Question

For a ramjet engine, combustion in the burner(whose cross-sectional area is constant as shown in the following figure) may be represented approximately as heating of a perfect gas with constant specific heat ratio...

For a ramjet engine, combustion in the burner (whose cross-sectional area is constant as shown in the following figure) may be represented approximately as heating of a perfect gas with constant specific heat ratio. Neglecting frictional effects, determine the stagnation pressure loss due to heating (i.e., derive the ratio of outlet and inlet stagnation pressures) and the ratio of outlet and inlet stagnation temperatures in terms of the Mach numbers M2 and M4. State all the assumptions made in the derivations. Flameholders Burning zone 4

Answer 1

Assumptions: - a) Area of Burner is constant b) friction does not exist during through burner. c) Gas in perfect gas with constant specific heat and ratio solution: - PO_4/PO_2 , T_O4/T_O2 equations appliable in this process: (1) P = rhoRT, ii) PV = constant iii) p + rhov^2 = constant first applying impulse function, at 2 and 4, P_2 + rho_2v_2^2 = P_4 P_4V_4^2 from , ideal gas relation, P_2 + P_2/RT_2 . v_2^2 = P_4 + P_4/RT_4 . V_4^2 {m = V/squareroot yRT m^2 = V^2/YRT} P_2 + P_2/RT_2 /m_2^2yRT_2 = P_4 + P_4/RT_4 . m_4^2 yRT_4 P_2 + rho_2ym_2^2 = P_4 + P_4ymu^2 P_2[1 + ym_2^2] = P_4[1 + ym_4^2] rightarrow 1 relation between static pressure and pressure at state 2, P_2^byT_2^y = P_O_2^1 - yT_O2^y T_2/T_o2 = (P_2/p_o2)^y - 1/y {because T_o2/T_2 = 1 + (y - 1)/2 M_2^2} therefore 1/1 + (y - 1)m_2^2/2 = (p_2/P_o2)^y - 1/y P_2 = P_o2[1/1 + (y - 1)m_2^2/2]^y/y - 1 rightarrow 2 similarly, P_4 = P_o4[1/1 + (0 - 1)m_4^2/2]y/y - 1 rightarrow 3