The Aerodynamics of an Oblique Biplane Emirates Aviation University, Dubai, UAE

Citation: Kim YH, Abdullah AN, Khan A, Devrath PK, Al Ghumlasi RA, et al. (2018) The Aerodynamics of an Oblique Biplane Emirates Aviation University, Dubai, UAE. Int J Astronaut Aeronautical Eng 3:019 Copyright: © 2018 Kim YH, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. *Corresponding author: Asma Najib Abdullah, B.Sc in Aeronautical Engineering, Emirates Aviation University, Dubai, UAE


Introduction
The Germans Luftwaffe had interest about the oblique biplane configuration during WWII due to its distinguished aerodynamic efficiency. Though the Luftwaffe could not complete the oblique winged fighter program "Messerschmitt P1109 [2]" due to the end of war, this idea was adopted by NACA in United States for further implementation and research [2]. Oblique Biplane would offer many advantages at high transonic and low supersonic speeds. However, a variety of uncertainties and technological difficulties associated with this unusual configuration have prevented its application to the operational aircrafts [3]. However, due to the advance of modern technologies, many reasonable solutions were proposed in order to overcome the technical difficulties that this configuration raised.
An Oblique Biplane is capable of sweeping at different angles ranging from 0° for take-off to 60° for cruising. The upper wing, right half, behaves like a forward swept wing and the left half, behaves like a backward swept wing. Vice Versa applies to the lower wing. This opposite rotation of the upper and lower wing around its pivot, cancels out the rolling moment created by each wing and the aircraft remains stable. The advantages of having this configuration is that it distributes the lift over about twice the wing span [1] as a conventional swept wing of the same span and due to its unique aerodynamic features, it shifts the neutral point of the wing and results in reduction of trim drag & the aerodynamic load on the fuselage and empennage. This unique characteristics leads to the increase in the range [4] and speed of the aircraft, hence the better fuel efficiency resulting in the less burdens on the engines to create the required amount of thrust [4]. This study investigates the potential of achieving improved aerodynamic performance and fuel efficiency of the fighter jet at a wide range of oblique angles with the best tail configuration (Conventional, Cruciform, T-Tail). This procedure will assist to identify the optimized wing oblique angle at which the aircraft will provide the better aerodynamic performance during the cruise. This research is targeting to achieve descriptive and applied knowledge about this unique aircraft configuration using computation and experimental approach, completely valid in nature.

Methodology
Progress flow chart-PHASE I Figure 1.

Fabrication of the aircraft components
For the Oblique wing Biplane in order to ensure  vroot v MAC C λ λ λ + +     +   the best lift is distributed around the airfoil and high lift is created, the supercritical airfoil SC417 is used. It is desirable to have an airfoil having a greater critical Mach number for high speed aircraft. The purpose of the supercritical airfoil is to increase the drag divergence Mach number.

Solid works
In order to have a reasonable wing length for the required characteristics, to be exact with the design wing geometry formulas were used. An initial sketch was made as shown in the Figure 2.

Wing calculations
The Mean Aerodynamic Chord of the wing was calculated using The span of the wing was decided based on the size of the wind tunnel test section.
To calculate the wing Planform area, the trapezoidal shape of the wing is considered [5]. Table 1 shows the values.
The steps carried in the calculation of the To solve the above equations [6], the aspect ratio, the taper ratio as well as the vertical tail volume coefficient is assumed.
The volume coefficient for all tails is taken from To solve those set of equations, the aspect ratio, taper ratio as well as the horizontal tail volume coefficient are assumed.

Cruciform tail
The results calculated for the cruciform tail in Table 3 used the assumptions [5] made in Table 4.
The values assumed for the vertical and       In addition to the previous mentioned equations, the vertical distance at which the horizontal tail is located in a cruciform tail configuration is found using Table 3 represents the parameters calculated for a Cruciform Tail.

Conventional tail calculations
The results calculated in Table 5 for the Conventional tail use the assumptions [5] made in Table 6.

T-Tail calculations
The horizontal tail volume coefficient is reduced by 5% compared to the other tail configurations due to the clean air experienced by the horizontal tail [5]. Moreover, 5% reduction is also applied to the vertical tail volume coefficient because of the end plate effect. Table 7 represents the assumptions made before calculating the parameters for a T-Tail.

Aircraft final look
The different Aircraft models are represented in Figure 4 with three different tail configurations to be tested in ANSYS.

Generated Mesh for the model
The Mesh is generated as shown in Figure 6 and

ANSYS Fluent Setup and Input Numbers
Step 1: Pressure-based selection After selecting double precession on the setup window, pressure-based solver is selected in Figure 8. Historically speaking, the pressurebased approach was developed for low-speed incompressible flows, while the density-based approach was mainly used for high-speed compressible flows. In both methods the velocity field is obtained from the momentum equations. In the density-based approach, the continuity equation is used to obtain the density field while the pressure field is determined from the equation of state. On the other hand, in the pressurebased approach, the pressure field is extracted by solving a pressure or pressure correction equation which is obtained by manipulating continuity and  altitude. The density is kept as an ideal gas, specific heat coefficient as 1006.43 (j/Kg.K), thermal conductivity is kept constant as 0.0242 (w/m.K) and lastly viscosity is 1.43226e-05 (Kg/m-s).

Step 4: Inlet condition
At the inlet the gauge pressure is kept at 16000 meter which is 10192 (Pa), Mach number is defined as 0.6 and in last the flow direction in Figure 11 is being set up as X-component of flow direction. momentum equations from aerodynamics analysis.
Step 2: Energy equation Next step after selecting pressure-based solution is to turn on the energy equation, Figure 9, for further calculation.

Step 3: Material selection
In the setup window, shown in Figure 10, the type of material is selected as "fluid". Next the fluid properties are being selected at the designed    Figure 14 shows the relation between the drag coefficient and the different sweep angles for the different tail configurations. As the sweep angle increases from 0 to 60 Degrees the drag coefficient starts reducing. At 0 Degrees, conventional tails accommodate the highest value of drag at about 0.051, whereas, cruciform shows the lowest value indicated as 0.041. As mentioned previously, the drag keeps on reducing with an increase in sweep angle. At 0 Degrees, the Biplane has the highest wing span. This explains why the three tail configurations experience the highest drag at this sweep angle due to excessive skin friction. As the span starts to change and reduce from 0 to 60, the drag also starts reducing. This is due to the cause that the total drag is directly proportional to the

Step 5: Lift direction selection
Lastly, lifting body and its direction is selected. Aircraft is kept as a lift creating body and according to the coordinates of the geometry Y-axis is the direction in which lift is being generated as shown in Figure 12. Drag is also defined in a similar manner.

Computational Analysis Results Discussion -Charts
Lift coefficient versus sweep angle Figure 13 illustrates the change in lift coefficient with change in the sweep angle. According to aerodynamic theory, lift increase with the increase in the Aspect Ratio [7], however, when the aspect ratio decreases contributing to a reduction in the wing-span, the tangential component of velocity increases with the sweep angle. From Figure 13, at 0 sweep angle, the aircraft with conventional tail has its maximum lift coefficient followed by the T-Tail and the least value is for Biplane with cruciform tail. With gradually increasing the sweep angle which results in a reduction in the Aspect ratio, the conventional tail is affected by the downwash of the wings compared to T-Tail and cruciform which results in an abrupt decrease in lift coefficient. At 30 Degree sweep angle Lift-to-drag ratio versus sweep angle Figure 15 shows the change in lift-to-drag coefficient versus sweep angle. At zero sweep angle, cruciform and T-Tail has same value for liftto-drag coefficient whereas the conventional has its least value of around 7.5. From the graph, all the numbers converge to a very near value of CL/  though the flow is characterised as a compressible flow and not many flow disturbances are observed as there is no fluctuation in the pressure coefficient. Due to the tapered wing [9], the induced drag produced doesn't significantly affect the lift generation [10] at the wing tips and is expected to create very small vortices. The interference drag plays a role at the junction between the wings and the pivot and it causes flow disturbances. The lower wing is affected more to the flow disturbances from the fuselage as well as the pivot laying on top of it. This contributes to an increase in the pressure coefficient.
Looking at the Mach Contour explains the flow pattern and shows the existence of shock waves if any.
In expanding over an aerodynamic shape, the flow velocity increase above the free stream value and if the free stream value is close enough to critical Mach number then the local Mach number will be supersonic in certain regions of the flow. The different colors on Figure 17 represent the difference in the Mach number over the surface of the aircraft. As noticed, the least velocity is observed in the areas where there is a stagnation [8]. Due to the curvature of the wing, the flow starts to accelerate moving upwards to the maximum curvature of the supercritical airfoil. Figure 18 shows the Mach Contour on a transverse plane. The Mach distribution is quite similar on the fuselage surface. At the wings surfaces, there is an abrupt the conventional tail will experience a uniform undisturbed fluid flow and will have less drag.
Based on the results obtained from ANSYS, the cruciform tail configuration is chosen for further analysis. As stated earlier, the optimum angle is chosen. The Oblique Biplane with a cruciform tail at 30 Degrees sweep angle shows the least value of drag compared to the other tail configurations as well as the highest Lift-to-Drag ratio. This makes 30 Degrees the optimum angle at cruise. The chosen tail at the optimum angle is tested in the transonic and the supersonic flow regime. Figure 16 shows the isometric view of pressure distribution over the surface of Biplane at 0 Degree sweep angle with Mach 0.6.Theoretically lift is generated by pressure imbalance [8] on the upper and lower surface of the wings. The pressure coefficient represented on the upper wing is negative indicating the generation of lift by the top surface of the two wings. Stagnation points are observed on some areas of the leading edge of the wing and the frontal area of the pivot as well as the tip of the fuselage nose. At such a point the pressure coefficient is almost 1. The pressure distribution over the surface of the wing is not very disturbed and appears to be relatively uniform until it reaches the trailing edge. This is the case as the wing is moving at a low Mach number so the compressibility effects are not very significant even

Degrees sweep angle
As the sweep angle is increased, the lift generation is also affected. The main contribution to the reduction in lift is because the aspect ratio of the wing has reduced by reducing the wing span. As mentioned earlier, the lift changes with the change change in the flow Mach number where it reaches to near sonic speed and a normal shock wave [7] is formed over the top surface of the wing, across which temperature, pressure, density of the fluid increase whereas the velocity decreases across the shock wave [7].  as areas like the tip of the fuselage nose and the leading edge of the tail as described earlier for the Oblique Biplane at 0 Degrees sweep. In such areas experiencing a stagnation point, the pressure coefficient is almost approaching 1.
As the flow moves further downstream the cross-sectional area of the fuselage increases and at the same time skin friction drag increases. The inclination in the fuselage nose helps to accelerate flow until it reaches to the wings-pivot area where in aspect ratio. This is because, in aerodynamics the main contributor to the lift component is the velocity perpendicular to the leading edge of the wing. As the sweep angle increases, the perpendicular velocity keeps on reducing, hence a reduction in lift as well as drag. This is seen on Figure 19 and Figure   20 representing 30 and 60 Degrees sweep angle. The stagnation points on the two models are highly predictable. The forward tip of the upper wing and the lower wing is perpendicular to the flow as well  The shock wave tends to be weak due to the non-perpendicular airflow over the wing surface. The higher the sweep angle the weaker the shock wave created at the same Mach number. Figure 22 represents the transverse section.

Degrees sweep angle
The flow distribution for the 60 Degrees follows almost the same pattern as that at 0 and 30 Degrees. However, the horizontal tail produces more lift compared to the previous sweep angles. This is because as the wing is swept further, the strength of the vortices reduces due to the reduction in the lift-induced drag [10].  Skin friction drag is a major contributor in the flow velocity over the wing surface. Starting from the leading edge of the wings the free stream flow comes in direct contact to the leading edge of the wings, where maximum pressure is felt and the fluid velocity is slowed down. As the air flows towards the trailing edge of the wing, it starts to experience a slight increase in the skin friction drag which causes drag at the rear part of the wings. At the pivot which is a circular mechanism that goes through the fuselage to hold the wings, the flow is perpendicular to its surface which behaves like a wall in front of the flow. From aerodynamics of the circular pivot, the fluid is smoothly moving around the frontal half of the pivot and the flow will be laminar [11] in that region. After that the flow tends to leave the surface and becomes turbulent. This phenomenon is due to the boundary layer separation on the rear half of the pivot. Here        On the wing surface the airspeed is faster than the speed of sound hence certain shock waves are created on the surface of the aircraft shown on Figure 26. Since the airfoil used on the wings is a supercritical airfoil, the formation of the shock waves is highly delayed to the trailing edge of the wing. Figure 27 shows the isometric view of pressure distribution at Mach 2.3. The force of drag is proportional to the coefficient of drag, to the square of the airspeed and to the air density. Since drag rises rapidly with speed, a key priority of supersonic aircraft design is to minimize this force by lowering the coefficient of drag and reducing the stagnation points over the surface of aircraft [12]. As seen from Figure 27, the surfaces of the aircraft generate a small amount of lift compared to the subsonic and transonic flow regimes. The wing clearly suffers from excessive shockwave formations and the pressure coefficient fluctuates between 1.3 to 1.8.

Degrees (Mach 2.3)
This is due to the fact that most of the surface of the aircraft is covered with shock waves that increase the wave drag on the aircraft and affect its performance. These locations include the rounded tip of the fuselage nose as well as the leading edge of the wings and the tail. Most of the parts of the aircraft are indicating a positive pressure coefficient greater than unity representing a highly compressible flow. As seen on the Figure 28, most of the aircraft is covered with a supersonic flow as expected.
Here, the flow mechanism changes due to the angle at which the wing is facing the free stream velocity and also due to the flow disturbances that occur around the pivot. As the flow climbs over the surface of the wing, it picks up speed starting from Mach 0.2 at the leading edge to almost Mach 2.2 at the trailing edge. This is shown on the red area over the wings on Figure 28.
Since the horizontal tail does not fall into the downwash region of the wing, it is not affected aerodynamically and can still generate a small amount of lift. This can be shown on the diagram where the velocity increases from the leading edge of the horizontal tail to its trailing edge and at the same time the pressure reduces due to the suction effect that creates the lift. 24 has contributed in the delaying the onset of shockwaves towards the trailing edge of the wing. However, the pressure coefficient has reduced by a very little increment due to the presence of a shock wave which promotes a supersonic region on the entire surface of the wing.
The lift generated by the plane at Mach 0.9 is satisfactory as long as there is no severe occurrence of strong shock waves.
The delay in the transonic drag rise that causes an increase in the pressure coefficient is an advantage of using the supercritical airfoil which weakens the shock wave on top of the wing.
Left half as backward swept wing and vice versa for the lower wing. From Figure 24, the flow is nearly high subsonic at the most leading edge of both wings with a Mach number ranging from 0.60 to 0.68. After the leading edge the flow start to accelerate over the surface of wing and the transition is obvious from subsonic to transonic and then to supersonic flow. A greater portion of the upper surface wing above the fuselage is covered by shock wave across which pressure, density, temperature and velocity drastically change. In comparison to upper wing, the wing below the fuselage has some disturbed flow around the pivot and fuselage area, where the flow Mach number is relatively decreased to subsonic. As the speed of a fluid approaches the speed of sound, many changes occur to the fluid and this is due to the compressibility effect experienced by the body moving through. Theoretically fuselages are designed to have minimum skin friction drag and the streamlines pass smoothly over the skin of fuselage with uniform Mach distribution. At the pivot, the fuselage accommodates a weak shock wave generated by the lower surface of the upper wing and a strong shock wave produced by the upper surface of the wing below the fuselage. From Figure 25, fluid flow is highly disturbed around the pivot, across which the Mach number drops to subsonic flow again and the flow remains subsonic at some area of the fuselage until it reaches the tail section.
Leading the discussion to Mach distribution over the horizontal and vertical tail as shown on Figure  26, the flow remains transient between subsonic and transonic over the vertical tail of Biplane ranging from Mach 0.7 to 0.85, whereas for the horizontal tail it experiences supersonic flow at its leading edge with a Mach number above one.  Figure 29. However, as we move further away from the mid-section of the bow shock, the area downstream of the bow shock Oblique shocks are created at the nose of the fuselage, the leading edge of the wing and at the tail of a supersonic aircraft [13]. The aircraft starts with a conical fuselage at the beginning with an increasing inclination until it meets the wing and pivot area. The fuselage nose has a blunt face and this promotes the formation of a weak shock or in other words a curved bow shock. Curved bow shocks [7] form at blunt bodies in a Supersonic

Wind Tunnel Apparatus
The following instruments were used in this experiment are: Therefore, when the airfoil is placed inside the test section a small gap must be left from both ends of the airfoil from the walls of the test section to avoid in accurate results.
• The necessary adjustments are made and are checked for one last time before the test section is closed and the experiment is ready to begin.

Wind tunnel operation
Start up: The procedure used to operate the wind tunnel initializing frame in Figure 31, is: 1. On control and instrumentation frame switch on the electrical isolator.
2. Speed Control is set to be minimum position (fully anticlockwise).

3.
For starting the flow of air, press the green START button.

4.
Then, gradually turn the speed control clockwise till desired speed is obtained for the experiment.
Shut down 1. Firstly, turn the speed control fully anticlockwise and then press red button to stop.  Similarly, Figure 34 shows the change in drag coefficient with respect to sweep angle. The graph follows the pattern of increase in drag with increasing sweep angle.

Wind tunnel procedure
The highest drag coefficient value is at 30   Figure 35 shows the effect of increasing the Mach number of the Oblique Biplane at 30 Degrees sweep angle and a cruciform tail. As the Mach number increases the compressibility effects become significant due to the changes in density. The aerodynamic forces acting on the aircraft highly depend on the changes in density at different flow regimes. The compressibility effect becomes more sincere as the speed of the aircraft increases. The fluctuations and disturbances that occur as the at 30 and 60 Degrees is increasing. This is because the wing on the 3D printed model started fluttering as the speed of air was increased. This caused a fluctuation in the drag value. However, if this issue was resolved, the drag should follow the same trend as that in ANSYS shown on Figure 34. The drag should reduce with increasing sweep. Due to the same issue the value of the Lift was also affected.  shares a significant increase as the flow turns into transonic and eventually supersonic as shown in Figure 39.

Lift-to-Drag ratio vs. Sweep angle: Swing wing vs. Oblique biplane
The Lift to Drag ratio represented on Figure 40 follows the same trend as that obtained from the Oblique Biplane. The Lift to drag ratio increases as the sweep angle increases from 0 to 60 Degrees. For a variable swept wing, the flow parallel to the wing has no effect on it, however, as the sweep angle is increased, the flow perpendicular to the wing gets slower (lesser) than the actual airflow [14], it consequently exerts less pressure on the wing. Therefore, the lift to drag ratio of the Swept wing reduces with an increasing sweep angle [14]. The same trend is followed by the Oblique Wing on Figure 41 at which the Lift to Drag ratio reduces with an increase in the sweep angle for a T-Tail and a Cruciform tail however, By comparing the two graphs for the variable swept wing and the Oblique wing, it is noticed that the Oblique wing has the highest value of lift to drag ratio at 0 Degrees which is the same case with a variable swept wing.

Lift-to-Drag ratio vs. Mach number: Supersonic aircraft vs. Oblique biplane
There is a huge emphasis on the aerodynamics of the flow when it comes to supersonic Mach aircraft increases its speed and in turn the Mach number can create sudden shock waves that have a direct effect on the lift and drag.
At Mach < 1, the compressibility effect can be ignored. So from Figure 35, at Mach 0.6 and 0.9, the compressibility effects are ignored and as seen there is no significant change in the Lift.
At Mach > 1, the compressibility effects become very significant and the density changes faster than the velocity of the aircraft. This causes a severe change in the lift generated by the aircraft as seen at Mach 2.3 on Figure 35.
Lift-to-Drag ratio: Delta wing vs. Oblique biplane Figure 36 illustrates the change in the lift coefficient with change in drag coefficient for delta wing. The cross-sectional area of a delta wing is higher compared to the Oblique wings which results in induced drag of the lifting wing. By comparing CL versus CD of delta wings and Oblique wings on Figure 36 and Figure 37, it is seen that they follow the same trend, as the lift coefficient decreases; the drag also decreases with it.

Lift-to-Drag ratio vs. Mach number: Variable sweep wing vs. Oblique biplane
As shown in Figure 38, the Oblique Biplane using a Cruciform tail follows the same general trend of variable sweep wings in Figure 38. The drag remains almost constant at low subsonic speed however it  as that in Figure 42. Typically, the Lift-to-Drag ratio of a supersonic aircraft is half that of a subsonic one [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. However, since the size of the model numbers. As shown on Figure 42, the Lift-to-Drag ratio at subsonic speeds is higher compared to that seen in supersonic. Figure 43 shares the same trend   It is clearly seen from the results obtained that, Oblique wing has reduced drag coefficient as the sweep angle increases in comparison with a conventional symmetrically swept design. Fundamentally, this is due to the increased length of an Oblique wing, which is twice as long as a symmetric wing. Moreover, the research shows that Oblique wings tend to perform better at high subsonic or transonic Mach numbers and very low supersonic Mach numbers due to the formation of excessive shock waves at higher Mach numbers. It is also found that for higher Mach numbers, 30 on which the test was conducted is very small, it is expected that the lift and drag values will be lesser than that of an actual, bigger model because of the size limitation.

Conclusion
The purpose of this research was to investigate the potential of achieving improved aerodynamic performance and efficiency of flight at a wide range of oblique angles with different tail configurations (conventional, T-Tail, cruciform) on an Oblique Biplane.  degrees is not very sufficient and will be a victim of excessive wave drag. Increasing the sweep angle will improve the performance at high subsonic and supersonic flow regimes.
Based on the tabulated results, the model with the cruciform tail configuration is chosen as the most effective candidate for the aircraft because of its adequate and relevant aerodynamic performance.
It is believed that reducing the effect of drag and shock waves occurrence on the surface of the Oblique Biplane will render the Aircraft fuel efficient. The Oblique Biplane can be the future fighter jet aircraft because of its high value performance in terms aerodynamics, cost, structural design and weight.