CN107131073B - A kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method - Google Patents

A kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method Download PDF

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CN107131073B
CN107131073B CN201710343087.6A CN201710343087A CN107131073B CN 107131073 B CN107131073 B CN 107131073B CN 201710343087 A CN201710343087 A CN 201710343087A CN 107131073 B CN107131073 B CN 107131073B
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formula
heating tube
heat
pipe
working medium
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CN107131073A (en
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刘繁茂
张磊
蒋彭
罗芳芝
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Hunan University of Science and Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02G—HOT GAS OR COMBUSTION-PRODUCT POSITIVE-DISPLACEMENT ENGINE PLANTS; USE OF WASTE HEAT OF COMBUSTION ENGINES; NOT OTHERWISE PROVIDED FOR
    • F02G1/00—Hot gas positive-displacement engine plants
    • F02G1/04—Hot gas positive-displacement engine plants of closed-cycle type
    • F02G1/043—Hot gas positive-displacement engine plants of closed-cycle type the engine being operated by expansion and contraction of a mass of working gas which is heated and cooled in one of a plurality of constantly communicating expansible chambers, e.g. Stirling cycle type engines
    • F02G1/053—Component parts or details
    • F02G1/055—Heaters or coolers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F03—MACHINES OR ENGINES FOR LIQUIDS; WIND, SPRING, OR WEIGHT MOTORS; PRODUCING MECHANICAL POWER OR A REACTIVE PROPULSIVE THRUST, NOT OTHERWISE PROVIDED FOR
    • F03G—SPRING, WEIGHT, INERTIA OR LIKE MOTORS; MECHANICAL-POWER PRODUCING DEVICES OR MECHANISMS, NOT OTHERWISE PROVIDED FOR OR USING ENERGY SOURCES NOT OTHERWISE PROVIDED FOR
    • F03G6/00—Devices for producing mechanical power from solar energy
    • F03G6/06—Devices for producing mechanical power from solar energy with solar energy concentrating means
    • F03G6/068—Devices for producing mechanical power from solar energy with solar energy concentrating means having other power cycles, e.g. Stirling or transcritical, supercritical cycles; combined with other power sources, e.g. wind, gas or nuclear
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02G—HOT GAS OR COMBUSTION-PRODUCT POSITIVE-DISPLACEMENT ENGINE PLANTS; USE OF WASTE HEAT OF COMBUSTION ENGINES; NOT OTHERWISE PROVIDED FOR
    • F02G2254/00—Heat inputs
    • F02G2254/30—Heat inputs using solar radiation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/40—Solar thermal energy, e.g. solar towers
    • Y02E10/46—Conversion of thermal power into mechanical power, e.g. Rankine, Stirling or solar thermal engines

Abstract

The invention discloses a kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design methods, include the following steps: the calculating for 1) determining Stirling thermal engine operating main design parameters；2) calculating of the pipe number, pipe range of heat dump heating tube；3) spatial position and shape of the heating tube of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump are designed.The present invention provides a set of practical calculation method for the design of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump, tube bundle formula heat dump heating tube pipe number and length calculation based on basic input heat and the Best Size Ratio can be provided from Stirling thermal engine operating main design parameters；The tube bundle formula heat dump high reliablity that the present invention designs, maintenanceability is good, and can guarantee that the heat exchange amount of heating tube bundle can satisfy design requirement.

Description

A kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method
Technical field
The invention belongs to solar energy Stirling heat engine heat dump technical fields, are specifically related to a kind of this spy of disc type solar energy Woods heat engine tube bundle formula heat dump design method.
Background technique
The heat exchanger assemblies performance of disc type solar energy Stirling thermal engine operating is the key that guarantee overall performance.As optical and thermal The interface of energy conversion, heat dump performance are to reflect one of the determinant of heat exchanger assemblies performance.With the suction of other purposes Hot device is compared, and the technical requirements of solar light-heat power-generation heat dump are higher, is mainly reflected in solar light-heat power-generation heat absorption The heat flow density that device is born is bigger, and heat flux distribution is more uneven, and Reliability And Maintainability requires more stringent.Due to too The coefficient of heat transfer of sunlight and heating tube outer surface is lower, and in order to ensure reaching certain heat exchange amount, the external surface area of heating tube is answered It is larger as far as possible.Therefore, solar energy Stirling tubular type heat dump mostly uses greatly the heating tube being made of many small-bore heating tubes Cluster.The performance for guaranteeing heating tube bundle is the common-denominator target of solar energy Stirling tubular type heat dump design.It is current and not formed complete Heat dump design method, therefore there is an urgent need to a kind of complete disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design sides Method instructs the design of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump.
Summary of the invention
In order to solve the above technical problem, the present invention provides a kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dumps to set Meter method, the tube bundle formula heat dump reliability with higher which designs, preferable maintenanceability, and can guarantee The heat exchange amount of heating tube bundle can satisfy design requirement.
The technical solution adopted by the present invention is that: a kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method, Include the following steps:
1) according to the effective power P of Stirling thermal engine operating0, averaging loop pressure Pm, revolving speed n, working medium power conversion coefficient ζ, tiltedly Disk inclination angle theta, hot chamber temperature TE, cold chamber temperature TC, calculate Stirling thermal engine operating Bill number Bn, cylinder bore DCY, hot chamber volume VE, cold Chamber volume VC；
2) calculating of the pipe number, pipe range of heat dump heating tube；
2.1) first by hot chamber volume VE, cold chamber volume VCCalculate Stirling engine cycle function WCE, then calculate and consider heat Total hot Q of input substantially after lossH；
2.2) according to Average mass flow rate mHWith unit flow area working medium flow GH, calculate heat dump and heat intraductal working medium The reynolds number Re in flow fieldHWith nusselt number NuH, and then convection transfer rate h is calculatedH；
2.3) according to thermal conduction study fundamental relation or the caloric receptivity Q ' of single heat pipeHCalculation formula, and obtain total basic Input hot QHPass through the caloric receptivity Q ' of single heat pipeHWith heating tube number NHAnother calculation formula of expression, then obtained with step 2.1) Total hot Q of input substantiallyHFormula simultaneous, heating tube pipe number N can be obtainedHWith pipe range lH；
3) spatial position and shape of the heating tube of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump are designed.
In above-mentioned disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method, in step 1), by formulaCalculate Stirling thermal engine operating Bill number Bn；By formula:It is straight to calculate cylinder Diameter DCY；In formula: νpmFor piston slip speed, Z is Stirling thermal engine operating cylinder body number,For the power conversion factor of working medium, ω For the cycle frequency of Stirling thermal engine operating；By formula:Hot chamber instantaneous volumetric is calculated, by public affairs Formula:Cold chamber instantaneous volumetric is calculated, maximum is taken to hot chamber instantaneous volumetric and cold chamber instantaneous volumetric Value obtains hot chamber volume VEWith cold chamber volume VC；In formula: α is swash plate angle of eccentricity, and R is swash plate reference radius.
In above-mentioned disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method, in step 2.1), according to formulaThe circulation function for calculating Stirling thermal engine operating, in formula:τ is temperature ratio, τ=chiller temperature TK/ heter temperature TH；κ be swept volume ratio, κ= Cold chamber range volume VC/ hot chamber range volume VE；For the phase-lead angle of the circulatory system；β is angle variables,
By formula:Calculate total base after considering heat loss The hot Q of this inputH。
In above-mentioned disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method, in step 2.2), by formula:Calculate Average mass flow rate mH；In formula: MfhmaxFor the maximum ratio of hot-zone working medium Amount；MfhminFor the minimum scale amount of hot-zone working medium；M is the mole of hot-zone working medium；MWFor the molal weight of working medium；FhtFor working medium Flowing time ratio；
By formula:Unit of account flow area working medium flow GH, in formula: mHFor heating tube Average mass flow rate； AHFor heating tube flow area, AH=NH·dH 2π/4, NHFor the heating tube pipe number of heat dump；dHFor the internal diameter of heating tube；
By formula:Calculate reynolds number ReH, in formula: RHHFor the hydraulic radius of heating tube, RHH= 0.5dH；GHFor the working medium flow of heating tube unit flow area；uGHFor the dynamic viscosity of working medium in heating tube；
By formula:Calculate the nusselt number of intraductal working medium； In formula: fHFor the Darcy resistance coefficient of heating tube intraductal turbulance flowing, expression formula are as follows: fH=(1.82lgReH-1.64)-2； PrHFor the Prandtl number for heating intraductal working medium；lHFor the length of heating tube；CtHFor Ge Nilinsiji formula correction factor, CtH= (TH/THW)0.45, wherein TH/THW=0.5~1.5, THWFor heat pipe outer wall temperature, CtH=0.965, THFor heter temperature.
In above-mentioned disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method, in step 2.3), every heat pipe Absorb heat Q 'HAre as follows: Q 'H=QH/NH, and the caloric receptivity of single heating tube may be expressed as: Q ' according to thermal conduction study relational expressionH=π dH·lH·hH·(THW-TH)；Heating tube pipe number N can be obtainedHWith pipe range lHCalculation formula:
Then heating tube pipe number N is calculatedHWith pipe range lH；
In formula: λ is the thermal coefficient of intraductal working medium, and η is efficiency of heat engine cycle, η=1-TC/TE；DopFor diameter of piston rod； SpFor piston range；THWFor heat pipe outer wall temperature；ΔQ'EFor the heat loss in power cycle system.
It further include heat dump in step 2 in above-mentioned disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method The optimization of pipe number, pipe range, concrete operations are as follows:
According to the Best Size Ratio formula of heating tube:It obtains and examines Consider the mathematical model of heating tube the heat exchange length and pipe number of flow resistance and period heat exchange loss and output power:
And Calculate pipe number, the pipe range of the heating tube of the Best Size Ratio；
In formula:Its In: FCrFor regenerator volumetric flow rate correction factor, FCkFor cooler volumetric flow rate correction factor, NKFor cooling tube pipe number, NHFor Heat dump heating tube number, uGHFor the dynamic viscosity of helium, FCkFor cooler volumetric flow rate correction factor, E3、E4For intermediate variable； fβH、fγH、fδHFor correction factor, in which: fβH=-356 βH+ 100, fγH=0.01 γH -11, fδH=-75.7TH/TC+152；TH For heter temperature, TKFor chiller temperature；
Intermediate variableFormula In, For the phase-lead angle of the circulatory system；
Regenerator volumetric flow rate correction factor
In formula:
Cooler volumetric flow rate correction factor
In formula:
χkFor the unhelpful volumetric ratio of cooler, χRFor the unhelpful volumetric ratio of regenerator；
Intermediate variable
In formula: γ is the specific heat ratio of helium, γ=1.66；PrkFor the Prandtl number of the water in cooler.
Compared with prior art, the beneficial effects of the present invention are: the present invention is disc type solar energy Stirling thermal engine operating tube bundle formula Heat dump design provides a set of practical calculation method, can provide and be based on from Stirling thermal engine operating main design parameters The tube bundle formula heat dump heating tube pipe number and length calculation of basic input heat and the Best Size Ratio；The tube bundle formula that the present invention designs Heat dump high reliablity, maintenanceability is good, and can guarantee that the heat exchange amount of heating tube bundle can satisfy design requirement.
Detailed description of the invention
Fig. 1 is disc type solar energy Stirling thermal engine operating tube bundle formula heat dump pipe number of the present invention and length calculation flow chart.
Fig. 2 is disc type solar energy Stirling thermal engine operating tube bundle formula heat dump heating tube hub line curve graph.
Fig. 3 is projection of the disc type solar energy Stirling thermal engine operating tube bundle formula heat dump heating tube hub line curve in axial plane Figure.
Fig. 4 is projection of the disc type solar energy Stirling thermal engine operating tube bundle formula heat dump heating tube hub line curve in sagittal plane Figure.
Fig. 5 is 1KW disc type solar energy Stirling thermal engine operating tube bundle formula heat dump threedimensional model.
Specific embodiment
Present invention will be explained in further detail with example with reference to the accompanying drawing.
As shown in Figure 1, the present invention the following steps are included:
1) calculating of Stirling thermal engine operating main design parameters is determined.
Input effective power P0, averaging loop pressure Pm, revolving speed n, working medium power conversion coefficient ζ, swashplate angle θ, hot chamber temperature Spend TE, cold chamber temperature TCEtc. known parameters, heat engine Bill's number calculation formula bePiston cylinder diameter calculation is public Formula isIn formula: νpmFor piston slip speed, Z is Stirling thermal engine operating cylinder body number, For the power conversion factor of working medium, ω is the cycle frequency of Stirling thermal engine operating；By formula: Hot chamber instantaneous volumetric is calculated, by formula:Cold chamber instantaneous volumetric is calculated, hot chamber is instantaneously held Long-pending and cold chamber instantaneous volumetric is maximized to obtain hot chamber volume VEWith cold chamber volume VC；In formula: α is swash plate angle of eccentricity, and R is oblique Disk reference radius.
2) calculating, optimization of the pipe number, pipe range of heat dump heating tube.
2.1) calculating of basic input heat.
The circulation function of Stirling thermal engine operating is calculated firstFormula Inτ is temperature ratio, τ=chiller temperature TK/ heter temperature TH；κ is swept volume ratio, κ =cold chamber range volume VC/ hot chamber range volume VE；For the phase-lead angle of the circulatory system；β is angle variables,
Obtain total basic input heat are as follows:And calculate consideration Total after heat loss inputs hot Q substantiallyH。
2.2) calculating of convection transfer rate.
Calculate Average mass flow rateIn formula: MfhmaxMost for hot-zone working medium Large scale amount；MfhminFor the minimum scale amount of hot-zone working medium；M is the mole of hot-zone working medium；MWFor mole weight of working medium, helium For 4g/mol；ω is the cycle frequency of Stirling thermal engine operating；FhtFor the flowing time ratio of working medium.
The working medium flow of heating tube unit flow areaIn formula: mHFor heating tube Average mass flow rate；AHFor Heating tube flow area, AH=NH·dH 2π/4, NHFor the heating tube number of heat dump.
Then the Reynolds number of intraductal working medium is calculated:In formula: RHHFor the hydraulic radius of heating tube, RHH =1/2dH；GHFor the working medium flow of heating tube unit flow area；uGHFor the dynamic viscosity of working medium in heating tube.
The nusselt number that heating intraductal working medium is calculated using Ge Nilinsiji formula, is obtained:In formula: NuHFor the nusselt number of intraductal working medium；fHFor heating tube The Darcy resistance coefficient of interior turbulent flow, expression formula are as follows: fH=(1.82lgReH-1.64)-2；ReHFor heating intraductal working medium Reynolds number；PrHFor the Prandtl number for heating intraductal working medium；dHFor the internal diameter of heating tube；lHFor the heat exchange length of heating tube；CtHFor Ge Nilinsiji formula correction factor, the C for gas working mediumtH=(TH/THW)0.45, wherein: TH/THW=0.5~1.5, THWFor Heat pipe outer wall temperature, CtH=0.965, THFor heter temperature.
2.3) heating tube pipe number NHWith pipe range lHCalculating.
Another expression formula of nusselt number is obtained according to thermal conduction study basic theories first:H in formulaH For the forced-convection heat transfer coefficient of intraductal working medium and heating tube wall, W/ (m2·K)；dHTo heat bore；λ is intraductal working medium Thermal coefficient.Assuming that it is Q ' that every heat pipe, which absorbs heat,H, then Q 'HIt is represented by Q 'H=QH/NH, and the caloric receptivity of single heat pipe It may be expressed as: Q ' according to thermal conduction study basic relational expressionH=π dH·lH·hH·(THW-TH)；Then final heating tube pipe number NHWith pipe Long lHCalculation formula can be written as: And calculate heating tube pipe number NHWith pipe range lH, in formula: λ is the thermal coefficient of intraductal working medium, and η is efficiency of heat engine cycle, η=1-TC/ TE；DopFor diameter of piston rod；SpFor piston range；THWFor heat pipe outer wall temperature；ΔQ'EFor the heat in power cycle system Loss.
2.4) pipe number, the pipe range optimization of the heating tube based on the Best Size Ratio.
According to heating tube the Best Size Ratio formula:Obtain consideration The mathematical model of heating tube heat exchange length and pipe number including flow resistance and period heat exchange loss and output power:
Formula In:Wherein: NKIt is cold But pipe pipe number, NHFor heat dump heating tube number, FCrFor regenerator volumetric flow rate correction factor, uGHFor the dynamic viscosity of helium, FCk For cooler volumetric flow rate correction factor, E3、E4For intermediate variable；fβH、fγH、fδHFor related correction factor, wherein fβH=-356 βH+ 100, fγH=0.01 γH -11, fδH=-75.7TH/TC+152；THFor heter temperature, TKFor chiller temperature.
About intermediate variable E3:
In formula, θ ' is intermediate variable, For the phase-lead angle of the circulatory system.
Regenerator volumetric flow rate correction factor
In formula:
Cooler volumetric flow rate correction factor
In formula:
χkFor the unhelpful volumetric ratio of cooler, χRFor the unhelpful volumetric ratio of regenerator.
Intermediate variable E4:
In formula: γ is the specific heat ratio of helium, γ=Cp/Cr=1.66；PrkFor the Prandtl number of the water in cooler；
3) design of disc type solar energy Stirling thermal engine operating heat dump heating tube spatial position.
Solar energy Stirling heat dump heating tube bundle is formed using inner tube is nested with outer tube, and spatial form is designed as rounding Taper type.The center line of one section of involute heating tube, the projection in xoz plane is as shown in Fig. 2, may be regarded as the rounding of deformation Frustum face, this ensure that it is equidistant involute cluster in the projection of xoy plane, as shown in Figure 3.
The position of hot four cylinder of chamber characterizes the bottom radius of circle r of circular cone0, sun focal spot radius characterizes heat dump opening radius For rf, heat pipe length characterizes heat dump height zf.Three parameter description heating tube hub line spatial position change rule are defined first Rule, k characterize bus slope, and ψ characterizes base radius r0~rfRadius of curvature variation in progressive formation, θ is fixed in cylindrical-coordinate system Angle change relationship of the starting point in basic circle circumferencial direction on justice center line.Wherein θiniIt is starting heating tube hub line in base The angle of round circumferential direction, then the definition of three parameters can be written as:
K=zf/(rf 2-r0 2)1/2
ψ (r)=((r/r0)2·(k2+1)-1)1/2
θ (r)=ψ-k-tan-1k+θini
The parametrization equation of involute heating tube bundle center line in cartesian coordinate system are as follows:
X (r)=rcos (θ (r))
Y (r)=rsin (θ (r))
Z (r)=k (r2-r0 2)1/2
Embodiment
1: known parameters effective power P0For 1Kw, PmFor 2MPa, revolving speed n is 500r/min, and working medium power conversion coefficient ζ is 0.34, swashplate angle θ are 20 °, hot chamber temperature TEIt is 700 degree, cold chamber temperature TCIt is 45 degree；B is calculatedn=0.168, DCY= 5.62cm VE=88.67cm3, VC=77.36cm3。
2: calculating Stirling engine cycle function W firstCE=2.676Kw inputs hot Q substantiallyE=4.048, calculate total base This input heat is QH=4.448kW；Mfhmax=0.3453, Mfhmin=0.1230, Fht=0.284, mH=1.545g/s, then be based on The heat dump pipe number of basic input heat, length calculation formula is available is
3: regenerator volumetric flow rate correction factor F being calculated firstCr=0.65, cooler volumetric flow rate correction factor FCk=0.717.Then four intermediate variables are calculated Finally obtain heat dump pipe number, length calculation based on the Best Size Ratio Formula are as follows: lH=0.162NH 0.8-2.0261；By two mathematical model simultaneous solutions, the length l of single heat pipe can be solvedHWith The total heat pipe number N of heat dumpH, due to containing low order unknown number in equation group, here by Matlab software for calculation solution low order side Journey group, pipe range lHEnable is x, pipe number NHEnabling is y, and obtained equation group is as follows:
Real solution x=0.31, y=28 after finally obtaining accurately, it can thus be appreciated that 1kW effective power Stirling thermal engine operating absorbs heat Heating tube pipe number N needed for deviceH=28, every heat pipe pipe range lH=31cm.
4: on the basis of the mathematical model of involute heat pipe center line, working out the MATLAB program of heat pipe center line, fortune Line program generates the curvilinear coordinate .IBL file of involute heat pipe center line, imports the three-dimensional mould that Proe/E establishes involute heat pipe Type.1kW Stirling thermal engine operating heat dump is easy to determine its base radius r0=50mm, opening radius rf=105mm, height zf= 85mm, the relevant parameter for having obtained involute heat pipe center line are as shown in table 1.
1 involute heat pipe center line relevant parameter of table

Claims (2)

1. a kind of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method, includes the following steps:
1) according to the effective power P of Stirling thermal engine operating0, averaging loop pressure Pm, revolving speed n, working medium power conversion coefficient ζ, swash plate inclines Angle θ, hot chamber temperature TE, cold chamber temperature TC, calculate Stirling thermal engine operating Bill number Bn, cylinder bore DCY, hot chamber volume VE, cold chamber appearance Product VC；
By formulaCalculate Stirling thermal engine operating Bill number Bn；By formula:Meter Calculate cylinder bore DCY；In formula: νpmFor piston slip speed, Z is Stirling thermal engine operating cylinder body number,It is converted for the power of working medium Coefficient, ω are the cycle frequency of Stirling thermal engine operating；By formula:Hot chamber instantaneous volumetric is calculated, By formula:Cold chamber instantaneous volumetric is calculated, hot chamber instantaneous volumetric and cold chamber instantaneous volumetric are taken Maximum value obtains hot chamber volume VEWith cold chamber volume VC；In formula: α is swash plate angle of eccentricity, and R is swash plate reference radius；
2) calculating of heat dump pipe number, pipe range:
2.1) first by hot chamber volume VE, cold chamber volume VCCalculate Stirling engine cycle function WCE, then calculate after considering heat loss Total hot Q of input substantiallyH；According to formulaCalculate Stirling heat The circulation function of machine, in formula:τ is temperature ratio, τ=chiller temperature TK/ heter temperature TH；κ For swept volume ratio, κ=cold chamber range volume VC/ hot chamber range volume VE；For the phase-lead of the circulatory system Angle；β is angle variables,
Obtain the formula of total basic input heat:And it calculates and examines Total hot Q of input substantially after considering heat lossH；
2.2) according to Average mass flow rate mHWith unit flow area working medium flow GH, calculate heat dump and heat intraductal working medium flow field Reynolds number ReHWith nusselt number NuH, and then convection transfer rate h is calculatedH；
By formula:Calculate Average mass flow rate mH；In formula: MfhmaxFor hot-zone working medium Maximum ratio amount；MfhminFor the minimum scale amount of hot-zone working medium；M is the mole of hot-zone working medium；MWFor mole weight of working medium Amount；FhtFor the flowing time ratio of working medium；
By formula:Unit of account flow area working medium flow GH, in formula: mHFor heating tube Average mass flow rate；AHFor Heating tube flow area, AH=NH·dH 2π/4, NHFor the heating tube pipe number of heat dump；dHFor the internal diameter of heating tube；
By formula:Calculate reynolds number ReH, in formula: RHHFor the hydraulic radius of heating tube, RHH=0.5dH；GHFor The working medium flow of heating tube unit flow area；uGHFor the dynamic viscosity of working medium in heating tube；
By formula:Calculate the nusselt number of intraductal working medium；In formula: fHFor the Darcy resistance coefficient of heating tube intraductal turbulance flowing, expression formula are as follows: fH=(1.82lgReH-1.64)-2；PrHTo add The Prandtl number of hot intraductal working medium；lHFor the length of heating tube；CtHFor Ge Nilinsiji formula correction factor, CtH=(TH/THW)0.45, Wherein TH/THW=0.5~1.5, THWFor heat pipe outer wall temperature, CtH=0.965, THFor heter temperature；
2.3) according to thermal conduction study fundamental relation or the caloric receptivity Q ' of single heat pipeHCalculation formula, and it is hot to obtain total basic input QHPass through the caloric receptivity Q ' of single heat pipeHWith heating tube number NHAnother calculation formula of expression, then obtain with step 2.1) total Substantially hot Q is inputtedHFormula simultaneous, heating tube pipe number N can be obtainedHWith pipe range lH；
Every heat pipe absorbs heat Q 'HAre as follows: Q 'H=QH/NH, and the caloric receptivity of single heating tube can be indicated according to thermal conduction study relational expression Are as follows: Q 'H=π dH·lH·hH·(THW-TH)；Heating tube pipe number N can be obtainedHWith pipe range lHCalculation formula:
Then heating tube pipe number N is calculatedHWith pipe range lH；
In formula: λ is the thermal coefficient of intraductal working medium, and η is efficiency of heat engine cycle, η=1-TC/TE；DopFor diameter of piston rod；SpFor Piston range；THWFor heat pipe outer wall temperature；ΔQ'EFor the heat loss in power cycle system；
3) spatial position and shape of the heating tube of disc type solar energy Stirling thermal engine operating tube bundle formula heat dump are designed.
2. disc type solar energy Stirling thermal engine operating tube bundle formula heat dump design method according to claim 1, also wrapped in step 2 The optimization of heat dump pipe number, pipe range is included, concrete operations are as follows:
According to the Best Size Ratio formula of heating tube:Obtain consideration stream The mathematical model of heating tube the heat exchange length and pipe number of resistance and period heat exchange loss and output power:
And calculate the pipe number N of the heating tube of the Best Size RatioHWith pipe range lH；
In formula:Wherein: FCrFor regenerator volumetric flow rate correction factor, FCkFor cooler volumetric flow rate correction factor, NKFor cooling tube pipe number, NHFor heat absorption Device heating tube number, uGHFor the dynamic viscosity of helium, FCkFor cooler volumetric flow rate correction factor, E3、E4For intermediate variable；fβH、 fγH、fδHFor correction factor, in which: fβH=-356 βH+ 100, fγH=0.01 γH -11, fδH=-75.7TH/TC+152；THFor Heter temperature, TKFor chiller temperature；
Intermediate variableIn formula, For the phase-lead angle of the circulatory system；
Regenerator volumetric flow rate correction factor
In formula:
Cooler volumetric flow rate correction factor
In formula:
χKFor the unhelpful volumetric ratio of cooler, χRFor the unhelpful volumetric ratio of regenerator；
Intermediate variable
In formula: γ is the specific heat ratio of helium, γ=1.66；PrkFor the Prandtl number of the water in cooler.
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