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- Introduction The Spacex Falcon 9 Is A Contemporary Rocket Designed To Deliver Payloads Into Space The Rocket Consists O 3 (20.59 KiB) Viewed 53 times
solved.
This is the temperature boundary conditions :
T(x,L) = 212K.
T(0,Z) = 0K,
T(D,Z) = 0K.
Introduction The SpaceX Falcon-9 is a contemporary rocket designed to deliver payloads into space. The rocket consists of two stages, a lower primary (for atmospheric flight) and upper secondary (for vacuum flight). In this assignment you will analyse the thermal behaviour of a simplified model of the secondary rocket stage. A schematic of the rocket stage and simplified model is given in Figure 1: • Tapering of the rocket can be ignored so it may be modelled as a rectangle with a length L = 13.8 m and a diameter/width D = 3.7 m; • The rocket has fixed boundary temperatures (stated with respect to ambient temperature);
• The temperature profile of the rocket as a function of two-dimensional space, T(x,z), can be modelled with the Laplace governing equation given by: OPT OT + = 0 ar2 az2 (1) T = 212 K = T = 0 K T = OK L = 13.8m L T = 3382 K D = 3.7m Figure 1: Simplified model of the SpaceX Falcon-9 stage 2 rocket.
1. State the temperature boundary conditions mathematically. (2%) 2. With the aid of a diagram, briefly explain how computing the steady-state temperature а distribution for this problem can be solved using two simpler component problems. Keep your answer to <100 words. (3%)