Aircraft and Rocket Propulsion by Brian J. Cantwell

By Brian J. Cantwell

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The ambient temperature and pressure are T 0 = 216K 4 2 P 0 = 2 × 10 N ⁄ M . 28 × 10 J/kg . 0. A normal shock stands in front of the inlet. 5 3 P0 4 e M0 = 3 shock and the stagnation temperature at station 4 is T t4 = 2000K . 5 = 8 , A 1 = A 3 = A 4 and A 4 ⁄ A e = 3 . Determine the dimensionless thrust T ⁄ ( P 0 A 1 ) . Do not assume f<<1. Neglect stagnation pressure losses due to wall friction and burner drag. Assume that the static pressure outside the nozzle has recovered to the ambient value.

A typical thrust plot is shown below. 12 Ramjet thrust The optimization question is; at what Mach number should the ramjet operate for maximum thrust at a fixed τ λ ? 39) with respect to τ r and set the result to zero. ∂  T  ------------- = ∂ τ r  P 0 A 0 τλ      2 τ λ    τ λ τ r  1 – 3 τ r + 2 ----- τ r  + τ f  τ λ + τ λ τ r – 2 τ r -----  τr   τr     2γ   ------------  ---------------------------------------------------------------------------------------------------------------------------------------- = 0 γ – 1  2 τλ   ( τ f – τ λ ) τ r ----τr   .

Solution - The first point to recognize is that the stagnation pressure at station 4 exceeds the ambient by more than a factor of two - note the pressure outside the nozzle is assumed to have recovered to the ambient value. 1975 . 8 ° K . 19 3/21/11 Example - Ramjet with unstarted inlet m˙ f h f = ( m˙ a + m˙ f )h te – m˙ a h t0 . 0344 . 49) Now we need to determine the flow batween stations 1 and 3. To get started we will neglect the fuel addition for the moment. Knowing the Mach number at 4 and the stagnation temperatures at 3 and 4 we can use Rayleigh line results to estimate the Mach number at station 3.

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