16 Uncertainty Treatment Applications: High-Enthalpy Flow Ground Testing
533
The end part of all the design process is when all the experiments and simulations
converge into the actual flight conditions and we are able to put safety margins to
what has been tested and simulated to express our confidence in our tools. What
follows is a review of the most widely used methodology for extrapolation from
plasma wind tunnels and an account of the uncertainties we face when performing
such extrapolation to flight.
16.4.1 Local Heat Transfer Simulation Methodology
When facing a design challenge, engineers look at critical values that constrain
the parameters considered for the particular subsystem. When we look at the
thermal protection system for space vehicles, one of the most critical and important
parameters is the type of thermal protection materials we are going to use and (in
case of ablative materials) the thickness. These design parameters are intrinsically
associated to the heat flux absorbed by the vehicle surface while on the entry
trajectory.
To address this problem, one must identify the highest possible heat flux to
be encountered along the particular entry trajectory and use it as the limit to be
withstood. On the different points of the vehicle surface, one can identify the
stagnation region as the most likely part to suffer from the highest heat loads. It
is because of this that we aim at reproducing in the wind tunnel the same heat flux
on the stagnation point of our vehicle than that of the flight.
Following this line of thought, it is time to introduce the Local Heat Transfer
Simulation (LHTS) methodology depicted in Fig. 16.13
According to the literature in [9, 44–46], the heat flux equation can then be
generalized as:
q w = A P r
−2/3 (ρ w μ w )
B (ρ e μ e )
C
ρ e μ e β e (H e − h w ) = f (H e , ρ e , β e , h w )
(16.32)
A direct consequence of this fact is that the ground testing of the heat flux is
possible without a complete reproduction of the flight conditions. Indeed, as the
enthalpy, pressure and density are directly related, Kolesnikov [6] selects only three
different parameters to be matched in the ground testing facilities and in flight in
order to have the same stagnation point heat flux. These parameters are the total
enthalpy, total pressure, and velocity gradient at the edge of the boundary layer of
the vehicle/probe.
H
t
e = H
f
e
p
t
e = p
f
e
β
t
e = β
f
e
(16.33)
where β denotes the velocity gradient ∂u/∂x as a measure of the velocity deflection
when adapting aerodynamically to the vehicle shape with u and x as the transversal
component to the stagnation line of the velocity and space, respectively.
533
The end part of all the design process is when all the experiments and simulations
converge into the actual flight conditions and we are able to put safety margins to
what has been tested and simulated to express our confidence in our tools. What
follows is a review of the most widely used methodology for extrapolation from
plasma wind tunnels and an account of the uncertainties we face when performing
such extrapolation to flight.
16.4.1 Local Heat Transfer Simulation Methodology
When facing a design challenge, engineers look at critical values that constrain
the parameters considered for the particular subsystem. When we look at the
thermal protection system for space vehicles, one of the most critical and important
parameters is the type of thermal protection materials we are going to use and (in
case of ablative materials) the thickness. These design parameters are intrinsically
associated to the heat flux absorbed by the vehicle surface while on the entry
trajectory.
To address this problem, one must identify the highest possible heat flux to
be encountered along the particular entry trajectory and use it as the limit to be
withstood. On the different points of the vehicle surface, one can identify the
stagnation region as the most likely part to suffer from the highest heat loads. It
is because of this that we aim at reproducing in the wind tunnel the same heat flux
on the stagnation point of our vehicle than that of the flight.
Following this line of thought, it is time to introduce the Local Heat Transfer
Simulation (LHTS) methodology depicted in Fig. 16.13
According to the literature in [9, 44–46], the heat flux equation can then be
generalized as:
q w = A P r
−2/3 (ρ w μ w )
B (ρ e μ e )
C
ρ e μ e β e (H e − h w ) = f (H e , ρ e , β e , h w )
(16.32)
A direct consequence of this fact is that the ground testing of the heat flux is
possible without a complete reproduction of the flight conditions. Indeed, as the
enthalpy, pressure and density are directly related, Kolesnikov [6] selects only three
different parameters to be matched in the ground testing facilities and in flight in
order to have the same stagnation point heat flux. These parameters are the total
enthalpy, total pressure, and velocity gradient at the edge of the boundary layer of
the vehicle/probe.
H
t
e = H
f
e
p
t
e = p
f
e
β
t
e = β
f
e
(16.33)
where β denotes the velocity gradient ∂u/∂x as a measure of the velocity deflection
when adapting aerodynamically to the vehicle shape with u and x as the transversal
component to the stagnation line of the velocity and space, respectively.