Full text
Analysis of Unsteady Pressure Loads on the Themis T3 Vehicle in Unpropelled Backward Flight Tim Horchler and Mariasole Laureti German Aerospace Center (DLR) Spacecraft Department, Göttingen
SALTO •SALTO - reusable Strategic Space Launcher Technologies & Operations •funded by the European Union in the frame of the Horizon Europe programme •supports the ESA Themis programme •T1H hop tests •Technology maturation for T3 and future launcher configurations
Evaluate Unsteady Pressure Loads on the T3 Vehicle for Suband Supersonic Flight Conditions 3 1. Evaluate unsteady root-mean-square (RMS) pressure loads on the vehicle surface 2. Analyze pressure spectra at selected surface locations 3. Assess grid resolution for the scaleresolving simulations (iDDES)
Numerical Tool: DLR TAU Code 4 •General purpose CFD code developed by the DLR Institute of Aerodynamics and Flow Technology •2nd-order compressible FV Navier-Stokes Solver •Unstructrued/hybrid grids: adaptation, chimera and deformation •Various turbulence models: RANS (1-7 eqn.), LES, (iD)DES •Validated for a wide range of flows (subto hypersonic) •Models for high-temperature thermodynamics •Models for chemically reacting flows (real-gas and multi-phase thermodynamics, combustion models, thermal relaxation, …)
Simulation Setup •Thermally and calorically perfect gas 𝛾 = 1.4 •Time-accurate dual-time-stepping scheme with ΔT = 2 × 10−6 s •Total simulation time ~1.0 s ↔ Δ𝑓 = 1 Hz •Low-dissipation low-dispersion (LD2) central scheme with matrix dissipation •Improved delayed detached-eddy simulation (iDDES) •Hybrid mesh with 16.6 mio cells (baseline), strongly refined in region of interest •Full configuration
Investigated Operating Conditions: Unpropelled Transonic Glide Phase Property Unit Subsonic baseline Subsonic fine Supersonic Simulation time S 0.995 1.047 1.118 Mach number - 0.9 0.9 1.5 Angle of Attack deg 5 5 5 Wall temperature K 300 300 300 No of grid points mio 16.55 36.72 16.62
Data Evaluation Strategy 7 𝑝RMS 𝑝dyn =𝑝 − 𝑝 2 ൗ 12𝜌∞𝑢∞ 2 Surface RMS pressure Sr =𝑓 ∙ 𝐿𝑟𝑒𝑓 𝑢∞ PSD′=PSD 𝑓 ∙ 𝑢∞ 𝑞∞ 2∙ 𝐿𝑟𝑒𝑓 Single-point spectra 1. Sample at 𝑓 𝑠= 5 kHz 2. Low-pass filter at 𝑓 𝑐= 2 kHz 3. Convert to spectrum with sample-length of 1024 samples Turbulent time scale 𝐶 𝜏 = 𝐶 𝑘 ∙ Δ𝑇 = σ𝑛𝑝𝑛+𝑘 ′∙ 𝑝𝑛 ′ σ𝑛𝑝𝑛 ′2 with 𝑝′= 𝑝 − 𝑝 1. Calculate auto-correlation 2. Fit parabolic curve 3. Find first zero-crossing
Qualitative Flow Field Overview: Turbulent Strtuctures Q Isosurfaces 8 Ma = 0.9 Ma = 1.5 𝑄 = 𝑄′∙𝑢∞ 2 𝐷2
Qualitative Flow Field Overview: Turbulent Strtuctures Q Isosurfaces 9 Ma = 0.9 Ma = 1.5 𝑄 = 𝑄′∙𝑢∞ 2 𝐷2 Q-criterion based on post-shock velocity
Influence of Mesh Refinement on RMS Pressure 36.7 mio fine mesh vs. 16.6 mio baseline mesh 16 fine mesh baseline mesh Part Max RMS baseline Max RMS fine Baseplate 41.1 % 39.8 % Nozzle 42.2 % 40.5 % Body 20.0 % 19.2 % •Significantly finer structures visible in Q isosurfaces •Very little influence on RMS distribution •Small differences in the maximum RMS values ➢Robust setup for RMS pressure estimation
Conclusion •Provided analysis of unsteady pressure loads for the T3 vehicle •Identification of critical regions using RMS pressure maps on the surface •Very similar spatial distribution for Ma = 0.9 and Mach = 1.5 but different amplitude •Single-point spectral analysis with limited significance •Sampling statistics worse than initially anticipated •Turbulent time scale in the range of 2-2.5 ms reduces sample size drastically •Mesh resolution is sufficient on leeward side •Grid sensor successfully applied to this case indicating good resolution •RMS pressure values insensitive to grid refinement → robust quantity 17
Outlook •Experimental campaign measuring T3 unsteady aerodynamics conducted at DLR Cologne (Ansgar Marwege): •Comparison between CFD and wind tunnel data •Can unsteady wind tunnel CFD data be extrapolated to flight? •Comparison of (time-averaged) unsteady simulation results with RANS •Compare global coefficients, e.g. lift, drag, moment coefficients, etc. •Transonsic regime difficult for RANS models, how large are the errors? 18
Thank you!
