2.2.1 General explanation and understanding of the TSE
An agreement on the exact principles/mechanism of the temperature separating process has not been universally reached, but several explanations have been put forward by researchers[4, 8, 51-60]. Hilsch[4] presumed that the centrifugal force and the internal friction produce a low pressure region at the axis of the VT, and the expansion of the fluid near the wall to the central of the tube leads to a temperature drop. At the same time, the inward expanding fluid transfers its kinetic energy to the peripheral fluid by some kind of internal friction, thus increasing its temperature.
Kassner and Knoernschild[8] analysed the friction laws and the energy transfer in a circular flow, and suggested that the temperature separation is caused by a conversion from an irrotational flow to a rotational flow in the VT. When the fluid enters the VT chamber, it rotates as an irrotational flow. For a viscous fluid, the shear force works on two annular layers, thus reducing the velocity difference between them and converting the flow in to rotational flow. This process results in a kinetic energy transfer from the inner rotating layers to outer layers by friction. At the same time, the
pressure difference between the peripheral and the central layers leads to a temperature drop towards the centre. In addition, the pressure differential between the hot end and the cold end along the axis leads to an expansion of the fluid and a drop in fluid temperature towards the cold orifice along the axial direction.
Deissler and Perlmutter[61] derived the energy balance in the VT and believed that the inner fluid does shear work on the outer fluid when it spirals inwards, and this work produces most of the energy/temperature separation. This shear work consists of three energy terms (turbulent dissipation, kinetic energy and potential/pressure energy), and the turbulent dissipation produces most of the heating for the outer fluid, while the cooling is generated mainly by the negative kinetic and potential/pressure energy terms[61].
Kurosaka[62] put forward an analytical explanation based on acoustic theories, stating that the streaming coming from the vortex whistle (a pure-tone noise in swirling flow) forces the Rankine vortex (an initial swirl in the VT) to become a forced vortex, and this transformation, to a substantial degree, leads to the temperature separation, and he also experimentally verified it by examining the influence of the intensity of the vortex whistle at a tuned frequency on the TSE[62].
Polihronov and Straatman[63]studied the thermodynamics of the flow rotation in a rotating reference frame (considering the Coriolis force and centrifugal force) instead of an inertial frame of reference. They concluded the cooling effect is a result of an adiabatic expansion process, during which the fluid overcomes the centrifugal force and does work on its surroundings by keeping the frame rotating when it spirals towards the centre.
Xue et al[64] used an experimental visualization method to investigate the TSE in VT. A low velocity water flow is supplied to an acrylic VT which is immersed in a water tank. Air bubbles, small plastic particles or hydrogen bubbles are used to visualize the flow streamlines and calculate the water velocities. They observed that the expanded water from the nozzle flows through the vortex chamber out of the cold end without reaching the hot end, and the rebounced fluid from the hot throttle turns back at several axial locations (setting up multi-circulation) to the periphery of the VT and moves towards the hot exit. Then, they concluded that the cooling effect is the result of the expansion from the nozzle, and the heating effect is mainly due to viscous friction in
the multi-circulation.
Lewins and Bejan[65] used a VT heat exchanger theory (in which the fluid is assumed to have a constant specific heat capacity) to understand the flow process and to correlate the TSE with the VT length, fluid specific heat, thermal conductivity and the mass flow rate. As shown in Figure 2.3, the VT is regarded as a heat exchanger, in which the hot and the cold stream flow in the opposite directions, and the Number of Transfer Units (NTU) method[66] is used to analyse the heat transfer rate between them. Their approach is applied by Cao[28] to show the relation between the TSE with the VT length, the fluid thermal diffusivity and the volume flow rate. Cao validated his work by comparing his results with the experimental data from Hilsch[4] (Figure 2.4). The discrepancies arose due to the fact that the conditions used in the experiments were slightly different to that in the calculation; a constant pressure gas was fed into the VT in experiment, and thus the inlet volume flow rate would vary slightly at different µc. However, in the calculation, a fixed inlet volume flow rate was employed.
Figure 2.3 Schematic diagram of the VT counter flow heat exchanger[28]
Figure 2.4 Comparison of the experimental[4] and calculated results[28]
Ahlborn and Gordon[54] attempted to use the concept of a classic refrigeration cycle to understand the energy transfer process in the VT. As shown in Figure 2.5, the flow
Inlet, Tin, ṁin Hot end Th, (1-µc) ṁin Th Cold end Tc, µ∙ṁin Q Layer
▪ Experiment results, Hilsch Calculated results, Cao
C ooli ng e ff ec t (°C ) 0 10 20 30 40 0 0.2 0.4 0.6 0.8 1 Cold mass flow ratio µc
undergoes through four typical processes of a refrigeration cycle: 1) the condensing process 2-3 in which the secondary flow is cooled by the expanded fluid from the nozzle (the authors believe that the fluid at the nozzle outlet has the lowest temperature within the VT); 2) the cooled fluid then undergoes an expansion process 3-4 in which the pressure drops from the peripheral part (high pressure region) to the central part (low pressure region) of the VT; 3) the evaporating process 4-1 in which the expanded fluid absorb heat along the axis of the VT moving toward the cold end; 4) the compression process 1-2, the heated fluid moves back from the inner part to the peripheral high pressure regions.
Figure 2.5 Schematic of the classic refrigeration cycle in the VT[54]
2.2.2 Remarks
Various theories have been suggested by researchers attempting to explain or to gain a better understanding the temperature separation mechanism, and among them, transfer of the kinetic energy caused by fluid friction or shear stress is probably the most widely adopted one. When the fluid enters the VT chamber, it experiences a change from a free vortex to a forced vortex flow which can be regarded respectively as a change from an irrotational flow to a rotational flow. For viscous fluid, the shear forces in the irrotational flow slow down the rotating speed and generate viscous friction.
Specific heat capacity has been taken as constant by researcher when applying the heat exchanger theory to correlate the TSE with the VT length and operating conditions. However, for many existing refrigerants, the specific heat capacity should not be taken as a constant as it varies noticeably under different conditions, and the author is not convinced that the current VT heat exchanger theory is accurate enough to be applicable to common refrigerants.
Secondary flow Cold end Heat rejection Energy absorption Expansion 4 3 2 1 Nozzle From primary flow High pressure Low pressure