High temperature low flow rate flow meter and optimization method thereof

Abstract

The application discloses a high-temperature low-flow-rate flowmeter and an optimization method thereof, the high-temperature low-flow-rate flowmeter comprising a heating pipe and a Venturi tube, a heating device being arranged outside the heating pipe; the Venturi tube makes the temperature of the heated liquid metal tend to be uniform; one temperature measuring point is arranged before the inlet of the heating pipe and after the outlet of the Venturi tube respectively, so as to obtain the temperature of the liquid metal before and after heating; the mass flow rate of the liquid metal is calculated based on an energy balance formula; the optimization method comprises the following steps: determining the pressure loss and the thermal non-uniformity factor corresponding to the design variable through modeling and numerical simulation; taking the minimum pressure loss and the minimum thermal non-uniformity factor as the optimization target, obtaining an optimal geometric parameter solution set through the Pareto front method in combination with the model and the simulation result; and further selecting the design variable with the minimum pressure loss and the highest stirring efficiency. The application can realize accurate measurement of the liquid metal flow rate under the high-temperature super-low-flow-rate working condition, and balance the temperature uniformity and the pressure loss.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of flow measurement, in particular to a high-temperature low-flow-rate flowmeter and an optimization method thereof. BACKGROUND

[0002] Accurate measurement of coolant flow rate in reactor fuel assemblies is one of the important factors to ensure the safe operation of liquid metal cooled reactors (LMRs), especially the flow rate of liquid metal under accident conditions may be as low as 0.01-0.05 m / s. Limited by high temperature, ultra-low flow rate and other factors, traditional differential pressure type, electromagnetic type flowmeter and other flowmeters are difficult to realize accurate and stable measurement of liquid metal. The thermal flowmeter is not affected by high temperature, but the low Prandtl number characteristics of liquid metal and the weak turbulence intensity under ultra-low flow rate result in that liquid metal is prone to serious temperature stratification, which affects the accurate measurement of temperature and reduces the measurement accuracy of the thermal flowmeter. SUMMARY

[0003] The purpose of the present application is to provide a high-temperature low-flow-rate flowmeter and an optimization method thereof for accurate measurement of liquid metal flow rate under high-temperature ultra-low flow rate conditions.

[0004] Technical solution: The high-temperature low-flow-rate flowmeter of the present application comprises a heating pipe and a Venturi tube connected in series, wherein a heating device is arranged outside the heating pipe for heating the liquid metal flowing through the heating pipe; the Venturi tube makes the temperature of the heated liquid metal tend to be uniform; one temperature measuring point is arranged before the inlet of the heating pipe and one temperature measuring point is arranged after the outlet of the Venturi tube, respectively for obtaining the temperature T in of the liquid metal before heating and the temperature T out of the liquid metal after heating; the mass flow rate of the liquid metal is calculated based on the following energy balance formula:

[0005]

[0006] wherein, represents the mass flow rate of the liquid metal; P represents the heating power of the heating device; c p represents the specific heat capacity of the liquid metal.

[0007] Further, the heating device adopts an electric heating belt, and the electric heating belt is wound outside the heating pipe.

[0008] Further, the temperature measuring point adopts a conventional industrial temperature sensor.

[0009] The high-temperature low-flow rate flowmeter utilizes the Venturi effect of the Venturi tube to stir the liquid metal, and the Venturi tube is an important means to improve the temperature uniformity and is also the main reason for pressure loss. Considering the influence of the geometric parameters of the Venturi tube on the flow characteristics and the measurement accuracy, the application further proposes an optimization method of the high-temperature low-flow rate flowmeter, so as to realize the multi-objective optimization of the pressure loss and the temperature uniformity.

[0010] The optimization method comprises:

[0011] (1) a parameterized model of the high-temperature low-flow rate flowmeter is established, the geometric parameters of the Venturi tube are taken as design variables related to the optimization target, numerical simulation is performed on the model, and the optimization target value is obtained; the optimization target comprises pressure loss and thermal non-uniformity factor; the smaller the thermal non-uniformity factor is, the more uniform the temperature distribution of the liquid metal is; the larger the thermal non-uniformity factor is, the more non-uniform the temperature distribution of the liquid metal is;

[0012] (2) taking the minimum pressure loss and the minimum thermal non-uniformity factor as the optimization target, the optimal geometric parameter solution set is obtained by the Pareto front optimization method in combination with the model and the simulation result.

[0013] Further, the optimization method further comprises:

[0014] (3) through simulation analysis and simulation verification, the geometric parameters with the minimum pressure loss and the highest stirring efficiency are selected from the optimal geometric parameter solution set, so that the balance between the temperature uniformity and the pressure loss is optimized.

[0015] Further, the thermal non-uniformity factor is expressed as:

[0016]

[0017] Wherein, E t is the thermal non-uniformity factor; T max is the maximum temperature; T min is the minimum temperature; A is the cross-sectional area of the pipe fluid domain perpendicular to the flow direction; T i is the local temperature based on each grid size in the cross section of the pipe fluid domain perpendicular to the flow direction; T ave is the cross-sectional average temperature of the pipe fluid domain perpendicular to the flow direction;

[0018]

[0019] Wherein, is the area of the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction; is the local temperature based on each grid size in the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction;

[0020]

[0021] where r is the radius of the cross section of the pipe fluid domain perpendicular to the flow direction; is the distance from the center of the cross section of the pipe fluid domain perpendicular to the flow direction to the thermal boundary layer;

[0022]

[0023] where T in is the temperature at the inlet of the flowmeter; c p is the specific heat capacity of the liquid metal; is the mass flow rate of the liquid metal;

[0024]

[0025] where p is the density of the liquid metal; v is the flow velocity of the liquid metal;

[0026]

[0027] where d t is the thickness of the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction; d is the thickness of the velocity boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction; Pr is the Prandtl number;

[0028]

[0029] where m is the dynamic viscosity of the liquid metal; l is the thermal conductivity of the liquid metal.

[0030] Further, the mixing efficiency is expressed as:

[0031]

[0032] where h is the mixing efficiency, s max is the peak value of the thermal heterogeneity factor before mixing, s s is the value of the stable thermal heterogeneity factor.

[0033] Further, a parametric modeling of the high-temperature low-flow-rate flowmeter is performed using CAD software.

[0034] Further, a numerical simulation of the high-temperature low-flow-rate flowmeter model is performed using CFD software.

[0035] Further, the design variables include the curvature of the Venturi tube and the throat diameter.

[0036] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: The high-temperature, low-flow-rate flow meter provided by this invention utilizes the Venturi effect of a Venturi tube to agitate heated liquid metal, thereby improving temperature uniformity and achieving accurate measurement of liquid metal flow rate under high-temperature, ultra-low-flow-rate conditions. The optimization method for the high-temperature, low-flow-rate flow meter provided by this invention achieves a balance between temperature uniformity and pressure loss by optimizing the geometric parameters of the Venturi tube, significantly improving the accuracy and reliability of the high-temperature, low-flow-rate flow meter. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of a high-temperature, low-flow-rate flow meter provided in an embodiment of the present invention;

[0038] Figure 2 This is a flowchart of the optimization method for a high-temperature, low-flow-rate flow meter provided in an embodiment of the present invention;

[0039] Figure 3 This is a Pareto front plot in an embodiment of the present invention;

[0040] Figure 4 These are three representative optimized models in the embodiments of this invention;

[0041] Figure 5 The variation of the thermal non-uniformity factor between the three optimal models and the unoptimized model in the embodiments of the present invention at a flow rate of 0.05 m / s;

[0042] Figure 6 These are the changes in thermal non-uniformity factors of the three optimization models in this embodiment of the invention under different flow rates;

[0043] Figure 7 These are the pressure losses of the three optimization models in this invention at different flow rates. Detailed Implementation

[0044] The invention will now be further described with reference to the accompanying drawings.

[0045] like Figure 1 As shown, this embodiment of the invention provides a high-temperature, low-flow-rate flow meter, including a heating tube 1 and a venturi tube 2 connected together. A heating device is externally mounted on the heating tube 1 to heat the liquid metal flowing through it. The venturi tube 2 ensures the heated liquid metal reaches a uniform temperature. A temperature measuring point is located before the inlet of the heating tube 1 and after the outlet of the venturi tube 2, respectively, to obtain the temperature T of the liquid metal before heating. in and the temperature T of the heated liquid metal out The mass flow rate of liquid metal is calculated based on the following energy balance formula:

[0046]

[0047] wherein, represents the mass flow rate of the liquid metal; P represents the heating power of the heating device; c p represents the specific heat capacity of the liquid metal.

[0048] In this embodiment, the heating device uses an electric heating belt, and the electric heating belt is wound outside the heating pipe. The temperature measuring point uses a conventional industrial temperature sensor.

[0049] As Figure 2 shown, the embodiment of the present application also provides an optimization method for the high-temperature low-flow-rate flowmeter, which combines CAD software and CFD software, uses the pre-Pareto front optimization method to obtain an optimization scheme, and specifically includes the following steps:

[0050] (1) A parameterized model of the high-temperature low-flow-rate flowmeter is established by using CAD software, the geometric parameters of the Venturi tube are taken as design variables related to the optimization target, the model is imported into CFD (computational fluid dynamics) software for numerical simulation, and an optimization target value is obtained.

[0051] In this embodiment, the design variables include the curvature and throat diameter of the Venturi tube. The optimization targets include pressure loss and thermal non-uniformity factor, wherein the thermal non-uniformity factor is an index proposed by the present application for quantitatively evaluating the temperature uniformity of the liquid metal after heating and stirring. The thermal non-uniformity factor is expressed as:

[0052]

[0053] wherein, E t is the thermal non-uniformity factor; T max is the maximum temperature; T min is the minimum temperature; A is the cross-sectional area of the pipe fluid domain perpendicular to the flow direction; T i is the local temperature based on each grid size on the cross section of the pipe fluid domain perpendicular to the flow direction; T ave is the cross-sectional average temperature of the pipe fluid domain perpendicular to the flow direction;

[0054]

[0055] wherein, is the area of the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction; is the local temperature based on each grid size in the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction;

[0056]

[0057] wherein, r is the radius of the cross section of the pipe fluid domain perpendicular to the flow direction; the distance from the center of the cross section of the fluid domain of the pipe perpendicular to the flow direction to the thermal boundary layer;

[0058]

[0059] where T in is the temperature at the inlet of the flow meter; c p is the specific heat capacity of the liquid metal; is the mass flow rate of the liquid metal;

[0060]

[0061] where p is the density of the liquid metal; v is the flow velocity of the liquid metal;

[0062]

[0063] where d t is the thickness of the thermal boundary layer in the cross section of the fluid domain of the pipe perpendicular to the flow direction; d is the thickness of the velocity boundary layer in the cross section of the fluid domain of the pipe perpendicular to the flow direction; Pr is the Prandtl number;

[0064]

[0065] where m is the dynamic viscosity of the liquid metal; l is the thermal conductivity of the liquid metal.

[0066] The smaller the thermal heterogeneity factor, the more uniform the temperature distribution of the liquid metal; the larger the thermal heterogeneity factor, the more non-uniform the temperature distribution of the liquid metal.

[0067] (2) Taking the minimum pressure loss and the minimum thermal heterogeneity factor as the optimization objectives, a multi-objective optimization is performed by the Pareto front optimization method, in combination with the CAD model and the simulation results of the CFD software, to obtain a set of optimal geometric parameter solutions.

[0068] The Pareto front diagram obtained by the optimization provides multiple schemes with relatively good performance. Through the optimization, the temperature uniformity of the liquid metal after heating is significantly improved, and the pressure loss is effectively reduced. The numerical simulation and the parameter optimization results show that different geometric structures can achieve different combinations between the mixing efficiency and the flow resistance.

[0069] As Figure 3 shown, each point on the boundary of the Pareto front diagram represents an optimal geometric structure. These solutions are non-dominated solutions, i.e., optimizing one objective (such as reducing the pressure loss) will inevitably lead to a compromise in another objective (such as the thermal heterogeneity factor).

[0070] (3) Further simulation analysis and simulation verification are performed on the optimal solution set by a CFD software, and a geometric parameter with the smallest pressure loss and the highest stirring efficiency is selected from the optimal geometric parameter solution set.

[0071] The stirring efficiency is expressed as:

[0072]

[0073] wherein η is the stirring efficiency, σ max is the peak value of the thermal non-uniformity factor before stirring, σ s is the value of the stable thermal non-uniformity factor.

[0074] As Figure 4 shown, in order to reduce the amount of calculation and further analyze the pressure loss and temperature uniformity performance under different low flow rates, the present application selects three representative optimization models from the lower left corner of the Pareto frontier diagram for comparison. The three optimization models are numbered as model 1, model 2 and model 3. The purpose of selecting these three models is to study their performance under different flow conditions, especially the trade-off between pressure loss and temperature uniformity.

[0075] As Figure 5 shown, there is a difference in the thermal non-uniformity factor distribution of the three optimized models and the model without stirring strategy at a flow rate of 0.05 m / s. The flowmeter with stirring strategy can achieve more uniform temperature distribution in a shorter flow distance, and the stirring effect of the three optimal models at a flow rate of 0.05 m / s is basically the same.

[0076] As Figure 6It can be seen that, before the mixing, the thermal non-uniformity factor increases with the increase of the flow distance due to the accumulation of temperature gradient caused by the heating of the inner wall of the pipe. The lower the flow rate, the higher the peak value of the thermal non-uniformity factor, indicating that the temperature distribution of the liquid metal before mixing is very uneven. With the increase of the flow rate, the peak value of the thermal non-uniformity factor gradually decreases. This indicates that a higher flow rate helps to improve the uniformity of the temperature distribution, because the increase of the flow rate can enhance the convective heat transfer, thereby homogenizing the temperature distribution faster. However, when the flow rate is further increased, although the mixing region can still significantly reduce the thermal non-uniformity factor, the peak value has been significantly reduced compared with the low flow rate, so the effect of mixing on the overall temperature distribution becomes relatively limited. Under high flow rate conditions, the relative advantage of this mixing strategy is weakened. At the same time, under the flow rate of 0.01 m / s, the improvement of the mixing region on the thermal non-uniformity factor is more significant and stable, indicating that the mixing strategy based on the Venturi effect proposed in the present application is more suitable for ultra-low flow rate conditions. For higher flow rates, although the mixing strategy is still effective, the improvement is significantly reduced, and the importance of mixing is relatively weakened. Therefore, if the flow rate exceeds the applicable range, other optimization designs may need to be used to further improve the temperature uniformity. In addition, it can also be seen from Figure 6 It can also be seen that, after the mixing region, the thermal non-uniformity factor of model 2 tends to be stable, while models 1 and 3 still need a certain flow distance to reach a stable state. This indicates that after mixing, the liquid metal still needs to undergo a certain mixing to be completely homogenized. This delay may increase the length requirement of the pipe design, and models 1 and 3 may not be suitable for systems with compact space or high temperature uniformity requirements.

[0077] It can also be seen that, after the mixing region, the thermal non-uniformity factor of model 2 tends to be stable, while models 1 and 3 still need a certain flow distance to reach a stable state. This indicates that after mixing, the liquid metal still needs to undergo a certain mixing to be completely homogenized. This delay may increase the length requirement of the pipe design, and models 1 and 3 may not be suitable for systems with compact space or high temperature uniformity requirements. Figure 7 It can be seen from Table 1 that, as the flow rate increases, the pressure drop of the three models increases significantly, and the pressure drop of model 3 increases the fastest, followed by model 2 and model 1. In addition, within the given flow rate range, model 3 has the highest mixing efficiency, followed by model 2 and model 1. From the analysis of mixing efficiency and pressure loss, it can be seen that model 3 achieves high mixing efficiency at the expense of more flow resistance performance; while model 1 slightly reduces the mixing efficiency in pursuit of low pressure drop; in contrast, model 2 achieves the best balance between pressure loss and mixing efficiency. Therefore, the best geometry of the flow meter mixing strategy suitable for liquid metal high-temperature ultra-low flow rate conditions finally recommended by the present application is model 2, i.e. Figure 4 (b) shown.

[0078] Table 1 Mixing efficiency of three optimized models at different low flow rates

[0079]

[0080] In conclusion, the optimized flowmeter structure of the application not only realizes the minimization of pressure loss and thermal non-uniformity factor, but also achieves the best balance between stirring efficiency and pressure loss. The optimized scheme not only significantly improves the uniformity of liquid metal temperature, but also effectively reduces the energy loss of the system.

Claims

1. A method of optimizing a high temperature, low flow rate flow meter, comprising: The high-temperature, low-flow-rate flow meter includes a heating tube and a venturi tube connected together. A heating device is installed outside the heating tube to heat the liquid metal flowing through it. The venturi tube ensures that the temperature of the heated liquid metal is uniform. A temperature measuring point is installed before the heating tube inlet and after the venturi tube outlet to obtain the temperature of the liquid metal before heating. and the temperature of the heated liquid metal The mass flow rate of liquid metal is calculated based on the following energy balance formula: ； wherein represents the mass flow of the liquid metal; represents the heating power of the heating device; represents the specific heat capacity of the liquid metal; The optimization method comprises: (1) establishing a parameterized model of the high-temperature low-flow rate flowmeter, taking geometric parameters of the Venturi tube as design variables related to an optimization target, performing numerical simulation on the model to obtain an optimization target value, and optimizing the target value, wherein the optimization target comprises pressure loss and a thermal non-uniformity factor; the smaller the thermal non-uniformity factor, the more uniform the temperature distribution of the liquid metal; the larger the thermal non-uniformity factor, the more non-uniform the temperature distribution of the liquid metal; (2) taking minimum pressure loss and minimum thermal non-uniformity factor as the optimization target, obtaining an optimal geometric parameter solution set by a Pareto front optimization method in combination with the model and the simulation result.

2. The optimization method of claim 1, wherein, Further comprising: (3) selecting geometric parameters with minimum pressure loss and highest stirring efficiency from the optimal geometric parameter solution set through simulation analysis and simulation verification.

3. The optimization method of claim 2, wherein, The thermal non-uniformity factor is expressed as: ； wherein, is a thermal non-uniformity factor; is a maximum temperature; is a minimum temperature; is a cross-sectional area of the pipe fluid domain perpendicular to the flow direction; is a local temperature on the cross-section of the pipe fluid domain perpendicular to the flow direction based on each grid size; is a cross-sectional average temperature of the pipe fluid domain perpendicular to the flow direction; ； wherein, A is the area of the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction; T is the local temperature within the thermal boundary layer in the cross section of the pipe fluid domain perpendicular to the flow direction based on each grid size. ； wherein R is the radius of the cross section of the fluid domain of the pipe perpendicular to the flow direction; R is the radius of the cross section of the fluid domain of the pipe perpendicular to the flow direction; ； wherein, is the temperature at the inlet of the flowmeter; is the specific heat capacity of the liquid metal; is the mass flow rate of the liquid metal; ； wherein, is the liquid metal density; is the liquid metal flow rate; ； wherein is the thermal boundary layer thickness in the cross section of the pipe flow domain perpendicular to the flow direction; is the velocity boundary layer thickness in the cross section of the pipe flow domain perpendicular to the flow direction; is the Prandtl number; ； wherein, is the dynamic viscosity of the liquid metal; is the thermal conductivity of the liquid metal.

4. The optimization method of claim 2, wherein, The stirring efficiency is expressed as: ； wherein, is the stirring efficiency, is the peak value of the thermal inhomogeneity factor before stirring, is the value of the stable thermal inhomogeneity factor.

5. The optimization method of claim 2, wherein, The high-temperature low-flow rate flowmeter is parameterized modeled by using CAD software.

6. The optimization method of claim 2, wherein, The high-temperature low-flow rate flowmeter model is numerically simulated by using CFD software.

7. The optimization method of claim 2, wherein, The design variables comprise an arc of the Venturi tube and a throat diameter.

8. The optimization method of claim 1, wherein, The heating device adopts an electric heating belt, and the electric heating belt is wound outside the heating pipe.

9. The optimization method of claim 1, wherein, The temperature measuring point adopts a conventional industrial temperature sensor.

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