CN110991023B - Method for calculating temperature distribution and boundary power density in sleeve type heat flow channel - Google Patents
Method for calculating temperature distribution and boundary power density in sleeve type heat flow channel Download PDFInfo
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Abstract
The invention discloses a method for calculating temperature distribution and boundary power density in a sleeve type heating flow channel, which comprises the following steps: let q beWδ T and λ are the linear power density, the temperature distribution peak and the equivalent thermal conductivity at the central heating channel boundary, respectively. Firstly, an equivalent model of a sleeve type heating channel to be estimated is established, and the geometric dimension of the equivalent model and the strength of an internal heat source are determined. Then q is obtained according to the law of heat conduction and the law of energy conservationWThe relation between delta T and lambda and the dimensionless temperature peak value are distributed along the axial direction delta T (x, lambda)/delta T, and the value of lambda is obtained iteratively. Finally, substituting the lambda into delta T (x, lambda) to combine delta T, lambda and qWThe relation between delta T and qWDistribution along the axial direction. The method is simple to operate and high in precision, and can be used for calculating the transverse heat transfer capacity and the temperature distribution of the thermal devices such as the double-pipe heat exchanger and the nuclear reactor closed fuel assembly; in addition, the temperature peak value in the sleeve type heating device can be obtained, and the method has important significance for determining the hot spot and the safety limit value of the heating device.
Description
Technical Field
The invention belongs to the field of heat exchanger design calculation and nuclear reactor thermal safety analysis calculation, and particularly relates to a method for calculating temperature distribution and boundary line power density in a sleeve type heating flow channel.
Background
Energy is an important material basis for the survival and development of human society, and is an important source for supporting the progress of industry. In the energy industry today, double pipe heating devices are widely found in heat exchangers, nuclear reactor cores employing closed fuel assemblies, and vertical natural circulation steam generators. When the thermal process equipment is designed, the determination of the transverse heat transfer capacity of the heating channel is important for mastering the temperature distribution, the heat exchange capacity and the safety limit value of the heating device.
Central heating channel boundary power density q leading from central heating channel to cooling channelWThe lateral heat transfer capability and safety characteristics of such heating devices are characterized. At present, the power density q of the boundary line of the central heating channelWThe research of (2) mainly adopts a CFD simulation method and an experimental method. The internal geometric structure of the sleeve type heating assembly is generally complex, a flow channel is long and narrow, and the size difference between a central heating channel and an edge cooling channel is large, so that difficulty is brought to grid division, and the problems of poor grid quality, low space filling efficiency, excessive occupied computational memory and the like are easily caused; moreover, on some local detail of the flow channel, the calculation grid is often different from the real situation, so that the simulation result has a large uncertainty error, and the reliability of the calculation result is low.
Power density q of central heating channel boundary lineWIt is also difficult to measure directly by experiment. Because the internal geometry of the sleeve type heating assembly is generally complex and the working environment is special, the arrangement of the temperature measuring device is difficult, and the positions and the number of temperature measuring points are limited greatly. In addition, when the thermocouple/thermal resistance thermometer is adopted to directly measure the temperature of the inner wall of the middle heating channel, the flow field and the temperature field are often greatly influenced, and therefore the reliability of the measurement result is low.
At present, in theoretical analysis and calculation of the sleeve type heating channel, the average temperature T of the section of the heating channel is mostly adoptednSubstitute heating channel wall temperature TWSubstituted into the convective heat transfer relation qW＝h(TW-Th) Calculating the power density q of the boundary line of the central heating channelW. (wherein T ishIs the average temperature of the fluid in the edge cooling channel) is easy to overestimate the wall temperature of the heating channel, thereby overestimating the transverse heat transfer capacity in the heating device, and therefore, the result of the method is lack of conservation when the thermal safety analysis and calculation of the heating device are carried out.
Disclosure of Invention
The technical problem solved by the invention is as follows: aiming at the defects of the prior art, a method for calculating the temperature distribution and the boundary line power density in a sleeve type heating flow channel is provided, and the methodThe method is characterized in that a sleeve type fluid heating channel is simplified into a corresponding equivalent geometric model, and a Fourier heat conduction law of solid heat conduction is combined to derive a temperature peak value delta T and a boundary line power density q of a central heating channelWSemi-theoretical semi-empirical relationship therebetween. Effectively avoids the defects of high computational overhead and poor channel geometric reduction degree of the CFD method and the problem of lack of conservation of the traditional estimation method, and can accurately estimate the power density q of the boundary line of the central heating channel as far as possible while effectively saving computational resourcesW。
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for calculating temperature distribution and boundary line power density in a sleeve type heating flow channel specifically comprises the following steps:
step 1: establishing a corresponding equivalent model and boundary conditions according to the actual arrangement condition of the sleeve type heating flow channel to be estimated, and enabling the sleeve type heating flow channel to be estimated to be equivalent to a cylindrical or prismatic equivalent model containing a uniform internal heat source and a corresponding edge cooling channel;
the internal geometric structure of the sleeve type heating component is complex, the flow channel is long and narrow, the size difference between the central heating channel and the edge cooling channel is large, and the direct experimental measurement or theoretical analysis and calculation are difficult; in contrast, the central heating channel is simplified into a cylindrical or prismatic channel which is regular in shape and convenient to calculate and a corresponding edge cooling channel, and theoretical calculation is carried out; simplifying the uniformly cooled heating channel into a uniformly cooled cylindrical channel containing an internal heat source, and simplifying the non-uniformly cooled heating channel into a non-uniformly cooled prismatic channel containing an internal heat source;
step 2: determining the radius R of a cylindrical equivalent model or the side length a of a prismatic equivalent model based on the principle of sectional area equality according to the geometric dimension of the flow section of the heating channel to be estimated;
radius of equivalent cylindrical passage
Length of sides of equivalent prismatic channels
Wherein A is the sectional area of the original heating channel (containing a heating rod);
and step 3: calculating the heat source intensity in the equivalent geometric model according to the size of the equivalent model determined in the step 2 and the power of a heat transfer line from the central heating channel to the edge cooling channel;
the power density of a boundary line for transferring heat from a center heating channel to an edge cooling channel at a certain point is set as qWIt is believed that the temperature amplitude in the central heating channel is caused by the transverse heat transfer from the central heating channel to the edge cooling channel, so that the temperature distribution in the central heating channel has the same linear power density q as that of the heat transfer from the central heating channel to the edge cooling channel with the internal heat sourceWThe temperature distribution in the cylindrical or prismatic equivalent geometric model of (a) is similar; the internal heat source strength of the equivalent geometric model is set as QVThen Q isV＝qWA; a is the sectional area of the original heating channel (containing a heating rod);
and 4, step 4: according to the Fourier heat conduction law, assuming that the equivalent thermal conductivity coefficient lambda is constant on the whole flow channel, the peak value delta T ═ T of the temperature distribution in the equivalent heating channel is obtainedmax-TWAnd equivalent heating channel boundary power density qWIn which T ismaxTo the maximum temperature in the equivalent heating channel, TWIs the temperature at the boundary of the equivalent heating channel;
the one-dimensional steady-state heat conduction formula with an internal heat source is
The temperature in the cylinder or prism containing uniform internal heat source is distributed in a parabolic way, and the power density q of the boundary line of the central heating channelWAnd the temperature peak value δ T ═ Tmax-TWProportional to the equivalent thermal conductivity, λ, qWK · λ δ T (k is a constant obtained by solving a heat conduction equation);
and 5: according to the specific heat c of the fluidpTotal heating power Q, edge cooling channel mass flow WhAnd central heating channel mass flow WnMeter for measuringCalculate the total temperature rise from the entrance to the exit of the casing
Then combining the law of energy conservation of the central heating channel and the edge cooling channel and the convection heat exchange formula of the edge cooling channel to derive a dimensionless temperature peak value along the axial distribution expression delta T (x, lambda)/delta T;
since there is a non-heating section of sufficient length after the heating section where the temperature difference between the central heating channel and the edge cooling channel will be flattened, it is assumed that the temperature rise of the central heating channel and the edge cooling channel from the inlet of the heating section to the outlet of the module are approximately equal, both at;
according to the law of conservation of energy of the central heating channel, the method comprises the following steps:
cpWn·dTn＝(q-qW)·dx＝(q-kλδT)·dx
wherein q is the linear power density of the heating element in the central heating channel, TnAverage temperature of the central heating channel;
according to the formula of convection heat exchange of the edge channel, the method comprises the following steps:
wherein alpha is the convective heat transfer coefficient of the edge channel, P is the heat circumference of the edge channel, ThIs the edge cooling channel average temperature; according to the law of conservation of energy of the edge channel, there are:
cpWh·dTh＝qW·dx＝kλδT·dx
the three formulas are combined to obtain:
solving the ordinary differential equation without dimension to obtain a dimensionless temperature peak value along the axial distribution expression delta T (x, lambda)/delta T;
step 6: based on the steps5 obtaining a dimensionless temperature peak value along the axial direction distribution expression delta T (x, lambda)/delta T and delta T, lambda and qWJudging whether the equivalent thermal conductivity coefficient lambda converges or not by a Gauss-Seidel iteration method and through the residual error of the equivalent thermal conductivity coefficient lambda and the heat flow of the inflow edge channel to obtain the value of the equivalent thermal conductivity coefficient lambda;
the size δ T (x, λ) of the temperature peak depends on the cross-sectional location x and the equivalent thermal conductivity λ; in an iterative process, the specific heat c of the fluid is first givenpTotal heating power Q, edge cooling channel mass flow WhAnd central heating channel mass flow WnGiving an iteration initial value of lambda, substituting the iteration initial value into a delta T (x, lambda) expression, and calculating the distribution of the peak value delta T of the temperature distribution in the equivalent heating channel on the whole central channel;
the length of the heating section is set to be L1The length of the non-heating section is L2(ii) a Since the equivalent thermal conductivity λ is constant over the entire flow channel as described in step 4, it is possible to prevent the occurrence of the heat loss due to the heat transfer
Wherein
Average linear power density over the entire flow channel boundary;
q is to beWSubstituting k, lambda and delta T into the formula to obtain
According to the above formula, obtain
Calculating new equivalent thermal conductivity coefficient lambdatemp(ii) a According to qWK lambda delta T to obtain the power density of the boundary line of the central heating channelqWDistribution over the heating channel. Since the temperature rises of the central channel and the edge channel from the inlet of the heating section of the assembly to the outlet of the assembly are approximately equal, the total heat flow flowing into the edge channel is
Should be in contact with
Equal; so that the central heating channel boundary hot wire power density q is finally heatedWIntegration over the entire channel
And
comparing the new equivalent thermal conductivity lambdatempCompared with the lambda of the previous step if
And
λtempthe relative error between the prior lambda and the prior lambda is less than 0.1 percent, and then q is considered to beWAnd lambda meets the convergence standard, and then a lambda value obtained by calculation is output; otherwise, updating the lambda value to lambdatempThe value of (2) is substituted back into a delta T (x, lambda) expression, and iterative computation is carried out again until convergence;
and 7: substituting the equivalent thermal conductivity coefficient lambda obtained in the step 6 into a delta T (x, lambda) expression to obtain the distribution of the peak value delta T of the temperature distribution in the equivalent heating channel along the axial direction; combined with delta T, q derived from step 6WThe relation between the two parameters is obtained to obtain the power density q of the boundary line of the central heating channelWDistribution along the axial direction.
Compared with the prior art, the invention has the following advantages:
the method of the invention combines the Fourier heat conduction law of solid heat conduction to derive the temperature peak value delta T and the boundary line power density q of the central heating channel by simplifying the sleeve type fluid heating channel into a corresponding equivalent geometric modelWSemi-theoretical semi-empirical relationship therebetween. Effectively avoids the defects of high computational overhead and poor channel geometric reduction degree of the CFD method and the problem of lack of conservation of the traditional estimation method, and can accurately estimate the power density q of the boundary line of the central heating channel as far as possible while effectively saving computational resourcesW。
Drawings
FIG. 1 is a schematic view of a 19 bundle sleeve type heating channel heating section and an equivalent heating channel structure.
Fig. 2 is a schematic view of the overall structure of a 19-bundle-sleeve type heating channel.
FIG. 3 is a flow chart of a computing method of the present invention.
Detailed Description
The following describes the present invention in further detail with reference to the flow chart of fig. 3, taking a 19-bundle-sleeve heating assembly as an example. The heating device has a heating section length L1Is L, the length of the non-heating section L20.35L; the axial line power of the heating section is uniform. The invention specifically comprises the following steps:
step 1: the arrangement of the bushing-type heating channel to be studied was analyzed. The structure of the heating section of the 19-rod bundle sleeve type heating channel is shown in figure 1. 19 heating rods are arranged in a cylindrical heating sleeve according to triangular grid cells. An annular cooling channel is provided around the central heating channel for cooling the central heating channel. As can be seen from fig. 1, the heating channel geometry has strong symmetry, thus simplifying it into a cylindrical equivalent heating channel containing a uniform internal heat source and a corresponding annular cooling channel.
Step 2: according to the geometric dimension of the flow section of the heating channel to be researched and according to the principle that the sectional areas are equal, the radius R of the equivalent cylindrical heating channel is determined. Specifically, the heating channel containing 19 bundles of rods is homogenized into an equivalent cylindrical central heating channel containing an internal heat source, and the section of the equivalent cylindrical central heating channel is maintainedThe product is equal to the original heating channel, and the radius of the cylindrical channel can be obtained
Wherein A is the cross-sectional area of the original heating channel (including the heating rod).
And step 3: according to the size (radius R or side length a) of the equivalent model determined in the step 2, the internal heat source intensity Q of the equivalent geometric model is calculated through the power of a heat transfer line led from the central heating channel to the edge cooling channelV. Specifically, as shown in FIG. 1, the linear power density of heat transfer from the central heating channel to the edge cooling channel at a certain point is set as qW(ii) a Then according to the law of conservation of energy:
and 4, step 4: according to the Fourier heat conduction law, the equivalent heat conductivity coefficient lambda of the heating channel is considered as a constant, and the peak value delta T-T of the temperature distribution in the equivalent heating channel is obtainedmax-TWAnd power density q of central heating channel boundary lineWThe relation between them. Specifically, the method comprises the following steps:
the fourier thermal conductivity equation is listed:
the corresponding boundary conditions are:
T＝Tmaxr ═ 0 (4-2) to give:
let δ T equal to Tmax-TWThen, there are:
by combining formula (3-1) again, it is possible to obtain:
and 5: according to specific heat c of working mediumpTotal heating power Q, edge channel mass flow WhAnd center channel mass flow WnCalculating the total temperature rise
Delta T-q obtained from the previous stepWAnd the expression is combined with the central heating channel, the edge channel energy conservation law and the edge channel convection heat exchange formula to derive the dimensionless temperature peak value axial distribution expression delta T (x, lambda)/delta T.
Specifically, since there is a sufficiently long non-heated section following the heated section, as shown in FIG. 2, the temperature rise of the central channel, the edge channel from the inlet of the heated section of the module to the outlet of the module, assuming approximately equal temperature rise, is Δ T. According to the law of conservation of energy, the average boundary heat flux density of the heating channel is calculated
Wherein Q is the total heating power, cpIs the specific heat of the fluid, WhAnd WnFluid mass flow L through the edge cooling channels and the central heating channel, respectively1And L2The lengths of the heated and non-heated sections, respectively.
According to the law of conservation of energy of the central heating channel:
cpWn·dTn＝(q-qW)·dx＝(q-4πλδT)·dx
(5-3)
according to the convection heat exchange formula of the edge channel:
taking differential on two sides:
according to the law of conservation of energy of the edge channel:
cpWh·dTh＝qW·dx＝4πλδT·dx
(5-6)
wherein q is the linear power of the heating section, Tn、ThThe average temperature of the central heating channel and the average temperature of the edge cooling channel are respectively, and alpha is the convection heat transfer coefficient between the fluid of the edge cooling channel and the wall surface.
Simultaneous 5-3, 5-5, 5-6 formula:
for a uniform heating assembly, there are:
finally, obtaining:
wherein
Step 6: and (4) obtaining the value of the equivalent thermal conductivity coefficient lambda by a Gauss-Seidel iteration method (judging whether convergence is caused by the residual error of the equivalent thermal conductivity coefficient lambda and the heat flow of the inflow edge channel) based on the dimensionless temperature peak value obtained in the step (5) along the axial distribution expression delta T (x, lambda)/delta T.
The size δ T (x, λ) of the temperature peak depends on the cross-sectional location x and the equivalent thermal conductivity λ. In an iterative process, the specific heat c of the fluid is first givenpTotal heating power cpEdge channel mass flow WhAnd center channel mass flow WnSetting parameters of the constant heating section, giving an iteration initial value of lambda, substituting the iteration initial value into a delta T (x, lambda) expression, and calculating the distribution and integral average of the delta T on the whole central channel
Since the temperature rises of the central channel and the edge channel from the inlet of the heating section of the assembly to the outlet of the assembly are approximately equal, the total heat flow flowing into the edge channel is
Average linear power density
Then according to the result obtained in step 4
Calculating new equivalent thermal conductivity coefficient lambdatemp(ii) a Then according to qWObtaining the boundary line power density q of the central heating channel by 4 lambda pi delta TWDistribution over the heating channel. Finally, q isWIntegration over the entire channel
And
comparing the new equivalent thermal conductivity lambdatempCompared to λ of the previous step. If it is not
And
λtempthe relative error between the prior lambda and the prior lambda is less than 0.1 percent, and then q is considered to beWAnd λ satisfy a convergence criterion. If q isWAnd the sum lambda meets the convergence standard, and then the calculated lambda value is output. Otherwise, updating the lambda value to lambdatempThe value of (c) is substituted back into the expression of delta T (x, lambda), and iterative calculation is carried out again until convergence.
And 7: and (4) substituting the equivalent thermal conductivity coefficient lambda obtained in the step (6) into a delta T (x, lambda) expression to obtain the distribution of the temperature peak value delta T along the axial direction. And q derived from step 6WObtaining the power density q of the boundary line of the central heating channel as 4 lambda pi delta TWDistribution along the axial direction.
Claims (1)
1. A method for calculating temperature distribution and boundary line power density in a sleeve type heating flow channel is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1: establishing a corresponding equivalent model and boundary conditions according to the actual arrangement condition of the sleeve type heating flow channel to be estimated, and enabling the sleeve type heating flow channel to be estimated to be equivalent to a cylindrical or prismatic equivalent model containing a uniform internal heat source and a corresponding edge cooling channel;
simplifying the uniformly cooled heating channel into a uniformly cooled cylindrical channel containing an internal heat source, and simplifying the non-uniformly cooled heating channel into a non-uniformly cooled prismatic channel containing an internal heat source;
step 2: determining the radius R of a cylindrical equivalent model or the side length a of a prismatic equivalent model based on the principle of sectional area equality according to the geometric dimension of the flow section of the heating channel to be estimated;
radius of equivalent cylindrical passage
Length of sides of equivalent prismatic channels
Wherein A is the cross-sectional area of the original heating channel containing the heating rod;
and step 3: calculating the heat source intensity in the equivalent geometric model according to the size of the equivalent model determined in the step 2 and the power of a heat transfer line from the central heating channel to the edge cooling channel;
the power density of a boundary line for transferring heat from a center heating channel to an edge cooling channel at a certain point is set as qWIt is believed that the temperature amplitude in the central heating channel is caused by the transverse heat transfer from the central heating channel to the edge cooling channel, so that the temperature distribution in the central heating channel has the same linear power density q as that of the heat transfer from the central heating channel to the edge cooling channel with the internal heat sourceWThe temperature distribution in the cylindrical or prismatic equivalent geometric model of (a) is similar; the internal heat source strength of the equivalent geometric model is set as QVThen Q isV＝qWA; a is the sectional area of the original heating channel containing the heating rod;
and 4, step 4: according to the Fourier heat conduction law, assuming that the equivalent thermal conductivity coefficient lambda is constant on the whole flow channel, the peak value delta T ═ T of the temperature distribution in the equivalent heating channel is obtainedmax-TWAnd equivalent heating channel boundary power density qWIn which T ismaxTo the maximum temperature in the equivalent heating channel, TWIs the temperature at the boundary of the equivalent heating channel;
the one-dimensional steady-state heat conduction formula with an internal heat source is
The temperature in the cylinder or prism containing uniform internal heat source is distributed in a parabolic way, and the power density q of the boundary line of the central heating channelWAnd the temperature peak value δ T ═ Tmax-TWProportional to the equivalent thermal conductivity, λ, qWK · λ δ T, k being a constant;
and 5: according to the specific heat c of the fluidpTotal heating power Q, edge cooling channel mass flow WhAnd central heating channel mass flow WnCalculating the total temperature rise from the inlet to the outlet of the sleeve
Then combining the law of energy conservation of the central heating channel and the edge cooling channel and the convection heat exchange formula of the edge cooling channel to derive a dimensionless temperature peak value along the axial distribution expression delta T (x, lambda)/delta T;
since there is a non-heating section of sufficient length after the heating section where the temperature difference between the central heating channel and the edge cooling channel will be flattened, it is assumed that the temperature rise of the central heating channel and the edge cooling channel from the inlet of the heating section to the outlet of the module are approximately equal, both at;
according to the law of conservation of energy of the central heating channel, the method comprises the following steps:
cpWn·dTn＝(q-qW)·dx＝(q-kλδT)·dx
wherein q is the linear power density of the heating element in the central heating channel, TnAverage temperature of the central heating channel;
according to the formula of convection heat exchange of the edge channel, the method comprises the following steps:
wherein alpha is the convective heat transfer coefficient of the edge channel, P is the heat circumference of the edge channel, ThIs the edge cooling channel average temperature; according to the law of conservation of energy of the edge channel, there are:
cpWh·dTh＝qW·dx＝kλδT·dx
the three formulas are combined to obtain:
solving the ordinary differential equation without dimension to obtain a dimensionless temperature peak value along the axial distribution expression delta T (x, lambda)/delta T;
step 6: dimensionless temperature peak based on step 5The expressions δ T (x, λ)/Δ T and δ T, λ, q are distributed along the axial directionWJudging whether the equivalent thermal conductivity coefficient lambda converges or not by a Gauss-Seidel iteration method and through the residual error of the equivalent thermal conductivity coefficient lambda and the heat flow of the inflow edge channel to obtain the value of the equivalent thermal conductivity coefficient lambda;
the size δ T (x, λ) of the temperature peak depends on the cross-sectional location x and the equivalent thermal conductivity λ; in an iterative process, the specific heat c of the fluid is first givenpTotal heating power Q, edge cooling channel mass flow WhAnd central heating channel mass flow WnGiving an iteration initial value of lambda, substituting the iteration initial value into a delta T (x, lambda) expression, and calculating the distribution of the peak value delta T of the temperature distribution in the equivalent heating channel on the whole central channel;
the length of the heating section is set to be L1The length of the non-heating section is L2(ii) a Since the equivalent thermal conductivity λ is constant over the entire flow channel as described in step 4, it is possible to prevent the occurrence of the heat loss due to the heat transfer
Wherein
Average linear power density over the entire flow channel boundary;
q is to beWSubstituting k, lambda and delta T into the formula to obtain
According to the above formula, obtain
Calculating new equivalent thermal conductivity coefficient lambdatemp(ii) a According to qW＝k·λδTObtaining the power density q of the boundary line of the central heating channelWDistribution over the entire heating channel; since the temperature rises of the central channel and the edge channel from the inlet of the heating section of the assembly to the outlet of the assembly are approximately equal, the total heat flow flowing into the edge channel is
Should be in contact with
Equal; so that the central heating channel boundary hot wire power density q is finally heatedWIntegration over the entire channel
And
comparing the new equivalent thermal conductivity lambdatempCompared with the lambda of the previous step if
And
the relative error between the prior lambda and the prior lambda is less than 0.1 percent, and then q is considered to beWAnd lambda meets the convergence standard, and then a lambda value obtained by calculation is output; otherwise, updating the lambda value to lambdatempThe value of (2) is substituted back into a delta T (x, lambda) expression, and iterative computation is carried out again until convergence;
and 7: substituting the equivalent thermal conductivity coefficient lambda obtained in the step 6 into a delta T (x, lambda) expression to obtain the peak value delta T of the temperature distribution in the equivalent heating channel along the axial directionThe distribution of (a); combined with delta T, q derived from step 6WThe relation between the two parameters is obtained to obtain the power density q of the boundary line of the central heating channelWDistribution along the axial direction.
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