Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures NASA Workshop on Innovative Finite Element Solutions to Challenging Problems May 18, 2000 Michael C. Lindell and Ruth M. Amundsen Structural & Thermal Analysis Branch NASA Langley Research Center Hampton, Virginia Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Outline

2 Hyper-X Introduction Analysis Challenges Aero-Thermo-Structural Analysis Process Thermal Analysis Methods & Results Structural Analysis Methods & Results Conclusions NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures

Hyper-X Introduction 3 Goal: To validate, in flight, propulsion and related technologies for air-breathing hypersonic aircraft. Product: Two vehicles capable of Mach 7 and one vehicle capable of Mach 10. Schedule: First Mach 7 flight in late 2000. Payoff: Increased payload capacities and reduced costs for future vehicles by eliminating on-board oxygen fuel requirements.

NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures 4 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Hyper-X Vehicle and Booster on B-52 5 NASA LaRC/Lindell/Amundsen/05-18-00

Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Hyper-X During Pegasus Boost 6 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Hyper-X Separating for Free Flight 7 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures

Hyper-X Engine Test 8 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Hyper-X Flight Hardware 9 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures

Hyper-X Analysis Challenges 10 Hypersonic flight introduces extreme heat loads into vehicle leading edges (wings, tails, and nose). High temperature materials and coatings are required to distribute heat and carry resulting loads. Accurate generation and incorporation of heat loads requires tight integration between aeroheating analysis, thermal analysis, and structural analysis.

Loading conditions require nonlinear analysis with temperature-dependent material properties. NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Aero-Thermo-Structural Analysis Process trajectory information Pro/Engineer design geometry SHABP aeroheating Fay-Riddell

aeroheating iteration Q MSC/PATRAN modeling T Q T PATRAN Thermal thermal analysis T

MSC/NASTRAN structural analysis 11 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Aero-Thermo-Structural Analysis Process Design in Pro/Engineer Aeroheating analysis in SHABP from IGES geometry

Import Pro/E model directly to MSC/PATRAN Thermal analysis in MSC/PATRAN Thermal Less manual model development due to geometry import Include aerodynamic heating and pressure loads from SHABP Different aeroheating and thermal meshes can be utilized Extensive FORTRAN in PATRAN Thermal to interpolate aeroheating over both time and 3D space Stagnation point heating done using Fay-Riddell Iteration between thermal and aeroheating to capture skin temperature Structural analysis in MSC/NASTRAN

12 Less manual model building due to sharing with thermal analyst Different thermal and structural meshes can be utilized Uses temperatures interpolated directly from thermal model Nonlinear static analysis performed at discrete trajectory points under thermal and mechanical loads NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Analysis Methods

Properties All properties done as temperature-dependent 3D orthotropic where needed (on C-C) Aeroheating fluxes On surfaces, aerodynamic heating from SHABP dependent on Mach, altitude, skin temperature, geometry Interpolated in time and space onto PATRAN model On leading edges from Fay-Riddell dependent on Mach, altitude, skin temperature, geometry Factors applied for gap heating, cove heating, etc. Iteration between Q and T to come to closure Uncertainty factor F(time) applied to flux after closure

Other boundary conditions 13 Radiation to atmosphere (changing temperature with descent) Contact resistance between parts and across welds Radiation within cavities All boundary conditions done on geometry to facilitate remesh NASA LaRC/Lindell/Amundsen/05-18-00

Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Analysis Model C-C leading edge Wing body 66,000 nodes Brick and tet elements 14 Mesh density at LE 0.1 x 0.1 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures

Thermal Analysis Model Details Weld detail Internal body structure 15 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Analysis Model Details Detail of leading edge mesh 16

NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Aeroheating Flux Details Flux change across surface At each of 18 trajectory points, the flux across the surface varies These effects must be combined in the thermal solver 1.2

Flux (Btu/ft2-s) 1.0 0.8 0.6 0.4 0.2 Flux change with time 0.0 0 17 20

40 60 80 Time (s) 100 120 140 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Analysis Results

Results in F at 127 s 18 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Analysis Results Results on body in F at 127 s 19 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Predicted Transient

3500 Temperature (F) 3000 apex LE center body skin body apex body bulk 2500 2000 1500 1000 500 0

0 20 20 40 60 80 Time (s) 100 120 140

NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal Analysis Results Two outer emissivities run on body with little difference painted = 0.8 unpainted = 0.3 Contact resistance of leading edge varied 5E-4 to 5E-3 Btu/in2-s-F with little effect

Contact resistance at weld varied 0.1 to 1.0 Btu/in2-s-F with little effect 21 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Structural Analysis Methods

22 Temperatures from thermal analysis interpolated through MSC/Patran onto structural finite element mesh. Analysis performed using MSC/Nastran v70.5. Initial linear analysis run for yield assessment. Nonlinear analysis performed using temperaturedependent material properties (elastic modulii and coefficients of thermal expansion). Temperature-dependent stress/strain curves used in nonlinear solutions for materials experiencing yield. Discrete trajectory points analyzed to determine worst

case loads for strain and deflection (not always the hottest case). Strain results evaluated in light of short duration, single use conditions. Deflection results used to specify initial cold clearances. NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Mach 10 Wing Finite Element Model 23 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures

Mach 10 Wing Internals 24 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Thermal/Structural Load Interpolation 25 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures

Mach 10 Wing Linear Analysis 26 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Yield Assessment Using model temperatures for a given trajectory point, compute the temperature-dependent yield stress at each node using Y(T).

Compute the linear Von Mises stress at each node. Compute the ratio of Von Mises stress to the temperaturedependent yield stress at each node. Generate a contour plot of the yield stress ratio. 27 Problem: How extensive is the yielding? Yield stress is a function of temperature and therefore also a function of position throughout the wing. Determine an approximate relationship between temperature and yield stress (e.g., piecewise linear), Y(T).

NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Mach 10 Wing Yield Assessment 28 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Mach 10 Wing Nonlinear Analysis 29

NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Typical Stress/Strain Curve for Wing 30 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Mach 10 Wing Nonlinear Analysis 31 NASA LaRC/Lindell/Amundsen/05-18-00

Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Mach 10 Wing Nonlinear Analysis 32 NASA LaRC/Lindell/Amundsen/05-18-00 Nonlinear Thermal/Structural Analysis of Hypersonic Vehicle Hot Structures Conclusions

33 Tight integration of aeroheating, thermal, and structural analyses, each based on full 3-D geometry, was worthwhile and efficient. 3-D analysis captured effects that simpler 2-D analysis would have missed. Deflected shape from structural analysis can be fed back into aeroheating analysis to assess impact of deformation on flow and heating characteristics. NASA LaRC/Lindell/Amundsen/05-18-00