or linearized analytical approaches used by other investigators to the solution of combustion instability starting from the ‘time lag’ concept suggested by von Kármán and developed by Summerfield, Tsien, Crocco, Barrère, and others. Then, the non-linear analysis is developed which is useful for both the design of liquid rocket chambers (steady state) and for the investigation of combustion instability (non-steady state). The model used allows incorporation of the most advanced information of the aerothermochemical processes involved as they are obtained from available experimental and analytical investigations.

Starting with the basic equations of aerothermochemistry, as written by von Kármán in 1955, the analysis is developed correlating the design parameters of pressure, temperature, gas velocity and cross-sectional area variation. The analysis incorporates the liquid phase (injector spray and droplet histories), the liquid-vapor transition (evaporation of propellants), as well as the energy release histories. It is shown that all the parameters can be determined and their individual influences evaluated and it is established that additional information is needed on the evaporation and shattering of drops in high-pressure environment at elevated temperatures. The set of simultaneous equations is solved by numerical methods.

Next, the non-steady, non-linear study of longitudinal combustion instability is presented and an extension to three-dimensional analysis is proposed.

For both the steady-state analysis (design) and the non-steady one (instability), realistic chamber pressures and chamber dimensions are used and a 100000 lb liquid oxygen-liquid hydrogen rocket motor is chosen. The steady-state analysis shows the important correlation of the design parameters. The result of the non-steady analysis are illustrated by the effects of realistic disturbances (both step-functions and oscillatory disturbances) which are introduced at various times and at various spatial positions. The obtained non-steady behavior of the rocket chamber agrees well with measured oscillatory behavior of actual rocket motors.

Finally, recent experimental results are presented of liquid propellant droplet evaporation under high-pressure (up to several times critical pressure) and high-temperature conditions. It is shown that the existing models for drop evaporation lack reality and that a new non-steady analysis is needed for the correlation of drop vaporization under supercritical conditions. The experimental apparatus and methodology are presented which were used in the experiments. The time-histories of drop temperature and drop radius are shown and heat and mass transfer coefficients are derived for use in rocket design. Drop shattering and spray breakup are discussed also both at atmospheric and at high-pressure conditions.

A 5-min film is shown relating to droplet evaporation and spray and drop shattering.

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Abbreviations

A :

chamber cross-sectional area, amplitude in forcing function

A i :

injector area

A t :

throat area

B :

amplitude in forcing function

C D :

drag coefficient

C d :

discharge coefficient

C l :

specific heat of liquid

c p :

specific heat at constant pressure

D :

drop diameter

D ABf :

binary diffusion coefficient at film temperature

e :

internal energy

F :

thrust

f :

forcing function

g :

gravitational constant

h :

mean heat transfer coefficient

I s :

specific impulse [F/w ̇= V e /g]

k :

thermal conductivity

k xm :

mass transfer coefficient

L* :

characteristic chamber length [V C /A t ]

ṁ :

mass rate of flow propellant

M :

momentum addition to gas per unit of time and unit of distance

M l :

mass of liquid drop

N Nu :

Nusselt number [hD/k]

N Pr :

Prandtl number [µCp/k]

N Re :

Reynolds number [D(u—V)ϱ/μ]

N Sc :

Schmidt number [μ mf /ϱ mf D ABf ]

N sh p :

Sherwood number [k xm D/ ϱ mf D ABf ]

p :

pressure

P c :

chamber pressure

P i :

injector pressure

Q :

energy addition to gas per unit of time and unit of distance

Q l :

heat transferred to liquid

Q v :

heat transferred to drop

r :

drop radius

t :

time

t 0 :

initial time

T :

temperature

T l :

temperature of liquid

u :

gas velocity

V :

drop velocity

V c :

chamber volume

V e :

exhaust velocity

V l :

drop volume

ẇ :

propellant weight flow rate

W :

evaporation rate from drop

We :

Weber number [ ϱ t D(u—V)|u—V|/σl]

x :

axial distance

x 0 :

initial distance

Δ :

difference

λ :

latent heat of liquid, factor in forcing function

μ :

viscosity

μ mf :

mixture viscosity at film temperature

ϱ :

density

ϱ g :

gas density

ϱ l :

liquid density

ϱ mf :

mixture density evaluated at film temperature

σl :

surface tension of liquid

ψ :

mass addition to gas per unit of time and unit of distance

ω, ω′ :

frequencies in forcing function.

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Authors and Affiliations

  1. Illinois Institute of Technology, Chicago, Ill., USA

    T. Paul Torda

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  1. T. Paul Torda
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Editors and Affiliations

  1. Centro Studi Trasporti Missilistici, Rome, Italy

    G. A. Partel

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© 1970 Reidel Publishing Company, Dordrecht, Holland

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Torda, T.P. (1970). Analytical and Experimental Investigations of Aerothermochemical Processes in Liquid Propellant Rocket Motors. In: Partel, G.A. (eds) Space Engineering. Astrophysics and Space Science Library, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7551-7_16

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  • DOI: https://doi.org/10.1007/978-94-011-7551-7_16

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