Rankine Combined Vortex Research Articles

A gas jet impacting a cavity

A subsonic air jet impinging upon a cavity is studied to explain the resultant heating phenomenon. Flow visualization within the cavity shows a large central vortex dominating the flow pattern. Velocity measurements inside the cavity are made using a hot-wire anemometer. Temperature is measured with a copper-constantan thermocouple. The velocity field within the cavity is described by a modified Rankine combined vortex. An uncommon form of the energy equation is used to account for turbulent heating in adverse pressure gradients. A theoretical solution is developed to model the temperature field in the cavity. There is a good agreement between the calculated and measured temperatures. The heating effect is related to Ranque-Hilsch tubes.

Waterspout Wind, Temperature and Pressure Structure Deduced from Aircraft Measurements

Abstract During September 1974 in the Lower Florida Keys, the first successful penetrations of mature waterspouts were accomplished by a specially instrumented research aircraft. Throughout the course of each penetration, the measurement system recorded the temperature, the pressure and the three-dimensional velocity field near and within the visible funnel. Multiple penetrations of both cyclonic and anticyclonic waterspouts in various life-cycle stages were achieved. The results indicate that the waterspout funnel structure exhibits 1) a warm central core region, 2) positive vertical velocities of 5–10 m s−1 outside of the warm core, and 3) tangential velocities and horizontal pressure gradients with characteristics similar to but with magnitudes greater than those of the dust devil. A scale analysis of each term in the governing equations of motion suggests a simplified set of modeling equations. The simple Rankine-combined vortex model with cyclostrophic flow explains approximately 75% of the total mea...

A kinematical consideration on behavior of a front within a typhoon area

Considering that a front is a substantial line, the behavior of a pre-existing front is investigated kinematically within a typhoon area in middle latitudes. The wind field of a typhoon is represented by the Rankine combined vortex to determine the deformation and displacement of the pre-existing front from trajectories of each point constituting the front by Petterssen's method of successive approximations. Comparison of the results thus obtained for the cases of typhoons Doris and Winnie, 1966, with those by the surface analysis shows good agreement.

WATERSPOUTS AND TORNADOES OVER SOUTH FLORIDA1

Abstract An analysis of the Lower Matecumbe Key 1967 waterspout data is presented. It was found that the flow field synthesized across the spray vortex of the second, larger waterspout is closely approximated by a Rankine-combined vortex with solid rotation over a circle 24 m in diameter. Five major tornadoes were documented in the Greater Miami area during 1968, and this anomalous number is ascribed to the development of strong localized zones of convergence on the mesoscale along or slightly inland from the southeast coast where the prevailing southwesterly tropospheric flow interacts with the sea breeze induced by the Florida Peninsula. On the other hand, the large number of waterspouts documented in the Lower Keys during the summer of 1968 were spawned by cumulus congestus cloud lines embedded in a very warm undisturbed trade-wind flow. Extensive documentation of close-range observations was obtained for an unusually large “tornadic waterspout” that passed through a crowded coastal marina in Miami. Ev...

Solitary waves in rotating fluids

This paper describes some experiments in rotating flows in which solitary waves were observed.In one set of experiments the waves were generated on a swirling flow whose circumferential velocity distribution resembled that of the Rankine combined vortex. This flow was established by stirring the liquid in a large cylindrical container, in much the same way as one stirs a cup of tea, and it was often found at the cessation of the stirring that a wave had been generated. This wave propagated along the vortex core and was reflected at the bottom of the container and at the free surface of the liquid and displayed the remarkable permanence characteristic of solitary waves. It appears that, to a first approximation, the speed of the waves may be calculated simply from the depression of the free surface of the liquid at the centre of the vortex. These waves are the rotating-fluid counterpart to the solitary waves in fluids of great depth recently discussed by Benjamin (1967b) and by Davis & Acrivos (1967).In a second set of experiments, solitary waves were generated in a long cylindrical tube and are analogous to the familiar solitary wave of open-channel flows. The theory indicates that these waves are possible in any swirling flow in which the angular velocity is distributed non-uniformly. Thus, a long liquid-filled tube was started rotating about its axis with a uniform angular velocity, and waves were generated before the fluid had reached a state of uniform rotation. Using the known velocity distribution for a tube of infinite length, comparisons have been made between the observed wave forms and the theoretical calculations of Benjamin (1967a). There is good agreement between the observed wave forms and the theoretical predictions.

Analytical Studies on the Flow Patterns of Liquid in a Cylindrical Mixing Vessel

Analytical studies were attempted to make clear the flow patterns of the liquid in the cylindrical mixing vessel without baffles, as the experimental results had already been obtained as shown in the previous reports.We could not well explain the details of the liquid flow patterns in the vessel by means of the so-called “Rankine's combined vortex” model (Refer to Fig. 1 and Eq.(1)). Therefore, we studied three important factors contributing to the momentum transfer in the agitated liquid; i.e., the liquid viscosity, the displacement of the liquid by the agitating impeller and the secondary circulation flow which is induced by the discharge flow from the tips of the impeller blades.In the range where Reynolds number was very small, the momentum transfer due to the viscosity effect was found to be predominant, so that the analytical results, obtained upon the assumption that the effects of the two factors other than the liquid viscosity are negligible, had a tendency to show good agreement with the experimental data on the tangential velocity distribution of the liquid in the vessel, as shown in Figs. 4 and 5.On the other hand, in the turbulent flow range where Reynolds number was very large, the secondary circulation flow had considerably important effects on the liquid flow pattern. Considering its contribution to the momentum transfer (Refer to Fig. 6), Eqs.(10) and (13) were analytically derived to express the tangential velocity distribution of the agitated liquid. The comparisons between the experimental data and the calculated results by these equations are shown in Fig. 8. They show good agreement.Furthermore, there were obtained data on the distributions of the turbulent kinematic viscosity and the static pressure in the vessel, as shown in Figs. 9 and 10, respectively.These results are considered to show the utility of the analysis.