INCAS BULLETIN, Volume 9, Issue 3/ 2017, pp. 3 – 11 (P) ISSN 2066-8201, (E) ISSN 2247-4528 Determination of a Two Variable Approximation Function with Application to the Fuel Combustion Charts Irina-Carmen ANDREI* *Corresponding author INCAS ‒ National Institute for Aerospace Research “Elie Carafoli”, B-dul Iuliu Maniu 220, Bucharest 061126, Romania, andrei.irina@incas.ro, icandrei28178@gmail.com DOI: 10.13111/2066-8201.2017.9.3.1 Received: 22 May 2017/ Accepted: 20 July 2017/ Published: September 2017 Copyright©2017. Published by INCAS. This is an “open access” article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 5 th International Workshop on Numerical Modelling in Aerospace Sciences, NMAS 2017, 17-18 May 2017, Bucharest, Romania, (held at INCAS, B-dul Iuliu Maniu 220, sector 6) Section 1 – Launchers propulsion technologies and simulations of rocket engines Abstract: Following the demands of the design and performance analysis in case of liquid fuel propelled rocket engines, as well as the trajectory optimization, the development of efficient codes, which frequently need to call the Fuel Combustion Charts, became an important matter. This paper presents an efficient solution to the issue; the author has developed an original approach to determine the non-linear approximation function of two variables: the chamber pressure and the nozzle exit pressure ratio. The numerical algorithm based on this two variable approximation function is more efficient due to its simplicity, capability to providing numerical accuracy and prospects for an increased convergence rate of the optimization codes. Key Words: approximation of two-variable functions, Propellant Combustion Charts, liquid propulsion, rocket engines 1. INTRODUCTION Thrust evaluation or thrust prediction at different flight regimes, as well as the analysis of flight dynamics and trajectory optimization are important milestones for both the design and performance analysis of liquid propelled rocket engines. For a realistic and accurate prediction of the rocket engines global on- and off-design performances, the Propellant Combustion Charts [1] are required which provide graphically the correlations between the chamber pressure c p , exit pressure conditions e p (i.e. burned gas expelled at ambient pressure or in vacuum) and mixture ratio r (which expresses the ratio of Oxygen to Fuel O/F), adiabatic flame temperature c T (also referred as the Chamber Temperature), gas molecular weight w M and specific heat ratio  , (also referred as the adiabatic power coefficient), for different types and combinations of fuel and oxidizer, [1]. Fig. 1 ÷ Fig. 4 shows the Combustion Charts for the study case: Liquid Oxygen and Kerosene (n-Dodecane, 12 26 CH ), [1].