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In this study, we conducted numerical simulations for a nonslender BWB type planform with a rounded leading edge and span of 2.0 m to analyze the effect of the sideslip angle on the planform at a freestream velocity of 60 m/s. The Reynolds number based on the mean chord length was

There is an advantage of a high lift-to-drag ratio aerodynamically in the BWB (blend wing body) type planform, of which the recent models are the 1303 UCAV (unmanned combat air vehicle) developed by the US AFRL and SACCON (Stability And Control CONfiguration) by NATO RTO AVT-161, than the conventional fixed wing one. This is because the BWB-type planform shows the aerodynamic features of the delta wing with the leading edge vortex. The primary leading edge vortex is generated from the interaction between the separated shear layer at the leading edge and the freestream. The secondary leading edge vortex occurs when the reattached flow is separated again by the adverse pressure gradient in the spanwise direction. The vortex lift is an additional lift provided by the local suction pressure near the leading edge. The nonlinear behavior of the pitching, rolling, and yawing moments is created by movement of the vortex [

The behavior of the vortex on this type of planform is sensitive to some parameters such as the swept angle [

Loeser et al. [

Yayla et al. [

In the present study, we conducted numerical simulations on the geometry of the BWB-type planform and compared aerodynamic coefficients with the experimental results by Shim et al. [

The geometry in the present study was the same as that in the experiment by Shim et al. [

BWB-type planform and geometric parameters.

Figure

Coordinate system and sign convention of moment.

We set the computational domain to box type with length in the streamwise direction of 20C (C is the root chord length) and width in the spanwise direction of 14C. The height in the vertical direction changed linearly from 10C at the inflow boundary to 24C at the outflow boundary. The grid inside the computational domain was generated with commercial software, ICEM-CFD of ANSYS [

Computational domain and grid details.

We solved incompressible Navier-Stokes equations with the second-order discretization scheme in space and time and corrected the pressure-velocity using a SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. We used the

We set the freestream velocity to 60 m/s as in Shim et al. [

Model and flow parameters.

Conditions | Unit | Present model |
---|---|---|

Span | mm | 2,000 |

MAC | mm | 708.3 |

Swept angle | ° | 47 |

Washout | ° | -5 |

Freestream velocity | m/s | 60 |

Angle of attack | ° (deg) | -4~16 with |

Sideslip angle | ° (deg) | 0, 2, 4, 6, 8, 14, 20 |

The grid system and numerical schemes including the turbulence model were validated by comparison with experimental results by Shim et al. [

Lift and drag coefficients for angle of attack.

Lift coefficient

Drag coefficient

Pressure coefficient of four stations (

Figure

Lift, drag, and side force coefficients for angle of attack.

Lift coefficient

Drag coefficient

Side force coefficient

Skin friction lines and pressure coefficient contours at angle of attack 12°.

We plotted the coefficients of pitching, rolling, and yawing moments to investigate the effect of sideslip angle in Figure

Pitching, rolling, and yawing moment coefficient for angle of attack.

Pitching moment coefficient

Rolling moment coefficient

Yawing moment coefficient

As expected, the rolling and yawing moment coefficients were markedly affected by the sideslip angle. At a sideslip angle of zero, the rolling and yawing moment coefficients were nearly zero, except at large angles of attack (16° in the rolling moment and 12°-16° in the yawing one). Even though the ideal value of this coefficient at a sideslip angle of zero should be zero, the grid along the symmetric plane (root chord,

As the angle of attack increased at a non-zero sideslip angle, the rolling moment coefficient increased until an angle of attack of 10° or 12° and decreased thereafter. The angle of attack with the maximum rolling moment value increased with the sideslip angle. Loeser et al. [

The yawing moment coefficient also showed a strong nonlinear behavior with variation in the sideslip angle. Like the rolling moment coefficient, an exactly zero moment could not be obtained due to the asymmetric grid structure and highly separated flow structures. As the angle of attack increased, the yawing moment coefficient showed little change until an angle of attack of 8-10°. However, there was a rapid decrease in the coefficient with a peak and then an abrupt increase. The magnitude of the peak increased with the angle of the sideslip. Similarly with the side force coefficient, the nonlinear characteristics of the yawing moment coefficient occurs near the angle of attack, 12°~14°, which can be inferred from the asymmetric leading edge vortex between both side wings. The negative yawing moment coefficient means that the balance of the

For a more detailed analysis of the sideslip angle effect, we plotted the sideslip force, rolling moment, and yawing moment with respect to the sideslip angle in Figure

Side force, rolling moment, and yawing moment coefficients for the side slip angle.

Side force coefficient

Rolling moment coefficient

Yawing moment coefficient

The rolling moment coefficient was positive, and the slope of

Similarly, the yawing moment coefficients showed a nonlinear behavior after an angle of attack of 12°. At small angles of attack, there was little change with increasing sideslip angle. However, at an angle of attack of 12°, the magnitude of the coefficient and the gradient of

We investigated the highly nonlinear behaviors of the aerodynamic force and moment coefficients in more detail from a physics perspective by analyzing flow field parameters including contours and streamlines. Figures

Skin friction lines and pressure coefficient contours at angle of attack 0°.

Skin friction lines and pressure coefficient contours at angle of attack 16°.

At an angle of attack of zero, as the sideslip angle increased, the rolling moment coefficient decreased linearly with a negative slope at a sideslip angle of zero (Figure

On the contrary, two cases in which there was a non-zero angle of attack showed different flow patterns with positive values and slopes of the rolling moment coefficient. Increases in the sideslip angle caused the spanwise velocity component to increase and then the pressure of the lower surface (not shown here) on the windward wing increased into a positive rolling moment. As shown in Figures

Figure

Skin friction lines and skin friction contours at angle of attack 12°.

There are five distinct flow types for a blunt leading edge swept wing: (1) the incipient separation that coalesces into (2) the leading edge vortex that induces (3) the secondary vortex separation, which is bracketed by (4) the inner attached flow and (5) an inner vortex separation. Frink et al. [

Frink et al. [

In Figure

Streamwise vorticity contours (upper) and streamlines (lowers) at the side slip angle 8°.

Figure

Streamlines and streamwise vorticity contours at

Streamlines

Streamwise vorticity contours

Here we reported simulation results for the nonslender BWB-type planform with variation in angle of attack (-4°-16°) and sideslip angle (0°-20°). We analyzed aerodynamic force and moment coefficients as well as flow structures over the upper surface based on the flow mechanism around the delta wing. The side force coefficients and rolling/yawing moment coefficients showed a highly nonlinear behavior with respect to the sideslip angle while the lift and drag force coefficients changed very little with respect to the sideslip angle. As the sideslip angle increased, the pitch break, which is related to the pitching moment coefficient, was delayed up to an angle of attack of 12° compared to 8° at the zero sideslip angle, and the magnitude of increase in pitching moment decreased thereafter. The rolling moment coefficient increased until an angle of attack of 10° or 12° and then decreased thereafter. Among the three moment coefficients, the yawing moment coefficient showed the highest nonlinear behavior as the sideslip angle varied. We plotted the side force and rolling/yawing moment coefficients with respect to the sideslip angle for detailed analysis of the sideslip angle effect. At a small angle of attack, the side force and two moment coefficients showed a linear behavior with respect to magnitude and rate of change in the angles. However, we observed highly nonlinear behaviors at large angles of attack. At angles of attack of 12° or 16° in the present model, the side force and yawing moment coefficients had values with opposite signs or slopes when compared with results at smaller angles of attack. We confirmed that the present aerodynamic coefficient results are similar to Loeser’s experimental results [

We interpreted the nonlinear behaviors of aerodynamic coefficients through analysis of the contours of pressure and skin friction coefficients. Movement to the apex of the leading edge vortex caused the planform to have pitch break with an abrupt increase in the pitching moment. Different decreasing rates of suction pressure at the leading edge of the wings on the windward and leeward sides gave rise to nonlinear changes in the rolling moment. The yawing moment demonstrated the opposite tendency at an angle of attack of 12° due to movement of the primary vortex with high skin friction to the inboard. We also identified the five flow types, which are well known in blunt leading edge swept wings, by the skin friction lines and off-body streamlines at large angles of attack and sideslip angles, in particular 16° and 20°, respectively, while we observed only primary attachment and separation by the primary vortex at most angles.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This research was supported by the Agency for Defense Development (UD170056JD).