Vortex Lattice Method arrangement for a wing. The different panels along with the bound vortices and control points can be observed [30]

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... first enters the geometrical points to model the wing, tailplane, flaps, rudder, ailerons and elevators. Then, according to the choice of the user, each lifting surface is divided into a specific number of panels that make up the lattice. Each of these panels has bound and trailing vortices, which form the horseshoe vortex, and control points. Fig. 4 shows the Vortex Lattice Method arrangement for a wing as used in Tornado. We can see from Fig. 4 that the wing is divided into a specific number of panels and each panel has its set of bound and trailing vortices, and a control point. The bound vortex and the trailing vortices of every panel induce a downwash velocity at control ...

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... Then, according to the choice of the user, each lifting surface is divided into a specific number of panels that make up the lattice. Each of these panels has bound and trailing vortices, which form the horseshoe vortex, and control points. Fig. 4 shows the Vortex Lattice Method arrangement for a wing as used in Tornado. We can see from Fig. 4 that the wing is divided into a specific number of panels and each panel has its set of bound and trailing vortices, and a control point. The bound vortex and the trailing vortices of every panel induce a downwash velocity at control points of all the panels. Once the downwash velocity due to the all the bound and trailing vortices ...

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... stated earlier, Tornado works on the VLM and it follows the VLM procedure where lifting surface under consideration is divided into a lattice of panels, and each of these panels consists of vortex segments and control points as shown in Fig. 4. The influence of these vortex segments on all the control points is determined to form the influence coefficient matrix. This influence coefficient matrix is equated against the local flow conditions to satisfy the flow tangency condition at every panel giving the strength (circulation) of the vortex segments of all the panels of the ...

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... panel containing its own set of bound and trailing vortex segments that make up the horseshoe vortex. The bound vortex is placed at ¼ of the local chord length of each panel with two trailing vortices extending from its either ends. Also, a control point is placed at 3/4 of the local chord length at the midpoint of the bound vortex on each panel. Fig. 4 shows the arrangement of the vortex ...

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... panels in the span-wise and chord-wise directions according to the values entered by the user. Each of these panels has its own set of bound and two trailing vortices, at either ends of the bound vortex, forming a horseshoe vortex. The two trailing vortices from each panel form the wing wake. All these panels also have control points as shown in Fig. 4. As pointed out in Section 2, and like the method followed in Whirl, the velocity induced by all the horseshoe vortices on the control points of all the panels are determined to form the influence coefficient matrix. Also, the total flow velocity at all the control points is determined to form the boundary condition vector. Using the ...

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... the same time step of 0.001 seconds was used for both the approaches. The change of vorticity along the blade in the span-wise direction (Helical Wake Modelling approach) Figure 45 represents the wake formation in the Helical Wake Modelling approach for a time step of 0.001 seconds. We can see that there are significant gaps in the helical wake. ...

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... Fig. 24. And Fig. 30, we can observe that the convergence based on the number of panels was achieved at around the same number of panels for both the propellers in the Helical Wake Modelling approach. From Fig. 25 and Fig. 31, we can observe that the convergence based on the wake length was achieved at the same value of the wake length for ...

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... Fig. 40 and Fig. 42, we can observe that the axial velocity increases in the wake streamwise direction for both the VRM and the Helical Wake modelling approaches. This happens because the vortex system produced by the propeller increases in length in the stream-wise direction, as mentioned in Section 2.1.1. It can also be observed form Fig. 40 ...

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... Fig. 40 and Fig. 42, we can observe that the axial velocity increases in the wake streamwise direction for both the VRM and the Helical Wake modelling approaches. This happens because the vortex system produced by the propeller increases in length in the stream-wise direction, as mentioned in Section 2.1.1. It can also be observed form Fig. 40 and Fig. 42 ...

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... happens because the vortex system produced by the propeller increases in length in the stream-wise direction, as mentioned in Section 2.1.1. It can also be observed form Fig. 40 and Fig. 42 that the axial velocity becomes constant after the modelled wake length of 10*propeller diameter is reached. Thus, we can say that Whirl calculates axial velocity accurately up till the modelled wake length, which is 10*propeller diameter in Fig. 40 and Fig. 43, and beyond the modelled wake length, the axial velocity calculated by Whirl would be null and void, for both the approaches. ...

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... 40 and Fig. 42, we can observe that the axial velocity increases in the wake streamwise direction for both the VRM and the Helical Wake modelling approaches. This happens because the vortex system produced by the propeller increases in length in the stream-wise direction, as mentioned in Section 2.1.1. It can also be observed form Fig. 40 and Fig. 42 that the axial velocity becomes constant after the modelled wake length of 10*propeller diameter is reached. Thus, we can say that Whirl calculates axial velocity accurately up till the modelled wake length, which is 10*propeller diameter in Fig. 40 and Fig. 43, and beyond the modelled wake length, the axial velocity calculated by ...

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... the stream-wise direction, as mentioned in Section 2.1.1. It can also be observed form Fig. 40 and Fig. 42 that the axial velocity becomes constant after the modelled wake length of 10*propeller diameter is reached. Thus, we can say that Whirl calculates axial velocity accurately up till the modelled wake length, which is 10*propeller diameter in Fig. 40 and Fig. 43, and beyond the modelled wake length, the axial velocity calculated by Whirl would be null and void, for both the ...

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... 41 and Fig. 43, we can observe that the tangential velocity remains almost constant in the wake stream-wise direction for both the Helical Wake Modelling and the VRM approaches. This happens because unlike the axial velocity, the tangential velocity doesn't rely on the vortex system length that increases in the wake stream-wise direction. From Fig. 40 and Fig. 42, Fig 41 and Fig. 43, we can observe that the graphs have smoother curves in case of the VRM approach as compared to the Helical Wake Modelling approach. This happens because the vortex rings form a sort of tube with almost negligible gaps between them, as observed in Fig. 44; and this causes the calculation of velocities in ...

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... that increases in the wake stream-wise direction. From Fig. 40 and Fig. 42, Fig 41 and Fig. 43, we can observe that the graphs have smoother curves in case of the VRM approach as compared to the Helical Wake Modelling approach. This happens because the vortex rings form a sort of tube with almost negligible gaps between them, as observed in Fig. 44; and this causes the calculation of velocities in the wake to be more stable in case of the VRM approach. In case of the Helical Wake Modelling approach, the helical wake has significant gaps, as observed in Fig. 45; and these gaps cause the calculation of velocities in the wake to be relatively more abrupt resulting in the 'not so ...

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... approach. This happens because the vortex rings form a sort of tube with almost negligible gaps between them, as observed in Fig. 44; and this causes the calculation of velocities in the wake to be more stable in case of the VRM approach. In case of the Helical Wake Modelling approach, the helical wake has significant gaps, as observed in Fig. 45; and these gaps cause the calculation of velocities in the wake to be relatively more abrupt resulting in the 'not so smooth curves' when compared with the curves obtained from the VRM ...