Numerical Simulation of Internal Flow Field in Turbo-Expander

As everyone pays more attention to energy consumption, it is very meaningful to use natural gas pressure energy for power generation and turbo-expander is an important part of power generation devices. In this paper, the turbo-expander model for pressure energy generation is meshed and numerically simulated based on fluent, and the pressure distribution and velocity distribution in the turbo-expander are obtained. The volute profile is Archimedes spiral, and the impeller is modeled by cfturbo. The main conclusions are as follows: when the number of grids is more than 2.2 million, the simulation results are less affected by the number of grids. The internal basin of the turbo-expander has obvious pressure gradient and velocity gradient. Due to the negative pressure at the elbow of the inlet pipe of the centrifugal effect, the existence of the blade leads to the change of the flow direction. Different watershed planes have different pressure and velocity distributions. The velocity and pressure of the watershed plane near the impeller outlet and the volute outlet are often smaller, but the flow vortex is more intense.


Introduction
As everyone pays more attention to energy consumption, more and more scholars pay more attention to the recovery of natural gas pressure energy. It is very meaningful to use natural gas pressure energy for power generation and turbo-expander is an important part of power generation devices. Turbo-expander is a machine that converts pressure energy into other forms of energy when high pressure gas expands, which is widely used in the acquisition of cooling capacity and pressure energy generation. As important components of turbo-expander, the design and flow field analysis of volute and impeller are very important to improve the performance of turbo-expander. Anna et al [1] analyzed the huge energy loss in the process of gas pipeline transportation. The energy loss in the process of decompression can be first converted into mechanical energy, and then converted into electrical energy through the generator. An oil-free twin-screw expander was designed for high-pressure gas pressure energy recovery device, and the rotor, bearing and other components were discussed. The feasibility and convenience of screw expander in the recovery and utilization of natural gas pressure energy were proved by experiments. Li et al [2] proposed a new system for the recovery of natural gas pressure energy, and combined the byproduct energy and low-grade heat of the pressure regulating station. The integrated system consists of two subsystems. The natural gas expansion subsystem can recover the pressure energy of natural gas. The Rankine cycle subsystem can recover the cold energy and low-grade heat of natural gas, so as to maximize the recovery of natural gas pressure energy. Deymi et al [3] used turbine expansion system to replace the surge station to use high pressure energy for the production of electricity and freshwater and  [4] studied the feasibility of using turbo-expander to replace expansion valve in natural gas pressure regulating station, so as to effectively utilize the energy lost by gas pipeline pressure regulation and finally achieve good results. Li Qiusheng [5] studied the influence of the relative position of diversion shell and impeller on the performance of submersible pump. Guo Xiang [6] takes IS80-65-160 centrifugal pump as the research object, analyzes the change of internal flow and external characteristics of centrifugal pump, and puts forward the partition method of steady performance curve.
In natural gas pressure energy power generation projects, turbo expanders are often used as core components. The turbo-expander model studied in this paper is mainly used for pressure energy generation. The analysis of internal flow field is helpful to understand the shortcomings of volute and impeller structure, which is convenient for future improvement and saves experimental cost.

Geometric model and numerical model
In this paper, the turbo-expander is mainly used for pressure energy power generation. The high-pressure gas is inflowed from the volute inlet to promote the impeller rotation. The impeller crankshaft drives the magnetic coupling and generator to complete the power generation. The modeling of the volute used is mainly based on the constant velocity normal line proposed by Stepanoff [7] . Assuming that the fluid inside the volute is uniform and the velocity is constant, the Archimedes spiral can be obtained. The profile equation adopted is shown below.
When the rotor speed is small, the power function expanded by the above equation is only the first two, and the general expression of Archimedes spiral can be obtained. Then, the following equation can be obtained by appropriate deformation. The values of m, A and B affect the clearance between volute and impeller. Fig.1 is the Archimedes spiral line corresponding to different m values, and the inner circle is the outer diameter contour of the impeller. From inside to outside, the corresponding m values are 0.05, 0.1, 0.15 and 0.2 respectively.

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(2) Fig. 1 Archimedes spiral Based on the Archimedes spiral equation, the volute is modeled by UG, as shown in Fig.2, where A = 1.02, R 2 = 110mm, m = 0.06, B = 0. Fig.3 is the 220mm impeller generated by cfturbo, and the blade height is 10mm. The mass conservation equation is as follows: The momentum conservation equation is as follows: The energy conservation equation is as follows: Turbulence control equation uses RNG k~ ε two-equation model, where k equation is as follows: ε equation is as follows: * In the formula, k is turbulent kinetic energy, is turbulent kinetic energy generation rate, is turbulent dissipation rate, is equivalent viscosity coefficient, and ， * ， 、 、 、 are all empirical values. In order to minimize the influence of grid number on simulation results, grid independence verification is needed to reduce the error factor of grid number on simulation results. Ensure inlet flow 0.5kg/s, outlet pressure 0.4MPa and rotor speed 600rpm unchanged. The ratio of inlet pressure to outlet pressure is monitored when the number of turbine model grids is 52w, 108w, 160w, 226w and 280w respectively. The turbulence model used in the simulation is RNG k-ε model, flow inlet, pressure outlet, and non-slip boundary conditions. As shown in Fig.4, when the grid mass is above 220 w, the turbine expansion ratio is less affected by the number of grids. Therefore, in order to ensure the accuracy of the simulation calculation and the less use of computational resources, the following simulation analysis shows that the number of grids is about 2.2 million.

Methods and Material
In the simulation process, the steady-state mrf model is used. In order to facilitate the later comparison with the experiment and consider the safety, air is selected instead of natural gas for simulation. The turbulence model used in the numerical simulation is the RNG ε model, the mass flow inlet boundary, the pressure outlet boundary, and the expandable wall function. In this paper, the turbo-expander is designed and modeled based on Archimedes equation, which is used for pressure energy generation. When the high pressure gas flows from the inlet, the volute shrinks and drives the impeller to rotate, and the crankshaft drives the magnetic coupling and generator to generate electricity successfully. Because the torque of the device is too large, the rotor speed is only about 600rpm during the experiment. It is necessary to reasonably analyze the change of the internal flow field of the turbo-expander to improve the experimental efficiency. Fig.7 and Fig.8 are the pressure distribution and velocity vector distribution when inlet flow is 0.5kg/s and outlet pressure is 0.4Mpa. Turbo-expander impeller speed is 600rpm, inlet pressure is 0.508Mpa, expansion ratio is 1.27. When the airflow passes through the inlet, due to the sudden change of airflow velocity direction, the elbow has a strong centrifugal force, and the pressure drops to the negative pressure. At the same time, it is accompanied by a large velocity distribution, and then tends to be stable. When the airflow drives the impeller to rotate in a steady state, there will be vortexes in the basin between the blades, and the vortex intensity near the inlet section is stronger and the pressure is greater. With the reduction of cross section, the pressure tends to decrease gradually. Fig.9 is the internal