CN114385960A - Energy average temperature-based dividing wall type heat exchanger performance calculation method - Google Patents
Energy average temperature-based dividing wall type heat exchanger performance calculation method Download PDFInfo
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Abstract
The invention discloses a dividing wall type heat exchanger performance calculation method based on energy average temperature, which comprises the following steps: inputting the working conditions of the dividing wall type heat exchanger; according to the working medium flowing mode, carrying out weighted average on inlet temperatures at two sides by taking the heat capacity flow rate of the fluid at two sides as a weight, and calculating the energy average temperature; calculating the convective heat transfer coefficient according to the convective heat transfer characteristic databases at the two sides of the heat transfer unit; calculating the convective heat transfer thermal resistance between the wall surface and the fluid on the two sides and the heat conduction thermal resistance of the solid wall surface of the dividing wall type heat exchanger according to the convective heat transfer coefficients on the two sides, and calculating the total heat transfer coefficient; redefining the number of heat transfer units and calculating; and calculating the outlet temperature and the on-way temperature distribution of the fluid at two sides according to the number of the heat transfer units and the energy average temperature, and calculating the total heat exchange amount. The invention realizes the non-iterative direct calculation of the heat transfer performance of the dividing wall type heat exchanger, improves the design calculation efficiency, more finely obtains the heat transfer performance of the dividing wall type heat exchanger and provides a new idea for the design calculation of the dividing wall type heat exchanger.
Description
Technical Field
The invention belongs to the technical field of heat exchangers, and particularly relates to a dividing wall type heat exchanger performance calculation method based on energy average temperature.
Background
The heat exchanger is widely applied to the traditional industry, is a carrier for energy exchange between fluid working media, and plays a key role in multiple fields such as refrigeration air conditioners, electric power, ships, gas turbines, aerospace and the like. Especially in the gas turbine and aerospace field, the heat exchanger is applied to various occasions such as fuel cooling of unmanned aerial vehicles, indirect cooling and heat regeneration of large-scale gas turbines on the ground, fuel and air cooling inside aircraft engines and the like, and is a key component for solving the heat problem and improving the energy utilization rate. Therefore, the heat exchanger technology is also a bottleneck technology developed in the field, and the quality of the performance of the heat exchanger is directly related to the final performance of the equipment. In recent years, with the continuous development of heat exchanger design and manufacturing technology, heat exchangers are gradually developed towards the direction of refinement, compaction and weight reduction, and technical innovation in each industrial direction puts forward more complex and severe flowing heat exchange requirements on the heat exchangers. Accordingly, it is necessary to develop a heat exchanger performance calculation method based on the conventional heat exchanger design calculation method.
The logarithmic mean temperature difference method is a traditional heat exchanger design calculation method which is used for nearly one hundred years and is almost used in heat exchanger design of all flow and structure forms. Taking the forward flow as an example, the expression form of the method is
Q＝LMTD KA
Wherein LMTD is the logarithmic mean temperature difference, t is the temperature, K is the total heat transfer coefficient, and A is the total heat transfer area. The logarithmic mean temperature difference method can calculate the mean heat transfer temperature difference in the heat exchanger according to the known inlet and outlet temperatures of the fluids at two sides, and further calculate the heat transfer quantity according to the Newton's cooling law; the balance relation between the heat transfer quantity and the enthalpy difference of the fluid working medium at the inlet and the outlet needs to be solved iteratively for the temperature at the fluid outlet. The method can accurately solve the performance of the heat exchanger, and the reliability of the heat exchanger is verified in a large number of engineering applications. The performance calculation method provided by the invention can omit iterative solution in the calculation process, improve the calculation efficiency and acquire more precise and comprehensive heat transfer performance information.
The present invention has been made in view of this situation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a dividing wall type heat exchanger performance calculation method based on energy average temperature. In order to solve the technical problems, the invention adopts the technical scheme that:
a dividing wall type heat exchanger performance calculation method based on energy average temperature comprises the following steps:
inputting working conditions of the dividing wall type heat exchanger according to the thermal environment of the dividing wall type heat exchanger;
calculating the energy average temperature of the two streams of fluid, performing weighted average on the inlet temperatures of the two sides by taking the heat capacity flow rate of the two streams of fluid as a weight according to the flowing mode of the working medium and the heat capacity flow rate of the two streams of fluid, and calculating the energy average temperature;
calculating the convective heat transfer coefficient, and obtaining the convective heat transfer coefficient of the fluid working medium at the two sides of the dividing wall type heat exchanger according to the convective heat transfer characteristic database at the two sides of the heat transfer unit;
calculating the total heat transfer coefficient of the dividing wall type heat exchanger, calculating the convective heat transfer thermal resistance between the wall surface and the fluid on the two sides according to the convective heat transfer coefficients on the two sides, and calculating the total heat transfer coefficient according to the thermal conductivity thermal resistance of the solid wall surface of the dividing wall type heat exchanger;
defining the number of heat transfer units and calculating, wherein the number of the heat transfer units is defined as the product of the sum of the inverses of the heat capacity flow rates of the fluid working media at the two sides and the total heat transfer coefficient and the total heat transfer area;
and step six, calculating the outlet temperature and the on-way temperature distribution of the fluid at two sides according to the number of the heat transfer units and the energy average temperature, and further acquiring the total heat exchange quantity.
Furthermore, the dividing wall type heat exchanger is an integral forward flow type heat exchanger and an integral reverse flow type heat exchanger.
Further, the operating conditions of the step-one intermediate wall heat exchanger include: inlet flow, temperature, pressure; physical property parameters of fluid working media on two sides; the dividing wall type heat exchanger has the structural form and the structural parameters.
Further, the calculation formula of the energy average temperature of the concurrent flow type heat exchanger in the second step is
tave＝(W1t1,in+W2t2,in)/(W1+W2)，
The energy average temperature of the counter-flow heat exchanger is calculated by the formula
tave＝(W1t1,in-W2t2,out)/(W1-W2)，
Where t is the temperature and W is the heat capacity flow rate, i.e., the product of the specific heat capacity and the mass flow.
Further, in the third step, the basic heat transfer unit form is obtained through the working conditions input in the first step, the empirical correlation formula adopted by the calculation of the heat transfer characteristics of the fluid at the two sides is determined according to the unit heat transfer form, and the convective heat transfer coefficient between the fluid working medium at the two sides and the wall surface of the dividing wall type heat exchanger is calculated according to the Reynolds number range.
Further, the calculation formula of the heat transfer unit number redefined in the step five is
NTU＝(1/W1+1/W2)KA，
The expression of the number of heat transfer units of the counter-flow heat exchanger is
NTU＝(1/W1-1/W2)KA，
Wherein K is the total heat transfer coefficient, and A is the total heat transfer area of the dividing wall type heat exchanger.
Further, in the sixth step, the expression of the outlet temperature of the concurrent heat exchanger is
ti,out＝tave+e-NTU(ti,in-tave)，
The expression of the outlet temperature of the counter-flow heat exchanger is
t1,out＝tave+e-NTU(t1,in-tave)，t2,out＝tave+eNTU(t2,in-tave)。
Further, in the second step, the expression of the energy average temperature of the counter-flow heat exchanger is deduced again, so that the expression can be directly calculated by input parameters, and the obtained expression is
tave＝(e-NTUW1t1,in-W2t2,in)/(e-NTUW1-W2)。
Further, the on-way temperature distribution of the fluid on two sides can be obtained through a calculation method, and the expression is
For the concurrent flow heat exchanger: t is ti(x)＝tave+e-NTU[0→x](ti,in-tave)；
For a counter-flow heat exchanger:
wherein, t1Representing the on-way temperature, t, of fluid flowing in the same direction as the coordinate axis in a counterflow heat exchanger2Representing the on-way temperature of the fluid flowing opposite to the coordinate axis, L representing the total flowing length, and x representing the flowing distance of the fluid; NTU [0 → x]Represents the number of heat transfer elements from 0 to the x position, i.e., the number of heat transfer elements corresponding to the heat transfer area from 0 to the x position.
Further, the calculation formula of the total heat exchange amount is Q ═ W1|t1,out-t1,in|＝W2|t2,out-t2,in|。
Further, the heat transfer unit forms comprise uniform cross-section channels, finned tube bundles, smooth tube bundles and the like.
After the technical scheme is adopted, compared with the prior art, the invention has the following beneficial effects.
According to the invention, through the working condition input of the dividing wall type heat exchanger, the calculation of the energy average temperature of two streams of fluid, the analysis of the convection heat exchange performance of the two sides of the fluid, the calculation of the total heat transfer coefficient of the dividing wall type heat exchanger, the definition and calculation of the number of heat transfer units of the dividing wall type heat exchanger and the calculation of the outlet temperature of the two sides of the fluid and the total heat exchange quantity of the dividing wall type heat exchanger, the non-iterative direct calculation of the heat transfer performance of the dividing wall type heat exchanger is realized, the calculation efficiency is improved, the heat transfer performance of the dividing wall type heat exchanger is more finely obtained, and a new thought is provided for the design calculation of the dividing wall type heat exchanger.
In the field of heat exchanger optimization, the performance calculation method is introduced, so that the defects in the aspect of structure can be seen more vividly, the structure optimization efficiency is effectively improved, and the optimization design convergence is improved.
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention to its proper form. It is obvious that the drawings in the following description are only some embodiments, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:
FIG. 1 is a schematic flow chart of a calculation method of the present invention;
FIG. 2 is a simplified schematic of a heat transfer process in an embodiment of the present invention;
FIG. 3 is a schematic representation of an in-line temperature profile in an embodiment of the present invention;
FIG. 4 is a schematic representation of the residual of the iterative calculation in the comparative example of the present invention.
It should be noted that the drawings and the description are not intended to limit the scope of the inventive concept in any way, but to illustrate it by a person skilled in the art with reference to specific embodiments.
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 will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and the following embodiments are used for illustrating the present invention and are not intended to limit the scope of the present invention.
In the description of the present invention, it should be noted that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; may be directly connected or indirectly connected through an intermediate. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
As shown in fig. 1 to 4, the method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature of the invention comprises the following steps:
inputting working conditions of the dividing wall type heat exchanger according to the thermal environment of the dividing wall type heat exchanger;
calculating the energy average temperature of the two streams of fluid, performing weighted average on the inlet temperatures of the two sides by taking the heat capacity flow rate of the two streams of fluid as a weight according to the flowing mode of the working medium and the heat capacity flow rate of the two streams of fluid, and calculating the energy average temperature;
calculating the convective heat transfer coefficient, and obtaining the convective heat transfer coefficient of the fluid working medium at the two sides of the dividing wall type heat exchanger according to the convective heat transfer characteristic database at the two sides of the heat transfer unit;
calculating the total heat transfer coefficient of the dividing wall type heat exchanger, calculating the convection heat transfer resistance between the specific wall surface and the fluid at two sides and the heat conduction resistance of the solid wall surface of the dividing wall type heat exchanger according to the convection heat transfer coefficient, and calculating the total heat transfer coefficient;
defining the number of heat transfer units and calculating, wherein the number of the heat transfer units is defined as the product of the sum of the inverses of the heat capacity flow rates of the fluid working media at the two sides and the total heat transfer coefficient and the total heat transfer area;
and step six, calculating the outlet temperature and the on-way temperature distribution of the fluid at two sides according to the number of the heat transfer units and the energy average temperature, and further acquiring the total heat exchange quantity.
Inputting the inlet flow, temperature and pressure of fluid working media at two sides in the step one based on the thermal environment of the dividing wall type heat exchanger; inputting physical parameters of fluid working media at two sides or the change rule of the physical parameters along with temperature and pressure; and (4) setting the structural form and structural parameters of the dividing wall type heat exchanger. And determining the temperature limit of the fluid working medium outlets at two sides according to the heat exchange requirement of the dividing wall type heat exchanger and the reliable working temperature range of the fluid working medium. The inlet temperature of the fluid working medium at two sides is known quantity, while the outlet temperature is unknown quantity, which accords with the input boundary of the performance calculation of the general heat exchanger.
And calculating the energy average temperature of the two streams of fluid, wherein the dividing wall type heat exchanger is an integral forward flow type heat exchanger or an integral reverse flow type heat exchanger. For the concurrent heat exchanger, the energy average temperature calculation takes the heat capacity flow rate of the fluid on two sides as weight to carry out weighted average on the inlet temperature on two sides, namely tave＝(W1t1,in+W2t2,in)/(W1+W2) Where t is temperature, W is heat capacity flow rate, and it is also true that the inlet temperatures at both sides are replaced with the outlet temperatures at the same time. For the counter-flow heat exchanger, the energy average temperature calculation takes the heat capacity flow rate of the fluid on two sides as weight to carry out weighted average on the inlet temperature on one side and the outlet temperature on the other side, the weight of the heat capacity flow rate of the fluid on the side opposite to the coordinate axis in the flow direction is taken as a negative value, namely tave＝(W1t1,in-W2t2,out)/(W1-W2) It is also true that the inlet/outlet temperatures of the fluids on both sides are replaced with the outlet/inlet temperatures, respectively. The two expressions of the energy average temperature do not change along the way, and the temperature in the formula can be taken as the temperature of the fluid on two sides corresponding to the position of any flow direction. Namely, the on-way temperature distribution of the two-side fluid can be obtained through a formula.
And (4) drawing up a structure according to the dividing wall type heat exchanger input in the step one, and obtaining basic heat transfer unit forms of the fluid channels at two sides, including but not limited to uniform cross-section channels, fin tube bundles, smooth tube bundles and the like. And respectively determining an empirical correlation formula to be adopted for calculating the heat transfer characteristics of the fluid at the two sides according to the type of the heat transfer unit, and calculating the convective heat transfer coefficient between the fluid working medium at the two sides and the wall surface of the dividing wall type heat exchanger according to the Reynolds number range. And calculating the convective heat transfer thermal resistance between the wall surface and the fluids at the two sides according to the convective heat transfer coefficients at the two sides, further considering the heat conduction thermal resistance of the solid wall surface of the dividing wall type heat exchanger, and calculating the total heat transfer thermal resistance between the fluids at the two sides of the dividing wall type heat exchanger by taking the sum of the convective heat transfer thermal resistance and the heat conduction thermal resistance as the total heat transfer thermal resistance between the fluids at the two sides of the dividing wall type heat exchanger, thereby calculating and obtaining the total heat transfer coefficient K of the dividing wall type heat exchanger.
Redefining the number of heat transfer units of the dividing wall type heat exchanger based on the calculated total heat transfer coefficient K and the total heat transfer area A of the dividing wall type heat exchanger. The number of heat transfer units defined in the present invention is clearly distinguished from the number of heat transfer units in the conventional "heat transfer effectiveness-heat transfer unit number method". For a concurrent heat exchanger, the number of heat transfer units is defined as the product of the sum of the inverses of the heat capacity flow rates of the two-side fluid working media, the total heat transfer coefficient K and the total heat transfer area A, and the expression is NTU ═ 1/W1+1/W2) KA; for the counter-flow heat exchanger, the heat capacity and flow rate of the fluid working medium on the side opposite to the direction of the coordinate axis should be negative, the invention does not take the fluid working medium 2 as the counter-flow working medium, and the expression of the counter-flow heat transfer unit number is NTU ═ 1/W1－1/W2)KA。
And directly calculating the outlet temperature of the fluid working media at two sides of the dividing wall type heat exchanger on the basis of the defined energy average temperature and the number of the heat transfer units. For a concurrent heat exchanger, the expression of the outlet temperature is ti,out＝tave+e-NTU(ti,in-tave) (ii) a For a counter-flow heat exchanger, the outlet temperature expression of the counter-flow heat exchanger is t for the fluid 1 with the flow direction consistent with the coordinate axis direction1,out＝tave+e-NTU(t1,in-tave) For the fluid 2 with the direction opposite to the coordinate axis, the outlet temperature expression is t2,out＝tave+eNTU(t2,in-tave). Correspond toThe total heat transfer capacity of the dividing wall type heat exchanger can be obtained by the outlet temperature result. Therefore, the invention provides the method for calculating the outlet temperature and the total heat exchange quantity of the heat exchanger with two basic flow forms of integral forward flow and integral reverse flow, and the method can accurately, simply and conveniently calculate the performance of the dividing wall type heat exchanger.
Preferably, in the method for calculating the energy average temperature of the counter-flow heat exchanger, the expression of the energy average temperature is tave＝(W1t1,in-W2t2,out)/(W1-W2) Wherein t is2,outIs an unknown quantity, so the energy average temperature cannot be directly solved. To facilitate the solution, the expression of the mean temperature of the energy in the countercurrent is deduced again here, written as tave＝(e- NTUW1t1,in-W2t2,in)/(e-NTUW1-W2). In the formula, the number of the counter-flow heat transfer units can be obtained by known quantity, and the other variables are known quantity. Therefore, the rewritten expression can directly solve the countercurrent energy average temperature.
By analogy with the solution method and conclusion of the outlet temperature, the on-way temperature analytic solution of the fluid working media at the two sides of the dividing wall type heat exchanger can be directly written. For a concurrent heat exchanger, the expression of the two side along-path temperature is ti(x)＝tave+e-NTU[0→x](ti,in-tave) (ii) a For the counter-flow heat exchanger, the expressions of the on-way temperatures on the two sides are respectively t1(x)＝tave+e-NTU[0→x](t1,in-tave) And t2(x)＝tave+eNTU[x→L](t2,in-tave) Where t is1Representing the on-way temperature, t, of fluid flowing in the same direction as the coordinate axis in a counterflow heat exchanger2Representing the on-way temperature of the fluid flowing opposite to the coordinate axis, L representing the total flowing length, and x representing the flowing distance of the fluid; NTU [0 → x]Represents the number of heat transfer elements from 0 to the x position, i.e., the number of heat transfer elements corresponding to the heat transfer area from 0 to the x position. Therefore, the method provides an analytic solution of the on-way temperature distribution of the fluid on two sides, and perfects the heat transfer of the dividing wall type heat exchanger with a brief conclusionTemperature field information of the process.
The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature is characterized in that the performance of the heat exchanger can be directly solved according to the known quantity, and compared with the traditional logarithmic average temperature difference method, the method omits the step of iteration of the outlet temperature. The method can be applied to the structure optimization design of the dividing wall type heat exchanger, the performance calculation process of the optimization design is effectively simplified, the structure optimization efficiency is increased, and the algorithm convergence of the optimization design is improved.
Example one
As shown in fig. 1 to 4, in the method for calculating the performance of the dividing wall type heat exchanger based on the average energy temperature according to the present embodiment, taking a counter-flow type heat exchanger as an example, the following steps are performed:
inputting inlet flow, temperature and pressure of fluid working media at two sides of the dividing wall type heat exchanger according to the thermal environment of the dividing wall type heat exchanger; inputting physical parameters of fluid working media at two sides or the change rule of the physical parameters along with temperature and pressure; and (4) setting the structural form and structural parameters of the dividing wall type heat exchanger. Wherein, the specific input parameters are shown in table 1, the heat transfer process diagram is shown in figure 2, and the working condition parameters are given by referring to the water-cooling air heat exchanger;
step two, according to the formula tave＝(e-NTUW1t1,in-W2t2,in)/(e-NTUW1-W2) Calculating the energy average temperature of the two streams of fluid, performing weighted average on the inlet temperatures of the two sides by taking the heat capacity flow rate of the two streams of fluid as a weight according to the flowing mode of the working medium and the heat capacity flow rate of the two streams of fluid, and calculating the energy average temperature;
calculating the convective heat transfer coefficient, and obtaining the convective heat transfer coefficient of the fluid working medium at the two sides of the dividing wall type heat exchanger according to the convective heat transfer characteristic database at the two sides of the heat transfer unit;
step four, calculating the total heat transfer coefficient of the dividing wall type heat exchanger, calculating the heat transfer convection resistance between the specific wall surface and the fluid at two sides and the heat transfer heat resistance of the solid wall surface of the dividing wall type heat exchanger according to the heat transfer convection coefficient, and calculating the total heat transfer coefficientThe heat transfer coefficient is 800W/(m)2K) and a total heat transfer area of 1m2As shown in table 1;
step five, according to NTU ═ 1/W1－1/W2) KA calculates the number of heat transfer units, and the calculated value is-1.0084;
step six, according to the formula t1,out＝tave+e-NTU(t1,in-tave) Calculating the outlet temperature of the fluid 1 with the same direction of the flow direction and the coordinate axis; according to the formula t2,out＝tave+eNTU(t2,in-tave) The outlet temperature of the fluid flowing opposite to the coordinate axis, i.e. fluid 2, is calculated.
The expression of the energy average temperature in step two is tave＝(W1t1,in-W2t2,out)/(W1-W2) Wherein t is2,outIs unknown quantity, so that it can not be directly solved, and for convenient solution, the formula t is used2,out＝tave+eNTU(t2,in-tave) Brought into tave＝(W1t1,in-W2t2,out)/(W1-W2) In the process, re-derivation is carried out to obtain the expression of the energy average temperature of the counter-flow heat exchanger as tave＝(e-NTUW1t1,in-W2t2,in)/(e-NTUW1-W2) The known quantities are introduced into the formula according to Table 1 to obtain TaveIs 265.16K, t1,outIs 341.90K, t2,out322.79K; through the calculation formula Q of the total heat exchange quantity being W1|t1,out-t1,in|＝W2|t2,out-t2,inAnd the total heat exchange quantity Q is further calculated to be 40.95 kW.
TABLE 1
| t1,in | m1 | cp,1 | t2,in | m2 | cp,2 |
| 293.15K | 0.2kg/s | 4200J/(kg·K) | 423.15K | 0.4kg/s | 1020kJ/(kg·K) |
| W1 | W2 | K | A | NTU | Tave |
| 840W/K | 408W/K | 800W/(m2·K) | 1m2 | -1.0084 | 265.16K |
| t1,out | t2,out | Q | |||
| 341.90K | 322.79K | 40.95kW |
The embodiment adopts a specific heat transfer process case to demonstrate the method of the invention in a full flow, and completes the performance calculation of the dividing wall type heat exchanger in a sequential calculation mode without iteration. According to conventional input, the parameters of the inlet fluid at two sides and the total heat transfer capacity of the dividing wall type heat exchanger, namely the total heat transfer coefficient K and the total heat transfer area A, are given according to boundary conditions, and the outlet temperature and the temperature distribution of the fluid at two sides are directly given in the form of analytical solution. The invention has the advantages of clear mathematical model of the heat transfer process and simplified performance calculation process of the dividing wall type heat exchanger.
Comparative example 1
As shown in fig. 1 to 4, in order to further illustrate the advantages of the method of the present invention compared to the conventional heat exchanger performance calculation method based on the logarithmic mean temperature difference, the input parameters of the above embodiment are solved by using the conventional method.
The brief flow of the conventional method is as follows: assuming, within reasonable limits, an outlet temperature t of the fluid 11,outCalculating the outlet temperature t of the fluid 2 according to the conservation of energy of the fluid on two sides2,outSubstituting the inlet and outlet temperatures of the fluid on the two sides into a logarithmic mean temperature difference calculation formula:
LMTD＝[(t1,out-t2,in)-(t1,in-t2,out)]/ln[(t1,out-t2,in)/(t1,in-t2,out)]
calculating average heat transfer temperature difference, and comparing heat exchange quantity Q calculated by heat transfer equation1LMTD KA and enthalpy difference Q between fluid inlet and outlet2＝cp,1m1|T1,out-T1,inI compare if Q1And Q2If the difference value is within the allowable range, the iteration converges, otherwise, the assumed 'outlet temperature of the fluid 1' is adjusted according to the difference value and the magnitude relation of the two, and the process is repeated until the convergence is reached.
With the gradient-based fast iterative method, the residual of the iterative computation is shown in FIG. 4, where the residual is defined as (Q)2-Q1)/Q2. Under the condition of the input parameters of the first embodiment, the residual error after about 120 steps can be reduced to the power of-4 of 10, and more accurate convergence is achieved. The converged fluid outlet temperatures of the two sides are 341.89K and 322.80K respectively, and the deviation from the accurate value calculated by the method of the invention exists in the second place after the decimal point.
This comparative example illustrates that: the traditional method and the method of the invention can obtain basically the same heat transfer result, but compared with the accurate analytic solution of the invention, the traditional iterative solution can only obtain the numerical solution, and has a certain deviation; the traditional method needs iteration of a certain order of magnitude, the iteration is carried out 120 times in the comparison example, and the calculation is complicated, but the method can be executed according to the flow sequence, so that the heat transfer performance calculation result can be obtained without iteration, and only 1 time of calculation is needed. In addition, the iterative process of the traditional method will receive the influence of factors such as initial values, boundary conditions and the like, and the convergence of the iterative process needs a certain means to be ensured, so that the workload is further increased. Therefore, the method can effectively improve the calculation efficiency of the traditional heat transfer calculation method, save iteration to simplify the calculation process and improve the stability.
Without loss of generality, the method of the present invention is described in the first embodiment by taking a counter-flow heat exchanger as an example, and the same conclusion as above can be similarly obtained by substituting the method into a counter-flow heat exchanger.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A dividing wall type heat exchanger performance calculation method based on energy average temperature is characterized by comprising the following steps:
inputting working conditions of the dividing wall type heat exchanger according to the thermal environment of the dividing wall type heat exchanger;
calculating the energy average temperature of the two streams of fluid, carrying out weighted average on the inlet temperatures of the two sides by taking the heat capacity flow rate of the two sides of fluid as a weight according to the flowing mode of the working medium and the heat capacity flow rate of the two sides of fluid, and calculating the energy average temperature;
calculating the convective heat transfer coefficient, and obtaining the convective heat transfer coefficient of the fluid working medium at the two sides of the dividing wall type heat exchanger according to the convective heat transfer characteristic database at the two sides of the heat transfer unit;
calculating the total heat transfer coefficient of the dividing wall type heat exchanger, calculating the convective heat transfer thermal resistance between the wall surface and the fluid on the two sides according to the convective heat transfer coefficients on the two sides, and calculating the total heat transfer coefficient according to the thermal conductivity thermal resistance of the solid wall surface of the dividing wall type heat exchanger;
defining the number of heat transfer units and calculating, wherein the number of the heat transfer units is defined as the product of the sum of the inverses of the heat capacity flow rates of the fluid working media at the two sides and the total heat transfer coefficient and the total heat transfer area;
and step six, calculating the outlet temperature and the on-way temperature distribution of the fluid at two sides according to the number of the heat transfer units and the energy average temperature, and further calculating the total heat exchange amount.
2. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 1, wherein the method comprises the following steps: the dividing wall type heat exchanger is an integral forward flow type heat exchanger and an integral reverse flow type heat exchanger.
3. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 1, wherein the method comprises the following steps: the working conditions of the step-one intermediate-wall heat exchanger include: inlet flow, temperature, pressure; physical property parameters of fluid working media on two sides; the dividing wall type heat exchanger has the structural form and the structural parameters.
4. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 2, wherein the method comprises the following steps: the calculation formula of the energy average temperature of the concurrent flow heat exchanger is tave＝(W1t1,in+W2t2,in)/(W1+W2) The energy average temperature calculation formula of the counter-flow heat exchanger is tave＝(W1t1,in-W2t2,out)/(W1-W2) Where t is temperature and W is heat capacity flow rate.
5. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 1, wherein the method comprises the following steps: in the third step, the basic heat transfer unit form is obtained through the working conditions input in the first step; determining an empirical correlation formula adopted by calculation of the heat transfer characteristics of the fluid at two sides according to the form of the heat transfer unit; and calculating the convection heat transfer coefficient between the fluid working media at the two sides and the wall surface of the dividing wall type heat exchanger according to the Reynolds number range.
6. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 2, wherein the method comprises the following steps: the calculation formula of the heat transfer unit number redefined in the step five comprises the following steps: the expression of heat transfer unit of forward flow heat exchanger is NTU ═ 1/W1+1/W2) KA, the expression of the number of heat transfer units of the counter-flow heat exchanger is NTU ═ n (1/W1-1/W2) KA, wherein K is the total heat transfer coefficient, and A is the total heat transfer area of the dividing wall type heat exchanger.
7. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 2, wherein the method comprises the following steps: in the sixth step, the expression of the outlet temperature of the concurrent heat exchanger is ti,out＝tave+e-NTU(ti,in-tave) The expression of the outlet temperature of the counter-flow heat exchanger is t1,out＝tave+e-NTU(t1,in-tave)，t2,out＝tave+eNTU(t2,in-tave)。
8. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 2, wherein the method comprises the following steps: in the second step, the expression of the energy average temperature of the counter-flow heat exchanger is deduced again, and the obtained expression is tave＝(e-NTUW1t1,in-W2t2,in)/(e-NTUW1-W2)。
9. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 5, wherein the method comprises the following steps: the heat transfer unit forms comprise uniform cross-section channels, finned tube bundles and smooth tube bundles.
10. The method for calculating the performance of the dividing wall type heat exchanger based on the energy average temperature as claimed in claim 1, wherein the method comprises the following steps: the on-way temperature distribution calculation expression is
For the concurrent flow heat exchanger: t is ti(x)＝tave+e-NTU[0→x](ti,in-tave)
For a counter-flow heat exchanger:
wherein, t1Representing the on-way temperature, t, of fluid flowing in the same direction as the coordinate axis in a counterflow heat exchanger2Representing the on-way temperature of the fluid flowing opposite to the coordinate axis, L representing the total flowing length, and x representing the flowing distance of the fluid; NTU [0 → x]Represents the number of heat transfer elements from 0 to the x position, i.e., the number of heat transfer elements corresponding to the heat transfer area from 0 to the x position.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115143818A (en) * | 2022-08-31 | 2022-10-04 | 新乡市特美特热控技术股份有限公司 | Novel heat exchanger made of titanium and aluminum alloy and design method thereof |
| CN115290693A (en) * | 2022-07-12 | 2022-11-04 | 北京航空航天大学 | Improved method for measuring heat convection coefficient outside micro-fine tube based on double working media |
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| CN115290693A (en) * | 2022-07-12 | 2022-11-04 | 北京航空航天大学 | Improved method for measuring heat convection coefficient outside micro-fine tube based on double working media |
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| CN115143818A (en) * | 2022-08-31 | 2022-10-04 | 新乡市特美特热控技术股份有限公司 | Novel heat exchanger made of titanium and aluminum alloy and design method thereof |
| CN115143818B (en) * | 2022-08-31 | 2023-01-06 | 新乡市特美特热控技术股份有限公司 | Design method of titanium and aluminum alloy heat exchanger |
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