Jawaharlal Nehru Technological University Hyderabad B.Tech IV AERO ENGINE DESIGN Previous Question Paper (July/August - 2022 - R18)

Compressible flow relationships describe how fluid properties such as pressure, density, temperature, and velocity change as a gas flows at high speeds where density variations become significant. These relationships are governed by the conservation of mass, momentum, and energy, combined with the equation of state for an ideal gas.

The most prominent relationships include:

1. Stagnation Properties: These represent the state of the fluid if it were brought to rest isentropically. The stagnation temperature (T₀) is related to static temperature (T) and Mach number (M) by:
   T₀ / T = 1 + ((γ - 1) / 2) * M²
2. Isentropic Flow Relations: For adiabatic, reversible flow, the ratios of stagnation to static properties depend solely on the Mach number and the ratio of specific heats (γ):
   P₀ / P = (1 + ((γ - 1) / 2) * M²)^(γ / (γ - 1))
   ρ₀ / ρ = (1 + ((γ - 1) / 2) * M²)^(1 / (γ - 1))
3. Area-Mach Number Relation: This governs flow through variable area ducts (like nozzles and diffusers), showing how the Mach number changes with cross-sectional area (A):
   A / A* = (1 / M) * [(2 / (γ + 1)) * (1 + ((γ - 1) / 2) * M²)]^((γ + 1) / (2 * (γ - 1)))
   where A* is the sonic throat area where M=1.
4. Normal Shock Relations: When supersonic flow encounters a shock wave, it undergoes a discontinuous change in properties. The Rankine-Hugoniot relations define the jump conditions across the shock, such as the pressure ratio:
   P₂ / P₁ = 1 + (2 * γ / (γ + 1)) * (M₁² - 1)
5. Prandtl-Meyer Function: This describes the expansion of supersonic flow around a convex corner, relating the turning angle (ν) to the Mach number.

These relationships are fundamental to the design of engine inlets, nozzles, and compressor blades, as they dictate the performance limits and shock wave formations within aero-engine components.

A mission profile is a graphical or tabulated representation of the sequence of phases an aircraft undergoes during a complete flight, from engine start to engine shutdown. It is essential for determining fuel requirements, engine sizing, and performance constraints. The standard mission profile consists of the following phases:

1. Engine Start and Warm-up: The engine is started, and systems are checked. Fuel consumption is low but constant during this period.
2. Taxi and Take-off: The aircraft moves to the runway and performs a high-thrust take-off. This phase consumes significant fuel due to maximum rated thrust requirements.
3. Climb: The aircraft ascends to its cruise altitude. This phase requires high power settings to overcome gravity and drag, resulting in high fuel burn rates.
4. Cruise: The longest phase of the mission, where the aircraft maintains a constant altitude and speed. The engine operates at an efficient cruise thrust setting to minimize specific fuel consumption (SFC).
5. Loiter: If required, the aircraft circles at a specific altitude and speed, often near the destination, waiting for landing clearance. This phase focuses on endurance and fuel efficiency.
6. Descent: The aircraft reduces altitude and speed towards the destination airport. Engine power is typically reduced to idle or low settings.
7. Landing and Taxi-in: The aircraft touches down, decelerates, and taxis to the gate.
8. Reserve Fuel: A mandatory portion of fuel is set aside for contingencies, such as holding patterns, diversions to alternate airports, or unexpected weather delays.

The total fuel weight is calculated by integrating the fuel flow rate over the time duration of each phase, ensuring that the engine design meets the thrust-to-weight and fuel efficiency requirements across these varying operational conditions.