Rocket Propulsion Thrust Coefficient Characteristic Velocity and Ideal Nozzle Expansion AE4451 Propulsion Thurst Coefficient 1 Copyright 2005 2006 by Jerry M Seitzman All rights reserved Thrust Coefficient c Define thrust coeff Also steady thrust Can combine with ideal nozzle results ue m ue pe pa Ae 1 pe 2 RTo 1 po 1 m choked At Thurst Coefficient 2 Copyright 2005 2006 by Jerry M Seitzman All rights reserved At po po RTo 2 1 1 1 AE4451 Propulsion 1 Ideal Thrust Coefficient 2 2 c 1 1 1 1 1 p 1 e po pe pa Ae po po At Ideal thrust coefficient is only function of Ae At pa po recall pe po fn a nozzle characteristic Note c fn To MW Thrust coeff depends mostly on pressure distribution in thrust chamber c from normalizing by poAt po At AE4451 Propulsion Thurst Coefficient 3 Copyright 2005 2006 by Jerry M Seitzman All rights reserved Characteristic Velocity Can define similar parameter to characterize combustor p A c o t characteristic velocity m For ideal case 1 1 m choked At po RTo 2 1 1 c ideal 1 1 1 R To 2 MW Note c fn To MW c c Thurst Coefficient 4 Copyright 2005 2006 by Jerry M Seitzman All rights reserved po At po At m m AE4451 Propulsion 2 Ideal Thrust Coefficient Mom vs Press 2 2 2 c 1 1 1 1 1 p 1 e po pe pa Ae po po At pe pa Ae m ue po At po At 1st term contribution to thrust by exit velocity momentum 2nd term contribution to thrust by exit pressure AE4451 Propulsion Thurst Coefficient 5 Copyright 2005 2006 by Jerry M Seitzman All rights reserved Comparison of Terms Compare terms for different nozzle designs 2 0 1 pa po 0 01 1 5 pe p o C 1 0 0 5 0 0 Thrust Coeff Velocity Term Pressure Term pe po 0 5 1 0 Converging nozzle Velocity term 0 1always provides thrust Pressure 0 01 term can increase or decrease thrust 0 001 100 1 Thurst Coefficient 6 Copyright 2005 2006 by Jerry M Seitzman All rights reserved 1 2 10 AAee A A t AE4451 Propulsion 3 Comparison of Terms Look at exit versus ambient pressure 2 0 1 pa po 0 01 1 5 c max 0 5 pe pa 0 0 0 01 Thrust Coeff Velocity Term Pressure Term 1 2 pe po 0 5 1 0 Converging nozzle 0 1 p e p o C 1 0 1 0 001 100 10 AAee A A t maximum thrust if perfectly expanded AE4451 Propulsion Thurst Coefficient 7 Copyright 2005 2006 by Jerry M Seitzman All rights reserved Effect of Ambient Pressure on c 2 2 pa po 0 2 0 1 8 Can get higher thrust coeffient by reducing ambient pressure increasing rocket pressure 0 001 1 6 C 1 4 0 0025 1 2 0 01 1 0 0 025 0 1 0 8 0 6 0 4 0 2 1 2 0 0 1 Thurst Coefficient 8 Copyright 2005 2006 by Jerry M Seitzman All rights reserved 10 A AA A eA t t ee A 100 1000 AE4451 Propulsion 4 Normalize by Converging Nozzle c 1 8 1 4 C C conv Large needed for 0 001 optimum c for small pa po 0 0025 Optimum for 0 01 c Isp varies 0 025 with altitude 0 1 pa for po 1000 psia shock at exit pa po 10 100 1000 0 015 sea level for single nozzle best AeA A Ae A t A 0 001 60 000 ft closer to low alt opt pa po 0 1 6 1 2 1 0 max thrust line 0 8 0 6 0 4 0 2 1 2 0 0 1 AE4451 Propulsion Thurst Coefficient 9 Copyright 2005 2006 by Jerry M Seitzman All rights reserved Flow Separation pa 1 8 1 6 C C conv 1 4 1 2 1 0 0 8 0 6 0 4 0 2 0 0 pa po 0 As pa increases from optimum pa pe flow eventually 0 0025 separates inside nozzle K 2 5 overexpanded 0 01 4 0 and before normal shock 0 025 appears at exit 0 1 Separated Flow oblique shocks enter nozzle Region Summerfield found 1 2 Normal shock at exit this generally occurred for K pa pe sep 2 5 4 1 10 100 pe 25 40 pa AeA A t e A Thurst Coefficient 10 Copyright 2005 2006 by Jerry M Seitzman All rights reserved 0 001 AE4451 Propulsion 5