A method and device for calculating the onset of film boiling with a fouled surface

Abstract

The application discloses a method and device for calculating a film boiling start point of a fuel rod with a contaminated surface, and belongs to the field of nuclear power. The method comprises the following steps: establishing a surface heat exchange model of the fuel rod with the contaminated surface according to a fuel rod cladding model with the contaminated surface and thermal parameters, and calculating a heat conduction coefficient and a permeability of the contaminated area; calculating a gas film thickness of the film boiling start; and calculating a minimum value of the gas film thickness according to a pressure balance and an energy conservation equation, and taking the minimum value as a film boiling start heat flux density. The method can accurately calculate the film boiling start heat flux density under the influence of the contamination, and improve the accuracy of a systematic analysis of the influence of the contamination on the thermal hydraulic performance of the reactor.

Description

Technical Field

[0001] This invention belongs to the field of nuclear power, specifically relating to a method and apparatus for calculating the initiation point of film boiling on a fouled surface. Background Technology

[0002] During long-term operation of pressurized water reactor nuclear power plants, fouling gradually accumulates on the fuel cladding surface, altering its heat exchange characteristics and consequently affecting boiling heat transfer behavior. Currently, research on film boiling processes on fouled surfaces is insufficient, and analysis of the impact of fouling on reactor thermal-hydraulic characteristics using heat transfer models cannot accurately predict different boiling conditions. Therefore, providing a method for calculating the initiation point of film boiling on fouled surfaces is of significant importance for improving the analysis of the impact of fouling on reactor thermal-hydraulic characteristics. Summary of the Invention

[0003] The purpose of this invention is to provide a method for calculating the initiation point of film boiling on fouled surfaces, thereby improving the accuracy of the analysis of the thermal-hydraulic characteristics of fouled surfaces. This invention also provides a calculation device.

[0004] According to one embodiment of the present invention, a method for calculating the initiation point of film boiling on a contaminated surface is provided, the method comprising the following steps:

[0005] Step a): Provide a fouled fuel rod cladding model and thermal parameters, establish a fouled fuel rod cladding surface heat transfer model based on the fouled fuel rod cladding model and thermal parameters, and calculate the thermal conductivity and permeability of the fouled region based on the fractal theory and the fouled fuel rod cladding surface heat transfer model.

[0006] Step b): Establish a steam chimney model and calculate the film thickness at the start of film boiling based on the diameter of the steam chimney;

[0007] Step c): Calculate the heat flux density corresponding to the minimum gas film thickness based on the pressure balance and energy conservation equations, and use it as the initial heat flux density for film boiling.

[0008] Furthermore, in some embodiments, in step a), the fouled fuel rod cladding model includes fouling thickness, fouling porosity, maximum pore diameter, minimum pore diameter, and fouling solid-phase thermal conductivity; the thermal parameters include mainstream fluid temperature, mainstream fluid velocity, operating pressure, and hydraulic diameter.

[0009] Furthermore, in some embodiments, in step a), the thermal conductivity k of the fouled area is... fractal The calculation method is as follows:

[0010] ;

[0011] The method for calculating the permeability K of the fouled area is as follows:

[0012] ;

[0013] Where, k series k is the equivalent thermal conductivity of the fouling series connection. p Let be the equivalent thermal conductivity of the fractal parallel fouling, Φ be the porosity of the fouling, and D be the equivalent thermal conductivity of the fractal parallel fouling. f Let D be the fractal dimension of the pore volume. T Let λ be the fractal dimension of the tortuous capillary path of the dirt. max This represents the maximum pore diameter.

[0014] Furthermore, in some embodiments, in step b), the steam chimney model includes a steam chimney diameter and a steam chimney inclination angle.

[0015] Furthermore, in some embodiments, in step b), the gas film thickness δ v The calculation method is as follows:

[0016] δ v =d ch· sinθ

[0017] Where d ch Let θ be the diameter of the steam chimney, and θ be the inclination angle of the steam chimney.

[0018] Furthermore, in some embodiments, the method for calculating the initial heat flux density q of film boiling is as follows:

[0019] ;

[0020] Where, q b For boiling heat transfer heat flux density,

[0021] ;

[0022] σ(T) is the surface tension of the liquid at temperature T, h lv The latent heat of vaporization of water, λ is the dirt contact angle. max v is the maximum pore diameter l v is the kinematic viscosity of the liquid. v Where is the vapor kinematic viscosity, K is the fouling permeability, L is the fouling thickness, and δ is the fouling viscosity. v f represents the thickness of the vapor film within the fouling layer. ch The area of ​​the fouled steam chimney is the percentage of the total area, d is the length of steam escaping along the gas film, θ is the tilt angle of the steam chimney, and T is the total area of ​​the fouled steam chimney. sat T is the liquid saturation temperature. b The temperature of the mainstream fluid is given, h0 is the heat transfer coefficient of the fouling surface, and u is the temperature of the mainstream fluid.f For the dynamic viscosity of the liquid, α m α is the thermal diffusivity of the dirt. m =k fractal / ρc pf ρ is the dirt density, c pf This refers to the specific heat capacity of the dirt.

[0023] Furthermore, in some embodiments, the dirt thickness L, the dirt porosity Φ, and the maximum pore diameter λ are further specified. max Steam chimney diameter d ch Steam chimney inclination angle θ, and equivalent thermal conductivity k of fouling in series. series The equivalent thermal conductivity k of the parallel fractal of the dirt p Mainstream fluid temperature T b Measurements were taken through experiments.

[0024] According to another aspect of the present invention, a computing device is provided, the computing device including a memory and a processor, wherein the memory stores a program for calculating the initiation point of film boiling on a fouled surface, and when the program for calculating the initiation point of film boiling on a fouled surface is executed by the processor, the method for calculating the initiation point of film boiling on a fouled surface provided in any of the foregoing embodiments can be implemented. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the nucleus boiling state in one embodiment;

[0026] Figure 2 This is a schematic diagram of the nucleus boiling critical point state in one embodiment;

[0027] Figure 3 This is a schematic diagram of heat transfer within the fouling in one embodiment.

[0028] The meanings of the reference numerals in the attached diagram are as follows: 1-Fouling unit; 2-Bubbles; 3-Steam chimney; 4-Fouling; 5-Fuel rod cladding.

[0029] The purpose of the above-described drawings is to provide a detailed description of the present invention so that those skilled in the art can understand the technical concept of the invention, and is not intended to limit the invention. For the sake of brevity, the above-described drawings only schematically depict the structures related to the technical features of the present invention, and do not depict the complete structure and all details strictly according to actual scale. Detailed Implementation

[0030] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings.

[0031] The term "embodiment" as used herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment herein. The phrase appearing in various places in the specification does not necessarily refer to the same embodiment, nor is it limited to mutually exclusive, independent, or alternative embodiments. Those skilled in the art will understand that the embodiments herein can be combined with other embodiments without causing structural conflicts.

[0032] In this article, "multiple" means at least two.

[0033] During nuclear power plant operation, the high-temperature and high-pressure environment of the primary coolant inevitably leads to the dissolution of metal ions such as Fe and Ni. Combined with components already present in the primary coolant, such as LiOH and H3BO3, these ions accumulate on the fuel rod cladding surface over time. The presence of this fouling layer affects the heat transfer performance of the fuel rod cladding surface, thus influencing boiling heat transfer behavior and potentially leading to film boiling, increasing the risk of accidents. However, current research lacks sufficient information on the occurrence of film boiling in the presence of a fouling layer. This makes it difficult to accurately determine the initiation point of film boiling in the presence of a fouling layer, hindering the accurate prediction of different boiling conditions using relevant physical models when analyzing the impact of fouling on reactor thermal-hydraulic characteristics. This restricts further improvements in the safety management of pressurized water reactor nuclear power plants.

[0034] To address the aforementioned problems, one embodiment of the present invention provides a method for calculating the initiation point of film boiling on a fouled surface, so as to accurately predict the heat flux density when film boiling occurs on the cladding surface of a fuel rod with fouling deposits, thereby providing a basis for determining the node of boiling condition transition on a fouled surface.

[0035] Specifically, the method includes the following steps:

[0036] Step a): Provide a fouled fuel rod cladding model and relevant thermal parameters, and establish a surface heat transfer model of the fouled fuel rod cladding based on the fouled fuel rod cladding model and thermal parameters. The fouled fuel rod cladding model is as follows: Figure 1 , Figure 3 As shown, fouling 4 is deposited on the surface of the fuel rod cladding 5. The uncovered areas of the fuel rod cladding 5 form porous steam chimneys 3. Because the heat exchange conditions in the steam chimneys 3 are better than in the area containing fouling 4, bubbles 2 preferentially form within the steam chimneys 3. The fouling unit 1 containing the steam chimneys 3 is used as the basic analytical unit. Arrow a represents coolant flow, arrow b represents the steam flow after coolant vaporization on the surface of the fuel rod cladding 5, and arrow c represents the flow process of steam accumulating on the surface of the fuel rod cladding 5 and leaving the surface of the fuel rod cladding 5.

[0037] In the calculation process of this invention embodiment, the permeability K and thermal conductivity k of the fouling are first determined based on fractal theory and heat transfer model. fractal .

[0038] Specifically,

[0039] ;

[0040] .

[0041] Where, k series k is the equivalent thermal conductivity of the fouling series connection. p Let be the equivalent thermal conductivity of the fractal parallel fouling, Φ be the porosity of the fouling, and D be the equivalent thermal conductivity of the fractal parallel fouling. f Let D be the fractal dimension of the pore volume. T Let λ be the fractal dimension of the tortuous capillary path of the dirt. max This is the maximum pore diameter.

[0042] By cutting samples from the fuel rod cladding under given operating conditions, the fouling thickness L, fouling porosity Φ, and maximum pore diameter λ can be measured and determined using an optical microscope or a scanning electron microscope. max Steam chimney diameter d ch 1. Steam chimney inclination angle θ; 2. Mainstream fluid temperature T under test conditions. b D is obtained through thermocouple measurements; the measurement results, combined with fractal theory and public databases, can be further calculated to obtain D. f D T k series and k p The mainstream fluid velocity, operating pressure, and hydraulic diameter in the thermal parameters can be determined based on the specific operating conditions being simulated.

[0043] Step b): Establish a steam chimney model and calculate the film thickness δ at the onset of film boiling. v .

[0044] Based on the structural characteristics of the fouling unit 1, the calculation process in this embodiment of the invention assumes that the steam chimney 3 will restrict the growth of the bubble 2, combined with... Figure 2 Assuming that a thinnest vapor film exists at the beginning of film boiling, the thickness of the vapor film is δ. v With the diameter d of bubble 2 b Quite, d b It can be based on the diameter d of the steam chimney 3 ch The angle θ of the steam chimney is calculated and determined, i.e., δ v =d ch· sinθ.

[0045] Step c): Calculate the heat flux density corresponding to the minimum gas film thickness based on the pressure balance and energy conservation equations, and use it as the initial heat flux density for film boiling.

[0046] First, calculate the heat flux density q during boiling heat transfer. b :

[0047] ;

[0048] Combination Figure 3 In the formula, L-δ v =δ f .

[0049] Further calculations yielded the initial heat flux density for film boiling:

[0050] .

[0051] Where σ(T) is the surface tension of the liquid at temperature T, h lv The latent heat of vaporization of water, λ is the dirt contact angle. max v is the maximum pore diameter l v is the kinematic viscosity of the liquid. v Where is the vapor kinematic viscosity, K is the fouling permeability, L is the fouling thickness, and δ is the fouling thickness. v f represents the thickness of the vapor film within the fouling layer. ch The area of ​​the fouled steam chimney is the percentage of the total area, d is the length of steam escaping along the gas film, θ is the angle of inclination of the steam chimney, and T is the total area of ​​the fouled steam chimney. sat T is the liquid saturation temperature. b The temperature of the mainstream fluid is given, h0 is the heat transfer coefficient of the fouling surface, and u is the temperature of the mainstream fluid. f For the dynamic viscosity of the liquid, α m α is the thermal diffusivity of the dirt. m =k fractal / ρc pf ρ is the dirt density, c pf This refers to the specific heat capacity of the dirt.

[0052] Among them, the kinematic viscosity of the liquid v l , where v is the kinematic viscosity of steam. v Liquid saturation temperature T sat , Heat transfer coefficient of dirt surface h0, Dynamic viscosity of liquid u f ρ of dirt density and c of dirt specific heat capacity pf It can be obtained by querying relevant databases.

[0053] The method for calculating the starting point of film boiling on a contaminated surface provided in the above embodiments can be implemented using the computing device provided in another embodiment of the present invention.

[0054] The computing device includes a memory and a processor, wherein the memory stores a program for calculating the initiation point of film boiling on a dirt-covered surface; when the processor executes the program, it obtains the various parameters required for the calculation process through manual input or automatic retrieval by the system, and can implement the method for calculating the initiation point of film boiling on a dirt-covered surface provided in the above embodiments, and make an accurate prediction of the heat flux density at the moment when film boiling occurs on a dirt-covered surface.

[0055] The method for calculating the initiation point of film boiling on fouled surfaces provided in this invention is based on fractal theory and heat transfer model, combined with the steam chimney structure characteristics of the fouled surface. By establishing a reasonable physical model, it can accurately simulate and calculate the heat transfer process of the critical state of film boiling, thereby obtaining an accurate initiation point of film boiling on fouled surfaces, improving the accuracy of the analysis of the impact of fouling on the thermal-hydraulic characteristics of reactors, and improving the safety design and safety management level of pressurized water reactor nuclear power plants.

[0056] The purpose of the above embodiments is to provide a more detailed description of the present invention in conjunction with the accompanying drawings, so that those skilled in the art can understand the technical concept of the present invention. Within the scope of the present invention, any optimization or equivalent substitution of the technical features involved falls within the protection scope of the present invention.

Claims

1. A method for calculating the initiation point of film boiling on a contaminated surface, characterized in that, Includes the following steps: Step a): Provide a fouled fuel rod cladding model and thermal parameters. Based on the fouled fuel rod cladding model and the thermal parameters, establish a surface heat transfer model for the fouled fuel rod cladding. Calculate the thermal conductivity and permeability of the fouled region based on fractal theory and the surface heat transfer model. The fouled fuel rod cladding model includes fouling thickness, fouling porosity, maximum pore diameter, minimum pore diameter, and the thermal conductivity of the fouling solid phase. The thermal parameters include mainstream fluid temperature, mainstream fluid velocity, operating pressure, and hydraulic diameter. The thermal conductivity k of the fouled region... fractal The calculation method is as follows: ； The method for calculating the permeability K of the fouled area is as follows: ； Where, k series k is the equivalent thermal conductivity of the fouling series connection. p Let be the equivalent thermal conductivity of the fractal parallel fouling, Φ be the porosity of the fouling, and D be the equivalent thermal conductivity of the fractal parallel fouling. f Let D be the fractal dimension of the pore volume. T Let λ be the fractal dimension of the tortuous capillary path of the dirt. max Maximum pore diameter; Step b): Establish a steam chimney model and calculate the film thickness at the start of film boiling based on the diameter of the steam chimney; the steam chimney model includes the steam chimney diameter and the steam chimney inclination angle, and the film thickness δ. v The calculation method is as follows: d v =d ch· sinθ, Where d ch Where θ is the diameter of the steam chimney, and θ is the inclination angle of the steam chimney; Step c): Based on the pressure balance and energy conservation equations, calculate the heat flux density corresponding to the minimum gas film thickness, which is used as the initial heat flux density for film boiling. The calculation method for the initial heat flux density q for film boiling is as follows: ； Where, q b For boiling heat transfer heat flux density, ； σ(T) is the surface tension of the liquid at temperature T, h lv The latent heat of vaporization of water, λ is the dirt contact angle. max v is the maximum pore diameter l v is the kinematic viscosity of the liquid. v Where is the vapor kinematic viscosity, K is the fouling permeability, L is the fouling thickness, and δ is the fouling thickness. v f represents the thickness of the vapor film within the fouling layer. ch The area of ​​the fouled steam chimney is the percentage of the total area, d is the length of steam escaping along the gas film, θ is the angle of inclination of the steam chimney, and T is the total area of ​​the fouled steam chimney. sat T is the liquid saturation temperature. b The temperature of the mainstream fluid is given, h0 is the heat transfer coefficient of the fouling surface, and u is the temperature of the mainstream fluid. f For the dynamic viscosity of the liquid, α m α is the thermal diffusivity of the dirt. m =k fractal / ρc pf ρ is the dirt density, c pf This refers to the specific heat capacity of the dirt.

2. The method for calculating the starting point of film boiling on a contaminated surface according to claim 1, characterized in that, Fouling thickness L, fouling porosity Φ, maximum pore diameter λ max Steam chimney diameter d ch Steam chimney inclination angle θ, and equivalent thermal conductivity k of fouling in series. series The equivalent thermal conductivity k of the parallel fractal of the dirt p Mainstream fluid temperature T b Measurements were taken through experiments.

3. A computing device, comprising a memory and a processor, characterized in that, The memory stores a program for calculating the initiation point of film boiling on a fouled surface. When the processor executes the program for calculating the initiation point of film boiling on a fouled surface, the method for calculating the initiation point of film boiling on a fouled surface as described in any one of claims 1 or 2 can be implemented.

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