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Modeling
This page discusses some aspects of flow modeling using panel methods
Wakes are sheets of vorticity shed aft of lifting surfaces. In potential flow, wakes are sheets of varying doublet strength (vorticity) representing the inviscid limit of the true viscous wake shed by the lifting surface. This shed vorticity is responsible for downwash on the lifting surface, which reduces lift and produces induced drag.
A doublet panel induces a jump in velocity potential between its two faces. This means that the velocity potential is discontinuous across the wake sheet. As such, the velocity potential on the outer surface of the body is discontinuous where the wake is shed from the body, typically sharp trailing edges. As the inner potential is continuous at such intersections, it is necessary for there to be a discontinuity in doublet strength at these intersections. At edges which shed wake panels, the strength of these wake panels is determined by the difference in doublet strength between the two panels forming that edge. This ensures that a line vortex is not formed at wake-shedding edges, even though the doublet strength on the body is discontinuous.
Within MachLine, wakes are generated automatically, but the user has some freedom in specifying how this should be done. For example, if the user desires to perform a nonlifting analysis, then they may specify that there be no edges on the body at which the doublet strength is discontinuous and no wake panels shed. The user may also specify the maximum flow-turning angle which is allowed on the surface before a wake is shed.
In supersonic flows, influences do not propagate upstream. Thus, in many cases, it is unnecessary to explicitly model the wake (for example, on a single straight wing with supersonic trailing edges). In this case, however, the doublet strength still must be discontinuous along edges from which the wake is shed, even though the wake itself is not present. This may be affected by specifying in the input file that a wake is present but it is not to be appended.
How exactly MachLine models the wake is set in the input file, described here.
There are multiple different ways or formulations in which the mass-flux boundary condition may be enforced in potential flow methods, several of which are implemented in MachLine. The formulation is specified in the input file, described here.
With the Morino formulation, the inner perturbation potential is chosen to be zero. From this, the source strengths are calculated explicitly as a function of the freestream velocity to satisfy the zero mass-flux boundary condition. A set of control points is then placed within the body and the doublet strengths are solved for such that the perturbation potential at each of these control points is zero.
With the source-free formulation, the inner total potential is chosen to be zero. The choice means that the source strengths are all zero, meaning source contributions never have to be calculated. As with the Morino formulation, a set of control points is placed within the body and the doublet strengths are solved for such that the total potential at each of these control points is zero.