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Objective
The objective of this design project was to develop a fictional engine tailored to meet the requirements of a defined mission for an aircraft traveling from New York to London. Although the supersonic aircraft was designed for commercial application, the primary focus was on designing and analyzing its propulsion system, specifically the inlet geometry of the engine.
The design process was divided into two sections. The first section involved designing the supersonic inlet to accommodate ambient conditions and achieve the desired number of shocks & maximize pressure recovery using Oswatitsch’s Principle. The second section conducted a parametric analysis by contrasting the performance of the fictional engine and the SR-71 Blackbird's J58 engine.
Oswatitsch's Principle
Stagnation Pressure Ratio across Oblique Shock
To perform engine analysis, several assumptions were made to account for various processes. The cross-sectional area of each engine section was assumed to be circular and the nozzle process was assumed to undergo losses across different sections: inlet, diffuser, compressor, burner, and turbine. Although the components were not considered isentropic, they were assumed to be adiabatic. Pressure loss estimates were based on historical data from the J58 engine. When J58-specific values were unavailable, data from similar engines were used to approximate the parameters.
Additionally, the engine was assumed to operate under a turbojet cycle rather than a ramjet cycle, despite being a hybrid of both. The exit nozzle was considered perfectly expanded, with the exit pressure equal to the ambient pressure.
For the turbine blades' inlet, a material was required to determine the maximum allowable temperature at the combustion chamber exit. Due to the extremely high temperatures of the exhaust gases, the turbine blades face a risk of failure, potentially leading to catastrophic consequences. While most modern turbojets use materials rated for turbine inlet temperatures between 1500 and 2000 K, a higher threshold of 2500 K was selected to enhance efficiency, as greater maximum allowable temperatures generally improves turbine performance. Furthermore, the afterburner was designed for a maximum temperature of 2750 K, as it was expected to operate at a higher temperature than the turbine inlet.
SR-71 Blackbird's J58 engine airflow
Results
Supersonic engine inlet rendition
The image and table on the left illustrates the supersonic engine's inlet, displaying the deflection and shock angles. In its simplest form, when supersonic airflow encounters a ramped geometry, it deflects inward, generating an oblique shockwave. Using Oswatitsch’s Principle, when the normal components of each supersonic flow are equal, the pressure recovery is at a maximum such that the oblique shockwaves intersect with the inlet's cowl.
To validate the recovery pressure, the graph on the right provides the expected pressure recovery for an inlet Mach of 3.2 for the condition of three oblique shocks and one normal shock. As the normal shock Mach number for each oblique shock was expected to be the same, the stagnation pressures must be the same across each oblique shock. The expected pressure recovery was 0.79 whereas the computed pressure recovery for the designed geometry was 0.793. The error was approximately 0.38%, therefore the computed pressure recovery was acceptable.
Optimum pressure recovery for various number of shockwaves.
The table on the left displays the results of executing parametric analysis on the engine. The stagnation temperature and pressure at the inlet of the compressor were determined using isentropic relations such that the pressure recovery of the inlet was incorporated from the supersonic inlet geometry design. The computed values must be smaller compared to the remaining segments of the engine - namely the compressor, combustion chamber, and turbine.
At the entrance to the combustion chamber, the stagnation temperature and pressure were higher than the compressor inlet due to its purpose of increasing the air pressure, resulting in an increase in temperature. In addition, the losses across each segment were accounted for through efficiency factors and compression ratios.
In order to produce thrust, the exit velocity must exceed the inlet velocity. Since the exit velocity of 3,070 m/s was greater than the inlet velocity of 944 m/s, the engine was able produce thrust. The air mass flow rate of the engine was determined using the density of air at 60,000 ft, the inlet area, and the inlet velocity. The computed air mass flow rate of 110 kg/s was acceptable as it is within magnitude of the J58 air mass flow rate of 140 kg/s. The fuel-to-air ratio was calculated using the stagnation temperature ratio between the turbine inlet and combustion chamber with consideration of the heating value of kerosene, 45 MJ. The resultant fuel-to-air ratio was 0.0276 whereas the published value at Mach 2.80 at 19.8 km altitude was 0.033. Despite the freestream Mach number not matching the provided Mach data, the fuel-to-air ratio is expected to decrease with increasing Mach numbers, thus validating the calculated fuel-to-air ratio of the fictional engine.
For future designs, the assumptions made will need to be revised, as not all are applicable when designing a real engine, particularly due to their contribution to errors in certain parameters. For example, the exit area was calculated to be 3.35 m², which was larger compared to existing engine exit areas during cruise.
Check out my project repository on GitHub for the project report & code.
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