## **Altitude-compensating and thrust-optimized rocket nozzles**

## PhD Student: Kyll Schomberg

## Rocket nozzle contour design

The function of a supersonic nozzle within a rocket engine is to convert the thermal energy of the combustion products into kinetic energy in order to produce thrust. Two main schools regarding the philosophy of rocket nozzle design currently exist:

• Ideal contours – An ideal contour that produces uniform and axial flow at the nozzle exit via isentropic turning of the flow can be generated using the method of characteristics. However, an ideal contour can only be described by a list of points in space which limits control of the design and increases the difficulty of manufacture.

• Optimal thrust design – A unique contour can be generated to maximise thrust for a given prescribed length by using the calculus of variations. However, all thrust-optimised contours suffer from transient side loading that occurs during engine start-up which increases the mass of the engine and increases the chance of structural failure.

As you can see, both categories of nozzle design are currently subject to inherent flaws. A unique rocket nozzle design method that is capable of addressing these flaws would therefore result in a net benefit in any conventional rocket engine. **To achieve this, I am currently investigating the use of an arc-based method for design of a rocket nozzle contour. **

All conventional (fixed-area) rocket nozzles face another avenue of efficiency loss which occurs due to the considerable decrease in atmospheric pressure throughout flight. This causes two main issues:

• A Limit on the maximum area ratio (and therefore vacuum thrust coefficient) due to the need to avoid flow separation during operation at sea level

• A reduction in thrust efficiency in the order of 15% due to a pressure differential that exists at all altitudes other than the design condition (one specific altitude point) Both sources of inefficiency stem from the fixed area in a conventional nozzle design.

A continual variation in nozzle area can be achieved through utilisation of the local ambient conditions to limit the expansion of the combustion products. A nozzle concept that achieves this is known as ‘altitude-adaptive’ and will ideally result in high thrust efficiency under all flow conditions. To increase the understanding of such nozzles, **I am currently investigating is the altitude-adaptive expansion-deflection nozzle.**

## The arc-based nozzle design method

The use of an arc-based design method allows complete spatial control and description of the contour using simple trigonometric relations. In this method, the expansion and turning curves are represented by a finite series of circular arc segments. This process allows the rapid approximation of any given nozzle contour by using a conical nozzle as scaling function.

The arc-based design method has been used to approximate both and ideal and thrust-optimised nozzle contour:

• Ideal – A truncated ideal contour (similar to that used in the LE-7 rocket engine) can be approximated to within less than 1% by using either one (KS1) or two (KS2) arc segments in the expansion curve combined with a single turning curve. Although the performance of the two variants in this case was equal, a large variation in flowfield structure was observed. The significant influence of the expansion curve represents a novel concept in the field.

• Thrust-optimised – A thrust optimised parabola contour (similar to that used in the Vulcain rocket engine) can be replicated using any number of equivalent nozzle variants. Application of the arc-based design method identified that a thrust-optimal contour can be replicated (and the thrust slightly increased) using the arc-based method. Furthermore, avoidance of the undesirable separation regimes can be achieved without a reduction in nozzle thrust.

By combining the features discovered in this process, a rocket nozzle contour that provides a net benefit over existing designs can be achieved. **Such a nozzle would produce greater thrust, have less mass and increase the safety of operation and ultimately reduce launch and engine costs. **

## The expansion-deflection (ED) nozzle

The ED nozzle uses a central flow deflector to redirect the exhaust towards the nozzle wall. This facilitates the creation of a recirculating wake region within the nozzle that limits the expansion of the combustion products with respect to the local ambient conditions. The adaption process prevents overexpansion of the flow and will theoretically result in ideal efficiency at all altitudes. I am investigating two main areas regarding the design and operation of the ED nozzle:

• Flow deflector design – The influence that the flow deflector has on the performance of the ED nozzle is poorly understood. Only a single design method exists for the flow deflector and the effect of geometric variation restricted to a limited number of parameters and vacuum operating conditions. I am currently investigating the effect of flow deflector geometry on ED nozzle thrust using a factorial-based design of experiments approach. The influence of the flow deflector has been shown to be high, and careful design is required for high thrust.

• Numerical analysis of the ED nozzle – Although the ED nozzle has existed in literature since 1960, interest in the concept is a recent affair. Because of this, attempts to conduct a numerical analysis to increase understanding of the flow field are limited. I am currently investigating a number of numerical methods for describing the ED nozzle flow field. The selected numerical approach has been shown to have a considerable effect of the solution. However, the result varies with respect to the subject of investigation i.e. thrust or flow features and suggests that the numerical approach must be tailored to reduce solution time.

A comprehensive geometry and numerical analysis is required in order to fully assess the merit of the ED nozzle concept. It is important to note that an efficient ED nozzle would result in a considerable increase in thrust and reduction in mass over existing designs. **The inherent capability of altitude-adaption would be a requirement in any single stage launch system, which may reduce the cost of transporting payload into orbit by an order of magnitude. **

## Publications

Schomberg, K., Olsen, J., Neely, A.J., Doig, G.**Effect of the Contour Shock on Restricted Shock Separation**Journal of Propulsion and Power (accepted, in press)

Schomberg, K., Olsen, J., Neely, A.J., Doig, G.**Suppressing Restricted Shock Separation in a Rocket Nozzle Using Contour Geometry**.

Journal of Propulsion and Power, **32**, 5: 1298-1301.

Schomberg, K., Doig, G., Olsen, J.**Design of High Area-Ratio Nozzle Contours Using Circular Arcs**.

Journal of Propulsion and Power, Vol. **32**, No. 1, pp. 188-195

Schomberg, K., Doig, G., Olsen, J.**Design of High Area-Ratio Nozzle Contours Using Circular Arcs**.

Journal of Propulsion and Power, Vol. 32, No. 1, pp. 188-195

Schomberg, K., Doig, G., Olsen, J.**Computational Simulation of an Altitude Adaptive Nozzle Concept**

Applied Mechanics and Materials Vol. 553 pp 223-228.

Schomerg, K., Olsen, J., Neely, A.J., Doig, G.**Suppressing Restricted Shock Separation in a Rocket Nozzle Using Contour Geometry.**

51st AIAA/SAE/ASEE Joint Propulsion Conference at Propulsion and Energy 2015, 27-29 July, Orlando, Florida.

Schomberg, K., Doig, G., Olsen, J., Neely, A.J.**Numerical Analysis of a Linear Expansion Nozzle at Open Wake Flow Conditions**.

16th Australian International Aerospace Congress, 23-24 February 2015, Melbourne, Australia.

Schomberg, K., Olsen, J., Neely, A., Doig, G.

Design of an Arc-Based Thrust-Optimised Rocket Nozzle Contour

6th European Conference for Aeronautics and Space Sciences, Krakow, Poland.

Schomberg, K., Doig, G., Olsen, J., Neely, A.J.

**Geometric Analysis of the Linear Expansion Deflection Nozzle at Highly Overexpanded Flow Conditions**.

AIAA Joint Propulsion Conference, Cleveland, OH, July 2014.

Schomberg, K., Doig, G., Olsen, J.

**Design of High Area Nozzle Contours Using Circular Arcs**.

AIAA Joint Propulsion Conference, Cleveland, OH, July 2014.

Schomberg, K., Doig, G., Olsen, J., Neely, A.J.**Experimental Analysis of a Linear Expansion-Deflection Nozzle at Highly Overexpanded Conditions**.

19th Australasian Fluid Mechanics Conference, 8-11 December 2014, Melbourne.

Schomberg, K., Doig, G., Olsen, J “**Computational Analysis of Pintle Variation in a Linear Expansion Nozzle**”, 13th Australian Space Science Conference. Sydney, Australia – Best Paper Award.

Schomberg, K., Doig, G., Olsen, J. **Computational simulation of an altitude adaptive nozzle concept**.

1st Australasian Conference on Computational Mechanics, October 2013.

Schomberg, K., Doig, G., Olsen, J.

Computational analysis of pintle variation in an expansion-deflection nozzle.

13th Australian Space Science Conference, Sydney, October 2013.

Schomberg, K., Olsen, J. **“Altitude compensation in expansion-deflection nozzles”,** 18th Australian Fluid Mechanics Conference, 2012. Launceston, Australia.