Unified Engineering                                                                           Spring Term 2006

Problem P5. (Propulsion) L.O.’s B, C & E

Using the integral momentum equation, compare the thrust of two candidate nozzles for a combustion chamber with conditions pc, Tc, and atmospheric pressure patm.  Assume the flow is quasi-static and adiabatic.

Combustion chamber temperature = 4000 K

Combustion chamber pressure = 5 MPa

Nozzle throat area = 0.0005 m^2

Gas constant = 300 J/kg-K

Ratio of specific heats = 1.3

Atmospheric pressure = 0.101325 MPa

a) Simple converging nozzle (strongly under-expanded), with exit (throat) area At.  What are the thrust and the Isp for this nozzle?

b) Same throat area as in a), but with an added nozzle bell to give a nozzle flow matched to the outside pressure patm.  What is the exit area of this nozzle?  What are the thrust and the Isp for this nozzle?

[Note: To solve this problem you will have to use relationships from thermodynamics (steady flow energy equation) and fluid mechanics (compressible flow relations).  These can all be found in the Unified Propulsion notes (Chapters V and VI).]