Question

When heat is added in a constant area duct without friction (i.e., in Rayleigh flow), which of the following statements is true?

• A. Total temperature and total pressure decrease for both supersonic and subsonic flows at inlet
• B. Total temperature increases and total pressure decreases for both supersonic and subsonic flows at inlet
• C. Total temperature and total pressure increases for supersonic flows at inlet
• D. Total temperature remains constant and total pressure decreases for subsonic flows at inlet

Hint:

Rayleigh flow involves thermal effects — always consider energy changes and pressure loss.

Answer 1

The Correct Option is B

To solve this problem, we must understand the behavior of Rayleigh flow, which is the flow of a compressible fluid in a constant area duct where heat is added or removed without friction. In Rayleigh flow, the following key points should be noted:

• Total Temperature (T_t): The total temperature, or stagnation temperature, increases when heat is added. This is due to the conservation of energy principle, where the added heat increases the energy of the system, thus increasing the total temperature for both supersonic and subsonic flows.
• Total Pressure (P_t): The total pressure decreases due to the irreversible nature of heat addition. Despite being a frictionless process, entropy increases, leading to a loss in total pressure for both supersonic and subsonic flows.

Given the above principles, the statement that "Total temperature increases and total pressure decreases for both supersonic and subsonic flows at inlet" accurately describes the behavior of Rayleigh flow.