Simulation on stirling reverse osmosis desalination power system

In this article, a new power system based on the Stirling engine and hydraulic free piston engine is proposed to provide power for reverse osmosis (RO) desalination. First, the design of the Stirling free piston RO desalination power system was carried out, and the size parameters of the main structures such as the regenerator, heater, cooler, power piston, and valve distribution piston were obtained. A physical model was established to simulate the process of the Stirling engine driving the RO desalination power system based on finite element CFD. The flow field distribution cloud map and output power of the Stirling engine were analyzed. The results indicate that the gas motion of the Stirling engine is stable, and the entire power system can operate normally.


Introduction
Freshwater resources are extremely scarce worldwide, but they are essential [1].RO seawater desalination is one of the important methods for obtaining fresh water currently available [2].Its power input is mostly high-pressure pumps, which consume a large amount of electrical energy and have weak energy adaptability.
The Stirling engine uses gas as the working fluid, and the gas moves back and forth through external heating and expansion in the working chamber, thus it can also be called a hot gas engine [3].In research, people mostly use first-order Schmidt models with ideal factors and second-order isothermal and adiabatic models to analyze thermodynamic processes because these methods are simple to calculate and suitable for preliminary design [4].With the advancement of technology, people have begun to consider non-ideal factors to improve and study these models.Ding [5] et al. considered the heat transfer loss and pressure loss of heat exchangers in an adiabatic model.
The Stirling engine, as an externally heated piston-type power machine, has strong adaptability to heat sources [6].The free-piston engine developed on the basis of traditional engines eliminates rigid transmission mechanisms such as cranks and connecting rods, and uses non-rigid media as the receiver of mechanical energy for piston translation, maintaining the periodicity of motion [7].At present, the hydraulic free piston structure using hydraulic energy as the energy storage method has been applied in internal combustion engines, namely hydraulic free piston engines.Moujery and Hong [8] established an analysis model based on the energy-saving law, taking into account the main heat loss of the engine and reducing its result error.Although the calculation process was complex, the error of the results was reduced.Although these studies have reduced errors and improved efficiency, the changes in velocity and temperature fields caused by oscillating flow cannot be observed.With the development of CFD technology, analyzing multidimensional flow fields becomes easier.Xiao et al. [9] demonstrated a new parameter analysis method that combines ISAM multi-objective optimization and CFD, which can be redesigned.The heat exchanger in the Type I Stirling engine was studied to investigate the effect of size and death volume of the heat exchanger on engine performance.By redesigning the heat exchanger, the efficiency was improved by 1.6%.In [10], further 3D simulations were conducted on the Type A Stirling engine, and the fitting results showed a deviation of 12-18% from the experimental results.
In this paper, an RO desalination power system based on a Stirling engine and a hydraulic freepiston engine is proposed.The process of the Stirling engine driving the RO desalination power system is simulated using finite element CFD.In order to further improve energy utilization and reduce the energy cost of desalination, the internal variation of the flow field is explored.

The power system schematic diagram
The Stirling free piston reverse osmosis desalination power system mainly consists of three parts, first of which is β Type Free Living，the Stirling engine, followed by the hydraulic cylinder section of the hydraulic free piston, and finally the RO seawater desalination component.The specific structural schematic diagram of the power system is shown in Figure 1. 1. expansion chamber 2. heater 3. regenerator 4. cooler 5. compression chamber 6. power piston spring 7. pump chamber piston 8. piston connecting rod 9. drainage check valve 10.RO membrane component 11. pump chamber 12. compression chamber piston 13. compression accumulator 14. frequency control valve 15. pump compression chamber 16. suction check valve 17. oil supply accumulator 18. power piston 19.gas distribution piston spring 20.gas distribution piston

The working principle of the power system
Starting with the piston assembly on the far left, the pump compression chamber is filled with hydraulic fluid, and the pump chamber is filled with water.After the heater is preheated, it will push the piston assembly to move from left to right.The gas in the air chamber and the compressed energy accumulator will work, and the drainage process will be completed after moving to the right.Subsequently, under the action of compressing the accumulator and the gas inside the chamber, it begins to move in the opposite direction to absorb water.During the movement of the piston assembly, the gas distribution piston is pushed by helium gas.During a reciprocating motion of the piston assembly, energy storage and discharge are completed in the corresponding compression accumulator, and drainage and suction are also completed in the pump chamber.Under normal circumstances, the piston components continuously move back and forth, and the system operates normally.

Mathematical models
ρ -Fluid density, u i -velocity component Momentum Equation: p -static pressure, F i -volumetric force in the i-direction, ρu i 'u j '-Reynolds stress, and τ ij -stress tensor

Physical models
The free piston Stirling engine has numerous components and is complex internally.Therefore, in order to reduce simulation calculation time, it has been simplified, as shown in Figure 2, which is the simplified three-dimensional physical model of the free piston Stirling engine.

Initial and boundary conditions
The actual Stirling cycle is complex, and many factors affect the efficiency of the thermal cycle.Therefore, it needs to be simplified and assumed:  Neglecting clearance leakage between piston and cylinder;  No temperature difference between helium and solid in the regenerator;  Ignoring heat transfer between the model and the external sector;  Assuming the piston motion is sinusoidal.The movement of the power piston and valve piston is achieved through UDF: v p =-25ꞏ0.036ꞏπꞏcos(50ꞏπꞏt+π/2) (4) The model of the power system is given in Table 1 with the parameter and initial criteria settings.
Table 1.Model parameters and initial condition settings.

Results
Figure 3 shows the relationship between pressure and volume in a Stirling engine.Three closed curves represent the relationship between stress and volume in the left chamber, right chamber, and total chamber, respectively.The areas enclosed by each part represent the work done by each chamber.It can be known that the compression chamber does negative work and the expansion chamber does positive work, and the total work done by the entire chamber is equal to the difference in work done by the right chamber and the lift section.When the area enclosed by the expansion chamber is larger and the area enclosed by the compression chamber is smaller, the output power is greater, indicating the better performance of the Stirling engine.By calculating the work done by the Stirling engine within a cycle, the output power can be calculated to be 284.42J and 6.58 KW.Since the designed rated power is 6 KW, it meets the requirement of power exceeding the rated power in the initial design stage.As shown in Figure 4, the velocity distribution cloud map inside the Stirling engine shows that in case (a), low-temperature helium travels from the right ventricle to the left ventricle.Due to the smaller diameter of the regenerator, the gas flow rate in the regenerator increases.When it has already passed through the regenerator and entered the expansion chamber, the velocity decreases.In case (b), most of the gas enters the expansion chamber and reaches its lowest velocity.Then, it gradually flows towards the compression chamber, causing oscillations in the regenerator channel, resulting in a decrease in gas flow velocity in the regenerator and reaching its lowest velocity.In case (c), a large amount of high-temperature gas enters the right chamber.As the volume of the right chamber increases during this process, the gas velocity passing through the regenerator increases, leading to an increase in the outlet velocity of the right chamber and the formation of obvious eddies in some areas of the compression chamber.The generation of these eddies will inevitably consume some energy, so it is necessary to optimize the structure and try to avoid the generation of eddies to reduce energy consumption when designing an engine.In case (d), the gas in this process continues to flow towards the compression chamber.However, due to the small change in the volume of the compression chamber, the gas flow velocity in the regenerator decreases to the minimum again, and the outlet velocity of the compression chamber also decreases compared to the previous moment.The figure illustrates the stress force field profile within the entire output system at the beginning of the drainage period, for example, in Figure 5.The stress gradient in the pump chamber is obvious along the direction of piston movement, and the pressure near the piston is relatively high.In the beginning, the pressure in the energy storage compression chamber is greater than that in the energy storage chamber, indicating that gas is mainly stored in the energy storage and the right chamber when the booster pump starts working.The pump chamber pressure gradually decreases during the draining process.As the size of the pump chamber is reduced, the stress should have increased.However, in reality, due to the presence of acceleration and the same increase as the volume decreases, the stress in the pump chamber has been decreasing.When the drainage is completed, the pressure decreases to the minimum value, which is still greater than the osmotic pressure, and the entire process meets the requirements.Figure 6 shows the distribution of the pressure field in the output system at the end of the water absorption process.The stress values in the pump chamber are basically equal at the end of the suction process, reaching a maximum pressure value of 0.7 MPa during the suction process.This indicates that the pressure in the entire pump chamber tends to be balanced at the end of the suction stage, preparing for the next working cycle.

Conclusions
 A new power system is proposed to provide power for RO desalination, explain the working principle of the entire power system, and verify that the Stirling free piston RO desalination power system can operate normally. The pressure cloud diagram of water absorption and drainage can indicate that the pressure in the pump chamber tends to be balanced. Using the steady-state preheating value as the starting value for transient simulation, the velocity field distribution of the Stirling engine at different times and the stable gas changes in each chamber were obtained. The simulation results obtained can serve as theoretical support for future experiments.

Figure 1 .
Figure 1.The power system schematic diagram.

Figure 2 .
Figure 2. Physical model of the dynamical system.

Figure 4 .
Figure 4. Cloud map of velocity field distribution.