1. ProceduresforModelingTurbofan:
To beginmodelingourturbojetcore as a turbofanengine,we hadtoinclude the additionof a
bypasschannel aroundthe existingcore.Airflowsthroughthe bypasswithanegligiblyhighervelocity
than free stream(therefore modelledasequal tofree streamvelocityof 166.67[
𝑚
𝑠
]).An increase in
thrustis obtainedthroughthe combinationof massflow originatingfromthe bypass[ 𝑚 𝑓̇ ] andmass flow
throughthe core [𝑚̇ 𝑐].We assumedtemperaturethroughthe bypassisequal toambienttemperature
of 216.67 K,whichinfluencesthe total temperatureof mixedaircalculatedbythe sumof bothmass
flowratesas such:
𝑚̇ 0 = 𝑚̇ 𝑓 + 𝑚̇ 𝑐 (2.1)
Mass flowrate of our bypassiscalculatedbyan equationandgivenvalue foundonNASA’swebsite for
turbojetandturbo jetengines.ForourPrattand WhitneyF-100-PW-229 model turbofanengine,bypass
ratiowas givenasa 0.3. This value isa ratioof massflow ratesby the givenequation:
𝑏𝑝𝑟 =
𝑚 𝑓̇
𝑚 𝑐̇
(2.2)
It iswiththisequationandour givenratioof 0.3 that we are able tosolve formass flow rate of this
particularbypass.
Thisair mixture isthenexpelledthroughacommonnozzle asdetailedinthe originalproblem
withan exitareaof .15[𝑚2]. The temperature of the new airmixture 𝑚̇ 0 ismodelledasa weighted
average of the temperaturesandoriginal comprisingmassflow rates:
𝑇0 = 𝑇 𝑐 (
𝑚̇ 𝑐
𝑚̇ 0
) + 𝑇 𝑓 (
𝑚̇ 𝑓
𝑚̇ 0
) (2.3)
where T0 is the newtemperature of ourmixture.Thisdropintemperature iscompensatedforthe
mixture’sincreasein massflowrate,whichrelatestoahigherforce outputfora turbofanengine versus
a turbojet.Exitvelocityiscalculatedusingthiscommonexitpointandnew airmixture byourfirstlawof
Thermodynamics:
𝐸 = 𝑄 − 𝑊𝑐𝑣 + 𝑚̇ 𝑐ℎ 𝑐 + 𝑚̇ 𝑓ℎ 𝑓 − 𝑚̇ 0ℎ0 +
1
2
𝑚̇ 𝑐 𝑉𝑐
2 +
1
2
𝑚̇ 𝑓 𝑉𝑓
2
−
1
2
𝑚̇ 0 𝑉0
2
(2.4)
⇒ 𝑉0 = √
2
𝑚̇ 0
(𝑚̇ 𝑐ℎ 𝑐 + 𝑚̇ 𝑓ℎ𝑓 − 𝑚̇ 0ℎ0 +
1
2
𝑚̇ 𝑓 𝑉𝑓
2
) (2.5)
Finally,thrustisprovidedusingexitvelocityby:
𝑇 = ( 𝑚̇ 𝑐 + 𝑚̇ 𝑓) 𝑉0 (2.6)