THESE de DOCTORAT - cerfacs

A
About the π c ′ = 0 assumption
A.1 When is π ′ T
equal to zero?
Let us recall the equation of conservation of the total energy through a compressor. It is defined
as
ρ 1 u 1 h t,1 + W = ρ 2 u 2 h t,2
(A.1)
where W is the work done by the compressor. This equation can be also written as
π T ρ 1 u 1 h t,1 = ρ 2 u 2 h t,2
(A.2)
where π T is the total enthalpy ratio between the upstream and downstream flow. Equation
(A.1) can be re-written as
ρ 1 u 1 h t,1 + ρ 1 u 1 ∆h t = ρ 2 u 2 h t,2
(A.3)
where ∆h t = ∆(Uv θ ) is related to the conservation of the rothalpy (see Fig. A.1)
I = h t,1 − U 1 v θ1 = h t,2 − U 2 v θ2
(A.4)
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