2 Geometry model implementation The geometry implementation process starts from the reference Common Research Model (CRM) CAD files available [15], and is carried out with the purposes of:

(1)

15

2 Geometry model implementation

The geometry implementation process starts from the reference Common Research Model (CRM) CAD files available [15], and is carried out with the purposes of:

 Validate the numerical model, referred to the CRM swept wing, by using wind tunnel results;

 Compare the reference model with a curved planform wing geometry: the planform curvature is realized only on outer sections between the kink (i.e. end of the Yehudi break) and the tip of the wing by shearing backward the airfoils.

 Ensure that the CAD process could be parameterized, so that, with a simple change of parameters, the aircraft model and the fluid domain could be modified.

 Provide an automated procedure to generate a similar structured mesh for the different CAD geometries.

The first two considerations force high accuracy in the modeling phase, with particular care required in the verification of tolerances to keep equal geometric features. Therefore the curved models maintain the same fuselage, fairing and wing from side-of-body to kink sections as the original CRM geometry. The model is modified only in the outer part of the wing. Semi-span, reference surface, twist angle, sections chord, aspect ratio, leading edge sweep angle at the kink remain all the same as listed in Chapter 1.

The accomplishment of the last two points makes the geometry implementation process very complex and restrictive. While the CAD design make use of parameters and laws in CATIA, the mesh generation is performed in Ansys ICEM CFD through its Replay function. The blocks elements (vertex, edges and faces) has to be associated to the variable geometry (points, lines, surfaces) in order to generate the mesh.

The Replay function allows recording of all the commands performed on ICEM by writing a script, then it is possible to read the script and perform the same commands. In the script file, the blocking and the geometric elements are codified by numbers, which does not vary with shape changes related to different planforms. Instead, substituting an element with a new one (even if in the same place, with the same shape and features) does change its distinguishing number.

The solution to the thesis demands is to build an adaptive geometry model which in the initial configuration is just like the CRM, while being able to obtain curved wing configurations simply changing some parameters without replacing its geometric elements.

(2)

16

2.1 CATIA build process for swept wing

The answer to the aforementioned requirements is to redesign, starting from the CRM available semi-model, the wing structure between kink and tip sections, making it adaptive to a desired curved configuration and finally rebuild the wing skin. The basic structure of wing consists of multiple airfoils distributed along the spanwise direction, leading and trailing edges splines, as well as many other splines which connects corresponding points on the airfoils.

The coordinate system is chosen such that the x direction corresponds to the fuselage longitudinal axis, positive from nose to tail, the y axis is normal to the symmetry plane, positive from root to tip, and the z axis is right handed.

The first step involves the import of the CRM CAD model in CATIA V5-6R2017, then 26 intersection profiles between kink and tip are obtained. 14 planes perpendicular to the y direction are placed in correspondence of the original geometric sections, see Table 1-2. Other 12 planes are built halfway between the previous ones, hence 734.539 mm equally spaced. With the Intersection command 26 profiles are obtained, corresponding to the airfoil profiles of the CRM model.

(3)

17

Figure 2-2 Wing airfoil copies and cross-planes for zero values of translation

At this point, the translated copies of the sections are generated using the Translation command. The copies can be easily moved along the x direction conferring to the structure the capability to adjust itself in whatever curved configuration.

Along the each airfoil there are 262 points already present in the original geometry. Each of the 262 splines joins the corresponding points of the 26 sections, completing the wing structure. These allow to provides high accuracy tolerances on the surface.

Figure 2-3 Wing structure composed by sections and guidelines as reference for the surface

Finally the Surface Multisection command exploits the 26 translated airfoils as cross-sections and the 262 spline as guidelines for the surface generation.

The aforementioned process completes the generation of both swept and curved wing configurations. The difference lies in the translation distance of the airfoil sections: for the

(4)

18

swept wing they are fixed to zero, while for the curved configuration the values are adjusted in accordance with the 3rd order polynomial law which defines the planform shape of the wing.

2.2 Curved wing Planform shape: polynomial law

The curved wing is obtained from the swept geometry model, by moving the 26 airfoil sections in accordance to the desired curved planform shape. As consequence of translations the wing configuration changes without replacing its elements.

By definition the planform shape of the wing is the projection of leading edge in the xy plane; the projection has to coincide with the polynomial law. In order to make it possible, the airfoils have to move along x direction by a quantity equal to the difference between the polynomial spline and the original leading edge projection.

It is possible to write the 3rd order polynomial law in mathematical form as follows: 𝑠(𝑡) = 𝑎 ∙ 𝑡3_{+ 𝑏 ∙ 𝑡}2_{+ c ∙ 𝑡 + 𝑑}

Where t is the span distance measured from kink in the coordinate system in Figure 2-4.

Figure 2-4 Curved wing coordinate system and polynomial lawparameters  bk/2 is the distance between kink section and simmetry plane;

 b/2 is the wing span measured from the simmetry plane;

(5)

19

In order to obtain the polynomial coefficients, four geometrical conditions are imposed: introduction of a local reference frame with origin in the kink leading edge, continuity of tangency, tip translation and sweep angle at the tip.

 𝑠(0) = 0

 s'(0) = tan⁡(𝛬_{𝑘𝑖𝑛𝑘})

 𝑠(1) = ∆_𝑡𝑖𝑝

 s'(1) = tan⁡(𝛬_𝑡𝑖𝑝) The resulting coefficient are:

 𝑎 = −2 ∙ 𝑥̅𝑡𝑖𝑝+∆𝑡𝑖𝑝 𝑦̅𝑡𝑖𝑝−𝑦̅𝑘𝑖𝑛𝑘+ tan(𝛬𝑘𝑖𝑛𝑘) + tan(𝛬𝑡𝑖𝑝)  𝑏 = 3 ∙ 𝑥̅𝑡𝑖𝑝+∆𝑡𝑖𝑝 𝑦̅𝑡𝑖𝑝−𝑦̅𝑘𝑖𝑛𝑘− 2 ∙ tan(𝛬𝑘𝑖𝑛𝑘) − tan(𝛬𝑡𝑖𝑝)  𝑐 = tan(𝛬𝑘𝑖𝑛𝑘)  𝑑 = 0 Where:  x̅_tip = 14,09490196 m  y̅_tip = 29,38152874 m  y̅kink = 10,87116444 m  𝛬_{𝑘𝑖𝑛𝑘} = 37,28935°

2.3 Generated models

Four different configuration are realized and studied in this work: the swept one matching the original CRM, and three curved wing models.

Model ∆tip Λtip

Swept 0 37.3

6 m 53° 6 m 53°

6.4 m 59° 6.4 m 59°

3 m 45° 3 m 45°

Table 2-1 Geometric model features

Where

 ∆_𝑡𝑖𝑝is the tip traslation compared to the swept configuration;

(6)

20 In the following figures are depicted:

 The drawing of CRM swept configuration in Figure 2-5;

 The comparison of the three curved wing models with the swept wing geometry. From Figure 2.6 to Figure 2.11, the different configurations are analyzed, respectively the 6 m 53°, 6.4 m 59° and 3 m 45°. It should be noted that only the variable quantities are quoted, while the others remains fixed.

(7)

21

Figure 2-6 CRM and 6 m 53° curved planform wing comparison

(8)

22

Figure 2-8 CRM and 6.4 m 59° curved planform wing comparison

(9)

23

Figure 2-10 CRM and 3 m 45° curved planform wing comparison

(10)

24

The changes in geometrical boundary conditions leads to three different leading edge curves, showed in Figure 2-12. The sweep angle has to avoid any inflection point, so the first derivative s’(t) is monotonically increasing, see Figure 2-13.

Figure 2-12 Curved planform wing, leading edge comparison

Figure 2-13 Curved planform wings, Leading edge sweep angle comparison

10,87 12,87 14,87 16,87 18,87 20,87 22,87 24,87 26,87 28,87 -25 -20 -15 -10 -5 0 y [m] x [m ]

Leading edges comparison

3 m 45° 6 m 53° 6.4 m 59° 0 0,2 0,4 0,6 0,8 1 1,2 0 10 20 30 40 50 60 70 First derivative 3 m 45° 6 m 53° 6.4 m 59°

(11)

25

2.4 Fluid domain implementation: far-field and sheath

In order to analyze the aerodynamic behavior of the four models (one swept wing and three curved wing) it is convenient to generate a geometric entity representing the entire fluid domain. Thus, a set of volumes and surfaces are built all around the aircraft. They are very useful for control of the mesh setup as will be described in the next chapter for blocking association.The control volumes establish a high density region, a sort of sheath, around the aircraft which is divided in two main components, one around the wing and one surrounding the fuselage. Outside this sheath, the remaining fluid domain ends with rectangular faces extending far enough where the flow have no effect on the model. The geometry implementation for the fluid domain, including far and near field regions, is unique and enforceable to each kind of wing. Also, the fluid domain is adaptive by simply adjusting parameters, again without replacing any geometric element.

2.4.1 Control volumes generation around the wing

Around the tip airfoil, in the Sketcher workbench, the offset of the profile is generated through the Offset command except for the trailing edge. The offset is closed by a circumference arc and two connecting spline, as shown in Figure 2-14. After this, 8 points out of 262 in the airfoil are selected to be the vertices of the control volumes together with one leading and three trailing edges points. From the 12 points, corresponding cross-segments connects and trim both airfoil and offset into 12 arches.

(12)

26

Each segment have parametric values for angles, as the offset curve for distance. All the dimensions and angles quoted in the figure can be changed by means of parameters except the 12 aforementioned points which have to be replaced manually into CATIA environment. The angles are numbered from leading to trailing edge and the offset is the sheath thickness.

Table 2-2 Tip section, sketch features

Finally, joining the selected segments and arches in the command 3D Profiles, twelve regions are outlined, the ones that will be used to shape the mesh blocks in ICEM.

Figure 2-15 Tip 3D profiles defining closed regions

leading

angle

trailing

angle angle 1 angle 2 angle 3 angle 4 angle 5

upper wing

value 87,15762° 90° 85° 90° 90° 90° 52,52617° change

method parametric parametric parametric parametric parametric parametric parametric

lower wing

value 87,15762° 90° 85° 90° 90° 90° 59,17966° change

point 1 point 2 point 3 point 4 offset

tip section upper wing

value 133 87 64 43 150 mm change

method manual manual manual manual parametric

lower wing

value 258 218 195 174 150 mm change

(13)

27

The previous procedure is repeated in other three sections, respectively the kink (Fig. 2-16), one near the root (Fig. 2-17) and the last beyond the root (Fig. 2-18). This is due to the non-planar wing-body intersection. It requires two sections: one before the root obtained from intersection; one after the root obtained extending the guidelines from kink to near root sections. The sheath volumes develop inside the fuselage before being split with the latter.

Figure 2-16 Kink section, sketch of the wing profile (yellow), construction lines (white)

Table 2-3 Kink section, sketch features

leading

angle

trailing

upper wing

value 90° 90° 90° 90° 90° 90° 45°

change method

parametric parametric parametric parametric parametric parametric parametric

lower wing

value 90° 90° 90° 90° 85° 90° 45°

change

kink section

upper wing

value 133 87 64 43 150 mm

change

method manual manual manual manual parametric lower

wing

value 258 218 195 174 150 mm change

(14)

28

Figure 2-17 Near root section, sketch of the wing profile (yellow), construction lines (white)

.

leading

angle

trailing

upper wing

value 90° 90° 90° 90° 90° 90° 45°

change

method parametric parametric parametric parametric parametric parametric parametric lower

wing

value 90° 90° 90° 90° 90° 90° 45°

change

Near root

section

upper wing value 133 87 64 43 150 mm change method

manual manual manual manual parametric

lower wing

value 258 218 195 174 150 mm

change

method manual manual manual manual parametric

(15)

29

Table 2-5 Beyond root sketch features

The twelve regions defined in each of the 4 sections are the references for the multi-section volumes respectively from the tip to the kink and from the kink to the multi-section beyond the root.

Figure 2-18 Beyond root section, sketch of the wing profile (yellow), construction lines (white)

leading

angle

trailing

upper wing

value 90° 90° 85° 90° 90° 90° 45°

change

method parametric parametric parametric parametric parametric parametric parametric lower

wing

value 90° 90° 85° 90° 90° 90° 45°

change

Beyond

root section

upper wing value 133 87 64 43 150 mm change

method manual manual manual manual parametric lower

wing

value 258 218 195 174 150 mm change

(16)

30

The command used is the Multi-Section Volume. Starting from the trailing edge of the tip-kink part, the input parameters correspond to the two sections 3D Profiles, the trailing edge spline, as guideline, and the vertices of 3D profiles as coupling points.

Figure 2-19 Control volumes around the wing

The other eleven volumes are generated in a similar way except for the guidelines, that increase from one to four. Three different guidelines are associated to the edges of the previously generated volume, while the last one belongs to the spline which connects two correspondent points of the 3D profiles used. For volumes between tip and beyond root the implementation is the same.

Figure 2-20 Control volumes kink-tip and kink -root

(17)

31

Figure 2-21 Wing control volumes, upper view

Figure 2-22 Wing control volumes, lower view

In the tip, 3D profiles are obtained in a similar way, with some added complexity: from Extrusion of the previously generated volumes and intersection with the wing tip surface, 10 offset profiles are obtained in yz planes sketches; offsets provide reference points for 10 splines connecting and closing the volumes sides around the tip in 3D Profiles. In the end, the outer edges of the volumes built between tip and kink sections represent two guidelines for the Multi-Section Volume command in the side part.

Finally the tip shell is completed by the Surface Connection forward and a Multi-Section Surface in the after part. For the surface connection two curves and two conditions of tangency are necessary: the two curves are respectively the forward side tip pod edge and the joined curve composed by the edges of the volumes in the leading edge region; the tangency is related to the tip pod surface and to the kink-tip control volumes. In the after

(18)

32

region instead, the Multi-Section Surface has as references the ending edge of the side tip pod and the joined curve of kink-tip control volumes edges in front of the trailing edge.

Figure 2-23 Tip pod outer side view

Figure 2-24 Tip pod inner side view

2.4.2 Control surfaces generation around the fuselage

The process followed for the control surfaces around the fuselage is very close to the one used in the tip shell. 15 sections are used instead of the 10 for the tip, while the joined curves extrapolated from the fuselage offset in the symmetry plane are exploited. The sheath thickness for swept and curved configurations is 300 mm. It could be changed by a parameter.

(19)

33

Figure 2-25 Fuselage control volume and building sections

Figure 2-26 Control volumes for swept wing configuration

(20)

34

Around the wing there is the need to accurately control the edges perpendicular to the lifting surface in the wing boundary layer, therefore the cells density and its shape to be aligned with the flow. On the fuselage instead, the lack of defined sections and corresponding points in each one, does not allow to split the sheath in the longitudinal direction in a simple way.

The control volumes and surfaces are exploited to easily associate structured mesh blocking elements (vertices, edge and faces) to CAD parametric points, curves and surfaces. This is the reason why also the intersections curves between wing and fuselage sheaths themselves and with the wing-body geometry are viewed, then imported in ICEM.

Figure 2-28 Control intersections

2.4.3 Far-field generation

The far-field is made up of 6 rectangular surfaces. First the symmetry and the lateral sketch are created with desired dimensions.

(21)

35

Figure 2-29 Far-field dimensions in mm

Later the shells are obtained end subsequently filled exploiting the command Fill Surfaces with a depth of 635 m.

Figure 2-30 Far-field surface

This kind of rectangular section far-field is used in two out of three configurations compared in this thesis. The last one shows a semispherical domain designed directly on ICEM environment by exactly inscribing the half-sphere in the parallelepiped.