Analytical Solution of Chamber Effective Length in the Axial Engine

In this research chamber effective length, which is the minimum chamber length required for complete combustion, for a dilute monopropellant spray, constant area, one dimensional and fixed volume engine is analytically predicted. A new evaporation rate in the form of d^k+1 relation, instead of d² law, is introduced. In case of controlling the vaporization by radiative heat transfer, k is equal to zero, and when molecular processes control the vaporization, k will be equal to unity and in some cases the vaporization data need the value of k greater than one to fit properly to related equation. Development of this approach can be used in design of combustion chambers with optimum length and with using vaporization rate of R = R₀〈r〉₀^k/〈r〉^k. Spray equation and distribution function in one-dimensional coordinate in direction of chamber axis is used as governing equations. Multiplying velocity and displacement variables by the simplified spray equation and some manipulation lead to a final form of integral equation. Definition of β₁β₃ as criteria will simplify the complex integral equation to a solvable relation. Results provide dimensionless velocity of droplets (from initial state to completely vaporization) and the chamber effective length for various values of k. The results obtained by employing d^k+1 relation show that increasing k increases in the droplet vaporization rate as well as the oxidizer velocity and decreases in the chamber effective length.