CN111723466B - Explicit heat transfer calculation method of double-pass reverse cross-flow heat exchanger - Google Patents
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Abstract
An explicit heat transfer calculation method of a double-pass reverse cross-flow heat exchanger comprises the following steps: step 1. Heat capacity flow rate CP of known Heat flow H And the heat capacity rate CP of the cold flow C Calculating the ratio of the heat capacity rates; step 2, calculating G parameters; step 3, calculating a D parameter; step 4, calculating an effective factor P of the double-pass cross-flow heat exchanger 1‑2 The method comprises the steps of carrying out a first treatment on the surface of the Step 5. Known effective factor P of double-pass Cross-flow Heat exchanger 1‑2 And the ratio R of the heat capacity rate, and a temperature difference correction coefficient F is obtained T The method comprises the steps of carrying out a first treatment on the surface of the Step 6, obtaining an X parameter; step 7, determining the outlet temperature T of the hot and cold material flows H2 ，T C2 The method comprises the steps of carrying out a first treatment on the surface of the Step 8, according to a heat balance equation, according to the heat capacity flow rate CP of the heat fluid H Or the heat capacity rate CP of the cold fluid C Inlet and outlet temperature T of hot and cold material flow H1 ，T H2 Or T C1 ，T C2 And solving the heat transfer quantity Q of the heat exchanger. The invention does not depend on the outlet temperature, and is particularly suitable for solving the operational heat transfer problem.
Description
Technical Field
The invention relates to a heat transfer calculation method of a heat exchanger, in particular to an explicit heat transfer calculation method of a double-pass reverse cross flow (shell-liquid mixing, tube-liquid non-mixing and countercurrent) heat exchanger.
Technical Field
In the prior art, the heat exchanger is a common device in chemical industry, petroleum, steel, automobiles, food and other industrial departments, and plays an important role in production. Particularly in chemical production, the heat exchanger can be used as a heater, a cooler, a condenser, an evaporator, a reboiler and the like, and has wide application. The traditional heat transfer calculation method is mainly two, namely a logarithmic mean temperature difference method (LMTD method) and a heat transfer efficiency-heat transfer unit number method (epsilon-NTU method). As cold and hot stream inlets in heat exchangersIf logarithmic average temperature difference method is adopted when temperature or other operation conditions are changed, the temperature difference correction coefficient F is obtained by inquiring the corresponding temperature difference correction coefficient diagram through a trial and error algorithm assuming the outlet temperature T The average heat transfer temperature difference is calculated according to the cross-flow logarithmic average temperature difference and the temperature difference correction coefficient, and whether the heat load is consistent or not is checked, so that the calculation process is complex, the precision is poor, the efficiency is low and the use is inconvenient; if the heat transfer efficiency-heat transfer unit number method is adopted, the functional relation between the heat transfer efficiency and the heat transfer unit number needs to be known, and the analytic relation between the heat transfer efficiency-heat transfer unit number is difficult to obtain and cannot be used for flow patterns such as cross-flow heat exchange.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides an explicit heat transfer calculation method of a double-pass reverse cross-flow (shell-liquid mixing and tube-liquid non-mixing) heat exchanger. The method is based on the heat conservation relation and the heat transfer process equation, and performs mathematical deduction on the relation among various parameters, so that an explicit heat transfer calculation method independent of outlet temperature is established, and the method is particularly suitable for solving the operational heat transfer problem.
The technical scheme adopted by the invention is as follows:
an explicit heat transfer calculation method of a double-pass reverse cross-flow heat exchanger comprises the following steps:
step 1. Heat capacity flow rate CP of known Heat flow H And the heat capacity rate CP of the cold flow C According to formula (1), the ratio R of the heat capacity rates is calculated:
wherein, CP H Is the heat capacity rate of the hot fluid, i.e. the product of mass flow and specific heat capacity; CP (control program) C Is the heat capacity rate of the cold fluid, i.e. the product of mass flow and specific heat capacity;
step 2. Knowing the heat capacity flow rate CP of the cold flow C Total heat transfer coefficient U, heat transfer area A and number of units in series of heat exchanger N SHELLS G is calculated according to the formula (2)Parameters:
wherein U is the total heat transfer coefficient; a is a heat transfer area; n (N) SHELLS The number of the heat exchanger units connected in series;
step 3. Knowing the ratio R of the G parameter calculated in step 2 and the heat capacity rate calculated in step 1, calculating the D parameter according to formula (3):
step 4. Knowing the G parameter calculated in step 2, calculating the ratio R of the D parameter calculated in step 3 and the heat capacity flow rate calculated in step 1, and calculating the effective factor P of the double-pass cross-flow heat exchanger according to the formula (4) 1-2 ：
Step 5. Known effective factor P of double-pass Cross-flow Heat exchanger 1-2 And the ratio R of the heat capacity rate, and obtaining a temperature difference correction coefficient F according to a formula (5) T For a double-pass cross-flow heat exchanger, F T The expression of (2) is:
wherein R is not equal to 1; f for different flow patterns T The expressions are different;
step 6. According to the total heat transfer coefficient U, heat transfer area A, heat capacity ratio R, heat capacity ratio CP of cold fluid C And a temperature difference correction coefficient F T The X parameter is calculated according to formula (6):
step 7 knowing the inlet temperature T of the hot and cold stream H1 、T C1 The ratio R of heat capacity and the X parameter calculated in the step 6, and the outlet temperature T of the hot and cold material flows is obtained according to formulas (7) and (8) H2 ，T C2 ：
(R-1)T H1 +R(X-1)T C1 +(1-RX)T H2 ＝0 (7)
(X-1)T H1 +X(R-1)T C1 +(1-RX)T C2 ＝0 (8)
Wherein T is H1 Is the inlet temperature of the hot fluid; t (T) H2 Is the outlet temperature of the hot fluid; t (T) C1 Is the inlet temperature of the cold fluid; t (T) C2 For the outlet temperature of the cold fluid, the inlet temperature T is known for the operational heat transfer problem H1 And T C1 U, A, CP H And CP C Then the simultaneous equations (7) and (8) solve for the outlet temperature T H2 And T C2 ；
Step 8, according to a heat balance equation, according to the heat capacity flow rate CP of the heat fluid H Or the heat capacity rate CP of the cold fluid C Inlet and outlet temperature T of hot and cold material flow H1 ，T H2 Or T C1 ，T C2 Solving the heat transfer quantity Q of the heat exchanger by adopting a formula (9):
Q＝CP H (T H1 -T H2 ) Or q=cp C (T C2 -T C1 ) (9)。
The invention provides an explicit heat transfer calculation method of a double-pass reverse cross flow (shell-liquid mixing, tube-liquid non-mixing and countercurrent) heat exchanger, which solves the heat transfer problem of the double-pass reverse cross flow (shell-liquid mixing, tube-liquid non-mixing) heat exchanger under the condition that the outlet temperature of cold and hot material flows is not known. The method can avoid complicated calculation steps such as trial calculation and image checking, reduces errors in the calculation process, has high calculation efficiency, and is particularly suitable for solving the operational heat transfer problem.
Compared with the prior art, the invention has the beneficial effects that: heat transfer problems for two-pass reverse cross-flow (shell-liquid mixing, tube-liquid non-mixing, counterflow) heat exchangers if the heat capacity CP of the hot fluid is known H Cold (cold)Heat capacity flow rate CP of fluid C Total heat transfer coefficient U, heat transfer area A, inlet temperature T of hot and cold material flow H1 And T C1 Number N of heat exchangers connected in series SHELLS The outlet temperature T of hot fluid and cold fluid can be directly solved without complicated operations such as trial and error, image checking and the like H2 And T C2 The temperature difference correction coefficient of the heat exchanger, the average heat transfer temperature difference and the heat load of the heat exchanger.
Description of the drawings:
FIG. 1 is a schematic diagram of a two-pass reverse cross-flow (shell-liquid mixing, tube-liquid non-mixing, counterflow) heat exchanger.
FIG. 2 shows the temperature difference correction factor F of a two-pass reverse cross-flow (shell-liquid mixing, tube-liquid non-mixing, counterflow) heat exchanger T A drawing.
The specific embodiment is as follows:
in order to better illustrate the application effect of the present invention, the method will be described with reference to specific application examples.
The invention will be described in further detail with reference to the following examples, which are intended to facilitate an understanding of the invention and are not to be construed as limiting in any way.
As shown in FIG. 1, a certain two-way reverse cross-flow (shell-liquid mixing, tube-liquid non-mixing, countercurrent) heat exchanger has a total heat exchange area of 20m 2 The cooling device is used for cooling oil with a mass flow of 2kg/s and a temperature of 120 ℃, the specific heat capacity of the oil is 2100J/kg.K, the inlet temperature of water is 30 ℃, and the flow is 1.2kg/s. The heat transfer coefficient of the heat exchanger is 275W/m 2 K, the specific heat capacity of water was 4200J/kg.K. The outlet temperatures of the water and oil at the heat exchanger were calculated.
This problem is known:
U＝275W/m 2 ·K，A＝20m 2 ，T H1 ＝393K，q1＝2kg/s，T C1 ＝303K，q2＝1.2kg/s，c pH ＝2100J/kg·K，c pC ＝4200J/kg·K，N SHELLS ＝1。
an explicit heat transfer calculation method of a double-pass reverse cross-flow (shell-liquid mixing and tube-liquid non-mixing) heat exchanger comprises the following steps:
step 1: the ratio R of the heat capacity rate is calculated according to formula (1).
Step 2: the G parameter is calculated according to equation (2).
Step 3: d parameters are calculated according to equation (3).
Step 4: calculating the effective factor P of the heat exchanger according to the formula (4) 2-4 。
Step 5: obtaining a temperature difference correction coefficient F according to a formula (5) T 。
Step 6: the X parameter is calculated according to equation (6).
Step 7: simultaneously equations (7) and (8), the outlet temperature T of the hot and cold streams is determined H2 ，T C2 。
(R-1)T H1 +R(X-1)T C1 +(1-RX)T H2 ＝0
(X-1)T H1 +X(R-1)T C1 +(1-RX)T C2 ＝0
Namely:
(1.2-1)×393+1.2×(1.2308-1)×303+(1-1.2×1.2308)T H2 ＝0
(1.2308-1)×393+1.2308×(1.2-1)×303+(1-1.2×1.2308)T C2 ＝0
combining the above equations to obtain T H2 ，T C2 ：
T H2 ＝340.74K
T C2 ＝346.55K
Step 8: and (3) solving the heat transfer quantity Q of the heat exchanger according to the formula (9).
Q＝CP H (T H1 -T H2 )＝2100×2×(393-340.74)＝219492J
Q＝CP C (T C2 -T C1 )＝4200×1.2×(346.55-303)＝219492J。
For comparison, we can solve this problem by the conventional logarithmic mean temperature difference method. In solving such an operational heat transfer problem, the conventional method first needs to assume the outlet temperature T of a thermal fluid H2 The heat load Q1 of the heat exchanger is calculated according to the energy conservation equation of the hot fluid, and the outlet temperature T of the other fluid is calculated according to the heat balance equation H1 Then, the logarithmic average temperature difference is obtained, and the temperature difference correction coefficient diagram of the double-pass reverse cross flow (shell-liquid mixing and tube-liquid non-mixing) heat exchanger is checked, and the temperature difference correction coefficient F is obtained in FIG. 2 T Then, according to a heat transfer rate equation, the heat load Q2 of the heat exchanger is calculated, and finally, whether Q2 is equal to Q1 is compared to judge whether the assumed outlet temperature is reasonable or not; if the calculation results before and after the heat load of the heat exchanger are inconsistent, the assumption of the outlet temperature is unreasonable, a new outlet temperature is needed to be assumed again, calculation is carried out again until the heat load of the heat exchanger calculated by the heat balance equation and the heat transfer rate equation is equal, and at the moment, the calculation is finished, and the corresponding outlet temperature is the temperature to be calculated. The specific process is as follows:
1) Assume that:
T H2 ＝360K
according to Q H ＝CP H (T H1 -T H2 )＝CP C (T C2 -T C1 )＝Q C
The method comprises the following steps: q1=2100×2× (393-360) =4200×1.2× (T) C2 -303)＝138600J
Thus: t (T) C2 ＝330.5K
Then:
looking up a temperature difference correction coefficient diagram, and obtaining the following steps in FIG. 2: f (F) T ＝1.0
According to the heat transfer rate equation, the heat load is calculated: q2=uaΔt LM F T ＝275×20×60×1＝330000J
Q2+.q1, indicating that the outlet temperature assumption is unreasonable;
2) Now assume again that:
T H2 ＝340.74K
the above calculation process is repeated:
Q H ＝CP H (T H1 -T H2 )＝CP C (T C2 -T C1 )＝Q C
Q1＝2100×2×(393-340.74)＝4200×1.2×(T C2 -303)＝219492J
T C2 ＝346.55K
looking up a temperature difference correction coefficient diagram, and obtaining the following steps in FIG. 2: f (F) T ＝0.96
Q2＝UAΔT LM F T ＝275×20×41.94×0.96＝221443
At this time: q2≡q1 (q2/q1=1.009)
Compared with the prior art, the method is a dominant heat transfer calculation method, repeated trial and error is not needed, and the traditional method is complicated, has low calculation efficiency and is inconvenient to solve the problem of operation type heat transfer. Therefore, the invention is used for solving the problem of operation type heat transfer, and has simple and convenient use and high calculation efficiency.
The foregoing embodiments have described the technical solutions and advantages of the present invention in detail, and it should be understood that the foregoing embodiments are merely illustrative of the present invention and are not intended to limit the invention, and any modifications, additions, substitutions and the like that fall within the principles of the present invention should be included in the scope of the invention.
Claims (1)
1. An explicit heat transfer calculation method of a double-pass reverse cross-flow heat exchanger is characterized by comprising the following steps:
step 1. Heat capacity flow rate CP of known Heat flow H And the heat capacity rate CP of the cold flow C According to formula (1), the ratio R of the heat capacity rates is calculated:
wherein, CP H Is the heat capacity rate of the hot fluid, i.e. the product of mass flow and specific heat capacity; CP (control program) C Is the heat capacity rate of the cold fluid, i.e. the product of mass flow and specific heat capacity;
step 2. Knowing the heat capacity flow rate CP of the cold flow C Total heat transfer coefficient U, heat transfer area A and number of units in series of heat exchanger N SHELLS The G parameter is calculated according to formula (2):
wherein U is the total heat transfer coefficient; a is a heat transfer area; n (N) SHELLS The number of the heat exchanger units connected in series;
step 3. Knowing the ratio R of the G parameter calculated in step 2 and the heat capacity rate calculated in step 1, calculating the D parameter according to formula (3):
step 4, knowing the G parameter calculated in the step 2, calculating the ratio R of the D parameter calculated in the step 3 and the heat capacity flow rate calculated in the step 1, and calculating the effective factor P of the double-pass reverse cross-flow heat exchanger according to the formula (4) 1-2 ：
Step 5. Known effective factor P of double-pass reverse cross-flow heat exchanger 1-2 And the ratio R of the heat capacity rate, and obtaining a temperature difference correction coefficient F according to a formula (5) T For a double-pass reverse cross-flow heat exchanger, F T The expression of (2) is:
wherein R is not equal to 1;
step 6. According to the total heat transfer coefficient U, heat transfer area A, heat capacity ratio R, heat capacity ratio CP of cold fluid C And a temperature difference correction coefficient F T The X parameter is calculated according to formula (6):
step 7 knowing the inlet temperature T of the hot and cold stream H1 、T C1 The ratio R of heat capacity and the X parameter calculated in the step 6, and the outlet temperature T of the hot and cold material flows is obtained according to formulas (7) and (8) H2 ，T C2 ：
(R-1)T H1 +R(X-1)T C1 +(1-RX)T H2 ＝0 (7)
(X-1)T H1 +X(R-1)T C1 +(1-RX)T C2 ＝0 (8)
Wherein T is H1 Is the inlet temperature of the hot fluid; t (T) H2 Is the outlet temperature of the hot fluid; t (T) C1 Is the inlet temperature of the cold fluid; t (T) C2 For the outlet temperature of the cold fluid, the inlet temperature T is known for the operational heat transfer problem H1 And T C1 U, A, CP H And CP C Then the simultaneous equations (7) and (8) solve for the outlet temperature T H2 And T C2 ；
Step 8, according to a heat balance equation, according to the heat capacity flow rate CP of the heat fluid H Or the heat capacity rate CP of the cold fluid C Inlet and outlet temperature T of hot and cold material flow H1 ，T H2 Or T C1 ，T C2 Solving the heat transfer quantity Q of the heat exchanger by adopting a formula (9):
Q＝CP H (T H1 -T H2 ) Or q=cp C (T C2 -T C1 ) (9)。
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