CN103258097A - Optimum design method of pipeline length of organic Rankine cycle heat exchanger considering flow pattern - Google Patents

Optimum design method of pipeline length of organic Rankine cycle heat exchanger considering flow pattern Download PDF

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CN103258097A
CN103258097A CN2013101816489A CN201310181648A CN103258097A CN 103258097 A CN103258097 A CN 103258097A CN 2013101816489 A CN2013101816489 A CN 2013101816489A CN 201310181648 A CN201310181648 A CN 201310181648A CN 103258097 A CN103258097 A CN 103258097A
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CN103258097B (en
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孙志强
朱启的
周孑民
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Central South University
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Abstract

The invention discloses an optimum design method of the pipeline length of an organic Rankine cycle heat exchanger considering a flow pattern. When organic working media are in a single-phase flow state, an average Nu of one section is calculated to get heat exchange amount of the section, the heat exchange amount is compared with actual heat exchange amount, and a pipe length value of the section is determined. When the organic working media are in a two-phase flow state, a convective heat-transfer coefficient calculation method of a corresponding flow pattern is selected to obtain a convective heat-transfer coefficient of the section, heat exchange amount of the section is calculated according to the convective heat-transfer coefficient value and an assumed pipe length in the end, the heat exchange amount is compared with the actual heat exchange amount, the pipe length of each dividing section is determined, and the pipeline length of the heat exchanger can be obtained. Computational accuracy of the heat exchange amount is obviously improved through consideration of flow pattern changes of media in the process of two-phase evaporation and condensation, and the optimum design method can be applied to determination of pipeline lengths of organic Rankine cycle heat exchangers using various commonly-used fluids.

Description

Consider the organic Rankine circulation heat exchanger duct length Optimization Design of flow pattern
Technical field
The present invention relates to a kind of organic Rankine circulation heat exchanger duct length Optimization Design of considering flow pattern.
Technical background
Within 2011, China GDP is about 7.30 trillion dollars, and the primary energy total quantity consumed is 26.13 hundred million tons of oil equivalents.China GDP accounts for 10.47% of world GDP total amount, but the energy for this reason consumed accounts for 21.29% of world's total energy consumption.Statistics shows, ten thousand yuan of GDP energy consumptions of China are 2.03 times of world average level, 2.38 times of the U.S., 4.18 times of Germany, 4.40 times of Japan.China's industrial energy consumption accounts for more than 70% of whole society's energy consumption, and the industrial energy consumption height is the main cause that causes China's per Unit GDP Energy Consumption high.And 60% – 65% of industrial energy consumption transforms for the waste heat that carrier is different, temperature is different, wherein, middle-low temperature heat quantity is extremely huge, but, because its grade is low, substantially can not be recycled by traditional water vapor power cycle.
In the face of so severe energy crisis and higher GDP energy consumption, find the only way that new forms of energy and research and development power-saving technology have become China's sustainable economic development.With regard to China's current situation, the renewable and clean energy resources such as development geothermal energy and sun power, reclaim the middle-low temperature heat resource that wide, the traditional water vapor power cycle of industrial process amount multiaspect is difficult to the high efficiente callback utilization and can not only effectively alleviate the situation of domestic energy supply anxiety, but also be conducive to improve environment.Waste heat, geothermal energy and the sun power etc. of industrial process discharge all belong to middle low-temperature heat source, and, in middle-low temperature heat recovery field, organic Rankine circulation becomes the desirable approach of high efficiente callback middle-low temperature heat because of advantages such as its efficiency are high, simple in structure and cost of investment is low.Therefore, optimal design seems especially important as the evaporator of organic Rankine circulation vitals and the duct length of condenser.
In existing evaporator and condenser tubes Design of length method, be to select a certain experimental formula to be calculated substantially, and do not consider the flow pattern in two-phase evaporation and condensation process, therefore caused the computational accuracy of heat exchanger tube length low.Simultaneously, the narrow application range of experimental formula, be unfavorable for research, popularization and the application of organic Rankine circulation.
Summary of the invention
The purpose of this invention is to provide a kind of organic Rankine circulation heat exchanger duct length Optimization Design, it has considered the flow pattern in two-phase evaporation and condensation process, computational accuracy is high, and can be applicable to use the determining of organic Rankine circulation heat exchanger duct length of various fluids commonly used.
Technical solution of the present invention is as follows:
In heat transfer process, when organic working medium is the single-phase flow state (supercooled liquid or gaseous state), at first according to the division segment pipe range initial value of supposition, utilize the Gnielinski formula to calculate the average nusselt number of this section nu, and then average according to this nunumber calculates the heat exchange amount of this section, and compares with actual heat exchange amount, if not identical, change and divides segment pipe range value, until its relative error is less than or equal to 1%; When organic working medium is the two-phase flow state, at first the pipe range of segment is divided in supposition, then according to evaporation or condensing temperature, round tube inside diameter d, the working medium mass velocity g, the heat flow density of dividing segment q(pipe range based on supposition) and average gas massfraction xdetermine this section residing two-phase evaporation or condensation flow pattern, and then choose convective heat-transfer coefficient calculating formula under corresponding flow pattern to obtain the convective heat-transfer coefficient of this section, the heat exchange amount of last this section of length calculation according to this convective heat-transfer coefficient value and supposition, and compare with actual heat exchange amount, if not identical, change and divide segment pipe range value, until its relative error is less than or equal to 1%.The pipe range of two-phase evaporation and the every division segment of condensation process can be determined in this way, and then the duct length of whole evaporator and condenser can be obtained.
The present invention, by considering the variations in flow patterns of working medium in two-phase evaporation and condensation process, has significantly improved the computational accuracy of heat exchange amount, can be applicable to use organic Rankine circulation heat exchanger duct length definite of various fluids commonly used.
The accompanying drawing explanation
Fig. 1 is definite process flow diagram of evaporator pipeline length;
Fig. 2 is definite process flow diagram of condenser tubes length;
Fig. 3 is layering two-phase flow cross sectional representation;
Fig. 4 is two-phase evaporation flow regime map;
Fig. 5 is the changing trend diagram of two-phase evaporation heat transfer coefficient with the gaseous mass mark;
Fig. 6 is two-phase condensation flow regime map;
Fig. 7 is the changing trend diagram of two-phase condensation coefficient with the gaseous mass mark.
Embodiment
, duct length determines when evaporator and condenser single phase flow heat transfer
The present invention has chosen the Gnielinski formula that accuracy in computation is the highest up to now and has calculated the convective heat-transfer coefficient under working medium single-phase flow state in evaporator and condenser.Under evaporator and condenser single-phase flow state, definite step of duct length is as follows:
Step 1: according to working medium and heat source fluid, divide the working medium kinetic viscosity under the section medial temperature μ i , specific heat capacity at constant pressure c p,i and coefficient of heat conductivity k i calculate the Prandtl number of working medium at these two kinds of temperature pr i (for gas, only needing to calculate the Prandtl number of dividing under section working medium medial temperature), wherein the Prandtl number calculating formula is
Figure 318233DEST_PATH_IMAGE001
；
Step 2: according to the density under the working medium medial temperature ρ i , kinematic viscosity υ i mass rate with working medium
Figure 383141DEST_PATH_IMAGE002
, the flow velocity of calculating working medium u i and Reynolds number re i , its concrete calculating formula is respectively
Figure 906527DEST_PATH_IMAGE003
，
Figure 133108DEST_PATH_IMAGE004
；
Step 3: suppose ithe pipe range of dividing section is l j,i ;
Step 4: according to the Gnielinski formula, calculate nusselt number nu i , its concrete calculating formula is
Figure 941445DEST_PATH_IMAGE005
，
To liquid
，
Figure 922357DEST_PATH_IMAGE007
，
To gas
Figure 585419DEST_PATH_IMAGE008
，
Figure 48762DEST_PATH_IMAGE009
，
In formula, l j,i be idivide section the j+1inferior calculating pipe range; f i for the mobile Darcy resistance coefficient of intraductal turbulance, press Fu Luonianke (Filonenko) formula
Figure 455472DEST_PATH_IMAGE010
calculate.
Step 5: according to nu f, i the relative error of unit of account time heat transfer capacity, its calculating formula is
Figure 517231DEST_PATH_IMAGE011
If Δ i 1%, change idivide the pipe range of section l j, i , repeating step 3 ~ step 4; If Δ i ≤ 1%, l j, i be idivide the pipe range of section.
Step 6: calculate the pipeline total length under evaporator or condenser single-phase flow state l, its calculating formula is
Figure 85616DEST_PATH_IMAGE012
，
In formula, nfor the duct segments research number under evaporator or condenser single-phase flow state.
, duct length determines during the heat exchange of evaporator biphase gas and liquid flow
1) drafting of evaporator flow pattern of gas-liquid two-phase flow figure and flow pattern determines
Two-phase is evaporated to flow pattern and be divided into stratified flow (stratified flow, S), wavy stratified flow (stratified-wavy flow, SW), slug flow/wavy stratified flow (slug/stratified-wavy flow, Slug+SW), slug flow (Slug flow, Slug), annular flow (annular flow, A), intermittent flow (intermittent flow, I), dry stream (dryout flow, D) and eight kinds of mist flows (mist flow, M).The concrete drawing process of its flow regime map is as follows:
Step 1: according to evaporating temperature t evap(in order to calculate working medium gaseous state and the liquid thermal physical property parameters such as density), round tube inside diameter d, the working medium mass velocity gand gaseous mass mark xcalculate the ratio of xsect gas area occupied
Figure 364151DEST_PATH_IMAGE013
, the shared xsect of liquid and gas the dimensionless area a ldwith a vd, the layering angle of circumference θ strat, dimensionless liquid is high h ldwith dimensionless gas-liquid two-phase interphase girth p id, as shown in Figure 3, in figure, 1 is gas, 2 is liquid.Concrete calculating formula is as follows:
，
In formula, ρ vwith ρ lbe respectively the density of gaseous state and liquid refrigerant; gfor acceleration of gravity; σfor the working medium surface tension.
Figure 661457DEST_PATH_IMAGE015
，
In formula, across-sectional area for interior conduit in evaporator;
Figure 899278DEST_PATH_IMAGE016
，
Figure 399529DEST_PATH_IMAGE017
，
Figure 85726DEST_PATH_IMAGE018
，
Figure 355033DEST_PATH_IMAGE019
。
Step 2: the transition value of the calculation of parameter " I – A " of trying to achieve according to hot working fluid physical parameter and step 1;
Figure 530799DEST_PATH_IMAGE020
，
In formula, μ lwith μ vbe respectively the dynamic viscosity coefficient of gaseous state and liquid refrigerant;
Step 3: the transition value of calculating " S – SW "
，
And work as x< x iAthe time, g strat= g strat( x iA);
Step 4: calculate transition value g wavy
Figure 244120DEST_PATH_IMAGE022
，
In formula, the Wei Bo number
Figure 633513DEST_PATH_IMAGE023
, Froude number .
(a) in interval x< x iA, when g wavy? g? g wavy( x iA) time, this zone is slug flow;
(b) in interval x< x iA, when g wavy( x iA) g? g strat( x iA) time, this zone is slug flow/wavy stratified flow;
(c) in interval x? x iA, when g wavy? g? g stratthe time, this zone is wavy stratified flow.
Step 5: according to working as the density of geothermal heat flow parameter q, the transition value of calculating " A – D ".
Figure 127128DEST_PATH_IMAGE025
，
In formula, core pond evaporation critical heat flux density , h lVfor evaporation latent heat.
When g strat( x i )>= g dryout( x i ) time, g dryout( x i )= g strat( x i );
When g wavy( x i )>= g dryout( x i ) time, g wavy( x i )= g dryout( x i ).
Step 6: the transition value of calculating " D – M ".
，
When g dryout( x i )>= g mist( x i ) time, g dryout( x i )= g mist( x i ).
By constantly increasing progressively the gaseous mass mark x, follow above-mentioned calculation procedure, finally can draw out the two-phase evaporation flow regime map under specified criteria, as shown in Figure 4.
Step 7: according to the mass velocity under concrete state gwith each flow pattern transition value be known two-phase now evaporation flow pattern.
2) evaporator Heat transfer of gas-liquid two-phase coefficient determines
The calculating formula difference of the two-phase evaporation heat transfer coefficient of different flow patterns, concrete condition is as follows:
If a) flow pattern is mist flow, its convective heat-transfer coefficient
Figure 495026DEST_PATH_IMAGE028
，
In formula, re hfor the homogeneous phase Reynolds number; pr vfor the gas phase Prandtl number; yfor composite factor; λ vfor the gas phase coefficient of heat conductivity.Its concrete calculating formula is
Figure 394848DEST_PATH_IMAGE029
，
Figure 23276DEST_PATH_IMAGE030
，
In formula, c pv specific heat capacity at constant pressure for the working medium gaseous state.
Figure 685464DEST_PATH_IMAGE031
；
B) if, when flow pattern is intermittent flow, annular flow, stratified flow, slug flow, slug flow/wavy stratified flow and wavy stratified flow, the computation process of its convective heat-transfer coefficient is as follows:
Step 1: calculate dry angle of circumference θ dry.
I) if flow pattern is intermittent flow, annular flow and slug flow, dry angle of circumference equals zero;
If ii) flow pattern is stratified flow, dry angle of circumference θ dry= θ strat;
If iii) flow pattern is wavy stratified flow, dry angle of circumference
；
If iv) flow pattern is slug flow/wavy stratified flow, dry angle of circumference
。
Step 2: calculate thickness of liquid film δ.
If δ? d/ 2, δ= d/ 2.
Step 3: calculate gas semiconvection heat transfer coefficient, its calculating formula is
Figure 706936DEST_PATH_IMAGE035
In formula, the gas phase Reynolds number
Figure 566307DEST_PATH_IMAGE036
.
Step 4: calculate liquid semiconvection heat transfer coefficient, its calculating formula is
Figure 175143DEST_PATH_IMAGE037
，
Wherein, h cbwith h nbcalculating formula be respectively
Figure 145373DEST_PATH_IMAGE038
，
In formula, Renault number of liquid membrane
Figure 218372DEST_PATH_IMAGE039
; Liquid Prandtl number
Figure 186328DEST_PATH_IMAGE040
; λ lfor the liquid phase coefficient of heat conductivity.
Figure 846241DEST_PATH_IMAGE041
，
In formula, pressure drop
Figure 620162DEST_PATH_IMAGE042
; mfor the working medium molal weight.
Step 5: calculate total convective heat-transfer coefficient, its calculating formula is
。
C) if flow pattern is dry stream, its convective heat-transfer coefficient
Figure 952103DEST_PATH_IMAGE044
Wherein, x diwith x debe respectively dry starting point and end point, its calculating formula is
Figure 847564DEST_PATH_IMAGE046
In certain mass speed gunder, by constantly increasing progressively the gaseous mass mark x, follow above-mentioned calculation procedure, finally can calculate the two-phase evaporation heat transfer coefficient under specified criteria, as shown in Figure 5.
3) duct length determines
According to above-mentioned calculating gained two-phase evaporation convection heat transfer coefficient hwith supposition the idivide segment pipe length l i can calculate idivide the relative error of the unit interval heat transfer capacity of section, its calculating formula is
Figure 399549DEST_PATH_IMAGE047
In formula,
Figure 771625DEST_PATH_IMAGE048
with
Figure 639087DEST_PATH_IMAGE049
be respectively the medial temperature of i division section heat source fluid and working medium;
Figure 692493DEST_PATH_IMAGE050
with
Figure 594590DEST_PATH_IMAGE051
be respectively idivide the specific enthalpy of section working medium entrance and exit place working medium.
If Δ i 1%, change idivide the pipe range of section l i , the double counting Δ i ; If Δ i ≤ 1%, l i be idivide the pipe range of section.
The total pipeline length gauge formula of evaporator two-phase region is
，
In formula, nfor the duct segments research number under evaporator two-phase flow state.
, duct length determines during the heat exchange of condenser biphase gas and liquid flow
1) drafting of condenser flow pattern of gas-liquid two-phase flow figure and flow pattern determines
Two-phase condensation flow pattern is divided into to stratified flow (stratified flow, S), wavy stratified flow (stratified-wavy flow, SW), annular flow (annular flow, A), intermittent flow (intermittent flow, I), mist flow (mist flow, M) and six kinds of bubble flows (bubbly flow, B).The concrete drawing process of its flow regime map is as follows:
Step 1: according to round tube inside diameter d, the working medium mass velocity gand condensing temperature t condunder the hot working fluid physical parameter, calculate homogeneous phase gas space mark
Figure 197052DEST_PATH_IMAGE053
, Rouhani-Axelsson gas space mark
Figure 913204DEST_PATH_IMAGE054
, logarithmic mean gas space coefficient
Figure 935387DEST_PATH_IMAGE013
, liquid dimensionless cross-sectional area a ld, gaseous state dimensionless cross-sectional area a vd, the layering angle of circumference θ strat, dimensionless liquid is high h ldwith dimensionless interphase girth p id.Its concrete calculating formula is as follows:
Figure 586948DEST_PATH_IMAGE055
Figure 927537DEST_PATH_IMAGE056
Figure 385063DEST_PATH_IMAGE057
Figure 199436DEST_PATH_IMAGE015
Figure 84215DEST_PATH_IMAGE016
Figure 413565DEST_PATH_IMAGE017
Figure 845126DEST_PATH_IMAGE019
Step 2: according to the transition value of the calculation of parameter " S – SW " of calculating in the thermal physical property parameter of working medium and step 1.
Figure 900807DEST_PATH_IMAGE058
Step 3: the transition value of calculating " SW – I " and " SW – A ".
Figure 655136DEST_PATH_IMAGE059
When x? x wavyminthe time, g wavy= g wavy( x wavymin), wherein x wavyminfor g wavyget minimum value in interval (0,1) g wavy( x wavymin) time local gaseous mass mark.
Step 4: the transition value of calculating " I – A ".
Figure 720044DEST_PATH_IMAGE060
Step 5: the transition value of calculating " I – M " and " A – M ".
Figure 305746DEST_PATH_IMAGE061
In formula, .
When x? x mistminthe time, g mist= g mist( x mistmin), wherein x mistminfor g wavyget minimum value in interval (0,1) g wavy( x mistmin) time local gaseous mass mark.
Step 6: the transition value of calculating " M – B ".
。
Follow above-mentioned calculation procedure, finally can draw out the two-phase condensation flow regime map under specified criteria, as shown in Figure 6.The reason that does not occur bubble flow in figure is that this flow pattern only appears under high-quality speed, higher than illustrated mass velocity scope.
According to the mass velocity under concrete situation gcan determine two-phase condensation flow pattern now with each flow pattern transition value.
2) condenser Heat transfer of gas-liquid two-phase coefficient determines
The calculating formula difference of the two-phase condensation convective heat-transfer coefficient of different flow patterns, its concrete calculation procedure is as follows:
Step 1: the dry angle of calculating different two-phase condensation flow patterns.
If a) annular flow, intermittent flow and mist flow, dry angle of circumference θ drybe zero, the inside surface roughness modifying factor f i calculating formula be
Figure 869649DEST_PATH_IMAGE064
；
B) if wavy stratified flow, layering angle of circumference θ strat, dry angle of circumference θ drywith the inside surface roughness modifying factor f icalculating formula be respectively
Figure 972920DEST_PATH_IMAGE065
Figure 436262DEST_PATH_IMAGE066
；
C) if stratified flow, dry angle of circumference θ dryequal the layering angle of circumference θ strat.
Step 2: calculate the convection current condensation coefficient h c.
Figure 344438DEST_PATH_IMAGE067
In formula, liquid Reynolds number
Figure 639153DEST_PATH_IMAGE068
.
Step 3: calculate pipe top membrane type condensation coefficient h f.
Figure 410800DEST_PATH_IMAGE069
Step 4: calculate total condensation convective heat-transfer coefficient h tp.
Figure 423755DEST_PATH_IMAGE070
In formula, rfor the pipe inside radius.
Follow above-mentioned calculation procedure, finally can calculate the two-phase condensation coefficient under specified criteria, as shown in Figure 7.
3) duct length determines
According to above-mentioned calculating gained two-phase condensation convective heat-transfer coefficient h tpwith supposition the idivide segment pipe length l i can calculate idivide the relative error of the unit interval heat transfer capacity of section, its calculating formula is
Figure 368577DEST_PATH_IMAGE071
In formula, with
Figure 224462DEST_PATH_IMAGE073
be respectively the medial temperature that i divides section working medium and heat eliminating medium;
Figure 724713DEST_PATH_IMAGE050
with
Figure 473226DEST_PATH_IMAGE051
be respectively idivide the specific enthalpy of section sender property outlet and porch working medium.
If Δ i 1%, change idivide the pipe range of section l i , the double counting Δ i ; If Δ i ≤ 1%, l i be idivide the pipe range of section.
The duct length calculating formula of condenser two-phase region is
Figure 680217DEST_PATH_IMAGE052
，
In formula, nfor the duct segments research number under condenser two-phase flow state.
According to above-mentioned calculation procedure, to the organic Rankine circulating evaporator that uses R600 and condenser tube progress row calculating.Result of calculation is based on following condition: 1) mass rate of heat source fluid and specific heat capacity at constant pressure are respectively 1kgs -1and 1kJkg -1k -1; 2) cooling water inlet temperature and cooling water side pressure are respectively 283.15K and 101.325kPa; 3) minimum temperature difference of evaporator and condenser diabatic process is respectively 10K and 1K; 4) evaporating temperature, condensing temperature and environment temperature are respectively 333.15K, 293.15K and 288.15K; 5) evaporator and condenser round tube inside diameter are 20mm, wall thickness 2.5mm.
1) splitting scheme of evaporator liquid segment is: divide equally by worker quality liquid section temperature, and divide the number of segment=round (evaporating temperature-working medium evaporator temperature)+1.Each result of calculation of dividing the segment pipe range is as shown in table 1.In table, data show, the relative error that the evaporator liquid segment of application the inventive method calculating gained is divided the segment pipe range is less, and maximal value is only 0.987%, and average relative error is 0.445%.
2) splitting scheme of evaporator and condenser Gas-liquid phase region is: divide equally the number of division segment=100 by the Working medium gas massfraction.Each result of calculation of dividing the segment pipe range is as shown in table 2 and table 3.In table, data show, the evaporator of application the inventive method calculating gained and the relative error of condenser gas-liquid two-phase Division segment pipe range are all less, and maximal value is respectively 0.999% and 0.938%, and average relative error is respectively 0.563% and 0.471%.
3) splitting scheme of condenser gas section is: divide equally by Working medium gas section temperature, and divide the number of segment=round (working medium condenser inlet temperature-condensing temperature)+1.Each result of calculation of dividing the segment pipe range is as shown in table 4.In table, data show, the relative error that the condenser gas section of application the inventive method calculating gained is divided the segment pipe range is less, and maximal value is only 0.938%, and average relative error is 0.337%.
Table 1
Table 2
Figure 569304DEST_PATH_IMAGE079
Table 3
Figure 958697DEST_PATH_IMAGE081
Table 4.

Claims (3)

1. an organic Rankine circulation heat exchanger duct length Optimization Design of considering flow pattern, it is characterized in that: in organic Rankine cycle heat exchange process, when organic working medium is the two-phase flow state, at first suppose that working medium evaporation or condensation divide the pipe range of segment, then according to evaporation or condensing temperature, round tube inside diameter d, the working medium mass velocity g, the heat flow density of dividing segment qwith the average gas massfraction xdetermine the residing evaporation of this division segment or condensation two-phase flow pattern, and then choose convective heat-transfer coefficient calculating formula under corresponding flow pattern to obtain the convective heat-transfer coefficient of this division segment, the heat exchange amount of last this section of division segment length calculation according to this convective heat-transfer coefficient value and supposition, and compare with actual heat exchange amount, if not identical, change and divide segment pipe range value, until its relative error is less than or equal to 1%; The pipe range of every division segment under certain cycle characteristics parameter can be determined in this way, and then the duct length of whole evaporator and condenser can be obtained; In evaporator and condenser, working medium, when the single-phase flow state, selects the Gnielinski formula to calculate its convective heat-transfer coefficient, comprises the following steps:
Step 1: according to the working medium kinetic viscosity under working medium and heat source fluid medial temperature μ, specific heat capacity at constant pressure c p and coefficient of heat conductivity kcalculate the Prandtl number of working medium at these two kinds of temperature pr, only need calculate the Prandtl number of dividing under section working medium medial temperature for gas, wherein the Prandtl number calculating formula is
Figure 576914DEST_PATH_IMAGE001
；
Step 2: according to the density under the working medium medial temperature ρ, kinematic viscosity υmass rate with working medium
Figure 906264DEST_PATH_IMAGE002
, the flow velocity of calculating working medium uand Reynolds number re, its concrete calculating formula is respectively
Figure 668946DEST_PATH_IMAGE003
，
Figure 72245DEST_PATH_IMAGE004
；
Step 3: according to the Gnielinski formula, calculate nusselt number nu, its concrete calculating formula is
Figure 393505DEST_PATH_IMAGE005
，
To liquid
，
Figure 9480DEST_PATH_IMAGE007
，
To gas
，
Figure 523562DEST_PATH_IMAGE009
，
In formula, lfor pipe range; ffor the mobile Darcy resistance coefficient of intraductal turbulance, press the Filonenko formula
Figure 561925DEST_PATH_IMAGE010
calculate.
2. a kind of organic Rankine circulation heat exchanger duct length Optimization Design of considering flow pattern according to claim 1, it is characterized in that: in evaporator, working medium is when biphase gas and liquid flow, calculate the coefficient of heat transfer of pipeline according to the convective heat-transfer coefficient calculating formula based on two-phase evaporation flow pattern, comprise the following steps:
Step 1: according to evaporating temperature t evap, round tube inside diameter d, the working medium mass velocity gand gaseous mass mark xcalculate the ratio of xsect gas area occupied
Figure 164945DEST_PATH_IMAGE011
, the shared xsect of liquid and gas the dimensionless area a ldwith a vd, the layering angle of circumference θ strat, dimensionless liquid is high h ldwith dimensionless gas-liquid two-phase interphase girth p id;
Concrete calculating formula is as follows:
Figure 870732DEST_PATH_IMAGE012
，
In formula, ρ vwith ρ lbe respectively the density of gaseous state and liquid refrigerant; gfor acceleration of gravity; σfor the working medium surface tension;
Figure 205899DEST_PATH_IMAGE013
，
In formula, across-sectional area for interior conduit in evaporator;
，
Figure 639734DEST_PATH_IMAGE015
，
Figure 200028DEST_PATH_IMAGE016
，
Figure 706096DEST_PATH_IMAGE017
Step 2: the transition value of the calculation of parameter of trying to achieve according to hot working fluid physical parameter and step 1 " have a rest stream – annular flow ";
Figure 984630DEST_PATH_IMAGE018
，
In formula, μ lwith μ vbe respectively the dynamic viscosity coefficient of gaseous state and liquid refrigerant;
Step 3: the transition value of calculating " Fen Ceng Liu – wavy stratified flow ";
Figure 433847DEST_PATH_IMAGE019
，
And work as x< x iAthe time, g strat= g strat( x iA);
Step 4: calculate transition value g wavy;
Figure 848648DEST_PATH_IMAGE020
，
In formula, the Wei Bo number
Figure 853513DEST_PATH_IMAGE021
, Froude number
(a) in interval x< x iA, when g wavy? g? g wavy( x iA) time, this zone is slug flow;
(b) in interval x< x iA, when g wavy( x iA) g? g strat( x iA) time, this zone is slug flow/wavy stratified flow;
(c) in interval x? x iA, when g wavy? g? g stratthe time, this zone is wavy stratified flow;
Step 5: according to working as the density of geothermal heat flow parameter q, calculate the transition value of " Huan Zhuan Liu – is dry to flow ";
Figure 774381DEST_PATH_IMAGE023
，
In formula, core pond evaporation critical heat flux density
Figure 810733DEST_PATH_IMAGE024
, h lVfor evaporation latent heat;
When g strat( x i )>= g dryout( x i ) time, g dryout( x i )= g strat( x i );
When g wavy( x i )>= g dryout( x i ) time, g wavy( x i )= g dryout( x i );
Step 6: the transition value of calculating " dry Liu – mist flow " (" D – M ");
Figure 720920DEST_PATH_IMAGE025
，
When g dryout( x i )>= g mist( x i ) time, g dryout( x i )= g mist( x i );
Step 7: according to mass velocity gjudge the now residing two-phase evaporation of working medium flow pattern with the transition value of each flow pattern;
Step 8: choose corresponding convection heat transfer' heat-transfer by convection calculating formula according to evaporation flow pattern of living in and carry out the calculating of the coefficient of heat transfer, concrete condition is as follows:
(1) if flow pattern is mist flow, its convective heat-transfer coefficient
Figure 708468DEST_PATH_IMAGE026
，
In formula, re hfor the homogeneous phase Reynolds number; pr vfor the gas phase Prandtl number; yfor composite factor; λ vfor the gas phase coefficient of heat conductivity; Its concrete calculating formula is
，
Figure 322169DEST_PATH_IMAGE028
，
In formula, c pv specific heat capacity at constant pressure for the working medium gaseous state;
Figure 167371DEST_PATH_IMAGE029
；
(2) if, when flow pattern is intermittent flow, annular flow, stratified flow, slug flow, slug flow/wavy stratified flow and wavy stratified flow, the computation process of its convective heat-transfer coefficient is as follows:
A) calculate dry angle of circumference θ dry;
I) if flow pattern is intermittent flow, annular flow and slug flow, dry angle of circumference equals zero;
If ii) flow pattern is stratified flow, dry angle of circumference θ dry= θ strat;
If iii) flow pattern is wavy stratified flow, dry angle of circumference
Figure 642215DEST_PATH_IMAGE030
；
If iv) flow pattern is slug flow/wavy stratified flow, dry angle of circumference
Figure 466952DEST_PATH_IMAGE031
；
B) calculate thickness of liquid film δ
Figure 710851DEST_PATH_IMAGE032
If δ? d/ 2, δ= d/ 2;
C) calculate gas semiconvection heat transfer coefficient, its calculating formula is
Figure 729885DEST_PATH_IMAGE033
In formula, the gas phase Reynolds number
Figure 692025DEST_PATH_IMAGE034
;
D) calculate liquid semiconvection heat transfer coefficient, its calculating formula is
Figure 320452DEST_PATH_IMAGE035
，
Wherein, h cbwith h nbcalculating formula be respectively
Figure 356541DEST_PATH_IMAGE036
，
In formula, Renault number of liquid membrane
Figure 623442DEST_PATH_IMAGE037
; Liquid Prandtl number
Figure 72878DEST_PATH_IMAGE038
; λ lfor the liquid phase coefficient of heat conductivity;
Figure 239417DEST_PATH_IMAGE039
，
In formula, pressure drop
Figure 457909DEST_PATH_IMAGE040
; mfor the working medium molal weight;
E) calculate total convective heat-transfer coefficient, its calculating formula is
Figure 881062DEST_PATH_IMAGE041
；
(3) if flow pattern is dry stream, its convective heat-transfer coefficient
Figure 614532DEST_PATH_IMAGE042
Wherein, x diwith x debe respectively dry starting point and end point, its calculating formula is
Figure 348876DEST_PATH_IMAGE043
Figure 421874DEST_PATH_IMAGE044
。
3. a kind of organic Rankine circulation heat exchanger duct length Optimization Design of considering flow pattern of stating according to claim 2, it is characterized in that: in condenser, working medium is when biphase gas and liquid flow, calculate the coefficient of heat transfer of pipeline according to the convective heat-transfer coefficient calculating formula based on two-phase condensation flow pattern, comprise the following steps:
Step 1: according to round tube inside diameter d, the working medium mass velocity gand condensing temperature t condunder the hot working fluid physical parameter, calculate homogeneous phase gas space mark
Figure 389830DEST_PATH_IMAGE045
, Rouhani-Axelsson gas space mark
Figure 548279DEST_PATH_IMAGE046
, logarithmic mean gas space coefficient , liquid dimensionless cross-sectional area a ld, gaseous state dimensionless cross-sectional area a vd, the layering angle of circumference θ strat, dimensionless liquid is high h ldwith dimensionless interphase girth p id; Its concrete calculating formula is as follows:
Figure 751170DEST_PATH_IMAGE047
Figure 952344DEST_PATH_IMAGE048
Figure 535772DEST_PATH_IMAGE049
Figure 895395DEST_PATH_IMAGE014
Figure 205154DEST_PATH_IMAGE015
Figure 842589DEST_PATH_IMAGE016
Step 2: according to the transition value of the calculation of parameter of calculating in the thermal physical property parameter of working medium and step 1 " a minute layer stream – wavy stratified flow ";
Figure 860410DEST_PATH_IMAGE050
Step 3: the transition value of calculating " Fen layer wave Liu – intermittent flow " (" SW – I ") and " Fen layer wave Liu – annular flow ";
When x? x wavyminthe time, g wavy= g wavy( x wavymin), wherein x wavyminfor g wavyget minimum value in interval (0,1) g wavy( x wavymin) time local gaseous mass mark;
Step 4: the transition value of calculating " Jian Xie Liu – annular flow " (" I – A ");
Figure 695828DEST_PATH_IMAGE052
Step 5: the transition value of calculating " Jian Xie Liu – mist flow " (" I – M ") and " Huan Zhuan Liu – mist flow " (" A – M ");
Figure 116707DEST_PATH_IMAGE053
In formula,
Figure 873310DEST_PATH_IMAGE054
;
When x? x mistminthe time, g mist= g mist( x mistmin), wherein x mistminfor g wavyget minimum value in interval (0,1) g wavy( x mistmin) time local gaseous mass mark;
Step 6: the transition value of calculating " Wu Zhuan Liu – bubble flow " (" M – B ");
Figure 587188DEST_PATH_IMAGE055
；
Step 7: according to mass velocity gcan determine the now residing two-phase condensation of working medium flow pattern with the transition value of each flow pattern;
Step 8: choose corresponding convection heat transfer' heat-transfer by convection calculating formula according to condensation flow pattern of living in and carry out the calculating of the coefficient of heat transfer, detailed process is as follows:
(1) calculate the dry angle of different two-phase condensation flow patterns;
If a) annular flow, intermittent flow and mist flow, dry angle of circumference θ drybe zero, the inside surface roughness modifying factor f i calculating formula be
；
B) if wavy stratified flow, layering angle of circumference θ strat, dry angle of circumference θ drywith the inside surface roughness modifying factor f icalculating formula be respectively
Figure 261993DEST_PATH_IMAGE057
Figure 350035DEST_PATH_IMAGE058
；
C) if stratified flow, dry angle of circumference θ dryequal the layering angle of circumference θ strat
(2) calculate the convection current condensation coefficient h c
Figure 679385DEST_PATH_IMAGE059
In formula, liquid Reynolds number
Figure 675023DEST_PATH_IMAGE060
;
(3) calculate pipe top membrane type condensation coefficient h f
Figure 907683DEST_PATH_IMAGE061
Wherein, qthe pipe range of value based on supposition;
(4) calculate total condensation convective heat-transfer coefficient h tp
Figure 166626DEST_PATH_IMAGE062
In formula, rfor the pipe inside radius.
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CN106126803B (en) * 2016-06-20 2019-01-11 珠海格力电器股份有限公司 Refrigeration system analogy method and device
CN106404829A (en) * 2016-08-31 2017-02-15 上海交通大学 CHF measuring method based on heat flux correction
CN106404829B (en) * 2016-08-31 2019-06-21 上海交通大学 Based on the modified CHF measurement method of hot-fluid
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CN108956692A (en) * 2018-08-29 2018-12-07 仲恺农业工程学院 Mass dryness fraction transition formula evaporator performance calculation method and its dryness measurement device
CN108956692B (en) * 2018-08-29 2023-06-30 仲恺农业工程学院 Dryness jump type evaporator thermodynamic performance calculation method and dryness measurement device thereof
CN109376447A (en) * 2018-11-08 2019-02-22 湖南科技大学 Extract the surface air cooler optical tube length calculation method of super long tunnel percolating water cooling capacity
CN109446692A (en) * 2018-11-08 2019-03-08 湖南科技大学 Extract water flow velocity optimization method in the surface air cooler light pipe of super long tunnel percolating water cooling capacity
CN109668750A (en) * 2019-01-06 2019-04-23 东北电力大学 A kind of passage aisle heat exchange equipment heat transfer deterioration prediction technique in parallel based on pressure drop signal analysis
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