# Presentation: 004103

## 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**

## Outline

**Hyper-X Introduction**
**Analysis Challenges**
**Aero-Thermo-Structural Analysis Process**
**Thermal Analysis Methods & Results**
**Structural Analysis Methods & Results**
**Conclusions**

## Hyper-X Introduction

**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.**

## Slide 4

## Hyper-X Vehicle and Booster on B-52

## Hyper-X During Pegasus Boost

## Hyper-X Separating for Free Flight

## Hyper-X Engine Test

## Hyper-X Flight Hardware

## Hyper-X Analysis Challenges

**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.**

## Aero-Thermo-Structural Analysis Process

- MSC/NASTRAN
*structural analysis*

- Pro/Engineer
*design geometry*

- PATRAN Thermal
*thermal analysis*

- MSC/PATRAN
*modeling*

- SHABP
*aeroheating*

*trajectory *
*information*

- Fay-Riddell
*aeroheating*

*iteration*

**T**

## 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**
- 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

## 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**
- 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

## Thermal Analysis Model

**66,000 nodes**
**Brick and tet elements**
**Mesh density at LE 0.1” x 0.1”**

**Wing body**

**C-C leading edge**

## Thermal Analysis Model Details

**Thermal Analysis Model Details**

**Internal body structure**

**Weld detail**

## Thermal Analysis Model Details

**Detail of leading edge mesh**

## Aeroheating Flux Details

**Aeroheating Flux Details**

**At each of 18 trajectory points, the flux across the surface varies**
**These effects must be combined in the thermal solver**

**Flux change with time**

## Thermal Analysis Results

**Results in °F at 127 s**

## Thermal Analysis Results

**Results on body in °F at 127 s**

## Thermal Predicted Transient

## 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

## Structural Analysis Methods

**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 temperature-dependent 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.**

## Mach 10 Wing Finite Element Model

## Mach 10 Wing Internals

## Thermal/Structural Load Interpolation

## Mach 10 Wing Linear Analysis

## Yield Assessment

**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).**
**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 temperature-dependent yield stress at each node.**
**Generate a contour plot of the yield stress ratio.**

## Mach 10 Wing Yield Assessment

## Mach 10 Wing Nonlinear Analysis

## Typical Stress/Strain Curve for Wing

**Typical Stress/Strain Curve for Wing**

## Mach 10 Wing Nonlinear Analysis

## Mach 10 Wing Nonlinear Analysis 

## Conclusions

**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.**