Sådhanå (2021) 46:76 Indian Academy of Sciences

https://doi.org/10.1007/s12046-021-01584-6Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

Rocket nozzles: 75 years of research and development

SHIVANG KHARE1 and UJJWAL K SAHA2,*

1 Department of Energy and Process Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway 2 Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India e-mail: [email protected]; [email protected]

MS received 28 August 2020; revised 20 December 2020; accepted 28 January 2021

Abstract. The nozzle forms a large segment of the rocket engine structure, and as a whole, the performance of a rocket largely depends upon its aerodynamic design. The principal parameters in this context are the shape of the nozzle contour and the nozzle area expansion ratio. A careful shaping of the nozzle contour can lead to a high gain in its performance. As a consequence of intensive research, the design and the shape of rocket nozzles have undergone a series of development over the last several decades. The notable among them are conical, bell, plug, expansion-deflection and dual bell nozzles, besides the recently developed multi nozzle grid. However, to the best of authors’ knowledge, no article has reviewed the entire group of nozzles in a systematic and comprehensive manner. This paper aims to review and bring all such development in one single frame. The article mainly focuses on the aerodynamic aspects of all the rocket nozzles developed till date and summarizes the major findings covering their design, development, utilization, benefits and limitations. At the end, the future possibilities of development are also recommended.

Keywords. Rocket nozzle; aerodynamics; thrust; expansion ratio; nozzle contour; shock wave; method of characteristics; efficiency.

1. Introduction divided by the area of throat). Lesser design complexity and weight, maximum performance, and ease of manufacture The nozzles were invented with a primary motive to change are some of the main desirable features of a rocket nozzle. the flow characteristics such as velocity and pressure. In The development of novel rocket nozzles [10] for launch 1890, Carl Gustaf Patrik de Laval developed a convergent- vehicles faces a challenging design problem. In order to divergent (CD) nozzle that had the ability to increase a steam meet the performance of nozzle at higher altitudes, the jet to a supersonic state [1, 2]. A typical CD nozzle and the nozzles are designed with high area ratios. However, this variation of velocity, temperature, pressure across the length would generate over-expanded flow conditions when oper- of nozzle is shown in figure 1. This nozzle was termed as a de ated at sea level. A nozzle is said to be an over-expanded Laval nozzle and was later used for rocket propulsion. An one when its exit pressure is less than the ambient pressure. American engineer Robert Goddard was the first to integrate These conditions lead to an unsteady internal flow separa- a de Laval nozzle with a combustion chamber, thereby tion resulting in the generation of side loads which may increasing the rocket efficiency and attaining the supersonic cause damage to the whole launch system. The generation of velocities in the region of Mach 7 [2, 3]. high magnitude side loads inside the nozzles is one of the For space propulsion, the rocket [4, 5] is the main system most important issues under consideration in designing the that stores its own propellant mass and ejects this mass at reusable, robust, and efficient launch vehicles [11–13]. high speed in order to provide thrust. A rocket engine [6–9] generates this thrust by accelerating the exhaust gases to the desired speed and direction. In simple words, the nozzle 1.1 Brief overview utilizes the pressure generated inside the combustion Rocket nozzles comes in a variety of configurations like chamber to enhance the magnitude of thrust by accelerating ideal, conical, bell, plug, expansion-deflection (E-D) and the combustion products to a high supersonic velocity. The dual bell besides the recently developed multi nozzle grid nozzle exit velocity can be controlled by the nozzle (MNG). An ideal nozzle is defined as the one that produces expansion ratio or the area ratio (i.e., the exit area of nozzle an isentropic flow (i.e., without internal shocks) and gives a uniform velocity at the exit. The contour of such a nozzle *For correspondence can be designed with the help of method of characteristics 76 Page 2 of 22 Sådhanå (2021) 46:76

The first conceptual analysis of plug nozzles was conducted in 1950s [21]. Though the performance benefits were claimed in most of the literatures, however, the plug noz- zles did not gain the hardware flight status. In the future, this might change as the rocket engine having a linear plug nozzle is foreseen as the propulsion system for the RLV X-33 concept of the Lockheed Martin Corporation [21, 24, 25]. In the E-D nozzle, the flow from the chamber is directed radially outward and away from the axis of nozzle. The flow is diverted towards the curved contour of the outer diverging nozzle wall [26]. The hot gas flow moving out of the chamber expands around a central plug. The E-D nozzle concept had been the subject of various experimental and analytical investigations. These studies revealed the poor altitude-compensation capabilities of E-D nozzle and were in fact poorer than the plug nozzles Figure 1. Variation of velocity, temperature and pressure across because of over-expansion and aspiration losses. For noz- the length of a De Laval nozzle [2]. zles with high expansion-ratio and comparatively smaller length, an E-D nozzle performs superior than a comparable [14–16] (detailed in section 2). The conical type has his- bell nozzle of equal length. This is due to the lesser torically been the most common contour for rocket nozzles divergence losses as compared to the bell nozzle [24]. In a because of its design simplicity and ease of manufacture dual bell nozzle, two shortened bell type of nozzles are [16, 17]. In a conical nozzle, the exit velocity is essentially joined into one with an inflection point between them. In one-dimensional (1D) corresponding to the area ratio, but 1949, Cowles and Foster were the first to introduce the dual the flow is not in an axial direction across the outlet area bell concept, and it was patented by Rocketdyne in 1960s leading to performance loss due to flow divergence [27–29]. It is still in the conceptual stage but seems to be a [17, 18]. In the late 1930s and early 1940s, German sci- strong candidate for future rocket engines [30]. In recent entists performed extensive nozzle research [16, 19]by times, a newer concept of Multi Nozzle Grid (MNG) came considering all aspects of designing. They opined that there into the limelight where a thin and lightweight plate with was no major benefit in using contours with high com- multiple small nozzles can be used instead of a lengthy and plexities. However, this was applicable only for low area heavy single nozzle. The saving in length is in direct pro- ratio nozzles like V-2 rocket [16, 17]. Because of its high portion to the square root of the number of small nozzles divergence losses, the conical type short nozzles find their (nozzlettes) in MNG (i.e., MNG with hundred nozzlettes is application in small thrusters and solid rocket boosters, ten times smaller than an equivalent single nozzle) [31–33]. where simple fabrication is desired over aerodynamic per- formance [17]. On increasing the cone angle, the thrust loss of a conical nozzle gets enhanced due to flow divergence. 1.2 Present objective This thrust loss can be minimized by contouring the nozzle wall and this type is referred to as the bell nozzle. This is As evident from above, various shapes of rocket nozzles because, by doing this, the flow can be made to turn closer have been evolved over the past 75 years, however, there is to the axial direction [18]. Usually, the calculus of varia- not a single article that gives a comprehensive review of all tions is the simple and direct approach for designing the the types of nozzles developed till date. The present article nozzle contours [14, 18]. Guderley and Hantsch [20] mainly deals with the aerodynamic features of ideal, coni- investigated the problem of finding the nozzle exit area and cal, bell, plug, expansion-deflection, dual bell, and multi its contour to generate the optimum thrust for given values nozzle grid type rocket nozzles. The review summarizes all of ambient pressure and nozzle length. However, the the facts and figures in a systematic way incorporating method was not accepted widely until a simplified tech- several features of rocket nozzles such as design, devel- nique, as detailed later, was proposed by Rao [14]. In opment, utilization, benefits and limitations along with Ariane 5 Vulcan or Space Shuttle Main Engine (SSME), recommendations. the conventional bell-type nozzle was used to expand the propellant products [21]. On the other hand, the plug nozzle is an altitude-compensating type rocket nozzle, where a 2. Ideal nozzle traditional CD nozzle expands the flow to a fixed area ratio regardless of the freestream conditions. The free jet When there is a parallel uniform flow with the exit pressure boundary that acts as a virtual outer wall on a plug nozzle matching with the ambient pressure at the nozzle exit, the expands to match the freestream ambient pressure [22, 23]. nozzle thrust becomes maximum. Such type of nozzle is Sådhanå (2021) 46:76 Page 3 of 22 76 termed as an ideal nozzle. The ratio of area at exit Ae to uniform flow at the exit. To attain a uniform flow at exit, area at throat At of such a nozzle [18] can be expressed by the minimum length of the nozzle required for various Eq. (1). values of expansion ratio (computed for c = 1.23) is shown in figure 2 [3]. In computing these lengths of the nozzle, it "# = 1=2 ðÞcþ1 =2ðÞc1 ðÞ1=c ðÞc1 =c 1 2 Ae c 1 2 pa pa was found that at the downstream of throat, a sharp corner ¼ 1 At 2 c þ 1 Pc Pc should be eluded. Hence, a wall contour of a radius of ð1Þ curvature equal to 0.4 times the radius of throat was used [18, 43]. From figure 2, it is clear that the ideal nozzle that where c is the isentropic exponent. The ratio pa/pc is very gives the maximum thrust performance is heavy and less for the rocket engines working at high altitudes, and lengthy. The following sections deal with the ways of hence more expansion ratios for the ideal nozzles is needed. decreasing the length of nozzles without much decrement A rocket engine working over a wide range of altitudes will in the performance. give optimum performance when the nozzle expansion ratio is variable. Because of very high temperatures involved, the mechanical variation of expansion ratio is not easy. Thus, 3. Conical nozzle an appropriate fixed expansion ratio is selected by consid- ering the performance requirements over the complete path The application of a conical nozzle was very common in of the rocket. The performance of nozzle divergent section early rocket engines. The principal appeal of the conical can be calculated (Eq. (2)) in terms of its vacuum thrust nozzle is that it is easy to manufacture and it has the coefficient Cfv [18] and can be expressed as: flexibility of converting an existing design to lower or higher area ratio without much redesign. A typical conical Fv Cfv ¼ ð2Þ nozzle configuration is depicted in figure 3. On the basis of pcAt length, performance and weight, the best compromised a where F is thrust when discharging to vaccum, p and A diverging angle ( ) for a conical nozzle is 15 [17, 36, 44]. v c t are the combustion chamber pressure and area of the nozzle The thrust coefficient of a 15 conical nozzle is only 1.7% throat, respectively. The vacuum thrust coefficient of an lesser than the ideal nozzle and changes slightly with alti- ideal nozzle is a function of isentropic exponent c and the tude [18]. Thus, the performances and lengths of newer nozzles are often compared with a 15 conical nozzle. The nozzle area expansion ratio Ae/At. The thrust coefficient of an ideal nozzle [18] working in limitation of conical nozzle being heavier and longer can be mitigated by increasing the divergent cone half-angle (a). an ambient pressure pa, is given by In a conical nozzle, the performance loss takes place at a pa Ae lower altitude as higher ambient pressure leads to flow Cf ¼ Cfvi : ð3Þ Pc At separation and over-expansion. The major disadvantage of conical nozzles includes the trade-off between the diver- The above equation is known as the 1D thrust coefficient gence angle and the nozzle length [45]. equation. The flow divergence in the conical nozzle leads to a The uniform exit flow can be obtained when the nozzle reduction in thrust as the flow direction is not completely wall configuration is designed by the method of charac- teristics [14–16, 34]. With the help of this method, the system of partial differential equations can be converted to ordinary differential equations that are valid along the characteristic curves that represent the path of propagation of disturbances in supersonic flows. A characteristic may be defined as a curve along which the governing partial dif- ferential equations reduce to an ’interior operator’s that is a total differential equation known as the compatibility equation. Thus, along a characteristic, the dependant vari- ables may not be specified arbitrarily being compelled to satisfy the compatibility equation [35–39]. High-speed computing machines are required for the wall contour computation. Foelsch [40–42] gave an approximation through which the nozzle contour can be obtained by manual computation. The length of an ideal nozzle can be decreased by permitting all the expansion to occur just at Figure 2. Length (calculated) comparison of several types of the throat downstream and then constructing the nozzle nozzle (MNG: Multi Nozzle Grid, E-D: Expansion-Deflection contour to turn the flow such that it can attain an axial nozzle) [3]. 76 Page 4 of 22 Sådhanå (2021) 46:76

(NPR) shows that shock location moves towards the nozzle exit as the NPR increases. Balabel et al [49] studied the turbulent gas flow dynamics in a two-dimensional (2D) CD nozzle and the associated physical phenomena were anal- ysed for different operating conditions. Results showed that, in predicting the point of separation and the position of shock wave, the realizable v2–f and the SST (Shear Stress Transport)k–x models gave better results in comparison to other models. Hoffman and Lorenc [50] investigated 2D gas particle flow effects in conical nozzles. Wehofer and Figure 3. Typical configuration of a conical nozzle. Moger [51] developed an analytical method to predict the inviscid transonic flow fields linked with CD and conver- gent conical nozzles. Jia et al [52] analysed numerically the axial at the exit. Malina [46] showed that the momentum at influence of the fire-in-the-hole staging event on the flow the exit was equal to the value calculated from 1D theory separation at the start-up and side loads of a conical nozzle multiplied by a correction factor, k [16, 17]. during flight. Jia et al [53] further investigated numerically the three-dimensional (3D) side loads and the associated 1 þ cosa k ¼ ð4Þ flow physics of a conical nozzle during the fire-in-the-hole 2 staging event of a multistage rocket. Zmijanovic et al [54] The magnitude of correction factor, k decreases as a studied the transverse secondary gas injection into the increases as shown in figure 4 [46]. supersonic flow of a CD nozzle to explain the influence of The conical nozzle thrust coefficient working into the fluidic thrust vectoring within the framework of a small vacuum (Cfvc) is given below [18] satellite launcher. The results demonstrated the possibility of attaining pertinent vector side forces with moderate þ / q 2 pe Ae 1 cos eVe Ae secondary to primary mass flow rate ratios ranging around Cfvc ¼ : þ ð5Þ pc At 2 pcAt 5%. They also revealed that the geometry and injector positioning had a high influence on the nozzle performance q where e,Ve,pe are the 1D density, velocity and pressure at and shock vector control system. Figure 6 shows the the nozzle exit. injection port and the scheme of separation alongside Darwell and Badham [47] revealed the possibility of nozzle wall. Zhang et al [55] performed the computational shock formation within the nozzle by the method of char- investigation of convergent conical nozzles. The influences acteristics. They found that by modifying the wall contour of base drag and the freestream Mach number on the cal- near the junction of the throat profile and the cone, the culated velocity coefficient were analysed. Sunley and shock formation could be eliminated. Khan and Shemb- Ferriman [56] carried out tests to study the jet separation in harkar [48] explained that one can capture the flow in a CD conical nozzles, and demonstrated that the pressure at nozzle in an overexpanded flow regime by employing a which the gas separates was neither constant nor computational fluid dynamics (CFD) code. They computed the flow features like after-shocks, location of shocks and lambda shocks in the CD nozzle. The centreline static pressure plot (figure 5) for different nozzle pressure ratio

Figure 5. Centreline static pressure (measured) plot for different Figure 4. Variation of k with a in graphical form [46]. nozzle pressure ratio (NPR) [48]. Sådhanå (2021) 46:76 Page 5 of 22 76

expansion of the working fluid that do not permit separation in this portion unless there are discontinuities in the nozzle contour [3]. The length of bell nozzle is generally given as a fraction of the reference conical nozzle length. As seen in figure 7, an 80% bell nozzle configuration that has the same expansion ratio (e)as15 half angle conical nozzle is 20% smaller in length. The exit angle of 80% and 60% bell nozzles are 8.5 and 11, respectively [3]. A near optimum contour of the bell nozzle can be designed by using a simple parabolic approximation pro- cedure given by Rao [14, 59, 60]. The parabolic approxi- mation of the bell nozzle design is shown in figure 8 [36], where at the upstream of throat T, the nozzle contour is a Figure 6. Scheme of the separation alongside nozzle wall [54]. circular arc whose radius is 1.5Rt. From T to the point N, the divergent portion of the nozzle contour is made up of a circular entrance section of radius 0.382Rt and from N to the exit E, it is a parabola [36]. independent of the nozzle length. Migdal and Kosson [57] The required data for the design of a specific bell nozzle studied the shock predictions in conical nozzles. Migdal are: diameter of throat Dt, initial wall angle of the parabola and Landis [58] investigated the performance of conical hn, nozzle exit wall angle he, area ratio e and nozzle axial nozzles by the application of method of characteristics. length from throat to exit plane Ln (or the desired fractional Table 1 summarizes the various numerical, experimental length Lf, based on a 15 conical nozzle) [36]. The varia- and analytical studies in the area of conical nozzles tions of wall angles hn and he with the expansion ratio at addressing the aerodynamic aspects such as flow separation different values of Lf are shown in figures 9 and 10, and the shock formation. respectively. It is evident in figure 9 that by increasing the expansion ratio of the bell nozzle, the value of hn increases. For a particular expansion ratio, the magnitude of hn is 4. Bell nozzle larger for lower fractional nozzle length. By choosing proper inputs, the optimum nozzle contours can be The bell type nozzle is the most commonly used shape in approximated. rocket engines. This category of nozzle provides significant The thrust loss can be minimized by contouring the benefits in terms of performance and size over the conical nozzle wall, as by doing this, the flow can be made to turn type nozzle. It has a high angle expansion section (20 to closer to the axial direction [18]. For contouring the nozzle 50) right behind the nozzle throat. This is followed by a walls, various methods have been suggested in the litera- gradual reversal of nozzle contour slope so that at the ture. Dillaway [61] computed nozzle contours by gradually nozzle exit the divergence angle is small, preferably below reducing the slope of nozzle wall as one approaches 10 half angle. It is possible to have large divergence angles towards the nozzle exit. In a contoured nozzle, there is a immediately behind the throat (20–50) because the high high dependency of exit flow on the nozzle contour and no relative pressure, the large pressure gradient, and the rapid simple relation such as Eq. (5) can be derived. The

Table 1. Major studies conducted on conical nozzle.

Investigators Year Nature of study Focus of study Migdal and Landis [58] 1962 Numerical Performance of conical nozzles Darwell and Badham [47] 1963 Numerical Shock formation Sunley and Ferriman [56] 1964 Experimental Jet separation Migdal and Kosson [57] 1965 Numerical Shock predictions Hoffman and Lorenc [50] 1965 Numerical Gas-particle flow effects Wehofer and Moger [51] 1970 Analytical Inviscid transonic flow fields Khan and Shembharkar [48] 2008 Numerical Location of shock Balabel et al [49] 2011 Numerical Turbulent gas flow dynamics Zmijanovic et al [54] 2014 Experimental and Numerical Fluidic thrust vectoring Zhang et al [55] 2015 Numerical Convergent conical nozzles Jia et al [52] 2015 Numerical Flow separation and side loads Jia et al [53] 2016 Numerical Side loads 76 Page 6 of 22 Sådhanå (2021) 46:76

Figure 7. Comparison of a 15conical nozzle (reference nozzle) h with 80% and 60% bell nozzles, all at an expansion ratio e of 25 Figure 10. Variation of wall angles e (calculated) with the e [3]. expansion ratio at different values of Lf (Lf = desired fractional length (m) [36].

of nozzle. The velocity (V), direction (h) density (q), and pressure (p) are calculated at a distance r from the axis of nozzle in the exit plane. According to Landsbaum [62], one can analyse the various truncated ideal nozzles of different expansion ratios and select the one which gives the best performance [63]. Farley and Campbell [64] investigated such truncated ideal nozzles experimentally and the results were found to be very close to the theoretical values. Figure 8. Parabolic approximation bell nozzle design configu- Ahlberg et al [65] presented the graphical technique for ration [36]. choosing the optimum nozzle contours from a family of truncated perfect nozzles. Rao [14] developed a method by using the calculus of variations to design the wall contour of the optimum thrust nozzle. For the same performance as that of 15 conical nozzle, the length required for the bell nozzle is shown in figure 2. Allman and Hoffman [66] examined a technique for the design of maximum thrust nozzle contours using direct optimization methods. The contour of the nozzle was given by second-order polynomial:

2 yðxÞ¼Aw þ Bwx þ Cwx ð7Þ

where the coefficients Aw,Bw, and Cw are determined by mentioning the attachment angle, the exit radius and by requiring that the polynomial contour attach continuously to the circular-arc initial expansion contour. The authors

Figure 9. Variation of wall angles hn with the expansion ratio e compared thrusts developed by the calculus of variation at different values of Lf [36]. contours (Rao’s method) with the thrusts generated by polynomial contours. It was concluded that both the methods predict essentially the same maximum thrust (i.e., contoured nozzle vacuum thrust coefficient can be evalu- for zero ambient pressure, the agreement was within 0.2%) ated as [18] justifying the proposed technique. Z Z p qV2cosh Frey et al [67] presented a new nozzle contouring tech- C ¼ 2prdr þ 2prdr ð6Þ fv p A p A nique called TICTOP (figure 11), merging both Truncated Ae c t Ae c t Ideal Contour (TIC) and Thrust Optimized Parabolic (TOP) where the integration is performed throughout the whole designs. The nozzle obtained is shock-free as the TIC area Ae of the exit plane, which is perpendicular to the axis design and does not induce restricted shock separation Sådhanå (2021) 46:76 Page 7 of 22 76

(RSS) which leads to high side loads. Simultaneously, it magnitude of which showed a high dependence on the permits a higher nozzle wall pressures at exit giving a better contour of nozzle. Asymmetry in flow separation was also margin of separation than the TOP design. Pilinski and observed at particular pressure ratios. Hagemann et al [78] Nebbache [68] analysed the separated flow numerically at tested two different types of nozzle, a thrust optimized and various NPRs in a TIC nozzle and the pattern of a free a truncated ideal nozzles, for the same performance data to shock separation (FSS) was obtained for very low and high explore the origin of different side loads. Results demon- pressure ratios. Between these two ranges of pressure strated the highest side load in the thrust optimized nozzle ratios, an uncommon cap shock pattern without reattach- when the separation pattern changed from free to restricted ment of the boundary layer appeared. Verma et al [69] shock separation. The side load measured in the truncated conducted tests campaign on a sub-scale TOP nozzle in ideal nozzle was only about 33.33% of side load in the order to investigate the link between unsteady characteris- thrust optimized nozzle. The comparison of both the nozzle tics of separation and reattachment shocks and the source of contours is shown in figure 12. Stark and Wagner [79] side loads in rocket nozzles. Lawrence and Weynand [70] performed tests to analyse the TIC nozzle flow field at low studied the separated flow in 2D and axisymmetric nozzles NPR. For NPR less than 10, a convex and for NPR greater having various wall contours. Nguyen et al [71] investi- than 20, a slight concave shaped Mach disks were found. gated the turbulent flow separation in an overexpanded Terhardt et al [80] studied the side-loads and flow separa- TOC nozzle. Nebbache and Pilinski [72] carried out com- tion in a TIC type nozzle experimentally and analytically. putational investigation of the flow in a TOC nozzle and Zhang et al [12] studied numerically the aeroelastic sta- analysed the structures of flow separation at various pres- bility for a rocket nozzle at the start-up. It was reported that sure ratios. Potter and Carden [73] described a method to the aeroelastic behaviour of rocket nozzles were strongly design the nozzles for low-density, high-speed flows with a dependent upon the wall thickness and the material prop- focus on treatment of very thick laminar boundary layers. erties of the wall. A comparison of different nozzle con- Baloni et al [74] performed 2D axisymmetric flow inves- tours is given in table 2, while the summary of major tigation within the bell type nozzle at off-design and design studies on bell nozzle is shown in table 3. conditions with the help of CFD software Fluent 6.3.26 and GAMBIT 2.4.6. Numerical simulation was conducted separately for two different flow conditions, i.e., hot and 5. Plug nozzle cold. Verma et al [75] carried out an experimental study to The plug nozzle is an advanced rocket nozzle that consists identify the source of several flow conditions that led to the of a primary nozzle whose shape is somewhat conventional generation of side load in a TIC nozzle. The main con- and a plug that helps an external expansion. The main tributors were found to be the transition in flow conditions, characteristics of this nozzle is its interaction with the i.e., the change in the circumferential shape of recirculation external ambient that can avoid the separation of flow portion inside the nozzle from a cylindrically dominated phenomena that affects a conventional bell nozzle. Such regime to a conical one and the end-effect regime that benefits arise from the generation of expansion fan at the initiated a highly unsteady condition of flow in the sepa- primary nozzle lip and its influence on the pressure beha- ration region preceding these transitions. Stark and Wagner viour along the plug wall [36]. [76] studied the separation of boundary layer and the The use of plug-type nozzles has been analysed inten- related flow field in a TIC nozzle. Verma [77] performed sively in recent years because of their various attractive experiments to investigate the separation of flow in a TIC performance and design features. The basic concept of a nozzle and reported that the off-design over-expanded plug nozzle is not new. The manufacturers of propulsion nozzle flow was dominated by shock-induced boundary systems and the Lewis Research Centre of NASA have layer separation that demonstrated fluctuating characteris- investigated their characteristics for several years [81]. The tics. The separation shock fluctuates back and forth, the early turbojets of Germany installed them to attain variation

Figure 11. The TICTOP design [67]. Figure 12. Comparison of Thrust optimized contour and Trun- cated ideal contour type nozzles [78]. 76 Page 8 of 22 Sådhanå (2021) 46:76

Table 2. Comparison of various nozzle contours.

Nozzle type Key features Conical Straight walls from throat to exit, incomplete flow turning Truncated ideal contour (TIC) Curved walls near throat transition to nearly straight walls near the exit, virtually complete flow turning, shortened version of the method of characteristics Thrust optimized contour (TOC) Curved walls near throat transition to nearly straight, walls near the exit, more sudden transition than TIC, virtually complete flow turning Thrust optimized parabola (TOP) Parabolic approximation of TIC, higher wall pressure at exit reduces risk of side loads

Table 3. Major studies conducted on bell nozzle.

Investigators Year Nature of study Focus of study Dillaway [61] 1957 Analytical 3D analysis of supersonic contoured nozzles Rao [14] 1958 Analytical Method to optimize the wall contour of nozzle Landsbaum [62] 1960 Numerical Design of bell-shaped nozzle contours Farley and Campbell [64] 1960 Experimental Cut off portions of ideal nozzles Ahlberg et al [65] 1961 Experimental and Numerical Optimization of truncated portions of ideal nozzles Lawrence and Weynand [70] 1968 Experimental Separated flow in 2D and axisymmetric nozzles having various wall contours Potter and Carden [73] 1968 Experimental and Numerical Design of nozzles for low-density and high-speed flows Terhardt et al [80] 2001 Experimental and Analytical Flow separation and side-loads in TIC nozzles Verma [77] 2002 Experimental Flow separation phenomena in a TIC nozzle Hagemann et al [78] 2002 Experimental Origin of side load in TIC and TOP Nguyen et al [71] 2003 Experimental Turbulent flow separation in TOC nozzles Pilinski and Nebbache [68] 2004 Numerical Separated flow in a TIC nozzle Verma et al [69] 2006 Experimental TOP nozzle Nebbache and Pilinski [72] 2006 Numerical Flow in an axisymmetric overexpanded TOC nozzle Stark and Wagner [79] 2006 Experimental Analysis of flow field in a TIC nozzle at low NPR Stark and Wagner [76] 2009 Experimental Boundary layer separation in a TIC nozzle Frey et al [67] 2017 Numerical TIC and TOP design Baloni et al [74] 2017 Numerical 2D axisymmetric flow analysis within the bell type nozzle Verma et al [75] 2017 Experimental Origin of side-load generation in TIC nozzle Zhang et al [12] 2017 Numerical Aeroelastic stability

of throat area [82]. The main attraction of a plug nozzle is Plug nozzles refer both to a full spike and a truncated that it is altitude compensating. In other words, where a spike nozzles. The contoured, full-length spike nozzle is conventional CD nozzle expands the flow to a fixed area normally referred to as a spike; while a conical, full-length ratio regardless of the freestream conditions, the free jet spike nozzle is defined as plug nozzle. The aerospike comes boundary that acts as a virtual outer wall on a plug nozzle from the idea of introducing an additional flow into the base expands to match the freestream ambient pressure. This region of the truncated spike, forming an ‘‘aerodynamic feature is useful for rockets used in launch vehicles, where spike’’ with the base flow. Basically, the base flow helps fill the NPR can range from low magnitude at launch to infinity in the area underneath the base and supports make up for in the vacuum of space. The schematic of the flow field near the performance loss from truncating the nozzle [3, 36, 85]. a plug nozzle at varying NPR is shown in figure 13 [83, 84]. The plug nozzle throat is situated as an annulus at the At or above design NPR, the plug nozzle behaves like a outer diameter (not all plug nozzles utilize an annular conventional CD nozzle ejecting the exhaust gases straight throat; some use engines clustered on a shared plug) with back axially (at design), or, resulting in a typical under- the exhaust gases flowing in an inward direction. At the expanded flow condition. For NPRs lesser than the design annulus outer edge or cowl-lip, the exhaust gases expand value, the jet boundary is pulled nearer to the plug by a suddenly to the ambient pressure. The expansion waves series of compression waves and expansion fans that occur generating from the cowl-lip controls the flow of exhaust naturally in an attempt to match the ambient pressure [84]. gases and the flow turning is affected by the surface of the Sådhanå (2021) 46:76 Page 9 of 22 76

Figure 13. Flow field of a plug nozzle with full length at different pressure ratios pc/pa, off-design [pc/pa \ (pc/pa)design] left, [pc/pa [ (pc/pa)design] right and design pressure ratio (centre) [83, 84]. plug. The design of the plug surface is such that the expansion of gases from a chamber pressure pc to an ambient pressure pa can take place smoothly producing a uniform flow at exit parallel to the axis of nozzle. The external diameter of such an ideal plug is same as the exit diameter of a uniform flow CD nozzle expanding the gases to the same ambient pressure pa. However, the plug nozzle is much smaller than an equivalent CD nozzle [18]. Krase [82] suggested simple approximate methods to design ideal plug nozzle contours by manual calculations. Berman and Crimp [81] studied the performance compar- ison between the conventional and the plug nozzles. As seen in figure 14, the plug nozzle shows a thrust benefit over a conventional nozzle when it is working at below design pressure ratio as the nature of flow in this case is Figure 14. Comparison of theoretical performances (calculated) self-adjusting [81, 86, 87]. of conventional and plug nozzles [81, 86, 87]. Rommel et al [21] performed computational investiga- tion of a plug nozzle and gave an understanding of the development of flow field at various ambient pressures. Figure 15 shows a typical conventional nozzle, a truncated and a full length plug nozzle. Ito et al [88] investigated the flow fields of a plug nozzle with the help of a numerical simulation. They designed the plug contour by the method of characteristics and various types of plug nozzles were considered by truncating the nozzle length at various positions. Results showed an increase of thrust performance of the contoured plug nozzle by about 5 to 6% than the Figure 15. Typical (a) conventional nozzle, (b) truncated nozzle conical plug nozzle, and the pressure distribution on the and (c) full length plug nozzle [21]. nozzle surface was unaffected by the external flow for the pressure ratios more than the designed point. Chutkey et al its design. Johnson et al [92] presented an optimization [89] analysed the flow fields associated with truncated analysis for plug nozzles with variable inlet geometry. annular plug nozzles of varying lengths. On the other hand, Besnard et al [93] presented the design, manufacturing and Shahrokhi and Noori [90] studied the flow properties of tests of a 1000 lbf thrust ablative annular aerospike engine. various aerospike nozzle shapes. They used the k-e turbu- Results showed that variations in c with temperature led to lence model and Navier-Stokes equations for the simulation small, albeit not null, differences in thrust and plume of flow field. A uniform cubic B-spline curve was used to characteristics. Further, the nozzle was found to be very generate the various plug shapes, and the best configuration efficient. Lahouti and Tolouei [94] carried out numerical was determined by considering the total thrust force as a modelling of external and internal flows of a truncated plug performance merit. Kumar et al [91] discussed the proce- nozzle with several amounts of base bleed in under-ex- dure to design a plug nozzle and the parameters governing pansion, optimum and over-expansion working conditions 76 Page 10 of 22 Sådhanå (2021) 46:76 to obtain the nozzle’s base thrust, base pressure distribution plug end. The approach that is used to optimize the contour and flow pattern. A variation of the non-dimensional total of conventional nozzles can also be used to optimize the base thrust (CFbase) with the pressure ratio (pa/pdes) for plug contour. The solution of such problems was discussed different amount of base bleed is shown in figure 16. by Rao [98], where he presented typical optimum plug Shanmuganathan et al [95] carried out the study of linear, contours. By the use of a plug, the reduction in length of the annular aerospike nozzles and the characteristics of its flow nozzle can be obtained as indicated in figure 15. field. They opined that the annular aerospike nozzle was As compared to other types, the major disadvantage of a better than the linear aerospike nozzle. plug nozzle lies with its high cooling requirements because The central plug body truncation is beneficial because it of higher heat fluxes and greater surface areas to be cooled eliminates the huge ideal length and heavy structural mass [21, 36]. The central plug of a spike nozzle if heated to of the well contoured body, and this truncation results in a higher values (greater than the material limitations) would different flow and performance behaviour as compared to require a secondary cooling system to be installed to cool the full length plug [3, 96]. At lesser pressure ratios, an open the plug and prevent failures. Overcoming this problem wake flow is established with a pressure level equal to the using secondary active cooling system greatly affects the ambient pressure. At a certain pressure ratio close to the mass of vehicle. The summary of major numerical and design pressure ratio of the full length plug nozzle, the base experimental studies of plug nozzles is shown in table 4.In flow suddenly changes its character and turns over to the case of plug nozzles, the key areas that have drawn atten- closed form, characterized by a constant base pressure that tion to the researchers are the optimization of the nozzles’ is no longer affected by the ambient pressure. Analyses contour and their truncation. indicated that smaller plug bodies with higher truncations leads to an earlier change in wake flow at pressure ratios below the design pressure ratio [24]. At the point of tran- 6. Expansion-deflection nozzle sition, the pressure inside the wake reaches below the ambient pressure, and the full base area generates a negative The expansion-deflection (E-D) nozzle is an altitude com- thrust. This loss of thrust depends on the percentage of pensating type rocket nozzle where the altitude compen- truncation and the total size of the base area. The results sation is attained through the interaction of exhaust gas demonstrated an increase in the thrust loss for smaller plug with the atmosphere. It looks similar to a bell nozzle, but a bodies as the total base area increases. Beyond the pressure ’pintle’ or ’centre body’ is placed at the throat and because ratio at transition, the pressure inside the closed wake of that the flow is diverted towards the wall [26]. The remains constant. A further decrease of the ambient pressure benefit with the centre body is that it makes the exhaust gas leads to a positive thrust contribution of the total base area to flow in a more outward direction than in bell nozzles. [24, 83]. An experimental investigation by Ruf and Due to this, the size of the nozzle decreases considerably as McConnaughey [97] stated that a 50% truncation of the plug compared to the conventional nozzles of the same expan- nozzle resulted in only a 0.5% reduction in its performance. sion ratio. This nozzle works in closed and open wake In order to avoid a flat base at the vertex of plug after the modes. In closed wake mode, the entire exit area of nozzle truncation, a larger cone angle could be used at the plug end. is filled by the exhaust gases. The ambient pressure at Berman and Crimp [81] showed the performance decrement which the transition of wake takes place from open to of only 1% by using cone half angles, even up to 30 at the closed modes is known as the design pressure. If the ambient pressure is further decreased, then the remaining expansion would occur outside the nozzle just like a bell nozzle and in that case there is no benefit of altitude compensation. In open wake mode, the ambient pressure controls the exit area of nozzle and the exhaust gas does not fill the complete nozzle. As the area ratio is controlled by the ambient pressure, the altitude compensation is achieved up to the design pressure [99, 100]. When there is a high chamber to ambient pressure ratio (pc/pa), the performance of the E-D nozzle is similar to that of a plug nozzle [18]. However, when the pressure ratio is lesser, the flow in a plug nozzle adjusts itself to the pressure at the cowl-lip. On the other hand, in an E-D nozzle, the flow adjusts itself to the pressure occurring behind the central plug. The combustion chamber of the E-D nozzle is small in size, and it has thus some benefits regarding Figure 16. Variation of total base thrust (calculated) with cooling requirements and weight. When a nozzle with very ambient pressure for different base bleeds [94]. Sådhanå (2021) 46:76 Page 11 of 22 76

Table 4. Major studies conducted on plug nozzle.

Investigators Year Nature of study Focus of study Krase [82] 1959 Numerical Design of ideal plug nozzle contours Berman and Crimp [81] 1961 Analytical Modification of plug end Rao [98] 1961 Numerical Optimization of plug contours Johnson et al [92] 1974 Numerical Optimization for axisymmetric plug nozzles Rommel et al [21] 1997 Numerical Flow field development at different ambient pressures Ruf and McConnaughey [97] 1997 Numerical Truncation of plug nozzle Ito et al [88] 2002 Numerical Designing of plug contour Besnard et al [93] 2002 Experimental Design and testing of thrust ablative annular aerospike engine Lahouti and Tolouei [94] 2006 Numerical External and internal flows of a truncated plug nozzle with base bleeds Shahrokhi and Noori [90] 2010 Numerical Flow properties of aerospike nozzle shapes Chutkey et al [89] 2014 Numerical Flow fields in truncated annular plug nozzles of varying lengths and Experimental Shanmuganathan et al [95] 2015 Numerical Flow field study of linear and annular aerospike nozzles Kumar et al [91] 2017 Numerical Design procedure of aerospike nozzle and Experimental

high expansion ratio is required, the best choice is an E-D nozzle because of its compact sized combustion chamber and smaller length [18]. Rao [101] studied the flow between the walls of the combustion chamber and the plug by using a series expansion and described the method of designing the optimum nozzle wall contour. Results showed that for the same performance as that of bell nozzle, the length of an E-D nozzle required was only 50% to that of bell nozzle length. The variation of the various nozzles thrust coeffi- cient with the altitude is shown in figure 17 [101]. Schomberg et al [100] studied the dependency of thrust coefficient on the E-D nozzle geometry when the flow conditions were highly over-expanded. Results show that the nozzle thrust depends upon the rate of change of area through the transonic region and the linear E-D type nozzle Figure 17. Variation of various nozzles thrust Performance has shown a higher thrust as compared to conventional (calculated) with altitude (E-D: Expansion-Deflection nozzle) nozzle when the flow conditions are highly over-expanded. [101]. The flow behaviour in open and closed modes in the E-D nozzle is shown in figure 18 [100]. Schomberg and Olsen [102] designed and tested the E-D nozzle at different theoretical altitude and were compared to experimental pressure ratios to represent operation over a range of the- static pressure readings and schlieren images. The corre- oretical altitudes (figures 19 and 20). They reported the lation between experimental and numerical static pressure efficiency of E-D nozzle to be more than the conventional values were found to be high for all operating conditions. CD nozzle. Wasko [103] studied the performance of plug Currao et al [105] reported the use of Pressure-Sensitive and E-D nozzles where the influence of base bleed were Paint (PSP) and infrared camera to a small linear asym- also analysed. Results showed that the performance of full metric nozzle. Their project aimed to validate numerical length plug nozzle was better, whereas the performance of results through the PSP measurements. Taylor et al [106] the E-D nozzle was only comparable to that of a conical CD studied the evacuation effect in E-D nozzles. Mueller and nozzle. Schomberg et al [26] compared the linear variant of Hall [107] analysed the region of separated flow within a an E-D nozzle to a conventional CD nozzle through an E-D type nozzle. Taylor and Hempsell [108] carried out the experimental investigation, and demonstrated that the thrust optimization of E-D nozzles for vacuum thrust. The major coefficient in the E-D type nozzle was 25–100% more than experimental and numerical studies in the area of E-D the CD nozzle across the tested range of pressure ratios. nozzles are summarized in table 5. In most of the cases, Schomberg et al [104] carried out numerical analysis of they are related to the design of optimum wall contour of E-D and CD nozzles. Results were noted over a range of nozzle, flow separation, and evacuation effects. 76 Page 12 of 22 Sådhanå (2021) 46:76

Figure 18. E-D nozzle flow behaviour in a open mode and b closed mode [109].

contour that is separated from the extension contour by an inflection in the wall. [110, 111] In 1949, Cowles and Foster first introduced the concept of a dual bell nozzle, and the design was patented by Rocketdyne in the 1960s [27–29]. As the CFD capabilities developed with time, the research activities gained attention in the 1990s. The confirmation of the feasibility of this nozzle was done by Horn and Fisher [27] by conducting tests at Rocketdyne and in Europe by the Future European Space Transportation Investigations Programme (FESTIP) at the European Space Agency (ESA) [27]. They investi- gated four contour combinations to find the extension contour that provided the most favourable flow transition characteristics and high altitude performance as compared Figure 19. Pressure distribution at a 450 kPa inlet [102]. to the performance of two baseline contours. The perfor- mance of the dual bell nozzles was demonstrated to be lesser than the theoretical optimum because of the losses linked with aspiration drag during low-altitude mode and non-optimum contour in high-altitude mode. Horn and Fisher found that even with such losses, a dual bell nozzle could deliver sufficient thrust to carry 12.1% additional payload as compared to a conventional CD nozzle having the identical expansion ratio. The first numerical analysis of dual bell nozzles was done by Goel and Jensen, which was published in 1995 [112]. Throughout the 2000s, in Europe and in the United States, various experimental and numerical investigations of dual bell nozzles were per- formed [24]. Modern studies focus on optimizing particular design variables of the dual bell nozzle such as the ideal contour and relative length of the extended section. With the help of nozzle wall inflection, this nozzle gives Figure 20. Pressure distribution at a 550 kPa inlet [102]. an altitude adaptation. Controlled and symmetrical sepa- ration of flow takes place at this wall inflection at low 7. Dual bell nozzle altitudes which leads to a less effective expansion ratio. The flow in the nozzle is attached to wall at higher altitudes Dual bell nozzles have been seen as a solution to maximize until the full geometrical expansion ratio is utilized. An the efficiency at high altitudes while eluding hazardous side improved vacuum performance is attained due to the higher loads at lower altitudes. As can be seen in figure 21, a dual expansion ratio [110, 113]. However, some additional bell nozzle consists of two different contours as opposed to performance losses are induced in dual bell nozzles. The one between the throat and exit. It is composed of a base main benefits of this nozzle lie with the control of flow Sådhanå (2021) 46:76 Page 13 of 22 76

Table 5. Major studies conducted on E-D nozzle.

Investigators Year Nature of study Focus of study Rao [101] 1960 Numerical Method of designing nozzle wall contour to yield optimum thrust and Experimental Mueller and Hall [107] 1968 Experimental Region of separated flow Wasko [103] 1968 Experimental Effects of base bleed Taylor and Hempsell [108] 2004 Numerical Optimization of E-D nozzles for vacuum thrust Taylor et al [106] 2010 Experimental Analysis of the evacuation effect in E-D nozzles Schomberg and Olsen [102] 2012 Experimental Designing and testing of E-D nozzles at different pressure ratios Schomberg et al [100] 2014 Numerical Effect of E-D nozzle geometry on calculated thrust coefficient and Experimental Schomberg et al [26] 2014 Experimental Comparison of linear variant of the E-D nozzle to a conventional CD nozzle Schomberg et al [104] 2014 Numerical Analysis of annular CD and E-D nozzles Currao et al [105] 2014 Experimental Application of PSP and Infrared camera to a small linear asymmetric nozzle

Figure 21. A typical dual bell nozzle.

separation and its design simplicity. While other altitude Figure 22. Two operation modes of dual bell nozzle: a sea level and b altitude mode [115]. compensating nozzle concepts have the limitations of mechanical complexity, cooling difficulty, and more weight and price tag. The dual bell nozzle provides an exceptional in an increase in the NPR. At a particular height, the blend of simplicity, lesser weight, performance and ease of transition NPR is reached and the separation point leaves cooling [24]. the contour inflection and moves rapidly to the nozzle exit. Kbab et al [114] designed the profile of a dual bell nozzle The extension then flows full (figure 22b). The thrust is and studied the flow behaviour using the method of char- enhanced due to the greater area ratio. acteristics. Genin et al [115] conducted experimental and The variation of specific impulse with altitude for a dual numerical studies on a dual bell nozzle for the evaluation of bell and two conventional nozzles is shown in figure 23 heat flux distribution. For both the operation modes (sea [115]. Schneider and Genin [116] analysed the effect of level and altitude), the heat flux value was found to increase various turbulence models and feeding pressure gradients in the region of the contour inflection. The heat flux value on the dual bell flow transition behaviour. They found increased by about 40% in altitude mode. In sea level mode improved results for the Reynolds stress turbulence and and during the sneak transition, the flow separation in the Spalart–Allmaras model. Genin et al [117] tested a planar region of the inflection increases this phenomenon. The two dual bell nozzle model under several test conditions in cold operation modes of a dual bell nozzle are depicted in fig- and hot flows. The analysis of the shock in the region of the ure 22. Under sea level conditions, the flow separates at the contour inflection gave an idea of the shape and position of contour inflection in a controlled and symmetrical way the separation front. In sea level mode, the numerical and (figure 22a). The generation of side load is continued to experimental results were in good agreement; and for decrease and the thrust enhances due to the small area ratio. higher NPR values, the calculated separation position was During flight, the ambient pressure reduces, which results situated further upstream than measured in the experiments. 76 Page 14 of 22 Sådhanå (2021) 46:76

Stark and Genin [118] studied the characteristics of side 7.1 Extendable nozzles load in a dual bell nozzle. Verma et al [119] did experi- mental investigation to study the Reynolds number effect Extendible nozzles were used as a substitute to dual bell on transition behaviour of dual bell nozzle for tests inside a nozzles earlier. This nozzle is commonly known as an high altitude simulation chamber. Verma et al [120] further extendible exit cone (EEC). It has a fixed low-area-ratio conducted experiments to investigate the dependency of section, which is enlarged to a higher area ratio by attaching transition behaviour on ambient pressure fluctuations in one or more nozzle cone extension parts. The specific dual bell nozzle. Toufik et al [121] studied the design of impulse of such nozzles increases by doubling or tripling dual bell nozzles and evaluated several wall parameters and the initial area ratio. This configuration permits very high performances with the help of the method of characteristics. area ratio nozzles to be bundled in a relatively short length Davis et al [28] developed the design procedure of dual bell that helps in decreasing vehicle inert mass. [125] nozzle contour and used it to analyse the nozzle that could be installed on a nanosatellite launcher or a sounding rocket. Verma et al [111] studied the unsteady flow con- 8. Multi nozzle grid ditions occurred during sneak transition by conducting cold-gas test on a subscale dual bell nozzle working under The Multi-Disciplinary Optimization (MDO) procedure sea level conditions. The results showed that the flow [31] creates a thin and lightweight Multi Nozzle Grid during sneak transition was highly unsteady and was the (MNG) plate (figure 24) instead of a lengthy and heavy major source of side load generation. Genin et al [122] single nozzle. The length saving is in direct proportion to performed the numerical and experimental studies to opti- the square root of the number of small nozzles (nozzlettes) mize the transitional behaviour through the variation in in the MNG (i.e., MNG with hundred nozzlettes is ten times extension geometry. Hagemann et al [123] had done the smaller than an equivalent single nozzle) [31–33]. Past analytical and experimental work to explore the aerody- study reveals the overall improvement in performance via namic characteristics of various dual bell nozzles. Frey and mass saving and nozzle efficiency. The mass saving results Hagemann [112] investigated various aspects of design for in substantial improvement of structural mass ratio, while the wall inflection and nozzle extension with focus on the improvement in nozzle efficiency is attained by using dependency of transition behaviour on the type of nozzle strategies that minimize thermodynamic losses yet increase extension. Results showed that two different types of noz- area ratio. Since the beginning of rocketry, the nozzle zle extensions (overturned and constant pressure) might designers mainly focused on how to increase the perfor- offer the sudden flow transition. Genin et al [124] investi- mance of a nozzle without enhancing its weight and length. gated computationally the flow behaviour in a dual bell The same task is just as important today with the devel- nozzle and analysed the two operation modes and the opment of advanced materials. MNG is the only nozzle transition from one mode to the other by changing the NPR. configuration where the nozzle length (i.e., plate thickness) Table 6 summarizes the experimental, analytical and to throat diameter can be less than one, yet is capable of numerical studies of the dual bell nozzles. providing extremely high area ratio [31]. Chasman et al [31] have studied the MDO to design an innovative multi- nozzle configuration. Later on, Chasman et al [32] have carried out the hot-fire tests of 91 nozzlettes MNG con- figuration characterized by exceedingly high nozzle erosion at an average rate of 0.5 lb./sec. The high erosion of copper infiltrated tungsten, traditionally considered being ‘‘a well- defined refractory material’’ underlines the need to match the structural material of the nozzle with the environment of propellant by-products. Material experts are in the opinion that the excessive erosion observed, occurred due to the sensitivity of tungsten to flow of hot carbon monoxide through the nozzlettes. Such sensitivity is inde- pendent of nozzle configuration and would also prevail in conventional single nozzle. Chasman et al [33] further studied the viscous losses of MNG in hybrid motor tests. The viscous losses in the flow through the MNG dropped the efficiency by 3% as compared to that of an Equivalent Single Nozzle (ESN). It can be mentioned here that a single nozzle that shares the same scaled nozzle contour and overall throat area as well as exit area is called an ESN. But Figure 23. Variation of specific impulse with altitude for a dual bell and two conventional nozzles [115]. when compared to a conventional single nozzle (CSN) that Sådhanå (2021) 46:76 Page 15 of 22 76

Table 6. Major studies conducted on dual bell nozzle.

Investigators Year Nature of study Focus of study Horn and Fisher [27] 1994 Experimental Performance characteristics of dual bell nozzles Frey and Hagemann [112] 1999 Analytical Dependence of the transition behaviour on and Experimental the type of nozzle extension Hagemann et al [123] 2002 Analytical Aerodynamic characteristics and Experimental Stark and Genin [118] 2010 Experimental Characteristics of side load Genin et al [124] 2012 Numerical Flow behaviour in a dual bell nozzle Genin et al [122] 2013 Numerical Optimization of the transitional behaviour through variation and Experimental of extension geometry Genin et al [115] 2013 Numerical Determination of heat flux distribution. and Experimental Genin et al [117] 2013 Numerical Planar dual bell nozzle under several test conditions and Experimental Verma et al [119] 2013 Experimental Reynolds number influence on dual bell transition behaviour Verma et al [120] 2014 Experimental Influence of ambient pressure fluctuations on the dual bell transition behaviour Davis et al [28] 2015 Numerical Dual bell nozzle contour design procedure and Experimental Verma et al [111] 2015 Experimental Unsteady flow conditions encountered during sneak transition Schneider and Genin [116] 2016 Numerical Effect of various turbulence models and feeding pressure gradients on dual bell flow transition behaviour Toufik et al [121] 2016 Numerical Design of dual bell nozzle Kbab et al [114] 2017 Numerical Design of dual bell nozzle profile

characteristics of all the rocket nozzles starting from the ideal to the MNG types are shown in table 9. The performance comparison of various nozzles is shown in figure 25. The nozzle thrust coefficient, CF for an ideal nozzle (in this figure, the ideal nozzle refers to a variable area-ratio nozzle having the optimum expansion for each chamber pressure to ambient pressure ratio, pc/pa) is shown together with those of the high area-ratio aero- Figure 24. Schematic of Multi Nozzle Grid (MNG) [31]. dynamic spike and bell nozzles. As is evident, the CF curve of the aerodynamic spike follows the ideal nozzle perfor- mance (altitude-compensation), rather than dropping off rapidly like the bell design at low pc/pa (i.e., sea level) operating points. All the nozzles have a higher CF at a high are commonly used in air vehicles, the MNG system may pc/pa (i.e., vacuum). improve the performance by more than 11% because of its mass and length savings. The major experimental studies in the area of MNG are shown in table 7. 9. Losses in rocket nozzles In summary, a list of rocket engines stating their appli- cations and the type of nozzles used along with their cor- The two important losses encountered in rocket nozzles are responding nozzle area ratio are shown in table 8, while the summarized below:

Table 7. Major studies conducted on Multi Nozzle Grid (MNG).

Investigators Year Nature of study Focus of study Chasman et al [31] 2005 Experimental MDO method for MNG design Chasman et al [32] 2005 Experimental Nozzle erosion in a MNG Chasman et al [33] 2012 Experimental Viscous losses of MNG in hybrid motor tests 76 Page 16 of 22 Sådhanå (2021) 46:76

Table 8. Key features of few rocket engines used in the past [43].

Rocket engines Application Nozzle used Nozzle area ratio RS-1801 Lunar excursion module ascent engine 72% Bell 45.6 AJ10-138 Titan III transtage Bell 40 YLR99-RM-1 X15 Aircraft; Pioneer spacecraft Conical 9.8 YLR113-AJ-1 Rocket sled Conical 5.7 RL10A-3-3 Centaur upper stage Bell 57 AJ10-137 Apollo service module Bell 62.5 LR91-AJ-5 Titan II stage Bell 49.2 LR89-NA-7 Atlas MA-5 Booster engine 100% Bell 8 J-2 S-II and S-IV stages of Saturn V Bell 27.5 F-1 S-1C stage of Saturn V Bell 16 Model 8093 Centaur ACS and ullage orientation Conical 15 M2A Comsat positioning and orientation Conical 40 SE-7 Gemini attitude control 80% Bell (Scarfed) 40.2 PD6000179 Titan III transtage ACS Optimized Bell 49 SE-7-1 Saturn SIV-B ullage 80% Bell (Scarfed) 40

Table 9. Characteristics of various rocket nozzles.

Types of nozzle Characteristics Ideal Give maximum thrust performance Long and heavy Conical Easier manufacturing Easier optimization Flow at exit is not completely axial Requires a trade-off between divergence angle and nozzle length Pressure thrust is not optimum at all altitudes Bell Lesser length as compared to conical nozzle Performance is higher as compared to conical nozzle Manufacturing is difficult Pressure thrust is not optimum at all altitudes Optimization is difficult Plug Flow separation can be avoided Allow near optimum expansion at all altitudesu¨ Less noisy Lesser size as compared to conventional nozzle Cooling of central plug is difficult E-D Allow near optimum expansion at all altitudes Size is lesser as compared to conventional nozzle Easier cooling Combustion chamber is compact Performance is low as compared to plug nozzle Higher throat heat fluxes relative to a conventional bell nozzle with an equal throat area Dual bell Can carry more payload as compared to conventional nozzles Controlled flow separation Easier cooling Higher performance and reliability Difficult to optimize the wall contour Lesser side loads Lower weight Difficult to manufacture MNG Better performance as compared to other types of nozzles Lesser length Sådhanå (2021) 46:76 Page 17 of 22 76

c. Injection of fluid into a side portion of the diverging nozzle section causing an asymmetrical distortion of the supersonic exhaust flow [130]. d. Separate thrust-producing unit that is not a part of the main propulsion system providing flow through one or more of its own nozzles [131].

11. Conclusion and recommendation

Rocket nozzle designers are always being challenged to Figure 25. Nozzle performance comparison (calculated) [126]. search for the resolution to use a smaller size nozzle in harvesting a higher specific impulse while maximizing the cost saving and simplifying the structural complexity. Lesser weight, maximum performance, and ease of manu- 9.1 Two-phase flow loss facture are some of the main desirable features of a rocket Solid rocket motors (SRMs) carrying evenly mixed ener- nozzle. This review paper attempts to analyse the major getic solid propellants have several benefits such as high research work done in the area of rocket nozzles during the reliability, structural simplicity, and ease of maintenance. last 75 years. Some of the salient points from the present Hence, such SRMs are extensively used as boosters for review work are summarized below. spacecraft/launch vehicles. However, the co-existence of • The thrust of a rocket nozzle becomes optimum when high-energy metal additives and the oxides generated in the there is a parallel uniform flow at the exit and having chamber during the working process may lead to loss of the exit pressure equal to the ambient pressure, but this two-phase flow resulting in poor performance of the SRMs. makes the nozzle longer and heavier. • A conical nozzle is easier to manufacture and has the flexibility of converting the existing design to lower or 9.2 Impingement Loss higher area ratio without much redesign. The thrust coefficient of a 15 conical nozzle is only 1.7% lesser The impingement of a thruster exhaust plume on spacecraft than the ideal nozzle. structures lead to loss of thrust depending on the configu- • The shock formation in a conical nozzle can be ration of the surfaces affected. Mitigating the effects of the eliminated by modifying the wall contour near the interaction between rocket exhaust plumes and neighboring junction of throat profile and cone. The numerical structures is a perpetual problem in the spacecraft propul- results show that the realizable v2–f and the SST k–x sion system design. The plume shear against the interior models give better results as compared to other models cylindrical surface results in an effective thrust loss, while in predicting the position of separation point and the the plume impingement against the cylinder base generally shock wave in the conical nozzle. The major disad- has a negligible effect on the net axial thrust. [3, 127] vantage lies with the trade-off between the divergence angle and the nozzle length. • 10. Thrust vector control in rocket nozzles Bell type nozzle is the most commonly used shape in rocket engines. This type of nozzle offers significant benefits in terms of size and performance over the Rocket propulsion systems deliver a push in the direction of conical nozzle. The thrust loss experienced in a conical desired end point, but such systems can also provide tor- nozzle due to the flow divergence can be decreased to ques in order to rotate the vehicle in conjunction with the some extent by the bell nozzle. The side load measured propulsive force. The thrust vectors direction can be con- in the truncated ideal nozzle is about 33.33% of side trolled using the mechanisms described below. These load in the thrust optimized nozzle. The use of the mechanisms can influence a vehicle’s yaw, pitch, and roll parabolic approximation procedures seems to be the rotations. [128–131]. The thrust vector control mechanisms easier method to optimize the bell nozzle contour. can be divided into four groups: • The length of a plug nozzle is significantly lesser than a. Mechanical deflection of the main nozzle or thrust an equivalent CD nozzle. These types of nozzles are chamber [128]. meant for altitude compensating. The main property of b. Insertion of heat-resistant movable bodies into the a plug nozzle is its interaction with the external exhaust jet; these experience aerodynamic forces and ambient that is capable to eliminate the flow separa- cause deflection of part(s) of the exhaust gas flow [129]. tion. Plug nozzle shows a thrust benefit over a 76 Page 18 of 22 Sådhanå (2021) 46:76

conventional CD nozzle when it is working below importance. Based on the results presented in this review design pressure ratio. The thrust performance of a and a look at which designs have received greatest attention contoured plug nozzle is around 5–6% more than the till date, the dual bell and MNG nozzles seems to be the conical plug nozzle. A 50% truncation in plug nozzle two most attractive candidates; the dual bell nozzle because results in only a 0.5% loss in its performance. The of its simplicity, and the MNG nozzle due to its lesser major disadvantage of such nozzles lies with its length. relatively high cooling requirements. • The length of an E-D nozzle is approximately the same to that of a plug nozzle for an equivalent thrust Acknowledgements performance. For the same performance as that of a bell nozzle, the length of an E-D nozzle required is The authors wish to place on record their sincere gratitude only 50% to that of a bell nozzle. The thrust coefficient to all the authors of classical and popular papers/reports/ of an E-D nozzle is 25-100% more than the CD nozzle. theses which formed the framework of the present review As the combustion chamber of a rocket engine with an work. Appreciation is extended to all the sources of E-D nozzle is compact in size, it has certain benefits figures and data used in this work. A list of these sources regarding cooling requirements and weight. When has been included in the references, and the authors there is a need of a very high expansion ratio, the best apologize if due recognition to any source is left out choice is the E-D type nozzle. inadvertently. • Dual bell nozzles have the advantage of maximum efficiency at high altitudes while no side loads at low List of symbols 2 altitudes. This nozzle provides sufficient thrust to carry Ae Nozzle exit area (m ) 2 12.1% more payload as compared to a conventional At Throat area (m ) CD nozzle having the same expansion ratio. The main Cfv Vacuum thrust coefficient benefits of a dual bell nozzle are its ability to control Cfvc Conical nozzle vacuum thrust coefficient flow separation, besides its design simplicity and high Cfvi Ideal nozzle vaccum thrust coefficient reliability. The heat flux value in a dual bell nozzle CFbase Total base thrust increases in the region of the contour inflection for CF Thrust coefficient both the operation modes. The flow during sneak CF,X Axial thrust coefficient transition is highly unsteady and is the major origin of CFi Ideal thrust coefficient side-load generation in the dual bell nozzle preceding Dt Throat diameter (m) the final transition. Other altitude compensating noz- Fv Thrust when discharging to vaccum zles have the limitations of mechanical complexity, HN Nozzle projected height (m) cooling difficulty, and more weight and price tag. The Isp Specific impulse (sec) dual bell nozzle provides an exceptional amalgam of L Nozzle length (m) performance, simplicity, lesser weight, and ease of Ln Nozzle axial length from throat to exit plane (m) cooling. LN Nozzle projected length (m) • In MNG, the length saving is in direct proportion to the Lf Desired fractional length (m) square root of the number of nozzlettes. This is the pa Ambient pressure (Pa) only nozzle configuration where the nozzle length (i.e., pc Chamber pressure (Pa) plate thickness) to throat diameter can be less than one, pdes Design pressure (Pa) yet is capable of providing extremely high area ratio. pe Pressure at the exit (Pa) Viscous losses in the MNG drop the efficiency by 3% pt Stagnation pressure (Pa) as compared to that of the ESN. However, as compared pw Wall pressure (Pa) to a CSN, the MNG system may improve the R Radius of circular arc (m) performance by more than 11% because of mass and Rt Throat radius (m) length savings. Ve Nozzle exit velocity (m/s As evident from the above comprehensive literature Greek symbols review, each design has its specific strengths and weak- a Divergent cone half-angle (deg.) nesses, and there is no design that stands out as clearly q Density at the exit of nozzle (kg/m3) superior to the others. Rather, the selection of a particular e c Isentropic exponent design results from a careful trade-off between different e Nozzle expansion ratio or area ratio factors such as application, performance, reliability, h Nozzle convergent cone section half-angle (deg.) mechanical complexity, manufacturability, weight, and h Nozzle exit wall angle (deg.) cost. The ‘winning’ concept from such a trade-off is further e h Initial wall angle of the parabola (deg.) influenced by how these factors are ranked in order of n Sådhanå (2021) 46:76 Page 19 of 22 76

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