A graphical version of this slide is also available. The interactive Java applet EngineSim is also available. This program solves these equations and displays the thrust and fuel flow values for a variety of turbine engines. In the text only version presented here, * denotes multiplication, / denotes division, and ^ denotes exponentiation. Referring to our station numbering, free stream conditions are noted by a "0" subscript, the entrance to the inlet is station "1" and the exit of the inlet (entrance to the compressor) is station "2".
Most modern passenger and military aircraft are powered by gas turbine engines, which are also called jet engines. There are several different types of jet engines, but all jet engines have some parts in common. All jet engines have an inlet to bring free stream air into the engine. The inlet sits upstream of the compressor and, while the inlet does no work on the flow, there are some important design features of the inlet. Because the inlet does no thermodynamic work, the total temperature (Tt) through the inlet is constant.
Inlet Total Temperature Ratio: Tt2 / Tt0 = 1
The total pressure (pt) across the inlet can change, however, because of several flow effects. Aerodynamicists characterize the inlet's pressure performance by the inlet total pressure recovery, which measures the amount of the free stream flow conditions that are "recovered". The pressure recovery (pt2 / pt0) depends on a wide variety of factors, including the shape of the inlet, the speed of the aircraft, the airflow demands of the engine, and aircraft maneuvers. There are some simple equations for the pressure recovery that are used as standards. (Mil. Spec. stands for Military Specifications. "M" is the Mach number)
Mil. Spec., M > 1 : pt2 / pt0 = ni * ( 1 - .075 * [M - 1] ^1.35)
Mil. Spec., M < 1 : pt2 / pt0 = ni * 1
Recovery losses associated with the boundary layers on the inlet surface or flow separations in the duct are included in the inlet efficiency factor (ni = pt2 / pt1). For subsonic flight speeds, these are the only losses. At supersonic flight speeds, there are additional losses created by the shock waves necessary to reduce the flow speed to subsonic conditions for the compressor. The magnitude of the recovery loss depends on the specific inlet design and is usually determined experimentally. The Mil. Spec. loss is a good first estimate at that value for most inlets. Actual inlet performance may be greater, but are usually less than Mil. Spec.
There is an additional propulsion performance penalty charged against the inlet called spillage drag. Spillage drag (D spill), as the name implies, occurs when an inlet "spills" air around the outside instead of conducting the air to the compressor face. The amount of air that goes through the inlet is set by the engine and can change with altitude and throttle setting. The inlet is usually sized to pass the maximum airflow (mdot i) that the engine can ever demand and, for all other conditions, the inlet will spill the difference between the actual engine airflow and the maximum air demanded.
Spillage Drag Equation: D spill = K * (mdot i * [V1 - V0] + A1 * [p1 - p0])
Where V is the velocity, A1 is the inlet capture area, and p is the static pressure. As the air is spilled over the external cowl lip, the air is accelerated and the pressure will decrease. This produces a lip suction effect that partially cancels out the drag due to spilling. Inlet aerodynamicists account for this effect with a correction factor (K) that multiplies the theoretical spillage drag. Typical values of K range from .4 to .7. But for a given inlet the value is determined experimentally. The form of the theoretical spillage drag is very similar to the thrust equation, with a mass flow times velocity term and a pressure times area term.
As the air is brought from free stream to the compressor face, the flow may be distorted by the inlet. At the exit of the inlet (the compressor face), one portion of the flow may have a higher velocity or higher pressure than another portion. The flow may be swirling, or some section of the boundary layer may be thicker than another section because of the inlet shape. The rotor blades of the compressor move in circles around the central shaft. As the blades encounter distorted inlet flow, the flow conditions around the blade change very quickly. The changing flow conditions can cause flow separation in the compressor (a compressor stall) and can cause structural problems for the compressor blades. A good inlet must produce high pressure recovery, low spillage drag, and low distortion.
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