Method for analyzing influence of cavitation and temperature on performance of nuclear primary pump wave seal

Abstract

The application provides an analysis method for the influence of cavitation and temperature on the sealing performance of a nuclear main pump. The method comprises selection of a cavitation model, judgment of fluid flow state, setting of boundary conditions and analysis of the influence on sealing performance. Three different calculation models are selected, and sealing performance parameters under changes in film thickness and rotational speed are calculated. Comparison of the calculation results of the three models shows that: (1) when the film thickness is small, the cavitation effect has a greater influence on the opening force, and the opening force is obviously promoted, and the viscosity-temperature effect reduces the opening force. When the film thickness is large, the cavitation effect is weakened or even disappears, and the influence of the viscosity-temperature effect on the opening force and leakage exceeds the cavitation effect. (2) When the rotational speed is low, the cavitation area is small, and the change in the opening force is not obvious, but the viscosity-temperature effect still has a very obvious promoting effect on the leakage. When the rotational speed is high, the influence of the cavitation effect on the opening force is greater than that of the viscosity-temperature effect, and the cavitation effect promotes the increase of the opening force, and the influence of the viscosity-temperature effect on the opening force is small.

Description

Technical Field

[0001] This invention belongs to the technical field of analysis of the influence of cavitation and temperature on the cavitation sealing performance of nuclear main pumps, and in particular relates to a method for analyzing the influence of cavitation and temperature on the cavitation sealing performance of nuclear main pumps. Background Technology

[0002] A liquid film exists in the end-face gap of non-contact mechanical seals when the opening force is large, a theory that has been experimentally confirmed. However, research on the load-bearing and lubrication mechanisms of this liquid film is still insufficient. Mayer studied a sealing model with deep grooves on the surface, which can generate large hydrodynamic pressure and can be applied in high-pressure, high-speed fields. Key et al. proposed a mechanical seal with rectangular grooves on the surface and found that under pressure, the rectangular grooves undergo end-face waviness deformation, which generates a dynamic pressure that, together with the static pressure, provides load support. Mylonas et al. designed a multi-cone convergent gap model based on a single-cone convergent hydrostatic mechanical seal, providing an important basis for the design of mechanical seals for nuclear main pumps. Djamai et al. developed a finite element model to analyze the influence of operating parameters and geometric parameters on sealing performance. Their research found that under high-pressure conditions, the hydrostatic effect can provide a sufficiently large sealing opening force. Young and Lebeck designed and studied a waviness seal structure with radial taper that combines hydrostatic and dynamic pressure effects. The stationary ring's tapered convergent surface provides the hydrostatic opening force, while the waviness surface provides the dynamic opening force, making it suitable for high-pressure, high-speed environments. Gagan et al. presented a method for predicting the operation of axisymmetric seals, and the predicted results showed good agreement with experimental results.

[0003] Research on mechanical seals in China started relatively late. Gu Yongquan, based on Mayer's hydrodynamic sealing theory, was among the first to conduct research on the structure, theory, and materials of mechanical seals. Han Jie et al. established radial taper and circumferential waviness mechanical seal models and studied the influence of waviness and taper on sealing characteristics under steady-state conditions. Luo Xian et al. studied different groove shapes, waviness, and taper on the surface of mechanical seals and analyzed the impact of changes in groove shape, taper, and waviness on sealing performance. Sun Yu conducted flow field analysis on the upstream pump spiral groove seal structure using Fluent software, calculated the changes in the local flow field under the groove root sharp corner and rounded corner structures, observed the particle deposition and end face wear of the pump groove, and verified the feasibility of self-cleaning of spiral groove seal particles. Zhang Qiangqiang studied the influence of manufacturing process errors of the sealing ring on sealing performance and proposed a new end face sealing structure based on the advantages of laser processing in free-form surface processing. Wang Xiaoxue et al. studied the working mechanism of the wave-face hydrodynamic seal and found that this type of seal usually has a large static pressure. The opening force is mainly provided by the static pressure effect, while the hydrodynamic pressure plays a role when the pressure is low.

[0004] Regarding cavitation in mechanical seals, foreign scholars have conducted extensive research on cavitation mechanisms, proposing cavitation boundary conditions such as Sommerfeld boundary, semi-Sommerfeld boundary, Reynolds boundary, and JFO boundary. Christopherson proposed a method of setting the negative pressure to zero, assigning pressures less than the cavitation pressure as the cavitation pressure; his calculation results show good agreement with experiments. Jacobsson and Floberg proposed a new boundary condition based on sliding bearing experiments. This condition, based on mass conservation, considers the rupture and regeneration of the liquid film. The sliding bearing pressure distribution calculated using this boundary condition shows excellent agreement with experiments, and Olsson provided a mathematical proof of this boundary condition, which is named the JFO boundary condition. Qiu et al. used the JFO boundary condition to predict the cavitation situation in circular groove mechanical seals; the cavitation region and sealing parameters basically agree with the experimental results. Brunetière et al. established a modified Reynolds equation that can solve gas, liquid, and cavitation flows based on the gas-liquid two-phase flow theory. Comparing the prediction results with those using JFO boundary conditions and experimental results, the results show that the prediction of liquid film cavitation can be achieved better by adjusting the mass fraction of gas in the fluid.

[0005] In the field of mechanical seal cavitation research, there is a considerable amount of domestic research focusing on spiral groove seals. Li Zhentao studied the cavitation boundaries of the inner and middle grooves in upstream and downstream pumps for end-face spiral groove seals, as well as the variation of cavitation boundaries with structural and operating parameters. He then built a spiral groove end-face seal test bench to investigate the cavitation conditions and sealing performance under different operating parameters for the inner and outer grooves. The results showed that the simulation and experimental results were in good agreement in both trend and numerical values. Ma Xuezhong et al., based on the Reynolds equation and the cavitation equation, used JFO cavitation theory to study spiral groove seals, analyzing the influence and mechanism of cavitation effect under dynamic lubrication. They proposed a cavitation suction end-face seal using the cavitation effect as a suction concept, and simulation calculations showed that it has good reverse suction capability and load-bearing performance. Liu Ying et al. solved the Reynolds equation based on JFO cavitation boundary conditions and analyzed the influence of structural and operating parameters on the waviness sealing performance. Han Ting took spiral groove mechanical seals as the research object, analyzed the mechanism of surface roughness on cavitation characteristics and sealing performance, and studied the influence of geometric parameters on sealing performance when the spiral groove end face is rough.

[0006] However, in current technologies, the liquid film in the waviness-sealed gap is only micrometer-thick. Driven by the rotation of the rotating ring, the fluid undergoes circumferential motion, generating a large amount of viscous shear frictional heat. Simultaneously, due to the waviness, the fluid in one cycle forms a high-pressure zone and a low-pressure zone. When the pressure in the low-pressure zone is lower than the saturated vapor pressure, cavitation occurs. Therefore, this invention will analyze the influence of cavitation and viscosity-temperature effects on sealing performance under different film thicknesses and rotational speeds, taking into account the occurrence of cavitation. Summary of the Invention

[0007] The purpose of this invention is to solve the problems in the prior art and to propose an analysis method for the influence of cavitation and temperature on the waviness sealing performance of nuclear main pumps.

[0008] This invention is achieved through the following technical solution: This invention proposes a method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump, specifically including:

[0009] Cavitation model selection: The ZGB cavitation model is selected. This model ignores the effects of surface tension, non-condensable gas and turbulent kinetic energy. In this model, the pressure inside the cavitation bubble in the cavitation region is equal to the local saturated vapor pressure, the bubble diameter is a fixed value, and the mass transport rate is described by the volume fraction of the vaporization core.

[0010] Fluid flow state determination: The change in the flow factor τ is used to determine whether the fluid is in a laminar or turbulent state;

[0011] Boundary condition settings: Set boundary conditions according to the boundary type;

[0012] Sealing performance impact analysis: The effects of cavitation and temperature on sealing performance were analyzed under different film thicknesses and rotational speeds. The sealing performance calculation results of three models were compared during the analysis. Specifically, the three models are: HD1 model uses a laminar flow model, does not consider cavitation and viscosity-temperature effects, and solves the NS equation and continuity equation, i.e., a hydrodynamic lubrication model; HD2 model uses a laminar flow model, enables the cavitation model, and solves the NS equation, continuity equation, and vapor phase transport equation, where the cavitation model is the ZGB cavitation model; THD model uses a laminar flow model, considers cavitation and viscosity-temperature effects, enables the energy equation and viscous frictional heat in the laminar flow model, and solves the NS equation, continuity equation, vapor phase transport equation, and energy equation, i.e., thermodynamic lubrication (THD), where fluid viscosity changes with temperature are introduced through a UDF.

[0013] Furthermore, the transport equation is:

[0014]

[0015] In the formula, R e R is the evaporation term in the phase transition process. cThis represents the condensation term during the phase change process; α represents the phase volume fraction; the subscript v represents the vapor phase.

[0016] If p≤p v

[0017]

[0018] If p>p v

[0019]

[0020] In the formula, F vap F is the evaporation term constant; cond R is the condensation term constant; B α is the cavitation radius (m); nuc This represents the volume fraction of nucleation sites.

[0021] Furthermore, in the process of determining the fluid flow state, the flow in the sealing gap consists of Couette flow and Poiseuille flow;

[0022] When the sealing ring operates without a pressure gradient, the rotation of the rotating ring drives the fluid to rotate, resulting in Couette flow. The Reynolds number in this case is denoted as Re. c :

[0023]

[0024] In the formula, r is the radius of the sealing ring (m); ω is the angular velocity of the sealing ring (1 / s); and h is the thickness of the liquid film (m).

[0025] When Re c <Re cl At that time, the flow is laminar, when Re c >Re ct At that time, the flow is turbulent;

[0026] When the sealing ring is not rotating and a pressure gradient exists, the flow is Poiseuille flow, and the Reynolds number is denoted as Re. p :

[0027]

[0028] In the formula, V r The radial velocity of the fluid in the sealing ring gap;

[0029] When Re p <Re pl At that time, the flow is laminar, when Re p >Re pt At that time, the flow is turbulent;

[0030] Flow factor τ:

[0031]

[0032] When τ < 9 / 16, the flow is laminar; when τ > 1, the flow is turbulent.

[0033] The fluid flow in the sealing ring is laminar.

[0034] Furthermore, in setting the boundary conditions, since the sealing ring has periodic characteristics, one period is used for calculation. The two end faces of the period are named P1 and P2, and P1 and P2 are set as periodic boundary conditions, i.e., periodic boundary conditions.

[0035] p(r,0)=p(r,2π / k)

[0036] In the formula, k is the wave number.

[0037] Furthermore, during operation, the main pump's wave seal has a rotating ring fixed on the main shaft that rotates with it, set as a rotating wall surface with a rotation speed of 1500 rpm and a temperature boundary condition of 'couple', i.e., a coupled heat exchange surface. The stationary ring is stationary and is set as a no-slip boundary condition with a temperature boundary condition of 'couple'. The pressures at the inlet and outlet of the sealing ring are known, and the inlet and outlet boundary conditions are given as pressure inlet and pressure outlet. The temperature of the sealing medium at the inlet is known and is set as a constant-temperature inlet boundary condition. Other conditions are set as wall boundary conditions.

[0038] Furthermore, when the wave seal ring is working, the wall surface on the outer diameter side of the moving ring rotates relative to the fluid in the sealing cavity. At this time, the fluid in the sealing cavity is undergoing forced convection heat transfer, and the formula for calculating the convection heat transfer coefficient is:

[0039]

[0040] In the formula, Re b For the fluid rotation and stirring action, Re b =ωD r 2 / v; ω is the angular velocity (rad / s); Re a Re is the correlation coefficient with fluid flow around the fluid. a =UD r / v; U is the axial velocity of the fluid around the moving ring (m) 2 / s); v is the kinematic viscosity (m³ / s); 2 / s); Pr is the Prandtl number, Pr = μc p / k; λ is the thermal conductivity (w / m·K);

[0041] The outer diameter sidewall of the stationary ring is relatively stationary with respect to the fluid inside the sealed cavity. The formula for calculating the convective heat transfer coefficient is:

[0042] α=0.023λRe 0.8 Pr 0.4 / δ

[0043] In the formula, δ is the clearance on the outer diameter side of the stationary ring (m); Re is the Reynolds number, Re=Vδ / υ; V is the average axial flow velocity of the sealing medium around the stationary ring (m / s).

[0044] Furthermore, the equations are discretized in time and space using the finite volume method; the coupling between pressure and velocity is solved using the SIMPLE algorithm; the spatial discretization of the pressure field adopts a second-order discretization scheme, and the difference schemes for the momentum equation and the energy equation adopt the QUICK scheme.

[0045] Furthermore, we define the relative rate of change of leakage between the THD model and the HD1 model as η1, and the relative rate of change of leakage between the THD model and the HD2 model as η2:

[0046]

[0047]

[0048] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump.

[0049] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump. Attached Figure Description

[0050] Figure 1 This is a schematic diagram illustrating the change in flow state;

[0051] Figure 2 This is a schematic diagram of the sealing boundary conditions for the wave size.

[0052] Figure 3 A comparison chart of models showing the change of opening force with film thickness;

[0053] Figure 4 A comparison chart of models showing leakage rate as a function of membrane thickness;

[0054] Figure 5 Radial temperature distribution at different rotational speeds;

[0055] Figure 6 A comparison chart of the opening force versus rotational speed models;

[0056] Figure 7A comparison chart of models showing leakage rate as a function of rotational speed;

[0057] Figure 8 This is a schematic diagram showing the relationship between the average temperature of the fluid and the change in leakage rate. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] Combination Figures 1-8 This invention proposes a method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump. The method specifically includes:

[0060] Cavitation model selection: The ZGB cavitation model is selected. This model ignores the effects of surface tension, non-condensable gas and turbulent kinetic energy. In this model, the pressure inside the cavitation bubble in the cavitation region is equal to the local saturated vapor pressure, the bubble diameter is a fixed value, and the mass transport rate is described by the volume fraction of the vaporization core.

[0061] Fluid flow state determination: The change in the flow factor τ is used to determine whether the fluid is in a laminar or turbulent state;

[0062] Boundary condition settings: Set boundary conditions according to the boundary type;

[0063] Sealing performance impact analysis: The effects of cavitation and temperature on sealing performance were analyzed under different film thicknesses and rotational speeds. The sealing performance calculation results of three models were compared during the analysis. Specifically, the three models are: HD1 model uses a laminar flow model, does not consider cavitation and viscosity-temperature effects, and solves the NS equation and continuity equation, i.e., a hydrodynamic lubrication model; HD2 model uses a laminar flow model, enables the cavitation model, and solves the NS equation, continuity equation, and vapor phase transport equation, where the cavitation model is the ZGB cavitation model; THD model uses a laminar flow model, considers cavitation and viscosity-temperature effects, enables the energy equation and viscous frictional heat in the laminar flow model, and solves the NS equation, continuity equation, vapor phase transport equation, and energy equation, i.e., thermodynamic lubrication (THD), where fluid viscosity changes with temperature are introduced through a UDF.

[0064] cavitation model

[0065] When the fluid dynamic pressure is high and the static pressure drops below the fluid's saturated vapor pressure, cavitation bubbles will be generated locally in the fluid. In waviness seals, the presence of waviness creates a high-pressure zone and a low-pressure zone within the sealing ring. Cavitation often occurs in the low-pressure zone, so a cavitation model needs to be included in the simulation calculation.

[0066] The Mixture model is a simplified Euler multiphase flow model with a wide range of applications. It can also be used for homogeneous multiphase flow models with strong coupling and identical phase velocities, and for calculating the viscosity of non-Newtonian fluids. The Mixture model can simulate multiphase flow of n phases (fluids or particles) by solving the momentum, continuity, and energy equations of the mixture, the volume fraction equations of the secondary phases, and the algebraic expression for relative velocities.

[0067] The Mixture model does not have the same computational accuracy as the Euler model, but there is a relatively mature cavitation model among the mixed models that is more efficient and stable and can well replace the Euler model. Therefore, this invention chooses the Mixture model for calculation.

[0068] In this invention, the primary phase is water and the secondary phase is water vapor. The Rayleigh-Plesset equation provides the basic laws governing steam generation and condensation. Other cavitation models are all based on this equation. This invention selects the ZGB (Zwart-Gerber-Belamri) cavitation model, which ignores the effects of surface tension, non-condensable gases, and turbulent kinetic energy. This model assumes that the pressure inside the cavitation bubble in the cavitation region is equal to the local saturated vapor pressure, the bubble diameter is a fixed value, and the mass transport rate is described by the volume fraction of the vaporization core.

[0069] The transport equation is:

[0070]

[0071] In the formula, R e R is the evaporation term in the phase transition process. c This represents the condensation term in the phase transition process; α represents the phase volume fraction; the subscript v represents the vapor phase;

[0072] If p≤p v

[0073]

[0074] If p>p v

[0075]

[0076] In the formula, F vap F is the evaporation term constant; condR is the condensation term constant; B α is the cavitation radius (m); nuc This represents the volume fraction of nucleation sites.

[0077] Flow state judgment

[0078] Because the liquid film in the sealing gap is too thin, commonly used methods for judging the flow state are not applicable. This invention proposes a method to judge the laminar and turbulent flow states of a fluid by using the change in the flow factor τ. Figure 1 Represents the fluid flow state and τ, Re p Re c The relationship between parameters.

[0079] In the process of determining the fluid flow state, the flow in the sealing gap consists of Couette flow and Poiseuille flow;

[0080] When the sealing ring operates without a pressure gradient, the rotation of the rotating ring drives the fluid to rotate, resulting in Couette flow. The Reynolds number in this case is denoted as Re. c :

[0081]

[0082] In the formula, r is the radius of the sealing ring (m); ω is the angular velocity of the sealing ring (1 / s); and h is the thickness of the liquid film (m).

[0083] When Re c <Re cl At that time, the flow is laminar, when Re c >Re ct At that time, the flow is turbulent;

[0084] When the sealing ring is not rotating and a pressure gradient exists, the flow is Poiseuille flow, and the Reynolds number is denoted as Re. p :

[0085]

[0086] In the formula, V r The radial velocity of the fluid in the sealing ring gap;

[0087] When Re p <Re pl At that time, the flow is laminar, when Re p >Re pt At that time, the flow is turbulent;

[0088] Flow factor τ:

[0089]

[0090] When τ < 9 / 16, the flow is laminar; when τ > 1, the flow is turbulent.

[0091] The sealing medium for the Bodu seal is water at 50°C with a dynamic viscosity of 5.494 × 10⁻⁶. -4 Pa·s, density is 988.1 kg / m³ 3 The sealing ring rotates at 1500 rpm, has an outer diameter of 0.15125 m and an inner diameter of 0.14025 m, and a liquid film thickness of approximately 1 μm to 10 μm. The radial velocity can be determined from simulation results, with a maximum radial velocity of 23.754 m / s. The calculated Reynolds number Re c The maximum is 427.07, Re p The maximum value is 427.21, which is significantly less than Re. cl and Re pl According to the definition of the flow factor τ, τ is 0.325, which is much smaller than 9 / 16 of the laminar flow boundary, so the fluid flow state in the sealing ring is laminar.

[0092] Boundary condition settings

[0093] In setting boundary conditions, since the sealing ring has periodic characteristics, one period is used for calculation. The two end faces of the period are named P1 and P2, and P1 and P2 are set as periodic boundary conditions.

[0094] p(r,0)=p(r,2π / k)

[0095] In the formula, k is the wave number.

[0096] In the calculation, Fluent assumes that the flow fields of P1 and P2 are consistent, and the two are similar to an interface connection.

[0097] Under high pressure, the sealing medium flows into the outer diameter of the sealing ring and out through the inner diameter. A schematic diagram of the boundary conditions is shown below. Figure 2 As shown.

[0098] During operation, the main pump's wave seal features a rotating ring fixed to the main shaft, rotating with it. This rotating ring is configured as a rotating wall surface at 1500 rpm, with a coupled temperature boundary condition (coupled heat exchange surface). The stationary ring remains stationary, with a no-slip boundary condition and a coupled temperature boundary condition. The pressures at the sealing ring inlet and outlet are known, and the inlet and outlet boundary conditions are given as pressure inlet and pressure outlet. The temperature of the sealing medium at the inlet is known and is set as a constant-temperature inlet boundary condition. Other boundary conditions are set as wall boundary conditions. Specific boundary condition settings are given in Table 1.

[0099] Table 1 Boundary Condition Settings

[0100]

[0101] When the wave seal ring is working, the wall surface on the outer diameter side of the moving ring rotates relative to the fluid in the sealing cavity. At this time, the fluid in the sealing cavity is undergoing forced convection heat transfer. The formula for calculating the convection heat transfer coefficient is:

[0102]

[0103] In the formula, Re b For the fluid rotation and stirring action, Re b =ωD r 2 / v; ω is the angular velocity (rad / s); Re a Re is the correlation coefficient with fluid flow around the fluid. a =UD r / v; U is the axial velocity of the fluid around the moving ring (m) 2 / s); v is the kinematic viscosity (m³ / s); 2 / s); Pr is the Prandtl number, Pr = μc p / k; λ is the thermal conductivity (w / m·K);

[0104] The outer diameter sidewall of the stationary ring is relatively stationary with respect to the fluid inside the sealed cavity. The formula for calculating the convective heat transfer coefficient is:

[0105] α=0.023λRe 0.8 Pr 0.4 / δ

[0106] In the formula, δ is the clearance on the outer diameter side of the stationary ring (m); Re is the Reynolds number, Re=Vδ / υ; V is the average axial flow velocity of the sealing medium around the stationary ring (m / s).

[0107] Effects of cavitation and temperature on sealing performance at different film thicknesses

[0108] To further investigate the impact of cavitation and viscosity-temperature effects on sealing performance, this invention will simulate three different computational models and compare the sealing performance calculation results of the three models. The HD1 model uses a laminar flow model, does not consider cavitation and viscosity-temperature effects, and solves the NS equation and continuity equation, i.e., the Hydrodynamic Lubrication (HD) model. The HD2 model uses a laminar flow model, enables the cavitation model, and solves the NS equation, continuity equation, and vapor phase transport equation, where the cavitation model is the ZGB cavitation model. The THD model uses a laminar flow model, considers cavitation and viscosity-temperature effects, enables the energy equation and viscous frictional heat in the laminar flow model, and solves the NS equation, continuity equation, vapor phase transport equation, and energy equation, i.e., Thermohydrodynamic Lubrication (THD), where the fluid viscosity change with temperature is introduced through a UDF.

[0109] This invention employs the finite volume method to discretize the equations in both time and space. The SIMPLE algorithm is used to solve for the coupling of pressure and velocity. The spatial discretization of the pressure field uses a second-order discretization scheme, while the difference schemes for the momentum and energy equations use the QUICK scheme.

[0110] Figure 3 The figure shows the variation of liquid film opening force with base film thickness calculated by three models. Since the HD1 model does not consider cavitation in its calculation, a large number of negative pressure zones appear in the liquid film when the film thickness is small. Since the opening force is the area integral of the liquid film pressure, the presence of negative pressure has a negative effect on the opening force. As can be seen from the figure, because the cavitation model in the HD2 model limits the minimum fluid pressure, it eliminates the negative effect of negative pressure zones on the opening force. When the film thickness is less than 3 μm, the opening force calculated by the HD2 model is higher than that of the HD1 model due to the cavitation effect. After 3 μm, the cavitation effect disappears, and the opening forces calculated by the two models are equal.

[0111] The THD model, considering thermal-fluid coupling, incorporates an energy equation and a cavitation model. Under small film thicknesses, the opening force is higher than the HD1 model but lower than the HD2 model. The comparison shows that after adding the energy equation and viscous frictional heat, the increased temperature leads to a decrease in fluid viscosity, reducing the dynamic pressure effect, thus resulting in a lower opening force for the THD model compared to the HD2 model. However, since the negative impact of increased temperature outweighs the positive impact of cavitation, the opening force of the THD model is still greater than that of HD1 when the film thickness is small. As the film thickness gradually increases, the cavitation effect gradually decreases, and the influence of the viscosity-temperature effect gradually becomes dominant, reaching its maximum at 3 μm when the cavitation effect disappears. Thereafter, with further increases in film thickness, the viscous frictional heat effect gradually weakens, and the difference between the THD model and the other two models gradually decreases.

[0112] The fluid in the sealing ring primarily consists of Poiseuille flow driven by pressure difference and Couette flow influenced by viscous forces. Due to cavitation, water below its saturated vapor pressure turns into steam, creating bubbles in the sealing ring that impede fluid flow and reduce leakage at the outlet. As the fluid temperature rises, its viscosity decreases—a phenomenon known as the viscosity-temperature effect. This decrease in viscosity weakens the Couette flow, reducing the amount of fluid moving with the rotating ring and making the fluid flow more easily. At this point, Poiseuille flow intensifies, increasing leakage at the outlet.

[0113] Define the relative rate of change of leakage between the THD model and the HD1 model as η1, and define the relative rate of change of leakage between the THD model and the HD2 model as η2:

[0114]

[0115]

[0116] Figure 4 For different calculation models of leakage variation with film thickness, the leakage of the THD model is consistently greater than that of the other two models. However, since the viscosity-temperature effect gradually decreases with increasing film thickness, the gap between THD and the other two models gradually decreases. Because the cavitation effect disappears after 3 μm, the comparative change rates of the models begin to overlap at 3 μm, after which the relative change is dominated only by the viscosity-temperature effect. From the relative change trends of the three models, it can be seen that at small film thicknesses, the influence of the viscosity-temperature effect decreases sharply with increasing film thickness. However, the promoting effect of reduced viscosity on leakage is greater than the hindering effect of cavitation on fluid leakage. Furthermore, since the weakening trend of the cavitation effect with film thickness is greater than that of the viscosity-temperature effect, η1 increases significantly before 3 μm. Subsequently, due to the disappearance of the cavitation effect and the weakening of the viscosity-temperature effect, η1 and η2 gradually decrease with increasing film thickness, and the rate of decrease slows down during this process.

[0117] The comparison of the effects of viscosity-temperature effect and cavitation effect on sealing performance with film thickness shows that when the film thickness is small, the cavitation effect has a greater impact on the opening force than the viscosity-temperature effect, while the viscosity-temperature effect has a greater impact on the leakage. When the film thickness is large, due to the weakening or even disappearance of the cavitation effect, the viscosity-temperature effect dominates the impact on both the opening force and the leakage.

[0118] Effects of cavitation and temperature on sealing performance at different rotational speeds

[0119] At different input rotational speeds, the relative sliding speeds between the moving and stationary rings differ, resulting in varying heat generation from viscous friction. This leads to different fluid temperature variations at different rotational speeds. Furthermore, changes in rotational speed affect the liquid film pressure distribution, which in turn influences the cavitation volume fraction. This invention will investigate the effects of viscosity-temperature effects and cavitation effects on sealing performance parameters as a function of rotational speed.

[0120] The present invention uses a geometric model with a basic membrane thickness of 2μm for calculation, with a working pressure of 5.3MPa, a rotation speed of 500~3000rpm, and an inlet temperature of 323.15K.

[0121] The liquid film thickness gradually increases radially after the dam area, so the liquid film thickness is larger at the inlet and smallest at the outlet within the dam area. Figure 5 The figure shows the radial temperature distribution of the fluid domain at different rotational speeds. It can be seen that along the radial direction, the temperature is lower at the inlet. Due to the gradual decrease in liquid film thickness, the temperature gradually increases along the flow direction, but the rate of increase gradually decreases, reaching its maximum at the outlet. With increasing rotational speed, the fluid temperature distribution significantly improves, the temperature difference at the outlet increases exponentially, and the temperature difference between the inlet and outlet also becomes larger. Furthermore, the rate of temperature increase is almost directly proportional to the rate of increase in rotational speed. This demonstrates that increasing rotational speed has a significant impact on fluid temperature, and these temperature changes will be reflected in the fluid's physical properties, thus affecting sealing performance.

[0122] Figure 6 To compare the results of the three calculation models when the opening force changes with the rotational speed, the figure shows that the opening force of the HD1 model decreases with increasing rotational speed. This is because the increase in speed causes a drop in fluid pressure in the low-pressure zone, resulting in negative pressure, which in turn affects the opening force. Since both the HD2 and THD models use cavitation models, the low-pressure zone is controlled, while the high-pressure zone gradually increases with increasing rotational speed under the influence of dynamic pressure effect. Therefore, when no cavitation occurs below 1500 rpm, the opening force of the HD2 and THD models gradually decreases. However, when the rotational speed is above 1500 rpm, the generation of cavitation and the expansion of the high-pressure zone cause the opening force to gradually increase.

[0123] When the speed is below 1500 rpm, the opening force of the THD model is lower than that of the other two models, but the difference is not significant. When the speed is above 1500 rpm, the gap between the HD2 model and the THD model and the HD1 model gradually increases with the increase of cavitation effect. Due to the existence of viscosity-temperature effect, the opening force of the HD2 model is greater than that of the THD model, but the difference is much smaller than that of the HD1 model. This indicates that as the speed increases, the positive impact of cavitation effect on opening force is greater than the negative impact of viscosity-temperature effect, and the influence of cavitation effect gradually becomes dominant.

[0124] Figure 7Comparing the leakage rate models with rotational speed, the graph shows that the leakage rates of models HD1 and HD2 gradually decrease with increasing rotational speed, while the leakage rate of the THD model gradually increases, and the increase is much greater than the decrease in leakage rates of models HD1 and HD2. The leakage rate of model HD2 is less than that of model HD1, due to the cavitation effect preventing fluid leakage. However, the difference between the two models gradually narrows with increasing rotational speed, indicating that the cavitation effect's hindering effect on fluid flow decreases with increasing rotational speed. The leakage rate of model THD is significantly greater than the other two models. As the rotational speed increases, viscous frictional heat increases, leading to a gradual increase in leakage. At 500 rpm, the leakage rate of model THD is already greater than that of model HD2, indicating that at low rotational speeds, the promoting effect of the viscosity-temperature effect on leakage is greater than the hindering effect of cavitation. This difference increases with increasing rotational speed, and the rate of increase accelerates. Therefore, it can be seen that the viscosity-temperature effect plays a dominant role in the change of leakage rate with rotational speed.

[0125] Figure 8 The figure reflects the relationship between the fluid average temperature and η1 with rotational speed in the THD model. As can be seen from the figure, the change in fluid average temperature is almost proportional to the change in rotational speed. η1 is small at low rotational speeds, but as the rotational speed increases, the fluid average temperature increases, the viscosity-temperature effect on leakage increases, and η1 gradually increases. Moreover, at higher rotational speeds, the trend is almost consistent with that of fluid average temperature.

[0126] The comparison of the effects of viscosity-temperature and cavitation on sealing performance with varying rotational speed shows that at lower speeds, both cavitation and viscosity-temperature effects are weak, and the change in opening force is not significant. However, the promoting effect of viscosity-temperature on leakage is still very pronounced even at low speeds. At higher speeds, the cavitation effect has a greater impact on the opening force than the viscosity-temperature effect, while the viscosity-temperature effect has a much greater impact on leakage than the cavitation effect.

[0127] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump.

[0128] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump.

[0129] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0130] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0131] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0132] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0133] The above provides a detailed analysis of the influence of cavitation and temperature on the sealing performance of the nuclear main pump. Specific examples are used to illustrate the principles and implementation methods of the invention. The above descriptions of the embodiments are only for the purpose of helping to understand the method and core ideas of the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

Claims

1. A method for analyzing the influence of cavitation and temperature on the waviness sealing performance of a nuclear main pump, characterized in that, Specifically, it includes: Cavitation model selection: The ZGB cavitation model is selected. This model ignores the effects of surface tension, non-condensable gas and turbulent kinetic energy. In this model, the pressure inside the cavitation bubble in the cavitation region is equal to the local saturated vapor pressure, the bubble diameter is a fixed value, and the mass transport rate is described by the volume fraction of the vaporization core. Fluid flow state determination: using flow factor τ The changes in fluid flow can be used to determine whether the flow is laminar or turbulent. Boundary condition settings: Set boundary conditions according to the boundary type; Sealing performance impact analysis: The effects of cavitation and temperature on sealing performance were analyzed under different film thicknesses and rotational speeds. During the analysis, the sealing performance calculation results of three models were compared. Specifically, the three models are: HD1 model uses a laminar flow model, does not consider cavitation and viscosity-temperature effects, and solves the NS equation and continuity equation, i.e., a hydrodynamic lubrication model; HD2 model uses a laminar flow model, enables the cavitation model, and solves the NS equation, continuity equation, and vapor phase transport equation, where the cavitation model is the ZGB cavitation model; THD model uses a laminar flow model, considers cavitation and viscosity-temperature effects, enables the energy equation and viscous frictional heat in the laminar flow model, and solves the NS equation, continuity equation, vapor phase transport equation, and energy equation, i.e., thermodynamic lubrication (THD), where fluid viscosity changes with temperature are introduced through a UDF. The transport equation is: In the formula, R e This refers to the evaporation term in the phase transition process; R c This refers to the condensation term in the phase transition process. α Volume fraction of phase; subscript v For vapor phase; like p ≤ p v like p>p v In the formula, F vap This is the constant for the evaporation term; F cond This is the condensation term constant; R B Where is the cavitation radius; α nuc This represents the volume fraction of nucleation sites. In the process of determining the fluid flow state, the flow in the sealing gap consists of Couette flow and Poiseuille flow; When the sealing ring operates without a pressure gradient, the rotation of the rotating ring drives the fluid to rotate, resulting in Couette flow. The Reynolds number in this case is denoted as Re. c : In the formula, r The radius of the sealing ring; ω The angular velocity of the sealing ring rotation; h The thickness of the liquid film; When Re c <Re cl At that time, the flow is laminar, when Re c >Re ct At that time, the flow is turbulent; When the sealing ring is not rotating and a pressure gradient exists, the flow is Poiseuille flow, and the Reynolds number is denoted as Re. p : In the formula, V r The radial velocity of the fluid in the sealing ring gap; When Re p <Re pl At that time, the flow is laminar, when Re p >Re pt At that time, the flow is turbulent; Flow factor τ : when τ At time <9 / 16, the flow is laminar. τ When the value is greater than 1, the flow is turbulent. The fluid flow in the sealing ring is laminar.

2. The method according to claim 1, characterized in that, In setting boundary conditions, since the sealing ring has periodic characteristics, one period is used for calculation. The two end faces of the period are named P1 and P2, and P1 and P2 are set as periodic boundary conditions. In the formula, k For wave number.

3. The method according to claim 2, characterized in that, During operation, the main pump's wave seal has a rotating ring fixed on the main shaft that rotates with it, set as a rotating wall surface at 1500 rpm, with a temperature boundary condition of "couple," i.e., a coupled heat exchange surface. The stationary ring is stationary, set as a no-slip boundary condition, with a temperature boundary condition of "couple." The pressures at the inlet and outlet of the sealing ring are known, and the inlet and outlet boundary conditions are given as pressure inlet and pressure outlet. The temperature of the sealing medium at the inlet is known and set as a constant-temperature inlet boundary condition. Other conditions are set as wall boundary conditions.

4. The method according to claim 3, characterized in that, When the wave seal ring is working, the wall surface on the outer diameter side of the moving ring rotates relative to the fluid in the sealing cavity. At this time, the fluid in the sealing cavity is undergoing forced convection heat transfer. The formula for calculating the convection heat transfer coefficient is: In the formula, Re b For the fluid rotation and stirring action, Re b = ωD r 2 / v ; ω Re is the angular velocity; a Re is the correlation coefficient with fluid flow around the fluid. a = UD r / v ; U The axial velocity of the fluid surrounding the moving ring; v Kinematic viscosity; Pr is the Prandtl number, Pr = μc p / k ; λ Thermal conductivity; The outer diameter sidewall of the stationary ring is relatively stationary with respect to the fluid inside the sealed cavity. The formula for calculating the convective heat transfer coefficient is: In the formula, δ The outer diameter clearance of the stationary ring; Re is the Reynolds number, Re = Vδ / v ; V The average axial velocity of the sealing medium around the stationary ring.

5. The method according to claim 1, characterized in that, The equations are discretized in time and space using the finite volume method; the coupling of pressure and velocity is solved using the SIMPLE algorithm; the spatial discretization of the pressure field adopts a second-order discretization scheme, and the difference schemes of the momentum equation and the energy equation adopt the QUICK scheme.

6. The method according to claim 1, characterized in that, Define the relative change rate of leakage between the THD model and the HD1 model. η 1. Define the relative change rate of leakage between the THD model and the HD2 model. η 2: 。 7. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium for storing computer instructions, characterized in that, When the computer instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-6.

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