2 Geometry model implementation The geometry implementation process starts from the reference Common Research Model (CRM) CAD files and is carried out with the purpose to achieve the thesis aims:

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2 Geometry model implementation

The geometry implementation process starts from the reference Common Research Model (CRM) CAD files and is carried out with the purpose to achieve the thesis aims:

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

 Compare the reference model with a curved planform wing geometry with a camber realized only on sections between the kink (i.e. end of the Yehudi break) and the tip by shearing the wing profiles. Therefore the swept and curved models maintain the same fuselage, fairing, wing from side-of-body to kink stations of the original CRM geometry. Leading edge angle at the kink, semi span, wing plan surface, twisted angle, sweep angle at kink leading edge, root chord, tip chord and aspect ratio of wing remain the same listed in Chapter 1 [16].

 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.

 Ensure that the association of blocking elements to the variable geometry, can be automated by using the replay function on ICEM.

The accomplishment of last two point makes the geometry implementation process very hard and restrictive. The Replay window allows recording of all the commands performed on ICEM by writing a script, then it is possible to read the script and perform the commands previously recorded. In the script file, the blocking and the geometry elements are codified by numbers which doesn’t change with the shape of elements. Obviously deleting an element (edges points surfaces) and replacing it with a new one, even if in the same place, with the same shape and features, its distinguishing number or part name changes.

In order to ensure the replay works, the geometry components have to be the same, even if they can still change their shape. The solution to the thesis demands is to build an adaptive geometry model which, in the starting configuration, is just like the CRM and is able to reach curved wing configurations simply changing some parameters without replacing its geometry elements.

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2.1 CATIA build process for swept wing

The answer to the four aforementioned guidelines is to redesign the wing structure between kink and tip stations, starting from the CRM, making it movable and adaptable to a curved configuration and finally rebuild the wing on the new structure by using the SURFACE MULTISECTION command. The fundamental structure of wing consists of the multiple airfoils along the span and the spline (among that leading and trailing edges) which connects the wing sections from kink to tip.

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 in the spanwise direction, and the z axis is right handed.

The first step consists of the import the CRM cad model on CATIA V5-6R2017, then 26 intersection profiles from kink to tip are obtained. 14 planes perpendicular to the “y” direction are placed in correspondence of the original geometric sections. 12 planes, instead, are built halfway between the previous ones at a distance of 734,53854 mm. With the INTERSECTION command 26 sections wing, corresponding to the airfoil profiles of CRM model, are obtained.

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Figure 2-2 Wing sections and planes

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 onto whatever curved configuration.

Along the airfoils there are 262 points already present in the original geometry. Each of the 262 splines generated joins the corresponding points at the 26 sections, completing the wing structure.

Figure 2-3 Wing structure

Finally the SURFACE MULTISECTION command exploits the 26 translated airfoils as sections and the 262 spline as guidelines for the surface generation.

The process afore mentioned allows the generation of swept and curved wing configurations. The differences lie in the airfoil section translation distances: for the swept

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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 Catia build process for curved wing

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

2.2.1 Planform shape: polynomial law

By definition the planform shape of the wing is always the projection of leading edge on “xy” plane; in the thesis it has to coincide with the polynomial spline. In order to make it possible, the airfoils have to move back or forward by a quantity equal to the distance, measured along “x” direction, between the polynomial spline and the edge of airfoil projection on “xy” plane.

It is possible to write the polynomial in mathematical form as follows: 𝑠(𝑡) = 𝑎 ∙ 𝑡3+ 𝑏 ∙ 𝑡2+ c ∙ 𝑡 + 𝑑

Where “t” is the span distance from the kink in the following coordinate system:

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 bk/2 is the distance between kink section and simmetry plane;

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

 ΛLE(t) is the swept angle at leading edge as function of local coordinate “t”.

In order to obtain the polynomial coefficients, four geometrical conditions are imposed: introduction of a relative reference frame with origin in the kink, tangency of kink-tip leading edge to the root-kink leading edge, tip shift and swept angle at the tip.

 𝑠(0) = 0  s'(0) = 𝛬_{𝑘𝑖𝑛𝑘}  𝑠(1) = ∆_𝑡𝑖𝑝  s'(1) = 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(𝛬_{𝑘𝑖𝑛𝑘})  𝑑 = 0 Where:  x̅_tip = 14,09490196 m  y̅_tip = 29,38152874 m  y̅_kink = 10,87116444 m  𝛬_{𝑘𝑖𝑛𝑘} = 37,28935°

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2.3 Generated models

Four different configuration are realized and studied in this work: the swept ones, that matches the CRM, and three curved models.

model ∆tip Λtip

swept 0 37,3

6000 53° 6m 53°

6400 59° 6,4m 59°

3000 45° 3m 45°

Table 2-1 geometry model features

Where

 ∆_𝑡𝑖𝑝is the tip traslation compared to the swept configuration;  ∆_𝑡𝑖𝑝is the swept angle of leading edge at the tip.

In the following figures are depicted:

 The drawing of CRM swept configuration;

 The comparison of the three curved models with the swept wing geometry. It should be noted that only the variable quantities are quoted, while the others don’t change. Starting from the Figure 2.6 to Figure 2.11, are analyzed the 6000 53°, 6400 59° and 3000 45° configurations.

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Figure 2-6 CRM and 6000 53° curved planform wing comparison

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The changes in geometrical boundary conditions leads to three different leading edge curves:

Figure 2-12 Curved planform wings, Leading edges comparison

In order to avoid recess along the wing span, the curvature of leading edges has to be always increasing. In Figure 2.13 the leading edge curvature is analyzed

Figure 2-13 Curved planform wings, Leading edge curvature comparison

0 0.2 0.4 0.6 0.8 1 1.2 0 5 10 15 20 25 x/wingspan LE d is ta n ce

Leading Edge Comparison

3000 45° 6400 59° 6000 53° 0 0.2 0.4 0.6 0.8 1 1.2 0 5 10 15 20 25 30 35 x/wingspan LE cu rv at u re Curvature Comparison 3000 45° 6400 59° 6000 53°

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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 required the generation of the geometric model representing the entire fluid domain. Around the aircraft, a set of volume and surfaces are built. They are very useful for mesh setup as mentioned in Chapter 3.The control volumes establish a sort of sheath around the aircraft which is divided in two main components, one around the wing and one surrounding the fuselage. Surrounding this sheath there is the remaining fluid domain which ends with rectangular faces. The geometry implementation for the fluid domain is unique, enforceable to every kind of model developed with the aforementioned process, by simply adjusting some parameters and without replacing geometry elements.

2.4.1 Control volumes generation around the wing

Around the tip airfoil, in the SKETCH environment, the offset of profile without trailing edge is generated through the OFFSET command. After that, the offset is closed by an arch and two connecting spline. At this time a spline, entirely included inside tip profile, is built and divided by 8 segments ending in 8 of 262 airfoil points. From the 8 points plus the trailing edge ones start another 10 segments which split the offset into 12 arches.

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Table 2-2 Tip section, sketch features

All the dimensions and angles quoted in the figure can be changed by means of parameters except the eight afore mentioned 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. Finally by selecting segments and arches in the command 3D PROFILES, six regions are outlined.

Figure 2-15 Tip 3D profiles

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

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The previous procedure is repeated for kink section, and the near root section

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

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

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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

lower wing

value 90° 90° 90° 90° 90° 90° 45°

change

Near root

section

upper wing value 133 87 64 43 150 mm change

lower wing

value 258 218 195 174 150 mm

change

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Table 2-5 beyond root sketch features

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

lower wing

value 90° 90° 85° 90° 90° 90° 45°

change

Beyond

root section

upper wing value 133 87 64 43 150 mm change

lower wing

value 258 218 195 174 150 mm

change

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The six regions defined in each of the 4 aforementioned sections are the bases for the multi-section volumes that goes from tip to kink and from kink to the section beyond the root.

The command used in the sheath implementation is the MULTI-SECTION VOLUME. Starting from the trailing edge of tip-kink portion, the input parameters are the corresponding bases, as sections, the trailing edge spline, as guide line, and the vertices of 3D profiles as points coupling.

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. One guide belongs to the splines which connect two points of the 3D profile and three different guides represent the edges of the volume generated before. In the section between tip and beyond root the implementation is the same.

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Figure 2-21 Wing control volumes, upper view

Figure 2-22 Wing control volumes, lower view

Finally the tip shell is built by exploiting the MULTI-SECTION VOLUME command in the middle section, the SURFACE CONNECTION in the forward part, and the MULTI-SECTION SURFACE in the back. In the middle region are used 8 tip offset as sections and two spline, composed by the external edge of the control volumes, as guidelines. For the surface connection two curves are necessary (the first section offset and the union of the edges belonging to the volume in the trailing edge region) and two conditions of tangency (tangency to tip shell middle region and to the kink tip control volumes). In the back section instead, the ended section of middle tip pod and again the union of control volume borders in front of trailing edge are exploited.

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Figure 2-23 Tip pod

Figure 2-24 Tip pod inner side

2.4.2 Control surfaces generation around the fuselage

The generation process followed for the control surfaces around the fuselage is very close to the tip one. 15 sections are used instead of the 8 for the tip, while, in place of the tip pod guidelines, the unified curves extrapolated from the fuselage offset in the symmetry plane are exploited. The sheath thickness for swept and curved configurations is 300 mm.

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Figure 2-25 Fuselage control volume and buliding sections

Figure 2-26 Control volumes for swept wing configuration

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Around the wing, the volumes are preferred to surfaces because there is the necessity to associate the edge perpendicular to the lifting surface in order to control the mesh in the wing boundary layer. The fuselage is a surface less notable for the aerodynamic point of view, hence the precedent adjustments is not required.

The control volumes and surfaces are exploited to associate vertices, edge and faces to points, lines and surfaces. This is the reason why also the lines of intersections of the two sheath between themselves and the aircraft geometry are extracted.

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.

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Later the shells are obtained end subsequently filled exploiting the command FILL SURFACES with a depth of 635000 m.

Figure 2-30 Far field surface

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