Second-Order Parabolic Equation to Model, Analyze, and Forecast Thermal-Stress Distribution in Aircraft Plate Attack Wing–Fuselage
Abstract
:1. Problem Introduction
2. Technical Characteristics of the P64 OSCAR B Aircraft
Plate-Attack Wing–Fuselage: Geometrical and Physical Characteristics
3. Proposed Model
3.1. Physical–Mathematical Modeling: Background
3.1.1. Heat Equation
3.1.2. Constitutive Laws
3.2. Initial and Boundary Conditions
3.3. Steady-State Case
4. Preliminary Lemmas
- 1.
- if on and in , then in ;
- 2.
- the following estimation of stability holds:
5. Model Realization in COMSOL-Multiphysics®
5.1. Model Physics
5.2. Model Geometry
5.3. Parameter Setting
5.4. Fixed-Constraint Setting
5.5. Plate Heat Transmission
5.6. Mesh Creation
5.7. Choice of Significant Temperatures
5.8. Boundary-Condition Setting
5.9. Determination of Heat-Transfer Coefficients h
6. Relevant Results
6.1. Simulations in Steady-State Conditions
6.2. Simulations in Dynamic Conditions
7. Experimental Investigations by IR Thermal Imaging and Result Comparison
7.1. Pretreatment with Penetrating Liquids
7.2. IR Thermography: Brief Overview
7.3. Thermographic Investigation at −18 (°C)
7.4. Thermographic Investigation at 15 (°C)
7.5. Thermographic Investigation at 30 (°C)
8. Conclusions and Perspectives
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
NDT and E | Nondestructive Testing and Evaluation |
UT | Ultrasound Technique |
ECs | Eddy Currents |
P64 OSCAR | The aircraft under study |
IR | Infrared Thermography |
PDE | Partial Differential Equation |
FEM | Finite Element Method |
UV | Ultraviolet Radiation |
FLIR SC660 | A type of thermal camera |
alloy 2024, 3630N | Special aluminum-copper alloy and special steel, respectively |
C | Carbon |
Chromium | |
Molybdenum | |
Manganese | |
Silicon | |
S | Sulfur |
P | Phosphorus |
Euclidean n-dimensional space | |
t | Temporal variable |
T | Absolute temperature |
D | Diffusion coefficient |
f | External heat source |
Density | |
r | Rate of heat per unit of mass |
V | Volume |
e | Internal energy |
Heat flux vector | |
External normal vector | |
k | Thermal conductivity |
Specific heat at constant pressure | |
Boundary of V | |
Stefan–Boltzmann constant | |
Surface emissivity | |
External absolute temperature | |
h | Heat-transfer coefficient |
Cylinder | |
Parabolic frontier | |
Lateral part of | |
Diffusive term | |
Convective term | |
Reactive term | |
, | Bounded functions in |
Plate attack wing–fuselage temperature | |
, , | Markers |
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Length | 7.24 (m) | Wingspan | 10 (m) |
Weight | 600 (kg) | Maximum take-off weight | 1100 (kg) |
Engine | Lycoming 0-360 180 (HP) | Cruise speed | 250 (km/h) |
Autonomy | 4, 5 (h) | Maximum cruising altitude | 5000 (m a.s.l.) |
Symbol | Standard Values | Symbol | Standard Values |
---|---|---|---|
477 (J/(kg K)) | k (thermal conductivity) | 42.7 (W/(m K) | |
Thermal expansion coefficient | 12.3 (1/K) | (density) | 7850 (kg/mq) |
Young’s module | 200 (Pa) | Poisson’s coefficient | 0.28 (dimensionless) |
(°C) | Flight Altitude (m) | (°C) | Flight Altitude (m) | (°C) | Flight Altitude (m) |
---|---|---|---|---|---|
−3.25 | 500 | 11.75 | 500 | 31.75 | 500 |
−6.50 | 1000 | 8.50 | 1000 | 28.50 | 1000 |
−9.75 | 1500 | 5.25 | 1500 | 25.25 | 1500 |
−13.00 | 2000 | 2.00 | 2000 | 22.00 | 2000 |
−19.50 | 3000 | −4.50 | 3000 | 15.50 | 3000 |
−22.75 | 3500 | −775 | 3500 | 12.25 | 3500 |
−26.00 | 4000 | −11.00 | 4000 | 9.00 | 4000 |
−29.25 | 4500 | −14.25 | 4500 | 5.75 | 4500 |
h | h | h | |||
---|---|---|---|---|---|
0 | 0.3671 | 15 | 0.4235 | 35 | 0.4482 |
−16.25 | 0.3681 | −1.25 | 0.3631 | 13.75 | 0.4269 |
−32.5 | 0.3371 | −17.50 | 0.3658 | −2.5 | 0.3628 |
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Angiulli, G.; Calcagno, S.; De Carlo, D.; Laganá, F.; Versaci, M. Second-Order Parabolic Equation to Model, Analyze, and Forecast Thermal-Stress Distribution in Aircraft Plate Attack Wing–Fuselage. Mathematics 2020, 8, 6. https://doi.org/10.3390/math8010006
Angiulli G, Calcagno S, De Carlo D, Laganá F, Versaci M. Second-Order Parabolic Equation to Model, Analyze, and Forecast Thermal-Stress Distribution in Aircraft Plate Attack Wing–Fuselage. Mathematics. 2020; 8(1):6. https://doi.org/10.3390/math8010006
Chicago/Turabian StyleAngiulli, Giovanni, Salvatore Calcagno, Domenico De Carlo, Filippo Laganá, and Mario Versaci. 2020. "Second-Order Parabolic Equation to Model, Analyze, and Forecast Thermal-Stress Distribution in Aircraft Plate Attack Wing–Fuselage" Mathematics 8, no. 1: 6. https://doi.org/10.3390/math8010006
APA StyleAngiulli, G., Calcagno, S., De Carlo, D., Laganá, F., & Versaci, M. (2020). Second-Order Parabolic Equation to Model, Analyze, and Forecast Thermal-Stress Distribution in Aircraft Plate Attack Wing–Fuselage. Mathematics, 8(1), 6. https://doi.org/10.3390/math8010006