CN115292846B - Cooling tower modeling method based on heat transfer - Google Patents

Cooling tower modeling method based on heat transfer Download PDF

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CN115292846B
CN115292846B CN202210977950.4A CN202210977950A CN115292846B CN 115292846 B CN115292846 B CN 115292846B CN 202210977950 A CN202210977950 A CN 202210977950A CN 115292846 B CN115292846 B CN 115292846B
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王中昊
周永诚
刘金福
于达仁
李文峰
李中华
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Harbin Institute of Technology
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Abstract

A cooling tower modeling method based on heat transfer relates to the technical field of cooling tower modeling. The invention aims to solve the problems that the existing cooling tower model cannot meet the optimization requirement due to iterative computation, and the model capable of meeting the optimization requirement is poor in accuracy. According to the cooling tower modeling method based on heat transfer, a cooling tower mechanism model based on heat dissipation capacity is established by analyzing heat transfer resistance and heat transfer temperature difference in a cooling tower by utilizing a heat transfer theory, and the model has a simplified analytic formula and does not need to be subjected to iterative calculation unlike a traditional model which needs to be subjected to a large number of iterative calculation; meanwhile, the geometric property of the cooling tower is generalized to be a constant, only the change of the inlet and outlet conditions of the cooling tower is considered, and the relation between the cooling heat dissipation capacity of the cooling tower and the mass flow of air and cooling water is emphasized, so that the model is simpler, higher in accuracy and capable of meeting the requirement of variable parameter solving in the operation optimization process of the refrigerating unit.

Description

Cooling tower modeling method based on heat transfer
Technical Field
The invention belongs to the technical field of cooling tower modeling.
Background
There is a great deal of refrigeration demand in modern industrial production or building air conditioning systems, and water-cooled units are widely used in the refrigeration field due to the advantages of high specific heat capacity of water, no toxicity and the like. According to whether the cooling water is recycled, the water cooling unit can be divided into a direct water cooling unit and a circulating water cooling unit, and the latter has remarkable advantages in terms of saving fresh water and reducing the thermal pollution of water sources.
The circulating water cooling unit mainly comprises three parts: heat exchanger, cooling tower and water pump. The cooling tower has the main heat dissipation task, various structures, and a schematic diagram of a counter-flow cooling tower is shown in fig. 1. During operation of the counter-flow cooling tower, cooling water is sprayed from the upper part of the cooling tower to the lower part of the cooling tower through the conical nozzle under the action of the water pump, outdoor air enters from the lower part of the cooling tower under the action of the axial flow fan and flows out from the upper part of the cooling tower after cooling the cooling water, and a large amount of fillers arranged on the inner wall surface of the cooling tower can enlarge the heat exchange area and time of the cooling water and the outdoor air so as to enhance the heat exchange effect, and the whole process comprises the heat transfer (heat transfer of the cooling water and saturated air) and mass transfer (air tends to be saturated) processes.
In recent years, under the large background of advocating low-carbon energy conservation, the problem of energy conservation and optimization of a refrigerating unit is particularly important due to further improvement of refrigeration demands in various industries, and a cooling tower is used as a key part in the refrigerating unit, so that the problem of modeling is very large.
There are two major classical models of cooling towers, the Merkel model proposed by Merkel and the e-NTU model proposed by Jaber and Webb, respectively. The Merkel model makes three key assumptions that simplify the cooling tower problem to be calculated, but these assumptions also make it impossible for the Merkel model to accurately describe the heat and mass transfer processes within the cooling tower. The e-NTU model is based on the same assumption as the Merkel model, and by applying the e-NTU method directly to the cooling tower equations, the problem is further simplified compared to conventional numerical solutions. However, these two models have significant drawbacks in practical applications, such as the Merkel model is solved numerically, the solution involves iterative calculations, and cooling tower geometry specifications are provided. The values of the key parameters UA in the e-NTU model vary with changes in cooling water and air flow, are difficult to determine, and involve iterative calculations as well, providing initial conditions, initial solutions, cooling tower geometry specifications, etc. These drawbacks make these two classical models unable to meet the requirements of variable parameter solution in the optimization process due to the iterative computation when facing the cooling tower operation optimization problem.
At present, some students do other work on modeling of the cooling tower, but the models still have defects, such as incapability of being applied to solving optimization problems due to iterative calculation; some can give analytic solutions to meet the requirement of optimal solution, but have the problem of poor accuracy and the like.
Disclosure of Invention
The invention aims to solve the problem that the existing cooling tower model cannot meet the optimization requirement due to iterative computation and the model capable of meeting the optimization requirement is poor in accuracy, and provides a cooling tower modeling method based on heat transfer.
A cooling tower modeling method based on heat transfer, comprising the steps of:
step one: according to the convection heat exchange theory, obtaining the water convection heat resistance R in the heat transfer process of the water and the air in the cooling tower w Air convection thermal resistance R a Is represented by the expression:
Figure BDA0003798133760000021
wherein m is w And m a Mass of water and air, b 1 And b 2 Are all constant and
Figure BDA0003798133760000022
Figure BDA0003798133760000023
S 1 and S is 2 Are constants for representing proportional relation, c p1 And c p2 Constant pressure specific heat capacity, mu, of water and air respectively 1 Sum mu 2 Dynamic viscosity, k, of water and air respectively 1 And k 2 Thermal conductivity coefficients of water and air, D 1 And D 2 Characteristic dimensions of the water and air flow channels, respectively, A 1 And A 2 The heat exchange areas of water and air are respectively, and i and j are constants determined by fitting according to actual operation data;
step two: due to the convective resistance R of water w Thermal resistance R of air convection a The following relation is formed between the total thermal resistance R:
R＝R w +R a ，
the total thermal resistance R can be expressed as:
Figure BDA0003798133760000024
wherein c 1 ＝b 1 ，
Figure BDA0003798133760000025
c 3 ＝i；
Step three: since the equivalent heat transfer temperature difference in a cooling tower is a weighted average of the outlet temperature difference and the inlet temperature difference, there are:
ΔT＝c 4 ΔT in +(1-c 4 )ΔT out in the third formula of the formula,
wherein DeltaT in ＝t w,o -t a,i,sw ，ΔT out ＝t w,i -t a,o,sw ，c 4 As the weight coefficient, t w,i And t w,o Respectively the inlet temperature and the outlet temperature of cooling water, t a,i,sw And t a,o,sw Saturated air inlet and outlet temperatures, respectively;
step four: according to the theory of heat transfer theory, the total thermal resistance R is used for calculating the heat dissipation capacity
Figure BDA0003798133760000031
Figure BDA0003798133760000032
Step five: substituting the formula II and the formula III into the formula IV to obtain a cooling tower model expression:
Figure BDA0003798133760000033
further, according to the convection heat exchange theory, the flow characteristic expression of the total thermal resistance R in the fluid heat transfer process in the cooling tower is as follows:
Figure BDA0003798133760000034
where nu= SRe i Pr j ，
Figure BDA0003798133760000035
Nu is the Newsaint number, re is the Reynolds number, pr is the Planet number, k is the fluid heat conductivity coefficient, D is the characteristic dimension of the fluid flow channel, A is the fluid heat exchange area, S is the constant representing the proportional relationship, v is the fluid flow velocity, ρ is the fluid density, c p Constant pressure specific heat capacity for fluid, μ is hydrodynamic viscosity.
Further, the fluid mass expression is known according to the law of conservation of mass:
Figure BDA0003798133760000036
transforming the above equation to obtain an expression for the fluid density ρ:
Figure BDA0003798133760000037
the expression of the fluid density ρ is taken into the flow characteristic expression of the total thermal resistance R during the fluid heat transfer in the cooling tower:
Figure BDA0003798133760000038
wherein b is a constant and
Figure BDA0003798133760000039
thereby making it possible toObtaining the convective heat resistance R of water in the heat transfer process of water and air in the cooling tower in the step one w Air convection thermal resistance R a Is an expression of (2).
Further, the cooling tower model described above is obtained under the following assumption:
(1) The heat and mass transfer process is only carried out in the direction perpendicular to the flow;
(2) The Lewis factor is constant;
(3) In the energy balance, the amount of water lost by evaporation is negligible;
(4) The cross-sectional area of the cooling tower and the temperature distribution of any cross-sectional area in the water flow are uniform;
(5) The enthalpy value of the saturated air is in linear relation with the wet bulb temperature in a certain range;
(6) The change in the density of the air during its flow through the cooling tower is ignored.
According to the method, a cooling tower mechanism model based on heat dissipation capacity is established by utilizing a theory related to heat transfer science and analyzing heat transfer resistance and heat transfer temperature difference in a cooling tower, and the model has a simplified analytic type and does not need to be subjected to iterative computation, unlike a traditional model which needs to be subjected to a large number of iterative computation; meanwhile, the geometric property of the cooling tower is generalized to be a constant, only the change of the inlet and outlet conditions of the cooling tower is considered, and the relation between the cooling heat dissipation capacity of the cooling tower and the mass flow of air and cooling water is emphasized, so that the model is simpler, higher in accuracy and easy to apply to engineering realization, and the requirement of variable parameter solving in the operation optimization process of the refrigerating unit can be met.
Drawings
FIG. 1 is a schematic diagram of a counterflow cooling tower;
FIG. 2 is a schematic diagram of a heat and mass transfer process for a certain cross section in a cooling tower;
fig. 3 is a graph of a heat and mass transfer process.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The first embodiment is as follows: referring to fig. 2 and 3, a modeling method for a cooling tower based on heat transfer according to the present embodiment includes the following steps:
this embodiment is based on the following assumption:
(1) The heat and mass transfer process is only carried out in the direction perpendicular to the flow;
(2) The Lewis factor is constant;
(3) In the energy balance, the amount of water lost by evaporation is negligible;
(4) The cross-sectional area of the cooling tower and the temperature distribution of any cross-sectional area in the water flow are uniform;
(5) The enthalpy value of the saturated air is in linear relation with the wet bulb temperature in a certain range;
(6) The change in the density of the air during its flow through the cooling tower is ignored.
The heat transfer and mass transfer process between the cooling water and the air in the cooling tower is equivalently simplified into the heat convection process between the cooling water and the saturated air and between the saturated air and the main air flow. Therefore, the present embodiment considers that the total heat transfer resistance in the cooling tower is divided into two parts, namely the water convection resistance R w Air convection thermal resistance R a . The cooling water in the supercooling tower has a cross section taken from an infinite small micro-element in the flow direction, and the process is shown in fig. 2. In the figure, t a Is the temperature of main stream air, DEG C; t is t a,sw Saturated air temperature, deg.c; t is t w Cooling water temperature, DEG C; the I-I layer is a heat exchange layer of cooling water and saturated air, and the thermal resistance is R w The method comprises the steps of carrying out a first treatment on the surface of the The II-II layer is a heat exchange layer of saturated air and main air flow (unsaturated), and the thermal resistance is R a 。
Based on the abovePrinciple, in the present embodiment, the water convection thermal resistance R w Thermal resistance R of air convection a The following relation is formed between the total thermal resistance R:
R＝R w +R a (1)。
since the flow of cooling water and air in the cooling tower is mainly driven by the water pump and the axial flow fan, the flow of cooling water and air can be regarded as forced convection. According to the convection theory, the flow characteristics of the total thermal resistance R in the heat transfer process of the fluid in the cooling tower can be expressed as follows:
Figure BDA0003798133760000051
where nu= SRe i Pr j ，
Figure BDA0003798133760000052
Nu is the Newsaint number, re is the Reynolds number, pr is the Planet number, k is the fluid heat conductivity coefficient, D is the characteristic dimension of the fluid flow channel, A is the fluid heat exchange area, S is the constant representing the proportional relationship of two sides of the equation, v is the fluid flow velocity, ρ is the fluid density, c p Constant pressure specific heat capacity for fluid, μ is hydrodynamic viscosity.
The fluid mass expression is known according to the law of conservation of mass:
Figure BDA0003798133760000053
transforming equation (3) to obtain an expression of the fluid density ρ:
Figure BDA0003798133760000054
then bringing equation (4) into equation (2) yields:
Figure BDA0003798133760000055
wherein b is a constant and
Figure BDA0003798133760000061
then the convection heat resistance R of the water in the heat transfer process of the water and the air in the cooling tower can be obtained according to the convection heat exchange theory w Air convection thermal resistance R a Is represented by the expression:
Figure BDA0003798133760000062
wherein m is w And m a Mass of water and air, b 1 And b 2 Are all constant and
Figure BDA0003798133760000063
Figure BDA0003798133760000064
S 1 and S is 2 Are constants for representing proportional relation, c p1 And c p2 Constant pressure specific heat capacity, mu, of water and air respectively 1 Sum mu 2 Dynamic viscosity, k, of water and air respectively 1 And k 2 Thermal conductivity coefficients of water and air, D 1 And D 2 Characteristic dimensions of the water and air flow channels, respectively, A 1 And A 2 The heat exchange areas of water and air are respectively, and i and j are constants determined by fitting according to actual operation data;
further, the total thermal resistance R can be expressed as follows in connection with equation (1):
Figure BDA0003798133760000065
wherein c 1 ＝b 1 ，
Figure BDA0003798133760000066
c 3 ＝i。
The curve of the heat and mass transfer process in the cooling tower is shown in figure 3, 1 is the air inlet state point; 2 is the air outlet status point; i.e 1 And i 2 Enthalpy values at the air inlet and outlet respectively; t is t w,i And t w,o Cooling water inlet and outlet temperatures, respectively; t is t a,i And t a,o The inlet and outlet temperatures of the main air flow are respectively; t is t a,i,sw And t a,o,sw The inlet temperature and the outlet temperature of saturated air are respectively the same as the wet bulb temperature at the inlet and the outlet of the main air flow; delta T in Is the inlet temperature difference; delta T out Is the outlet temperature difference. Since the equivalent heat transfer temperature difference in a cooling tower is a weighted average of the outlet temperature difference and the inlet temperature difference, there are:
ΔT＝c 4 ΔT in +(1-c 4 )ΔT out (8)，
wherein DeltaT in ＝t w,o -t a,i,sw ，ΔT out ＝t w,i -t a,o,sw ，c 4 Is a weight coefficient.
And according to the theory related to heat transfer theory, the total thermal resistance R is used for calculating the heat dissipation capacity
Figure BDA0003798133760000071
Figure BDA0003798133760000072
Finally, substituting the formula (8) and the formula (7) into the formula (9) to obtain a cooling tower model expression:
Figure BDA0003798133760000073
the cooling tower mechanism model based on the heat dissipation capacity is established in the embodiment facing the cooling tower operation optimization requirement. Specifically, an idealized assumption is made on the actual mass and heat transfer process in the cooling tower, the concept of boundary layer thermal resistance is introduced, and a heat transfer equation between cooling water and air, namely, the heat dissipation capacity is equal to the ratio of temperature difference to thermal resistance, is established. According to the relation between the thermal resistance of the fluid boundary layer and a plurality of typical dimensionless numbers, the thermal resistance of the boundary layer is expressed as a function composed of cooling water flow, air flow and a plurality of parameters to be identified. By analyzing the heat exchange process in the cooling tower, a parameter to be identified, namely weight, is introduced, so that the equivalent heat transfer temperature difference is a weighted average of the outlet temperature difference and the inlet water temperature difference. The model parameters are identified by using the actual data, a mechanism model of the cooling tower based on the heat dissipation capacity and provided with an analytic model is established, and the model of the cooling tower provided by the embodiment has good accuracy and can meet the operation optimization solving requirement of the cooling tower.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.

Claims (3)

1. A method of modeling a cooling tower based on heat transfer, comprising the steps of:
step one: according to the convection heat exchange theory, obtaining the water convection heat resistance R in the heat transfer process of the water and the air in the cooling tower w Air convection thermal resistance R a Is represented by the expression:
Figure FDA0004225897500000011
wherein m is w And m a Mass of water and air, b 1 And b 2 Are all constant and
Figure FDA0004225897500000012
Figure FDA0004225897500000013
S 1 and S is 2 To characterize the constants of the proportional relationships of the respective thermal resistance expressions, c p1 And c p2 Constant pressure specific heat capacity, mu, of water and air respectively 1 Sum mu 2 Dynamic viscosity, k, of water and air respectively 1 And k 2 Thermal conductivity coefficients of water and air, D 1 And D 2 Characteristic dimensions of the water and air flow channels, respectively, A 1 And A 2 The heat exchange areas of water and air are respectively, and i and j are constants determined by fitting according to actual operation data;
step two: due to the convective resistance R of water w Thermal resistance R of air convection a The following relation is formed between the total thermal resistance R:
R＝R w +R a ，
the total thermal resistance R can be expressed as:
Figure FDA0004225897500000014
wherein c 1 ＝b 1 ，
Figure FDA0004225897500000015
c 3 ＝i；
Step three: since the equivalent heat transfer temperature difference in the cooling tower is a weighted average of the outlet temperature difference and the inlet temperature difference, there are:
ΔT＝c 4 ΔT in +(1-c 4 )ΔT out in the third formula of the formula,
wherein DeltaT in ＝t w,o -t a,i,sw ，ΔT out ＝t w,i -t a,o,sw ，c 4 As the weight coefficient, t w,i And t w,o Respectively the inlet temperature and the outlet temperature of cooling water, t a,i,sw And t a,o,sw Saturated air inlet and outlet temperatures, respectively;
step four: according to the theory of heat transfer theory, the total thermal resistance R is used for calculating the heat dissipation capacity
Figure FDA0004225897500000016
Figure FDA0004225897500000021
Step five: substituting the formula II and the formula III into the formula IV to obtain a cooling tower model expression:
Figure FDA0004225897500000022
2. the modeling method of a cooling tower based on heat transfer according to claim 1, wherein the flow characteristic expression of the total thermal resistance R in the heat transfer process of the fluid in the cooling tower is:
Figure FDA0004225897500000023
where nu= SRe i Pr j ，
Figure FDA0004225897500000024
Nu is the Newsai number, re is the Reynolds number, pr is the Planet number, k is the fluid heat conductivity coefficient, D is the characteristic dimension of the fluid flow channel, A is the fluid heat exchange area, S is the constant representing the left-right proportional relationship of the fluid expression, v is the fluid flow velocity, ρ is the fluid density, c p Constant pressure specific heat capacity for fluid, μ is hydrodynamic viscosity.
3. The method of modeling a cooling tower based on heat transfer of claim 2, wherein the fluid mass expression is known from the law of conservation of mass:
Figure FDA0004225897500000025
transforming the above equation to obtain an expression for the fluid density ρ:
Figure FDA0004225897500000026
the expression of the fluid density ρ is taken into the flow characteristic expression of the total thermal resistance R during the fluid heat transfer in the cooling tower:
Figure FDA0004225897500000027
wherein b is a constant and
Figure FDA0004225897500000028
thereby obtaining the convective heat resistance R of the water in the heat transfer process of the water in the cooling tower and the air in the step one w Air convection thermal resistance R a Is an expression of (2).
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