CN113782105A - Method for analyzing flow heat transfer characteristics of liquid metal lead bismuth alloy under swinging condition - Google Patents
Method for analyzing flow heat transfer characteristics of liquid metal lead bismuth alloy under swinging condition Download PDFInfo
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Abstract
The invention discloses a method for analyzing the flow heat transfer characteristics of a liquid metal lead-bismuth alloy under a swing condition, which comprises the following steps of 1, carrying out structural parameter modeling according to a lead-bismuth alloy flow channel, inputting an initial flow field, a temperature field and a pressure field as static state calculation initial values; 2. calling a physical property relation of the lead-bismuth alloy, introducing a turbulent flow Plantt model, obtaining a flow field, a temperature field and a pressure field in a static state, and taking the flow field, the temperature field and the pressure field as working conditions of a swinging condition to calculate an initial value; 3. setting a swing condition to calculate a time step, calling a pulsating speed inlet boundary condition, and setting a pulsating amplitude and a period; 4. calling an external force field calculation function under a swinging condition, and setting a swinging amplitude and period; 5. and setting the swinging motion time, and calculating the flow and heat transfer characteristics of the lead-bismuth alloy under the swinging condition until the single time step calculation convergence and the swinging motion time reach the calculation requirement. The invention provides a method for the design and safety analysis of the lead bismuth reactor in ocean engineering application.
Description
Technical Field
The invention relates to the field of thermal hydraulic power of a lead-bismuth reactor, in particular to a method for analyzing the flow heat transfer characteristics of a liquid metal lead-bismuth alloy under a swing condition.
Background
The lead bismuth reactor refers to a reactor taking lead bismuth alloy as a coolant. Under the background of scarcity of natural resources such as land energy and the like, the ocean resources are gradually valued, and the lead bismuth reactor is considered to be widely applied to ocean engineering due to the characteristics of compact structural design, good inherent safety, good economy and the like. In a marine environment, the ship on which the lead bismuth reactor is arranged rotates, so that the lead bismuth reactor receives additional force. The flow heat transfer characteristics of the reactor coolant lead bismuth alloy under the swing condition are different from those of the reactor coolant lead bismuth alloy under the land stationary condition, and the design and safety analysis of the reactor are influenced by related thermal hydraulic engineering. Therefore, the research on the flow heat transfer characteristic of the lead-bismuth alloy under the swing condition has great significance for understanding the flow heat transfer mechanism of the lead-bismuth alloy, providing a design basis for reactor design and providing powerful support for reactor analysis software development.
At present, in the application of ocean engineering, a pressurized water reactor is a widely applied and mature reactor type. As a novel reactor, the research of various countries on the lead-bismuth reactor is still in a lasso stage. In the research on terrestrial lead bismuth stacks, many countries have conducted experimental and theoretical studies, including the study of the flow heat transfer of lead bismuth alloys in various bundle channels and other types of flow channels. However, the analysis and research on the flow heat transfer characteristics of the lead-bismuth alloy under the rocking condition are still lacked.
Disclosure of Invention
In order to make up the defects of the prior art, the invention aims to provide a method for analyzing the flow heat transfer characteristics of a liquid metal lead-bismuth alloy under a swing condition, which can construct a lead-bismuth alloy flow environment and set the physical properties of a lead-bismuth alloy working medium aiming at the characteristics of a flow channel in a lead-bismuth reactor, select a proper turbulence Plantt model, develop the thermodynamic and hydraulic calculation of the lead-bismuth alloy under a static condition and obtain the initial state of dynamic swing condition calculation; setting the boundary condition of the inlet of the flow channel according to the swing condition of the lead-bismuth stack, setting the swing amplitude, period and movement duration, and obtaining the flow heat transfer characteristic of the lead-bismuth alloy under the swing condition through a low Reynolds number turbulence model.
In order to achieve the purpose, the invention adopts the following technical scheme to implement:
a method for analyzing the flow heat transfer characteristics of a liquid metal lead-bismuth alloy under a swinging condition comprises the following steps:
step 1: establishing a lead-bismuth alloy flow channel model and inputting steady-state parameters, wherein the method comprises the steps of establishing a geometric model according to the lead-bismuth alloy flow channel, and inputting an initial temperature field, a velocity field and a pressure field of the flow channel according to the running parameters of a lead-bismuth reactor to serve as static and steady-state calculation initial values;
step 2: calling a physical property relation of the lead-bismuth alloy, calling a turbulent flow Prandtl model, starting a Reynolds stress turbulence model in a computational fluid mechanics program, carrying out static thermal hydraulic calculation of the liquid metal lead-bismuth, and converging a to-be-calculated residual curve to 10-5Then obtaining a temperature field, a velocity field and a pressure field in the flow channel as initial values for calculating the flow heat transfer of the lead-bismuth alloy under the condition of swinging motion;
the method comprises the following steps of (1) introducing a lead-bismuth alloy physical property relational expression optimization calculation in consideration of the influence of physical property setting of the liquid lead-bismuth alloy on the flow and heat exchange of the liquid lead-bismuth alloy; the physical property relation of the liquid lead-bismuth alloy is as follows:
ρLBE＝11096-1.3236T (1)
Cp,LBE＝159-2.72×10-2T+7.12×10-6T2 (2)
λLBE＝3.61+1.517×10-2T-1.741×10-6T2 (3)
in the formula:
ρLBEdensity of Pb-Bi alloy/kg-m-3
T-temperature of lead bismuth alloy/K
Cp,LBE-lead bismuth alloy heat capacity/J.K-1
λLBE-lead bismuth alloy thermal conductivity/W.m-1·K-1
μLBE-dynamic viscosity/Ns.m of lead bismuth alloy-2
Introducing a turbulent flow Plantt model for optimizing and simulating the turbulent heat exchange process of the liquid lead-bismuth alloy in the lead-bismuth alloy:
turbulent plangtian model:
in the formula:
Prt-turbulent Plantt number
PetTurbulent Peclet number
vt-turbulent viscosity/pas
v-viscosity/pas
Pr-Plantt number
Alpha-thermal diffusivity per m2·s-1
And step 3: setting unit time step length calculated by the swing condition, calling a pulse speed inlet boundary condition, and setting the inlet boundary condition of the lead-bismuth alloy flow channel as sinusoidal pulse flow fluctuation so as to simulate system flow fluctuation of the lead-bismuth reactor under the swing condition. Setting the pulse amplitude and period at the same time;
the pulse speed adopts a sine form, and system flow fluctuation of the lead-bismuth reactor under the swinging condition is simulated, and is expressed as follows:
in the formula:
uminlet boundary pulsating speed
us-flow rate of lead bismuth alloy of lead bismuth reactor system under static condition
AuAmplitude of pulsation
T1-pulse period
t-time of rocking movement
And 4, step 4: calling the calculation function of the additional external force field of the lead-bismuth alloy under the condition of the swinging motion, calculating the additional external force applied to the lead-bismuth alloy, and setting the amplitude and the period of the swinging motion;
when the ship loading the reactor system is in a marine environment, the ship non-inertial system can translate and rotate relative to the inertial system; the additional external force generated due to the rocking motion at this time can be expressed as follows
Fa＝ρa＝ρ(acen+at+aC)＝-ρ[α×(α×r)+β×r+2α×ur] (8)
In the formula:
Fa-additional external force
Rho-density of Pb-Bi alloy
a-total additional acceleration
acenCentripetal acceleration
at-tangential acceleration
aC-coriolis acceleration
Alpha-rocking angular velocity
Beta-rocking angular acceleration
Coordinates of r-Pb-Bi alloy fluid particles
urFlow velocity of fluid particles of lead bismuth alloy
The rocking angle, angular velocity and angular acceleration are set to trigonometric forms. For a vertical lead bismuth alloy flow channel, considering the influence of gravity, the lateral additional external force perpendicular to the flow direction can be expressed as follows:
in the formula:
Rho-density of Pb-Bi alloy
y ', z' -non-inertial coordinate system coordinates
Theta-rocking angle
θmaxAmplitude of rocking motion
T2Period of rocking motion
t-time of rocking movement
Angular velocity of alpha-rocking motion
Angular acceleration of beta-roll motion
And 5: setting the swinging time, and calculating the flow and heat transfer characteristics of the lead-bismuth alloy under the swinging condition; if the calculation residual continuously fluctuates and the calculation cannot be converged, the unit time step length needs to be adjusted and the calculation is restarted; if the calculated residual tends to be stable and does not fluctuate any more, the calculation is shown to be convergent, and whether the swing motion time length meets the calculation requirement or not is judged at the moment; if the swing calculation time length meets the calculation requirement, stopping the calculation, and obtaining the calculation result of the flow heat transfer of the lead-bismuth alloy under the swing motion condition; otherwise, increasing a unit time step, taking the last time step calculation result as an initial condition, and continuing to calculate the flow heat transfer characteristics of the lead-bismuth alloy under the swinging condition until the swinging movement time length reaches the calculation requirement.
Compared with the prior art, the invention has the following advantages:
1. the analysis method can solve the flow heat transfer characteristic of the lead-bismuth alloy under the condition of swinging, and fills the existing calculation blank;
2. the analysis method of the invention adds a swing condition additional force model and a turbulence Plantt model, and can more accurately calculate the coolant flow characteristic and the heat transfer characteristic of the flow channel of the lead-bismuth reactor under the swing motion condition.
3. The method can be used for modeling according to an actual flow channel, inputting the amplitude, the period and the movement duration of the swinging motion according to the actual condition of the swinging motion, and inputting the boundary condition of the flow channel according to the actual flow fluctuation of the system caused by the swinging motion, thereby ensuring the calculation accuracy of the flow heat transfer of the lead-bismuth alloy.
Drawings
FIG. 1 is a block diagram of the computational process of the present invention.
FIG. 2 is a schematic diagram of the rocking motion of the circular tube channel.
FIG. 3 is a diagram of the change of the Nurseel number of the dimensionless heat exchange coefficient of a certain section of the lead bismuth alloy in the rocking time length under a certain rocking motion condition.
Detailed Description
The process of the present invention is described in further detail below with reference to the accompanying drawings and the detailed description:
as shown in FIG. 1, the method for analyzing the flow heat transfer characteristics of the liquid metal lead-bismuth alloy under the condition of swing comprises the following steps:
step 1: the method comprises the steps of establishing a lead-bismuth alloy flow channel model and inputting steady-state parameters, wherein the steps of establishing a geometric model according to the lead-bismuth alloy flow channel, inputting an initial temperature field, a velocity field and a pressure field of the flow channel according to the running parameters of a lead-bismuth reactor, and using the initial temperature field, the velocity field and the pressure field as static and steady-state calculation initial values.
Step 2: calling a physical property relation of the lead-bismuth alloy, calling a turbulent flow Prandtl model, starting a Reynolds stress turbulence model in a computational fluid mechanics program, carrying out static thermal hydraulic calculation of the liquid metal lead-bismuth, and converging a to-be-calculated residual curve to 10-5And then obtaining a temperature field, a velocity field and a pressure field in the flow channel as initial values for calculating the flow heat transfer of the lead-bismuth alloy under the condition of swinging motion.
The method comprises the following steps of (1) introducing physical property relational expression optimization calculation of the lead-bismuth alloy in consideration of the influence of physical property setting of the liquid lead-bismuth alloy on flow and heat exchange of the liquid lead-bismuth alloy; the physical property relation of the liquid lead-bismuth alloy is as follows:
ρLBE＝11096-1.3236T (1)
Cp,LBE＝159-2.72×10-2T+7.12×10-6T2 (2)
λLBE＝3.61+1.517×10-2T-1.741×10-6T2 (3)
in the formula:
ρLBEdensity of Pb-Bi alloy/kg-m-3
T-temperature of lead bismuth alloy/K
Cp,LBE-lead bismuth alloy heat capacity/J.K-1
λLBE-lead bismuth alloy thermal conductivity/W.m-1·K-1
μLBE-dynamic viscosity/Ns.m of lead bismuth alloy-2
Introducing a turbulent flow Plantt model for optimizing and simulating the turbulent heat exchange process of the liquid lead-bismuth alloy in the lead-bismuth alloy:
turbulent plangtian model:
in the formula:
Prt-turbulent Plantt number
PetTurbulent Peclet number
vt-turbulent viscosity/pas
v-viscosity/pas
Pr-Plantt number
Alpha-thermal diffusivity per m2·s-1
And step 3: setting unit time step length calculated by the swing condition, calling a pulse speed inlet boundary condition, and setting the inlet boundary condition of the lead-bismuth alloy flow channel as sinusoidal pulse flow fluctuation so as to simulate system flow fluctuation of the lead-bismuth reactor under the swing condition. The pulse amplitude and period are set simultaneously.
The pulse speed adopts a sine form, and system flow fluctuation of the lead-bismuth reactor under the swinging condition is simulated, and is expressed as follows:
in the formula:
uminlet boundary pulsating speed
us-flow rate of lead bismuth alloy of lead bismuth reactor system under static condition
AuAmplitude of pulsation
T1-pulse period
t-time of rocking movement
And 4, step 4: and calling the calculation function of the additional external force field of the lead-bismuth alloy under the condition of the swinging motion, calculating the additional external force applied to the lead-bismuth alloy, and setting the amplitude and the period of the swinging motion.
When the vessel carrying the reactor system is in a marine environment, the vessel non-inertial system translates and rotates relative to the inertial system. The additional external force generated due to the rocking motion at this time can be expressed as follows
Fa＝ρa＝ρ(acen+at+aC)＝-ρ[α×(α×r)+β×r+2α×ur] (8)
In the formula:
Fa-additional external force
Rho-density of Pb-Bi alloy
a-total additional acceleration
acenCentripetal acceleration
at-tangential acceleration
aC-coriolis acceleration
Alpha-rocking angular velocity
Beta-rocking angular acceleration
Coordinates of r-Pb-Bi alloy fluid particles
urFlow velocity of fluid particles of lead bismuth alloy
The rocking angle, angular velocity and angular acceleration are set to trigonometric forms. For a vertical lead bismuth alloy flow channel, considering the influence of gravity, the lateral additional external force perpendicular to the flow direction can be expressed as follows:
in the formula:
Rho-density of Pb-Bi alloy
y ', z' -non-inertial coordinate system coordinates
Theta-rocking angle
θmaxAmplitude of rocking motion
T2Period of rocking motion
t-time of rocking movement
Angular velocity of alpha-rocking motion
Angular acceleration of beta-roll motion
And 5: and setting the swinging motion time, and calculating the flow and heat transfer characteristics of the lead-bismuth alloy under the swinging condition. If the calculation residual continuously fluctuates and the calculation cannot be converged, the unit time step length needs to be adjusted and the calculation is restarted; if the calculated residual tends to be stable and does not fluctuate any more, the calculation is shown to be convergent, and whether the swing motion time length meets the calculation requirement or not is judged at the moment; if the swing calculation time length meets the calculation requirement, stopping the calculation, and obtaining the calculation result of the flow heat transfer of the lead-bismuth alloy under the swing motion condition; otherwise, increasing a unit time step, taking the last time step calculation result as an initial condition, and continuing to calculate the flow heat transfer characteristics of the lead-bismuth alloy under the swinging condition until the swinging movement time length reaches the calculation requirement.
The effect of the present invention is described below with reference to a specific calculation object, taking the schematic diagram of the circular tube channel swinging motion shown in fig. 2 as an example, first, through step 1, a geometric model is established according to the lead-bismuth alloy flow channel, which is exemplified as a circular tube channel, and an initial temperature field, a velocity field and a pressure field of the flow channel are input according to the operating parameters of the lead-bismuth reactor, which are used as initial values for static and steady state calculation; calling a physical property relation of the lead-bismuth alloy according to the step 2, calling a turbulence Prandtl model, and starting a Reynolds stress turbulence model to obtain a temperature field, a velocity field and a pressure field in the flow channel; setting the calculated unit time step length according to the step 3, and calling a pulsating speed inlet boundary condition; calling the function of calculating the additional external force field of the lead-bismuth alloy under the condition of swinging motion according to the step 4, and calculating the additional external force applied to the lead-bismuth alloy; setting the swinging motion time according to the step 5, calculating the flowing and heat transfer characteristics of the lead-bismuth alloy under the swinging condition, outputting the cloud pictures of the flow field and the temperature field in the flow channel under the swinging condition, and the overall and local flow resistance characteristics and heat transfer characteristics of the flow channel, wherein fig. 3 shows the change picture of the Nossel number of the dimensionless heat exchange coefficient of the local section of the fully developed section of the flow channel in the swinging time. The calculation analysis method is helpful for evaluating the influence of an external force field caused by swing on the flow heat transfer characteristic of the lead-bismuth alloy, and provides a research basis for the application of the lead-bismuth cooling reactor in ocean engineering.
Claims (1)
1. A method for analyzing the flow heat transfer characteristics of a liquid metal lead-bismuth alloy under a swing condition is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a lead-bismuth alloy flow channel model and inputting steady-state parameters, wherein the method comprises the steps of establishing a geometric model according to the lead-bismuth alloy flow channel, and inputting an initial temperature field, a velocity field and a pressure field of the flow channel according to the running parameters of a lead-bismuth reactor to serve as static and steady-state calculation initial values;
step 2: calling a physical property relation of the lead-bismuth alloy, calling a turbulent flow Prandtl model, starting a Reynolds stress turbulence model in a computational fluid mechanics program, carrying out static thermal hydraulic calculation of the liquid metal lead-bismuth, and converging a to-be-calculated residual curve to 10-5Then obtaining a temperature field, a velocity field and a pressure field in the flow channel as initial values for calculating the flow heat transfer of the lead-bismuth alloy under the condition of swinging motion;
the method comprises the following steps of (1) introducing a lead-bismuth alloy physical property relational expression optimization calculation in consideration of the influence of physical property setting of the liquid lead-bismuth alloy on the flow and heat exchange of the liquid lead-bismuth alloy; the physical property relation of the liquid lead-bismuth alloy is as follows:
ρLBE＝11096-1.3236T (1)
Cp,LBE＝159-2.72×10-2T+7.12×10-6T2 (2)
λLBE＝3.61+1.517×10-2T-1.741×10-6T2 (3)
in the formula:
ρLBEdensity of Pb-Bi alloy/kg-m-3
T-temperature of lead bismuth alloy/K
Cp,LBE-lead bismuth alloy heat capacity/J.K-1
λLBE-lead bismuth alloy thermal conductivity/W.m-1·K-1
μLBE-dynamic viscosity/Ns.m of lead bismuth alloy-2
Introducing a turbulent flow Plantt model for optimizing and simulating the turbulent heat exchange process of the liquid lead-bismuth alloy in the lead-bismuth alloy:
turbulent plangtian model:
in the formula:
Prt-turbulent Plantt number
PetTurbulent Peclet number
vt-turbulent viscosity/Pa·s
v-viscosity/pas
Pr-Plantt number
Alpha-thermal diffusivity per m2·s-1
And step 3: setting unit time step length calculated by a swing condition, calling a pulse speed inlet boundary condition, setting the inlet boundary condition of a lead-bismuth alloy flow channel as sinusoidal pulse flow fluctuation so as to simulate system flow fluctuation of a lead-bismuth reactor under the swing condition, and setting pulse amplitude and period;
the pulse speed adopts a sine form, and system flow fluctuation of the lead-bismuth reactor under the swinging condition is simulated, and is expressed as follows:
in the formula:
uminlet boundary pulsating speed
us-flow rate of lead bismuth alloy of lead bismuth reactor system under static condition
AuAmplitude of pulsation
T1-pulse period
t-time of rocking movement
And 4, step 4: calling the calculation function of the additional external force field of the lead-bismuth alloy under the condition of the swinging motion, calculating the additional external force applied to the lead-bismuth alloy, and setting the amplitude and the period of the swinging motion;
when the ship loading the reactor system is in a marine environment, the ship non-inertial system can translate and rotate relative to the inertial system; the additional external force generated due to the rocking motion at this time is expressed as follows
Fa＝ρa＝ρ(acen+at+aC)＝-ρ[α×(α×r)+β×r+2α×ur] (8)
In the formula:
Fa-additional external force
Rho-density of Pb-Bi alloy
a-total additional acceleration
acenCentripetal acceleration
at-tangential acceleration
aC-coriolis acceleration
Alpha-rocking angular velocity
Beta-rocking angular acceleration
Coordinates of r-Pb-Bi alloy fluid particles
urFlow velocity of fluid particles of lead bismuth alloy
The swing angle, the angular velocity and the angular acceleration are set to be in the form of trigonometric functions, and for a vertical lead-bismuth alloy flow channel, the influence of gravity is considered, and the transverse additional external force perpendicular to the flow direction is expressed as follows:
in the formula:
Rho-density of Pb-Bi alloy
y ', z' -non-inertial coordinate system coordinates
Theta-rocking angle
θmaxAmplitude of rocking motion
T2Period of rocking motion
t-time of rocking movement
Angular velocity of alpha-rocking motion
Angular acceleration of beta-roll motion
And 5: setting the swinging time, and calculating the flow and heat transfer characteristics of the lead-bismuth alloy under the swinging condition; if the calculation residual continuously fluctuates and the calculation cannot be converged, the unit time step length needs to be adjusted and the calculation is restarted; if the calculated residual tends to be stable and does not fluctuate any more, the calculation is shown to be convergent, and whether the swing motion time length meets the calculation requirement or not is judged at the moment; if the swing calculation time length meets the calculation requirement, stopping the calculation, and obtaining the calculation result of the flow heat transfer of the lead-bismuth alloy under the swing motion condition; otherwise, increasing a unit time step, taking the last time step calculation result as an initial condition, and continuing to calculate the flow heat transfer characteristics of the lead-bismuth alloy under the swinging condition until the swinging movement time length reaches the calculation requirement.
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| CN115577583A (en) * | 2022-09-06 | 2023-01-06 | 西安交通大学 | Analysis method for flow-induced vibration of lead-based reactor wire winding positioning fuel rod |
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| CN115994495A (en) * | 2022-11-24 | 2023-04-21 | 西安交通大学 | Calculation method for flow heat transfer characteristics of liquid metal lead bismuth in loop system under motion condition |
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