CN113591329B - Numerical method based on cold source temperature of shell-and-tube condenser in cross-season organic Rankine cycle system - Google Patents
Numerical method based on cold source temperature of shell-and-tube condenser in cross-season organic Rankine cycle system Download PDFInfo
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Abstract
The invention discloses a numerical calculation method based on the cold source temperature of a shell-and-tube condenser in a cross-season organic Rankine cycle system, relates to the technical field of heat transfer performance of the shell-and-tube condenser, and particularly relates to a method for determining the cold source temperature of the shell-and-tube condenser in the cross-season operation process of the organic Rankine cycle system. The method comprises the following specific steps: determining meteorological parameters, selecting types of cooling towers and calculating the heat power of the cooling towers through Meteorom meteorological software, and setting the evaporation temperature t of the working medium eva Mass flow q of working medium m Flow q of cold source v The heat exchange area A of the shell-and-tube condenser is combined with Matlab and simultaneously called a Refprope 9.1 database according to a given formula, a cooling tower model and the organic Rankine cycle system are subjected to coupling calculation, and a calculation method which is more consistent and closer to the cold source temperature in the actual operation process of the cross-season organic Rankine cycle is established.
Description
The technical field is as follows:
the invention relates to the technical field of heat transfer performance of a shell-and-tube condenser, in particular to a numerical calculation method for determining cold source temperature of the shell-and-tube condenser in the operation process of a cross-season organic Rankine cycle system.
Background art:
at present, a Logistic model, namely T is generally adopted for a method for calculating the cold source temperature of a cooling system in a cross-season organic Rankine cycle water ＝0.813T environment +3.316. In the actual heat transfer process, the temperature of a cold source of the organic Rankine cycle cooling system is closely related to factors such as dry-bulb temperature, wet-bulb temperature, relative humidity, atmospheric pressure and cooling capacity of a cooling tower. Obviously, the organic Rankine cycle cold source temperature calculated by only the Logistic model formula is unreasonable. In general, the basic flow of an organic rankine cycle is as follows: the working medium in the liquid storage tank flows through the working medium pump after being pressurized by the working medium pumpThe flow meter is sent to the tube side of the evaporator, the working medium is changed into high-temperature high-pressure steam after absorbing heat emitted by heat conducting oil in the evaporator, then the working medium steam is sent to the single-screw expander to push the expander to rotate, the working medium is changed into exhaust gas with reduced temperature and pressure after being discharged from the expander, the pressure of the exhaust gas is slightly reduced after entering the oil separator, then the exhaust gas enters the condenser to be condensed, and the working medium discharged from the condenser is collected by the liquid storage tank and is recycled by the working medium pump.
The invention content is as follows:
the purpose of the invention is as follows: aiming at the existing problems, the invention provides a method for calculating the temperature of a cold source in the actual running process of an organic Rankine cycle, which is more accordant and closer to the actual running process of the organic Rankine cycle and is based on Matlab and Meteonorm meteorological software and simultaneously calls a Refprope 9.1 database to perform coupling calculation on a cooling tower model and a cross-season organic Rankine cycle system.
The technical scheme is as follows: a numerical method based on the temperature of a cold source of a shell-and-tube condenser in a cross-season organic Rankine cycle system comprises the following steps:
the first step is as follows: obtaining the local dry bulb temperature t through Meteorom meteorological software g Wet bulb temperature t s Relative humidity phi, and atmospheric pressure P a
The second step is that: selecting the model of the cooling tower, and calculating the characteristic number of the cooling tower according to the following formula
Ω'＝Bλ 1 m (1)
Wherein omega' is the characteristic number of the cooling tower, B and m are related to the type of the filler of the cooling tower, and lambda 1 As the gas-water ratio of the cooling tower
The third step: setting the evaporation temperature t of the working medium eva Mass flow q of working medium m Cold source flow q v Shell and tube condenser heat exchange area A, t in the first iteration process 2 ＝t s (t 2 For the water temperature of the cooling tower, a subsequent iteration process t 2 Will change)
The fourth step: setting the condensation temperature t in the first iteration k Lower limit t of k1 ＝t s ，t k2 ＝t eva Intermediate condensation temperature t km ＝(t k1 +t k2 ) (subsequent iteration process t) k1 、t k2 Will change)
The fifth step: calculating the heat release of the shell-and-tube condenser:
in the formula h 2 、h 3 Inlet and outlet enthalpy values of working medium side of condenser in kJ-kg -1 Through t km Refprop9.1 is called to query.
And a sixth step: calculating the outlet temperature of cooling water of the shell-and-tube condenser
T without considering heat dissipation loss w1 ＝t 2 ,t w2 ＝t 1 (t w1 Is the inlet water temperature t of the condenser w2 Is the outlet water temperature t of the condenser 1 Is the water temperature t of the cooling tower 2 Water temperature at the outlet of the cooling tower) formula rho 1 、C p Density of cooling water kg m -3 And specific heat capacity kJ. K (kg) -1 ，
The seventh step: calculating the water-side heat transfer coefficient of the shell-and-tube condenser:
in the formula d i Is the inner diameter of a heat exchange pipe of a shell-and-tube condenser, and the unit is m
The eighth step: calculating the heat transfer coefficient of the working medium side of the shell-and-tube condenser:
in the formula, r is the latent heat of vaporization of the working medium, kJ.kg -1 ，ρ 2 Is the density of the working medium, kg.m - 3，λ 2 Is the coefficient of thermal conductivity of working medium, w (m.k) -1 Eta is dynamic viscosity of working medium, pa.s, R Shell side Is the shell-side thermal resistance, R, of a shell-and-tube condenser Pass Is the tube side thermal resistance. d o Is the outer diameter of a heat exchange tube of a shell-and-tube condenser, and the unit is m and d i Is the inner diameter of a heat exchange pipe of a shell-and-tube condenser, and the unit is m and lambda 3 Heat conductivity coefficient w (m.k) for condenser heat exchange tube -1 And assume that during the first iteration t km -t wp ＝10℃(t wp Is the assumed temperature of the outer wall of the heat exchange tube of the condenser), h can be calculated by the formula (7) Working medium H to be calculated Working medium Substituting into equation (8), t can be calculated w If | t w -t wp |<At 0.01 deg.C, proceeding the ninth step, otherwise let t wp ＝t w And repeating the eighth step until t is satisfied w -t wp |<Up to 0.01 ℃. T can be calculated by the eighth step w (actual temperature of outer wall of condenser heat exchange tube), h Working medium
The ninth step: calculating the logarithmic mean temperature difference in a shell-and-tube condenser
The tenth step: calculating comprehensive heat transfer coefficient of shell-and-tube condenser
In the formula R Shell side Is the shell-side thermal resistance, R, of a shell-and-tube condenser Pass Is tube pass thermal resistance, η 0 For rib efficiency, d o Is the outer diameter of the heat exchange tube of a shell-and-tube condenser, and the unit is m
The eleventh step: calculating heat transfer capacity of shell-and-tube condenser
The twelfth step: the heat release P of the shell-and-tube condenser obtained by the fifth step condenser Comparing with the heat transfer P of the shell-and-tube condenser calculated in the eleventh step, i.e. adopting dichotomy, if P is condenser >P, then t k2 ＝t km Otherwise t k1 ＝t km If | t is satisfied k1 -t k2 |<And if the temperature is 0.01 ℃, performing the tenth step, and otherwise returning to the fourth step for recalculation.
And a thirteenth step of: calculating the cooling number of a cooling tower
Δt＝t 1 -t 2 And when Δ t<At 15 ℃, it can be simplified to the following formula:
wherein the relevant parameter can be calculated by:
P tg ＝98.065*10 (0.0141966-3.142305*(1000/tg-1000/373.15) +8.2*log 10 (373.15 /tg)-0.0024804*(373.15-tg)) (14)
i 1 ″＝1.005*(t 1 -273.15)+(2500+1.842*(t 1 -273.15))*0.622*P t1 /(P a -P t1 ) (19)
the empirical formula for K is:
if it is used
Outputting the final result t 1 、t 2 Otherwise, let t 2 ＝t 2 +0.0001, the third step is carried out again.
In the formula, omega is the cooling number of the counter-flow cooling tower, K is the coefficient of heat taken away by the evaporated water, C w Specific heat of cooling water in kJ. Kg. Degree.C.) -1 ，P t1 、P t2 At a temperature of t 1 、t 2 Corresponding to the saturation vapor pressure, i, of the humid air 1 ″、i m ″、i 2 "respectively means that the temperature is the water temperature t 2 Average water temperature t m Water temperature t in tower 1 Saturated air enthalpy of time, i 1 、i m 、i 2 The specific enthalpies of the tower inlet air, the average state air and the tower outlet air are respectively shown.
Compared with the prior art, the invention has the following beneficial effects:
the main purpose of the invention is to accurately simulate the influence of a cooling system on the cross-season organic Rankine cycle system, obtain a result most conforming to the actual organic Rankine cycle operation condition by adjusting relevant parameters such as the evaporation temperature, the mass flow, the cold source flow and the heat transfer area of a shell-and-tube condenser of the organic working medium and applying a numerical simulation method, and couple environmental factors, a cooling tower and the like with the organic Rankine cycle. The method used in the invention can be greatly close to the actual operation state, and a matching relation with better precision between the organic Rankine cycle numerical simulation and the experimental verification is constructed.
Description of the drawings:
FIG. 1 is a flow chart of the organic Rankine cycle system and cooling tower model coupling calculation
FIG. 2 shows the inlet water temperature t of the shell-and-tube condenser under different working conditions and different cold source flows across seasons w1 (namely the water temperature t at the outlet of the cooling tower 2 ) Water temperature diagram t at outlet of shell-and-tube condenser w2 (namely the water temperature t entering the cooling tower 1 )
The specific implementation mode is as follows:
the present invention will be further described with reference to the following examples and drawings, but the present invention is not limited to the following examples.
According to the theoretical calculation model established, refprope 9.1 database is called simultaneously based on Matlab and Meteonorm meteorological software, related calculation programs are compiled, and a cooling tower model and an organic Rankine cycle system are subjected to coupling calculation. As shown in fig. 1, a numerical method based on the cold source temperature of a shell-and-tube condenser in an organic rankine cycle system comprises the following steps:
obtaining dry bulb temperature t of 3 months, 6 months, 9 months and 12 months in Beijing 2020 by Meteorom meteorological software g Wet bulb temperature t s Relative humidity phi, and atmospheric pressure P a
Selecting the model of the cooling tower, and calculating the characteristic number of the cooling tower according to the following formula
Ω'＝Bλ 1 m (1)
Wherein omega' is the characteristic number of the cooling tower, B and m are related to the type of the filler of the cooling tower, and lambda 1 For the gas-water ratio of the cooling tower, by referring to the handbook related to the cooling tower, B =1.57, m =0.57, λ in the embodiment 1 ＝1。
Setting the working medium to R123, t eva ＝111.15℃、q m ＝1500kg·h -1 、q v ＝4m3·h -1 ～20m3·h -1 、
A＝57m 2
Calculating the heat release of the shell-and-tube condenser:
in the formula h 2 、h 3 The enthalpy value of the inlet and the outlet of the working medium side of the condenser is kJ.kg -1 Through t km Refprop9.1 is called to query.
Calculating the outlet temperature of cooling water of the shell-and-tube condenser
T without considering heat dissipation loss w1 ＝t 2 ,t w2 ＝t 1 (t w1 Is the inlet of a condenserTemperature of mouth water, t w2 Is the outlet water temperature t of the condenser 1 Is the water temperature t of the cooling tower 2 Water temperature at the outlet of the cooling tower) formula rho 1 、C p Is the density kg.m of cooling water -3 And specific heat capacity kJ (kg. K) -1
Calculating the water-side heat transfer coefficient of the shell-and-tube condenser:
in the formula d i Is the inner diameter of a heat exchange pipe of a shell-and-tube condenser d i =0.0168m, unit m
Calculating the heat transfer coefficient h of the working medium side of the shell-and-tube condenser Working medium And the temperature t of the outer wall of the condenser tube and the heat pipe w ：
In the formula R Shell side ＝0.14×10 -3 ，R Pass ＝0.18×10 -3 ，d o ＝0.019m。
Calculating the logarithmic mean temperature difference in a shell-and-tube condenser
Calculating comprehensive heat transfer coefficient of shell-and-tube condenser
In the formula R Shell side ＝0.14×10 -3 ，R Pass ＝0.18×10 -3 ，η 0 ＝85％，d o ＝0.019m。
Calculating heat transfer capacity of shell-and-tube condenser
The calculated heat release P of the shell-and-tube condenser condenser Comparing with heat transfer P of shell-and-tube condenser, if P condenser >P, then t k2 ＝t km Otherwise t k1 ＝t km
Calculating the cooling number of a cooling tower
Δt＝t 1 -t 2 And when Δ t<At 15 ℃, it can be simplified to the following formula:
wherein the relevant parameter can be calculated by:
P tg ＝98.065*10 (0.0141966-3.142305*(1000/tg-1000/373.15) +8.2*log 10 (373.15 /tg)-0.0024804*(373.15-tg)) (14)
i 1 ″＝1.005*(t 1 -273.15)+(2500+1.842*(t 1 -273.15))*0.622*P t1 /(P a -P t1 ) (19)
the empirical formula for K is:
if it is not
Outputting the final result t 1 、t 2 Otherwise, let t 2 ＝t 2 +0.0001 until the condition is satisfied
In the formula, omega is the cooling number of the counter-flow cooling tower, K is the coefficient of heat taken away by the evaporated water, C w Specific heat of cooling water in kJ. Kg. Degree.C.) -1 ，P t1 、P t2 At a temperature of t 1 、t 2 Is wet airGas corresponding saturated vapor pressure, i 1 ″、i m ″、i 2 "respectively indicates the temperature as the water temperature t 2 Average water temperature t m Water temperature t in tower 1 Saturated air enthalpy of hour, i 1 i m i 2 The specific enthalpies of the inlet air, the average air and the outlet air are respectively shown.
Through the calculation of the flow chart, the change condition of the cold source temperature under the condition of different cold source flow under the operation working condition of the cross-season organic Rankine cycle system can be accurately solved, as shown in the attached figure 2.
In conclusion, the numerical calculation method for the Refprope 9.1 database is simultaneously called by coupling the cooling tower model and the cross-season organic Rankine cycle system based on Matlab and Meteonorm meteorological software, so that the calculation method which is more consistent and closer to the cold source temperature in the actual operation process of the organic Rankine cycle is established.
Claims (4)
1. A numerical method based on the cold source temperature of a shell-and-tube condenser in a cross-season organic Rankine cycle system is characterized by comprising the following steps of:
the first step is as follows: obtaining the local dry bulb temperature t through Meteorom meteorological software g Wet bulb temperature t s Relative humidity φ and atmospheric pressure P a ；
The second step is that: selecting the model of the cooling tower, and calculating the characteristic number of the cooling tower according to the following formula
Ω'＝Bλ 1 m (1)
Wherein omega' is the characteristic number of the cooling tower, B and m are related to the type of the filling material of the cooling tower, and lambda is 1 The gas-water ratio of the cooling tower;
the third step: setting the evaporation temperature t of the working medium eva Mass flow q of working medium m Flow q of cold source v Shell and tube condenser heat exchange area A, t in the first iteration process 2 ＝t s ，t 2 For the temperature of the water leaving the cooling tower, the subsequent iteration process t 2 Will change;
the fourth step: set to be firstCondensing temperature t in the course of sub-iteration k Lower limit t of k1 ＝t s Upper limit of t k2 ＝t eva Intermediate condensation temperature t km ＝(t k1 +t k2 ) /2, subsequent iterative procedure t k1 、t k2 Will change;
the fifth step: calculating the heat release of the shell-and-tube condenser:
in the formula h 2 、h 3 Inlet and outlet enthalpy values of working medium side of condenser in kJ-kg -1 Through t km Refprop9.1 is called to inquire;
and a sixth step: calculating the outlet temperature of cooling water of the shell-and-tube condenser
T without considering heat dissipation loss w1 ＝t 2 ,t w2 ＝t 1 ，t w1 Is the inlet water temperature t of the condenser w2 Is the outlet water temperature t of the condenser 1 The water temperature t of the cooling tower 2 The temperature of the water discharged from the cooling tower is used as the temperature of the water discharged from the cooling tower; where ρ is 1 、C p Is the density kg.m of cooling water -3 And specific heat capacity kJ (kg. K) -1 ；
The seventh step: calculating the water-side heat transfer coefficient of the shell-and-tube condenser:
in the formula d i The inner diameter of a heat exchange tube of a shell-and-tube condenser is m;
eighth step: calculating the side heat transfer coefficient of the working medium of the shell-and-tube condenser:
in the formula, r is the latent heat of vaporization of the working medium, kJ.kg -1 ，ρ 2 Is the density of the working medium, kg.m - 3，λ 2 Is the coefficient of thermal conductivity of working medium, w (m.k) -1 Eta is dynamic viscosity of working medium, pa.s, R Shell side Is the shell-side thermal resistance, R, of a shell-and-tube condenser Pass Is tube pass thermal resistance, d o Is the outer diameter of the heat exchange tube of a shell-and-tube condenser, and the unit is m and d i Is the inner diameter of a heat exchange pipe of a shell-and-tube condenser, and the unit is m and lambda 3 Heat conductivity coefficient w (m.k) for condenser heat exchange tube -1 ；
Suppose that during the first iteration, t km -t wp ＝10℃，t wp H can be calculated for the assumed temperature of the outer wall of the heat exchange tube of the condenser through a formula (7) Working medium H to be calculated Working medium Substituting into equation (8), t can be calculated w If | t w -t wp |<At 0.01 deg.C, proceeding the ninth step, otherwise let t wp ＝t w And repeating the eighth step until t is satisfied w -t wp |<Up to 0.01 deg.C, t can be calculated by the eighth step w 、h Working medium ，t w The real temperature of the outer wall of the heat exchange tube of the condenser;
the ninth step: calculating the logarithmic mean temperature difference in a shell-and-tube condenser
The tenth step: calculating comprehensive heat transfer coefficient of shell-and-tube condenser
In the formula R Shell side Is the shell-side thermal resistance, R, of a shell-and-tube condenser Pass Is tube pass thermal resistance, η 0 For rib efficiency, d o The outer diameter of a heat exchange tube of a shell-and-tube condenser is m;
the eleventh step: calculating heat transfer capacity of shell-and-tube condenser
The twelfth step: the heat release P of the shell-and-tube condenser obtained by the fifth step condenser Comparing with the heat transfer P of the shell-and-tube condenser calculated in the eleventh step, i.e. adopting the idea of dichotomy if P condenser >P, then t k2 ＝t km Otherwise t k1 ＝t km If | t is satisfied k1 -t k2 |<Performing the tenth step at the temperature of 0.01 ℃, and returning to the fourth step for recalculating if the temperature is not equal to the preset temperature;
the thirteenth step: calculating the cooling number of a cooling tower
Δt＝t 1 -t 2 And when Δ t<At 15 ℃, it can be simplified to the following formula:
wherein the relevant parameter can be calculated by:
P tg ＝98.065*10 (0.0141966-3.142305*(1000/tg-1000/373.15) +8.2*log 10 (373.15/tg)-0.0024804*(373.15-tg)) (14)
i 1 ”＝1.005*(t 1 -273.15)+(2500+1.842*(t 1 -273.15))*0.622*P t1 /(P a -P t1 ) (19)
the empirical formula for K is:
if it is not
Outputting the final result t 1 、t 2 Otherwise, let t 2 ＝t 2 +0.0001, the third step is carried out again.
2. The numerical method for the cold source temperature of the shell-and-tube condenser in the cross-season organic Rankine cycle system according to claim 1, wherein Ω is the cooling number of a counter-flow cooling tower, K is the coefficient of heat taken away by the amount of evaporated water, and C is w Specific heat of cooling water in kJ. Kg. Degree.C.) -1 ，P t1 、P t2 At a temperature of t 1 、t 2 Corresponding to the saturated vapor pressure, i 1 ”、i m ”、i 2 "respectively indicates that the temperature is the water temperature t 2 Average water temperature t m Water temperature t in tower 1 Saturated air enthalpy of time, i 1 、i m 、i 2 The specific enthalpies of the tower inlet air, the average state air and the tower outlet air are respectively shown.
3. The numerical method based on the shell-and-tube condenser cold source temperature in the cross-season organic Rankine cycle system according to claim 1, characterized in that: solving by adopting a dichotomy idea; the upper limit of the dichotomy is the evaporation temperature t of the organic working medium eva The lower limit is the local wet bulb temperature t s The judgment conditions include: the absolute error between the upper limit temperature and the lower limit temperature is less than 0.01 ℃, at the moment, the relative error between the heat exchange quantity calculated in the heat transfer process of the shell-and-tube condenser and the heat quantity absorbed by the cold source is less than 0.01, and the relative error between the characteristic number and the cooling number of the cooling tower is less than 0.01.
4. The numerical method based on the temperature of the cold source of the shell-and-tube condenser in the cross-season organic Rankine cycle system according to claim 3, wherein the adopted structural parameters of the shell-and-tube condenser are as follows: 4 processes, 136 heat exchange tubes, wherein the length of the heat exchange tube is 2.4m, the outer diameter is 19mm, the wall thickness is 1.1mm, and the heat exchange area of the light tube is 19m 2 Rib factor 3.0, rib efficiency 85%; the structural parameters of the cooling tower are plastic bending waves and two-layer staggered arrangement, and the structural parameters can be obtained by referring to a related manual of the cooling tower: b =1.57, m =0.57, and the air-water ratio is always 1 by adjusting the cooling tower fan.
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