Skip to main content
SpringerLink
Log in

Mathematical modelling of a cryogenic engine

  • Published:
International Journal of Advances in Engineering Sciences and Applied Mathematics Aims and scope Submit manuscript

Abstract

Cryogenic propulsion systems using liquid hydrogen and liquid oxygen propellant combination are used in satellite launch vehicles in view of the higher specific impulse (ISP). Due to extreme low temperature of cryogenic propellant and low density and explosive nature of LH2, the development of cryogenic propulsion system is very complex and time consuming. In ISRO an indigenous cryogenic upper stage powered by an engine developing a nominal thrust of 73.5 kN in vacuum with a propellant loading of 12.8 tonnes is developed and successfully flight tested for the first time in GSLV D5 flight on 5th January 2014. A mathematical model is developed for finalizing the engine start and shut off sequence, ensuring smooth and safe ignition, predicting performance of subsystems under transient phase, nominal and off nominal conditions, control systems parameter settings and for the performance estimation of engine in sea level and flight. This paper highlights the configuration and working of a cryogenic engine, mathematical modelling of the engine, applications of the model in the cryogenic engine development and comparison of predicted values with the test results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

PC :

Main engine chamber pressure

PGGE:

Gas generator chamber pressure

PFPI:

Pressure at main fuel pump inlet

PHPD:

Pressure at main fuel pump delivery

POPI:

Pressure at main oxidizer pump inlet

POPD:

Pressure at main oxidizer pump delivery

PHCHE:

Pressure of hydrogen at coolant channel exit

POME:

Pressure of LOX at the exit of mixture ratio controller

PGTE:

Pressure at the exit of main turbine

POAE:

Pressure of LOX at the exit of absolute velocity regulator

PHBTI:

Pressure at hydrogen booster turbine inlet

PHBTD:

Pressure at hydrogen booster turbine exit

PFBO:

Pressure at fuel booster pump outlet

POBTI:

Pressure at oxygen booster turbine inlet

POBO:

Pressure at oxygen booster pump outlet

TFPI:

Fluid temperature at main fuel pump inlet

TOPI:

Fluid temperature at main oxidizer pump inlet

TOPD:

Fluid temperature at main oxidizer pump delivery

THCHE:

Fluid temperature of hydrogen at coolant channel exit

THBTD:

Fluid temperature at hydrogen booster turbine exit

mlox :

LOX flow rate

mf :

Hydrogen flow rate

ME:

Main engine

GG:

Gas generator

OBT:

Oxidizer booster turbine

FBT:

Fuel booster turbine

SE:

Steering engine

MOP:

Main oxidizer pump

V, U:

Velocity

f:

Friction factor, body force

L:

Length

At :

Throat area

A:

Turbine nozzle area

C*:

Characteristic velocity

hg:

Gas side convective heat transfer coefficient

hc:

Coolant side heat transfer coefficient

qc:

Heat flux due to convection

qr:

Heat flux due to radiation

q:

Combined heat flux

k:

Conductivity of the material

t:

Shell thikness

ηf:

Fin effectiveness

H:

Total enthalpy

C:

Concentration

τ:

Shear stress

μ:

Viscocity

ρ:

Density

P:

Pressure

Q, R:

Source terms

h:

Static enthalpy

E:

Total energy

e:

Internal energy

J:

Diffusion flux

References

  1. Huzel, D.K., Huang, G.H.: Modern Engineering for Design of Liquid Propellant Rocket Engines. American Institute of Aeronautics and Astronautics, Washington D.C. (1992)

    Google Scholar 

  2. Sutton, G.P.: Rocket Propulsion Elements: An Introduction to the Engineering of Rockets. Wiley, New York (1992)

    Google Scholar 

  3. Gordon, S., MCBride, B.J.: Computer Program for calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflection shocks and Chapman-Jougent Detonations, NASA SP-273 (1971)

  4. White, F.M.: Fluid Mechanics. McGraw-Hill Book Company, New York (1979)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cryogenic Propulsion and Stage Entity, ISRO, Thiruvananthapuram, Kerela, India

    V. Narayanan

  2. Cryogenic Propulsion Engines Group/ISRO, ISRO, Thiruvananthapuram, Kerela, India

    M. S. Suresh

  3. Engine Fluid System and Analysis Division/ISRO, ISRO, Thiruvananthapuram, Kerela, India

    N. Jayan & K. S. Bijukumar

Authors
  1. V. Narayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Suresh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Jayan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. S. Bijukumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. S. Bijukumar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Narayanan, V., Suresh, M.S., Jayan, N. et al. Mathematical modelling of a cryogenic engine. Int J Adv Eng Sci Appl Math 6, 183–194 (2014). https://doi.org/10.1007/s12572-015-0117-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12572-015-0117-2

Keywords

Search

Navigation