Implementation of an Unsteady PSP System in the NASA TDT NASA Langley Research Center daniel.reese@nasa.gov Daniel Reese, Sarah Peak, Kyle Goodman, Neal Watkins Transonic Dynamics Tunnel (TDT) - Continuous, closed-circuit - 16’×16’ slotted test section - 0.01 atm < P < 1 atm - 0 < Mach < 1.2 - Max Reynolds number of: - 9.6×106/ft ( in R-143a) - 3×106/ft ( in air) Wind Tunnel Facility & Launch Vehicle Model Launch Vehicle Model - Generic hammerhead used by Coe and Nute (NASA TM X-778, 1962) - 17.4” long payload section - 56 Kulites & 14 static pressure taps Perry et al. AIAA 2007-1770 2 Environmental Enclosures Enclosures - Maintain ambient pressure as facility P is reduced - Provide constant supply of cooling air for internal components - Allow for remote-operation (from control room) of all equipment housed within 3 Unsteady Flow System https://technology.nasa.gov/patent/LAR-TOPS-36https://doi.org/10.1103/APS.DFD.2015.GFM.V0015 4 Leaf blower with fluidic oscillator attachment creates impinging jet with known frequency independent of amplitude Test Objectives Run 784 Point 179 α = -2° Framerate = 5 kHz Leaf blower • Vary AOA -4°<α<4° • Vary pressure 56575° removed from calculation • Patch regions of “bad” data (e.g. registration targets, unpainted region) Phase 2: Intensity Mapping • Account for small model motion between frames by warping all subsequent images to align with first frame • Project each warped image onto the model grid Phase 3: Conversion to Pressure • Calculate intensity fluctuations for each frame relative to average of all frames 6 Unsteady pressure obtained from raw intensity data Data processing on NASA Advanced Supercomputer (NAS) • Collaborative effort with NASA Ames • Convert intensity movies to unsteady pressure mapped to grid 𝑃 = 𝐼𝑟𝑒𝑓 𝐼 − 1 ∗ 𝐺𝑎𝑖𝑛 𝐺𝑎𝑖𝑛 = 𝑎 + 𝑏𝑇 + 𝑐𝑇2 + 𝑑 + 𝑒𝑇 + 𝑓𝑇2 ∗ 𝑃𝑠𝑠 T = 𝑟 𝑇0 − 𝑇∞ + 𝑇∞ 𝑟 = 0.896 Kulite Comparison: Time History ∆Pressure Histories • Zone-averaged PSP shows agreement with Kulite average • Individual Kulites show spatial-dependence of pressure disturbance • Better agreement likely achievable with local averaging around unsteady pressure tap Small unsteady pressure disturbance resolved by uPSP system 7 Kulite Comparison: Spectral Analysis Fundamental frequency (+ higher harmonics) measured by uPSP system 8 Power Spectra • Zone-averaged PSP shows agreement with Kulite average • Individual Kulites show spatial-dependence of pressure disturbance • Fourth harmonic lost to noise in uPSP measurements Dynamic Mode Decomposition: Background 𝑋 = 𝑈Σ𝑉∗ → 𝑋′ = 𝐴𝑈Σ𝑉∗ 𝑈∗𝑋′𝑉Σ−1 = 𝑈∗𝐴𝑈 = à ÃW = 𝑊Λ Φ = 𝑋′𝑉Σ−1𝑊 ෠𝑌 𝑡 = Φ Λ𝑡 𝑧0 𝑋 = | | 𝑥1 𝑥2 | ⋯ 𝑥𝑚−1 | | | 𝑋′ = | | 𝑥2 𝑥3 | ⋯ 𝑥𝑚 | | | Define 2 matrices from uPSP data DMD tries to find a best fit linear operator A that advances X into X’ 𝑋′ ≈ 𝐴𝑋 DMD is a dynamical system of coupled spatial temporal modes timespace Eigenvalue decomposition of Ã: Decouple space and time Singular value decomposition (SVD) of 𝑋: Today, this is a ~370k×45k matrix We have leading eigenvalues and eigenvectors of A without ever having to compute A Reconstruct data using only dominant modes: Project A onto leading modes: In our case, A is ~370k×370k → 137B entries Continue analysis using only the r “most important” modes. Today: r=25, so à is only 25 × 25. 9 ෠𝑋 = | | 𝑥1 𝑥2 | ⋯ 𝑥𝑚 | | | 10 Temporal DMD Modes Radial distance associated with growth rate • Inside unit circle = decay • Outside unit circle = growth • On unit circle = oscillation Angle determines frequency of associated mode 25 modes consist of 12 complex conjugate pairs and one real value DMD eigenvalues (Λ) relate to temporal characteristics 11 “Eigen pressure distributions” show dominant spatial coherent modes Spatial DMD Modes DMD eigenvectors (Φ) relate to spatial structures involved in the modal dynamics Higher Modes + Real Imaginary Modes 1/2 Modes 3/4 Modes 5/6 Recall each (Φ) related to associated (Λ) so frequency of each mode is known Filtering through DMD Reconstruction of our data using only r=25 dominant modes: DMD Reconstruction 12 ෠𝑌 𝑡 = Φ Λ𝑡 𝑧0 Filtering in space and time Moving average filter in time (75 frames = 15 ms) 2D median filter in space (4x4 pix) Now combine space (Φ) and time (Λ) by reconstructing uPSP data… Reconstructed uPSP measurements show improved noise reduction Future Work 13 • Continue building on the post-processing tools developed for uPSP analysis • Apply uPSP system to actual “wind on” test in TDT using the Coe model • Determine the O2 concentration needed to perform uPSP in a low-pressure R134a environment • Apply all lessons learned for an upcoming experimental campaign for the space launch system (SLS) The best is yet to come!