japan-School of Aerospace Engineering

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Steady, 1-d, constant area, adiabatic flow with no external work but with friction • Conserved quantities-– since adiabatic, no work: ho=constant – since A=const: mass flux=ρv=constant≡G

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japanSchool of Aerospace EngineeringFanno Flow - ThermodynamicspTvM Steady, 1-d, constant area, adiabaticflow with no external work but withfriction Conserved quantitiesx, f?L since adiabatic, no work: ho=constant since A=const: mass flux=v=constantGAs you change h, combining: ho=h+G2/22=constantyou change (and v)since G and ho const. On h-s diagram, can draw Fanno Line line connecting points with same ho and vAE3450Fanno Flow -1Copyright 2001-2002 by Jerry M. Seitzman. All rights reserved.School of Aerospace EngineeringFanno Line Velocity change (due tofriction) associated withentropy change Friction can only increaseentropy can only approach M=1 friction alone can notallow flow to transitionbetween sub/supersonichhov=0M1vmaxsmaxs Two solutions given (v,ho,s): subsonic & supersonic change mass flux: new Fanno lineFanno Flow -2Copyright 2001-2002 by Jerry M. Seitzman. All rights reserved.AE34501School of Aerospace EngineeringFanno Line - Choking Total friction experienced M1by flow increases withlength of flow, e.g.,hduct length, Lho For long enough duct,Me=1 (L=Lmax) What happens if L>LmaxMeLM1 subsonic flow: must move tosdifferent Fanno line ( ), i.e., lower mass flux supersonic flow: get a shock ( )AE3450Fanno Flow -3Copyright 2001-2002 by Jerry M. Seitzman. All r

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