Category: Learn Blogs

Downwash & Induced Drag

The flow pattern at the tip of the finite wing generates a vortical flow field. The trailing vortices create a ‘downwash’ at the wing that rotates the freestream velocity downwards vectorially. These vortices make the resultant lift force vector rotate backward, which gives rise to a force that is in the direction of the flow. This is in addition to the ‘lift force’ (an upward force at right angles to the flow direction). This ‘drag force‘ is called the ‘induced drag’ as it is accompanied by the production of lift.

Linearized Theory

The above discussion regarding forces generated due to uniform motion of aerodynamic elements(airfoils/wings) does not necessarily apply to bird flights.
Birds generate both lift and thrust forces using the same aerodynamic surfaces, contrary to the mechanism of aerospace vehicles where the lift and thrust generation are decoupled.
An important aspect here relates to the unsteady nature of flapping-wing aerodynamics of birds. The complexity of the bird’s flight is associated with the interactive relationship between the wing’s motion and the aerodynamic and elastic forces, which are essentially nonlinear.

In nature, almost all turbulent flows are invariably ‘unsteady‘. What is prescribed as ‘steady‘ is the statistical averaged variable, provided that the flow has an energy equilibrium condition. In such cases, one correct formulation is the steady RANS.

Other pure unsteady statistical formulations exist, such as unsteady RANS (URANS).

In a specific flow problem, viz. flow around a bluff body, it is difficult to get a good solution for drag using RANS. The LES or hybrid DES formulations better address this type of problem.

Every system has a steady and a transient state. The steady-state of the system is reached when the state does not change its value in successive iterations. The transient state is the phase between the beginning and till steady state that has been achieved.

A 2D steady-state heat conduction equation:

A 2D transient state heat conduction equation:

Some of the steady-state methods are:

1. Jacobi method
2. Gauss-Seidel method
3. SOR method

Crank-Nicholson methods are used for transient state calculation.

SOR should be used in the steady-state analysis because it converges in fewer iterations and has lesser memory requirements than Jacobi.

In transient state analysis, the explicit scheme is faster. A steady-state solver is faster because of the mathematical simplification. There is no thermal diffusivity and no time integration. There will be no numerical diffusion, and the solution will always be stable, just that we have to choose a good CFL/courant number. (Courant No. = v * dt /dl, where, v = velocity of flow, dt= time step, dl = grid cell size).

The 1920’s and 1930’s in Germany were a time of great innovation in aircraft and propulsion design. This is due to a few factors, post World War-I politics, German government support and the coaching by old aeronautical geniuses.

During most of the 1920’s Germany was prohibited from developing or manufacturing military aircraft. This led the aviation enthusiasts to sailplane and gliding competitions. The sailplane competitions encouraged quick and inexpensive development of new ideas. These competitions trained an entire generation of aeronautical engineers. The aerodynamic edge was constantly extended along with the development of lightweight building techniques. The competitions culminated on a 950-meter peak in the Bavarian Alps called Wasserkuppe. This was where the Olympics of gliding were held every year. This area was perfect for gliding, gentle grass-covered slopes, which fell away into wide-open valleys. By 1937 there was a large complex of buildings catering to the gliding community.

 

The rise of the NSDAP party and Germany’s aspirations of regaining some of its power and prestige led the German government to wholeheartedly support the education of aeronautics in schools and the official support of the sailplane competitions. Sponsorships and grants for innovative ideas became plentiful in the 1930s. (Ransom, 2001).

Aeronautical greats such as Prandtl, Ahlborn and Lilienthal trained or inspired this new generation of engineers competing at Wasserkuppe. Prandtl derived the basis for much of the fluid dynamic theory used today. Prandtl was very interested in the glider competitions and became friends with a young engineer named Alexander Lippisch who would develop the Me-163 and much of the theory of Delta wings. Prandtl along with Lippisch went on to coach the teenage Horten brothers who would go on to almost 60 years of tailless aircraft research. Professor Ahlborn, through his study of a gliding seed called Zanonia (Macrocarpa) in the 1890’s inspired many tailless aircraft designs. Ahlborn documented the hydrodynamics of this tailless flying seed and ran the German Hydrodynamic Institute into the 1920’s. The Zanonia seed achieved stable flight by using a combination of swept wings with up to 10 degrees of washout at the tips. The washout at the tip provided a negative pitching moment, which countered the positive pitching moment of the center section. This information became the foundation for tailless aircraft theory developed by the Hortens and Lippisch as well as the British engineer John Dunne. Lilienthal who is Germany’s equivalent to the Wright brothers conducted a number of manned glider flights in the 1890’s also provided inspiration.