D. P. Mishra
4.5 ADVANCED ROCKET NOZZLE
namely, wall pressure, Mach number, wall roughness, and so on. Another criterion for flow separation is the following semiempirical relationship relating Pe, Pa, and Me [5]:
P
Pe M
a =
(
1 88. e-1)
-0 64. (4.16) where Me is the Mach number at the nozzle exit. In order to avoid flow separation, the nozzle exit area is chosen such that Pe must be greater than Pa(1.88Me − 1)−0.64 for a particular nozzle exit Mach number. In other words, an adverse pressure gradient is less likely to occur in the divergent section of the nozzle to avoid flow separation. With separation of flow, the nozzle may adapt to any altitude change as it provides higher pressure at the nozzle exit. Hence, it is expected to have a higher thrust under the flow separation condition for the same nozzle area ratio. However, flow separa- tion does not occur in a symmetrical manner, as shown in Figure 4.12.Rather flow separation in a practical system is found to occur in an asym- metrical manner, giving rise to side thrust. Hence, flow separation must be avoided for rocket propulsion applications.
has been designed and developed. A two-step extendible bell nozzle con- sisting of two segments is shown in Figure 4.13a. Initially, the extendible nozzle with a smaller exit area Ae1 is used for a certain range of low altitude.
Subsequently, a second segment is actuated using a special mechanism such that the nozzle exit area is increased to Ae2 at higher altitude for better per- formance. This kind of extendible nozzle has been employed successfully in several solid rocket engines and few liquid-propellant engines, particularly before initiation of ignition. A three-segment extendible nozzle has been devised but has not yet been used during flight due to additional complexi- ties. Some of the pertinent problems with the actuation mechanism, the seal between the nozzle segments, and the added weight are to be solved to make the extendible nozzle viable for future application in rocket engines.
4.5.2 Dual Bell–Shaped Nozzle
In order to overcome the problem of actuation mechanism of the extend- ible nozzle, a dual nozzle has been designed and developed by combining
Extendible segment Combustion
chamber Nozzle
Ae1 Ae2
Ae1 Ae2 First bell Second bell Combustion
chamber Nozzle (a)
(b)
Bump point
FIGURE 4.13 Schematic of (a) an extendible nozzle and (b) a dual bell–shaped nozzle.
the two segments of the nozzle with a hump between them as shown in Figure 4.13b. During low-altitude flight, the first bell nozzle segment with the smaller exit area Ae1 is operated for the expansion of gas as the flow separation occurs at the hump point and does not adhere to the larger exit area Ae2. In other words, the thrust is developed by the expansion of gas up to the exit area Ae1. In contrast, at higher altitude, due to lower ambi- ent pressure, gas expands further for a particular chamber pressure even beyond the hump point by getting attached up to the larger exit area Ae2. As a result, the nozzle operates at a higher area ratio and enhances perfor- mance even at higher altitude. However, there will be marginal decrease in performance compared to that of the extendible nozzle. This type of nozzle has been used to improve the performance of cryogenic engines on the space vehicle Araine 5.
4.5.3 Expansion–Deflection Nozzle
Both extendible and dual bell–shaped nozzles cannot adapt with changes in altitude in a continuous manner, but rather in a discrete manner dur- ing the flight of a rocket engine, and hence will have lower performance level. In order to adapt the nozzle to the changes in altitude in a continu- ous manner, two different types of nozzles have been developed, namely, (1) the expansion–deflection nozzle and (2) the aerospike nozzle, in which the free jet boundary helps in adjusting the expansion process automati- cally and in a continuous manner with changes in ambient pressure along with the altitude. A schematic of a typical expansion–deflection nozzle with annual cross section with the central body/plug is shown in Figure 4.14a.
In this case, gas flow from the combustion chamber is turned around the curved contour of the plug and moves outward away from its central axis along the curved and diverging surface of the bell nozzle. The purpose of the plug is to force the flow to remain attached to, or to stick to, the nozzle walls. An aerodynamic interface is formed between the inner gas layer along the curved diverging section and the ambient air. When ambi- ent pressure changes with altitude, hot gases fill the larger portion of the diverging section of the nozzle. In other words, this nozzle adapts well to altitude in a continuous manner.
4.5.4 Aerospike Nozzle
In the case of an aerospike nozzle, an aerospike/aerodynamic plug is placed in the center of the nozzle as shown in Figure 4.14b. Note that the flow moves inward toward its axis guided by the centrally placed aerospike. The outer gas
boundary is interfaced directly with ambient air. The expansion of gas flow around the aerospike gets adjusted directly with the changes in ambient pres- sure due to changes in altitude. At the designed pressure, the boundary will be almost parallel to the axis with similar performance as that of a conventional bell nozzle. But for higher ambient pressure, the boundary moves inward raising the exhaust pressure. On the other hand, if the boundary moves out- ward, it allows the gas to expand to a lower pressure. As a result, this kind of nozzle can perform in a far superior way than the designed condition com- pared to the conventional bell nozzle. The full parabolic contoured nozzle is much longer in order to achieve minimum flow losses when fluid is turned off around the aerospike. Hence, the nozzle with a truncated aerospike, as shown in Figure 4.14b, is designed to overcome this problem. Generally, the aerospike in the nozzle is truncated to such an extent that it provides least performance loss. Of course, with the use of a truncated aerospike, the nozzle becomes shorter and sturdier with minimum problems due to heat transfer.