# Uncertainty Quantification Analysis for Hypersonic CFD

Graduate Student: Andrew Weaver

Collaborators: Dr. Robert Greendyke (AFIT), Dr. Jose Camberos (AFRL)

The development of advanced hypersonic aerospace vehicles remains a strong focus of several programs pursued by US Air Force and NASA as well as European agencies. The design of hypersonic systems requires multidisciplinary studies involving structural mechanics, aerodynamics, propulsion and materials. Since both flight and on-the-ground experiments are expensive for hypersonic flight conditions, computational methods such as computational fluid dynamics (CFD) serve as critical tools in the analysis and design of such systems. While a deterministic CFD solution gives a single-point estimate for a fixed set of input parameters, in real-life hypersonic applications numerous uncertainties in the design, manufacture and operation must be addressed. With the modern computational capabilities it has become feasible to perform uncertainty quantification (UQ) analyses which are valuable to design processes. UQ indicates which parameters are contributing the most to the variability of an output quantity and introduces opportunities for design improvements.[1][2]

The purpose of this research is to provide an efficient method to quantify the uncertainties in flowfield properties of interest due to fluctuations in atmospheric conditions such as: freestream temperature, density, and velocity as well as modeling parameters such as collision integral coefficients. Thus, a Polynomial-chaos (PC) method which uses deterministic sampling is presented.[1][2] In applying this method to the FIRE II experiment at 1643 second trajectory point, it is observed that the output properties are most sensitive to the freestream velocity variations. Figure (1) shows the baseline temperature contour over the FIRE II forebody, and Fig. (2) shows the relative temperature uncertainty due to a 0.29% input velocity uncertainty. Note the higher uncertainties in the expansion region of the shoulder and across the shock near the outflow.

** Figure 1.**

*Translational Temperature Contour for Baseline Case*

**Figure 2.**Uncertainty in Translational Temperature Due to 0.29% Velocity Variations

**References**

[1] Weaver, A., “Analysis of Flowfield and Surface Heat Flux Uncertainties Under Typical Blunt-Body Re-entry Conditions,” Master's Thesis, Department of Aeronautical and Astronautical Engineering, Purdue University, Lafayette, IN, 2010.

[2] Weaver, A., Alexeenko, A., Greendyke, R., and Camberos, J., “Flowfield Uncertainty Analysis for Hypersonic CFD Simulations,” *48 ^{th} AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition*, 2010, also Paper AIAA-2010-1180.

[3] Weaver, A., Alexeenko, A., Greendyke, R., and Camberos, J., “Flowfield Uncertainty Analysis for Hypersonic Computational Fluid Dynamics Simulations,” *Journal of Thermophysics and Heat Transfer* 25 (1) 2011, pp. 10-20.