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Passive clearance control system :
Compressor discharge air and HP compressor air provide cooling airflow to protect the turbine casing against rapid temperature changes. The stationary parts in the high-pressure turbine section expand and contract more rapidly than the rotor due to pressure and temperature changes. The rotor also has a radial expansion due to rotational speed.
The turbine casing incorporates temperature controlled casing flanges with cooling air passages for the passive case clearance control system. The cooling air controls the expansion and contraction of the case to match the rotor and thus maintain desired clearances throughout all temperature ranges and operating conditions.
Figure shows (highlighted) air tubes (Bird Cage) that cools the HP and LP turbines. The air is taken from just aft of the fan and ducted through the cowls (not shown).
What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spread c(k1)-c(k2)?
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