CN115186606A - Checking method of multi-stream countercurrent plate-fin heat exchanger and computer program product - Google Patents
Checking method of multi-stream countercurrent plate-fin heat exchanger and computer program product Download PDFInfo
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Abstract
The invention provides a checking method and a computer program product of a multi-strand countercurrent plate-fin heat exchanger, which are high in calculation speed and high in precision, and aims to solve the technical problems that the CFD simulation algorithm of the conventional plate-fin heat exchanger is low in calculation speed and cannot be applied to an industrial large-scale plate-fin heat exchanger with hundreds of layers of fin channels. The method mainly comprises the following steps: inputting structural parameters and working condition parameters of the plate-fin heat exchanger, initializing a temperature field and a pressure field, fitting physical parameters of each fluid, constructing a heat conduction model of the fin, deducing to obtain a pressure field distribution, a partition plate temperature field and a fluid temperature field distribution equation set, and performing iterative solution on the equation set. The calculation method of the invention considers the axial heat conduction effect which causes the serious reduction of the heat exchanger capability in the low-temperature plate-fin heat exchanger, can calculate the overall pressure distribution and temperature field distribution of the countercurrent plate-fin heat exchanger in any arrangement mode, and reduces the cost and the period of the heat exchanger design.
Description
Technical Field
The invention belongs to a checking method of a heat exchanger, and particularly relates to a checking method of a multi-strand countercurrent plate-fin heat exchanger and a computer program product.
Background
The multi-flow plate-fin heat exchanger has the advantages of high heat transfer efficiency, large specific surface area and strong adaptability, and is widely applied to the field of low-temperature heat exchange. The CFD calculation of the plate-fin heat exchanger is discussed in a large number of existing documents, the method is only suitable for simulation of a single channel or a few channels, simulation of hundreds of layers of fin channels in the industry cannot be performed at all, and some researches consider the overall lumped parameter calculation of the plate-fin heat exchanger, and the method is high in calculation speed and poor in accuracy. In addition, the basic idea of the calculation method of the distribution parameter model is to divide the plate-fin heat exchanger into a plurality of small sections along the flow direction, so that the thermophysical properties of the working medium in each discrete section are approximately unchanged, but the axial heat conduction in the partition plate is not considered in the related method of the distribution parameter model.
Disclosure of Invention
The invention provides a checking method and a computer program product of a multi-strand countercurrent plate-fin heat exchanger, aiming at solving the technical problems that the simulation algorithm aiming at the multi-strand plate-fin heat exchanger at present cannot be applied to the simulation of hundreds of layers of fin channels, is high in calculation speed and poor in precision, and axial heat conduction in a partition plate is not considered.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a checking method of a multi-flow countercurrent plate-fin heat exchanger is characterized by comprising the following steps:
s1, arranging N partition plate temperature nodes in a partition plate along a main flow direction, so that N +1 fluid temperature nodes are formed in a fin channel along the main flow direction, and two adjacent fluid temperature nodes in a fin channel form a fluid unit; wherein N is an integer greater than 1;
s2, estimating the temperature range and the pressure range of each strand of fluid, initializing a fluid pressure field, a fluid temperature field and a partition plate temperature field, and fitting a spline surface or a spline curve by combining the physical properties of each strand of fluid;
s3, according to a spline surface fitting result, combining an f factor in a fin channel and parameters of the multi-stream countercurrent plate-fin heat exchanger, calculating the pressure drop of each fluid unit, further calculating to obtain the pressure field distribution of the whole fluid domain, combining the fluid pressure field initialized in the step S2, determining a pressure field residual error, if the pressure field residual error meets a convergence condition, taking the current pressure field as a check effect, and continuing to execute the step S4, otherwise, recalculating the pressure drop of each fluid unit, further calculating to obtain new pressure field distribution of the whole fluid domain, and determining the residual error of the pressure field according to the new pressure field distribution and the old pressure field distribution obtained by the previous iterative calculation until the pressure field residual error meets the convergence condition;
s4, obtaining the temperature gradient of the top of the fin and the temperature gradient of the root of the fin according to the one-dimensional heat conduction equation of the fin, and determining a partition plate temperature node calculation equation set and a fluid temperature node calculation equation set;
s5, determining the heat exchange coefficient h between the surface of the fin in each fluid unit and the fluid according to the j factor of the plate-fin heat exchanger, the physical property parameter of the fluid and the structural parameter of the fin in each layer of channel c,i Determining a partition plate temperature node influence coefficient and a fluid temperature node influence coefficient, solving a partition plate temperature node calculation equation set and a fluid temperature node calculation equation set by combining parameters of the multi-strand countercurrent plate-fin heat exchanger, and determining a fluid temperature field and a partition plate temperature field;
and S6, obtaining the temperature residual errors of the fluid temperature field and the partition plate temperature field, taking the obtained fluid temperature field, the partition plate temperature field and the current pressure field as check results if the temperature residual errors of the fluid temperature field and the partition plate temperature field meet the preset temperature residual error requirement, otherwise, repeatedly executing the steps S3 to S6 under the current fluid temperature field, the partition plate temperature field and the current pressure field until the temperature residual errors of the fluid temperature field and the partition plate temperature field meet the preset temperature residual error requirement.
Further, in step S3, the parameters of the multi-flow countercurrent plate-fin heat exchanger include the number of layers n of the heat exchanger, the arrangement manner, the overall size, the structural parameters and the working condition parameters of the fins in each layer of fin channel, and the working condition parameters of each layer of fin channel.
Further, in step S3, the overall dimensions include a length L along the flow direction and a length W perpendicular to the flow direction;
the structural parameters and the working condition parameters of the fins in each layer of fin channel are as follows:
if straight fins, including the fin height H i Wing pitch s i Thickness of wing t i ；
In the case of serrated fins, including the fin height H i Wing pitch s i Thickness of wing t i Pitch l i ；
If the fins are perforated, including the fin height H i Wing spacing s i Thick wing t i Pitch l i Pore void fraction phi i ；
The working condition parameter of each layer of fin channel comprises an inlet temperature value T in,i And inlet pressure P in,i Wherein i represents the number of the fin channel, and i is more than or equal to 1 and less than or equal to n +1.
Further, step S4 specifically includes:
s4.1, solving the following fin heat conduction equation
Wherein,
indicating heat exchange between fluid and fin, lambda s Represents the thermal conductivity of the fin, and T represents the temperature distribution in the fin;
s4.2, combining a fin heat conduction equation and a Fourier heat conduction law to obtain the temperature gradient at the top of the fin
Combining a fin heat conduction equation and a Fourier heat conduction law to obtain the temperature gradient of the root of the fin
Wherein ch and sh respectively represent hyperbolic cosine and hyperbolic sine;
θ i-i,k ＝T w,i,k -T ∞,i,k
θ i-i+1,k ＝T w,i+1,k -T ∞,i,k
T f,i,k representing the temperature value, T, of the fluid temperature node (fl, i, k) f,i,k+1 A temperature value representing a fluid temperature node (fl, i, k + 1); fl represents the fluid, k represents the serial number of the temperature node of the partition plate; f represents a friction factor; p i Represents the wet week; lambda [ alpha ] i,k Represents the thermal conductivity of the fin; a. The c,i Represents the cross-sectional area of heat conduction in the fluid cell; h is a total of c,i,k Representing the convective heat transfer coefficient between the fin surface and the fluid;
s4.3, according to the temperature gradient of the top of the fin
And temperature gradient of fin root
Determining a partition plate temperature node calculation equation set and a fluid temperature node calculation equation set by combining a Fourier heat conduction law and an energy conservation law satisfied by a control volume of a partition plate temperature node (w, i, k); wherein w represents a separator.
Further, in step S4.3, the system of calculation equations for the temperature node of the partition plate is as follows:
wherein, T f,i-1,k A temperature value representing a fluid temperature node (fl, i-1, k); t is a unit of f,i-1,k+1 Represents the temperature value of the fluid temperature node (fl, i-1, k + 1); t is f,i,k+1 A temperature value representing a fluid temperature node (fl, i, k + 1); t is a unit of w,i-1,k A temperature value representing a temperature node (w, i-1, k) of the partition; t is w,i+1,k A temperature value representing a temperature node (w, i +1, k) of the partition; t is a unit of w,i,k-1 A temperature value representing a temperature node (w, i, k-1) of the partition; t is w,i,k+1 A temperature value representing a temperature node (w, i, k + 1) of the partition; a. The f,i-1,k Represents the solution to the partition temperature node, T f,i-1,k The influence coefficient of (c); a. The f,i-1,k+1 When the solution to the partition temperature node is represented, T f,i-1,k+1 The influence coefficient of (a); a. The f,i,k When the solution to the partition temperature node is represented, T f,i,k The influence coefficient of (c); a. The f,i,k+1 When the solution to the partition temperature node is represented, T f,i,k+1 The influence coefficient of (a); a. The w,i-1,k When the solution to the partition temperature node is represented, T w,i-1,k The influence coefficient of (a); a. The w,i+1,k When the solution to the partition temperature node is represented, T w,i+1,k The influence coefficient of (a); a. The w,i,k-1 When the solution to the partition temperature node is represented, T w,i,k-1 The influence coefficient of (a); a. The w,i,k+1 When the solution to the partition temperature node is represented, T w,i,k+1 The influence coefficient of (a); n represents the total number of flow channels.
Further, in step S4.3, the fluid temperature node calculation equation set specifically includes:
if the fluid flows along the positive direction of the flow channel, the equation system for calculating the fluid temperature node is:
wherein, B f,i,k Representing calculated fluid temperature node, T f,i,k The influence coefficient of (a); b is w,i,k When representing the calculated fluid temperature node, T w,i,k The influence coefficient of (c); b w,i+1,k Representing calculated fluid temperature node, T w,i+1,k The influence coefficient of (c); b f,i,k+1 ＝B f,i,k +B w,i,k +B w,i+1,k ；
If the fluid flows along the negative direction of the flow channel, the equation system for calculating the fluid temperature node is as follows:
wherein, B f,i,k+1 Representing calculated fluid temperature node, T f,i,k+1 The influence coefficient of (c); b is w,i,k When representing the calculated fluid temperature node, T w,i,k The influence coefficient of (a); b is w,i+1,k When representing the calculated fluid temperature node, T w,i+1,k The influence coefficient of (a); b is f,i,k ＝B f,i,k+1 +B w,i,k +B w,i+1,k 。
Further, the f-factor in the fin channel in step S3 and the f-factor of the plate-fin heat exchanger in step S5 are obtained specifically by:
if the fins are saw-tooth fins:
wherein,
re represents a Reynolds number;
if the fins are straight fins:
the laminar flow region is calculated by:
the turbulence zone is calculated by:
in the formula D h,i Is the equivalent diameter;
if the fins are perforated fins:
lnj i,k ＝34.57583-15.92678lnRe i,k +2.137607(lnRe i,k ) 2 -0.09544151×(lnRe i,k ) 3
lnf i,k ＝28.78906-12.31399lnRe i,k +1.565191(lnRe i,k ) 2 -0.06736098(lnRe i,k ) 3 。
further, in step S5, the heat exchange coefficient h between the surfaces of the fins and the fluid in each fluid unit c,i,k Specifically obtained by the following formula:
wherein Pr is the Plantt number, lambda f Is the thermal conductivity of the fluid.
Further, in step S3, the calculating the pressure drop of each fluid unit specifically includes:
the pressure drop of the fluid unit formed by the fluid temperature node (fl, i, k) and the fluid temperature node (fl, i, k + 1) is obtained by:
wherein G is i Representing the mass flow rate of fluid in the channel of the ith layer of fins, D h,i Denotes the equivalent diameter of the fin in the i-th layer of fin channels, ρ denotes the density, f denotes the friction factor, ρ i,k Represents the fluid density, rho, determined by the kth fluid temperature node value of the ith layer of fin channel i,k+1 And (4) representing the fluid density determined by the k +1 fluid temperature node value of the ith layer of fin channel.
The invention also provides a computer program product comprising a computer program, which is characterized in that the program is executed by a processor to realize the steps of the checking method of the multi-flow counterflow plate-fin heat exchanger.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention relates to a checking method of a multi-strand countercurrent plate-fin heat exchanger, which considers the method of fluid physical property change and axial heat conduction effect, can guide the design checking calculation of a low-temperature plate-fin heat exchanger, can be applied to the simulation of hundreds of layers of fin channels, and has high calculation speed and high precision.
2. The method of the invention considers the axial heat conduction effect which causes the serious reduction of the heat exchanger capability in the low-temperature plate-fin heat exchanger, and can calculate the overall pressure distribution and temperature field distribution of the countercurrent plate-fin heat exchanger in any arrangement mode.
3. The invention also provides a computer program product capable of executing the steps of the method, which can be popularized and applied to realize monitoring on corresponding hardware equipment.
Drawings
FIG. 1 is a schematic three-dimensional structure of a multi-flow counterflow plate-fin heat exchanger;
FIG. 2 is a schematic diagram of a two-dimensional simplified model of a multi-flow counter-flow plate-fin heat exchanger;
FIG. 3 is a schematic diagram of the heat exchange between the fluid and the baffle in a multi-flow counter-flow plate-fin heat exchanger;
FIG. 4 is a schematic flow chart illustrating an embodiment of a method for calibrating a multi-flow counterflow plate-fin heat exchanger according to the present invention;
FIG. 5 is a schematic diagram of the fluid temperature distribution along the flow direction calculated by the embodiment of the checking method of the multi-flow counterflow plate-fin heat exchanger of the present invention;
FIG. 6 is a schematic diagram of outlet temperature distribution calculated by the checking method of the multi-flow countercurrent plate-fin heat exchanger according to the embodiment of the present invention;
fig. 7 is a schematic temperature enthalpy diagram of a calculation result of the checking method of the multi-flow countercurrent plate-fin heat exchanger according to the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
As shown in fig. 1 to 4, the present invention is a method for checking a multi-flow counterflow plate-fin heat exchanger considering an axial heat conduction process, which mainly comprises the following steps:
1) Acquiring parameters:
the number of layers N of the plate-fin heat exchanger, the arrangement, the overall dimensions such as the length L (length in the flow direction) and the width W (length perpendicular to the flow direction, i.e., the lateral direction), the number of nodes N +1 arranged in the flow channel in the flow direction, and the number of nodes N arranged in the partition plate in the flow direction are obtained.
The structural parameters and the working condition parameters of the fins in each layer of fin channel are as follows: if the fin is a straight fin, the fin height H is included i Wing pitch s i Thickness of wing t i (ii) a In the case of a sawtooth fin, the pitch l is in addition to the parameters of a straight fin i (ii) a If the fin is a perforated fin, the porosity phi is also included i 。
Setting working condition parameters of each layer of fin channel: inlet temperature value phi i And inlet pressure P in,i And i is the number of the fin channel and represents the ith layer of fin channel.
2) Model simplification
Assuming that the fluid is uniformly distributed at the inlet, only steady state calculation is considered, only the partition plate, the fin solid domain and the fluid domain in the fin channel are considered, the heat conduction term is neglected in the fluid, and the heat exchanger is considered to be insulated from the surrounding environment.
If there are N layers of fin channels in total, there are N +1 layers of partition plates in total, and N nodes are arranged in the partition plates along the main flow direction, there are N +1 nodes in total in the main flow direction in the fluid channel, and two temperature nodes in the flow channel may define one fluid unit (as shown by the shaded part in fig. 2), and then N +1 temperature nodes may define N fluid units. In fig. 2, a is the diaphragm control volume where the diaphragm temperature node (w, i, k) is located, and B is the fluid unit formed by the flow channel temperature node (fl, i, k) and the fluid temperature node (fl, i, k + 1).
3) Calculation of j factor and f factor of plate-fin heat exchanger
The j-factor and f-factor of the plate-fin heat exchanger can be used to determine the pressure drop and heat transfer coefficient in each fluid unit, and are calculated by using the following equations (1) and (2) for the serrated fins:
wherein α, θ, γ are respectively:
the following correlation is used for the flat fin laminar flow region to calculate:
the correlation for the straight fin turbulence zone is calculated using:
for the perforated fins, the correlation is adopted:
lnj i,k ＝34.57583-15.92678lnRe i,k +2.137607(lnRe i,k ) 2 -0.09544151×(lnRe i,k ) 3 (8)
lnf i,k ＝28.78906-12.31399lnRe i,k +1.565191(lnRe i,k ) 2 -0.06736098(lnRe i,k ) 3 (9)
when the f-factor in the fin channel is calculated, the pressure drop can be determined according to step 4).
When the j factor in the fin channel is obtained through calculation, a method for calculating the heat exchange coefficient of the surface of the fin needs to be supplemented, and comprises the following steps:
in the formula, λ f Is the thermal conductivity of the fluid, pr is the prandtl number:
where μ is the dynamic viscosity coefficient of the fluid, c p Is the specific heat capacity of the fluid.
4) Pressure drop calculation
The pressure drop in the fin channels includes two components, the pressure drop due to friction pressure drop and momentum change rate, and the pressure drop of the fluid unit defined by the fluid temperature nodes (fl, i, k) and (fl, i, k + 1) is calculated as follows:
given the inlet pressure, knowing the density ρ and the friction factor f in equation set (12), the outlet pressure for each layer of fin passages can be determined by point-by-point calculation according to equation (12).
5) Calculation of fluid and diaphragm temperature nodes
The fluid of adjacent fin passageway comes the heat transfer through the baffle, and the heat transfer of fluid and baffle divide into two parts, is the heat transfer of fin and baffle and the heat transfer of fluid self and baffle respectively, in order to try to get the heat conduction between baffle and the fin, need to try to get the temperature distribution along the direction of height in the fin earlier, and then obtain the heat conduction of fin root according to the Fourier heat conduction law. The one-dimensional heat conduction equation in the fin is:
in the formula (13), the reaction mixture is,
is the heat exchange between fluid and fins, and is used as a source term in the fin heat conduction equation, lambda s Is the thermal conductivity of the fin, in formula (13)T of (a) can be understood as the temperature distribution in the diaphragm, and the source term is calculated by:
in the formula, h c Is the convective heat transfer coefficient between the fin surface and the fluid, P i Is a wet week and meets
A c,i Is the cross section of heat conduction in the fluid unit and meets the requirement
The temperature values in the fluid unit formed by the fluid temperature nodes (fl, i, k) and (fl, i, k + 1) are:
the boundary condition satisfied by fin thermal conduction equation (13) in the fluid cell formed by the fluid temperature nodes (fl, i, k) and (fl, i, k + 1) is:
y＝0,T＝T w,i+1,k ；y＝H i ,T＝T w,i,k (16)
solving a given fin heat conduction equation (13), and then obtaining the temperature gradient of the top of the fin according to the Fourier heat conduction law
And temperature gradient of fin root
The method comprises the following steps:
in the formula, H i Is the fin height of the ith layer of fin channel, and ch and sh are hyperbolic cosine and hyperbolic sine respectivelyChord, θ i-i,k 、θ i-i+1,k And m e,i,k The calculation methods of (2) are respectively:
based on equation (17), the fourier heat transfer law, and the law of conservation of energy satisfied by the control volume in the separator numbered (w, i, k), a system of equations for solving the temperature node of the separator expressed in the form of influence coefficients can be derived:
the expressions of the influence coefficients in the above equations are:
t in the formula (20) sp Is the thickness of the partition plate of the plate-fin heat exchanger, lambda s Is the thermal conductivity of the solid domain of the separator; in the formula, subscripts are marked outside parenthesis, and if the subscript outside parenthesis is (i, k), the subscript marking of the parameter inside parenthesis is divided into three cases, if the parameter is L, W, N, t sp If the parameter is s, t and H, the subscript is i, if the parameter is lambda s ,h c ,m e Then subscript is (i, k); if the subscript outside the parenthesis is (i-1, k), the parameters inside the parenthesis are labeled according to the same concept. The parameter subscripts of subsequent similar formulas are all in this way.
The control volume of the fluid unit satisfies an energy conservation equation, and an equation set for calculating the fluid temperature node can be obtained through derivation:
the calculation expression of the influence coefficient in expression (21) is:
similarly, in the formula, subscripts are added to parentheses, and if the subscript outside the parentheses is (i, k), the subscripts of the parameters in the parentheses are classified into three cases, and if the parameters L, W, and N, no subscript is required, if the parameters s, t, and H, the subscript is i, and if the parameter λ is λ s ,h c ,m e Subscripts are (i, k); if the subscript outside the parenthesis is (i-1, k), the parameters inside the parenthesis are labeled according to the same idea.
If the fluid is flowing in the + x direction, the system of equations for the fluid temperature node can be calculated according to equation (21), and if the fluid is flowing in the-x direction, the fluid temperature node is calculated according to the following equation:
the method of calculating the influence coefficient in expression (23) is similar to expression (20).
6) Solving a system of equations
Solving the equation sets (19), (21), (23) and (12) can obtain the fluid temperature field distribution, the partition plate temperature field distribution and the fluid channel pressure field distribution of the plate-fin heat exchange whole body, and the influence coefficients of the equation sets are determined according to the method introduced in the step 5), so that the equation sets are nonlinear, and the equation sets cannot be solved simultaneously.
Here, a separate iterative solution is adopted, that is, different types of equation sets are solved separately in each iteration round, and the specific steps are as follows:
a. firstly, inputting overall and local structural parameters and working condition parameters of the plate-fin heat exchanger;
b. fitting spline curves or spline surfaces according to given working condition parameters aiming at different strands of fluids, and extracting required physical property data from a nist database;
c. in an iteration round, solving and carrying out internal iterative computation of a pressure field according to an equation set (12) until the residual error of the pressure field meets the convergence condition;
d. calculating the influence coefficient in the equation set (21) according to the pressure field determined in the step c, the physical property spline curve or spline curve parameter determined in the step b and the calculation method of the factor j introduced above, further determining the temperature field distribution in the partition plate by adopting a Gaussian-Seidel iteration method, and if the lower corner mark of each iteration is performed in a mode that the lower corner mark of T is from small to large, the method can be expressed as follows:
to accelerate the calculation, a hyper-relaxation factor is introduced:
T n0 ＝T n0-1 +α(T n0 -T n0-1 ),1＜α＜2 (25)
wherein, alpha is a super-relaxation iteration factor, and n0 is an iteration turn identifier;
e. determining influence coefficients in equation sets (21) and (23) according to the physical property spline curve or spline curve parameter determined in the step b, the pressure field distribution determined in the step c, the partition plate temperature field distribution determined in the step d and the heat exchange coefficient solving method discussed in the step 5), and solving the equation sets (21) and (23) by adopting a step calculation method.
f. And c, calculating the temperature residual error of the plate-fin heat exchanger, if the convergence condition is not met, continuing entering a new iteration from the step c, and otherwise, outputting a calculation result.
One embodiment of the present invention is as follows.
1) Given parameters
A precooler used in a Claude circulating helium liquefying system is selected, the precooler has three helium gases of high pressure, medium pressure and low pressure, each fluid adopts the same sawtooth-shaped fin channel, and the fin height is H i =3.8mm, wing pitch s i =1.4mm, pitch l i =3.0mm, fin thickness t i =0.2mm, inlet temperature values of the three streams are 44.2K, 10.3K and 45.8K, respectively, inlet pressures are 1.219MPa, 0.144MPa and 0.650MPa, respectively, and the three streams have 6, 20 and 13 layers, respectively, arranged for a total ofThere are 39 layers, the arrangement code of the channel is 232321321321232321232321232321232232232123123123123232, where 1, 2, and 3 are the number of each fluid, for example, the number of the first fluid is "1", and there are 6 layers in the first fluid, so there are 6 "1" in the arrangement code of the channel, and the arrangement mode of the channel of the three fluids is given as the reverse direction, the forward direction, and the reverse direction.
2) Model simplification and initialization
If it is assumed that the temperature distribution of the fluid along the z direction in each fin channel is uniform, as shown in fig. 1, the three-dimensional model can be simplified to the two-dimensional planar model shown in fig. 2, where N fin channels are shared in fig. 2, a partition plate is shared in total by N +1 layers, and N nodes are arranged in the partition plate along the main flow direction, so that N +1 nodes are shared in total in the main flow direction in the channel, and two temperature nodes in the flow channel can define one fluid unit (shown by the shaded portion in the figure), so that N +1 temperature nodes can define N fluid units. The fluid temperature and pressure are stored in the temperature nodes of the fluid channels and the temperature field data of the solid domain of the separator is stored in the temperature nodes of the separator.
The temperature nodes in each layer of fluid channels may be initially given as the inlet temperature values for that layer, while the initial temperature values given in the baffles may be interpolated from the adjacent initialized fluid temperature fields. To simplify the calculations, only the barrier, the fin solid domains and the fluid domains in the fin channels are considered, the heat transfer terms are ignored in the fluid, and the heat exchanger is considered to be thermally isolated from the surrounding environment.
3) Physical property fitting
The temperature and the pressure of different strands of fluid are different, the temperature interval and the pressure interval where different strands of fluid can be located are estimated, then a temperature pressure grid is divided in the temperature interval and the pressure interval, the fluid physical properties at different temperatures and pressures are obtained from a nist physical property database, then spline surface fitting is carried out, and subsequent calculation related to the fluid physical properties is extracted from a spline surface.
4) Determination of pressure field of plate-fin heat exchanger
The method comprises the following steps of formally entering an outer iteration calculation round, firstly determining the distribution of a pressure field according to the temperature field distribution of a fluid, wherein the inner iteration calculation of the pressure field distribution is a first calculation module in the outer iteration round, and the pressure drop comprises the pressure drop generated by friction pressure drop and momentum change rate:
in the formula, G i Is the mass flow rate of the fluid in each layer of fin channels, L is the length of the heat exchanger core along the flow direction, N is the number of fluid units arranged in the flow direction of the heat exchanger, D h,i The equivalent diameter of the plate-fin heat exchanger, subscript i is the number of the layer, f is the friction factor, ρ is the density, the fluid properties required for calculating the f-factor and ρ in each fluid unit are determined according to the qualitative temperature of the fluid unit, and for the fluid unit with the number (i, k), the method for calculating the qualitative temperature is as follows:
different fin structures adopt different methods to calculate the f factor, and the sawtooth type fin adopts the following method:
wherein α, θ, γ are respectively:
the f-factor is calculated for the laminar and turbulent flow regions of the straight fins using the following correlation, respectively:
the f-factor is calculated for the perforated fin using the correlation:
lnf i,k ＝28.78906-12.31399lnRe i,k +1.565191(lnRe i,k ) 2 -0.06736098(lnRe i,k ) 3 (9)
when the qualitative temperature of each fluid unit is known and an f factor calculation method is given, the pressure drop of each fluid unit can be determined according to the formula (12), the pressure value on each fluid temperature node is calculated point by point, the outlet pressure of each layer of fin channel is finally determined, the residual error of a pressure field is judged every time an iterative calculation round in the pressure field is passed, and the pressure field is used as the qualitative pressure of the fluid unit in the subsequent calculation of the iterative round outside the iterative calculation round until the residual error of the pressure field meets the convergence condition.
5) Calculation of the temperature field of the diaphragm
As shown in fig. 3, the fluid in the adjacent fin channel layers exchanges heat through the partition plates, and the heat exchange between the fluid and the partition plates is divided into two parts, namely, the heat exchange between the fins and the partition plates (D in fig. 3), and the heat exchange between the fluid itself and the partition plates (C in fig. 3), in order to obtain the heat conduction amount between the partition plates and the fins, the temperature distribution in the fins along the height direction needs to be obtained first, and then the heat conduction amount at the roots of the fins is obtained according to the fourier heat conduction law, and in order to obtain the heat conduction amount between the partition plates and the fins, the temperature distribution in the fins needs to be known first, in an actual situation, the heat conduction along the fluid flow direction and the heat conduction along the fin height direction exist in the fins, and in order to simplify the calculation, the heat conduction along the fin height direction only exists in the fins (as shown in fig. 3, the heat conduction along the y direction is considered only). The one-dimensional heat conduction equation of the fin is:
in the formula,
is the heat exchange between fluid and fins, and is used as a source term in the fin heat conduction equation, lambda s In order to obtain the temperature distribution of the fin in the fin height direction (y direction) in a certain fluid unit, the calculation method of the source term is as follows:
in the formula, h c Is the convective heat transfer coefficient between the fin surface and the fluid, P i Is a wet week and meets
A c,i Is the cross section of heat conduction in the fluid unit and meets the requirement
T ∞,i,k Is the fluid temperature value, as shown in equation (15).
The boundary condition satisfied by fin thermal conduction equation (13) in the fluid cell defined by fluid temperature nodes (fl, i, k) and (fl, i, k + 1) is:
y＝0,T＝T w,i+1,k ；y＝H i ,T＝T w,i,k (16)
solving a given fin heat conduction equation (13), and then obtaining the temperature gradients of the top and the root of the fin according to the Fourier heat conduction law as follows:
wherein H is wing height, ch and sh are hyperbolic cosine and hyperbolic sine respectively, and theta i-i,k 、θ i-i+1,k And m e,i,j,k The calculating methods of (2) are respectively:
based on equation (17), the fourier law of thermal conductivity, and the law of conservation of energy satisfied by the control volume in the diaphragm numbered (w, i, j), a system of equations for solving the temperature node of the diaphragm expressed in the form of influence coefficients can be derived:
the expressions of the influence coefficient a in the expression (19) are respectively:
t in formula (20) sp Is the thickness of the plate-fin heat exchanger partition plate.
In order to calculate the influence coefficient in equation (19), it is necessary to determine the heat exchange coefficient h in each fluid unit c And the calculation of the heat exchange coefficient is derived from the j factor correlation of the plate-fin heat exchanger.
For a zigzag fin channel, the following j-factor correlation is used:
the laminar and turbulent flow regions for the straight fins were calculated using the following correlations, respectively:
for the perforated fins, the correlation is adopted:
lnj i,k ＝34.57583-15.92678lnRe i,k +2.137607(lnRe i,k ) 2 -0.09544151×(lnRe i,k ) 3 (8)
when the j factor in the fin channel fluid unit is obtained through calculation, the convective heat transfer coefficient in the fluid unit can be obtained through calculation:
where μ is the dynamic viscosity coefficient of the fluid, c p Is the specific heat capacity of the fluid, λ f Is the thermal conductivity of the fluid and Pr is the prandtl number.
The heat exchange coefficients calculated in different fluid units in the plate-fin heat exchanger are different, so h c J factor, re, pr, lambda f And D h,i With subscripts (i, k).
The system of equations (19) actually contains N × (N + 1) equations, and the solution of the system of equations uses gaussian-Seidel (Gauss-Seidel) point iteration, and updates all the partition temperature nodes only once in each outer iteration round, and if each update is performed in a manner that the lower subscript of T is from small to large, it can be expressed as:
the first term on the right of equation (24) is the updated node, the second term is the un-updated node, and the third term
The convective heat transfer source term, which can be understood as the partition thermal conductivity equation, n0 is an iteration turn identifier in this equation. To speed up the convergence of the outer iterations, a hyper-relaxation iteration is introduced:
T n0 ＝T n0-1 +α(T n0 -T n0-1 ),1＜α＜2 (25)
t in the equation refers to the spacer temperature field distribution in each iteration.
6) Fluid temperature field calculation in finned passage
This is the third calculation module in the outer iteration round, the partition temperature node value required for calculating the fluid temperature node comes from step 5), the control volume of the fluid unit satisfies the energy conservation equation, and taking the fluid unit defined by the fluid temperature nodes (fl, i, k) and (fl, i, k + 1) as an example, the calculation equation set of the fluid temperature node flowing along the + x direction can be derived:
the expression of the influence coefficient B in equation (21) is:
if the fluid flows in the-x direction, the temperature node of the fluid is calculated according to the following system of equations:
the calculation of the influence coefficient B in equation (23) is similar to equation (21). Equations (21) and (23) can be solved by a stepwise calculation, i.e., a calculation is performed node by node along the flow direction.
7) Temperature residual calculation
And (3) calculating the residual error of the temperature field, namely comparing the partition plate and fluid temperature field determined in the step 5) and the step 6) with the old temperature field determined in the previous external iteration, and if the residual error does not meet the convergence condition, continuing to enter a new external iteration from the step 4), otherwise, outputting the temperature field and pressure field calculation results. Fig. 5 and 6 are the results of calculations for this embodiment, wherein fig. 5 extracts the on-stream fluid temperatures in a representative three-layer fin channel, fig. 6 extracts the outlet temperatures of each layer of fin channel, and fig. 7 is a temperature enthalpy diagram for further processing, i.e., combining the fluids of each layer in a plate fin heat exchanger into cold and hot fluids, respectively.
The invention can simplify and rapidly check and calculate the multi-flow countercurrent plate-fin heat exchanger with any structure and working condition, and particularly can introduce influence factors of physical property change and axial heat conduction.
The method of checking of the invention may also form a computer program product comprising a computer program which, when being executed by a processor, carries out the steps of a method of checking a multi-flow counterflow plate-fin heat exchanger.
In addition, all parameters of the present invention, with the index i, indicate that the parameter is related to the number of layers, and with the index (i, k) indicate that the parameter is related to both the number of layers and the number of fluid cells.
The present invention has been described in terms of the preferred embodiment, and it is not intended to be limited to the embodiment. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A checking method of a multi-flow countercurrent plate-fin heat exchanger is characterized by comprising the following steps:
s1, arranging N partition plate temperature nodes in a partition plate along a main flow direction, so that N +1 fluid temperature nodes are formed in a fin channel along the main flow direction, and two adjacent fluid temperature nodes in a fin channel form a fluid unit; wherein N is an integer greater than 1;
s2, estimating the temperature range and the pressure range of each strand of fluid, initializing a fluid pressure field, a fluid temperature field and a partition plate temperature field, and fitting a spline surface or a spline curve by combining the physical properties of each strand of fluid;
s3, according to a spline surface fitting result, combining an f factor in a fin channel and parameters of the multi-stream countercurrent plate-fin heat exchanger, calculating the pressure drop of each fluid unit, further calculating to obtain the pressure field distribution of the whole fluid domain, combining the fluid pressure field initialized in the step S2, determining a pressure field residual error, if the pressure field residual error meets a convergence condition, taking the current pressure field as a check effect, and continuing to execute the step S4, otherwise, recalculating the pressure drop of each fluid unit, further calculating to obtain new pressure field distribution of the whole fluid domain, and determining the residual error of the pressure field according to the new pressure field distribution and the old pressure field distribution obtained by the previous iterative calculation until the pressure field residual error meets the convergence condition;
s4, obtaining the temperature gradient of the top of the fin and the temperature gradient of the root of the fin according to the one-dimensional heat conduction equation of the fin, and determining a partition plate temperature node calculation equation set and a fluid temperature node calculation equation set;
s5, determining the heat exchange coefficient h between the surface of the fin in each fluid unit and the fluid according to the j factor of the plate-fin heat exchanger, the physical property parameter of the fluid and the structural parameter of the fin in each layer of channel c,i Determining a partition plate temperature node influence coefficient and a fluid temperature node influence coefficient, solving a partition plate temperature node calculation equation set and a fluid temperature node calculation equation set by combining parameters of the multi-strand countercurrent plate-fin heat exchanger, and determining a fluid temperature field and a partition plate temperature field;
and S6, obtaining the temperature residual errors of the fluid temperature field and the partition plate temperature field, if the temperature residual errors of the fluid temperature field and the partition plate temperature field meet the preset temperature residual error requirement, taking the obtained fluid temperature field, the partition plate temperature field and the current pressure field as check results, otherwise, repeatedly executing the steps S3 to S6 under the current fluid temperature field, the partition plate temperature field and the current pressure field until the temperature residual errors of the fluid temperature field and the partition plate temperature field meet the preset temperature residual error requirement.
2. The method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 1, further comprising: in the step S3, the parameters of the multi-flow countercurrent plate-fin heat exchanger include the number n of layers of the heat exchanger, the arrangement mode, the overall size, the structural parameters and the working condition parameters of the fins in each layer of fin channel, and the working condition parameters of each layer of fin channel.
3. The method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 2, further comprising: in step S3, the overall dimensions include a length L along the flow direction and a length W perpendicular to the flow direction;
the structural parameters and the working condition parameters of the fins in each layer of fin channel are as follows:
if straight fins, including the fin height H i Wing spacing s i Thickness of wing t i ；
If it is a sawtooth fin, including the fin height H i Wing pitch s i Thickness of wing t i Pitch l, pitch i ；
If the fins are perforated, including the fin height H i Wing pitch s i Thickness of wing t i Pitch l, pitch i Pore void fraction phi i ；
The working condition parameter of each layer of fin channel comprises an inlet temperature value T in,i And inlet pressure P in,i Wherein i represents the number of the fin channel, and i is more than or equal to 1 and less than or equal to n +1.
4. The method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 3, further comprising: the step S4 specifically comprises the following steps:
s4.1, solving the following fin heat conduction equation
Wherein,
indicating heat exchange between fluid and fin, lambda s Represents the thermal conductivity of the fin, and T represents the temperature distribution in the fin;
s4.2, combining a fin heat conduction equation and a Fourier heat conduction law to obtain the temperature gradient at the top of the fin
Combining a fin heat conduction equation and a Fourier heat conduction law to obtain the temperature gradient of the root of the fin
Wherein ch and sh respectively represent hyperbolic cosine and hyperbolic sine;
θ i-i,k ＝T w,i,k -T ∞,i,k
θ i-i+1,k ＝T w,i+1,k -T ∞,i,k
T f,i,k representing the temperature value, T, of the fluid temperature node (fl, i, k) f,i,k+1 A temperature value representing a fluid temperature node (fl, i, k + 1); fl represents the fluid, k represents the serial number of the temperature node of the partition plate; f represents a friction factor; p i Represents the wet week; lambda [ alpha ] i,k Represents the thermal conductivity of the fin; a. The c,i Represents the cross-sectional area of heat conduction in the fluid cell; h is c,i,k Representing the convective heat transfer coefficient between the fin surface and the fluid;
s4.3, according to the temperature gradient of the top of the fin
And temperature gradient of fin root
Determining a partition plate temperature node calculation equation set and a fluid temperature node calculation equation set by combining a Fourier heat conduction law and an energy conservation law satisfied by a control volume of a partition plate temperature node (w, i, k); wherein w represents a separator.
5. The method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 4, further comprising: in step S4.3, the partition temperature node calculation equation set is:
wherein, T f,i-1,k A temperature value representing a fluid temperature node (fl, i-1, k); t is a unit of f,i-1,k+1 Represents the temperature value of the fluid temperature node (fl, i-1, k + 1); t is a unit of f,i,k+1 A temperature value representing a fluid temperature node (fl, i, k + 1); t is a unit of w,i-1,k A temperature value representing a temperature node (w, i-1, k) of the partition; t is w,i+1,k A temperature value representing a temperature node (w, i +1, k) of the partition; t is w,i,k-1 A temperature value representing a temperature node (w, i, k-1) of the partition; t is a unit of w,i,k+1 A temperature value representing a temperature node (w, i, k + 1) of the partition; a. The f,i-1,k Represents the solution to the partition temperature node, T f,i-1,k The influence coefficient of (a); a. The f,i-1,k+1 When the solution to the partition temperature node is represented, T f,i-1,k+1 The influence coefficient of (a); a. The f,i,k Represents the solution to the partition temperature node, T f,i,k The influence coefficient of (a); a. The f,i,k+1 Represents the solution to the partition temperature node, T f,i,k+1 The influence coefficient of (c); a. The w,i-1,k When the solution to the partition temperature node is represented, T w,i-1,k The influence coefficient of (a); a. The w,i+1,k When the solution to the partition temperature node is represented, T w,i+1,k The influence coefficient of (a); a. The w,i,k-1 Represents the solution to the partition temperature node, T w,i,k-1 The influence coefficient of (c); a. The w,i,k+1 When the solution to the partition temperature node is represented, T w,i,k+1 The influence coefficient of (a); n represents the total number of flow channels.
6. The method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 5, further comprising: in step S4.3, the fluid temperature node calculation equation set specifically includes:
if the fluid flows along the positive direction of the flow channel, the equation system for calculating the fluid temperature node is:
wherein, B f,i,k When representing the calculated fluid temperature node, T f,i,k The influence coefficient of (c); b is w,i,k Representing calculated fluid temperature node, T w,i,k The influence coefficient of (c); b w,i+1,k When representing the calculated fluid temperature node, T w,i+1,k The influence coefficient of (c); b f,i,k+1 ＝B f,i,k +B w,i,k +B w,i+1,k ；
If the fluid flows along the negative direction of the flow channel, the equation system for calculating the fluid temperature node is as follows:
wherein, B f,i,k+1 When representing the calculated fluid temperature node, T f,i,k+1 The influence coefficient of (c); b w,i,k When representing the calculated fluid temperature node, T w,i,k The influence coefficient of (c); b w,i+1,k Representing calculated fluid temperature node, T w,i+1,k The influence coefficient of (a); b is f,i,k ＝B f,i,k+1 +B w,i,k +B w,i+1,k 。
7. The method of calibrating a multiple-flow counterflow plate-fin heat exchanger of claim 6, further comprising: the f-factor in the fin channel in the step S3 and the f-factor of the plate-fin heat exchanger in the step S5 are obtained specifically by the following method:
if the fins are saw-tooth fins:
wherein,
re represents a Reynolds number;
if the fins are straight fins:
the laminar flow region is calculated by:
the turbulence zone is calculated by:
in the formula D h,i Is the equivalent diameter;
if the fins are perforated fins:
lnj i,k ＝34.57583-15.92678lnRe i,k +2.137607(lnRe i,k ) 2 -0.09544151×(lnRe i,k ) 3
lnf i,k ＝28.78906-12.31399lnRe i,k +1.565191(lnRe i,k ) 2 -0.06736098(lnRe i,k ) 3 。
8. the method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 7, further comprising: in step S5, the heat exchange coefficient h between the surfaces of the fins and the fluid in each fluid unit c,i,k Specifically obtained by the following formula:
wherein Pr is the Plantt number, lambda f Is the thermal conductivity of the fluid.
9. The method for calibrating a multi-flow counterflow plate-fin heat exchanger of claim 8, further comprising: in step S3, the calculating the pressure drop of each fluid unit specifically includes:
the pressure drop of the fluid unit formed by the fluid temperature node (fl, i, k) and the fluid temperature node (fl, i, k + 1) is obtained by:
wherein G is i Represents the mass flow rate of the fluid in the channel of the ith layer of fins, D h,i Denotes the equivalent diameter of the fin in the i-th layer of fin channels, ρ denotes the density, f denotes the friction factor, ρ i,k Represents the fluid density, rho, determined by the kth fluid temperature node value of the ith layer of fin channel i,k+1 And (3) the fluid density determined by the k +1 th fluid temperature node value of the ith layer of fin channel.
10. A computer program product comprising a computer program characterized in that: the program when executed by a processor implements the steps of a method of calibrating a multi-flow counterflow plate fin heat exchanger as claimed in any one of claims 1 to 9.
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| CN116680838B (en) * | 2023-07-27 | 2024-04-26 | 东莞市鹏锦机械科技有限公司 | Heat transfer calculation method of plate-fin heat exchanger |
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