Analytical Solution of Chamber Effective Length in the Axial Engine Available to Purchase

In this research, effective length of one-dimensional combustion in a dilute monopropellant spray, constant area and fixed volume chamber is analytically predicted. A new evaporation rate in the form of d^k+1 relation is introduced. In the case of controlling vaporization by radiative heat transfer, k is equal to zero, and when molecular processes control the vaporization, k will be equal to one and in some cases vaporization data need the value of k greater than one to fit properly to related equation. Development of this approach can be used in the 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 the governing equation. Multiplying velocity and displacement variables by 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 chamber effective length for various values of k. The results obtained by employing d^k+1 relation show that increasing k increases in droplet vaporization rate as well as oxidizer velocity and decreases in dimensionless effective length of chamber. Also they show that for β₁β₃ ≥ 25 deviation of dimensionless velocity from published data by Dehghani et al. (2009) is less than 3%.