High-temperature low-flow-velocity flowmeter and optimization method thereof

Abstract

The invention discloses a high-temperature low-flow-velocity flowmeter and an optimization method thereof. The high-temperature low-flow-velocity flowmeter comprises a heating tube and a Venturi tube, and heating equipment is arranged outside the heating tube; the Venturi tube enables the temperature of the heated liquid metal to tend to be uniform; temperature measuring points are arranged in front of an inlet of the heating pipe and behind an outlet of the Venturi pipe respectively, and the temperature of the liquid metal before and after heating is obtained; the mass flow of the liquid metal is calculated based on an energy balance formula; the optimization method comprises the following steps: determining pressure loss and thermal non-uniformity factors corresponding to design variables through modeling and numerical simulation; taking the minimum pressure loss and the minimum thermal non-uniformity factor as optimization objectives, and obtaining an optimal geometric parameter solution set through a Pareto frontier method in combination with the model and a simulation result; and the design variable with the minimum pressure loss and the highest stirring and mixing efficiency is optimized. Accurate measurement of the liquid metal flow under the working condition of high temperature and ultralow flow velocity can be realized, and balance of temperature uniformity and pressure loss is realized.

Description

Technical Field

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

[0002] Accurate measurement of coolant flow in reactor fuel assemblies is one of the important factors to ensure the safe operation of liquid metal cooled reactors (LMRs). In particular, the flow rate of liquid metal under accident conditions may be as low as 0.01-0.05 m / s. Limited by factors such as high temperature and ultra-low flow rate, traditional differential pressure and electromagnetic flow meters are difficult to achieve accurate and stable measurement of liquid metal. Thermal flow meters are not affected by high temperatures, but the low Prandtl number characteristics of liquid metal and the weak turbulence intensity at ultra-low flow rates make liquid metal prone to severe temperature stratification, which affects the accurate measurement of temperature and reduces the measurement accuracy of thermal flow meters. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a high-temperature, low-flow rate flowmeter and an optimization method thereof, which can be used to accurately measure the flow rate of liquid metal under high-temperature and ultra-low flow rate conditions.

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

[0005]

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

[0007] Furthermore, the heating device adopts an electric heating belt, which is wound around the outside of the heating tube.

[0008] Furthermore, the temperature measurement points use traditional industrial temperature sensors.

[0009] The high temperature and low flow rate flowmeter described in the present invention utilizes the Venturi effect of the Venturi tube to stir the liquid metal. The Venturi tube is both an important means to improve temperature uniformity and the main cause of pressure loss. Considering the influence of the geometric parameters of the Venturi tube on the flow characteristics and measurement accuracy, the present invention further proposes an optimization method for the high temperature and low flow rate flowmeter to achieve multi-objective optimization of pressure loss and temperature uniformity.

[0010] The optimization method comprises:

[0011] (1) Establish a parametric model of a high-temperature, low-flow rate flowmeter, and use the geometric parameters of the venturi tube as design variables related to the optimization target; perform numerical simulation on the model to obtain the optimization target value; the optimization target includes pressure loss and thermal inhomogeneity factor; the smaller the thermal inhomogeneity factor, the more uniform the temperature distribution of the liquid metal; the larger the thermal inhomogeneity factor, the more non-uniform the temperature distribution of the liquid metal;

[0012] (2) Taking the minimum pressure loss and the minimum thermal non-uniformity factor as the optimization objectives, the optimal geometric parameter solution set is obtained by combining the model and simulation results through the Pareto frontier optimization method.

[0013] Furthermore, the optimization method also includes:

[0014] (3) Through simulation analysis and simulation verification, the geometric parameters with the minimum pressure loss and the highest mixing efficiency are selected from the optimal geometric parameter solution set to achieve the best balance between temperature uniformity and pressure loss.

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

[0016]

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

[0018]

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

[0020]

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

[0022]

[0023] Among them, T in is the flow meter inlet temperature; c p is the specific heat capacity of liquid metal; is the mass flow rate of liquid metal;

[0024]

[0025] Where, ρ is the density of liquid metal; v is the flow rate of liquid metal;

[0026]

[0027] Among them, δ t is the thickness of the thermal boundary layer in the cross section of the pipeline fluid domain perpendicular to the flow direction; δ is the thickness of the velocity boundary layer in the cross section of the pipeline fluid domain perpendicular to the flow direction; Pr is the Prandtl number;

[0028]

[0029] Among them, μ is the dynamic viscosity of liquid metal; λ is the thermal conductivity of liquid metal.

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

[0031]

[0032] Among them, η is the mixing efficiency, σ max is the peak value of thermal inhomogeneity factor before mixing, σ s is the value of the stable thermal non-uniformity factor.

[0033] Furthermore, CAD software is used to perform parametric modeling on the high-temperature and low-flow-rate flowmeter.

[0034] Furthermore, the high-temperature and low-flow-rate flowmeter model was numerically simulated using CFD software.

[0035] Further, design variables include the arc and throat diameter of the venturi.

[0036] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: The high-temperature, low-flow rate flowmeter provided by the present invention can improve the temperature uniformity by stirring the heated liquid metal through the Venturi effect of the Venturi tube, thereby realizing the accurate measurement of the liquid metal flow under high-temperature and ultra-low flow rate conditions. The optimization method of the high-temperature, low-flow rate flowmeter provided by the present invention achieves a balance between temperature uniformity and pressure loss by optimizing the geometric parameters of the Venturi tube, thereby significantly improving the accuracy and reliability of the high-temperature, low-flow rate flowmeter. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a schematic diagram of a model of a high-temperature and low-flow-rate flowmeter provided by an embodiment of the present invention;

[0038] Figure 2 It is a flowchart of an optimization method for a high-temperature and low-flow-rate flowmeter provided by an embodiment of the present invention;

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

[0040] Figure 4 These are three representative optimal models after optimization in the embodiments of the present invention;

[0041] Figure 5 is the change of thermal inhomogeneity factor of the three optimal models and the unoptimized model at a flow rate of 0.05 m / s in the embodiment of the present invention;

[0042] Figure 6 is the change of thermal non-uniformity factor of the three optimization models under different flow rates in the embodiment of the present invention;

[0043] Figure 7 : is the pressure loss of the three optimization models at different flow rates in the embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention will be further described below in conjunction with the accompanying drawings.

[0045] like Figure 1 As shown, an embodiment of the present invention provides a high-temperature and low-flow rate flowmeter, comprising a heating tube 1 and a venturi tube 2 connected to each other, wherein a heating device is arranged outside the heating tube 1 to heat the liquid metal flowing through the heating tube 1; the venturi tube 2 makes the temperature of the heated liquid metal tend to be uniform; a temperature measuring point is arranged before the inlet of the heating tube 1 and after the outlet of the venturi tube 2, respectively, for obtaining the temperature T of the liquid metal before heating in and the temperature of the heated liquid metal T out ; The mass flow rate of liquid metal is calculated based on the following energy balance formula:

[0046]

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

[0048] In this embodiment, the heating device uses an electric heating belt, which is wound around the outside of the heating tube. The temperature measurement point uses a traditional industrial temperature sensor.

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

[0050] (1) A parametric model of a high-temperature, low-flow rate flowmeter was established using CAD software, and the geometric parameters of the venturi tube were used as design variables related to the optimization target. The model was imported into CFD (computational fluid dynamics) software for numerical simulation to obtain the optimization target value.

[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 inhomogeneity factor, wherein the thermal inhomogeneity factor is an index proposed by the present invention for quantitatively evaluating the temperature uniformity of the liquid metal after heating and mixing. The thermal inhomogeneity factor is expressed as:

[0052]

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

[0054]

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

[0056]

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

[0058]

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

[0060]

[0061] Where, ρ is the density of liquid metal; v is the flow rate of liquid metal;

[0062]

[0063] Among them, δ t is the thickness of the thermal boundary layer in the cross section of the pipeline fluid domain perpendicular to the flow direction; δ is the thickness of the velocity boundary layer in the cross section of the pipeline fluid domain perpendicular to the flow direction; Pr is the Prandtl number;

[0064]

[0065] Among them, μ is the dynamic viscosity of liquid metal; λ is the thermal conductivity of liquid metal.

[0066] 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.

[0067] (2) Taking the minimum pressure loss and the minimum thermal non-uniformity factor as the optimization objectives, the Pareto frontier optimization method is used to combine the CAD model and CFD software simulation results to perform multi-objective optimization and obtain the optimal geometric parameter solution set.

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

[0069] like Figure 3 As shown in Figure 1, each point on the boundary of the Pareto front diagram represents an optimal geometric structure. These solutions are non-dominated solutions, that is, optimizing one goal (such as reducing pressure loss) will inevitably lead to a compromise of another goal (such as thermal inhomogeneity factor).

[0070] (3) The optimal solution set is further simulated and verified through CFD software, and the geometric parameters with the minimum pressure loss and the highest mixing efficiency are selected from the optimal geometric parameter solution set.

[0071] The mixing efficiency is expressed as:

[0072]

[0073] Among them, η is the mixing efficiency, σ max is the peak value of thermal inhomogeneity factor before mixing, σ s is the value of the stable thermal non-uniformity factor.

[0074] like Figure 4 As 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 invention selects three representative optimization models from the lower left corner of the Pareto front 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] Depend on Figure 5 As shown in the figure, there is a difference in the distribution of thermal inhomogeneity factors between the three optimized models and the model without mixing strategy at a flow rate of 0.05 m / s. The flowmeter with mixing strategy can achieve a more uniform temperature distribution in a shorter flow distance, and the mixing effects of the three optimal models at a flow rate of 0.05 m / s are basically the same.

[0076] Depend on Figure 6As shown, before mixing, the thermal inhomogeneity factor increases with the increase of flow distance, which is due to the accumulation of temperature gradients caused by heating of the inner wall of the pipeline. The lower the flow rate, the higher the peak value of the thermal inhomogeneity factor, indicating that the temperature distribution of the liquid metal before mixing is very uneven. As the flow rate increases, the peak value of the thermal inhomogeneity factor gradually decreases. This shows that a higher flow rate helps to improve the uniformity of temperature distribution, because the increase in flow rate can enhance convective heat transfer, thereby homogenizing the temperature distribution faster. However, when the flow rate increases further, although the mixing area can still significantly reduce the thermal inhomogeneity factor, the peak value has been significantly reduced compared to 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 the mixing strategy is weakened. At the same time, at a flow rate of 0.01m / s, the improvement of the thermal inhomogeneity factor in the mixing area is more significant and stable, indicating that the mixing strategy based on the Venturi effect proposed in the present invention is more suitable for ultra-low flow 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 be needed to further improve temperature uniformity. Figure 6 It can also be seen that the thermal inhomogeneity factor of model 2 has stabilized just after leaving the mixing area, while models 1 and 3 still need a certain flow distance to reach a stable state. This shows that after mixing, the liquid metal still needs to go through a certain amount of mixing before it can be completely homogenized. This delay may increase the length requirement of the pipeline design. For systems with compact space or high requirements for temperature uniformity, models 1 and 3 may not be applicable.

[0077] Combination Figure 7 As can be seen from Table 1, with the increase of flow rate, 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. Combining the analysis of mixing efficiency and pressure loss, it can be seen that Model 3 sacrifices more flow resistance performance while achieving high mixing efficiency; while Model 1 slightly reduces the mixing efficiency when pursuing low pressure drop; in contrast, Model 2 achieves the best balance between pressure loss and mixing efficiency. Therefore, the optimal geometric structure of the flowmeter mixing strategy suitable for liquid metal high temperature and ultra-low flow rate conditions finally recommended by the embodiment of the present invention is Model 2, that is, Figure 4 (b) as shown.

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

[0079]

[0080] In summary, the final optimized flowmeter structure of the present invention not only achieves the minimization of pressure loss and thermal inhomogeneity factor, but also achieves the best balance between mixing 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 high temperature and low flow rate flow meter, characterized in that: The invention comprises a heating tube and a venturi tube connected to each other, wherein a heating device is arranged outside the heating tube to heat the liquid metal flowing through the heating tube; the venturi tube makes the temperature of the heated liquid metal tend to be uniform; a temperature measuring point is arranged before the inlet of the heating tube and after the outlet of the venturi tube, respectively, to obtain the temperature T of the liquid metal before heating in and the temperature of the heated liquid metal T out ; The mass flow rate of liquid metal is calculated based on the following energy balance formula: in, represents the mass flow rate of liquid metal; P represents the heating power of the heating equipment; c p Represents the specific heat capacity of liquid metal.

2. The high temperature and low flow rate flow meter according to claim 1, characterized in that: The heating device adopts an electric heating belt, which is wound around the outside of the heating tube.

3. The high temperature and low flow rate flow meter according to claim 1, characterized in that: The temperature measurement points adopt traditional industrial temperature sensors.

4. An optimization method for a high temperature and low flow rate flow meter according to claim 1, characterized in that: include: (1) Establish a parametric model of a high-temperature, low-flow rate flowmeter and use the geometric parameters of the venturi tube as design variables related to the optimization objective; The model is numerically simulated to obtain the optimization target value; the optimization target includes pressure loss and thermal inhomogeneity factor; the smaller the thermal inhomogeneity factor, the more uniform the temperature distribution of the liquid metal; the larger the thermal inhomogeneity factor, the more non-uniform the temperature distribution of the liquid metal; (2) Taking the minimum pressure loss and the minimum thermal non-uniformity factor as the optimization objectives, the optimal geometric parameter solution set is obtained by combining the model and simulation results through the Pareto frontier optimization method.

5. The optimization method according to claim 4, characterized in that: Also includes: (3) Through simulation analysis and simulation verification, the geometric parameters with the minimum pressure loss and the highest mixing efficiency are selected from the optimal geometric parameter solution set.

6. The optimization method according to claim 5, characterized in that: The thermal non-uniformity factor is expressed as: Among them, E t is the thermal inhomogeneity factor; T max is the maximum temperature; T min is the minimum temperature; A is the cross-sectional area of ​​the pipeline fluid domain perpendicular to the flow direction; T i is the local temperature of the pipe fluid domain cross section perpendicular to the flow direction based on each grid size; T ave is the average cross-sectional temperature of the pipe fluid domain perpendicular to the flow direction; in, 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 in the thermal boundary layer of the pipe fluid domain cross section perpendicular to the flow direction based on each grid size; Where r is the radius of the pipe fluid domain cross section perpendicular to the flow direction; is the distance from the center of the pipe fluid domain cross section perpendicular to the flow direction to the thermal boundary layer; Among them, T in is the flow meter inlet temperature; c p is the specific heat capacity of liquid metal; is the mass flow rate of liquid metal; Where, ρ is the density of liquid metal; v is the flow rate of liquid metal; Among them, δ t is the thickness of the thermal boundary layer in the cross section of the pipeline fluid domain perpendicular to the flow direction; δ is the thickness of the velocity boundary layer in the cross section of the pipeline fluid domain perpendicular to the flow direction; Pr is the Prandtl number; Among them, μ is the dynamic viscosity of liquid metal; λ is the thermal conductivity of liquid metal.

7. The optimization method according to claim 5, characterized in that: The mixing efficiency is expressed as: Among them, η is the mixing efficiency, σ max is the peak value of thermal inhomogeneity factor before mixing, σ s is the value of the stable thermal non-uniformity factor.

8. The optimization method according to claim 5, characterized in that: The high temperature and low flow rate flowmeter is parametrically modeled using CAD software.

9. The optimization method according to claim 5, characterized in that: The high temperature and low flow rate flowmeter model is numerically simulated using CFD software.

10. The optimization method according to claim 5, characterized in that: Design variables include the arc and throat diameter of the venturi.

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