and the Implementation into Linear Plug Nozzles
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen
op dinsdag 21 juni 2005 om 13.00 uur
door
Menko Edward Nicolaas WISSE ingenieur lucht- en ruimtevaarttechniek
Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. P. G. Bakker.
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. ir. P. G. Bakker, Technische Universiteit Delft, promotor
Prof. dr. E. H. Hirschel, Universit¨at Stuttgart Prof. dr. ir. H. W. M. Hoeijmakers, Universiteit Twente
Prof. dr. H. G. Hornung, California Institute of Technology Prof. dr. ir. B. Koren, Technische Universiteit Delft / CWI
Dr.-ing. G. Hagemann, EADS Space Transportation
Ir. W. J. Bannink, Technische Universiteit Delft
Ir. W. J. Bannink en dr. ir. B. W. van Oudheusden hebben in belangrijke mate aan de totstandkoming van het proefschrift bijgedragen.
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ISBN 90-9019436-3
Copyright c 2005 by Menko Wisse
All rights reserved. No part of the material protected by this copyright notice may be produced or utilised in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the author.
Samenvatting
De grootste technologische uitdaging waar de ontwikkeling van de eerstvol-gende generatie lanceervoertuigen mee wordt geconfronteerd, is het ontwik-kelen van volledig herbruikbare systemen die in twee trappen of uiteindelijk in ´e´en trap een baan om de aarde moeten kunnen bereiken. Deze twee-traps (Two-Stage-To-Orbit, TSTO ) of enkeltwee-traps (Single-Stage-To-Orbit, SSTO ), herbruikbare lanceervoertuigen (Reusable Launch Vehicles, RLV ) kunnen de kosten voor het in een baan om de aarde brengen van ‘nuttige lading’ terugbrengen tot minder dan 10% van de huidige kosten. Deze ont-wikkeling kan echter alleen worden gerealiseerd door het ontwerpen van speciale voortstuwingssystemen die zijn voorzien van zogenaamde hoogte-aanpassende uitlaten (altitude-adaptive nozzles).
Het meest veelbelovende hoogteaanpassende uitlaatconcept is de ‘lineai-re tapuitlaat’ (linear plug nozzle). Dit zijn lineair naast elkaar geplaatste, binnenstebuiten gekeerde conventionele klokuitlaten (bell nozzles). Voorde-len van dit type uitlaat zijn: het aanpassingsvermogen naar veranderende omgevingsdruk; eenvoud en betrouwbaarheid, door afwezigheid van be-weegbare delen; laag motorgewicht, door het gemak van integratie in voer-tuigen en door een meer verdeelde stuwkrachtsbelasting; ingebouwde stuw-krachtrichtingsbesturing (thrust vector control ) door het regelen van de stuwkracht van de afzonderlijke modulaire motoren; en een goedkope ver-vaardiging van uitlaten voor grote voertuigen, doordat de uitlaat is op-gedeeld in meerdere gelijkvormige componenten. Het aanpassingsvermogen van het concept verdwijnt echter in de buurt van transsone snelheden (rond de geluidssnelheid) en bij hogere snelheden. Dit probleem wordt veroorza-akt door een lagedruk, tweedimensionale ‘compressibele rugstroming’ (base
flow ), gelegen achter de voertuigrug tussen de losgelaten externe buiten-stroming en de losgelaten brandstofuitlaatbuiten-stroming.
De compressibele rugstroming is een welbekend stromingsfenomeen, dat al jaren wordt bestudeerd en geanalyseerd, met name tijdens het begin van de raketontwikkeling eind jaren vijftig en in de jaren zestig. Een bevredi-gende beschrijving van de fysische processen die de rugstroming bepalen, is echter tot op dit moment nog niet gevonden. Een juist begrip van deze processen is echter essentieel in het kader van de ontwikkeling van externe-stromingsbestendige lineaire tapuitlaten en zeker voor het realiseren van enkeltrapsvoertuigen in het algemeen.
De complexiteit van de compressibele rugstroming wordt veroorzaakt door het bestaan van en de interactie van meerdere veschillende processen. Voor elk afzonderlijk ge¨ıdentificeerd proces in de complexe stroming rond de uitlaat van lanceervoertuigen, ook de lokale getallen van Reynolds mogen verondersteld worden zeer groot te zijn, ook al kunnen de lokale lengte-schalen relatief klein zijn. Dit is een gevolg van de tamelijk hoge snelhe-den, grote dichtheden en afmetingen van lanceervoertuigen, in combinatie met zeer lage viscositeit. Hierdoor mag een asymptotische benadering wor-den toegepast, waarin de verschillende elementen, waaruit de compressibele rugstroming bestaat, apart kunnen worden behandeld.
De asymptotische benadering maakt het analytische bewijs van het be-staan en de kwantificering van de bepalende rugstromingsfenomenen, zoals de stroomopwaartse invloed, de isentrope compressie voor heraanligging en de interactie van de nieuw ontwikkelde schuiflaag met de ge¨ expandeer-de grenslaag en het circulatiegebied, mogelijk. Uit expandeer-deze analyse zijn twee limietoplossingen naar voren gekomen. E´en is de welbekende ‘Chapman li-miet’, waarin de grenslaagdikte verwaarloosbaar wordt verondersteld ten opzichte van de schuiflaagdikte. De andere is een ‘nieuw ge¨ıdentificeerde li-miet’, waarin juist de schuiflaagdikte verwaarloosbaar wordt verondersteld ten opzichte van de grenslaagdikte. De overeenkomstige oplossingsmetho-den zijn verder aangepast om zo ook asymmetrische rugstromingen, door het toelaten van uitwisseling van massa en energie, alsmede het adiabatisch en niet-adiabatisch ruglekken (base bleed ), het rugverhitten (base heating) en het gelijktijdig gebruik van verschillende stoffen te kunnen behandelen. De asymptotische oplossingsmethode is verder aangepast voor rugstro-mingen stroomafwaarts van tapuitlaten. De schuiflaag, ontwikkeld tussen de brandstofuitlaatstroming en het circulatiegebied, kan hierdoor net zoals in de werkelijkheid worden afgebogen door reflecterende expansiegolven. Daarnaast zijn hiermee ook optimale ruglekpercentages van de tapuitlaat-rugstroming voor een maximale specifieke impuls bepaald en volgde uit de aan de voertuigrugstroming onderworpen parameterstudie dat de ‘re¨eele’ hete uitlaatgassen voor significant hogere rugdrukken en rugtemperaturen zorgen dan koude gassen zoals het gebruik van lucht tijdens windtunnelex-perimenten.
ne-gatieve gevolgen van rugstromingen te verminderen of zelfs helemaal te voorkomen door de toepassing van weldoordachtte en welgevormde achter-lichamen (after bodies). Als de stroming niet-viskeus wordt verondersteld, is gevonden dat een optimale bootstaart (Eng. boat tail) een rechtlijnige ge-ometrie heeft. De ‘geventileerde achterrandholte’ (Ventilated Trailing-Edge Cavity, VTEC ), bevestigd achter de voertuigrug, voorkomt de lage rug-drukken door het verplaatsen van het heraanhechtingspunt ver stroomaf-waarts. Hierdoor behoudt de brandstofuitlaatstroming het vermogen om haar hoogteaanpassende taken ook tijdens supersone vlucht uit te voeren.
Summary
The major technical challenge the development of next-generation launch-ers is facing today, is to achieve complete reusability in two stages to orbit or ultimately in one single stage. These Two-Stage-To-Orbit (TSTO) or Single-Stage-To-Orbit (SSTO) Reusable Launch Vehicles (RLV) may re-duce payload cost by a factor of ten or more. The challenge, however, can only be met by the design of special propulsion systems equipped with so called altitude-adaptive nozzles.
The most promising altitude-adaptive concept is that of the ‘linear plug nozzle’, a conventional bell nozzle turned inside out and arranged in a linear configuration. Advantages of this type of nozzle are: adaptability to varying ambient pressure; simplicity and reliability, because there are no movable parts; low engine weight, because of ease in vehicle integration and distributed thrust loads; built-in Thrust Vector Control (TVC) by throttling modular engines; and, cheap manufacturing of high-performance nozzles, because the nozzle is divided in multiple equivalent segments. The adaptability of the concept, however, ceases to exist around and beyond transonic velocities. The problem is related to the development of a low-pressure planar ‘compressible base flow’, located behind the vehicle base in the region between the separated external flow and the separated exhaust jet.
Compressible base flow is a well-known fluid-dynamic phenomenon, which has been studied and analysed for many years, especially during the onset of rocketry in the late 1950s and 1960s. However, a satisfying description of the physical processes driving the base flow has as yet not been determined. Nevertheless, a proper understanding of these processes is essential for the
development of a linear plug nozzle resisting external-flow effects, and is critical for the realisation of single-stage-to-orbit vehicles in general.
The complexity of compressible base flow lies in the composition and in-teraction of multiple processes. For every separate process that can be iden-tified in the complex flow around launch-vehicle nozzles, the local Reynolds number may be assumed high, even though corresponding length scales may be relatively small; this is a result of rather high velocities, densities and launch-vehicle sizes, and rather low viscosities. Consequently, an asymp-totic approach is allowed in which the different elements of compressible base flow are treated separately.
The asymptotic approach enables the analytical proof of existence and quantification of driving base-flow phenomena, such as upstream influence, isentropic compression before reattachment, and interaction of the develop-ing shear layer with the expanded boundary layer and circulatory region. From this analysis two limiting base-flow solutions are identified. One is the well-known ‘Chapman limit’, in which the boundary-layer thickness is assumed to be negligible in comparison with the shear-layer thickness. The other is a ‘newly-identified limit’, in which the shear-layer thickness is assumed to be negligible in comparison with the boundary-layer thick-ness. The corresponding solution methods have been adjusted to cope with asymmetric base-flow conditions (allowing the exchange of mass and en-ergy between the two flows), adiabatic and non-adiabatic base bleed, base heating, and the use of different species.
The asymptotic solution method has been further adjusted to cope with the base flow downstream of the actual plug nozzle as well. The shear layer, developed in between the jet exhaust and this base flow, is generally redirected by reflecting expansion waves. Optimal base-bleed percentages for the plug-nozzle base flow have been determined for maximal specific impulse. Subjecting the vehicle base flow solution to a parameter-variation analysis, reveals that real exhaust gases will produce significantly higher base pressures and temperatures than cold gases (air).
Clarifying the problem of base flow enables one to diminish or even avoid the negative consequences of base flow by application of a well-considered and well-shaped after body. For the case of inviscid flow the optimal conven-tional boat-tail shape is found to be linear. The ‘Ventilated Trailing-Edge Cavity (VTEC)’, attached to the vehicle base, moreover avoids the low base pressures by relocating the reattachment point farther downstream, so that the exhaust jet still retains the ability to fulfil its altitude-adaptive tasks at supersonic flight speeds.
Contents
Samenvatting (Summary, in Dutch) v
Summary ix 1 Introduction 1 1.1 Scope . . . 1 1.2 Objectives . . . 18 1.3 Approach . . . 18 1.4 Outline . . . 20 2 Linear-Plug-Nozzle Flow 21 2.1 Linear-Plug-Nozzle Design . . . 21 2.2 Altitude Adaptation . . . 23 2.3 Internal/External-Expansion Nozzle . . . 27 2.4 Plug Truncation . . . 28 2.5 External-Flow Effects . . . 29 2.6 Concluding Remarks . . . 30
3 Asymptotic Description of Base Flow 31 3.1 Introduction. . . 31
3.2 Asymptotic Approach . . . 33
3.3 Asymptotic Solution Methods . . . 58
3.4 Asymmetric Base Flow. . . 64
3.6 Concluding Remarks . . . 72
4 The Asymptotic Base-Flow Concept in Linear-Plug-Nozzle Flow 75 4.1 Exhaust in Quiescent Air . . . 76
4.2 External-Flow Influence . . . 94
4.3 Concluding Remarks . . . 109
5 Integration of After Bodies into the Linear Plug Nozzle 111 5.1 Boat Tailing. . . 111
5.2 Ventilated Trailing-Edge Cavity. . . 119
5.3 Concluding Remarks . . . 126
6 Conclusions 135 A Continuum Theory 141 A.1 Navier-Stokes Equations . . . 141
A.2 Perfect-Gas Equation of State . . . 143
A.3 Transport Properties . . . 143
A.4 Non-Dimensional Navier-Stokes Equations . . . 144
A.5 Euler Equations. . . 145
A.6 Boundary-Layer Equations . . . 145
A.7 Turbulent Boundary-Layer Equations . . . 146
B Boundary Conditions at a Solid Surface 149
References 151
Dankwoord (Acknowledgments, in Dutch) 157
Curriculum Vitae (in Dutch) 159
Curriculum Vitae 161
1
Introduction
1.1
Scope
The main objective of next-generation launchers is to achieve reusability, since it is assessed that this will reduce operational costs considerably. Nowadays, all launchers except one (the Space Shuttle) are fully expend-able systems, making launchings expensive. Single-stage-to-orbit (SSTO) or two-stage-to-orbit (TSTO) reusable launch vehicles (RLV) may reduce payload cost by a factor of ten or more. However, access-to-space with reduced or eliminated stages and frequent reusability of these vehicles is a technical challenge that can only be met by intelligent combination of light-weight structures and altitude-adapting engines. Yet, to date all op-erational launchers are equipped with conventional non-adaptable nozzles.
1.1.1
Conventional Nozzles
Conventional nozzles used in all today’s rocket engines are of the so called bell-type. This type of nozzle is an internal-expansion nozzle, which shape enables the exhaust gases to expand at design conditions to the ambient pressure. In this expansion process as well as in the mixing and combus-tion process some imperfeccombus-tions are encountered, lowering the theoretically-attainable performance values. Performance losses of two typical high-performance rocket engines, the Space Shuttle Main Engine (SSME) and the Vulcain-1 engine of the Ariane-5 engine, are tabulated in Table1.1, [25].
Performance losses SSME Vulcain 1 Imperfections in mixing and combustion 0.5 % 1.0 %
Friction 0.6 % 1.1 %
Divergence of exit flow 1.0 % 1.2 %
Chemical non-equilibrium 0.1 % 0.2 %
Non-adapted nozzle flow 0–15 % 0–15 %
Table 1.1. Performance losses in conventional rocket nozzles [25].
Among the sources of losses in the expansion process tabulated here are the viscous effects induced by turbulent boundary layers, the divergent nozzle-exit flow, and the chemical non-equilibrium effects, which may be neglected in H2− O2 rocket engines with chamber pressures above pc= 50
bar [39]. However, the most-significant performance loss is induced by the non-adaptability of the nozzle flow to off-design conditions.
Non Adaptability
The off-design performance losses are induced either in over-expanded con-ditions during operations at low-altitude or in under-expanded concon-ditions during operations at high altitude. Only at the design condition itself the expansion is close to ideal. The flow phenomena for these different condi-tions are illustrated in Fig.1.1. The design condition, in which the nozzle-exit pressure is equal to the ambient pressure (Fig.1.1b), is met at a certain altitude in the atmosphere. During low-altitude operations (Fig.1.1a) the ambient pressure is higher than the nozzle-exit pressure, and an oblique shock wave is required to adapt the exhaust jet to the ambient pressure. The oblique shock may or may not end up downstream into a normal shock, a Mach disk. Nonetheless, the expansion part of the nozzle where the ex-haust jet has expanded beyond the ambient pressure now produces drag, resulting in a loss of performance. On the other hand, at high-altitude operations (Fig. 1.1c) the ambient pressure is lower than the nozzle-exit pressure, and expansion waves are needed to adapt to the ambient pres-sure. An ideal nozzle would expand the exhaust jet to the ambient prespres-sure. However, in this case, the nozzle only produces thrust for the expansion part until the nozzle-exit pressure, resulting again in loss of performance. Side Loads
Since in the low-altitude regime the ambient pressure is higher than at the design condition, the exhaust jet may already separate inside the nozzle. The wall pressures behind the separation line are hereby increased towards the ambient pressure. However, the separation line has been shown to ex-perience a random movement along the nozzle wall [20], resulting in the possible generation of unsteady side loads. Reliable prediction of these side
fan expansion shocks
(a) Over-expanded condition
(b) Design condition
fan expansion
(c) Under-expanded condition
Figure 1.1. Altitude-varying flow phenomena for conventional bell nozzles. loads is still beyond the reach of modern theoretical models and remains a subject of on-going research. Yet, side loads may result in the complete destruction of the rocket nozzle, as was reported during the development of the hydrogen-oxygen J-2 second- and third-stage engine of the Saturn V launcher and on two occasions during the development of the SSME en-gine [52]. Therefore, maximal design pressure ratios are chosen to avoid the uncontrolled flow separation with possible side loads during the transient start-up of the rocket engine, consequently reducing the vacuum perfor-mance. This highly reduces the performances of rocket engines operating during the entire trajectory like the SSME and the Vulcain 1.
1.1.2
Altitude-Adaptive Nozzles
Table 1.1 reveals that the most considerable gain in performance may be obtained by enhancing the nozzles’ adaptation capabilities to the vari-ous ambient conditions encountered during the ascent trajectory. ‘Alti-tude adaptation’ is the widely used description for the ability of nozzles to adapt to varying ambient pressures at different altitudes. However, also the external-flow Mach number is an ascent trajectory variable that should be taken into account. Various concepts have been discussed by Hagemann
et al. [25]. They categorised nozzles with devices for controlled-flow separa-tion into one sub-group, denoted as ‘controlled-separasepara-tion nozzles’. To such a sub-group also belong the ‘dual-mode nozzles’. In the present disserta-tion, the findings have been summarised in a table (Table1.2). Inhere plug nozzles, expansion-deflection nozzles and variable-throat nozzles have also been categorised in a sub-group denoted as ‘continuous-adapting nozzles’. The table contains schematic illustrations of the various nozzles as well as different scores (denoted by the number of asterisks) for nozzle properties. Let us take them in order.
Controlled-Separation Nozzles
The primary emphasis of the controlled-separation nozzles is the reduction of side loads at sea level and during the rest of the low-altitude operation. Nozzle with fixed inserts. This nozzle is the least dramatic change to the baseline bell nozzle. A trip ring is attached to the inside of the conven-tional bell nozzle, which disturbs the turbulent boundary layer causing a controlled separation. The sea-level performance of the nozzle with a trip ring is lower than the performance of the conventional nozzle truncated at the trip-ring location, because of aspiration drag (drag induced by the act of inhaling) in the separated region. Since the transition behaviour to full expansion is quite uncertain, the low-altitude adaptation performance scores relatively low. At high altitudes with lower ambient pressures the jet reattaches at the nozzle wall. The only losses here are induced by the obstacle (trip ring), which are marginal and result in a high high-altitude adaptation performance. Since the trip rings may be attached to existing nozzles, it is simple and scores high on the performance of costs. However, one of the main problems is the ring resistance in high-temperature bound-ary layers and the exact circumferential fixing, resulting in low reliability. These problems together with the performance losses and uncertainties in transition are assumed to be responsible for the reduced interest in this concept.
Nozzle with temporary inserts. Nozzles with temporary inserts, which are removed at high-altitude operations, have the advantage over nozzles with fixed wall inserts that they do not experience wall discontinuities which decrease vacuum performance, resulting in even higher high-altitude adap-tation performances. The inserts may be either ablative or ejectable, and they may be designed as a complete secondary nozzle or as small steps. However, during low-altitude operations the nozzle still experiences aspi-ration drag, which together with a presumably not completely optimised insert contour lowers the low-altitude adaptation performance. In case of an ejectable insert, the ejection itself is highly unreliable. A mechanism should provide a sudden and symmetrical detachment. In any case, shocks are formed from the inserts during the transient ejection, which interact
Nozzles Lo w-al titud e adap tation High -al titu de adap tation Si m p licit y Re liabi lit y En gin e w eigh t Cos ts Ex te rnal-fl o w ad aptation Baseline bell nozzle F FFFF FFFFF FF FFF FFFFF FF Controlled-separation nozzles Nozzle with fixed inserts FF FFFF FFFFF FF FFF FFFFF FF Nozzle with temporary inserts FFF FFFFF FF FF FF FFF FF Nozzle with secondary gas injection FFF FFFF FFF FFF FF FFF F Dual-bell nozzle FFF FFFF FFFF FFFF FFF FFFF FF Extendible nozzle FFF FFFFF FF F FF FF FF Continuous-adapting nozzles Plug nozzle FFFFF FFFF FFF FFFFF FFFFF FFF F Expansion-deflection nozzle FFFF FFF FFF FFFFF FFFF FFF FF Variable-throat nozzle FFFFF FFFFF F F FF FF FFFF Dual-mode nozzles Dual-throat nozzle FFF FFFF FF F FF F FFF Dual-expander nozzle FFFF FFFF FF FF FF F FFF
Table 1.2. Critical comparison of the baseline bell and various altitude-adaptation nozzle concepts by granting scores to various nozzle properties, where increasing scores indicate favourable characteristics.
with the nozzle wall and induce pressure loads and local heat fluxes. A not very unlikely asymmetric ejection would result in the generation of side loads. The result could be catastrophic, not to speak of the possibil-ity of a downstream collision. Therefore, a good ejection mechanism would become very complex. Another method is to use combustible or ablative elements. During the ascent the element size continuously reduces until the complete element is consumed and the baseline bell nozzle emerges for optimal vacuum performance. The uncertainties here are the stability and temporary-defined surface-regression rates of the inserts, because of the local pressure and temperature fluctuations.
Nozzle with secondary gas injection. In this case the nozzle forces the ex-haust jet to separate in over-expanded condition at a desired location by injection of a secondary fluid in normal direction to the wall. The injection may be either active, from a high-pressure reservoir, or passive using vented holes in the nozzle wall. Since a large amount of injected fluid is required to enforce a significant flow separation, no net impulse gain is accomplished by using active injection. Concerning the vented nozzle, its slots are opened during low-altitude operations triggering flow separation, whereas its slots are closed during high-altitude operations for full expansion. This concept, however, only seems to work for low-altitude operations. At intermediate ranges in altitude the limited number of holes cannot enforce separation anymore and the thrust efficiency suddenly drops, lowering the low-altitude adaptation performance. Since the slots are connected to the vehicle-base pressure region which is lower than the ambient pressure, the nozzle tran-sition occurs at a lower altitude. This results in a reduced external-flow adaptation performance.
Dual-bell nozzle. The dual-bell nozzle concept consists of a typical inner nozzle, a wall inflection and an outer extension. At low altitudes the ex-haust jet separates at the inflection. The aspiration drag causes the thrust to be not completely adaptive at low altitudes. At high altitudes the flow is attached to the wall until the nozzle exit. However, performance losses are induced at the inflection. The relatively low aspiration pressure at low altitudes forces the transition to occur too early, leading to further losses in thrust. The transition behaviour, however, remains somewhat uncertain, but not as uncertain as that of the nozzle with fixed inserts. The dual-bell’s low-altitude performance is, therefore, comparable to the nozzle with tem-porary inserts and nozzle with secondary gas injection. The high-altitude adaptation performance is comparable to the nozzle with fixed inserts and nozzle with secondary gas injection, but it cannot obtain the baseline vac-uum performance of the nozzle with temporary inserts. Its main advantage is its simplicity, because of the absence of any movable parts, therefore, its high reliability, and costs reduction.
Extendible nozzle. The extendible nozzle is a concept with movable parts. At low altitudes the extension is in the retracted position and at high alti-tudes the extension is deployed. A minor performance loss is incorporated at low-altitude operations because of the non-optimal truncated inner noz-zle. The performance characteristics of altitude adaptation are therefore comparable to the nozzle with temporary inserts (ejectable nozzle). The main drawback is the requirement of mechanical devices for deployment of the extension, which reduces simplicity and reliability, and increases engine mass and costs. The engine’s reliability is further decreased, since the cool-ing devices on the extendible part also need to be flexible and the extension experiences strong vibrations in the retracted position because of engine noise.
Continuous-Adapting Nozzles
The primary emphasis of the continuous-adapting nozzles is on the adapta-tion capability at every altitude. This means that the area ratio of nozzle-jet exit area over throat area continuously adapts itself to the altitude or ambient pressure, actively or passively.
Plug nozzle. The plug nozzle is an example of a passive continuous-adapting nozzle. Roughly, one could say that the plug nozzle is a bell nozzle turned inside out with the injection rotated towards the centreline. Therefore, the exhaust jet is only constrained by the thrust producing solid surface on the inside, while the ‘invisible’ outer wall is not constrained by a solid surface but by the atmospheric ambient pressure. It is this ambient pressure to which the plume adapts. The jet is exhausted in the external part at a spe-cific angle. Since the outer part of the jet is subject to a sudden expansion to the ambient pressure, expansion waves are created travelling towards the inner ramp. The inner ramp is designed in such way that waves without strength are reflected over the complete ramp at the design condition. At altitudes lower than the design condition, the expansion fan is narrower and the ambient pressure is already reached at an intermediate position on the ramp. Downstream, the still continuously deflecting ramp causes the exhaust jet to gradually and almost inviscidly deflect to the centreline direc-tion. This results in extremely high low-altitude adaptation performances. However, at higher altitudes, where ambient pressures are lower than the design condition, no adaptation is present anymore. The design pressure ra-tio of chamber pressure over ambient pressure is, therefore, chosen as high as possible, increasing the high-altitude adaptation performance as well. Control problems of a constant throat height during manufacturing and thermal expansion, cooling of the annular throat with a tiny throat height, and control of combustion instabilities in the annular combustion chamber, are avoided by clustering the internal part into rectangular internal nozzle sections. Since there are no movable parts, the nozzle is simple and reli-able, although it is completely different from a baseline bell nozzle which
decreases the simplicity score and increases manufacturing costs. Moreover, the ease in vehicle-engine integration and distributed thrust loads reduces engine weight, which may be even more reduced by truncating the plug without much performance loss, although hereby a fluid-dynamically com-plex base-flow problem is created. However, the reduced weight induces a drop in operational costs. There are also additional advantages, as there is the ease of obtaining thrust vector control by throttling the various modu-lar nozzle chamber pressure ratios, and the segmentation principle dividing the plug nozzle into multiple modules, which makes manufacturing of very high-performance nozzles easier and cheaper. Though, the problem of the plug nozzle is that its adaptation capabilities ceases to exist around and beyond transonic speeds, leaving the plug nozzle with an extremely low mark for its external flow adaptation performance. This problem is also directly related to another base flow situated at the vehicle base or cowl.
Expansion-deflection nozzle. This nozzle is also meant as a passive contin-uous-adapting nozzle. It is a bell nozzle in which the throat is split by a central plug deflecting the exhaust jet outward. Its aerodynamic behaviour as a function of altitude is quite similar to plug nozzles, since the expansion process is controlled by a surrounding pressure. However, for the expansion-deflection nozzle the process is controlled from the inside. Therefore, this surrounding pressure is the pressure in the wake of the central plug, which is always lower than the ambient pressure because of the aspiration ef-fect, leading to an additional over-expansion. These losses result in poor altitude-adaptive capabilities, lower than those of plug nozzles. The advan-tages are further the same as for the plug nozzles. Yet, the external-flow adaptation is not as sensitive as for the plug nozzle since the adaptation is not controlled from the outside but from the inside. However, the inside control already resulted in over-expansion losses. Therefore, the net result for this condition is about the same.
Variable-throat nozzle. The variable-throat nozzle is a conventional bell nozzle with a throat area that may be varied by an axially moving me-chanical pintle, hereby varying the expansion-area ratio. In contrast to the plug nozzle and the expansion-deflection nozzle not the exit area is con-tinuously and passively controlled, but the throat area is concon-tinuously and actively controlled. Therefore, it allows an optimal expansion throughout the mission. However, the concept requires an actuator and a sophisticated control system, raising issues about the design complexity, cooling of the pintle and throat, reliability, and engine weight. Yet, this nozzle is remark-ably unaffected by external-flow influences, because the nozzle-exit area, which may possess the same frontal surface as the vehicle, remains the same and the exit pressure follows the ambient pressure, when the throat area is varied correctly during ascent.
Dual-Mode Nozzles
Dual-mode nozzles using one or two fuels offer two different modes dur-ing the ascent of the launch vehicle. The two-fuel concept involves the use of a dense moderate-performance propellant during lift-off to provide high thrust at the initial flight phase, and a better performing propellant at high altitudes, resulting in a higher specific impulse. The combustion chambers are located one inside the other in case of a dual-throat nozzle, or the conventional-bell thrust chamber is surrounded by an annular thrust chamber in case of a dual-expander nozzle. Both dual-mode nozzles pos-sess an acceleration-reduction capability, achieved by shutting down one of the two engines. In this way, losses due to over-expansion can be avoided, leading to an increase in specific impulse. However, their development and construction requires considerable technological effort.
Dual-throat nozzle. In this nozzle the combustion chambers are located one inside the other. At low altitude both thrust chambers run in parallel. At higher altitudes the outer chamber is shut off. However, for this nozzle the expansion process induces some significant losses in performance. At sea-level operation, separation occurs in the inner nozzle, before it merges with the outer flow, resulting in addition to the losses in performance in higher heat loads on the inner nozzle. Operating at high altitude with the outer chamber shut off, the interaction of the inner exhaust jet with the outer nozzle wall results in significant losses as well.
Dual-expander nozzle. This nozzle concept possesses two concentric thrust chambers and nozzles. It consists of a conventional bell nozzle surrounded by an annular thrust chamber. Both chambers have short primary noz-zles, the outer edge extended by a divergent nozzle extension. As for the dual-throat nozzle, both chambers operate at low altitudes. During this op-eration performance losses are not significant. At high altitude one of the chambers is shut off. Then, however, a strong expansion towards the shutt-off engine followed by a recompression shock at reattachment, induces a slight loss in performance.
Critical Comparison
Having reviewed all the altitude-adaptive nozzles separately, we may com-pare them and try to find out which concept provides the best properties. However, all the concepts have one or more weak points. Each property should be granted a weighing factor in order to obtain a total score for each nozzle concept. Nevertheless, this is a very arbitrary process and, since these weight functions will vary from one vehicle concept to the other, this quantitative task will be left unfulfilled. Yet, some qualitative remarks may still be made.
For instance, let us consider an existing launch vehicle with a baseline conventional bell nozzle, which endures the problem of generation of side
loads. A fast, simple, and low-cost solution would be to place a fixed insert, a trip ring inside the existing nozzle. A more structural, long-term solution would be a dual-bell nozzle, increasing off-design adaptation capabilities, yet simple to design and to incorporate in an existing launch vehicle, no moving parts and, therefore, reliable.
For a next-generation single-stage-to-orbit (SSTO) or two-stage-to-orbit (TSTO) concept, in which altitude adaptation becomes even more impor-tant, continuous-adapting nozzles may become more interesting, especially for SSTO concepts. Passive-adapting nozzles, like the plug nozzle and the expansion-deflection nozzle, have the advantage over the active-adapting nozzle, like the variable-throat nozzle, of ensuring low technological risk. The plug nozzle clearly outperforms the expansion-deflection nozzle. This view is supported by widespread interest into the plug nozzle. Although it has to overcome its weakness, the low external flow adaptation perfor-mance, further advantages of the plug nozzle, like the built-in thrust-vector-control capability, cheap manufacturing due to the segmentation principle, and the reduced engine weight seem to make this nozzle the ideal candidate for next-generation nozzles.
1.1.3
Plug-Nozzle Development in Historical Perspective
Not long ago the plug nozzle was only known to a handful of rocketry ex-perts. Over the years minor research had been conducted on the subject, and it appeared to become nothing more than a footnote in aerospace his-tory. Already explored by the Germans in World War II for use in the first turbojet engines, serious interest for rocket application seemed to be lack-ing until the unveillack-ing of Lockheed Martin’s winnlack-ing X-33 concept in the mid-1990s. The vehicle was intended to serve as a technology demonstrator for NASA’s indicated successor of the Space Shuttle, the next-generation single-stage-to-orbit reusable launch vehicle VentureStar, which was to be powered by the Rocketdyne XRS-2200 linear ‘aerospike’ engine. Since then, the engine concept has received widespread attention all over the world.The first serious studies on plug nozzles were conducted in Germany al-ready before World War II in 1937, in conjunction with the development of the turbojet engine. The Junkers Jumo-004 was the first turbojet engine to go into quantity production in the fall of 1944, and also the first engine equipped with plug nozzles. These engines were used to power the Messer-schmitt Me-262 twin-jet fighter (Fig.1.2), the world’s first operational jet combat aircraft, and the Arado Ar-234 series of bomber-reconnaissance air-craft. The engines were equipped with axially-movable plug centrebodies in order to be able to vary throat area for better performance.
After World War II the German technology was incorporated by the American manufacturers of air-breathing propulsion systems and the NASA Lewis Research Center in order to obtain high efficiencies at design and off-design conditions for turbojet and ramjet engines.
Figure 1.2. The Messerschmitt Me-262 twin-jet fighter powered by Junkers Jumo-004 turbojet engines.
The first research into annular plug nozzles for rocket application was conducted by General Electric in the 1950s, at that time still involved in rocket engines. They introduced the segmented combustor principle, divid-ing the engine in modules, ideal for very large rockets. The concept was bid to NASA for an F-1 engine proposal, the first stage engine of the Sat-urn V. However, there were not enough testing results to offer. The timing was wrong. In 1963 GE proposed an early SSTO concept [46], the first to employ a plug-nozzle propulsion system. It was intended to place a fully-assembled rotating space station into orbit. Although, it was never given a name, the plug-nozzle concept remained the baseline engine for future SSTO concepts.
Meanwhile, in the late 1950s also Rocketdyne started their research into annular plug-nozzle technology. Their concept evolved in what they call aerospike. This is a truncated ideal plug nozzle/truncated ideal spike, in which base bleed is added to the plug base flow, trying to restore the base drag losses induced by the truncation. In this way, the ideal spike is claimed to be restored in an aerodynamic way, resulting in an aerodynamic spike or ‘aerospike’. Similar work was underway in West Germany in the late 1960s to the early 1970s in support of a heavy-lift launch vehicle called Neptune [32], which was equipped with a propulsion concept consisting of an annular plug nozzle.
On 30 October 1968, NASA’s Manned Spacecraft Center (MSC) and Marshall Space Flight Center (MSFC) issued a joint Request For Propos-als (RFP) for an eight-month study of an Integral Launch and Re-entry Vehicle (IRLV), ‘Phase A’ of the Space Shuttle design and development cycle. They stated that the studies should concentrate rather on economy and safety than on optimised payload performance. The separate engine
(a) Hot oxygen/hydrogen firings on the 250K O2/H2 ADP annular
aerospike [36].
(b) Hot-plume
thrust-vector-control test on the linear aerospike
of Linear System Test Bed
no. 2 [36].
Figure 1.3. Rocketdyne’s shift from annular to linear aerospikes.
competition conducted by MSFC resulted in the two-position/extendible bell-type rocket engine as a winning concept. At that time, several aerospike engines (Fig.1.3a) had been successfully tested by Rocketdyne under a joint NASA-Air Force contract since 1960, but the technology was still consid-ered to be too immature. It was stated that the extendible bell engine had a significant programmatic advantage in the context of a main propulsion system for a 1970’s Space Shuttle, since it was believed that the availability of the aerospike critical path main propulsion system could unduly delay vehicle development and early flight operations [7]. On the other hand, it was mentioned that these concluding statements are pertinent to an early Space Shuttle only.
Therefore, the development of aerospike technology went on into the 1970s under NASA contracts. However, as the former aerospikes were all annular in shape often consisting of segmented combustors placed around the spike/plug, further cost reduction was claimed by linearly aligning the segmented combustors (Fig.1.3b). Rocketdyne demonstrated the feasibility of design, fabrication, and assembly of a full-scale linear-aerospike test-bed number 1 [22], which was employed with the segmented combustor concept, from April 1970 to June 1972. Test-bed number 2 (Fig.1.3b) demonstrated advanced thrust-vector-control concepts [31]. These studies were followed in 1976 and 1977 by a study conducted for NASA Lewis Research Cen-ter on a dual-fuel, modular, split-combustor linear-aerospike engine as an integrated engine for an SSTO reusable launch vehicle (RLV) [16]. It was actually a dual-expander nozzle incorporated in a plug nozzle instead of in a bell nozzle. In mode 1 for sea-level operation both the inner and outer combustors were used, resulting in moderate area ratios. In mode 2 for higher-altitude operation the outer engine was shut down. Then, the area
Figure 1.4. The first launch of the Space Shuttle (Columbia) from the Kennedy Space Center (KSC) on mission STS-1 on April 12, 1981. (Courtesy NASA)
ratio suddenly increased. In this way the engine was equipped with an extra adaptation feature in addition to the continuously altitude-adaptation feature of the plug-nozzle external part, which is however ac-tively controlled and is therefore not sensitive to external-flow effects.
The first orbital launch of the shuttle Space Transportation System (STS-1) involved the ‘Columbia’ and took place on April 12, 1981 (Fig. 1.4). The extendible bell was already replaced by a baseline bell engine. This replacement is a good example of the policy at that time, which implies choosing the safest path, albeit more expensive and less optimal. The re-sult is a partly reusable launch system, consisting of a reusable orbiter and expendible boosters and an expendible external tank. Relying on 1960s technology, the shuttle is therefore costly, labour intensive to operate, and the technology became rapidly out-of-date. The NASA policy change to “faster, better, cheaper” in the 1980s and 1990s encouraged the agency to avoid heavy reliance on supplemental boost systems. The goal for RLVs became developing self-boosting flight vehicles similar to aircraft, whose activities may be performed with much smaller launch crews, with more rapid turnaround times, and at greatly reduced costs. This might be ac-complished by single-stage-to-orbit (SSTO) or two-stage-to-orbit (TSTO) systems.
The U.S. National Aerospace Plane (NASP) X-30 program, started in 1985, was a first result of the philosophy change. It was an attempt to
Figure 1.5. National Aerospace Plane (NASP) X-30. (Courtesy NASA)
Figure 1.6. TSTO S¨anger space-trans-portation system. (Courtesy MBB)
develop an SSTO concept using a dual-mode ramjet-scramjet propulsion system, which is fully integrated in the vehicle design. It is obvious that the SSTO concept as well as the integrated engine makes this vehicle ideal for the application of plug-like nozzles. The goal was to achieve first flight in the early 1990s. However, soon it became clear that the required air-breathing technology was too complex to achieve a mission-capable vehicle even by the beginning of the 21st century. When the NASP program was cancelled in 1994, one realised that while developing the great amount of complex technologies required for an X-30-like vehicle, an operational, next-generation, launch vehicle would be needed in the meantime by the beginning of the 21st century to replace the ageing shuttle.
The overall objective of such a reusable-launch-vehicle design was to re-duce payload costs to approximately $1,100 to $2,200 per kilogram from the present Space-Shuttle payload costs of approximately $22,000 per kilo-gram [6]. Other goals were increased empty weight to around 35% (compa-rable to military aircraft, like the C-5A and C141A, later on scaled down to 10%), rapid aircraft-like turnaround, and small launch crews. This led to the development of X-33 concepts. After a competitive phase the con-tract was awarded to Lockheed-Martin Skunk Works in July 1996. The X-33 Advanced Technology Demonstrator (Fig. 1.7) is the one-half-scale lifting-body-type vertical-take-off horizontal-landing (VTHL) flight version of the at-that-time envisioned operational successor of the Space Shuttle, the VentureStar. It would be powered by two XRS-2200 linear-aerospike engines (Fig. 1.8), developed by Rocketdyne. Each engine employs 2x10 aligned combustion chambers. The full-sized RS-2200 engine, intended for the VentureStar, was to have 2x7 aligned combustion chambers. At the time
Figure 1.7. Lockheed-Martin Skunk Works’ X-33 ATD. (Courtesy NASA)
Figure 1.8. Boeing Rocketdyne’s XRS--2200 final test at NASA Stennis Space Center, August 6, 2001. (Courtesy NASA)
the final tests on the XRS-2200 aerospike were successfully completed in mid-2001, the X-33 program was already terminated. Problems with the hy-drogen fuel tank, made of lightweight composites which had to be replaced by heavier aluminum, and somewhat disappointing aerospike performance results, made SSTO access-to-space with the VentureStar a difficult task.
The reduced aerospike performance was encountered during the LASRE experiments [74], the first aerospike flight tests ever, conducted with a 20% half-span scale model of an X-33 fore-body and an XRS-2200 aerospike engine. This model (Fig.1.9a) was mounted on top of an SR-71 Blackbird high-speed research aircraft (Fig. 1.9b). Tests were performed from Mach 0.6 to Mach 3.2. The data was intended to define engine performance un-der realistic flight conditions, and to determine plume interactions with the base and the engine cowls. However, the problems with the tanks de-layed the hot-firing tests of LASRE too, and when the X-33 program was terminated, only cold-firing tests had been conducted with LASRE.
(a) LASRE aerospike.
(Courtesy NASA)
(b) LASRE mounted on the SR-71. (Courtesy NASA)
ramp nozzle dual−mode
scramjet inlet
single−expansion
Figure 1.10. Hyper-X X-43A experimental dual-mode scramjet vehicle. (Courtesy NASA)
The choice for the VentureStar concept as a Space Shuttle successor led to worldwide - read Russia [19, 18], Japan [58, 59, 60, 61, 35], and Eu-rope - interest in linear plug nozzles. In EuEu-rope this interest resulted in a first investigation in linear plug nozzles within the frame of the ESA Future European Space Transportation Investigations Programme (FES-TIP). In 1995 the FESTIP program was initiated in order to study possible reusable-launch-vehicle (RLV) concepts and to develop the related tech-nologies. The plug-nozzle investigation resulted in the basic understanding of the flow phenomena and performance characteristics [30]. In Germany this program was followed by the LION program on improved contour-design methods for the internal/external-expansion plug nozzle [24]. In the Netherlands the focus was mainly on the external-flow effects, which were found to deteriorate the altitude-adaptation capabilities in transonic and supersonic conditions [3, 70]. This resulted in a proposal and initial cal-culations on an alternative after body, the Ventilated Trailing-Edge Cav-ity (VTEC) [67]. These studies were followed in 2001 by an ESA-ESTEC Technical Research Programme (TRP) denoted Linear-Plug-Nozzle Inves-tigations (LPNI). The objective of this research project was to investigate the applicability of linear plug nozzles in full-scale vehicles. It included per-formance assessments, a feasibility study of thrust vector control (TVC) by throttling individual modules (both experimental and numerical), and en-gine manufacturing and launcher integration studies. Meanwhile, in 1999 a successor of the FESTIP program on launcher reusability was started,
denoted Future Launchers Technologies Programme (FLTP) [9]. This pro-gram is expected to provide a propro-grammatic decision on the initiation of a European development program in 2006-2007 for the next-generation Eu-ropean launchers. The technological development is expected to lead to a next-generation reusable launcher by 2015-2020.
For the long term, air-breathing engines are still envisioned to power launch vehicles [41]. The oxidiser amount that does not have to be taken along during launch will reduce vehicle size and weight considerably, re-ducing payload costs even further. The air-breathing cycle would then be a dual-mode scramjet operating from high-supersonic conditions (Mach 3) in ramjet mode, switching to scramjet mode at Mach 6 until mid-hypersonic conditions (Mach 10). This cycle was successfully flown up to Mach 7 on the Hyper-X X-43A experimental vehicle (Fig. 1.10) on March 27, 2004, and even up to Mach 10 on November 16, 2004. For future engines the cycle must be combined with another cycle to power the vehicle at least to supersonic velocities. For access-to-orbit the Rocket-Based Combined-Cycle (RBCC) engine would be the ultimate integration of air-breathing and rocket propulsion cycles. The integral rocket system may then perform as a low-speed system in the subsonic to supersonic range and as a high-speed system above the scramjet operating regime. Observe in Fig. 1.10
that the single-expansion ramp nozzle (SERN) of the integrated scramjet engine resembles the plug-nozzle ramp. Plug nozzles may therefore serve space vehicles far into the future, even beyond the introduction of opera-tional air-breathing engines.
1.1.4
Reduced Adaptability of Plug Nozzles due to Base
Flows
We have shown that plug nozzles have a big potential for the future. How-ever, as was mentioned in Section 1.1.2, it has to overcome a weakness: poor adaptation to transonic and supersonic external flows. At these con-ditions, the favourable altitude-adaptation characteristics deteriorate due to the effect of base flows, which are generated because of the addition of the external flow. In between these flows a base flow is formed, possessing a static pressure lower than the ambient pressure. The result is an exhaust-jet expansion to the wrong static pressure, hereby reducing the plug-nozzle performance.
The poor adaptation characteristics are a direct result of the physics pre-scribing base flow. If one would like to overcome the adaptation weakness, good understanding of the complex physics prescribing base flows seems to be a first requirement. Then, the acquired knowledge may help finding the best solution for the reduction of the performance-deteriorating effect. It seems, therefore, that gathering more information about the complex physics stipulating the base flow will prove to be a good investment.
1.2
Objectives
The adaptation to ambient pressure, relatively low weight, ease in vehi-cle integration and the absence of movable parts, makes the plug nozzle a strong competitor for inclusion in future air-breathing as well as non-air-breathing launchers. The adaptation capabilities, however, seriously de-teriorate in the transonic and supersonic flight regime. In these regimes low-pressure base flows are formed, resulting in aspiration drag and, more importantly, significant over expansion of the exhaust jet. For the per-formance of conventional nozzles, base flows were never assumed to play a major role. However, for plug-nozzle performance, they do which em-phasises the importance of good base-flow-physics understanding. The first objective of this study is, therefore, to understand the underlying processes determining the base flow, and to understand the effects of related param-eters using a suitable systematic approach.
Further, plug nozzles may be integrated into the launch vehicle in ev-ery way one can imagine. In order to do this the aft-part of the vehicle, the after body, has to be changed accordingly. The acquired knowledge on fundamental aspects of base flows, and their possible implications to the plug-nozzle overall performance, may result in new insights in conventional after-body optimisation or even in the development of completely new and exotic after bodies. The second objective of this study is therefore to in-corporate the acquired knowledge about base flows into the development of after bodies.
An additional base flow is formed because of truncation of the plug nozzle for engine thrust-to-weight optimisation reasons. The acquired knowledge about base flows may here lead to new insights in base-drag dependency on the different altitude-adaptation stages. The third objective is to incorpo-rate acquired base-flow knowledge into plug-nozzle base-flow understand-ing.
1.3
Approach
For a good understanding of base-flow physics both numerical and exper-imental investigations do not suffice. The problem is simply too complex. It requires an analytical approach.
Fluid flows in their most general form are being treated by the Boltzmann equations, describing the kinetic theory of microscopic interactions between molecules. However, in many fluid-dynamic problems more molecules take part in the process than there are stars in the ‘Milky Way’, making the problems time-consuming and practically insolvable in a reasonable period of time. Fluids in fluid-dynamic processes on these larger length scales start to behave in a macroscopic way. Let the Knudsen number (Kn) de-note the ratio between the microscopic (inter-particle distance) and
macro-scopic length scales. As the macromacro-scopic scale of the problem becomes much larger than the microscopic scale, Kn → 0, the fluid will start acting as a continuum. These problems may be treated with the classical continuum theory (Appendix A). As Kn < 0.001 the fluid flow may be considered a continuum, which is the case in most fluid-dynamic problems.
However, one should keep in mind that also in these problems, there are some phenomena which are concentrated in such small areas, that the local Knudsen number may become relatively high, for instance near stagnation points, where the starting boundary layer is of the same length scale as the inter-particle distance. Actually, every boundary layer interacts with the wall in a very small region. This is called the Knudsen layer. The flow conditions at the edge of the Knudsen layer provide the macroscopic flow equations with the necessary boundary conditions (AppendixB). The main macroscopic fluid-flow equations are the Euler (inviscid) and Navier-Stokes (viscous) equations. The Euler equations (A.17) can be found as a scaling limit of the Boltzmann equations. For the Navier-Stokes equations (A.1) this is much more difficult. Bardos, however, states in his overview of multi-scale analysis in fluid dynamics [4], that the Navier-Stokes equations and the Boltzmann equations should in some sense be embedded one into another, and one should be able to deduce each of them from the next one by some mathematical limit.
The conditions in which we are interested all have in common that they handle with fluids, which are dense enough to be described by the contin-uum theory. This enables us to use the Navier-Stokes equations, describing the conservation of mass, momentum and energy for a continuum. Further, since extreme pressures (> 1000 bar) and temperatures (< 30 K) are ex-cluded, the thermodynamic state of the treated gases is well described by the assumption of a perfect gas (A.5), in which the intermolecular forces are neglected. Within this assumption, radiation cooling, which is applied to every surface of hypersonic flight vehicles wherever possible [29], is excluded as well. Its cooling effect on the free-stream surface, as well as the base and the plug-ramp surface portions would somewhat change the outcome.
The key problem of this dissertation, compressible base flow in plug nozzles, is complex, because it consists of multiple processes. For conve-nience, the Navier-Stokes equations (A.1) may be transformed into a non-dimensional form (A.13). Since we assume reasonably high density and global length-scale values, high velocities, and low viscosity of gases, the global Reynolds number is in general very high (Re 1). This indicates that viscous effects are restricted to very small regions. However, it does not mean that its effects are negligible at all times. In cases of smooth plug-nozzle flows in which separation does not occur, it does, and the flow is well described by the Euler equations (A.17), which emerge from the non-dimensional Navier-Stokes equations (A.13) when adopting the correct length scales. Still near the wall there are viscous boundary layers, which are described by the boundary-layer equations (A.19), but they have
negli-gible effect on the inviscid region. This is certainly not the case in separated flows such as base flows. However, even on the length scales of the separate steady physical processes, occurring in base flow, the local Reynolds num-bers are large too (Relocal 1). Since the length scales of these separate
processes are asymptotically smaller or larger than the other, an asymp-totic approach may be adopted to tackle the complete base-flow problem, in which on the length scales of a specific separate process only that specific process is acting, and the others provide the boundary conditions. In this way, the base flow may be supposed to consist of multiple components, and these components might again consist of multiple sub-components.
In order to verify the approach and further made assumptions, the results need to be verified. This is done by comparison with experimental results, which are limited by the restriction of the experimental set-up.
1.4
Outline
The basis of plug-nozzle flow physics is treated in Chapter2. This chapter is concerned with the basic design, altitude-adaptation capabilities, incorpo-ration of an internal-expansion part, and an introduction to plug truncation and external-flow effects.
Plug truncation and external-flow effects introduce base-flow phenomena, which are further examined in Chapter 3. This chapter is devoted to the determination of base-flow parameters, description of the base-flow physical processes using an asymptotic approach, and the incorporation of these processes into a solution method for both symmetric and asymmetric base-flow configurations.
Then, the newly acquired knowledge is applied in Chapter 4 to plug--nozzle-related base flows, occurring due to truncation and external flows. Hereby, the effects of parameters affecting the base flows are explained as well as hysteresis effects.
In view of the strong relevance to base-flow behaviour and plug-nozzle performance, a number of topics related to after-body integration is treated in Chapter 5. In here, optimal shapes for the conventional boat tail are derived, as well as the treatment of a new exotic after-body geometry, the Ventilated Trailing-Edge Cavity (VTEC), which is a result of the new insights in base-flow and altitude-adaptation characteristics.
In Chapter6, the dissertation closes with the conclusions and recommen-dations resulting from this study.
2
Linear-Plug-Nozzle Flow
The basic contour design of the linear plug nozzle is a straightforward pro-cess, in principle based on the application of the inviscid irrotational su-personic Prandtl-Meyer flow theory [43] derived from the Euler equations (A.17). The contour is two-dimensional, since the segments are placed lin-early next to each other. The design conditions for a specific pressure ratio pc/p∞ of chamber pressure pc over external-flow static pressure p∞, and
in particular its off-design performance at pressure ratios lower than the design pressure ratio due to the adaptation capabilities to varying external-flow conditions, seem to make it the ideal nozzle which augments the ad-vantages of the conventional bell nozzle. However, the bell nozzle does have some advantages too over the plug nozzle. The bell-nozzle size and its after-body height is for instance smaller. It seems therefore wise to incorporate both the advantages into a hybrid nozzle. Let us first start introducing the basic sonic-inlet linear plug nozzle.
2.1
Linear-Plug-Nozzle Design
The basic design of a plug nozzle with sonic inflow [2] can be easily un-derstood. Let the sonic flow enter the plug nozzle with a certain tilt angle θthroat, see Fig. 2.1. At the lip of the vehicle aft end this flow gets in
con-tact with the ambient air, and a Prandtl-Meyer simple wave is thereby initiated. Now, the ramp of the plug nozzle is designed in such a way that
Figure 2.1. Schematics of the plug-nozzle design with sonic inflow.
the straight-line characteristics generated by the centred expansion fan are not disturbed by the reflected waves from the ramp. In other words, the ramp is a streamline of a centred expansion fan. In this way, inviscid thrust losses by means of the formation of shocks are prevented. As the flow is expanding to higher Mach numbers and lower static pressures, it is inclined towards the centreline direction, thereby approaching its design Mach num-ber Mdesign and design pressure ratio (pc/p∞)design.
Since the plug ramp is designed as a streamline of the Prandtl-Meyer flow the complete flow field can be described by a centred expansion fan. The Prandtl-Meyer angle reads
ν =r γ + 1 γ − 1arctan
r γ − 1 γ + 1(M
2− 1) − arctanpM2− 1, (2.1)
called after Prandtl and Meyer [43], being the turning angle of the flow from sonic to supersonic at a Mach number M . The derivation of this equation may be found in many textbooks on compressible flow, e.g. Anderson [1]. The deflection of the flow is constant along the straight characteristics shown in Fig. 2.1, and can be described by the sum of the initial throat angle θthroat and the Prandtl-Meyer angle ν: θ = θthroat+ ν. However, in
order to get a quantitative relation for the ramp, we need to specify the angle α and the length l of each expansion wave. For the angle α we find, since α = µ − θ:
α = µ − θthroat− ν, (2.2)
where µ is the Mach angle which is related to the Mach number: µ = arcsin 1
M. (2.3)
Since we assume continuity of mass, ρU A is constant over each character-istic line. Here, A is the passage area of the charactercharacter-istic line l normal to velocity direction, and is therefore described by: A = l sin µ = l/M . With the isentropic relations for density ρ and velocity U [1], continuity of mass gives: l lthroat = 2 γ + 1 1 + γ − 1 2 M 2 2(γ−1)γ+1 . (2.4)
Finally, we can write the relations for l, Eq. (2.4), and α, Eq. (2.2) into Cartesian co-ordinates (xramp, yramp) of the plug-nozzle ramp, reading
(xramp, yramp) = (l cos α, −l sin α) , (2.5)
where the origin of x and y is assumed at the lip.
So far, we have treated the design condition, but the main feature of the plug nozzle is its good off-design performance, at least for the con-dition where the ambient pressure is lower than the exit pressure (under expanded). The altitude-adaptation phenomenon is responsible for that good performance.
2.2
Altitude Adaptation
The altitude adaptation is the most attractive feature of the plug nozzle. It was briefly mentioned in the introduction, and is illustrated in Fig.2.2. It means that the plug nozzle is able to adapt its jet to the surrounding ambient pressure, without considerable thrust loss. The decreasing ambi-ent pressure with increasing altitude requires such an adaptable nozzle, especially for single-stage-to-orbit vehicles. Then, since the nozzle should carry the vehicle over the complete range of the launch, it would experi-ence even worse off-design conditions than multiple-stage vehicles, which may have different nozzle-design conditions for the multiple stages. There-fore, especially for single-stage-to-orbit vehicles the altitude adaptation is an indispensable feature. However, the adaptation is only present in under-expanded condition, illustrated in Fig.2.2a.
Hagemann [26], therefore, divides the plug-nozzle flow physics due to variations in nozzle pressure ratio pc/p∞ into three major categories: the
under-expanded condition in Fig. 2.2a, the design condition in Fig. 2.2b, and the over-expanded condition in Fig. 2.2c. The design condition has already been treated in the previous section. This condition is reached when the primary expansion to the ambient pressure results in a jet flow parallel to the centreline. For pressure ratios lower than that design pressure ratio (Fig. 2.2a), which actually occurs with increasing altitude, the altitude--adaptation process emerges.
First, we will explain which special phenomena are acting in the flow. There are actually four of these:
1. expansion waves reflecting from a solid body, 2. compression waves reflecting from a solid body,
3. expansion waves reflecting from a constant-pressure region, and 4. compression waves reflecting from a constant-pressure region.
(a) Under-expanded plug nozzle
(b) Plug nozzle, design condition
(c) Over-expanded plug nozzle
Figure 2.2. Flow phenomena on a plug nozzle at different pressure ratios pc/p∞.
These processes are illustrated in Fig.2.3. For instance in Fig.2.3a, we see the expansion waves reflecting from a solid surface, as for instance is the plug surface in Fig.2.2. This expansion wave turns the flow away from the body. In order to turn the flow back to the surface, the reflected waves have to be expansion waves too. If the body has a straight surface like in the figure, the reflected wave is of the same strength as the incoming wave. For compression waves reflecting from a solid surface, see Fig.2.3b, the reflected waves are compression waves of the same strength, in order to let the flow be able to follow the body surface. At a constant-pressure surface on the other side of the jet in Fig.2.2, the waves approach the constant-pressure region, see Fig.2.3c and d. As the expansion waves meet the boundary (Fig.2.3c), the pressure tends to decrease. In order to meet with the constant-pressure boundary condition, compression waves are reflected from the boundary with the same strength as the incoming expansion waves. Both, the incom-ing expansion waves as well as the reflected compression waves, deflect the
expansion waves
expansion waves
(a) Process 1: Expansion waves re-flecting on a solid body.
compression waves
compression waves
(b) Process 2: Compression waves reflecting on a solid body.
constant-pressure region
compression waves expansion waves
(c) Process 3: Expansion waves flecting on a constant-pressure re-gion.
constant-pressure region
expansion waves compression waves
(d) Process 4: Compression waves reflecting on a constant-pressure re-gion.
Figure 2.3. Reflected waves from a solid body and constant-pressure boundary.
flow inward. For approaching compression waves, see Fig.2.3d, the opposite occurs. In order to meet with the constant-pressure boundary, expansion waves are needed of the same strength, and both waves thereby deflect the flow outward. Concluding, we could say that assuming the body to be a flat surface, waves are reflected as waves of the same family and with the same strength, whereas from a region of constant pressure, waves are reflected as waves of the opposite family with the same strength.
In the case of the plug nozzle in under-expanded condition (Fig.2.2a), the ambient pressure is higher than for design conditions, so the flow will not fully expand to the centreline, but only to a certain point on the plug-nozzle ramp, where the ambient pressure is reached. Upstream of this point, we see expansion waves approaching the plug-nozzle ramp, which reflect from the ramp as neutral waves without strength. Behind the last expansion wave at which the ambient pressure was reached, the flow is initially uniform. How-ever, the plug ramp is concave, so the uniform flow is a little compressed, hereby generating compression waves. These compression waves are the ini-tiators of the adaptation process. First we see the compression waves being reflected at the constant-pressure region as expansion waves deflecting the jet upward (process 4, Fig.2.3). These expansion waves are then reflected
by the ramp as expansion waves (process 1), but with less strength because
of the compression from the concave ramp. These expansion waves are then reflected by the constant-pressure boundary as compression waves of the same strength (process 3). Finally, these compression waves are reflected
as compression waves at the plug ramp (process 2 ), and are somewhat
strengthened by the concave ramp. Note that again we have compression waves heading to the constant-pressure region, which means we arrived in process 4 again, and we will find the same processes again in the same
order: 4 // 1 2 OO 3 oo
Therefore, it is a continuous process which will eventually attenuate when the jet reaches the centreline. In this way a system of processes 1, 2, 3
and 4 adapts the exhaust flow gradually to the centreline direction, hereby
slowly fluctuating around the ambient pressure and not producing strong shocks. The absence of those shocks results in an almost ideal thrust, the attractive feature of the altitude-adaptation process.
On the other hand, at pressure ratios above the design pressure ratio (over expansion), see Fig. 2.2c, the dimensionless pressure distribution (p/pc) along the plug ramp remains the same as for the design pressure
ratio. Therefore, the ideal thrust will not be entirely reached. A different way to understand that thrust is lost in the over-expanded condition is to consider the entropy increasing shock. In inviscid flow, this is the only phenomenon which results in an entropy increase, and therefore a thrust loss. This shock can be found far downstream of the nozzle. It is neces-sary to deflect the flow back into the free-stream direction. First, take a look at the over-expanding expansion waves approaching the centreline in Fig.2.2c. Like in process 1, the expansion waves are reflected as expansion
waves of the same strength. Downstream, these expansion waves run into the constant-pressure boundary, where they will be reflected as compression waves, like in process 3 . These compression waves coalesce downstream
into the shock, responsible for the thrust loss.
In conclusion, we may say that the reason why the plug nozzle is so adaptable to altitude is that when the jet has expanded to the ambient pressure, the smooth concave form of the plug nozzle forces the jet to grad-ually deflect towards the centreline, according to the four altitude-adapting processes. This gradual adaptation avoids the production of strong thrust-decreasing shocks.
Figure 2.4. Schematics of the LION [24] internal/external-expansion nozzle.
2.3
Internal/External-Expansion Nozzle
The nice feature of the plug nozzle over the bell nozzle is its altitude-adaptive capability, however, some other properties of the bell nozzle are better. For instance, a bell nozzle is much smaller than a plug nozzle, hence weighs less, and its smaller wetted surface means less friction drag. Therefore, it seems plausible to combine these two and incorporate both their benign features into a new nozzle, the internal/external-expansion nozzle. One such nozzle is illustrated in Fig.2.4.
Let us build our new nozzle and start with a bell nozzle. The problem of the bell nozzle is its dramatic performance loss in the over-expanded condition, so this must be prevented. Assume now that the chamber pres-sure is limited to pc = 100 bar and the ambient pressure is always lower
than p∞= 1 bar, then the pressure ratio pc/p∞is always higher than 100.
Therefore, we do not need the altitude-adaptive capability up to this con-dition. The first part of the nozzle can be designed as an internal-expansion nozzle like the bell nozzle. Further downstream the pressure can become lower than the ambient pressure if the nozzle would maintain its bell-shape, and therefore this part can best be designed as a plug nozzle, the external-expansion part. Another feature of this internal/external-external-expansion plug nozzle is that the tilt angle is reduced significantly, thereby reducing the vehicle base too. This will become a very pleasant feature when we start considering the supersonic external-flow effects.
Different contour approaches can be used. In principle, a non-symmetric internal nozzle could be used to accelerate the flow to the desired uniform internal exit Mach number, which smoothly fits to the simple-expansion ex-ternal part. Another approach is to use a truncated symmetric bell-shaped nozzle, resulting in a non-uniform internal exit flow. The external plug con-tour has to be designed with the method of characteristics in such a way that the external plug nozzle exit will be uniform again. The symmetric internal nozzle’s benefit is the easy manufacturing. This approach is for instance used for the LION model [24] of Fig.2.4.
