The swirling round laminar jet

Abstract

The swirling round laminar jet in an unbounded viscous fluid is investigated in this paper. The axisymmetric laminar jet with a swirling velocity is simulated by a linear-momentum source and an angularmomentum source, both located at the origin. The first-order and the second-order solutions in the far field have been obtained by solving the complete Navier-Stokes equations. It is found that the first-order solution is the well-known round-laminar-jet solution without the swirling velocity obtained by Landau [2] and Squire [3]. The second-order solution represents a pure rotating flow. The swirling velocity predicted by the present solution is compared with that obtained by Loitsyanskii [15] and G6rtler [16], who solved the corresponding boundary-layer equations. It is found that the swirling velocity predicted by the present theory is smaller than that obtained from the boundary-layer equations.

Swirling jets for the mitigation of hot spots and thermal stratification in the VHTR lower plenum.

“…Vortex research in Cartesian coordinates includes the Green-Taylor vortex [Taylor and Green, 1937] and the helicoid vortex developed in Section 5.1.1 [Rodriguez andEl-Genk, 2008a, 2010d]. Various researchers selected spherical coordinates [Tsukker, 1955;Gol'Dshtik and Yavorskii, 1986;Hwang and Chwang, 1992], but the vast majority of the research found in the literature is in cylindrical coordinates [Rankine, 1858;Lamb-Oseen, 1932;Burgers, 1948;Loitsyanskiy, 1953;Gortler, 1954;Newman, 1959;Sullivan, 1959;Batchelor, 1964;Squire, 1965;Chepura, 1969;Martynenko, 1989;Aboelkassem, Vatistas, and Esmail, 2005;Rodriguez andEl-Genk, 2008a, 2010d]. Cylindrical coordinates are chosen primarily due to its geometric simplicity and excellent mapping of the vortex behavior onto a coordinate system-in particular, as a 3D vortex spins azimuthally as it stretches about the z axis, the vortex velocity field shape fills up a cylindrical geometry.…”

Recent Advances in Modeling Axisymmetric Swirl and Applications for Enhanced Heat Transfer and Flow Mixing

“…Vortex research in Cartesian coordinates includes the Green-Taylor vortex (Taylor and Green, 1937) and the helicoid vortex discussed herein El-Genk, 2008a, 2010b andd). Various researchers selected spherical coordinates (Gol'Dshtik and Yavorskii, 1986;Hwang and Chwang, 1992;Tsukker, 1955), but the vast majority of the research found in the literature is in cylindrical coordinates (Aboelkassem, Vatistas, and Esmail, 2005;Batchelor, 1964;Burgers, 1948;Chepura, 1969;Gortler, 1954;Lamb, 1932;Loitsyanskiy, 1953;Martynenko, 1989;Newman, 1959;Rankine, 1858;El-Genk, 2008a, 2010b andd;Sullivan, 1959;Squire, 1965). Cylindrical coordinates are chosen primarily due to its geometric simplicity and excellent mapping of the vortex behavior onto a coordinate system-in particular, as a 3D vortex spins azimuthally, stretching about the z axis, the vortex velocity field engulfs a cylindrical geometry.…”

Two Phase Flow, Phase Change and Numerical Modeling

“…Vortex research in Cartesian coordinates includes the Green-Taylor vortex (Taylor and Green, 1937) and the helicoid vortex discussed herein El-Genk, 2008a, 2010b andd). Various researchers selected spherical coordinates (Gol'Dshtik and Yavorskii, 1986;Hwang and Chwang, 1992;Tsukker, 1955), but the vast majority of the research found in the literature is in cylindrical coordinates (Aboelkassem, Vatistas, and Esmail, 2005;Batchelor, 1964;Burgers, 1948;Chepura, 1969;Gortler, 1954;Lamb, 1932;Loitsyanskiy, 1953;Martynenko, 1989;Newman, 1959;Rankine, 1858;El-Genk, 2008a, 2010b andd;Sullivan, 1959;Squire, 1965). Cylindrical coordinates are chosen primarily due to its geometric simplicity and excellent mapping of the vortex behavior onto a coordinate system-in particular, as a 3D vortex spins azimuthally, stretching about the z axis, the vortex velocity field engulfs a cylindrical geometry.…”