CN110060788A - A kind of general thermion nuclear reactor for space power supply thermal transient Analysis of Electrical Characteristics method - Google Patents
A kind of general thermion nuclear reactor for space power supply thermal transient Analysis of Electrical Characteristics method Download PDFInfo
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Abstract
A kind of general thermion nuclear reactor for space reactor core transient state pyroelecthc properties comprehensive analysis method, key step is as follows: 1, determining thermion nuclear reactor for space core structure and initial parameter 2, calculate current time thermion nuclear reactor for space core temperature distribution 3, the potential on calculating current time heap core electrode and current distribution 4, calculate current time reactor core output voltage, output electric current, electromotive power output 5, according to all known conditions, the calculating that step 2 carries out subsequent time is jumped to, cycle calculations are until reaching stable state；Method of the invention can calculate interchangeable heat ion space nuclear reactor power supply transient state pyroelecthc properties, and the available more accurate calculated result when calculating.
Description
Technical field
The present invention relates to nuclear reactor for space field of power supplies, and in particular to a kind of general thermion nuclear reactor for space heap
Core transient state pyroelecthc properties comprehensive analysis method
Background technique
With space exploration task demand be continuously increased and solar energy and chemical cell are in deep space mission or planet table
The space power producer of limitation in the task of face, technology maturation and high reliablity is following the main direction of development.Heat
Ion space nuclear reactor power supply is a kind of current research nuclear reactor for space power supply the most mature, and the U.S. and Russia are upper
The nineties in century has carried out a large amount of research work.Up to the present, Russia is still carrying out high-power thermion nuclear reactor
The research work of power supply.
Nuclear reactor for space is studied in the world at present, can all consider influence of the pyroelecthc properties to system substantially.It is international
On carried out the related pyroelecthc properties research of a large amount of thermion spaces heap, these researchs are broadly divided into two classes, and one kind is using examination
Proved recipe method measures the pyroelecthc properties of thermion nuclear reactor for space power supply, and one kind is anti-to thermion space core using theoretical model
Heap power supply is answered to be analyzed, but most experimental and theoretical analysis is all based on single thermionic fuel element in heap and carries out
, and focus on stable state pyroelecthc properties more.In order to determine the influence of reactor core transient state pyroelecthc properties, thermal-hydraulic is established to reactor core
Model, heat and power system model, thus for more fully and effectively assess thermion nuclear reactor for space pyroelecthc properties provide according to
According to.
Summary of the invention
In order to overcome the above-mentioned problems of the prior art, the purpose of the present invention is to provide a kind of general thermion is empty
Between nuclear reactor transient state pyroelecthc properties comprehensive analysis method, general thermion nuclear reactor for space entirety reactor core is carried out
Research, can accurately reflect the pyroelecthc properties of full heap, the thermion space nuclear reaction of different structure and power may be implemented
Heap pyroelecthc properties calculate, and reduce the requirement to the structure and parameter of thermion nuclear reactor for space, effectively increase this method
To the adaptability of different problems.
To achieve the goals above, this invention takes following technical schemes:
A kind of general thermion nuclear reactor for space reactor core transient state pyroelecthc properties comprehensive analysis method, this method include with
Lower step:
Step 1: thermionic fuel element structure and parameter being determined according to user demand, determine each layer of thermionic fuel element
Size, the temperature of the power distribution and coolant of fuel of structure, divide radial and axial node number according to demand；
Step 2: calculating current t moment thermion nuclear reactor for space core temperature distribution, the structure obtained using step 1
Establish the non-linear differential equation of heat balance group about the diabatic process of thermion nuclear reactor for space reactor core respectively with parameter；
General thermion nuclear reactor for space reactor core is made of thermionic fuel element and moderator matrix, thermion combustion
Expect element mainly by fuel region, fission gas gap, emitter, caesium gas-bearing formation, receiving pole, helium layer, stainless steel inner sleeve, cold
But agent and stainless steel outer sleeve pipe are constituted；
Reactor fission power is solved using the point reactor model dynamical equation of six groups of delayed neutrons is considered first；Point heap mould
Type considers the influence of delayed neutron counterincision Variable power and the Reactivity feedback of fuel, coolant and structure member simultaneously, because
This is the first order differential equation system of a coupling；Simultaneously as reactivity is time correlation variable, therefore equation group is non-linear
's；Point reactor model dynamical equation is calculated by formula (1) and formula (2)；
In formula:
P (t) --- t moment reactor fission power/W；
T --- calculate time/s；
Λ --- neutron generation time/s；
β --- total effective delayed neutron fraction；
βi--- i-th group of delayed neutron fraction；
λi--- decay coefficient/s of i-th group of delayed neutron-1；
Ci(t) --- the concentration/m of i-th group of delayed neutron of t moment-3；
nc--- delayed neutron group number；
ρ (t) --- total reactivity/$；
The reactivity of reactor can because out-pile reactivity introduce or heap in Reactivity feedback due to change；Pass through corresponding machine
Reason model or rule-of-thumb relation establish the reactive solving model of each section；The total reactivity of reactor is calculated by formula (3)；
ρ (t)=ρD(t)+∑ρi(t) formula (3)
In formula:
ρ (t) --- total reactivity/$；
ρD(t) --- reactivity/$ that control rotary drum and shutdown rotary drum introduce；
ρi(t) --- each material Reactivity feedback/$；
The Reactivity feedback considered in reactor physics model includes: UO2The temperature of the Doppler effect of fuel, electrode
Feedback, moderator temperature feedback and reflecting layer temperature feedback；It is most important for most of operating conditions of thermionic reactor
Be the positive-effect of moderator and the negative effect of thermionic fuel element；
The Doppler of fuel, which feeds back to formula (4), to be calculated:
In formula:
--- the Doppler of fuel feeds back；
TU--- fuel temperature/K；
T0--- reference temperature/K；
Emitter and receiving pole Reactivity feedback are calculated by formula (5):
In formula:
--- emitter and receiving pole Reactivity feedback；
TE--- emitter temperature/K；
TC--- receiving pole temperature/K；
Moderator Reactivity feedback coefficient is calculated by formula (6):
--- moderator Reactivity feedback；
TM--- zircoium hydride moderator temperature/K；
Wherein parameter phi is determined by formula (7):
Reflecting layer Reactivity feedback coefficient is calculated by formula (8):
In formula:
--- reflecting layer Reactivity feedback；
TR--- reflecting layer temperature/K；
Rotary drum reactivity is controlled to introduce by formula (9) calculating:
In formula:
ρD--- control rotary drum reactivity introduces；
θ --- control rotary drum rotational angle/degree；
Decay power mainly includes that the radioactive decay of neutron absorption product and fission product is decayed by simplification
Heat is solved and is calculated by formula (10) and formula (11):
In formula:
Pd(t) --- t moment reactor decay power/W；
Hi(t) --- the concentration/m of i-th group of fission product of t moment-3；
--- the share of i-th group of fission product；
--- decay coefficient/s of i-th group of fission product-1；
According to the reactor core general power that the solving model of fission power and decay power obtains, according to shared by each control volume of fuel
Power fraction be added in fuel control volume as inner heat source, in reactor core thermal-hydraulic solving model, by formula (12)
It calculates；
QV=P φ/V formula (12)
In formula:
QV--- volume inner heat source/Wm of fuel control volume-3；
P --- reactor general power/W；
φ --- fuel control volume heat release rate accounts for the share of reactor general power；
Volume/m of V --- fuel control volume3；
Middle submodel utilized above obtains inner heat source, and fuel region equation of heat balance is calculated by formula (13):
In formula:
ρU--- density/kgm of fuel pellet-3；
cU--- specific heat/Jkg of fuel pellet-1·K-1；
TU--- temperature/K of fuel pellet；
λU--- thermal coefficient/Wm of fuel pellet-1·K-1；
Radius/m of r --- fuel pellet；
QV--- heat source density/Wm of fuel control volume-3；
Emitter equation of heat balance is calculated by formula (14):
In formula:
ρE--- density/kgm of emitter-3；
VE--- volume/kgm of emitter-3；
cE--- specific heat/Jkg of emitter-1·K-1；
λG--- thermal coefficient/Wm of fission gas-1·K-1；
δG--- fission gas gap width/m；
εUE--- the emissivity of fuel and emitter surface；
εEC--- emitter and the emissivity for receiving pole surface；
λU--- thermal coefficient/Wm of fuel pellet-1·K-1；
ПE--- unit length emitter exterior surface area/m2；
AE--- emitter cross-sectional area/m2；
λCs--- thermal coefficient/Wm of caesium steam-1·K-1；
δCs--- caesium steam width of air gap/m；
φE--- transmitting electrode potential；
φC--- receive electrode potential；
E --- electron charge；
σ --- black body radiation constant, 5.67E-14W/ (mm2·K4)；
L --- emitter and receiving pole length；
χC--- receiving pole work function；
Receiving pole equation of heat balance is calculated by formula (15):
In formula:
ρC--- density/kgm of receiving pole-3；
VC--- volume/kgm of receiving pole-3；
cC--- specific heat/Jkg of receiving pole-1·K-1；
AC--- receiving pole cross-sectional area/m2；
λHe--- thermal coefficient/Wm of helium-1·K-1；
δHe--- helium width of air gap/m；
εIS--- stainless steel inner sleeve and the emissivity for receiving pole surface；
K --- Boltzmann constant；
Stainless steel inner sleeve equation of heat balance is calculated by formula (16):
In formula:
ρSI--- density/kgm of stainless steel inner sleeve-3；
cSI--- specific heat/Jkg of stainless steel inner sleeve-1·K-1；
ПC--- unit length receiving pole exterior surface area/m2；
εCS--- pole surface is received to the emissivity of stainless steel sleeve pipe；
Tf--- temperature/K of coolant；
ПSI--- unit length stainless steel exterior surface area/m2；
ASI--- stainless steel inner sleeve cross-sectional area/m2；
hfI--- coolant and the inner sleeve wall surface coefficient of heat transfer/Wm-2·K-1；
Above-mentioned thermion nuclear reactor for space reactor core heat transfer Nonlinear differential eguations are solved using GEAR algorithm, obtain electricity
The Temperature Distribution of pole；
Step 3, the potential and current distribution for calculating t moment heap core electrode, establish the electric potential balancing of emitter and receiving pole
Ordinary differential system:
Emitter electric potential balancing is calculated by formula (17):
In formula:
φE--- transmitting electrode potential；
J --- current density/Acm-2；
L --- electrode axial length/cm；
Formula (17) boundary condition is given by formula (18) and formula (19):
In formula:
Voutput--- emitter output voltage/V；
RE1--- emitter head end connection resistance/Ω；
RE2--- emitter end connection resistance/Ω；
Emitter electric potential balancing is calculated by formula (20):
In formula: φC--- receive electrode potential；
Wherein, formula (20) boundary condition is given by formula (21) and formula (22):
In formula:
RC1--- receiving pole head end connection resistance/Ω；
RC2--- receiving pole end connection resistance/Ω；
Using solution by iterative method potential and current distribution, Potential Distributing is first assumed, obtained according to Potential Distributing and Temperature Distribution
To current distribution, the ordinary differential system of electrode potential is solved using chasing method, new Potential Distributing is obtained, as iterative process
New Potential Distributing is iterated calculating until meeting required precision, just obtains the potential current distribution of electrode；
Step 4: according to the potential current distribution of acquired electrode, the concatenated connection type of thermionic fuel element, heat
The output power of ion space nuclear reactor power supply reactor core adds for single thermionic fuel element power with voltage with output voltage
It is a thermionic fuel element electric current with, electric current；
Step 5: according to the distribution of thermion nuclear reactor for space power supply core temperature, electrode potential current distribution, carrying out down
The calculating of one step, cycle calculations are until reaching end time；
Compared with prior art, the present invention has following outstanding feature:
General thermion nuclear reactor for space entirety reactor core is studied, can accurately reflect the thermoelectricity of full heap
Characteristic, the thermion nuclear reactor for space pyroelecthc properties that different structure and power may be implemented calculate, and reduce to thermion sky
Between nuclear reactor structure and parameter requirement, effectively increase this method to the adaptability of different problems.This method can calculate
The pyroelecthc properties of general thermion nuclear reactor for space power supply transient state run plan when being nuclear reactor for space power supply transient operation
Summary, electrical system control scheme etc. provide research method.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart.
Specific embodiment
Invention is further described in detail with reference to the accompanying drawings and detailed description:
A kind of general thermion nuclear reactor for space reactor core transient state pyroelecthc properties comprehensive analysis method of the invention, uses
GEAR algorithm solves the distribution of thermion nuclear reactor for space core temperature, solves electrode potential distribution using chasing method, iteration is asked
Solve each moment reactor core electromotive power output, output voltage, output electric current.As shown in Figure 1, this method detailed process includes with lower section
Face:
Step 1: thermionic fuel element structure and parameter being determined according to user demand, determine each layer of thermionic fuel element
Size, the temperature of the power distribution and coolant of fuel of structure, divide radial and axial node number according to demand；
Step 2: calculating current t moment thermion nuclear reactor for space core temperature distribution, the structure obtained using step 1
Establish the non-linear differential equation of heat balance group about the diabatic process of thermion nuclear reactor for space reactor core respectively with parameter；
General thermion nuclear reactor for space reactor core is made of thermionic fuel element and moderator matrix, thermion combustion
Expect element mainly by fuel region, fission gas gap, emitter, caesium gas-bearing formation, receiving pole, helium layer, stainless steel inner sleeve, cold
But agent and stainless steel outer sleeve pipe are constituted；
Reactor fission power is solved using the point reactor model dynamical equation of six groups of delayed neutrons is considered first；Point heap mould
Type considers the influence of delayed neutron counterincision Variable power and the Reactivity feedback of fuel, coolant and structure member simultaneously, because
This is the first order differential equation system of a coupling；Simultaneously as reactivity is time correlation variable, therefore equation group is non-linear
's；Point reactor model dynamical equation is calculated by formula (1) and formula (2)；
In formula:
P (t) --- t moment reactor fission power/W；
T --- calculate time/s；
Λ --- neutron generation time/s；
β --- total effective delayed neutron fraction；
βi--- i-th group of delayed neutron fraction；
λi--- decay coefficient/s of i-th group of delayed neutron-1；
Ci(t) --- the concentration/m of i-th group of delayed neutron of t moment-3；
nc--- delayed neutron group number；
ρ (t) --- total reactivity/$；
The reactivity of reactor can because out-pile reactivity introduce or heap in Reactivity feedback due to change；Pass through corresponding machine
Reason model or rule-of-thumb relation establish the reactive solving model of each section；The total reactivity of reactor is calculated by formula (3)；
ρ (t)=ρD(t)+∑ρi(t) formula (3)
In formula:
ρ (t) --- total reactivity/$；
ρD(t) --- reactivity/$ that control rotary drum and shutdown rotary drum introduce；
ρi(t) --- each material Reactivity feedback/$；
The Reactivity feedback considered in reactor physics model includes: UO2The temperature of the Doppler effect of fuel, electrode
Feedback, moderator temperature feedback and reflecting layer temperature feedback；It is most important for most of operating conditions of thermionic reactor
Be the positive-effect of moderator and the negative effect of thermionic fuel element；
The Doppler of fuel, which feeds back to formula (4), to be calculated:
In formula:
--- the Doppler of fuel feeds back；
TU--- fuel temperature/K；
T0--- reference temperature/K；
Emitter and receiving pole Reactivity feedback are calculated by formula (5):
In formula:
--- emitter and receiving pole Reactivity feedback；
TE--- emitter temperature/K；
TC--- receiving pole temperature/K；
Moderator Reactivity feedback coefficient is calculated by formula (6):
--- moderator Reactivity feedback；
TM--- zircoium hydride moderator temperature/K；
Wherein parameter phi is determined by formula (7):
Reflecting layer Reactivity feedback coefficient is calculated by formula (8):
In formula:
--- reflecting layer Reactivity feedback；
TR--- reflecting layer temperature/K；
Rotary drum reactivity is controlled to introduce by formula (9) calculating:
In formula:
ρD--- control rotary drum reactivity introduces；
θ --- control rotary drum rotational angle/degree；
Decay power mainly includes that the radioactive decay of neutron absorption product and fission product is decayed by simplification
Heat is solved and is calculated by formula (10) and formula (11):
In formula:
Pd(t) --- t moment reactor decay power/W；
Hi(t) --- the concentration/m of i-th group of fission product of t moment-3；
--- the share of i-th group of fission product；
--- decay coefficient/s of i-th group of fission product-1；
According to the reactor core general power that the solving model of fission power and decay power obtains, according to shared by each control volume of fuel
Power fraction be added in fuel control volume as inner heat source, in reactor core thermal-hydraulic solving model, by formula (12)
It calculates；
QV=P φ/V formula (12)
In formula:
QV--- volume inner heat source/Wm of fuel control volume-3；
P --- reactor general power/W；
φ --- fuel control volume heat release rate accounts for the share of reactor general power；
Volume/m of V --- fuel control volume3；
Middle submodel utilized above obtains inner heat source, and fuel region equation of heat balance is calculated by formula (13):
In formula:
ρU--- density/kgm of fuel pellet-3；
cU--- specific heat/Jkg of fuel pellet-1·K-1；
TU--- temperature/K of fuel pellet；
λU--- thermal coefficient/Wm of fuel pellet-1·K-1；
Radius/m of r --- fuel pellet；
QV--- heat source density/Wm of fuel control volume-3；
Emitter equation of heat balance is calculated by formula (14):
In formula:
ρE--- density/kgm of emitter-3；
VE--- volume/kgm of emitter-3；
cE--- specific heat/Jkg of emitter-1·K-1；
λG--- thermal coefficient/Wm of fission gas-1·K-1；
δG--- fission gas gap width/m；
εUE--- the emissivity of fuel and emitter surface；
εEC--- emitter and the emissivity for receiving pole surface；
λU--- thermal coefficient/Wm of fuel pellet-1·K-1；
ПE--- unit length emitter exterior surface area/m2；
AE--- emitter cross-sectional area/m2；
λCs--- thermal coefficient/Wm of caesium steam-1·K-1；
δCs--- caesium steam width of air gap/m；
φE--- transmitting electrode potential；
φC--- receive electrode potential；
E --- electron charge；
σ --- black body radiation constant, 5.67E-14W/ (mm2·K4)；
L --- emitter and receiving pole length；
χC--- receiving pole work function；
Receiving pole equation of heat balance is calculated by formula (15):
In formula:
ρC--- density/kgm of receiving pole-3；
VC--- volume/kgm of receiving pole-3；
cC--- specific heat/Jkg of receiving pole-1·K-1；
AC--- receiving pole cross-sectional area/m2；
λHe--- thermal coefficient/Wm of helium-1·K-1；
δHe--- helium width of air gap/m；
εIS--- stainless steel inner sleeve and the emissivity for receiving pole surface；
K --- Boltzmann constant；
Stainless steel inner sleeve equation of heat balance is calculated by formula (16):
In formula:
ρSI--- density/kgm of stainless steel inner sleeve-3；
cSI--- specific heat/Jkg of stainless steel inner sleeve-1·K-1；
ПC--- unit length receiving pole exterior surface area/m2；
εCS--- pole surface is received to the emissivity of stainless steel sleeve pipe；
Tf--- temperature/K of coolant；
ПSI--- unit length stainless steel exterior surface area/m2；
ASI--- stainless steel inner sleeve cross-sectional area/m2；
hfI--- coolant and the inner sleeve wall surface coefficient of heat transfer/Wm-2·K-1；
Above-mentioned thermion nuclear reactor for space reactor core heat transfer Nonlinear differential eguations are solved using GEAR algorithm, obtain electricity
The Temperature Distribution of pole；
Step 3, the potential and current distribution for calculating t moment heap core electrode, establish the electric potential balancing of emitter and receiving pole
Ordinary differential system:
Emitter electric potential balancing is calculated by formula (17):
In formula:
φE--- transmitting electrode potential；
J --- current density/Acm-2；
L --- electrode axial length/cm；
Formula (17) boundary condition is given by formula (18) and formula (19):
In formula:
Voutput--- emitter output voltage/V；
RE1--- emitter head end connection resistance/Ω；
RE2--- emitter end connection resistance/Ω
Emitter electric potential balancing is calculated by formula (20):
In formula: φC--- receive electrode potential；
Wherein, formula (20) boundary condition is given by formula (21) and formula (22):
In formula:
RC1- receiving pole head end connection resistance/Ω；
RC2- receiving pole end connection resistance/Ω；
Using solution by iterative method potential and current distribution, Potential Distributing is first assumed, obtained according to Potential Distributing and Temperature Distribution
To current distribution, the ordinary differential system of electrode potential is solved using chasing method, new Potential Distributing is obtained, as iterative process
New Potential Distributing is iterated calculating until meeting required precision, just obtains the potential current distribution of electrode；
Step 4: according to the potential current distribution of acquired electrode, the concatenated connection type of thermionic fuel element, heat
The output power of ion space nuclear reactor power supply reactor core adds for single thermionic fuel element power with voltage with output voltage
It is a thermionic fuel element electric current with, electric current；
Step 5: according to the distribution of thermion nuclear reactor for space power supply core temperature, electrode potential current distribution, carrying out down
The calculating of one step, cycle calculations are until reaching end time.
Claims (1)
1. a kind of general thermion nuclear reactor for space reactor core transient state pyroelecthc properties comprehensive analysis method, it is characterised in that: packet
Include following steps:
Step 1: thermionic fuel element structure and parameter being determined according to user demand, determine each layer structure of thermionic fuel element
Size, fuel power distribution and coolant temperature, divide according to demand radial with axial node number；
Step 2: calculating current t moment thermion nuclear reactor for space core temperature distribution, the structure and ginseng obtained using step 1
Number establishes the non-linear differential equation of heat balance group about the diabatic process of thermion nuclear reactor for space reactor core respectively；
General thermion nuclear reactor for space reactor core is made of thermionic fuel element and moderator matrix, thermionic fuel member
Part is mainly by fuel region, fission gas gap, emitter, caesium gas-bearing formation, receiving pole, helium layer, stainless steel inner sleeve, coolant
It is constituted with stainless steel outer sleeve pipe；
Reactor fission power is solved using the point reactor model dynamical equation of six groups of delayed neutrons is considered first；Point reactor model is same
When consider the influence of delayed neutron counterincision Variable power and the Reactivity feedback of fuel, coolant and structure member, therefore be
The first order differential equation system of one coupling；Simultaneously as reactivity is time correlation variable, therefore equation group is nonlinear；Point
Heap model dynamical equation is calculated by formula (1) and formula (2)；
In formula:
P (t) --- t moment reactor fission power/W；
T --- calculate time/s；
Λ --- neutron generation time/s；
β --- total effective delayed neutron fraction；
βi--- i-th group of delayed neutron fraction；
λi--- decay coefficient/s of i-th group of delayed neutron-1；
Ci(t) --- the concentration/m of i-th group of delayed neutron of t moment-3；
nc--- delayed neutron group number；
ρ (t) --- total reactivity/$；
The reactivity of reactor can because out-pile reactivity introduce or heap in Reactivity feedback due to change；Pass through corresponding mechanism mould
Type or rule-of-thumb relation establish the reactive solving model of each section；The total reactivity of reactor is calculated by formula (3)；
ρ (t)=ρD(t)+∑ρi(t) formula (3)
In formula:
ρ (t) --- total reactivity/$；
ρD(t) --- reactivity/$ that control rotary drum and shutdown rotary drum introduce；
ρi(t) --- each material Reactivity feedback/$；
The Reactivity feedback considered in reactor physics model includes: UO2The Doppler effect of fuel, electrode temperature feedback,
Moderator temperature feedback and reflecting layer temperature feedback；For most of operating conditions of thermionic reactor, it is most important that
The positive-effect of moderator and the negative effect of thermionic fuel element；
The Doppler of fuel, which feeds back to formula (4), to be calculated:
In formula:
--- the Doppler of fuel feeds back；
TU--- fuel temperature/K；
T0--- reference temperature/K；
Emitter and receiving pole Reactivity feedback are calculated by formula (5):
In formula:
--- emitter and receiving pole Reactivity feedback；
TE--- emitter temperature/K；
TC--- receiving pole temperature/K；
Moderator Reactivity feedback coefficient is calculated by formula (6):
--- moderator Reactivity feedback；
TM--- zircoium hydride moderator temperature/K；
Wherein parameter phi is determined by formula (7):
Reflecting layer Reactivity feedback coefficient is calculated by formula (8):
In formula:
--- reflecting layer Reactivity feedback；
TR--- reflecting layer temperature/K；
Rotary drum reactivity is controlled to introduce by formula (9) calculating:
In formula:
ρD--- control rotary drum reactivity introduces；
θ --- control rotary drum rotational angle/degree；
Decay power mainly includes that the radioactive decay of neutron absorption product and fission product by simplification obtains decay heat, is asked
Solution is calculated by formula (10) and formula (11):
In formula:
Pd(t) --- t moment reactor decay power/W；
Hi(t) --- the concentration/m of i-th group of fission product of t moment-3；
--- the share of i-th group of fission product；
--- decay coefficient/s of i-th group of fission product-1；
According to the reactor core general power that the solving model of fission power and decay power obtains, according to function shared by each control volume of fuel
Rate share is added in fuel control volume as inner heat source, for being calculated in reactor core thermal-hydraulic solving model by formula (12)；
QV=P φ/V formula (12)
In formula:
QV--- volume inner heat source/Wm of fuel control volume-3；
P --- reactor general power/W；
φ --- fuel control volume heat release rate accounts for the share of reactor general power；
Volume/m of V --- fuel control volume3；
Middle submodel utilized above obtains inner heat source, and fuel region equation of heat balance is calculated by formula (13):
In formula:
ρU--- density/kgm of fuel pellet-3；
cU--- specific heat/Jkg of fuel pellet-1·K-1；
TU--- temperature/K of fuel pellet；
λU--- thermal coefficient/Wm of fuel pellet-1·K-1；
Radius/m of r --- fuel pellet；
QV--- heat source density/Wm of fuel control volume-3；
Emitter equation of heat balance is calculated by formula (14):
In formula:
ρE--- density/kgm of emitter-3；
VE--- volume/kgm of emitter-3；
cE--- specific heat/Jkg of emitter-1·K-1；
λG--- thermal coefficient/Wm of fission gas-1·K-1；
δG--- fission gas gap width/m；
εUE--- the emissivity of fuel and emitter surface；
εEC--- emitter and the emissivity for receiving pole surface；
λU--- thermal coefficient/Wm of fuel pellet-1·K-1；
ПE--- unit length emitter exterior surface area/m2；
AE--- emitter cross-sectional area/m2；
λCs--- thermal coefficient/Wm of caesium steam-1·K-1；
δCs--- caesium steam width of air gap/m；
φE--- transmitting electrode potential；
φC--- receive electrode potential；
E --- electron charge；
σ --- black body radiation constant, 5.67E-14W/ (mm2·K4)；
L --- emitter and receiving pole length；
χC--- receiving pole work function；
Receiving pole equation of heat balance is calculated by formula (15):
In formula:
ρC--- density/kgm of receiving pole-3；
VC--- volume/kgm of receiving pole-3；
cC--- specific heat/Jkg of receiving pole-1·K-1；
AC--- receiving pole cross-sectional area/m2；
λHe--- thermal coefficient/Wm of helium-1·K-1；
δHe--- helium width of air gap/m；
εIS--- stainless steel inner sleeve and the emissivity for receiving pole surface；
K --- Boltzmann constant；
Stainless steel inner sleeve equation of heat balance is calculated by formula (16):
In formula:
ρSI--- density/kgm of stainless steel inner sleeve-3；
cSI--- specific heat/Jkg of stainless steel inner sleeve-1·K-1；
ΠC--- unit length receiving pole exterior surface area/m2；
εCS--- pole surface is received to the emissivity of stainless steel sleeve pipe；
Tf--- temperature/K of coolant；
ΠSI--- unit length stainless steel exterior surface area/m2；
ASI--- stainless steel inner sleeve cross-sectional area/m2；
hfI--- coolant and the inner sleeve wall surface coefficient of heat transfer/Wm-2·K-1；
Above-mentioned thermion nuclear reactor for space reactor core heat transfer Nonlinear differential eguations are solved using GEAR algorithm, obtain electrode
Temperature Distribution；
Step 3, the potential and current distribution for calculating t moment heap core electrode, establish the normal of the electric potential balancing of emitter and receiving pole
Differential equation group:
Emitter electric potential balancing is calculated by formula (17):
In formula:
φE--- transmitting electrode potential；
J --- current density/Acm-2；
L --- electrode axial length/cm；
Formula (17) boundary condition is given by formula (18) and formula (19):
In formula:
Voutput--- emitter output voltage/V；
RE1--- emitter head end connection resistance/Ω；
RE2--- emitter end connection resistance/Ω；
Emitter electric potential balancing is calculated by formula (20):
In formula: φC--- receive electrode potential；
Wherein, formula (20) boundary condition is given by formula (21) and formula (22):
In formula:
RC1--- receiving pole head end connection resistance/Ω；
RC2--- receiving pole end connection resistance/Ω；
Using solution by iterative method potential and current distribution, Potential Distributing is first assumed, electricity is obtained according to Potential Distributing and Temperature Distribution
Flow distribution is solved the ordinary differential system of electrode potential using chasing method, obtains new Potential Distributing, new as iterative process
Potential Distributing is iterated calculating until meeting required precision, just obtains the potential current distribution of electrode；
Step 4: according to the potential current distribution of acquired electrode, the concatenated connection type of thermionic fuel element, thermion
The output power and output voltage of nuclear reactor for space power supply reactor core are that single thermionic fuel element power and voltage sum it up, electricity
Stream is a thermionic fuel element electric current；
Step 5: according to the distribution of thermion nuclear reactor for space power supply core temperature, electrode potential current distribution, carrying out in next step
Calculating, cycle calculations are until reaching end time.
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| CN113793711A (en) * | 2021-09-13 | 2021-12-14 | 西安交通大学 | Method for analyzing coupling heat transfer characteristics of lithium-cooled nuclear reactor and Stirling generator |
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