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.
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.
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The major lift producing component of an aerospace vehicle is the wing surface and the control deflection is provided by the control surfaces.
When the control moment and the aerodynamic moment are balanced, this state is called the trim state of the vehicle.
For a statically stable vehicle(C.G. ahead of C.P.), the control moment generated by the actuator deflection produces the required AoA, and the moment produced is stabilizing the vehicle.
The case is different for a statically unstable vehicle (C.G. behind C.P.), where this creates a destabilizing moment.
The flying vehicle with a stable configuration can be designed without an autopilot theoretically. However, for precise control of lateral acceleration, autopilot is an integral element in the design procedure.
A trim-state is achieved when the aerodynamic moment generated due to AoA is balanced by the control moment generated due to fin deflection, i.e,
Aerodynamic Moment = Control Moment
The vehicle’s static stability is directly proportional to the distance between the C.G. and C.P., more the distance, the more is the control effort required to trim the vehicle.
For a high manoeuvring vehicle and where control effort needs to be optimized, it is desired to keep this distance as minimum as possible.
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:
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).