Aerodynamic physics of the Delta Wing – POST #100

Reference: ResearchGate

Delta wings are known as highly swept wings and that’s what makes them aerodynamically more efficient at a high angle of attack. Supersonic aircraft are equipped with such wing configurations. The high-speed aircraft have to fly at low speed for takeoff and landing. Therefore it is important to study their aerodynamic characteristics at low speed.

Delta wings are able to produce lift force for the value of angle of attacks at which convectional airfoil section wing would be stalled.

Flow Features over the Delta Wing

Reference: ResearchGate

The dominant feature of this flow is the two vortex patterns (Primary Vortex) that are shed from the vicinity of the highly swept leading edge. The angle of attack makes the flow asymmetric between the lower and upper surfaces of the delta wing and results in higher pressure on the bottom surface than the pressure on the upper surface of the delta wing. 

Thus the flow tries to curl around or rolls up from the vicinity of the leading edge of the bottom surface to the top surface resulting in the formation of a primary and secondary vortex. 

This is known as the Curling of the flow from the high pressure lower surface to the low pressure upper surface on the delta wing.
Reference: ResearchGate

Flow across the sharp edge or any corner separates due to viscous effect as shown in the above image. The 2 leading edges of the standalone delta wing act as the sharp edge from where flow separates and rolls up. As it does so there are two strong vortex structures (primary vortex) trapped inside, which are responsible for generating low pressure at the vortex core which is actually felt by the upper surface of the wing.

Reference: ResearchGate

As shown from the above coefficient of pressure distribution from the upper surface of the delta wing, this vortex stably creates huge suction peaks close to the upper surface leading edge and by this mechanism, they are able to sustain high lift up to a high angle of attack.  

Reference: ResearchGate

There is a lot happening at the upper surface of the delta wing, If we take close look at it, We would be able to locate the primary, and secondary vortex shedding through the wing edge. A secondary vortex sheds & forms underneath the primary vortex in the opposite sense.   

If we look at the vortex trace lines on the wing surface as shown in the above image we can see primary vortex separation line S1 and reattachment line A1. Similarly, we can see secondary vortex separation line S2 and reattachment line A1. The surface streamlines flow away from the reattachment line A1 & A2 whereas the surface streamlines tend to flow towards the separation line S1 & S2 & then simply lift off the surface along these lines.  

We can say the primary vortex is contained within the region between A1-S1 lines, this will help us to roughly estimate the size of the vortex but we can not locate the exact location of the vortex as it is an off-body feature. Similar observations can be made for the secondary vortex. We may also happen to have a tertiary vortex but not shown in the above picture.

The flow downstream is sort of undisturbed along with a series of straight-line rays emanating from the vertex of the triangular shape.  

Hence Delta wings are efficient at moderate and high angles of attack!

Pressure distribution on the delta wing

Spanwise Pressure distribution on the delta wing

In the above image, we can see the cross-sectional view of the delta wing with static pressure distribution on the top and bottom surfaces.

The leading-edge vortices that roll up are strong and stable because of the high value of vorticity, the local static pressure near the leading edges of the delta wing becomes extremely negative resulting in a suction effect due to the presence of primary and secondary vortex. Hence, the surface pressure on the top surface of the delta wing is reduced near the leading edge and is slightly higher (still lower than the ambient pressure) and reasonably constant over the middle of the wing.  

The spanwise variation of pressure over the bottom surface is essentially constant and higher than the freestream pressure. This results in a pressure difference between the upper and lower surface. This is how Lift force is generated on the delta wing and sustained over the large angle of attack.  

With the increase in AOA, suction becomes stronger on the top surface, and similarly pressure on the lower surface increases, and hence lift force also increases.  

Vortex flow structures on delta wing at different angles of attack  

Now, we will see how the vortex structure behaves when the angle of attack of the delta wing increases. 

Reference: NPTEL, Fundamentals of Theoretical and Experimental Aerodynamics

The suction of the leading edge vortices enhances the lift on a delta wing. For this reason, the lift coefficient curve of a delta wing exhibits an increase in lift coefficient for a value of AOA at which the convectional airfoil section wing would be stalled.

Aerodynamic characteristics from the lift curve of the Delta wing  

  1. The lift curve slope is smaller as compared to the airfoil.
  2. Lift continues to increase to the large value of AOA.
  3. A reasonable value of maximum lift coefficient ~ 1.5 is achieved at a near stall angle.
  4. In delta wings stall is delayed whereas in the airfoil section maximum lift coefficient is obtained at a much smaller AOA but stall occurs much earlier in the airfoil section.

Vortex Breakdown

Reference: ResearchGate

It is a dramatic phenomenon that occurs in the flow over the top surface of a delta wing at a high enough angle of attack. The leading-edge vortices begin to fall apart. Some were along the length of the vortex, This is called vortex breakdown.

The vortex exhibits spiral-type instabilities close to the wing tip as shown in the above image. The core twist in various directions. Further downstream the vortex core widens and a bubble-type structure is formed which finally leads to vortex breakdown, where the vortex suddenly bursts, forming a large bubble of chaotic flow.  

There is a significant loss of lift moment, and an increase in drag and roll in case of asymmetric vortex breakdown.  

Vortex Traces on a Delta Wing, Surface Flow visualization Vortex Prediction

Reference: motorsportengineer

Vortex Traces on a Delta Wing, We can see main primary vortices in red, being generated from pressure side of the wing to the suction side. Using the surface flow visualization technique, we can’t see vortex as it is an off body flow structure far away from the surface. What we can see, it’s effect on boundary layer that can help us to locate these vortices.

Surface flow visualization reveals the flow streamlines in the limit as a solid surface is approached. Colour oil applied to the surface of a wind tunnel model provides one example (the oil responds to the surface shear stress and forms a pattern).

Vortex rotation generate primary reattachment lines, that could be seen in flow trace visualization. If we see that kind of traces(reattachment lines), we can predict core of the vortex is bit offset at a certain distance from the surface.

As vortex is shedding through edge, there will be more vortex shedding in the opposite sense, it will grab the boundary layer and shed it in opposite sense. So it will going to have a secondary separation line as we can see in the above image.

It will also have a secondary reattachment line which is an area close to tangent to the surface. If in our flow visualization techniques, resolution is good enough we can see tertiary vortex trace as well.

We can see the width of the traces, for the primary vortex, it is the biggest and it should be as the primary vortex is the biggest one. Based on the surface flow visualization traces pattern we can predict the location of vortex.

Between Primary reattachment and Secondary separation line, Somewhere between these two lines and at a distance from the surface would be the location of primary vortex.

Finally Flow visualization can give us hint to predict the location of vortex offset to the surface.

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