Masters Theses

Date of Award

5-2006

Degree Type

Thesis

Degree Name

Master of Science

Major

Aerospace Engineering

Major Professor

Joseph Majdalani

Committee Members

Gary Flandro, Kenneth Kimble

Abstract

We consider the isentropic flow equations that relate pressures, temperatures, densities, and critical back pressure to their total quantities for a given flow Mach number and nozzle area ratio. Using proper substitutions, we bypass the Mach number and link these fundamental commodities directly to the local area expansion ratio. The transcendental equations we obtain are then solved asymptotically and presented in closed form to arbitrary order. Both subsonic and supersonic branches of the solution are identified and suitably treated. Two representations of the isentropic variables are introduced for both subsonic and supersonic cases. The first representation defines the isentropic variable as the total quantity divided by its local, while the second representation is described as the reciprocal of the first one. Expressions for the truncated errors for the supersonic case are first determined. Then, Bosley's technique is applied to confirm the truncation order for each approximation. The final expressions provide direct solutions for the main thermodynamic properties as function of the area expansion and gas compression ratios. This enables us to calculate these widely used quantities without resorting to numerical iteration, intermediate Mach number calculations, guesswork, or trial. The work increases our repertoire of isentropic flow approximations that are ubiquitously used in the propulsion and power generation industries.

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