On Source and Vortex Distributions in the Linearized Theory of Steady Supersonic Flow

The motion of the trailing vortices associated with a lifting wing is investigated by theoretical and visual-flow methods for the purpose of determining the proper vortex distribution to be used for downwash calculations. Both subsonic and supersonic speeds are considered in the analysis.It is found that the degree to which the vortices are rolled up depends upon the distance behind the wing and upon the lift coefficient, span loading, and aspect ratio of the wing. While the rolling up of the trailing vortices associated with high-aspectratio wings is of little practical importance, it is shown that, with low-aspect-ratio wings, the trailing vortex sheet may become essentially rolled up into two trailing vortex cores within a chord length of the trailing edge.The downwash fields associated with the two limiting cases of the flat vortex sheet and the fully rolled-up vortices are investigated in detail for both subsonic and supersonic speeds. The intermediate case in which the rolling-up process is only partially completed at the tail position is also discussed.

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“…The downwash within the vortex cores may be approximated by assuming that each core has a radius given by Eq. (17) and rotates as a solid body.…”

Section: Downwash At D » Ementioning

confidence: 99%

The Rolling Up of the Trailing Vortex Sheet and Its Effect on the Downwash Behind Wings

Spreiter¹,

Sacks²

1951

Journal of the Aeronautical Sciences

151

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“…The obtained results prove its applicability for multiple lifting surfaces with part span deflections and can include ground effect and wind tunnel interference. Robinson [18] worked with the hyperbolic characteristics of the differential equation satisfied by the velocity potential in linearised supersonic flow. This entailed the presence of fractional infinities in the fundamental solution of equations.…”

Section: Steady Vortex Lattice Methodsmentioning

confidence: 99%

Review of vortex lattice method for supersonic aircraft design

Joshi

Thomas

2023

Aeronaut. j.

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There has been a renewed interest in developing environmentally friendly, economically viable, and technologically feasible supersonic transport aircraft and reduced order modeling methods can play an important contribution in accelerating the design process of these future aircraft. This paper reviews the use of the vortex lattice method (VLM) in modeling the general aerodynamics of subsonic and supersonic aircraft. The historical overview of the vortex lattice method is reviewed which indicates the use of this method for over a century for development and advancements in the aerodynamic analysis of subsonic and supersonic aircraft. The preference of VLM over other potential flow-solvers is because of its low order highly efficient computational analysis which is quick and efficient. Developments in VLM covering steady, unsteady state, linear and non-linear aerodynamic characteristics for different wing planform for the purpose of several different types of design optimisation is reviewed. For over a decade classical vortex lattice method has been used for multi-objective optimisation studies for commercial aircraft and unmanned aerial vehicle’s aerodynamic performance optimisation. VLM was one of the major potential flow solvers for studying the aerodynamic and aeroelastic characteristics of many wings and aircraft for NASA’s supersonic transport mission (SST). VLM is a preferred means for solving large numbers of computational design parameters in less time, more efficiently, and cheaper when compared to conventional CFD analysis which lends itself more to detailed study and solving the more challenging configuration and aerodynamic features of civil supersonic transport.

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“…Assume now that the local incidence at the top surface is a for 0 < x < c/2 and -a for c/2 < x < c. For 0 < x < c/2 the pressure is then still given by (4.8) or (4.9), while for c/2 < x < c we now have instead of (4.5), (4)(5)(6)(7)(8)(9)(10) where J(r,y,r0) is still defined by (3.11). Carrying out the integration in (3.11), we have to take into account that r is now smaller than or equal to r0.…”

Section: Introductionmentioning

confidence: 99%