Background

If a mobile object emits a jet of fluid in one direction, the object itself is propelled in the opposite directiondue to Newton`s third law.This is the basis of jet propulsion and has extensive applications in both the natural and the human-engineered world, for example squids, scallops, traditional rockets and the modern airplane jet engine. However, there are practical difficulties in adapting these systems to reach low-Earth orbit in a repeatable, cost-efficient and sustainable way. One particular challenge is designing reusable propulsion systems which can work efficiently both within the atmosphere and above it.

Questions

1.(a) Draw a simplified diagram of the engine suitable for a control volume analysis of the thrust. Make sure that all relevant parameters are labelled on the diagram. Write out the full version of the momentum equation and briefly describe how each term in the equation relates to the physical engine.

(b) The engine is being tested in a controlled-atmosphere wind tunnel which matches the conditions at 25 km altitude and a speed of Mach 4. The engineers measure the thrust from the engine burning steadily and find that it is 2.5 × ?10?^6 N. Use the momentum equation and the data given below to estimate the speed of the exhaust gas leaving the engine, explaining the logic behind each step.

Air is entering the engine at Mach 4, since the engine would meet undisturbed air at that speed. The speed of sound at this altitude is 295 m/s. Assume that the P and T data at points 1 and 8 in figure 3 apply here, and take inflow and outflow mass flow rate (m ) ? from points 2 and 7.Assume that the cross-sectional areas of the inlet and outlet are 5 m2 and 1.5 m2 respectively. You may assume that all the air enters at a uniform speed and exits with another uniform speed. The thrust is equal in magnitude to the anchoring force needed to hold the engine in place.

2. Use the concepts relevant to gas power cycles for developing a simplified thermodynamic cycles for analysing the performance of the engine.

The following assumptions could be considered:

• The helium loop works on a closed Brayton cycle, and the air-breathing engine works on an open Brayton cycle. These can be analysed separately.

• The heat exchangers all work at constant pressure (if different input and output pressures are shown, take the average to find the constant pressure).

• Consider the expansion and compression processes in thecomponents such as nozzle,compressors and turbines to be isentropic.

To answer the questions below, use the data shown in Figure 3.

(a) Reconstruct the Helium Loop (shown in green in figures 2 and 3) using the above assumptions and calculate its thermal efficiency.

(b) Convert the open cycle on which the engine operates to an equivalent closed cycle for your analysis. The key components that form the open cycle of the engine (excluding the hydrogen tank and the pre-burner) are represented by states 1-2-3-4-6-7-8 in figure 3. Draw a diagram and explain all the stages in the cycle.

(c) Calculate the thermal efficiency of the equivalent closed cycle you described in part (b).

3. [There is a limit of 300 words for your answerto this question]

Choose one component in the engine (you can find the full list of labels for figure 1 below, and you should pick one component from this list). Write an analysis of that component based on the topics we have covered in this module (both fluid mechanics and thermodynamics). Be specific about the processes you discuss, and analyse the flow of fluids and energy through the component using the data in figure 3. Include concise calculations if appropriate. Make sure that you describe clearly how the engineering concepts apply. What are the priorities for designing your chosen component and can you suggest priorities for improving or developing it?