Search results
Results From The WOW.Com Content Network
In flow regions where vorticity is known to be important, such as wakes and boundary layers, potential flow theory is not able to provide reasonable predictions of the flow. [1] Fortunately, there are often large regions of a flow where the assumption of irrotationality is valid which is why potential flow is used for various applications.
The original problem was solved by Stokes in 1845, [9] but Geoffrey Ingram Taylor's name was attached to the flow because he studied its stability in a famous 1923 paper. [ 10 ] The problem can be solved in cylindrical coordinates ( r , θ , z ) {\\displaystyle (r,\\theta ,z)} .
The problem of potential compressible flow over circular cylinder was first studied by O. Janzen in 1913 [4] and by Lord Rayleigh in 1916 [5] with small compressibility effects. Here, the small parameter is the square of the Mach number M 2 = U 2 / c 2 ≪ 1 {\displaystyle \mathrm {M} ^{2}=U^{2}/c^{2}\ll 1} , where c is the speed of sound .
While the fluid mechanics of the original flow are unsteady when >, the new flow, called Taylor–Couette flow, with the Taylor vortices present, is actually steady until the flow reaches a large Reynolds number, at which point the flow transitions to unsteady "wavy vortex" flow, presumably indicating the presence of non-axisymmetric instabilities.
Von Kármán swirling flow is a flow created by a uniformly rotating infinitely long plane disk, named after Theodore von Kármán who solved the problem in 1921. [1] The rotating disk acts as a fluid pump and is used as a model for centrifugal fans or compressors.
The problem has a cylindrical symmetry and can be treated in two dimensions on the orthogonal plane. Line sources and line sinks (below) are important elementary flows because they play the role of monopole for incompressible fluids (which can also be considered examples of solenoidal fields i.e. divergence free fields).
A shift in the position of the reference point effectively adds a constant (for steady flow) or a function solely of time (for nonsteady flow) to the stream function at every point . The shift in the stream function, Δ ψ {\displaystyle \Delta \psi } , is equal to the total volumetric flux, per unit thickness, through the surface that extends ...
For example, in the laminar flow within a pipe with constant cross section, all particles travel parallel to the axis of the pipe; but faster near that axis, and practically stationary next to the walls. The vorticity will be zero on the axis, and maximum near the walls, where the shear is largest.