A study of flow characteristics in a low-pressure ejector installation

Production processes sometimes are accompanied by the release of hazardous substances, the composition and volume of which is determined by the production technology. When designing ventilation systems for paint departments, special attention is paid to safety concerns, since all paint coatings are corrosive and flammable substances. Besides, solvent vapors are explosive. For local ventilation of painting chambers, it is rational to use safe exhaust systems with an ejector, which works sturdily, regardless of the release of flammable and explosive impurities. The ejector is simple in design and can operate in a wide range of changes in the parameters of the state of airflow. The model of the ejection unit is synthesized using the universal modeling package ChemCad, which contains a highly developed database of airflow parameters, which allows for solving various applied problems. Numerical modeling was carried out using the software package FLUENT. In work, a calculation was carried out and a low-pressure ejector was designed for a typical painting booth. The calculation results are presented in the form of graphs and tables of pressures, velocities, flow rates in characteristic sections, pressure losses in the sections of the ejector installation.The ejection coefficient was also calculated.


Introduction
There are known studies in which to stabilize the operation of the exhaust ventilation system of buildings for various purposes it is proposed to design modular ejection systems [1][2][3][4][5][6].
When designing industrial ventilation, supply and exhaust systems are used based on the operation of fans. Such solutions are quite sufficient in assembly, packaging, and filling shops of industries that are not associated with the release of pollutants, and where the main task of ventilation is the comfortable stay of the working personnel in the room. If the production process is associated with the release of a large amount of heat, moisture, dust, flammable and explosive substances, then when designing ventilation systems, it is *Corresponding author:evgeniyav09@gmail.com necessary to take into account the peculiarities of the production technology [7][8][9] and the danger of using fans. In cases where the exhaust air contains explosive or destructive impurities acting on the fan, for example, in painting booths or in chamber dryers, when it is required to create insignificant dynamic pressures for the circulation of airflow, it is rational to use safe exhaust systems with an ejector. At the same time, ejection systems have low efficiency and therefore are used when other solutions are not possible. In the studies [10][11], a description and study of exhaust ventilation systems is given, where ejector installations have been used that work reliably, regardless of the volume of released flammable, explosive, and abrasive impurities.
Methods for calculating ejectors are well developed, but they do not allow for designing optimal solutions with minimal energy consumption. Problems of this kind are effectively solved using various modeling applications. In particular, the use of the ChemCad universal modeling program (UMP) allows for the calculating of the thermophysical properties of air flows with various contaminants. In [12][13] examples of solving applied problems using the UMP ChemCad are considered.
Computational fluid dynamics methods using the ANSYS (FLUENT) software package are also widely used to solve such applied problems [14][15][16][17][18]. Numerical methods make it possible to quickly and visually simulate the flow of air flows in characteristic sections of an ejector installation and design more efficient industrial ventilation systems [19][20][21][22].

Materials and methods
In this work, the object of research is a low-pressure ejector unit (Fig. 1). The ejection effect consists in the fact that the ejected stream (active), of high pressure, moves at a high speed, carries along with it the ejected stream (passive) of low pressure. Clean air, blown by a high-pressure fan 5 located outside the ventilated room, flows out of nozzle 1 into the mixing chamber 3, into which air from the receiving chamber 2 of the manned room is sucked in due to the pressure difference. Further, the mixture of active and passive streams flows through the diffuser 4, and the air duct and is discharged into the atmosphere. For painting a variety of products -from small parts to large-sized products, paint booths are designed. When simulating a low-pressure ejector, a painting booth with a size of 5.4 * 3.4 * 2.5 m 3 was considered. The air is supplied from the top, evenly over the entire area of the false ceiling. Air suction is carried out in the center of the chamber, through the floor, which is equipped with floor grilles throughout the entire area. The inlet and outlet pass through a cleaning system. The minimum temperature is 20-25 °С (in the drying mode up to 50°С). Air movement in the painting area is 20-25 cm/s. The air pressure in the chamber is slightly higher than the standard 100 kPa (atmospheric pressure or outside pressure).
For the calculation, the amount of air supply was taken as 6600 m 3 /h. To ensure the back pressure, it is required to remove 6000 m 3 /h of air with the resistance of the suction network ∆р2 = 230 Pa; the resistance of the pressure head of the ejector ∆р3 = 80 Pa; stirring factor w = 1.
When designing equipment based on the principles of ejection, it is necessary to determine the optimal shape and geometric dimensions of the ejector, as well as the characteristics of the fan, taking into account that the power consumed by its electric drive determines a significant share of the costs of the painting process.
The main design parameter of the ejector is the ejection coefficient, which is understood as the ratio of the flow rate of the active (blown by the fan) stream to the flow of the passive stream (sucked in from the painting chamber). The higher the ejection coefficient, the lower the flow rate of the supplied active stream, and, thus, the less electricity is consumed by the fan. The ejection coefficient itself is a function that depends on the geometric characteristics of the ejector, therefore, finding the optimal geometry of the ejector will reduce both operating and capital costs for installing the ventilation system.
The main purpose of calculating the ejector installation in this work is to obtain the values of pressures and velocities at any point of the model, flow rates at the boundaries, and also to calculate the ejection coefficient: Where GD -flow rate of the ejected (dirty) air; GC -flow of ejecting (clean) air, kg/s.

Low-pressure ejector simulation
In the simulation, the ejector is divided into three parts: a nozzle, a mixing chamber, and a diffuser (Fig. 1).
The pressure and temperature at the nozzle exit are determined by the equations (2) and (3): The main equation used in the simulation of the ejector: The nozzle outlet pressure is calculated as follows: Nozzle outlet temperatures: The speed of sound: Actual flow rate: The Mach number before mixing the active and ejected streams in the nozzle is expressed by the formula: In general, to obtain the critical Mach number in any section i, the following equation can be used: If we take into account equation (10), then the critical Mach number at the nozzle exit is calculated by the formula: By definition, the ratio for the ejection coefficient is calculated by the formula: The critical Mach number of the moving stream at the outlet from the nozzle before mixing with the ejected stream: When simulating the mixing process, one-dimensional continuity equations in combination with the equations of motion and energy can be combined into the following relations to calculate the critical Mach number and Mach number in the diffuser: To calculate the mixed active and ejected flow before the exhaust, the following equation is used: Mach number at the entrance and exit of the diffuser: It should be noted that the following equations are used to calculate the temperature and pressure at the diffuser inlet: (20) The speed of sound and the actual speed are determined by the following relationships: (24) The temperature and pressure at the outlet of the diffuser are calculated as follows: In order to calculate the outlet pressure from the ejector, we can use the following equations: (28) Thus, the output stream from the ejector is: (29) Equations (2) -(29) allow to calculate the ejector for a given performance. Problems of this kind are effectively solved using various modulating application programs. In particular, the use of the ChemCad universal modeling program (UMP) makes it possible to calculate the thermophysical properties of air streams with volatile components of various paints and varnishes. In [12][13] examples of solving applied problems using the UMP ChemCad are considered.

A numerical study of the flow in a low-pressure ejector system
A numerical study of the flow in a low-pressure ejector system was carried out using the licensed software package ANSYS® Academic Research Mechanical and CFD, Release 18.2. The system of differential equations of turbulent motion is closed using the «standard» model ( -kinetic energy of turbulent pulsations, -specific dissipation of turbulent energy). For modeling the boundary layer near impermeable surfaces, the Standard Wall Function is adopted.
Limit conditions: -at the inlet of the ejected (dirty) air, the flow rate GD was set, kg / s; -at the inlet of the ejecting (clean) air, the excess pressure Pn, created by the pump was set, Pa; -excess pressure Pout, Pa was set at the outlet from the ejector unit.   It is proposed to install a fan of the VTs5-35-8V1.01 brand, an AIM132M4 electric motor, and power consumption of 11 kW to the ejector. The rotational speed is 1500 rpm, the developed total pressure is 2900 -2060 Pa.   Fig. 3. The purpose of the calculation was to determine the pressure, velocities, flow rates in characteristic sections, pressure losses in the sections of the ejector installation, and also to calculate the ejection coefficient. The calculation results are presented in Tables 2-4 (Table 2) according to the designer's manual. In the performed numerical experiments, fans of models V-Ts14-46-4-04 and V-Ts4-70-4-01 can be used.