2001-32 Thermal Analysis of Fairchild Dornier 728Jet Wing/Fuselage Interface using MSC.Patran Thermal Paper number 2001-32 D. Konopka, J. Hyer, A. Schönrock Fairchild Dornier GmbH PO Box 1103 82230 Wessling / GERMANY +49 (0) 81 53-30 3649 David.Konopka@faidor.de Abstract Fairchild-Dornier is currently developing the 728JET, the first member of a completely new family of aircraft designed for high frequency utilization in the competitive and demanding regional jet market. Computational analysis methods have been used extensively throughout the development process to optimize all aspects of the design. This paper gives an overview of the wing-tank/fuselage thermal mathematical model. The model was created from an MSC.Nastran whole-aircraft finite-element mechanical model and translated via MSC.Patran into a thermal model. The fuel-laden wing and the fuselage have widely disparate thermal response rates. When exposed to an environmental shift in temperature, such as that seen during climb to altitude, the wing and fuselage respond thermally different. Thermal stresses are induced at the aircraft wing/fuselage interface, which must be considered by the stress engineer and in the design calculations. The method of nodal temperature derivation is demonstrated in this paper. 1
1.0 INTRODUCTION As part of a thorough design evaluation of aircraft structures, the stress resulting from thermal gradients must be considered. Naturally, in order to predict such stresses, the thermal gradients need to be defined and applied to the finite element geometry in a usable fashion. This paper presents the approach that was used to define thermal gradients through a flight transient for an aircraft structure. 2.0 PROBLEM DEFINITION The primary goal of this study is to identify the thermal gradients upon the wing and center fuselage structures. The major cause of these thermal differences is due to the disparate thermal capacity (or mass) of the wing tanks versus panel and frame sections of the fuselage. These differences in thermal capacity will produce uneven transient heating or cooling when the aircraft encounters a thermal shift in its environmental exposure. The wing with full tanks will react slowly to the surrounding temperature change, while panel sections will react almost immediately to an environmental shift. The environmental exposure shift examined is a take-off and climb from hot ground conditions to high altitude cold conditions. Such an encounter will induce cold temperatures on the fuselage skin panels while higher temperatures on the tank panels remain. A reverse temperature shift, from cold to hot during a descent, will induce a reverse, but still substantial gradient between these parts. 3.0 ANALYSIS As part of the study to define maximum gradients that would be found upon the aircraft structure, the definition of worst case mission segments was required. A series of possible flight paths were evaluated to identify situations that would exacerbate thermal gradients due to thermal shift in environmental exposure. Gradients would exist during both the climb and descent portion of the flight. 3.1 Geometry and Mesh A thermal finite element model comprised of the center fuselage and the wing was created for the 728 Jet. This center fuselage-wing thermal model was created from the finite element mesh established for the stress group. The meshed geometry is shown in Figure 1. 3.2 Calculation Method The thermal calculations were made using MSC.Patran Thermal, the thermal analysis preference selection of MSC.Patran. This module has a multitude of thermal analysis capabilities and modeling features. The features made use of through this analysis include transient analysis, advective heat flow, variable film coefficient convection, conduction, radiation as element and nodal heat flux, time dependent boundary conditions, 3D quadrilateral elements, and temperature dependent material properties. The solution is solved by QTRAN whose analysis technique or formulation of equations is that of thermal network where the problem is assembled into a collection of thermal resistances and potentials (capacitors). Elements are translated from finite element data to resistor-capacitor data through a routine in the PATQ code. Once all t he node to node and node to boundary resistor-capacitor equations are formulated, the QTRAN code uses a predictor-corrector algorithm for solution. 2
3.3 Material and Element Properties The model definition includes temperature dependent material properties for aluminum, steel, fuel and air. Additionally, it is through the use of time dependent density that the fuel mass is varied to simulate the removal of fuel from the tanks. The element properties were incorporated from the structural model. Over 2 000 properties are employed to define various thicknesses of the aircraft structure. Figure 1. Isometric view of Center Fuselage and Left Wing Model Geometry 3.4 Boundary Conditions The model includes several boundary conditions to model the various regions around the structure. Each panel includes two convective boundary conditions and where necessary a radiation boundary. 3.4.1 Boundary Temperatures The definition of the temperatures was necessary for convection boundary conditions. In the case of the fuel tanks, the tanks are modeled with a thermal capacity node during the flight. These fluid nodes, one for both the fuel and air of each tank, are then used to calculate temperatures that are used as boundary conditions for the internal tank panel surfaces. The other temperature boundaries are modeled as functions that vary with time. This was 3
handled within the thermal model with linear interpolation through an index table lookup procedure. The modeled center f uselage internals are comprised of a cabin, an underfloor region, and the belly fairing compartment. The belly faring compartment is further subdivided into subcompartments. Internal air modeling was performed and steady state temperature predictions exist at various altitude flight conditions. These steady state temperatures have been used to construct the temperature profile through the flight mission. For aircraft external temperatures, ambient temperatures were specified in the mission definition. Finally, the boundary layer, or adiabatic wall temperature was calculated based on the aircraft speed and altitude. 3.4.2 Convection To define the convective boundary from the boundary temperature the film coefficient must be defined. For heat transfer coefficients, values were ascertained from empirical correlations for appropriate flow conditions. The majority of film coefficients were modeled as constant values. Because the FE model utilizes two dimensional panel elements in three dimensional space, two boundary conditions have been assigned to each shell element, one for each side. The convective boundary condition around the aircraft exterior varies with the flight conditions and altitude. For the convective heat transfer between the exterior air and the aircraft, boundary conditions have been calculated with a film coefficient based on skin friction. An average film coefficient was used over all exposed regions of the wing and fuselage. 3.4.3 Radiation In addition to the convection boundary conditions, there were radiation boundary conditions modeled as heat fluxes. These included solar heat flux, radiation from the ECS heatexchanger surface, radiation from the engine bleed air pipe, reflected radiation from the ground, and radiation exchange between the sky from the aircraft surface. ECS is an abbreviation for Environmental Control System, which provides the cabin with air at temperatures around 20 C, taken from the engine compressors at temperatures around 500 C. The outside air temperature at high altitude can be less than 70 C. Steady state estimates were made for these components at various altitudes in a normal flight mission. A collection of these temperature estimates was assembled using interpolation for intermediate altitudes. In this way, a heat flux versus time profile was provided for the model. The radiation reflected from the ground was calculated assuming a worst case ground temperature. A radiation coupling between the sky and the upper exterior surfaces was created. A final form of heat transfer that will occur is the radiation between individual surfaces of the aircraft. Calculations were performed to check the significance of this heat transfer mode. These showed that part-to-part radiation for the most temperature variant surfaces did not exceed 5% of the convection boundary condition. In most cases this flux term was found to 4
be 1-2% of the convection term. Therefore, it was a valid assumption to neglect this additional modeling. 3.4.4 Fuel Modeling In order to provide boundary temperatures to the wing tanks from the fuel side, modeling of the fuel was performed. The fuel level in the tanks and the thermal capacitance associated with the fuel were features incorporated in the model. To model the fuel capacitance, fluid nodes were created to represent the fuel and the air in the tanks. MSC.Patran Thermal allows for capacitances to be assigned to individual nodes. Capacitor values which are input manually are then added to those created from the finite element mesh. The procedure has certain limitations. Primarily, the capacitor volume is a constant and cannot be varied during the calculations. For the center and outer fuel tanks, the volume changes during flight. (The feeder tank volume is held relatively constant.) To circumvent this restriction, the density of the fuel in each tank was varied to represent the change in fuel capacitance. The fuel mass during flight was described in the mission definitions. In addition to modeling the changing mass of the fuel tanks, a methodology was created to handle the changing fuel level in the tanks. This must entail a method to change the connection of a boundary condition from surfaces connected with fuel to surfaces connected with air. To do this, an intermediate region was established in each tank. These were the portions of the side, top and bottom of each tank that is in fuel contact when full, but as the tanks empty, are above the fuel level. To handle this change, a boundary condition comprised of two components was set up for these surfaces. The first component was connected to the fuel fluid node, and the second was attached to the air fluid node. Initially at time equal zero, the fuel connection is set to 100%, and the air connection is set to 0%. Then, as fuel level falls below the region of interest, the connection to fuel is set to 0% and the connection to air is set to 100%. The connections are varied with the percent of fuel and air during the transition phase. 4.0 DISCUSSIONS The environmental thermal shift will induce gradients upon the aircraft structure. Some key regions where these gradients will exist are: 1) top panel to center fuselage skin panel; 2) circumferentially around the fuselage; and 3) tank top panels to the tank bottom panels. To get a better understanding of these gradients, the nodal results were grouped and averaged for these components. The transient temperature results are shown for these component averages on Figure 2. These average temperatures are shown for the first 2500 seconds of the mission. 5
Mission 1.0e Climb Average Component Temperatures outer tank (u) outer tank (l) Temperature; Altitude (u) (l) fuse(u) fuse(l) feed tank (u) feed tank (l) fuselage top Keel-beam alt (1000ft) TAT SAT 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 time [sec] Figure 2. Predicted Transient Temperature Gradients for Various Model Components In Figure 3, the fuel and air temperature predictions for each tank are shown. The boundary layer temperature and the altitude have been added to the graphs for reference. The worst average gradients were estimated to occur at time equal 1900 seconds. This references a time in the mission determined to collectively apply the largest gradients upon the wing tanks and fuselage structure. Individually, other times may be found that produce slightly larger gradients for specific regions, but the 1900 second time captures the best group of large gradients. An example of this is at the Keel Beam. This part reacts at a much different rate to temperature changes than the other structures. This part reaches a larger gradient at a different time in the mission than most other regions. Therefore, if a time point of maximum gradient for the keel beam was selected, the other regions would not be near their maximum. 6
Mission 1.0 Climb Predicted Fuel System Temperatures Temperature; Altitude outer tank fuel outer tank air fuel air TAT feed tank fuel alt (1000ft) 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 time [sec] Figure 3. Transient Temperature Predictions for Fuel System Figure 4. High Altitude Temperature Contours, Wing and Fuselage Top View 7
For flight point time 1900 seconds, two views of temperature contours on the model are shown in Figures 3 and 4. At this time, the temperature gradients have reached their approximate maximum. The difference between outer and inner tank along with the fuselage temperatures becomes highly noticeable in the results. Figure 5. High Altitude Temperature Contours, Under Wing and Belly Fairing Region 5.0 CONCLUSIONS The thermal analysis provides an integral part of the aircraft design process. The contribution is an estimation of thermal gradients component of stress. The quantification of this component of stress is used to further optimise the aircraft design. The full stress is made up of several components including pressure loading, mechanical loading and the thermal gradients. The quantification through thermal analysis of the thermal load provides information for a component of stress that has historically been lumped into other loadings or assumed into the noise. The analysis will eventually be calibrated with flight test data. Economically, flight test can only provide thermal results at a relatively few discreet test point locations. Once calibrated with these discrete test measurements, the thermal analysis can fill-in the remaining results over the full aircraft. The approach has shown that a large and complex plate element meshed geometry designed for stress analysis can be used for thermal analysis. The existing tools within MSC.Patran Thermal enable the analyst to utilize the same mesh allowing the stress engineer to have temperature predictions specific to his meshed geometry. This also avoids 8
the recreation of a computational mesh for thermal purposes and any inherent errors associated with an interpolation process between dissimilar meshes. 6.0 ACKNOWLEDGEMENTS We would like to thank Walter Simon, of MSC.Software GmbH for his support and technical assistance in the creation and execution of this thermal model. 7.0 REFERENCES (1) MSC.Patran Thermal User s Guide, Volume 1: Thermal/Hydraulic Analysis, The MacNeal-Schwendler Corporation, Los Angeles, CA, Octo ber, 2000. (2) Kreith, F., Principles of Heat Transfer, 3 rd ed., Harper & Row, Publishers, Inc., 1973. 9