Rocket Nozzle Geometries - gatech.edu

1 1 Nozzle Geometries -1 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionNozzle GeometriesNozzle ConfigurationsNozzle Geometries -2 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionNozzle Configurations So far considered 1-d ideal nozzles primarily for over/underexpandedoperation Described one real effect flow separation Continue by looking at real Nozzle configurations ( Nozzle geometry) Converging section subsonic flow, favorable pressure gradient can use almost any shapewith minimal poloss Diverging section design goals high Isp, low Nozzle mass and length ConvergingDivergingThroat2 Nozzle Geometries -3 Copyright 2012, 2018 by Jerry M.

2 Seitzman. All rights Rocket PropulsionMajor Nozzle Configurations Four major types (based on diverging section) oldest, simplest design, easy to complex shape, high altitude compensating, annular or altitude compensating, shorter than other enclosed nozzles small, inexpensive thrusterslarge rockets +large static (X-33) and small flight teststatic tested, primarily for upper stagesNozzle Geometries -4 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionNozzle ConfigurationsFrom Sutton3 Nozzle Geometries -5 Copyright 2012, 2018 by Jerry M.

3 Seitzman. All rights Rocket PropulsionLinear Aerospike Nozzle From Boeing XRS-2200 test (X-33)Photo Credit: BoeingNozzle Geometries -6 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionNozzle GeometriesConical Nozzles4 Nozzle Geometries -7 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionConical Nozzles Diverging section consists of 2 of sphere begins at throat radius section begins at transition point N half angle Design parameters Rt, R1, , L1, L, Re,.. NRtReRNR1L1 LNLLC teteteRRRRAA Nozzle Geometries -8 Copyright 2012, 2018 by Jerry M.

4 Seitzman. All rights Rocket PropulsionConical Nozzle -Length Can write length in terms of design parameters NRtReRNR1L1 LNLLC1 LLLN sin11RL NeNRRL tan tan1cos1tan1cos11 RRRRRLtteN cos11 RRRtN sintan1cos111 RRRLt tancossin1cos121 RRtteRR 5 Nozzle Geometries -9 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionConical Nozzle -Length Continuing NRtReRNR1L1 LNLLC tancossin1cos121 RRLt coscos2 coscos12 tancos1111 RRLt 1cos11tan1 ttRRRLT ypical value: R1/Rt~ L/Rt75011311523191823152712 For = 50 L Nozzle Geometries -10 Copyright 2012, 2018 by Jerry M.

5 Seitzman. All rights Rocket PropulsionFlow Divergence Other effect of increasing nozzleangle flow divergence Some of the momentum increase produced by Nozzle is not aligned with Nozzle axis thrust reduction/loss For uniform |ue| can apply correction factor eaeeAppum 6 Nozzle Geometries -11 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionConical Nozzles Design Tradeoff Shorter lengthbut lower thrustfor higher cone-angle tradeoff between size/mass and Isp eaeeAppum tan1cos111 ttRRRL0204060800102030 Half-angle ( ) L/Rt( =50)2cos1 for spherical expansion15 Nozzle Geometries -12 Copyright 2012, 2018 by Jerry M.

6 Seitzman. All rights Rocket PropulsionNozzle GeometriesBell/Contoured Nozzles7 Nozzle Geometries -13 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionBell/Contoured Nozzles Contoured to minimize turning and divergence losses reducing divergence requires turning flow (more axial) can result in compressions, could lead to shock losses Goal is to design Nozzle contour such that all waves are isentropic and produce nearly axial flow at exitRtLCEECN ozzle Geometries -14 Copyright 2012, 2018 by Jerry M. Seitzman.

7 All rights Rocket PropulsionDesign Approachesfrom Method of characteristics (MOC) inviscidassumption (can use hybrid approachfor wall boundary layers) must account for variable speed of sound Approximate optimization method of Rao initial (near throat) section spherical transition to parabolaRao, Jet Propulsion 28, pp. 377-382 (1958)Rao, J. Amer. Rocket , pp. 1488-1494 (1961)Allman and Hoffman, AIAA J. 19, pp. 750-751 (1981)8 Nozzle Geometries -15 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionApproximate Optimization Approach Near throat region composed of twospherical sections before throat: R1/Rt= after throat and up to N: R1/Rt= N given by Parabola (after N) with slope matched at N 4 unknowns: P, Q, S, T` NNRtReR1 LLC sin1 RxN xyx y e cos11 RRytN 21 TxSQxPy 4 boundary conditions:1)2)3)4)0 NNyxNteNeyRyxLx ,Rao)( , supplied N Rao)( , supplied e Nozzle Geometries -16 Copyright 2012, 2018 by Jerry M.

8 Seitzman. All rights Rocket PropulsionApproximate Optimization Approach Output of approach is optimal contour given acceptable length L(shorter larger divergence e) Typically Lis specified relative to length of conical Nozzle with =15 ` NNRtReR1 LLCxyx y e tRfL9 Nozzle Geometries -17 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionApproximate Optimal Design Angles Shorter Nozzle larger initial and final angles Larger larger initial angle smaller final anglefrom Sutton N enever zero angleNozzle Geometries -18 Copyright 2012, 2018 by Jerry M.

9 Seitzman. All rights Rocket PropulsionApprox. Optimal Design Performance Less divergence loss for full length bell vs. conical 70% bell has nearly same divergence loss but shorter and with less mass never 100% efficientfrom Sutton10 Nozzle Geometries -19 Copyright 2012, 2018 by Jerry M. Seitzman. All rights Rocket PropulsionAltitude/Ambient Pressure Adjustment Can use variable expansion ratio nozzles extendable, two-step nozzles , RL-10B-2 on Delta IV 2ndstage Plug/aerospikeand ED nozzles requires full aerodynamic model to help determine Nozzle boundaries plug: outer boundary ED: inner boundary full aerospike: high performance but cooling difficult truncated aerospike: can still get high with short LNozzle Geometries -20 Copyright 2012, 2018 by Jerry M.

10 Seitzman. All rights Rocket PropulsionNozzle Length Comparison Ideal bell Nozzle is longest for given Aerospike(and E/D) nozzles have potential for lowest weightfrom Sutto