Time-Dependent Mars Entry Aeroheating Estimation from Simulated In-Depth Heat Shield Temperature Measurements

Abstract

There are substantial uncertainties in the computational models currently used to predict the heating environment and the Thermal Protection System material response during Mars entry. Flight data are required to quantify and possibly reduce such uncertainties as well as improve current computational tools. The Mars Science Laboratory Entry, Descent, and Landing Instrumentation suite will provide a comprehensive set of flight data that will include subsurface temperature measurements of its Phenolic Impregnated Carbon Ablator heatshield at different locations. The purpose of this paper is to investigate the time-dependent estimation of Mars Science Laboratory surface heating from simulated Mars Science Laboratory Entry, Descent, and Landing Instrumentation temperature data using inverse methods in the presence of random and bias measurement and model errors. The surface heat flux is indirectly reconstructed by estimating the discretized heat transfer coefficient profile as a function of time. Whole-time domain least-squares methods in conjunction with the Tikhonov regularization technique are applied to this problem. The performance of the estimation methods and the accuracy of the reconstructed surface conditions are investigated under different types of errors in the measurements, such as random noise and thermocouple lag. Furthermore, the effect of material property bias on the estimation of surface conditions is also studied.

Inverse Heat Conduction Methods in the CHAR Code for Aerothermal Flight Data Reconstruction

“…A too-small value of α will not provide the desired smoothing effect, but a too-large value will overly smooth the solution and introduce too much bias in the reconstructed temperature vector. As pointed out by Mahzari et al 13 , the value of α will depend on the magnitude of the unknowns (in their case, small values of the heat transfer coefficient in their reconstructions required regularization parameters that were orders of magnitude greater than those needed for heat flux reconstructions in the literature). Many authors resort to a trial-and-error method for defining appropriate values for α.…”

“…Since a finite-difference approximation to the sensitivity coefficients are evaluated for many realistic problem, evaluating this matrix can become costly if the numerical model for the system is expensive. As an example (described in more depth in Seciton III.D), a sequential reconstruction of the MSL dataset presented by Mahzari et al 13 would require the ablator material response model integrating 1.95 · 10 3 s of time to complete the reconstruction. By contrast, the whole domain reconstruction presented by Mahzari et al required the integration of 6.79 · 10 6 s, three orders of magnitude more effort!…”

“…However, if F is too large relative to M , the SSD reconstruction could rapidly become the most expensive. If we consider a numerical example, Mahzari et al 13 considered a time domain of t f ull = 130 s with a reconstruction frequency of 1 Hz (N = 1, and M = 130) and ν = 200 non-linear iterations for the MSL reconstruction. This means that a whole domain reconstruction requires 6.786 · 10 6 s of accumulated simulated time.…”

“…Neither is universally better than the other; the optimal choice comes down to the sensitivity coefficients of the specific problem. Some examples of sequential algorithms are the future time family of algorithms from Beck et al 8 , and some examples of whole domain algorithms are the Gauss-Newton method 13 and conjugate-gradient methods (with and without the adjoint equation) 6,14 . Perhaps a bit tangent but still related to this metric, space marching techniques 15,16 swap a spatial dimension for time and compute temperatures sequentially in space from the sensor location to the boundary.…”

Inverse Estimation of the Mars Science Laboratory Entry Aeroheating and Heatshield Response

“…The authors have traditionally defined the inverse problem as the estimation of the timedependent heat transfer coefficient profile. This approach was used for the inverse analysis of simulated MISP data [31] and Mars Pathfinder data [6]. Inverse methods are used to estimate heat transfer coefficient as a function of time while keeping the recovery enthalpy fixed to the CFD-calculated value and allowing FIAT to internally calculate surface ablation chemistry and material decomposition.…”