## Date of Award

12-2016

## Degree Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Aeronautics and Astronautics

## First Advisor

William A. Crossley

## Committee Chair

William A. Crossley

## Committee Member 1

Sally P. Bane

## Committee Member 2

Gregory A. Blaisdell

## Committee Member 3

Daniel A. DeLaurentis

## Committee Member 4

John P. Sullivan

## Abstract

This research describes a process to model surface pressure data sets as a function of wing geometry from computational and wind tunnel sources and then merge them into a single predicted value. The described merging process will enable engineers to integrate these data sets with the goal of utilizing the advantages of each data source while overcoming the limitations of both; this provides a single, combined data set to support analysis and design. The main challenge with this process is accurately representing each data source everywhere on the wing. Additionally, this effort demonstrates methods to model wind tunnel pressure data as a function of angle of attack as an initial step towards a merging process that uses both location on the wing and flow conditions (e.g., angle of attack, flow velocity or Reynold’s number) as independent variables. This surrogate model of pressure as a function of angle of attack can be useful for engineers that need to predict the location of zero-order discontinuities, e.g., flow separation or normal shocks.

Because, to the author’s best knowledge, there is no published, well-established merging method for aerodynamic pressure data (here, the coefficient of pressure *Cp*), this work identifies promising modeling and merging methods, and then makes a critical comparison of these methods. Surrogate models represent the pressure data for both data sets. Cubic B-spline surrogate models represent the computational simulation results. Machine learning and multi-fidelity surrogate models represent the experimental data. This research compares three surrogates for the experimental data (sequential—a.k.a. online—Gaussian processes, batch Gaussian processes, and multi-fidelity additive corrector) on the merits of accuracy and computational cost. The Gaussian process (GP) methods employ cubic B-spline CFD surrogates as a model basis function to build a surrogate model of the WT data, and this usage of the CFD surrogate in building the WT data could serve as a “merging” because the resulting WT pressure prediction uses information from both sources. In the GP approach, this model basis function concept seems to place more “weight” on the *Cp* values from the wind tunnel (WT) because the GP surrogate uses the CFD to approximate the WT data values. Conversely, the computationally inexpensive additive corrector method uses the CFD B-spline surrogate to define the shape of the spanwise distribution of the *Cp*while minimizing prediction error at all spanwise locations for a given arc length position; this, too, combines information from both sources to make a prediction of the 2-D WT-based *Cp* distribution, but the additive corrector approach gives more weight to the CFD prediction than to the WT data.

Three surrogate models of the experimental data as a function of angle of attack are also compared for accuracy and computational cost. These surrogates are a single Gaussian process model (a single “expert”), product of experts, and generalized product of experts.

The merging approach provides a single pressure distribution that combines experimental and computational data. The batch Gaussian process method provides a relatively accurate surrogate that is computationally acceptable, and can receive wind tunnel data from port locations that are not necessarily parallel to a variable direction. On the other hand, the sequential Gaussian process and additive corrector methods must receive a sufficient number of data points aligned with one direction, e.g., from pressure port bands (tap rows) aligned with the freestream. The generalized product of experts best represents wind tunnel pressure as a function of angle of attack, but at higher computational cost than the single expert approach. The format of the application data from computational and experimental sources in this work precluded the merging process from including flow condition variables (e.g., angle of attack) in the independent variables, so the merging process is only conducted in the wing geometry variables of arc length and span.

The merging process of *Cp* data allows a more “hands-off” approach to aircraft design and analysis, (i.e., not as many engineers needed to debate the *Cp*distribution shape) and generates *Cp* predictions at any location on the wing. However, the cost with these benefits are engineer time (learning how to build surrogates), computational time in constructing the surrogates, and surrogate accuracy (surrogates introduce error into data predictions). This dissertation effort used the Trap Wing / First AIAA CFD High-Lift Prediction Workshop as a relevant transonic wing with a multi-element high-lift system, and this work identified that the batch GP model for the WT data and the B-spline surrogate for the CFD might best be combined using expert belief weights to describe *Cp* as a function of location on the wing element surface. (Abstract shortened by ProQuest.)

## Recommended Citation

Haderlie, Jacob Courtney, "Modeling methods for merging computational and experimental aerodynamic pressure data" (2016). *Open Access Dissertations*. 929.

https://docs.lib.purdue.edu/open_access_dissertations/929