The VII procedure for the 3D model is similar in concept to the Direct method for the 2D case. However some approaches had to be adapted.
First, the geometry must be imported and interpreted. The file created by the APAME GUI to be used by the APAME SOLVER is read and interpreted by a routine implemented in MATLAB. This way the geometry and the flow conditions are imported into this environment. The geometric model imported into APAME GUI was obtained from a NASTRAN structural analysis file.
After the geometry was imported it is then interpreted. A routine implemented in MATLAB first finds the 3D trailing edge and then, for each trailing edge panel, assembles the correspondent streamwise section. These sections are then treated as 2D airfoils by the 2D Boundary Layer Solver. After the boundary layer is evaluated for all sections, the results are reassembled and passed to the 3D aero- dynamic model. A file containing the Transpiration velocity values for each of the 3D surface panels is then created. The APAME Solver is once again called to solve the inviscid problem but his time with the displacement correction.
As results are obtained, APAME integrates the pressure loads over the wing surface and outputs the aerodynamic coefficients. Velocity distribution at the wing surface is also imported back to MATLAB and is used in the following iteration for a new Boundary Layer solution. This iterative procedure is repeated until convergence. Figure 4.3 summarizes the calculation procedure implemented in this module.
?
Aerodynamic Analysis Definition(APAME ”.inp” file)
?
?
APAME Inviscid Flow Solver
?
Aerodynamic Loads and Coefficients(”.res” file) Read 3D Velocity field
Interpret Geometry and Results Organize results into 2D Streamwise sections
?
Velocity distribution on upper and lower surface Boundary Layers over 2D Wing Sections 2D Boundary Layer Equations(Repeat for each BL section)
First station
Thwaites method See [32].
Laminar Flow stations ( ˜n<9) Governing Equations:
Von Karman(Eq. 3.48) Shape Param.(Eq. 3.47)
Amplification(Eq. 3.63) Closure Equations:
Hk∗(Eq. 3.50a) H∗(Eq. 3.50b) Cf(Eq. 3.51) CD(Eq. 3.52)
Turbulent Flow stations Governing Equations:
Von Karman(Eq. 3.48) Shape Param.(Eq. 3.47) Lag Entrainment(Eq. 3.60)
Closure Equations:
Hk∗(Eq. 3.56) H∗(Eq. 3.50b)
Cf(Eq. 3.54) CD(Eq. 3.58)
?
δ∗over the Wing Sections
Calculate Transpiration Velocity(EQ. 3.69) Organize BL parameters to 3D
vnover Wing Surface panels
-
?
- Boundary Layer parameters along streamwise sections - Aerodynamic Coefficients and Loads
Figure 4.3: Aerodynamic Module computation flowchart.
4.3 Structural module
By dividing a complex geometry into several small simpler parts, know as Finite Elements, the Finite Element Method is a numerical method used for finding an approximate solution to partial differential equations.
Although the method can be used in many fields, including Aerodynamics or Heat Transfer, its use in Structural Mechanics is by far the most consensual, as very good results can be obtained in structural analysis with relatively low computational requirements. With various formulations and element types available, it is the standard for Structural Analysis in the industry across all engineering fields.
Several commercial software packages are available today implementing this kind of methods for several fidelity levels and offering embedded Multidisciplinary Analysis. Siemmens NX and MSC Pa- tran/Nastran both use NASTRAN as the structural solver. NASTRAN is an acronym for NASA Structural
Analysis, a FEM Solver developed in the 1960’s as a way to uniformize the use of structural solvers through its engineering centers. Other solutions like Ansys, Abaqus and others use proprietary solvers.
The Structural module is responsible for calculating the solution to the static structure problem. Its main component is NX NASTRAN, a commercial Finite Element Analysis tool that solves the struc- tural linear system consisting of the wing structure fixed at the root and loaded with several load cases corresponding to different aerodynamic loads.
First, the aerodynamic loads originated from the Aerodynamic Module are read. The aerodynamic pressure and the shear stresses are organized and passed to the NASTRAN structural analysis file, replacing any existent load cases. NX NASTRAN is then called and the results output file is generated containing, among other parameters, the nodal displacements.
4.4 Aeroelastic framework
In this section the implementation of the Aeroelastic framework, which is the main objective of this work, is presented. It was built around two main modules, the Aerodynamic Solver and the Structural Solver, presented in detail in previous sections.
The first step was to allow that the geometry is imported. To do so, the APAME Graphical User Interface (GUI) is used, as it already includes routines to import the discretized geometry from the analysis files used by NASTRAN, ABAQUS and other commercially available software. It is also during this step that the wake panels are added to the geometry, as well as the flow conditions and reference parameters are set.
From that point on, the file (*.inp) created by the APAME GUI to be used by the APAME SOLVER is read and interpreted by a routine implemented in MATLAB. This way the geometry and the flow conditions are imported into this environment.
At this point, the Aerodynamic solver takes the geometry and executes the iterative procedure de- scribed in Section 4.2. When the Aerodynamic solution is obtained, the aerodynamic loads, due to both the aerodynamic pressure and the shear stresses, are imported and included in the original NASTRAN structural analysis file. As the aerodynamic and structural meshes coincide at the wing surface due to having been imported from the same file, the loads are assigned back to each individual panel and the new structural analysis file is generated. Next, the framework calls NASTRAN to solve the static structural analysis as indicated by the new file.
Once the solution is achieved and the NASTRAN structural analysis output file is generated, the framework executes a routine to read and interpret the results. The surface node displacements are taken by the framework and the geometry is updated to the new deformed configuration by adding the displacements in X, Y and Z to the respective original node positions. The wake position is recalculated by taking the nodal displacements at the wing trailing edge.
This new geometry is then exported back to the APAME SOLVER input file and the cycle is repeated until convergence is reached.
The entire process is summarized in the flowchart of Figure 4.4.
'
&
$
%
- Structural and Aerodynamic Geometry Definition (NASTRAN ”.dat” file)
- Flight Conditions;
- Reference values
?
APAME GUI
?
Aerodynamic Analysis Definition(APAME ”.inp” file)
?
?
AERODYNAMIC MODULE
?
Aerodynamic Loads
LOAD TRANSFER (Aero to Struct)
?
Structural Analysis Definition(NASTRAN ”.dat” file)
?
STRUCTURAL MODULE
?
Nodal Displacements Results(NASTRAN ”.f04” file)
LOAD TRANSFER (Struct to Aero)
Deformed Aerodynamic Analysis Definition(APAME ”.inp” file)
-
?
- Displaced Geometry
- Aerodynamic Coefficients and Loads
Figure 4.4: Aeroelastic Framework Modules flowchart.