Based on the prepared counterflow vortex tube model with four inlets, the effect of the length of the vortex tube channel on the generation of cold and hot air is investigated. In the simulation were used standard equations of gas dynamics, which include the equations of continuity, conservation of momentum, total energy, and the state of an ideal gas. To consider turbulent effects was chosen a -\varepsilon$ turbulence model. Computational experiments were carried out in the OpenFOAM software using the sonicFoam solver. The prepared grid allowed modeling vortex tubes with the main channel length varying from 20 to 70 cm. All calculations were carried out under the same boundary conditions with constant pressure at the inlets and atmospheric pressure at the hot and cold outlets. The constructed model adequately reproduces the two-vortex structure of the air flow in the vortex tube. To obtain and process the results were used OpenFOAM utilities and a script implementing the algorithm for averaging the values at the tube outlets written in Python. The results were obtained on the temperatures and mass flow rates of air in cold and hot outlets of the vortex tube depending on the length of the device. According to the analysis of the obtained data, it was shown that increasing the length of the channel of the vortex tube significantly increases the production of cold air with a certain increase in its temperature. An increase in the temperature of the produced hot air with an increase in the length of the vortex tube was also noted.
Objective: Study dependence between length of main channel of the vortex counterflow tube and generation of cold and hot air.
Methods: A series of computational experiments were prepared for the study. The simulation used the finite volume method, implemented in the OpenFOAM software. A counterflow vortex tube model with four inlets was prepared. A gas dynamics was described by a standard system of equations that includes the following equations: continuity, conservation of momentum and total energy, closed by the equation of state of an ideal gas. To consider for turbulent effects was used a k-e turbulence model. In preparing results for analysis, in order to reduce the influence of turbulent pulsations on the values obtained, the following actions were carried out to average the values. In the first stage, averaging of values over the cross section at the outlets of the vortex tube was performed. For this, the corresponding section was divided into irregular subregions by the surfaceCut utility and the average value of physical quantity for the total area was calculated. After that, the area averages over several successive time steps were averaged over a period of time. The spatial cross sections used for averaging are determined by the geometry of the computational domain. To implement this algorithm was written a script in the Python programming language.
Results: During the computational experiment, data were obtained characterizing the values of temperature and mass flow in the cross sections of hot and cold outlets of the vortex tube. Analyzing the data corresponding to the cross section of the cold outlet was found a tendency for a monotonic increase of temperature and mass flow, converging to some values with increasing tube length. At the same time, the temperature rise, measured by the difference between the values for the shortest and longest tubes, is only 0.2%, while the mass flow rate increases by 7%. In other words, at the considered lengths, with an increase in the length of the tube we see a significant increase in the production of cold air with a certain increase in its temperature.
At the same time, considering the values obtained in the hot section of the vortex tube, we see a completely different picture. The mass flow rate of air at this outlet drops significantly with increasing tube length. For the considered lengths, one can observe a threefold drop in mass flow rate. When this occurs, the temperature of the outgoing air increases.
Conclusions: Shown dependences of temperature and mass flow rates of hot and cold air for vortex tubes, whose geometrical parameters differ only in the length of the main part of the tube. Noted the presence of two pronounced patterns in the change of physical parameters with increasing tube length. The first is that there is a redistribution temperature of the outgoing air in favor of the hot component with increasing tube length. But, at the same time increase length of the tube is accompanied by an increase in hydrodynamic resistance. This leads to a simultaneous increase in the temperature of hot air and a sharp reduction in its mass flow. The second - at the cold outlet, an increase length of the vortex tube channel leads to a significant increase in the production of cold air, along with a slight increase in its temperature.