Unsteady Heat Load Simulation for Hypersonic Cruise Optimization
Unsteady heat loads during the range cruise of a hypersonic vehicle propelled by a turbo/ram jet engines combination are considered. The unsteady heat load effects are simulated using a a realistic mathematical model. This model is coupled to the equation
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1
Introduction
A hypersonic flight sytem equipped with wings and air breathing engines can be considered a promising concept for an economic and safe access to space. It provides the capability of a range cruise so that the orbital stage can be released at a location distant from the takeoff site. A main problem at hypersonic speed concerns the high temperatures to which the vehicle is exposed. This is illustrated in Fig. 1, which shows areas where heat loading is particularly significant. An efficient thermal protection system is required to protect the structure of the flight system. It will be shown in this paper that the heat flux into the vehicle can be significantly reduced using optimal trajectory control.
/
Leading Edge
'"
Upper Surface
Lower Surface
\
Stagnation Point
Fig. 1. Areas with significant heat loading
M. Breuer et al. (eds.), High Performance Scientific and Engineering Computing © Springer-Verlag Berlin Heidelberg 2002
326
Wachter, Sachs
In recent years, important results have been achieved in the trajectory optimization of hypersonic vehicles [2,4,6], including effects of heat load and heat flux [5,11]. This paper presents results for an optimized range cruise, with special emphasis placed on a realistic simulation of the unsteady heat flux.
2 2.1
Modelling Flight System Dynamics Modelling
Modelling of the vehicle for trajectory optimization is based on point mass dynamics. The equations of motion read, with reference to a rotating spherical earth model [10], Fig. 2:
11 = ~
[T(V, h; a,OT) cos a - D(V, h;a)] - mg(h) sin, +
+w~r(h) sin" "y = m1v [T(V, h; a, OT) sina + L(V, h; a)]
V
+ cos, [ r( h)
-
g(h)
V +
w~r(h)] V
+
+ 2 WE, (1)
h = Vsin"
x=
m=
Vcos" -mjuel(V, h; a, OT).
State variables are speed V, flight path angle " altitude h, coordinate x and mass m. Control variables are angle of attack a and throttle setting OT.
v
mg Fig. 2. Forces acting on the vehicle
To describe the aerodynamics and powerplant characteristics a complex mathematical model is applied, including multifunctional dependencies for lift L, drag D and thrust T.
Unsteady Heat Load Simulation for Hypersonic Cruise Optimization 2.2
327
Heat Flux Modelling
A complex model for realistic simulation of the unsteady heat flux into the vehicle was developed [4]. A region at the lower side of the vehicle at half the distance between the nose and the liquid hydrogen tank is considered (Xle = 20 m). The wall structure of the thermal protection system is shown in Fig. 3. The thermal protection system consists of several layers of different material and thickness.
Outer Surface (Hot Airflow)
Inner Surface
Fig. 3. Wall structure with heat protection (5-1ayer model)
To model the heat flux, the wall is split up into n layers, Fig. 4. A onedimensional knot model is used to describe the heat flux from one layer to the other. The heat flux into the first layer can be described by ql
= qair
- qrad
=
qair(V, h,T1;a) -
E:CJ
[T{ - T!]
(2)
where qair and Tl depend on the flight condition. The heat
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