# Aerospike Aerodynamics

After introducing the aerospike nozzle, we alluded to how the introduction of a base bleed improves the thrust performance of the overall system. In this section, we will further explore the aerodynamic behavior of the aerospike and how this type of nozzle generates thrust.

### Thrust Characteristics:

The basic thrust characteristics of the aerospike nozzle can be better understood by referring to the following figure.

##### Example of an aerospike nozzle with a subsonic, recirculating flow [from Hill and Peterson, 1992]

The nozzle generates thrust in three ways. First, the thrusters in the toroidal chamber, located at the base of the nozzle, generate thrust as the fuel is combusted and exhausted. We shall label this thrust component F thruster, and we can compute this thrust using the equation

where

 F thruster = thrust force acting on the thruster = mass flow rate v exit = exhaust gas velocity at the nozzle exit p exit = pressure of the exhaust gases at the nozzle exit p∞ = ambient pressure of the atmosphere A exit = cross-sectional area of the nozzle exit θ = angle between the thrust axis and the vertical
We previously discussed how nozzles generate thrust when the exhaust gases expand against the nozzle walls. Although we used the bell nozzle to illustrate that discussion, the exhaust gases in a spike nozzle expand against the spike centerbody rather than outer walls. Thus, the expansion of the exhaust gases exerts a thrust force that we will call F centerbody.

where

 F centerbody = thrust force acting on the centerbody A centerbody = cross-sectional area of the centerbody moving along the nozzle axis p centerbody = pressure of the exhaust gases on the centerbody moving along the nozzle axis p∞ = ambient pressure of the atmosphere
Finally, we mentioned that the aerospike nozzle is so named because an "aerodynamic spike" is created through the addition of a secondary, circulating flow aft of the flat nozzle base. As the supersonic primary flow, consisting of the high-pressure gases exhausted from the thrusters, expands downstream of the base, the primary flow interacts with the subsonic, secondary flow causing it to circulate. This low-pressure flow then re-circulates upward to exert an additional thrust force on the base.

where

 F base = thrust force acting on the base p base = pressure of the re-circulating flow on the base p∞ = ambient pressure of the atmosphere A base = cross-sectional area of the base
Summing up these three thrust components yields the following relationship for the total thrust force (T) generated by an aerospike nozzle:

### Aerospike Flowfield:

The exact nature of the exhaust flowfield behind an aerospike nozzle is currently the subject of much research. The most notable features of a typical aerospike nozzle flowfield are shown in more detail below.

##### Flowfield characteristics of an aerospike nozzle [from Ruf and McConnaughey, 1997]

The primary exhaust can be seen expanding against the centerbody and then around the corner of the base region. The interaction of this flow with the re-circulating base bleed creates an inner shear layer. The outer boundary of the exhaust plume is free to expand to ambient pressure. Expansion waves can be seen emanating from the thruster exit lip, and these waves reflect from the centerbody contour to the free jet boundary. Compression waves are then reflected back and may merge to form the envelope shock seen in the primary exhaust.

At low altitude (high ambient pressure), the free boundary remains close to the nozzle (see below) causing the compression waves to reflect onto the centerbody and shear layer themselves. The waves impacting the centerbody increase pressure on the surface, thereby increasing the centerbody component of thrust. The waves impacting the shear layer, on the other hand, increase the circulation of the base flow thereby increasing the base component of thrust.

##### Shadowgraph flow visualization of an ideal isentropic spike at (a) low altitude and (b) high altitude conditions [from Tomita et al, 1998]

As the vehicle ascends, the pressure decreases and the free boundary expands further and further away away from the nozzle contour, as shown above. As it does so, the compression waves also move downstream and eventually cease to impact on the centerbody. The pressure profile on the contour becomes constant and no longer varies with ambient pressure. However, the secondary flow remains under the influence of ambient pressure for a much longer period. Only at very high altitudes do the compression waves impact downstream of the sonic line, at which point the base pressure becomes constant. The primary exhaust is then said to have enclosed the wake.

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