Supersonic MLN Thrust Correction at HT with Application to The Missile Trajectory

The aim of this work is to develop a new numerical calculation program making it possible to correct the thrust coefficient C_F and the exit Mach number M_E of an existing MLN by studying the effect of the stagnation temperature T₀ of the combustion chamber below the dissociation threshold of the molecules, based on the use of the HT model to, firstly, correct the flow in the nozzle, and then deduce the new corresponding values of (C_F)_C and (M_E)_C. The nozzle equipped with missiles and supersonic aircraft is determined using the PG model. This model is developed without dependence of T₀. In reality, and depending on the used propellants, the combustion chamber T₀ value can reach high values exceeding 500 K. Since T₀ can be high, the (C_F)_C and (M_E)_C cannot be those obtained by the PG model. They must respond to the behavior of T₀ effect, since the gas actually behaves like a gas at HT. Since the MLN has an unchanged contour, that is to say the mass of the nozzle is unchanged, it is necessary to correct the (C_F)_PG as well as, (M_E)_PG in order to further correct the other performances of the aerospace machines using the MLN, like the range, flight time, and maximum altitude of the supersonic missiles. An introduction of two new dimensionless coefficients λ and ψ making it possible to respectively determine the correction rate of (C_F)_C and (M_E)_PG compared to those determined by the manufacturers during the design of the MLN by the PG model. The calculation of the error between the obtained correction value and that given by the manufacturer is done for all parameters. The application is made for air and for three other gases H₂O (gas), CO and N₂. For example when (M_E)_PG = 3.00, T₀ = 3500 K, r_* = 1.00 and air, we will have a correction until 21.16% for (C_F)_C and 9.50% for (M_E)_C.