CN115618570A - Rapid calculation method for heat transfer characteristic of compact tubular heat exchange structure - Google Patents
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Abstract
The invention discloses a method for quickly calculating and analyzing heat transfer characteristics of a compact tubular heat exchanger, which comprises the following steps: step 1, establishing a mathematical model of a heat transfer coefficient of a shell side of a heat exchange structure based on a basic convection heat transfer theory and geometric characteristics of a compact tubular heat exchange structure; step 2, establishing a mathematical model of the heat transfer coefficient of the heat exchange structure at the tube side based on the basic theory of convective heat transfer; step 3, establishing a quasi-three-dimensional mathematical model of the steady-state convective heat transfer of the compact tubular heat exchange structure based on the porous medium theory and the volume average hypothesis; and 4, calculating and solving the temperature field based on the mathematical model established in the step. The method can quickly calculate and analyze the heat transfer characteristics of the compact tubular heat exchange structure under different spatial arrangement and geometric parameter conditions, particularly can obtain the temperature field distribution conditions of cold and hot fluid media of the heat exchange structure, and can predict the influence factors and the influence rules of the influence factors on the heat transfer characteristics.
Description
Technical Field
The invention relates to a rapid calculation and analysis method for heat transfer characteristics of a compact tubular heat exchanger, in particular to a set of mathematical model, a calculation method and a flow which can efficiently and rapidly calculate quasi-three-dimensional steady-state heat transfer characteristics of the compact tubular heat exchanger based on the structural characteristics of numerous staggered micro pipelines, so as to reasonably and efficiently obtain and analyze detailed heat transfer characteristics of the heat exchanger.
Background
In recent years, with the rapid development of science and technology and the rise of emerging subjects, new and higher requirements are put forward on heat exchangers, and compact heat exchangers have been developed rapidly in the industrial fields of petrochemical industry, thermal power, aerospace and the like since the 20 th century and the 30 th era. With the continuous perfection of the theory of intensified heat transfer and the continuous improvement of the level of mechanical manufacturing processes, many new compact heat exchangers with high efficiency are emerging, which generally have a small hydraulic diameter and a high specific surface area (ratio of heat exchange area to volume) of the heat exchange surface, exceeding 700m2/m3 on the gaseous fluid side. The heat transfer process can be further strengthened by reasonably designing the heat transfer surface, the flow mode and the like, so that the heat transfer effect is continuously improved. The technological development trends of the compact heat exchanger of today include: the heat transfer area per unit volume is continuously increased, and the application of new materials with high pressure and high temperature resistance and corrosion resistance, a micro-scale flow heat transfer mechanism, a new design method based on CFD (Computational Fluid Dynamics) simulation technology and the like are researched and applied.
However, the compact tube heat exchanger has the inherent characteristic that the number of the interlaced micro pipelines is large, and the solid three-dimensional modeling simulation analysis and evaluation of the three-dimensional flow and heat transfer process in the compact tube heat exchanger is very difficult and has huge calculation cost, so that an efficient three-dimensional calculation analysis method for the heat transfer characteristic of the compact tube heat exchanger needs to be explored. Aiming at the flow heat transfer process in the compact tubular heat exchanger, a set of quasi-three-dimensional mathematical model capable of efficiently and rapidly calculating and an evaluation method are established to reasonably and efficiently obtain and analyze the heat transfer performance of the heat exchanger, and scientific basis and theoretical support are provided for the development and perfection of design theory and technology of the compact tubular heat exchanger in multiple modern fields.
Disclosure of Invention
The invention aims to provide a theoretical prediction method for heat transfer characteristics of a compact tubular heat exchange structure so as to reasonably and efficiently obtain and analyze the heat transfer performance of a heat exchanger.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for rapidly calculating heat transfer characteristics of a compact tubular heat exchanger comprises the following steps:
and 4, calculating and solving the temperature field based on the mathematical model established in the steps 1 to 3.
The step 1 specifically comprises the following steps:
step 11, the shell side qualitative temperature adopts the average temperature of the shell side fluid inlet and outlet pipe bundles:
wherein, t' 1 Is the temperature of the hot fluid at the inlet, t ″) 1 For the temperature of the hot fluid at the outlet, subscript m denotes the average, subscript 1 denotes the shell side variable;
step 12, the shell side fluid reynolds number is described as:
the flow velocity at the smallest cross section of the tube bundle is described as:
where the subscript o denotes shell side, d o Is the outer diameter of the heat exchange tube u o Is the flow rate of the hot fluid, S 1 And S 2 Respectively transverse pitch, longitudinal pitch, v, of the tube bundle in rows of prongs o The kinematic viscosity of the fluid at the shell side qualitative temperature;
and step 13, selecting a Knudel number calculation relation for the heat transfer of the fluid passing through the cross row tube bundle:
wherein, pr fo Is the prandtl number of the shell-side fluid, pr wo Is the prandtl number of fluid in the shell side near-wall region;
step 14, based on the basic theory of convection heat transfer, the shell side heat transfer coefficient is as follows:
wherein λ is o Is the shell-side fluid thermal conductivity at shell-side qualitative temperature, d o Is the outer diameter of the heat exchange tube，Nu o The shell side Nussel number at the qualitative temperature;
accounting for tube wall temperature t based on shell side heat transfer coefficient w ＝t m1 -q/h o Wherein q is the heat flux density.
The step 2 specifically comprises the following steps:
step 21, adopting the average temperature of the inlet and the outlet of the fluid at the tube side as the tube side qualitative temperature:
wherein, t' 2 ,t″ 2 The inlet and outlet temperatures of the fluid in the pipe are respectively;
at step 22, the reynolds number of the tube side flow is described as:
wherein the subscript i denotes the tube side, d i Is the inner diameter of the heat exchange tube v i The kinematic viscosity u of the fluid in the tube at the tube side qualitative temperature i Is the flow rate of the fluid in the tube;
step 23, for the tube side layer flow heat transfer, selecting an experimental correlation formula provided by Sieder and Tate:
for turbulent heat transfer within a tube, the Knudsen number relationship is obtained by referring to the formula of Glynes:
wherein, pr i Is the Plantt number of the fluid on the tube side, d i And l is the tube diameter and the tube length, respectively, f i Darcy drag coefficient for turbulent flow within a pipe:
f i ＝(1.81 lg Re i -1.5) -2 (9)
λ i Is the coefficient of thermal conductivity of the fluid in the tube at the tube side qualitative temperature, d i Is the inner diameter of the heat exchange tube Nu i The Nussel number at the qualitative temperature.
The step 3 specifically comprises the following steps:
step 31, establishing an equivalent staggered micro-channel structure, wherein the flow direction of the airflow 1 is parallel to x 1 The flow direction of the gas flow 2 is parallel to x 2 And the gas flow 1 and the gas flow 2 simultaneously exchange heat with adjacent channels through the micro-channels. Because the actual wall thickness of the tube is thin, the thermal resistance of the tube wall is ignored, and the thermal diffusion item is ignored when forced convection heat transfer is the main heat transfer process, the volume average method is applied to establish the temperature control equation in the microstructure as follows:
wherein ρ and C p Respectively the density and the specific heat capacity at constant pressure of the fluid, u is the average speed in the flow channel, h fs For convective heat transfer coefficient, A fs And ε is the area ratio and porosity of the porous media model, respectively, T is the fluid temperature, subscript 1 and subscript 2 represent fluid 1 and fluid 2, respectively;
step 32, integrating the equations (11 a) and (11 b) in step 31 to obtain an integral equation of
ε 1 ρ 1 C p1 u 1 T 1 +h fs1 A fs (T 1 -T 2 )x 1 ＝C 1 (12a)
(1-ε 1 )ρ 2 C p2 u 2 T 2 -h fs2 A fs (T 1 -T 2 )x 2 ＝C 2 (12b)
Step 33, apply the edge condition x 1 ＝0，T 1 ＝T 10 And x 2 ＝0，T 2 ＝T 20 Substituting into the formulae (12 a) and (12 b) in step 32 to obtain the coefficient C 1 ＝ε 1 ρ 1 C p1 u 1 T 10 And C 2 ＝(1-ε 1 )ρ 2 C p2 u 2 T 20 A constant C 1 And C 2 And (3) respectively substituting the formula (12) and carrying out algebraic derivation to obtain an analytic solution of the temperature distribution of the fluid 1 and the fluid 2:
the step 4 specifically comprises the following steps:
step 41, firstly, determining initial design parameters of a heat exchange structure, including flow m, flow speed u and initial temperature t' of two heat exchange fluids; secondly, based on the qualitative temperature t m And further determining material physical property parameters and heat exchange characteristic parameters of the fluid working medium, including density rho and constant pressure specific heat capacity C of the fluid working medium p A heat conductivity coefficient lambda, a kinematic viscosity v and a heat transfer coefficient h; determining the porosity epsilon and the area ratio A of the porous medium model by combining the arrangement and the geometric parameters of the compact tubular heat exchange structure fs (ii) a Then, the relevant initial flow heat exchange conditions, physical parameters, geometric parameters and the like are taken as coefficients to be carried into formula (13) to obtain the T 1 And T 2 The system of equations (1);
step 42, calculating and solving the heat transfer equation set constructed in the step 41 to obtain the temperature distribution condition of the heat exchange structure; based on the micro-channel configuration of the heat exchange structure, dividing the flow channels of the fluid 1 and the fluid 2 into k multiplied by j grid units respectively, and calculating the temperature of the fluid in each grid unit in sequence, wherein the method comprises the following steps:
i: for j =1 line, T 2,k,j＝1 Is the inlet boundary temperature condition of the fluid 2, and the T of the fluid 1 is calculated by applying the equation (13 a) 1,k,j＝1 Along with position coordinate x 1 The change rule of (2); for k =1 line, T 1,k＝1,j Is the inlet boundary temperature condition of the fluid 1, and T is calculated by applying the equation (13 b) 2,k＝1,j Along with the position coordinate x 2 The change rule of (2); wherein subscript 2 denotes fluid 2,k and j denotes a grid cell number;
II: for j =2,T 2,k,j＝2 Is a fluid 2 unit T 2,k＝1,j＝2 Temperature condition of (1), calculating T by applying the formula (13 a) 1,k,j＝2 X is 1 The change rule of (2); for k =2,T 1,k＝2,j As fluid 1 unit T 1,k＝2,j＝1 Inlet boundary temperature condition, using equation (13 b) to calculate T 2,k＝2,j X is 2 The change rule of (2);
……
sequentially and alternately calculating the temperature values of the fluid 1 and the fluid 2 in the rows k and j until the temperature values in all the units k multiplied by j are calculated;
and 43, comparing the fluid outlet temperature and the pipe wall temperature obtained by calculation in the step 42 with the fluid outlet temperature and the pipe wall temperature initially set in the step 41, stopping calculation if the deviation between the fluid outlet temperature and the pipe wall temperature is less than 5% and the design requirements are met, and resetting the outlet temperature and the pipe wall temperature and repeating the steps 1 to 4 if the deviation between the fluid outlet temperature and the pipe wall temperature is not more than 5%.
Has the advantages that: the method can calculate and obtain the average heat exchange coefficient of the heat exchanger and the outflow temperature of the fluid working medium after heat exchange based on the conventional tube bundle heat exchanger theoretical analysis method, but cannot acquire the temperature field distribution of the heat exchange structure. Although three-dimensional temperature field distribution can be obtained by means of CFD simulation technology, the quantity of interlaced micro-pipelines in the compact tubular heat exchange structure is large, the solid three-dimensional modeling simulation analysis of the three-dimensional flow and heat transfer process in the compact tubular heat exchanger is very difficult, and the modeling and calculation costs are very large. The advantages of the invention are as follows: a rapid calculation model and a rapid calculation method for the quasi-three-dimensional steady-state heat transfer characteristics of a compact tubular heat exchange structure are provided. Based on the mathematical model and the calculation method, the heat transfer characteristics of the compact tubular heat exchange structure under different spatial arrangement and geometric parameter conditions can be calculated and analyzed, particularly the temperature field distribution conditions of cold and hot fluid media of the heat exchange structure can be obtained, meanwhile, the influence factors and the influence rules of the influence factors on the heat transfer characteristics can be predicted, and a foundation and a theoretical support are provided for the development and the perfection of the design theory and the technology of the heat exchange structure.
Drawings
FIG. 1 is a schematic view of a fork bank bundle structure;
wherein: s T ,S L The transverse pitch and the longitudinal pitch of the cross row tube bundle are respectively, d is the diameter of the heat exchange tube, and u is the flow velocity of fluid outside the tube;
FIG. 2 is a schematic diagram of a heat exchange structure, wherein (a) is a schematic diagram of a compact tubular heat exchange structure and (b) is an equivalent staggered micro-channel heat exchange structure;
FIG. 3 is a schematic diagram of computational meshing of flow heat transfer for an interleaved microchannel structure; wherein: i and j are grid number variables, m 1 And m 2 The flow rate of the heat exchange fluid;
FIG. 4 is a flow chart of compact tubular heat exchange structure temperature field calculation;
fig. 5 illustrates the cloud of the temperature distribution of the hot and cold fluids in the embodiment.
Detailed Description
The invention is further explained below with reference to the drawings.
The invention provides a mathematical model and a calculation method capable of efficiently and quickly calculating the quasi-three-dimensional steady-state heat transfer characteristic of a compact tubular heat exchanger based on the requirements of engineering calculation and design of the heat exchange characteristic of the tubular heat exchanger. The specific implementation process of the invention is shown in figure 4.
The invention relates to a method for calculating heat transfer characteristics of a compact tubular heat exchanger, which comprises the following steps of:
step 11, firstly, the initial design parameters of the heat exchange structure, including the inlet flow m of the shell side fluid o Speed u o And initial temperature t' 1 Are generally known to be deterministic.
Secondly, the outlet temperature and the pipe wall temperature of the shell side fluid after heat exchange are set as t ″ 1 And t w Calculating the qualitative temperature t of the fluid on the shell side by the formula (1) m1
Wherein, t' 1 Is the temperature, t ″, of the hot fluid at the inlet 1 Is the temperature of the hot fluid at the outlet; where the subscript m represents the average and the subscript 1 represents the shell side variables.
Qualitative temperature t based on preliminary determination m1 And wall temperature t w Then, the material physical parameters and the like corresponding to the shell side fluid working medium at the temperature can be further checked, including the density rho o Specific heat capacity C po Thermal conductivity lambda o And kinematic viscosity v o . Shell side fluid Plantt number Pr fo Determined according to fluid physical property parameters under qualitative temperature condition, pr wo And determining according to the fluid physical property parameters under the condition of the average wall temperature of the tube bundle.
Step 12, calculating the Reynolds number of the shell side fluid through the formula (2)
The flow velocity at the smallest cross section of the tube bundle is described as:
u o is the hot fluid flow rate. S 1 ,S 2 The transverse pitch and the longitudinal pitch of the cross-row tube bundle are shown in figure 1. V is o Is the fluid kinematic viscosity of the fluid at a qualitative temperature.
Step 13, for the heat transfer of the fluid across the tube bundle of the cross row, referring to an experimental correlation given by Ru Kawu scasts, selecting a nussel number calculation relation, and when the tube bundle of the cross row is less than 16 rows, adopting a tube row number correction coefficient shown in table 1.
Wherein, pr fo Is the prandtl number of the shell-side fluid, pr wo Is the prandtl number of fluid in the shell side near-wall region;
TABLE 1 Ru Kawu Skats correlation tube row number correction coefficient
Step 14, calculating the shell side heat transfer coefficient by the formula (5) based on the basic theory of convective heat transfer
λ o Is the shell-side fluid thermal conductivity at shell-side qualitative temperature, d o Is the outer diameter of the heat exchange tube. And may be based on shell side heat transferCoefficient accounting for the wall temperature t w ＝t m1 -q/h o And q is the heat flux density.
step 21, initial design parameters of the heat exchange structure, including inlet flow m of fluid on the tube side i Speed u i And initial temperature t' 2 Are generally known to be deterministic. The outlet temperature and the pipe wall temperature of the fluid at the pipe side after heat exchange are set as t ″ 2 Calculating the qualitative temperature t of the fluid on the tube side by the formula (6) m2
Qualitative temperature t based on preliminary determination m2 Then, the material physical parameters and the like corresponding to the fluid working medium at the tube side under the temperature can be further checked, including the density rho i Specific heat capacity C pi And a heat conductivity coefficient lambda i Kinetic viscosity v i And the Plantt number Pr of the fluid on the tube side fi 。
Step 22, calculating the Reynolds number of the fluid on the pipe side by the formula (7)
Wherein the subscript i denotes the tube side, d i Is the inner diameter of the heat exchange tube v i The kinematic viscosity u of the fluid in the tube at the tube side qualitative temperature i Is the flow rate of the fluid in the tube;
step 23, for laminar flow heat transfer in the pipe, an experimental correlation formula provided by Sieder and Tate is selected to calculate the Nu of the Nu i
For turbulent heat transfer in a pipe, the Knudsen number Nu is calculated by referring to the formula of Gernilins i
Wherein d is i And l is the tube diameter and the tube length, respectively, f i Darcy drag coefficient for turbulent flow within a pipe:
f i ＝(1.81lgRe i -1.5) -2 (9)
λ i Is the coefficient of thermal conductivity of the fluid in the tube at the tube side qualitative temperature, d i Is the inner diameter of the heat exchange pipe.
and establishing a quasi-three-dimensional mathematical model of the convection heat transfer of the fluid on the shell side and the tube side in the compact tubular heat exchange structure based on the volume average hypothesis and the porous medium theory by combining the structural characteristics of the compact tubular heat exchanger and the internal fluid flow heat exchange characteristics of the compact tubular heat exchanger.
Step 31, the actual dense tube bundle structure as shown in fig. 2 (a) is equivalent to the staggered microchannel structure as shown in fig. 2 (b). As shown in fig. 2 (b), the flow direction of the gas flow 1 is parallel to x 1 The flow direction of the gas flow 2 is parallel to x 2 The gas flow 1 and the gas flow 2 pass through the micro-channel and simultaneously carry out heat transfer with the adjacent channel. Since the actual wall thickness of the tube is very thin, the thermal resistance of the tube wall is negligible. The volume average method is used for establishing a temperature control equation in the microstructure as
Wherein ρ and C p Respectively the density and the specific heat capacity at constant pressure of the fluid, u is the average speed in the flow channel, h fs For convective heat transfer coefficient, A fs And ε is the area ratio and porosity, respectively, of the porous media model. T is the fluid temperature. Subscript 1 and subscript 2 denote fluid working substance 1 and fluid working substance 2, respectively.
Step 32, integrating the equations (11 a) and (11 b) in step 31 to obtain an integral equation of
ε 1 ρ 1 C p1 u 1 T 1 +h fs1 A fs (T 1 -T 2 )x 1 ＝C 1 (12a)
(1-ε 1 )ρ 2 C p2 u 2 T 2 -h fs2 A fs (T 1 -T 2 )x 2 ＝C 2 (12b)
Step 33, based on the model shown in FIG. 2, has x 1 ＝0，T 1 ＝T 10 And x 2 ＝0，T 2 ＝T 20 The edge value condition of (2). Substituting the boundary condition into the formulae (12 a) and (12 b) in step 32 to obtain the coefficient C 1 ＝ε 1 ρ 1 C p1 u 1 T 10 And C 2 ＝(1-ε 1 )ρ 2 C p2 u 2 T 20 . Will be constant C 1 And C 2 The formula (12) is respectively substituted, algebraic derivation is carried out, and the analytic solutions of the temperature distribution of the fluid 1 and the fluid 2 are obtained as follows:
step 4, calculating a quasi-three-dimensional temperature field of the heat transfer characteristic of the heat exchange structure, comprising the following steps:
step 41, through the steps 1 to 3: the initial design parameters of the heat exchange structure, including the flow rate and initial temperature of the two heat exchange fluids, are generally determined, i.e. u 1 、u 2 、T 10 And T 20 Determining; according to the qualitative temperature, the material physical property parameters, heat transfer coefficient and the like of the fluid working medium at the temperature can be further determined, namely rho 1 、ρ 2 、C p1 、C p2 、h fs1 And h fs2 (ii) a Determining the porosity and area ratio of the porous medium model, namely epsilon, by combining the arrangement and geometric parameters of the compact tubular heat exchange structure 1 And A fs And (4) determining. The values of these initial flow heat transfer conditions, physical parameters, geometric parameters, etc. are taken as coefficients to obtain the equation (13) for T 1 And T 2 The system of equations of (1).
And 42, calculating and solving the heat transfer equation set constructed in the step 41 to obtain the temperature distribution condition of the heat exchange structure. Based on the configuration of the heat exchange structure microchannel shown in fig. 2 (b), the fluid 1 and fluid 2 channels are respectively divided into k × j grid units, as shown in fig. 3, and the fluid temperature in each grid unit is sequentially calculated, the steps are as follows:
i: for j =1 column, T 2,k,j＝1 The value of (d) is the fluid 2 inlet boundary temperature condition. Calculation of T of fluid 1 Using equation (13 a) 1,k,j＝1 Along with the position coordinate x 1 The change rule of (2). For k =1 line, T 1,k＝1,j The value of (b) is the fluid 1 inlet boundary temperature condition. Calculation of T Using equation (13 b) 2,k＝1,j Along with the position coordinate x 2 The change rule of (2). Wherein subscript 2 denotes fluid 2,k and j denotes a grid cell number;
II: for j =2 columns, T 2,k,j＝2 Is a fluid 2 unit T 2,k＝1,j＝2 The temperature condition of (2). Calculating T by applying equation (13 a) 1,k,j＝2 X is 1 The change rule of (2). For k =2 lines, T 1,k＝2,j Is a fluid 1 unit T 1,k＝2,j＝1 Inlet boundary temperature conditions. Calculation of T Using equation (13 b) 2,k＝2,j X is 2 The change rule of (2).
……
And sequentially and alternately calculating the temperature values of the fluid 1 and the fluid 2 in the rows k and j until the calculation of the temperature values in all the k multiplied by j units is completed.
Step 43: comparing the fluid outlet temperature and the pipe wall temperature obtained by calculation in the step 42 with the fluid outlet temperature and the pipe wall temperature initially set in the step 41, stopping calculation when the deviation between the two is small (less than 5%) and the requirements are met, otherwise resetting the outlet temperature and the pipe wall temperature and repeating the steps 1 to 4, wherein the calculation flow is shown in fig. 4.
The present invention will be further described with reference to the following examples.
Examples
(1) Calculation of heat transfer coefficient of shell side of heat exchange structure
(1.1) taking a compact tubular heat exchange structure as an example, a geometric model diagram thereof is shown in fig. 2 (a), and known initial design conditions and parameters are shown in tables 2 and 3, respectively.
TABLE 2 initial design flow and temperature conditions for heat exchange structures
TABLE 3 geometric parameters of Heat exchange structures
(1.2) obtaining qualitative temperatures t based on the formula (1), the formula (2), the formula (4) and the formula (5) in the step 1, respectively m1 =642.0K, shell side Reynolds number Re o =453.0 shell side Nu number o =7.5, the heat convection coefficient of the shell side is h o ＝994.2。
(2) Calculation of heat transfer coefficient of heat exchange structure tube side
Combining the basic design parameters of tables 2 and 3, and respectively obtaining the qualitative temperature t based on the formula (6), the formula (7), the formula (8) and the formula (10) in the step 2 m2 =301.1K, shell side Reynolds number Re i =198.0, shell side Nu seel number Nu i =2.8, shell side convective heat transfer coefficient of h i ＝1192.4。
(3) Establishing a quasi-three-dimensional mathematical model of steady-state convection heat transfer of a compact tubular heat exchange structure, wherein the equation set is shown as a formula (13):
(4) Quasi-three-dimensional steady-state temperature field for calculating heat transfer characteristic of heat exchange structure
(4.1) the variable value obtained by the analysis is brought into the correlation coefficient of (13), namely the value about T is obtained 1 And T 2 The system of equations of (a). It is to be noted that the fluid physical parameter in formula (13) is a function of temperature, i.e.
The fitting relation of the nitrogen physical property parameters is as follows:
density: rho 1 ＝3.161942-0.009682608T+1.202177e10 -5 T 2 -5.189068e10 -9 T 3
Specific heat capacity: c p1 ＝1047.143-0.3461212T+0.0008111318T 2 -3.71728e10 -7 T 3
The fitting relation of the physical parameters of the supercritical helium is as follows:
density: rho 1 ＝100.7069-0.9549658T+0.004865611T 2 -1.438563e10 -5 T 3 +2.536484e10 -8 T 4 -2.623537e10 -11 T 5 +1.466367e10 -14 T 6 -3.414229e10 -18 T 7
Specific heat capacity: c p1 ＝5695.899-6.633854T+0.03764684T 2 -0.0001169575T 3 +2.119099e10 -7 T 4 -2.22886e10 -10 T 5 +1.259755e10 -13 T 6 -2.956371e10 -17 T 7
And (4.2) obtaining the temperature field of the heat exchange structure through iterative computation based on the established quasi-three-dimensional mathematical equation set of the steady-state convective heat transfer of the heat exchange structure and by combining the computation flow shown in the figure 4.
Fig. 5 shows a cloud diagram of the temperature distribution of the hot and cold fluids, and it can be seen from the diagram that the temperature of the hot fluid gradually decreases along the process (x direction), and the temperature distribution near the cold fluid inlet (z → 0) is obviously lower than that at the cold fluid outlet (z → 40), and the temperature gradient is relatively large. Similarly, the temperature distribution of the cold fluid also exhibits a similar law: the cold fluid temperature increases gradually along the way (z direction), and the temperature at the inlet (x → 0) of the hot fluid is obviously higher than the temperature distribution at the outlet (x → 40) of the hot fluid, and the temperature gradient is relatively large. The temperature difference between the inlet and the outlet of the hot fluid is the largest (504K) closest to the inlet of the cold fluid. The temperature difference between the hot fluid inlet and the hot fluid outlet farthest from the cold fluid inlet is the smallest (327K). The temperature difference between the inlet and the outlet of the cold fluid is the largest at the hot fluid inlet (496K). The temperature difference between the inlet and the outlet of the cold fluid farthest from the hot fluid inlet is the smallest (296K). In addition, the calculation result of the temperature difference between the inlet and the outlet of the cold fluid and documents [6] The experimental results are compared, the relative deviation of the two is less than 10%, and the reliability of the calculation model and the method is reflected.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. A method for quickly calculating heat transfer characteristics of a compact tubular heat exchanger is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a mathematical model of a heat transfer coefficient of a shell side of a heat exchange structure based on a basic convection heat transfer theory and geometric characteristics of a compact tubular heat exchange structure;
step 2, establishing a mathematical model of the heat transfer coefficient of the heat exchange structure on the tube side based on the basic theory of convective heat transfer;
step 3, establishing a quasi-three-dimensional mathematical model of the steady-state convective heat transfer of the compact tubular heat exchange structure based on the porous medium theory and the volume average hypothesis;
and 4, calculating and solving the temperature field based on the mathematical model established in the steps 1 to 3.
2. The method for calculating the heat transfer characteristics of a compact tube heat exchanger according to claim 1, wherein: the step 1 specifically comprises the following steps:
step 11, the shell side qualitative temperature adopts the average temperature of the shell side fluid inlet and outlet pipe bundles:
wherein, t' 1 Is the temperature, t ″, of the hot fluid at the inlet 1 For the temperature of the hot fluid at the outlet, subscript m denotes the average, subscript 1 denotes the shell side variable;
step 12, the shell side fluid reynolds number is described as:
the flow velocity at the smallest cross section of the tube bundle is described as:
where the subscript o denotes shell side, d o Is the outer diameter of the heat exchange tube u o Is the flow rate of the hot fluid, S 1 And S 2 Respectively transverse pitch, longitudinal pitch, v, of the tube bundle in rows of prongs o The kinematic viscosity of the fluid at the shell side qualitative temperature;
and step 13, selecting a Knudel number calculation relation for the heat transfer of the fluid passing through the cross row tube bundle:
wherein, pr fo Is the prandtl number of the shell-side fluid, pr wo Is the prandtl number of fluid in the shell side near-wall region;
step 14, based on the basic theory of convection heat transfer, the shell side heat transfer coefficient is as follows:
wherein λ is o Is the shell-side fluid thermal conductivity at shell-side qualitative temperature, d o Is the outer diameter of the heat exchange tube Nu o The shell side Nussel number at the qualitative temperature;
accounting for tube wall temperature t based on shell side heat transfer coefficient w ＝t m1 -q/h o Wherein q is the heat flux density.
3. The method for calculating the heat transfer characteristics of a compact tube heat exchanger according to claim 1, wherein: the step 2 specifically comprises the following steps:
step 21, adopting the average temperature of the inlet and the outlet of the fluid at the tube side as the tube side qualitative temperature:
wherein, t' 2 ,t″ 2 The inlet and outlet temperatures of the fluid in the pipe are respectively;
at step 22, the reynolds number of the tube side flow is described as:
wherein the subscript i denotes the tube side, d i Is the inner diameter of the heat exchange tube v i The kinematic viscosity u of the fluid in the tube at the tube side qualitative temperature i Is the flow rate of the fluid in the tube;
step 23, for the tube side layer flow heat transfer, selecting an experimental correlation formula provided by Sieder and Tate:
for turbulent heat transfer within a tube, the Knudsen number relationship is obtained by referring to the formula of Glynes:
wherein, pr i Is the Plantt number of the fluid on the tube side, d i And l is the tube diameter and the tube length, respectively, f i Darcy drag coefficient for turbulent flow within a pipe:
f i ＝(1.81lgRe i -1.5) -2 (9)
step 24, based on the basic theory of convective heat transfer, the heat transfer coefficient of the heat exchange structure at the tube side is described as
λ i Is the coefficient of thermal conductivity of the fluid in the tube at the tube side qualitative temperature, d i Is the inner diameter of the heat exchange tube Nu i The Nussel number at the qualitative temperature.
4. The method for calculating the heat transfer characteristics of the compact tube heat exchanger according to claim 1, wherein: the step 3 specifically comprises the following steps:
step 31, establishing an equivalent staggered micro-channel structure, wherein the flow direction of the airflow 1 is parallel to x 1 The flow direction of the gas flow 2 is parallel to x 2 The gas flow 1 and the gas flow 2 simultaneously exchange heat with adjacent channels through the micro-channels. Because the actual wall thickness of the tube is thin, the thermal resistance of the tube wall is ignored, and the thermal diffusion item is ignored when forced convection heat transfer is the main heat transfer process, the volume average method is applied to establish the temperature control equation in the microstructure as follows:
in the formula, rho and C p Respectively the density and the specific heat capacity at constant pressure of the fluid, u is the average speed in the flow channel, h fs For convective heat transfer coefficient, A fs And ε is the area ratio and porosity of the porous media model, respectively, T is the fluid temperature, subscript 1 and subscript 2 denote fluid 1 and fluid 2, respectively;
step 32, integrating the equations (11 a) and (11 b) in step 31 to obtain an integral equation of
ε 1 ρ 1 C p1 u 1 T 1 +h fs1 A fs (T 1 -T 2 )x 1 ＝C 1 (12a)
(1-ε 1 )ρ 2 C p2 u 2 T 2 -h fs2 A fs (T 1 -T 2 )x 2 ＝C 2 (12b)
Step 33, apply the edge condition x 1 ＝0，T 1 ＝T 10 And x 2 ＝0，T 2 ＝T 20 Substituting into the formulae (12 a) and (12 b) in step 32 to obtain the coefficient C 1 ＝ε 1 ρ 1 C p1 u 1 T 10 And C 2 ＝(1-ε 1 )ρ 2 C p2 u 2 T 20 A constant C 1 And C 2 And (3) respectively substituting the formula (12) and carrying out algebraic derivation to obtain an analytic solution of the temperature distribution of the fluid 1 and the fluid 2:
5. the method for calculating the heat transfer characteristics of a compact tube heat exchanger according to any one of claims 1 to 4, wherein: the step 4 specifically comprises the following steps:
step 41, firstly, determining initial design parameters of a heat exchange structure, including flow m, flow speed u and initial temperature t' of two heat exchange fluids; secondly, based on the qualitative temperature t m And further determining material physical property parameters and heat exchange characteristic parameters of the fluid working medium, including density rho and constant pressure specific heat capacity C of the fluid working medium p A heat conductivity coefficient lambda, a kinematic viscosity v and a heat transfer coefficient h; determining the porosity epsilon and the area ratio A of the porous medium model by combining the arrangement and the geometric parameters of the compact tubular heat exchange structure fs (ii) a Then, the relevant initial flow heat exchange conditions, physical parameters, geometric parameters and the like are taken as coefficients to be carried into formula (13) to obtain the T 1 And T 2 The system of equations of (a);
step 42, calculating and solving the heat transfer equation set constructed in the step 41 to obtain the temperature distribution condition of the heat exchange structure; based on the micro-channel configuration of the heat exchange structure, dividing the flow channels of the fluid 1 and the fluid 2 into k multiplied by j grid units respectively, and calculating the temperature of the fluid in each grid unit in sequence, wherein the method comprises the following steps:
i: for j =1 line, T 2,k,j＝1 Is the inlet boundary temperature condition of the fluid 2, and the T of the fluid 1 is calculated by applying the equation (13 a) 1,k,j＝1 Along with position coordinate x 1 The change rule of (2); for k =1 line, T 1,k＝1,j Is the inlet boundary temperature condition of the fluid 1, and T is calculated by applying the equation (13 b) 2,k＝1,j Along with the position coordinate x 2 The change rule of (2); wherein subscript 2 denotes fluid 2,k and j denotes a grid cell number;
II: for j =2,T 2,k,j＝2 Is a fluid 2 unit T 2,k＝1,j＝2 Using the temperature condition of (1), calculating T by using the formula (13 a) 1,k,j＝2 X is 1 The change rule of (2); for k =2,T 1,k＝2,j Is a fluid 1 unit T 1,k＝2,j＝1 Inlet boundary temperature condition, using equation (13 b) to calculate T 2,k＝2,j X is 2 The change rule of (2);
……
sequentially and alternately calculating the temperature values of the fluid 1 and the fluid 2 in the rows k and j until the temperature values in all the units k multiplied by j are calculated;
and 43, comparing the fluid outlet temperature and the pipe wall temperature obtained by calculation in the step 42 with the fluid outlet temperature and the pipe wall temperature initially set in the step 41, stopping calculation if the deviation between the two is less than 5% and the design requirements are met, and resetting the outlet temperature and the pipe wall temperature and repeating the steps 1 to 4 if the deviation between the two is not more than 5%.
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