THESE de DOCTORAT - cerfacs

138 Chapter A: About the π ′ c = 0 assumption
and
¯π T h ′ t,1 ¯v θ,1 = h ′ t,2 ¯v θ,2
(A.19)
Summarizing, the fluctuation of the parameter π
T ′ can be neglected if
v ′ θ,1 = v′ θ,2 and ¯π T h ′ t,1 ¯v θ,1 = h ′ t,2 ¯v θ,2 (A.20)
or
v ′ θ,1
= h′ t,1
v θ,1 ¯ ¯h t,1
or
v ′ θ,2
= h′ t,2
v θ,2 ¯ ¯h t,2
(A.21)
The parameter π T is related to the total pressure ratio π c as π T
variation of π c is written.
= π c
(γ−1)/γ . The fractional
π
T
′ = γ − 1 π c
′
¯π T γ ¯π c
(A.22)
It is observed then that making π ′ T = 0 is equivalent to make π′ c = 0, which is a clear simplification
for the definition of the differential equation of momentum in SNozzle. Indeed, doing
π ′ c = 0 means that p ′ t,2 /p′ t,1 = ¯π c