Free Swirl Research Articles

Cyclic Matroids

For integers and exceeding one, a matroid on elements is nearly -cyclic if there is a cyclic ordering of its ground set such that every consecutive elements of are contained in an -element circuit and every consecutive elements of are contained in a -element cocircuit. In the case , nearly -cyclic matroids have been studied previously. In this paper, we show that if is nearly -cyclic and is sufficiently large, then these -element circuits and -element cocircuits are consecutive in in a prescribed way, that is, is “ -cyclic.” Furthermore, we show that, given and where , every -cyclic matroid on elements is a weak-map image of the th truncation of a certain -cyclic matroid. If , this certain matroid is the rank- whirl, and if , this certain matroid is the rank- free swirl.

Evaluation of an accurate and consistent mathematical model of an elbow flowmeter derived from the Navier–Stokes equation

Models derived from the free swirl theory, forced swirl mathematical models, and regression models provide inaccurate predictions of the behavior of elbow flowmeters. To generate an accurate model, we employ the Navier–Stokes equation considering an orthogonal coordinate system according to a curved surface. Thereby, we derive a mathematical model to measure the parameters associated with elbow flowmeters. The effects of physical parameters such as geometric parameters, ratio of bend to diameter, and Reynolds number are investigated. We obtained a relative error below 0.5% upon comparison of the theoretical model calculations and experimental results. This indicates that the proposed model is accurate and useful for future research and industrial production design of elbow flowmeters.

Rayleigh–Taylor Instability of Swirling Annular Layer With Mass Transfer

The interfacial instability of Rayleigh–Taylor type at the cylindrical boundary involving the liquid phase and vapor phase of a fluid has been considered when the vapor is warmer than the liquid. We use viscous potential flow theory to include the viscosity at the interface. To examine the stability of the arrangement, the normal-mode analysis is performed together with the effect of heat as well as mass transfer and free swirl. The physical system consists of an annular fluid layer restricted in a cylinder with vapor phase in the core. This work investigates the effect of a variety of variables on the instability of the interface. It is found that when the heat transfer constant increases, the range of stability increases. Also, the range of stability increases faster in the presence of swirling.

Effect of free swirl flow on the rate of mass and heat transfer at the bottom of a vertical cylindrical container and possible applications

Rates of mass transfer at the base of a vertical cylindrical container were determined under decaying swirl flow by the electrochemical technique. Variables studied were swirl flow solution velocity, diameter of the tangential inlet nozzle and physical properties of the solution. The data were correlated by a dimensionless mass transfer equation. The equation can be used to predict the rate of heat loss from the bottom of swirl flow equipment as well as the rate of diffusion controlled corrosion of the bottom. The importance of the derived equation in the design and scale up of a cylindrical batch recirculating catalytic or electrochemical reactor with a catalyst layer or electrode at the bottom and a cooling jacket around the vertical wall suitable for conducting exothermic liquid – solid diffusion controlled reactions which need rapid temperature control to avoid the loss of heat sensitive catalysts or heat sensitive products was pointed out. Comparison of the present results with the results obtained using perpendicular inlet nozzle which generates parallel flow at the bottom and axial flow along the cylindrical container revealed the fact that although swirl flow produces higher rates of heat and mass transfer at the cylindrical wall than axial flow and the reverse is true at the container base. Relevance of the present study to the design and operation of membrane processes and heat recovery from hot pools of liquid metals and low melting alloys in the production stage was highlighted.

Semi-preserving development of a slightly heated free swirling jet

The paper formulates the concept of a semi-preserving developing of a free nonisothermal swirling jet. On the basis of experimental data it may be estimated that the semi-preserving conditions are established at the distance x − x0 ≈ (15−20) D. Also, it has been pointed out that self-preservation, which requires the turbulence structure to be similar during decay, may be considered as an asymptotic state of the semi-preserving development achieved in practice at a distance where $\overline{u_r u_{\phi}/ \overline(u_x u_r) \ll 1\cdot 0$.

Heat Transfer in Free Swirling Flow in a Pipe

The local heat transfer coefficient, for air flowing through a pipe with a swirling motion, was measured at various stations downstream of the swirling air inlet. The swirling motion of the air was produced by a single tangential slot, initially at 90 deg to the pipe axis, through which the air was introduced. The dimensions of the slot and the angle of tangency were varied and the resultant flow field inside the pipe was measured and expressed in the form of local “swirl numbers”. The augmentation of heat transfer was found to be a function of the swirl number and a correlation for this function is presented. At some locations, the augmentation can be as much as eight times the value for fully developed nonswirling turbulent flow.