APPLICATION OF MODERN DESIGN OF EXPERIMENTS TO CARS THERMOMETRY IN A SUPERSONIC COMBUSTOR

We have applied formal experiment design and analysis to optimize the measurement of temperature in a supersonic combustor at NASA Langley Research Center. We used the coherent anti-Stokes Raman spectroscopy (CARS) technique to map the temperature distribution in the flowfield downstream of an 1160 K, Mach 2 freestream into which supersonic hydrogen fuel is injected at an angle of 30 degrees. CARS thermometry is inherently a single-point measurement technique; it was used to map the flow by translating the measurement volume through the flowfield. The method known as “Modern Design of Experiments” (MDOE) was used to estimate the data volume required, design the test matrix, perform the experiment, and analyze the resulting data. MDOE allowed us to match the volume of data acquired to the precision requirements of the customer. Furthermore, one aspect of MDOE, known as response surface methodology, allowed us to develop precise maps of the flowfield temperature, allowing interpolation between measurement points. An analytic function in two spatial variables was fit to the data from a single measurement plane. Fitting with a cosine series bivariate function allowed the mean temperature to be mapped with 95% confidence intervals of ±30 K, comfortably meeting the precision requirement of ±50 K specified prior to performing the experiments. We estimate that applying MDOE to the present experiment saved a factor of five in data volume acquired, compared to experiments executed in the traditional manner. Furthermore, the precision requirements could have been met with less than half the data acquired. * Research Scientist, Member AIAA ** Senior Research Scientist, Member AIAA # Associate Professor, Senior Member AIAA Nomenclature F ratio of selected mean square values k number of regressors in a model (p-1) K kelvin n number of data points used to fit a response surface model p number of parameters in a model, including intercept (k+1) r radial axis from center of fuel jet, in polar coordinates R Ratio of explained to total sum of squares x spanwise axis in duct y vertical axis in duct z streamwise axis in duct σ standard error in the regression θ azimuthal axis about center of fuel jet, in polar coordinates ANOVA analysis of variance CARS coherent anti-Stokes Raman spectroscopy CIHW confidence interval half width df degrees of freedom LOF lack of fit MDOE modern design of experiments MSE residual mean square error (unexplained variance) PE pure error PIHW prediction interval half width RSM Response Surface Methodology, Response Surface Modeling SS sum of squares confounding Executing an experiment so that the change in response cannot be uniquely attributed to a specific factor Fcritical A threshold F statistic indicating minimum statistical significance level Specific setting of an independent variable LOF F ratio of lack of fit to pure error components of unexplained variance 22nd AIAA Aerodynamic Measurement Technology and Ground Testing Conference 24-26 June 2002, St. Louis, Missouri AIAA 2002-2914 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. 2 American Institute of Aeronautics and Astronautics model F ratio of model mean square to residual mean square model mean square variance that can be explained by model p statistic probability that a corresponding F statistic is not significant parameter space, design space Range of independent variable levels population a theoretical construct representing conceptually all the possible observations of a system sample a discrete number of observations site: Specific location in the design space (specific combination of independent variable levels)