Simulation Analysis of Vortex Tube Parameters for Desalination Device Using Ship Exhaust Heat

The waste heat energy of diesel exhaust of current small and medium-sized ships is a big waste, while the distillation method in marine desalination is energy-intensive and its equipment is large, as well as the reverse osmosis method is seriously polluting. In order to solve the above problems, a waste heat desalination device for small and medium-sized ships is designed based on the cold-heat separation effect of vortex tube. In this paper, based on the study of the vortex tube working principle, the parameters of the vortex tube are designed and calculated, and the optimum inlet temperature at a certain pressure is calculated to further determine the design parameters of the whole device. According to the basic laws of thermodynamics, a mathematical model is established to describe the changes in the state of diesel exhaust.


Introduction
According to Fulton et al [1~2], the principle of vortex tube effect can be understood: the vortex tube converts the kinetic energy in the high-pressure airflow into thermal energy of the airflow, and separates the airflow from hot and cold. High-pressure airflow in the vortex chamber: Airflow expansion in the inner layer works, losing kinetic energy and lowering the temperature. The outer airflow acquires kinetic energy and converts it into thermal energy during friction with the hot end tube. Eventually the vortex tube shows a temperature difference in the radial direction. The operating principle of the vortex tube is shown in Figure 1.

Model assumptions
In order to simplify the model and make the problem computationally convenient, without changing its underlying laws and principles, the following assumptions are made in this paper.
(1) Adequate mixing of exhaust and compressed gases.
(2) The gas is ideal and the specific heat Cp is constant.
(3) Ignoring the heat conduction through the wall of the pipe and considering the wall to be insulated from the outside.
(4) Exhaust gases and gas mixtures are incompressible fluids.

Mathematical model of mixer design
The following fixed parameters are set for model solving.

Model analysis.
The mixing module is designed as a venturi mixer, and the role of the venturi mixer is to make the exhaust gas coming out of the evaporator and the compressed gas mix efficiently. The use of venturi effect can improve the efficiency of rarefaction, help reduce the exhaust back pressure of diesel engines, thereby reducing the negative impact of the device on the exhaust.

Figure 2. Mixer
According to the requirements of the vortex tube, the optimum pressure of the mixer's discharge air is about 0.6 MPa and the optimum temperature is 40°C. Control of the gas state after mixing the compressed air with the exhaust gas is achieved by designing the compressed air flow rate.
The exhaust gas leaving the evaporator has a pressure of 0.25 MPa and a temperature of 353 K. According to the equation of state of the gas, the specific volume v1: (1) The compressed gas pressure is 0.8 MPa and the temperature is 293 K. According to the equation of state of the gas, the specific volume v2: The mixture is designed for a pressure of 0.6 MPa and a temperature of 313 K. According to the equation of state of the gas, the specific volume v3: When mixing, the exhaust gas exothermic Q1, compressed gas heat absorption Q2, the two processes are for the multi-variable process, and Q1 + Q2 = 0. Exhaust heat.
Heat absorbed by compressed gas.
Knowing that mass flow rate of the tail gas is 1350 kg/h, we can obtain Compressed gas flow. The flow rate of the mixer outlet is. (8)

2.3.2.
Modelling. Summarizing the above, the following mathematical model can be obtained to describe the mixing process of exhaust gas and compressed gas.

Analysis of results
The suitable range of inlet temperature of vortex tube is shown in Fig.6.   Figure 6. Result figure According to the analysis, as the inlet temperature of the vortex tube (i.e., outlet temperature of the mixer) increases, the cooling capacity per unit of power consumption of the vortex tube gradually increases, but the total cooling capacity gradually decreases. Based on the calculations, we selected 315 K as the optimum inlet temperature for the vortex tube and used this temperature to design the parameters for th e other devices in the system.

Research methodology
3.1.1. Simulation Thoughts. Simulate the cold and hot separation phenomenon of vortex tube under the condition of inlet pressure and temperature, and the lowest and highest total temperature that can be reached at the cold and hot ends respectively, and compare them with the measured data to verify their rationality, and then extend them to the seawater preheating calculation and water vapor condensation calculation under actual conditions to obtain reasonable results.