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140 Referred Parameter Turboshaft Engine Model<br />
The engine technology parameters SP0C and sfc0C are assumed to vary linearly with mass flow ˙m0C<br />
up to a limit ˙mlim, and constant thereafter at SPlim and sfclim. The mass flow at the reference condition<br />
is ˙mref = Pref/SPref, with the reference values SPref and sfcref. The functions are defined by the limit<br />
values, and by the intercept values SPzero and sfczero at ˙m0C =0. If ˙mref ≥ ˙mlim, the limit values<br />
are set to the reference values. If ˙mref < ˙mlim, the intercept values are projected from the reference<br />
values: SPzero = SPref − ˙mrefx, x =(SPlim − SPref)/( ˙mlim − ˙mref); and similarly for sfczero. Then for<br />
˙m0C < ˙mlim<br />
and for ˙m0C ≥ ˙mlim<br />
SP0C = SPzero + Ksp1 ˙m0C = Ksp0 + Ksp1 ˙m0C<br />
sfc0C = sfczero + Ksfc1 ˙m0C = Ksfc0 + Ksfc1 ˙m0C<br />
SP0C = SPlim<br />
sfc0C = sfclim<br />
From the limit and intercept values, the slopes are Ksp1 =(SPlim − SPzero)/ ˙mlim and Ksfc1 = (sfclim −<br />
sfczero)/ ˙mlim. Usually the effect of size gives Ksp2 ≥ 0 and Ksfc2 ≤ 0. The power at the limit is<br />
Plim = SPlim ˙mlim. Using ˙m0C = P0C/SP0C, the specific power equation can be solved for the mass flow<br />
given the power:<br />
˙m0C =<br />
⎧<br />
⎨<br />
⎩<br />
P0C/SPlim<br />
<br />
( K0<br />
2K1 )2 + P0C K0<br />
− K1 2K1<br />
P0C ≥ Plim or Ksp1 =0<br />
otherwise<br />
From this mass flow, SP0C and sfc0C are calculated, hence the fuel flow ˙w0C = sfc0CP0C. The specific<br />
thrust available at MCP is assumed to be constant, and the specification power turbine speed decreases<br />
with the mass flow:<br />
Fg0C = SF0C ˙m0C<br />
Nspec =<br />
Nopt0C = Nspec<br />
<br />
Nspec − KNs2/ <br />
˙m0C<br />
<br />
Nopt0C<br />
Nspec<br />
ref<br />
ref<br />
+ KNs2/ ˙m0C = KNs1 + KNs2/ ˙m0C<br />
Then the power and specific power at all ratings R are obtained from the ratios: P0R = rp0RP0C,<br />
SP0R = rs0RSP0C, PmechR = rm0RP0C.<br />
18–9 Engine Speed<br />
The model as described in the previous sections may not adequately account for variation of engine<br />
performance with engine speed, so it is also possible to define the parameters corresponding to a set<br />
of engine-speed ratios r = N/Nspec. Then the engine-performance and power-available quantities are<br />
linearly interpolated to obtain the values at the required engine speed N. If this option is used, then the<br />
correction based on P (N)/P (Nspec) =ηt(N)/ηt(Nspec) is not applied.<br />
18–10 Weight<br />
The engine weight can be a fixed input value, calculated as a function of power, or scaled with<br />
engine mass flow. As a function of power, the weight of one engine is:<br />
Wone eng = K0eng + K1engP + K2engP Xeng