This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Find sources: "Rankine vortex" – news · newspapers · books · scholar · JSTOR(April 2024)
The Rankine vortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine.
The vortices observed in nature are usually modelled with an irrotational (potential or free) vortex. However, in potential vortex, the velocity becomes infinite at the vortex center. In reality, very close to the origin, the motion resembles a solid body rotation. The Rankine vortex model assumes a solid-body rotation inside a cylinder of radius and a potential vortex outside the cylinder. The radius is referred to as the vortex-core radius. The velocity components of the Rankine vortex, expressed in terms of the cylindrical-coordinate system are given by[1]
where is the circulation strength of the Rankine vortex. Since solid-body rotation is characterized by an azimuthal velocity , where is the constant angular velocity, one can also use the parameter to characterize the vortex.
The vorticity field associated with the Rankine vortex is
At all points inside the core of the Rankine vortex, the vorticity is uniform at twice the angular velocity of the core; whereas vorticity is zero at all points outside the core because the flow there is irrotational.
In reality, vortex cores are not always circular; and vorticity is not exactly uniform throughout the vortex core.
^D. J. Acheson (1990). Elementary Fluid Dynamics. Oxford University Press. ISBN 0-19-859679-0.
The Rankinevortex is a simple mathematical model of a vortex in a viscous fluid. It is named after its discoverer, William John Macquorn Rankine. The...
}}} becomes non-zero, with direction roughly parallel to the vortex axis. The Rankinevortex is a model that assumes a rigid-body rotational flow where...
that rotation. This is the case, for example, in the central core of a Rankinevortex. The vorticity may be nonzero even when all particles are flowing along...
William John Macquorn Rankine FRSE FRS (/ˈræŋkɪn/; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor...
(disambiguation) Rankine (crater) Rankine power station Rankine theory RankinevortexRankine's method Rankine–Hugoniot equation Trouton–Rankine experiment...
to the idea of the Rankinevortex as shown in fig 2, which combines solid body rotation for small r {\displaystyle r} and vortex motion for large values...
Technology. Rankinevortex – a simpler, but more crude, approximation for a vortex. Lamb–Oseen vortex – the exact solution for a free vortex decaying due...
to a Rankinevortex, characterised by a slow, outward decrease in azimuthal velocities. RAFOS floats trapped in the core of the Lofoten Vortex revealed...
Operations Center (ROC) Radius of maximum wind (RMW) Rain-free base (RFB) Rankinevortex Rear flank downdraft (RFD) Ridge Roll cloud Remote sensing Rope tornado...
The turbine's hot exhaust powers a steam power plant (operating by the Rankine cycle). This is a combined cycle gas turbine (CCGT) plant. These achieve...
their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative...
in mercury at a temperature of 4.2 K. Cryogenicists use the Kelvin or Rankine temperature scale, both of which measure from absolute zero, rather than...
an infinitely old universe; this paradox was later extended by William Rankine. In final publication, Thomson retreated from a radical departure and declared...
blade surface. Tip vortex cavitation is caused by the extremely low pressures formed at the core of the tip vortex. The tip vortex is caused by fluid...
h+v^{2}/2} is constant, which is also constant across the shock wave (Rankine–Hugoniot conditions) and therefore we can write v × ω = − T ∇ s {\displaystyle...
SNAP-1 was a test platform that was never deployed, using cerium-144 in a Rankine cycle with mercury as the heat transfer fluid. Operated successfully for...
engine Water-fuelled car Water-returning engine Water turbine Working fluid Rankine cycle Hydroelectricity Singer, Charles Joseph; Raper, Richard. A history...
building on the publications of William Thomson, Helmholtz and William Rankine popularized the idea of the heat death of the universe. In fluid dynamics...
a temperature of 1.2 K was reached by combining a PTR with a superfluid vortex cooler. For getting the cooling, the source of the pressure variations is...
A; Ashjaee, M (2013). "The thermal efficiency improvement of a steam Rankine cycle by innovative design of a hybrid cooling tower and a solar chimney...
Morey (1930–32) by John W. Campbell The Lensman series (1934-1948) and The Vortex Blaster (1960) by E. E. Smith Empire (1945-1951), and Foundation series...
resonance. 1887 – Pierre Henri Hugoniot based on the work of Rankine, introduces the Rankine–Hugoniot conditions to model shock waves. 1887 – First models...
Fahrenheit) Johann Heinrich Lambert (foot-lambert) William John Macquorn Rankine (degree Rankine) Non-systematic units Alexander Graham Bell (bel) Marie Curie (curie)...
temperature using his hypothesis of molecular vortices 1850 – Rankine uses his vortex theory to establish accurate relationships between the temperature...
Relativistic Euler equations Helmholtz's theorems – 3D motion of fluid near vortex lines Kirchhoff equations Knudsen equation – Description of gas flow in...
1090/S0002-9947-99-02399-5. S2CID 53365869. Retrieved 2009-06-27. "Spiral vortex solution of Birkhoff–Rott equation". Association for Computing Machinery...