CN114925598A - Tubular heat exchanger heat exchange error reliability analysis method based on Kriging method - Google Patents
Tubular heat exchanger heat exchange error reliability analysis method based on Kriging method Download PDFInfo
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Abstract
The invention discloses a tubular heat exchanger heat exchange error reliability analysis method based on a Kriging method, and relates to the field of heat exchange analysis. Forming a parameter sample for training a kriging model by normal random sampling; obtaining a heat exchange efficiency response output value corresponding to the parameter sample extracted in normal distribution through numerical simulation calculation, wherein the heat exchange efficiency response output value is used as a training sample, and the rest are used as reference samples; establishing a kriging agent model and training the kriging agent modelRefining; comparing the calculation result of the trained kriging model with the comparison sample until the relative error of the calculation result meets the set precision requirement; for 10 obeying normal random distribution α Carrying out proxy calculation on each characteristic parameter sample; based on the calculation result of the kriging proxy model, the heat exchange error reliability of the heat exchanger is predicted by the Monte Carlo method, the heat exchange error reliability of the heat exchanger can be predicted by a small amount of numerical simulation calculation, and the calculation efficiency of the heat exchange error reliability of the heat exchanger is effectively improved.
Description
Technical Field
The invention relates to the field of heat exchange analysis, in particular to a tubular heat exchanger heat exchange error reliability analysis method based on a Kriging method.
Background
The method for strengthening heat exchange is divided into active strengthening heat exchange and passive strengthening heat exchange. The passive heat exchange enhancement technology does not use external power, and the purpose of enhancing heat exchange is achieved by improving the turbulence degree in the heat exchanger through the structure, arrangement and other modes of the heat exchanger. There are many types of passive heat exchange methods, and a method of simultaneously using two or more passive heat exchange technologies is called composite enhancement. The spiral corrugated pipe heat exchanger combines two passive enhanced heat exchange technologies of a spiral structure and a rough surface, and the corrugated structure spiral structure is applied to the pipe wall of the spiral pipe, so that the fluid generates a reverse rotating vortex to thin a thermal boundary layer, and the heat exchange efficiency is effectively improved.
The research on the flow heat exchange process of the spiral corrugated pipe is generally based on the structure parameter size of the spiral corrugated pipe as an accurate value. Rainieri indicates that for a high-viscosity working medium, the enhanced heat exchange effect generated by the corrugated pipe structure is not obvious, the change of physical properties along with temperature is a key working medium for promoting fluid instability to generate vortex in the flowing process of the corrugated pipe so as to realize enhanced heat exchange, and meanwhile, the generation of the vortex reduces the critical Reynolds number for starting to transit to the turbulent flow. The change of the heat exchange rate and the relative pressure of the spiral corrugated pipe is researched by adopting a numerical calculation mode for the Zach. The results show that the heat exchange rate of the helical bellows is independent of the inlet temperature and the surface temperature. Bozzoli teaches that spiral tubes with corrugations present a critical Dean number above which the corrugated walls are superimposed with the wall curvature, resulting in additional heat transfer enhancement.
In the background of the above-mentioned research, some researchers have conducted some studies on the flow heat transfer characteristics of the spiral corrugated tube. However, in these studies, there are few studies on the heat exchange characteristics of the spiral corrugated pipe heat exchanger under the condition that the structural parameters of the spiral corrugated pipe are random variables. In studies on spiral corrugated tube heat exchangers, flow conditions and randomness of the parameters of the corrugated tube structure are often neglected. Influenced by the processing technology and the actual measurement precision, in the actual application, the flow condition and the structural parameters of the corrugated pipe are random variables. The randomness of the structural parameters causes errors in the actual heat exchange of the spiral corrugated pipe heat exchanger. In order to ensure that the heat exchange error does not exceed the specified range, the reliability of the change of the heat exchange error of the helical bellows needs to be analyzed while the influence of the randomness of parameters on the heat exchange characteristics of the helical bellows is considered.
The traditional reliability calculation method needs to calculate response output values of a large number of samples, and often has the problems of large calculation amount and low calculation efficiency. Therefore, in order to efficiently perform predictive analysis on the heat exchange error of the spiral corrugated pipe, it is necessary to provide a method for efficiently and quickly analyzing the heat exchange reliability of the spiral corrugated pipe heat exchanger.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a tubular heat exchanger heat exchange error reliability analysis method based on a Kriging method, which predicts the tubular heat exchanger heat exchange error reliability through numerical simulation calculation and effectively improves the calculation efficiency of the heat exchange error reliability of the spiral corrugated pipe heat exchanger.
The technical scheme provided by the invention is as follows:
a tubular heat exchanger heat exchange error reliability analysis method based on a Kriging method comprises the following steps:
step 1: determining a related characteristic parameter x of the heat efficiency of the tubular heat exchanger, and forming a parameter sample for training a Kriging model by adopting a normal random sampling mode;
step 2: setting a variation coefficient by taking the relevant characteristic parameter x in the step 1 as a mean value, extracting the parameter samples in a normal distribution mode, and obtaining a heat exchange efficiency response output value corresponding to the extracted parameter samples as a training sample through numerical simulation calculation;
and 3, step 3: establishing a kriging agent model, and training the kriging agent model through the training sample;
and 4, step 4: calculating a heat exchange efficiency response output value corresponding to a parameter sample except the training sample as a reference sample;
and 5: carrying out proxy calculation on the comparison sample by using the trained kriging model, and comparing the calculation result with the comparison sample in the step 4 until the relative error of the calculation result meets the set precision requirement;
step 6: adopting the Krigin agent model meeting the precision requirement in the step 5 to carry out normal random distribution on the 10 α Calculating a kriging agent model by using the characteristic parameter samples, wherein alpha is more than or equal to 6; and (3) carrying out probability analysis by a Monte Carlo method based on the calculation result of the Krigin agent model, and carrying out analysis prediction on the reliability of the heat exchange error of the tubular heat exchanger.
The related characteristic parameter x: calculating a related characteristic parameter x of the heat exchange efficiency of the tubular heat exchanger by using the inlet diameter d and the mass flow M of the inflow working medium, wherein the related characteristic parameter x is shown as a formula (1):
x＝[M,d] (1)。
the flowing working medium of the tubular heat exchanger is water.
The specific process of the step 2 is as follows: simulating the flow in the heat exchange pipe and the heat exchange process by adopting a numerical simulation calculation mode, wherein a control equation obeyed by the numerical simulation calculation process is written into a tensor form in a Cartesian coordinate system (x, y, z), and the equation is shown as a formula (2) to a formula (9):
the continuous equation:
the momentum equation:
energy equation:
wherein T is temperature, rho is density, and P is pressure of the flowing working medium; mu.s t The dynamic viscosity is the dynamic viscosity of the heat exchange working medium during turbulent flow, and lambdat is the heat conductivity coefficient of the heat exchange working medium during turbulent flow; x is the number of i Instantaneous displacement of the flowing working medium in the direction i; x is a radical of a fluorine atom j Instantaneous displacement of the flowing working medium in the j direction; e is energy; pr is the Plantt number; pr (Pr) of t Is the Plantt number u of the turbulent flow of the heat exchange working medium i Is the flow velocity in the i direction in the coordinate, u j Is the flow velocity in the direction of j in the coordinate;
the turbulence model is a realzablek-epsilon model, wherein the equation of the turbulence energy k is shown in formula (5):
wherein, the equation of the turbulent dissipation rate epsilon is shown in the formula (6):
Γ k is a constant in the turbulence model; c 1 、C 2 Is a constant; represents the y-direction velocity; such asFormula (7):
wherein σ k Representing the prandtl number of turbulent kinetic energy; sigma ε The turbulence prandtl number, which represents the turbulence dissipation ratio, is shown in equation (8):
σ k ＝1.0,σ ε ＝1.2 (8)
the heat exchange efficiency response output value is a Nu which is a Nu of Nu and is used for expressing the intensity of convective heat exchange, and the calculation mode is as shown in a formula (9):
wherein h is the convective heat transfer coefficient; d h Is the equivalent diameter of the heat exchanger inlet cross section.
The kriging agent model g k (x) As shown in formula (10):
wherein f (x) { f 1 (x),...,f 4 (x) Expressed as a basis function, β ═ β 1 ,...,β 4 The coefficient is a undetermined coefficient of a regression function; z (x) is 0, variance σ, and the expectation created on the basis of the global simulation is 0 2 The covariance of (2) is as shown in equation (11):
Cov[z(x (i) ),z(x (j) )]＝σ 2 [R(x (i) ,x (j) )] (11)
R(x (i) ,x (j) ) Represents the correlation function of any two sample points, where x (i) Training samples in the ith kriging model; x is a radical of a fluorine atom (j) Training samples in the jth kriging model; i, j 1,2, 1 (i) ,x (j) ) In the case of Gaussian correlation functions, expressionsAs shown in equation (12):
wherein, theta k (k 1, 2.... m) is an unknown relevant parameter, kriging proxy model g k (x) The response estimate of (c) is:
wherein f is T (x) Transpose to odd functions;
the matrix is an estimated value of beta, g is a column vector formed by response values of training sample data, and F is an m multiplied by p order matrix formed by regression models at m sample points; r (x) is a vector of correlation functions between training sample points and prediction points;
wherein r is T (x) R (x) is a transposed matrix expressed as:
r T (x)＝{R(x,x (1) ),R(x,x (2) ),......,R(x,x (m) )} (14)
relevant parameter theta ═ theta 1 ,θ 2 ,......,θ m Structure of (1)The fitting precision of the formed kriging agent model is optimal, and the fitting precision is obtained by solving the maximum value of the maximum likelihood estimation, as shown in formula (17):
the specific process of the step 5 is as follows:
the reliability of the heat exchange error of the heat exchanger is a multidimensional integral, as shown in formula (18):
P s ＝∫……∫ G(x)＞0 f X (x)dx (18)
where X is the vector space of the relevant characteristic parameter X, f X (x) Is a joint probability density function of characteristic parameters, and a limit state function G (x), as shown in formula (19):
G(X)＝E rlim -E r (m,d) (19)
wherein E is r (m, d) is a response function of the heat exchange amount of the heat exchange pipe, E rlim Is an error limit value; g (x) is more than 0, the heat exchange error of the heat exchange tube is more than the thermal error limit value at the moment, and the probability density of the function G (x) is more than 0 is the reliability probability; the reliability probability value is obtained by integrating the probability density function of the basic random variable, as shown in formula (20):
wherein, the first and the second end of the pipe are connected with each other,
is a variable X i An edge probability density function of (i ═ 1,2,3.., n).
The required setting error of the precision requirement is less than +/-7.5 percent.
The specific process of the step 6 is as follows:
according to f X (x) Randomly sampling x, and if G (x) is less than 0, the heat exchange error in the simulation exceeds the limit once; if a total of N simulations were performed, N appeared for G (x) < 0 f Then exceedEstimated value of heat exchange error range probability
Comprises the following steps:
with reference to equation (20), the failure probability of the monte carlo method is:
wherein, I (x) is an indication function of x, when x is less than 0, I (x) is 1, when x is more than or equal to 0, I (x) is 0; i [ g ] X (x)]Removing the integration region from the irregular failure domain omega f Expanding to infinity; according to equation (22), the ith sample value of X is set to X i Then P is f Is estimated value of
Comprises the following steps:
the above-mentioned
And when the mean value is +/-7.5%, judging that the reliability of the heat exchange error is invalid.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
according to the method, the reliability of the heat exchange error of the heat exchanger can be predicted by a small amount of numerical simulation calculation based on the result of proxy calculation of a large number of characteristic parameter samples by a Krigin model and the Monte Carlo method, so that the calculation efficiency of the reliability of the heat exchange error of the heat exchanger is effectively improved.
Drawings
Fig. 1 is a flow chart of a method for analyzing reliability of heat exchange errors of a tubular heat exchanger based on a kriging method according to an embodiment of the present invention;
FIG. 2 is a schematic view of a helical bellows provided in accordance with an embodiment of the present invention;
wherein, fig. 2(a) is a structural schematic diagram of a helical bellows; FIG. 2(b) is a schematic view of a corrugated structure;
FIG. 3 is a flowchart of a Monte Carlo method according to an embodiment of the present invention;
fig. 4 is a reliability probability density distribution diagram provided by the embodiment of the invention.
Detailed Description
The following detailed description of the present invention is provided in connection with the accompanying drawings and examples.
The embodiment provides a tubular heat exchanger heat exchange error reliability analysis method based on a kriging method, as shown in fig. 1, the method includes the following steps:
step 1: determining a related characteristic parameter x of the heat efficiency of the tubular heat exchanger, and forming a parameter sample for training a Kriging model by adopting a normal random sampling mode;
the related characteristic parameter x: calculating a related characteristic parameter x of the heat exchange efficiency of the tubular heat exchanger by using the inlet diameter d and the mass flow m of the inflow working medium, wherein the formula (24) is as follows:
x＝[m,d] (23)
in this embodiment, the heat exchange working medium of the tubular heat exchanger is water, the geometric simulation model of the helical bellows is analyzed by a numerical simulation calculation method, and the size parameters of the helical bellows are shown in fig. 2(a) and 2(b), wherein the helical pitch L is 50mm, the helical pitch D is 100mm, the inlet diameter D is 16mm, the corrugation depth e is 1.5mm, the corrugation pitch P is 32mm, and the mass flow m of the inflow working medium is 0.85 kg/s; taking the inlet diameter d, the corrugation depth e, the corrugation pitch P and the mass flow m of the inflow working medium as relevant characteristic parameters x for calculating the heat exchange efficiency of the spiral corrugated pipe heat exchanger as follows:
x＝[e,P,m,d] (24)
forming a parameter sample for training a kriging model by adopting a normal random sampling mode;
step 2: setting a variation coefficient by taking the relevant characteristic parameter x in the step 1 as a mean value, extracting the parameter samples in a normal distribution mode, and obtaining a heat exchange efficiency response output value corresponding to the extracted parameter samples as a training sample through numerical simulation calculation;
simulating the flow in the heat exchange tube and the heat exchange process by adopting a numerical simulation calculation mode, wherein a control equation obeyed by the numerical simulation calculation process is written into a tensor form in a Cartesian coordinate system (x, y, z), and the tensor form is shown as a formula (25) to a formula (32):
the continuous equation:
the momentum equation:
energy equation:
wherein T is temperature, rho is density, and P is pressure of the flowing working medium; mu.s t Is the dynamic viscosity of the heat exchange working medium during turbulent flow, and lambdat is the heat conductivity coefficient of the heat exchange working medium during turbulent flow; x is the number of i Instantaneous displacement of the flowing working medium in the direction i; x is the number of j Instantaneous displacement of the flowing working medium in the j direction; e is energy; pr is the Plantt number; pr (Pr) t Is the Plantt number u of the turbulent flow of the heat exchange working medium i Is the flow velocity in the i direction in the coordinate, u j Is the flow velocity in the j direction in the coordinate;
the turbulence model is a realzablek-epsilon model, where the equation for the turbulence energy k is shown in equation (28):
wherein, the equation of the turbulent dissipation rate epsilon is shown as the formula (29):
Γ k is a constant in the turbulence model; c 1 、C 2 Is a constant; represents the y-direction velocity; as shown in equation (30):
wherein σ k Representing the prandtl number of turbulent kinetic energy; sigma ε A turbulent prandtl number representing a turbulent dissipation ratio, as shown in equation (31):
σ k ＝1.0,σ ε ＝1.2 (31)
the heat exchange efficiency response output value is Nu which is used for expressing the intensity degree of convective heat exchange, and the calculation mode is as shown in a formula (32):
wherein h is the convective heat transfer coefficient; d h Is the equivalent diameter of the heat exchanger inlet cross section;
taking the characteristic parameter value x in the step 1 as a mean value, setting a normal distribution with a coefficient of variation of 0.03, and extracting a sample for training a kriging model; the sample portion data for training is shown in table 1:
TABLE 1 partial training sample data
And 3, step 3: establishing a kriging agent model, and training the kriging agent model through the training sample;
and 4, step 4: calculating heat exchange efficiency response output values corresponding to parameter samples except the training samples through an equation (25) to an equation (32), and taking the heat exchange efficiency response output values as comparison samples;
the kriging agent model g k (x) As shown in formula (33):
wherein f (x) { f 1 (x),...,f 4 (x) Expressed as a basis function, β ═ β 1 ,...,β 4 The coefficient is a undetermined coefficient of a regression function; z (x) is 0, variance σ, and the expectation created on the basis of the global simulation is 0 2 The covariance of (a) is as shown in equation (34):
Cov[z(x (i) ),z(x (j) )]＝σ 2 [R(x (i) ,x (j) )] (34)
R(x (i) ,x (j) ) Represents the correlation function of any two sample points, where x (i) Training samples in the ith kriging model; x is the number of (j) Training samples in the jth kriging model; i, j 1,2, 1 (i) ,x (j) ) In the case of a gaussian correlation function, the expression is given by equation (35):
wherein, theta k (k 1, 2.... m) is an unknown relevant parameter, kriging proxy model g k (x) The response estimate of (c) is:
wherein f is T (x) Is the transposition of an odd function;
is an estimate of beta, g isTraining a column vector formed by response values of sample data, wherein F is an m multiplied by p order matrix formed by regression models at m sample points; r (x) is a vector of correlation functions between training sample points and prediction points;
wherein r is T (x) R (x) is a transposed matrix expressed as:
r T (x)＝{R(x,x (1) ),R(x,x (2) ),......,R(x,x (m) )} (37)
the correlation parameter θ ═ θ 1 ,θ 2 ,......,θ m The fitting precision of the kriging proxy model formed by the method is optimal, and the fitting precision is obtained by solving the maximum value of the maximum likelihood estimation, as shown in the formula (40):
and 5: carrying out proxy calculation on the comparison sample by using the trained kriging model, and comparing the calculation result with the comparison sample in the step 4 until the relative error of the calculation result meets the set precision requirement;
in this embodiment, the reliability of the heat exchange error of the spiral corrugated tube heat exchanger is a multidimensional integral, as shown in equation (41):
P s ＝∫……∫ G(x)＞0 f X (x)dx (41)
wherein, the related characteristic parameter X influencing the heat exchange error of the corrugated spiral pipe does not contain the temperature and the spiral structure parameter, X is the vector space of X, f X (x) Is a joint probability density function of characteristic parameters, a limit state function G (x), as shown in formula (42):
G(X)＝E rlim -E r (e,P,m,d) (42)
wherein E is r (E, P, m, d) is a response function of the heat exchange amount of the spiral corrugated pipe, E rlim Is an error limit value; for X belongs to X, G (X) is more than 0 and is called as a failure domain, the heat exchange error of the spiral corrugated pipe is more than a thermal error limit value, and the probability density of a function G (X) is more than 0 and is called as reliability probability; and (4) integrating the probability density function of the basic random variable to obtain a reliability probability value, as shown in the formula (43):
wherein the content of the first and second substances,
is a variable X i An edge probability density function of (i ═ 1,2,3.., n);
step 6: adopting the Krigin agent model satisfying the error precision in the step 5 to carry out the normal random distribution on the 10 α Calculating a Crick proxy model by using the characteristic parameter samples, wherein alpha is more than or equal to 6; based on the calculation result of the kriging agent model, as shown in fig. 3, performing probability analysis by a monte carlo method, and analyzing and predicting the reliability of the heat exchange error of the tubular heat exchanger;
according to f X (x) Randomly sampling x, and if G (x) is less than 0, the heat exchange error in the simulation exceeds the limit once; if a total of N simulations were performed, N appeared for G (x) < 0 f Then, the estimated value of the probability of exceeding the heat exchange error range
Comprises the following steps:
with reference to equation (43), the failure probability of the Monte Carlo method is:
wherein, I (x) is an indication function of x, when x is less than 0, I (x) is 1, when x is more than or equal to 0, I (x) is 0; i [ g ] X (x)]The integral area is divided from the irregular failure domain omega f Expanding to infinity; according to equation (45), the ith sample value of X is set to X i Then P is f The estimated values of (c) are:
in this embodiment, the kriging proxy model satisfying the error accuracy in the step 5 is adopted to perform the normal random distribution-compliant 10 pairs 6 Carrying out proxy calculation on characteristic parameter samples, wherein the distribution mode of sample parameters is shown in a table 2; and on the basis of the calculation result of the kriging agent model, predicting the reliability of the heat exchange error of the spiral corrugated pipe heat exchanger by a Monte Carlo method.
TABLE 2 distribution of sample parameters
The probability density distribution calculated by the monte carlo method is shown in fig. 4, and the heat exchange error reliability failure is determined as 7.5% of the proxy calculation result exceeding the mean value.
In this example, the knoop number average calculated by the proxy model is 561.89, and when the knoop number of the proxy calculation result is less than 519.47 and greater than 604.031, the heat exchange error of the spiral corrugated pipe heat exchanger exceeds the specified range and is considered as failure. According to the failure condition, a spiral corrugated pipe heat exchanger heat exchange error reliability analysis method based on a Kriging method is adopted to obtain that the heat exchange error reliability is 1-0.72% (failure probability) ═ 99.28%.
Claims (9)
1. A tubular heat exchanger heat exchange error reliability analysis method based on a Kriging method is characterized by comprising the following steps: the method comprises the following steps:
step 1: determining a related characteristic parameter x of the heat efficiency of the tubular heat exchanger, and forming a parameter sample for training a Krigin model in a normal random sampling mode;
and 2, step: setting a variation coefficient by taking the relevant characteristic parameter x in the step 1 as a mean value, extracting the parameter samples in a normal distribution mode, and obtaining a heat exchange efficiency response output value corresponding to the extracted parameter samples through numerical simulation calculation to serve as a training sample;
and 3, step 3: establishing a kriging agent model, and training the kriging agent model through the training sample;
and 4, step 4: calculating heat exchange efficiency response output values corresponding to parameter samples except the training samples to serve as comparison samples;
and 5: performing proxy calculation on the comparison sample by using the trained kriging model, and comparing the calculation result with the comparison sample in the step 4 until the relative error of the calculation result meets the set precision requirement;
step 6: adopting the Krigin agent model meeting the precision requirement in the step 5 to carry out normal random distribution on the 10 α Performing Krigin proxy model calculation on the characteristic parameter samples, wherein alpha is more than or equal to 6; and based on the calculation result of the kriging agent model, performing probability analysis by a Monte Carlo method, and analyzing and predicting the reliability of the heat exchange error of the tubular heat exchanger.
2. The method for analyzing the reliability of the heat exchange error of the tubular heat exchanger based on the Kriging method as claimed in claim 1, wherein the method comprises the following steps:
the related characteristic parameter x: calculating a related characteristic parameter x of the heat exchange efficiency of the tubular heat exchanger by using the inlet diameter d and the mass flow M of the inflow working medium, wherein the related characteristic parameter x is shown as a formula (1):
x＝[M,d] (1)。
3. the method for analyzing the reliability of the heat exchange error of the tubular heat exchanger based on the Kriging method as claimed in claim 2, wherein the method comprises the following steps: the flowing working medium of the tubular heat exchanger is water.
4. The method for analyzing the reliability of the heat exchange error of the tubular heat exchanger based on the Kriging method as claimed in claim 1, wherein the method comprises the following steps:
the specific process of the step 2 comprises the following steps: simulating the flow in the heat exchange pipe and the heat exchange process by adopting a numerical simulation calculation mode, wherein a control equation obeyed by the numerical simulation calculation process is written into a tensor form in a Cartesian coordinate system (x, y, z), and the equation is shown as a formula (2) to a formula (9):
the continuous equation:
the momentum equation:
energy equation:
wherein T is temperature, rho is density, and P is pressure of the flowing working medium; mu.s t The dynamic viscosity is the dynamic viscosity of the heat exchange working medium during turbulent flow, and lambdat is the heat conductivity coefficient of the heat exchange working medium during turbulent flow; x is the number of i Instantaneous displacement of the flowing working medium in the direction i; x is the number of j Instantaneous displacement of the flowing working medium in the j direction; e is energy; pr is the Plantt number; pr (Pr) of t Is the Plantt number u of turbulent flow of heat exchange medium i Is the flow velocity in the i direction in the coordinate, u j Is the flow velocity in the direction of j in the coordinate;
the turbulence model is a realzablek-epsilon model, wherein the equation of the turbulence energy k is shown in formula (5):
wherein, the equation of the turbulent dissipation ratio epsilon is shown in the formula (6):
Γ k is a constant in the turbulence model; c 1 、C 2 Is a constant; represents the y-direction velocity; as shown in formula (7):
wherein σ k Representing the prandtl number of turbulent kinetic energy; sigma ε The turbulent prandtl number, which represents the turbulent dissipation ratio, is shown in equation (8):
σ k ＝1.0,σ ε ＝1.2 (8)
the heat exchange efficiency response output value is a Nu which is a Nu of Nu and is used for expressing the intensity of convective heat exchange, and the calculation mode is as shown in a formula (9):
wherein h is the convective heat transfer coefficient; d is a radical of h Is the equivalent diameter of the heat exchanger inlet cross section.
5. The tubular heat exchanger heat exchange error reliability analysis method based on the kriging method according to claim 1, wherein:
the kriging agent model g k (x)，As shown in equation (10):
wherein f (x) { f 1 (x),...,f 4 (x) Expressed as a basis function, β ═ β 1 ,...,β 4 The coefficient is a undetermined coefficient of a regression function; z (x) is 0, variance σ, and the expectation created on the basis of the global simulation is 0 2 The covariance of (2) is as shown in equation (11):
Cov[z(x (i) ),z(x (j) )]＝σ 2 [R(x (i) ,x (j) )] (11)
R(x (i) ,x (j) ) Represents the correlation function of any two sample points, where x (i) Training samples in the ith kriging model; x is the number of (j) Training samples in the jth kriging model; i, j 1,2, 1 (i) ,x (j) ) In the case of a gaussian correlation function, the expression is given by equation (12):
wherein, theta k (k 1, 2.... m) is an unknown relevant parameter, kriging proxy model g k (x) The response estimate of (c) is:
wherein f is T (x) Transpose to odd functions;
the matrix is an estimated value of beta, g is a column vector formed by response values of training sample data, and F is an m multiplied by p order matrix formed by regression models at m sample points; r (x) between training sample point and prediction pointA vector of correlation functions;
wherein r is T (x) R (x) is a transposed matrix expressed as:
r T (x)＝{R(x,x (1) ),R(x,x (2) ),......,R(x,x (m) )} (14)
relevant parameter theta ═ theta 1 ,θ 2 ,......,θ m The fitting precision of the kriging proxy model is optimal, and the fitting precision is obtained by solving the maximum value of the maximum likelihood estimation, as shown in formula (17):
6. the method for analyzing the reliability of the heat exchange error of the tubular heat exchanger based on the Kriging method as claimed in claim 1, wherein the method comprises the following steps:
the specific process of the step 5 comprises the following steps:
the reliability of the heat exchange error of the heat exchanger is a multidimensional integral, as shown in formula (18):
P s ＝∫……∫ G(x)＞0 f X (x)dx (18)
where X is the vector space of the relevant characteristic parameter X, f X (x) Is a joint probability density function of characteristic parameters, a limit state function G (x), as shown in formula (19):
G(X)＝E rlim -E r (m,d) (19)
wherein E is r (m, d) is a response function of the heat exchange amount of the heat exchange pipe, E rlim Is an error limit value; g (x) is more than 0, the heat exchange error of the heat exchange tube is more than the thermal error limit value at the moment, and the probability density of the function G (x) is more than 0 is the reliability probability; and (3) integrating the probability density function of the basic random variable to obtain a reliability probability value, as shown in the formula (20):
wherein f is Xi (x i ) Is a variable X i An edge probability density function of (i ═ 1,2,3.., n).
7. The tubular heat exchanger heat exchange error reliability analysis method based on the Kriging method as claimed in claim 6, wherein: the accuracy requirement setting requirement error is less than +/-7.5%.
8. The method for analyzing the reliability of the heat exchange error of the tubular heat exchanger based on the Kriging method as claimed in claim 1, wherein the method comprises the following steps: the specific process of the step 6 is as follows:
according to f X (x) Randomly sampling x, and if G (x) is less than 0, the heat exchange error in the simulation exceeds the limit once; if a total of N simulations are performed, G (x) < 0 shows N f Then, the estimated value of the probability of exceeding the heat exchange error range
Comprises the following steps:
with reference to equation (20), the failure probability of the monte carlo method is:
wherein, I (x) is an indication function of x, when x is less than 0, I (x) is 1, when x is more than or equal to 0, I (x) is 0; i [ g ] X (x)]Removing the integration region from the irregular failure domain omega f Expansion to infinity; according to equation (22), the ith sample value of X is set to X i Then P is f Is estimated value of
Comprises the following steps:
9. the tubular heat exchanger heat exchange error reliability analysis method based on the kriging method according to claim 1, wherein: the above-mentioned
And when the average value is more than +/-7.5%, judging that the reliability of the heat exchange error is invalid.
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