CN105485954A - Design method for inertia pipe type pulse pipe cold finger optimally matched with linear compressor - Google Patents

Abstract

The invention discloses a design method for an inertia pipe type pulse pipe cold finger optimally matched with a linear compressor. The method comprises the eight steps that firstly, the inertia pipe type pulse pipe refrigerator cold finger is equivalent into an alternating current circuit; secondly, the pulse pipe cold finger impedance under optimal matching is calculated according to compressor parameters; thirdly, the volume flow rate of a compressor outlet is calculated; fourthly, the reasonable refrigerating temperature, the reasonable refrigerating capacity and the reasonable refrigerating efficiency target are set; fifthly, all components of the pulse pipe cold finger are endowed with initial values; sixthly, the impedance value of a connecting pipe inlet is calculated; seventhly, the refrigerating capacity and the refrigerating efficiency are calculated; and eighthly, whether the calculated impedance value, the calculated refrigerating capacity and the calculated refrigerating efficiency are equal to the theoretical optimal values or not is judged through comparison, if yes, the design is finished, and if not, the fifth step is repeated to adjust the initial parameters, and the sixth step, the seventh step and the eighth step are repeated. According to the design method, very positive significance is achieved for practical development of an efficient inertia pipe type pulse pipe refrigerator.

Description

With the method for designing of the inertia cast pulse tube cold finger of linear compressor Optimum Matching

Technical field

The present invention relates to refrigeration & cryogenic engineering field, particularly a kind of method for designing with the inertia cast pulse tube cold finger of linear compressor Optimum Matching.

Background technology

Pulse tube refrigerating machine is a significant innovation of regenerating type low-temperature refrigerator, which eliminate the cold junction displacer be widely used in conventional regenerating type low-temperature refrigerator (as Stirling and G-M refrigeration machine), achieve the low vibration of cold junction, low interference and without wearing and tearing; And the important improvement in structure optimization and pm mode, at typical warm area, its actual efficiency has also reached the peak of regenerating type low-temperature refrigerator.These remarkable advantages make pulse tube refrigerating machine become a big hot topic of Cryo Refrigerator research over nearly 30 years, all obtain a wide range of applications in Aero-Space, low-temperature electronics, superconduction industry and cryosurgery industry etc.

According to the difference of drive source, again pulse tube refrigerating machine is divided for the high frequency pulse tube cooler driven by linear compressor and two kinds, the low frequency pulse tube system refrigeration machine by G-M type driven compressor.The pulse tube refrigerating machine of the field application such as space flight and military affairs, because have very strict restriction to weight and volume, generally all adopts the linear compressor that lightweight high frequency operates, and the operating frequency of compressor is usually all at more than 30Hz.The high frequency pulse tube cooler driven by linear compressor, due to compact conformation, the outstanding advantages such as lightweight, volume is little, efficiency is high, running is reliable, life expectancy is long, becomes one of the most popular type of space flight infrared device cooling gradually.

Phase difference between pressure wave and mass flow is the key parameter that regenerating type low-temperature refrigerator produces refrigeration effect.In pulse tube refrigerating machine, the phase adjusted mode realizing the phase difference between pressure wave and mass flow has multiple, as aperture, air reservoir, bidirection air intake, multi-channel shunt, symmetric nozzle and asymmetric nozzle etc., the inertia tube that the mid-90 in 20th century grows up is then because phase modulation wide ranges, efficiency is high, potentiality are large, the outstanding advantages such as stable and reliable for performance, emphasize Aero-Space stable and reliable for performance and military field, become the dominant form of pulse tube refrigerating machine phase adjusted mode.

The structure of high frequency pulse tube cooler can be divided into two large divisions roughly: one, as the linear compressor of drive source, and two, remainder is except for the compressor referred to as pulse tube cold finger.Coupling between the two all has very important meaning in optimization compressor efficiency and raising refrigeration machine complete machine refrigeration performance.And the method for designing of inertia cast pulse tube cold finger with linear compressor Optimum Matching, the discussion that the system that has not yet to see is deep.

Summary of the invention

In view of the deficiencies in the prior art, the present invention proposes method for designing that is a kind of and the inertia cast pulse tube cold finger of linear compressor Optimum Matching.

The object of the invention is to, method for designing that is a kind of and the inertia cast pulse tube cold finger of linear compressor Optimum Matching is provided, can appropriate design inertia cast pulse tube cold finger by the method, realize the Optimum Matching with existing linear compressor, thus increase substantially the refrigeration performance of pulse tube refrigerating machine complete machine, promote the practical development of efficient inertia cast high frequency pulse tube cooler.

This method for designing comprises the following steps:

Step one: inertia cast high frequency pulse tube cooler comprises linear compressor 1, connecting leg 2, level aftercooler 3, regenerator 4, cool end heat exchanger 5, pulse tube 6, hot end heat exchanger 7, inertia tube 8, air reservoir 9; Wherein connecting leg 2, level aftercooler 3, regenerator 4, cool end heat exchanger 5, pulse tube 6, hot end heat exchanger 7, inertia tube 8 and air reservoir 9 constitute pulse tube cold finger 10, and linear compressor 1 is connected by connecting leg 2 with pulse tube cold finger 10; According to circuit analog model, the pressure in high frequency pulse tube cooler is equivalent to electromotive force, and volume flow rate is equivalent to electric current, flow resistance, fluid capacitance and inertia by the resistance be equivalent to respectively in circuit, electric capacity and inductance, whole high frequency pulse tube cooler cold finger equivalence can become alternating current circuit;

Step 2: the magnetic field intensity measuring magnet in given linear compressor 1, the area of piston, the mechanical damping of piston, the length of coil, the resistance of coil, the axial rigidity of flat spring and the size of mover quality, the expression formula of the electric efficiency after linear compressor 1 mates with pulse tube cold finger 10 is:

$\mathrm{\η}=\frac{\left|Z_a\right|{\mathrm{cos\θB}}^2{L}^2{A_p}^2}{\left|Z_a\right|{{\mathrm{cos\θA}}_p}^2{B}^2{L}^2+{\mathrm{bB}}^2{L}^2+R_e{A_p}^4\[{\left(\right|Z_a|cos\mathrm{\θ}+b/{A_p}^2)}^2+{\left(\right|Z_a|\sin \mathrm{\θ}+(m\mathrm{\ω}-k_x/\mathrm{\ω})/{A_p}^2)}^2\]}---\left(1\right)$

η in expression formula (1) is the conversion efficiency that the input electric work of linear compressor 1 is converted to pulse tube cold finger 10 porch sound merit; | Z _a| be the amplitude of pulse tube cold finger 10 impedance, θ is the phase angle of pulse tube cold finger 10 impedance, and B is the magnetic field intensity of magnet in linear compressor 1; L is loop length; A _pfor piston area; B is piston machine damping; R _efor coil resistance; M is mover quality, and ω is angular frequency; k _xfor flat spring axial rigidity; Based on the expression formula (1) of compressor electric motor efficiency, the amplitude of pulse tube cold finger 10 impedance under accomplished Optimum Matching, phase angle and running frequency;

Step 3: according to the maximum piston the run stroke of linear compressor 1, set suitable compressor piston stroke, and the volume flow rate size drawing linear compressor 1 exit according to the calculation expression (2) of piston face volume flow rate:

$\stackrel{\·}{U}\left(t\right)=A_p\mathrm{\ω}X---\left(2\right)$

In expression formula (2) for linear compressor (1) exit volume flow rate, A _pfor piston area, ω is angular frequency, and X is piston stroke;

Step 4: according to the application demand of reality, arranges the target cryogenic temperature of rational pulse tube cold finger 10, refrigerating capacity and refrigerating efficiency;

Step 5: give initial value to all parts of pulse tube cold finger 10, comprise cross-sectional area and the length of connecting leg 2, the level cross-sectional area of aftercooler 3, length and porosity, the cross-sectional area of regenerator 4, length, wire diameter sizes and porosity, the cross-sectional area of cool end heat exchanger 5, length and porosity, the cross-sectional area of pulse tube 6 and length, the cross-sectional area of hot end heat exchanger 7, length and porosity, the cross-sectional area of inertia tube 8 and length, and the volume of air reservoir 9;

Step 6: the volume flow rate of giving the blowing pressure and air reservoir 9 porch initial value, utilizes expression formula (3) and expression formula (4) to calculate dynamic pressure and the resistance value of air reservoir 9 entrance:

$p_9=\frac{{\mathrm{\γP}}_m}{{\mathrm{\ωV}}_{9}i}{\stackrel{\·}{U}}_9---\left(3\right)$

$Z_9=\frac{{\mathrm{\ωV}}_{9}i}{{\mathrm{\γP}}_m}---\left(4\right)$

P in expression formula (3) ₉for air reservoir 9 porch dynamic pressure, γ is adiabatic coefficent, P _mfor the blowing pressure, ω is angular frequency, V ₉for the volume of air reservoir 9, i is imaginary part, for air reservoir 9 inlet volumetric flow rate, Z in expression formula (4) ₉for the impedance of air reservoir 9; Expression formula (5), expression formula (6) and expression formula (7) is utilized to calculate the dynamic pressure of inertia tube 8 porch, volume flow rate and impedance:

$p_8=p_9+{\∫}_0^{l_8}(\frac{{\mathrm{\ω\ρ}}_{8}i}{A_8}+\frac{{\mathrm{\μS}}_8}{A_8^2{\mathrm{\δ}}_v}){\stackrel{\·}{U}}_{x-8}dx---\left(5\right)$

${\stackrel{\·}{U}}_8={\stackrel{\·}{U}}_9+{\∫}_0^{l_8}\frac{{\mathrm{\ωA}}_{8}i}{{\mathrm{\γP}}_m}{p}_{x-8}dx---\left(6\right)$

$Z_8=p_8/{\stackrel{\·}{U}}_8---\left(7\right)$

P in expression formula (5) ₈for inertia tube 8 porch dynamic pressure, p ₉for air reservoir 9 porch dynamic pressure, l ₈for the length of inertia tube 8, ω is angular frequency, ρ ₈for the density of Working medium gas in inertia tube 8, i is imaginary part, A ₈for the cross-sectional area of inertia tube 8, μ is dynamic viscosity, S ₈for the section girth of inertia tube 8, δ _vfor the viscous osmotic degree of depth, for being the volume flow rate of x position with air reservoir 9 entrance distance in inertia tube 8, in expression formula (6) for the volume flow rate of inertia tube 8 porch, for air reservoir 9 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-8for being the dynamic pressure of x position with air reservoir 9 entrance distance in inertia tube 8, the Z in expression formula (7) ₈for the impedance of inertia tube 8 porch; Expression formula (8), expression formula (9) and expression formula (10) is utilized to calculate the dynamic pressure of hot end heat exchanger 7 porch, volume flow rate and impedance:

$Z_7=p_7/{\stackrel{\·}{U}}_7---\left(10\right)$

P in expression formula (8) ₇for hot end heat exchanger 7 porch dynamic pressure, p ₈for inertia tube 8 porch dynamic pressure, l ₇for the length of hot end heat exchanger 7, ω is angular frequency, ρ ₇for the density of Working medium gas in hot end heat exchanger 7, i is imaginary part, for the porosity of hot end heat exchanger 7, A ₇for the cross-sectional area of hot end heat exchanger 7, r ₇for flow resistance in hot end heat exchanger 7, for being the volume flow rate of x position with inertia tube 8 entrance distance in hot end heat exchanger 7, in expression formula (9) for the volume flow rate of hot end heat exchanger 7 porch, for inertia tube 8 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-7for being the dynamic pressure of x position with inertia tube 8 entrance distance in hot end heat exchanger 7, the Z in expression formula (10) ₇for the impedance of hot end heat exchanger 7 porch; Expression formula (11), expression formula (12) and expression formula (13) is utilized to calculate the dynamic pressure of pulse tube 6 porch, volume flow rate and impedance:

p ₆＝p ₇(11)

${\stackrel{\·}{U}}_6={\stackrel{\·}{U}}_7+{\∫}_0^{l_6}\frac{{\mathrm{\ωA}}_{6}i}{{\mathrm{\γP}}_m}{p}_{6}dx---\left(12\right)$

$Z_6=p_6/{\stackrel{\·}{U}}_6---\left(13\right)$

P in expression formula (11) ₆for pulse tube 6 porch dynamic pressure, p ₇for hot end heat exchanger 7 porch dynamic pressure, in expression formula (12) for the volume flow rate of pulse tube 6 porch, for hot end heat exchanger 7 porch volume flow rate, l ₆for the length of pulse tube 6, ω is angular frequency, A ₆for the cross-sectional area of pulse tube 6, i is imaginary part, and γ is adiabatic coefficent, P _mfor the blowing pressure, the Z in expression formula (13) ₆for the impedance of pulse tube 6 porch; Expression formula (14), expression formula (15) and expression formula (16) is utilized to calculate the dynamic pressure of cool end heat exchanger 5 porch, volume flow rate and impedance:

$Z_5=p_5/{\stackrel{\·}{U}}_5---\left(16\right)$

P in expression formula (14) ₅for cool end heat exchanger 5 porch dynamic pressure, p ₆for pulse tube 6 porch dynamic pressure, l ₅for the length of cool end heat exchanger 5, ω is angular frequency, ρ ₅for the density of Working medium gas in cool end heat exchanger 5, i is imaginary part, for the porosity of cool end heat exchanger 5, A ₅for the cross-sectional area of cool end heat exchanger 5, r ₅for flow resistance in cool end heat exchanger 5, for being the volume flow rate of x position with pulse tube 6 entrance distance in cool end heat exchanger 5, in expression formula (15) for the volume flow rate of cool end heat exchanger 5 porch, for pulse tube 6 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-5for being the dynamic pressure of x position with pulse tube 6 entrance distance in cool end heat exchanger 5, the Z in expression formula (16) ₅for the impedance of cool end heat exchanger 5 porch; Expression formula (17), expression formula (18) and expression formula (19) is utilized to calculate the dynamic pressure of regenerator 4 porch, volume flow rate and impedance:

$Z_4=p_4/{\stackrel{\·}{U}}_4---\left(19\right)$

P in expression formula (17) ₄for regenerator 4 porch dynamic pressure, p ₅for cool end heat exchanger 5 porch dynamic pressure, l ₄for the length of regenerator 4, ω is angular frequency, ρ ₄for the density of Working medium gas in regenerator 4, i is imaginary part, for the porosity of regenerator 4, A ₄for the cross-sectional area of regenerator 4, r ₄for flow resistance in regenerator 4, for being the volume flow rate of x position with cool end heat exchanger 5 entrance distance in regenerator 4, in expression formula (18) for the volume flow rate of regenerator 4 porch, for cool end heat exchanger 5 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-4for being the dynamic pressure of x position with cool end heat exchanger 5 entrance distance in regenerator 4, g is the control source item that thermograde causes, the Z in expression formula (19) ₄for the impedance of regenerator 4 porch; Utilize the dynamic pressure of expression formula (20), expression formula (21) and expression formula (22) calculation stage aftercooler 3 porch, volume flow rate and impedance:

$Z_3=p_3/{\stackrel{\·}{U}}_3---\left(22\right)$

P in expression formula (20) ₃for level aftercooler 3 porch dynamic pressure, p ₄for regenerator 4 porch dynamic pressure, l ₃for the length of level aftercooler 3, ω is angular frequency, ρ ₃for the density of Working medium gas in level aftercooler 3, i is imaginary part, for the porosity of level aftercooler 3, A ₃for the cross-sectional area of level aftercooler 3, r ₃for flow resistance in level aftercooler 3, for being the volume flow rate of x position with regenerator 4 entrance distance in level aftercooler 3, in expression formula (21) for the volume flow rate of level aftercooler 3 porch, for regenerator 4 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-3for being the dynamic pressure of x position with regenerator 4 entrance distance in level aftercooler 3, the Z in expression formula (22) ₃for the impedance of level aftercooler 3 porch; Expression formula (23), expression formula (24) and expression formula (25) is utilized to calculate the dynamic pressure of connecting leg 2 porch, volume flow rate and impedance:

$p_2=p_3+{\∫}_0^{l_2}(\frac{{\mathrm{\ω\ρ}}_{2}i}{A_2}+\frac{{\mathrm{\μS}}_2}{A_2^2{\mathrm{\δ}}_v}){\stackrel{\·}{U}}_{x-2}dx---\left(23\right)$

${\stackrel{\·}{U}}_2={\stackrel{\·}{U}}_3+{\∫}_0^{l_2}\frac{{\mathrm{\ωA}}_{2}i}{{\mathrm{\γP}}_m}{p}_{x-2}dx---\left(24\right)$

$Z_2=p_2/{\stackrel{\·}{U}}_2---\left(25\right)$

P in expression formula (23) ₂for connecting leg 2 porch dynamic pressure, p ₃for level aftercooler 3 porch dynamic pressure, l ₂for the length of connecting leg 2, ω is angular frequency, ρ ₂for the density of Working medium gas in connecting leg 2, i is imaginary part, A ₂for the cross-sectional area of connecting leg 2, μ is dynamic viscosity, S ₂for connecting leg 2 section girth, δ _vfor the viscous osmotic degree of depth, for being the volume flow rate of x position with level aftercooler 3 entrance distance in connecting leg 2, in expression formula (24) for the volume flow rate of connecting leg 2 porch, for level aftercooler 3 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-2for being the dynamic pressure of x position with level aftercooler 3 entrance distance in connecting leg after level 2, the Z in expression formula (25) ₂for the impedance of connecting leg 2 porch;

Step 7: whether the volume flow rate of connecting leg 2 entrance calculated in contrast step 6 is equal with the volumetric flow rates that step 2 calculates, if equal, expression formula (26) and expression formula (27) is utilized to calculate refrigerating capacity and the refrigerating efficiency of pulse tube cold finger 10 respectively:

${\stackrel{\·}{Q}}_{cool}={\left(PV\right)}_5-(1-\mathrm{\ϵ})\left(C_p{P}_m\right({\stackrel{\·}{U}}_4-{\stackrel{\·}{U}}_5)/{\mathrm{\πR}}_g)---\left(26\right)$

$COP=\frac{Q_{cool}}{{\left(PV\right)}_2}---\left(27\right)$

In expression formula (26) for the refrigerating capacity of pulse tube cold finger 10, (PV) ₅for the sound merit of cool end heat exchanger 5 porch, ε is regenerator efficiency, C _pconstant pressure specific heat is held, P _mfor the blowing pressure, for regenerator 4 porch volume flow rate, for cool end heat exchanger 5 porch volume flow rate, π is pi, R _gfor gas constant, the COP in expression formula (27) is refrigerating efficiency, (PV) ₂for the sound merit of connecting leg 2 porch, then carry out step 8; If unequal, jump to step 5, the volume flow rate of adjustment air reservoir 9 porch initial value, and repeat step 6 and step 7;

Step 8: in comparison step six, the resistance value of connecting leg 2 entrance of gained and step one calculate the optimum pulse tube cold finger resistance value of gained, and the target refrigerating capacity simultaneously calculated in comparison step seven in the refrigerating capacity of gained and refrigerating efficiency and step 3 and refrigerating efficiency, if all equal, so designed, now the size of each parts of pulse tube cold finger 10 can realize the Optimum Matching with linear compressor 1.If have one not identical or all unequal, return step 6, the size value of adjustment pulse tube cold finger 10 all parts, then repeat step 6 to step 8.

The invention has the advantages that:

1 by the interaction relationship between linear compressor and pulse tube cold finger, obtains the interact relation of pulse tube cold finger to linear compressor electric efficiency;

The equivalence of inertia cast high frequency pulse tube cooler, by circuit analog model, is become alternating current circuit, enormously simplify the process of its analysis and optimization by 2;

3 propose the Optimum Matching that a kind of method for designing can obtain inertia cast high frequency pulse tube cooler and linear compressor.

Above-mentioned advantage make the inertia cast pulse tube cold finger designed by this method for designing can with existing linear compressor realize Optimum Matching; ensure the high electric efficiency of compressor and the high refrigerating efficiency of pulse tube cold finger, the practical development for high efficiency inertia cast high frequency pulse tube cooler has very positive meaning.

Accompanying drawing explanation

Fig. 1 is the invented inertia cast pulse tube refrigerating machine cold finger method for designing flow chart with linear compressor Optimum Matching that can realize;

Fig. 2 is inertia cast high frequency pulse tube cooler structural representation;

Wherein: 1 is linear compressor; 2 is connecting leg; 3 is level aftercooler; 4 is regenerator; 5 is cool end heat exchanger; 6 is pulse tube; 7 is hot end heat exchanger; 8 is inertia tube; 9 is air reservoir; 10 is pulse tube cold finger.

Detailed description of the invention

Below in conjunction with drawings and Examples, the specific embodiment of the present invention is described in further detail:

Fig. 1 is the invented inertia cast pulse tube refrigerating machine cold finger method for designing flow chart with linear compressor Optimum Matching that can realize;

Fig. 2 is inertia cast high frequency pulse tube cooler structural representation.

This method for designing comprises the following steps:

Step one: inertia cast high frequency pulse tube cooler comprises linear compressor 1, connecting leg 2, level aftercooler 3, regenerator 4, cool end heat exchanger 5, pulse tube 6, hot end heat exchanger 7, inertia tube 8, air reservoir 9; Wherein connecting leg 2, level aftercooler 3, regenerator 4, cool end heat exchanger 5, pulse tube 6, hot end heat exchanger 7, inertia tube 8 and air reservoir 9 constitute pulse tube cold finger 10, and linear compressor 1 is connected by connecting leg 2 with pulse tube cold finger 10; According to circuit analog model, the pressure in high frequency pulse tube cooler is equivalent to electromotive force, and volume flow rate is equivalent to electric current, flow resistance, fluid capacitance and inertia by the resistance be equivalent to respectively in circuit, electric capacity and inductance, whole high frequency pulse tube cooler cold finger equivalence can become alternating current circuit;

Step 2: the magnetic field intensity measuring magnet in given linear compressor 1, the area of piston, the mechanical damping of piston, the length of coil, the resistance of coil, the axial rigidity of flat spring and the size of mover quality, the expression formula of the electric efficiency after linear compressor 1 mates with pulse tube cold finger 10 is:

$\mathrm{\η}=\frac{\left|Z_a\right|{\mathrm{cos\θB}}^2{L}^2{A_p}^2}{\left|Z_a\right|{{\mathrm{cos\θA}}_p}^2{B}^2{L}^2+{\mathrm{bB}}^2{L}^2+R_e{A_p}^4\[{\left(\right|Z_a|cos\mathrm{\θ}+b/{A_p}^2)}^2+{\left(\right|Z_a|\sin \mathrm{\θ}+(m\mathrm{\ω}-k_x/\mathrm{\ω})/{A_p}^2)}^2\]}---\left(1\right)$

η in expression formula (1) is the conversion efficiency that the input electric work of linear compressor 1 is converted to pulse tube cold finger 10 porch sound merit; | Z _a| be the amplitude of pulse tube cold finger 10 impedance, θ is the phase angle of pulse tube cold finger 10 impedance, and B is the magnetic field intensity of magnet in linear compressor 1; L is loop length; A _pfor piston area; B is piston machine damping; R _efor coil resistance; M is mover quality, and ω is angular frequency; k _xfor flat spring axial rigidity; Based on the expression formula (1) of compressor electric motor efficiency, the amplitude of pulse tube cold finger 10 impedance under accomplished Optimum Matching, phase angle and running frequency;

Step 3: according to the maximum piston the run stroke of linear compressor 1, set suitable compressor piston stroke, and the volume flow rate size drawing linear compressor 1 exit according to the calculation expression (2) of piston face volume flow rate:

$\stackrel{\·}{U}\left(t\right)=A_p\mathrm{\ω}X---\left(2\right)$

In expression formula (2) for linear compressor (1) exit volume flow rate, A _pfor piston area, ω is angular frequency, and X is piston stroke;

Step 4: according to the application demand of reality, arranges the target cryogenic temperature of rational pulse tube cold finger 10, refrigerating capacity and refrigerating efficiency;

Step 5: give initial value to all parts of pulse tube cold finger 10, comprise cross-sectional area and the length of connecting leg 2, the level cross-sectional area of aftercooler 3, length and porosity, the cross-sectional area of regenerator 4, length, wire diameter sizes and porosity, the cross-sectional area of cool end heat exchanger 5, length and porosity, the cross-sectional area of pulse tube 6 and length, the cross-sectional area of hot end heat exchanger 7, length and porosity, the cross-sectional area of inertia tube 8 and length, and the volume of air reservoir 9;

Step 6: the volume flow rate of giving the blowing pressure and air reservoir 9 porch initial value, utilizes expression formula (3) and expression formula (4) to calculate dynamic pressure and the resistance value of air reservoir 9 entrance:

$p_9=\frac{{\mathrm{\γP}}_m}{{\mathrm{\ωV}}_{9}i}{\stackrel{\·}{U}}_9---\left(3\right)$

$Z_9=\frac{{\mathrm{\ωV}}_{9}i}{{\mathrm{\γP}}_m}---\left(4\right)$

P in expression formula (3) ₉for air reservoir 9 porch dynamic pressure, γ is adiabatic coefficent, P _mfor the blowing pressure, ω is angular frequency, V ₉for the volume of air reservoir 9, i is imaginary part, for air reservoir 9 inlet volumetric flow rate, Z in expression formula (4) ₉for the impedance of air reservoir 9; Expression formula (5), expression formula (6) and expression formula (7) is utilized to calculate the dynamic pressure of inertia tube 8 porch, volume flow rate and impedance:

$p_8=p_9+{\∫}_0^{l_8}(\frac{{\mathrm{\ω\ρ}}_{8}i}{A_8}+\frac{{\mathrm{\μS}}_8}{A_8^2{\mathrm{\δ}}_v}){\stackrel{\·}{U}}_{x-8}dx---\left(5\right)$

${\stackrel{\·}{U}}_8={\stackrel{\·}{U}}_9+{\∫}_0^{l_8}\frac{{\mathrm{\ωA}}_{8}i}{{\mathrm{\γP}}_m}{p}_{x-8}dx---\left(6\right)$

$Z_8=p_8/{\stackrel{\·}{U}}_8---\left(7\right)$

P in expression formula (5) ₈for inertia tube 8 porch dynamic pressure, p ₉for air reservoir 9 porch dynamic pressure, l ₈for the length of inertia tube 8, ω is angular frequency, ρ ₈for the density of Working medium gas in inertia tube 8, i is imaginary part, A ₈for the cross-sectional area of inertia tube 8, μ is dynamic viscosity, S ₈for the section girth of inertia tube 8, δ _vfor the viscous osmotic degree of depth, for being the volume flow rate of x position with air reservoir 9 entrance distance in inertia tube 8, in expression formula (6) for the volume flow rate of inertia tube 8 porch, for air reservoir 9 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-8for being the dynamic pressure of x position with air reservoir 9 entrance distance in inertia tube 8, the Z in expression formula (7) ₈for the impedance of inertia tube 8 porch; Expression formula (8), expression formula (9) and expression formula (10) is utilized to calculate the dynamic pressure of hot end heat exchanger 7 porch, volume flow rate and impedance:

$Z_7=p_7/{\stackrel{\·}{U}}_7---\left(10\right)$

P in expression formula (8) ₇for hot end heat exchanger 7 porch dynamic pressure, p ₈for inertia tube 8 porch dynamic pressure, l ₇for the length of hot end heat exchanger 7, ω is angular frequency, ρ ₇for the density of Working medium gas in hot end heat exchanger 7, i is imaginary part, for the porosity of hot end heat exchanger 7, A ₇for the cross-sectional area of hot end heat exchanger 7, r ₇for flow resistance in hot end heat exchanger 7, for being the volume flow rate of x position with inertia tube 8 entrance distance in hot end heat exchanger 7, in expression formula (9) for the volume flow rate of hot end heat exchanger 7 porch, for inertia tube 8 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-7for being the dynamic pressure of x position with inertia tube 8 entrance distance in hot end heat exchanger 7, the Z in expression formula (10) ₇for the impedance of hot end heat exchanger 7 porch; Expression formula (11), expression formula (12) and expression formula (13) is utilized to calculate the dynamic pressure of pulse tube 6 porch, volume flow rate and impedance:

p ₆＝p ₇(11)

${\stackrel{\·}{U}}_6={\stackrel{\·}{U}}_7+{\∫}_0^{l_6}\frac{{\mathrm{\ωA}}_{6}i}{{\mathrm{\γP}}_m}{p}_{6}dx---\left(12\right)$

$Z_6=p_6/{\stackrel{\·}{U}}_6---\left(13\right)$

P in expression formula (11) ₆for pulse tube 6 porch dynamic pressure, p ₇for hot end heat exchanger 7 porch dynamic pressure, in expression formula (12) for the volume flow rate of pulse tube 6 porch, for hot end heat exchanger 7 porch volume flow rate, l ₆for the length of pulse tube 6, ω is angular frequency, A ₆for the cross-sectional area of pulse tube 6, i is imaginary part, and γ is adiabatic coefficent, P _mfor the blowing pressure, the Z in expression formula (13) ₆for the impedance of pulse tube 6 porch; Expression formula (14), expression formula (15) and expression formula (16) is utilized to calculate the dynamic pressure of cool end heat exchanger 5 porch, volume flow rate and impedance:

$Z_5=p_5/{\stackrel{\·}{U}}_5---\left(16\right)$

P in expression formula (14) ₅for cool end heat exchanger 5 porch dynamic pressure, p ₆for pulse tube 6 porch dynamic pressure, l ₅for the length of cool end heat exchanger 5, ω is angular frequency, ρ ₅for the density of Working medium gas in cool end heat exchanger 5, i is imaginary part, for the porosity of cool end heat exchanger 5, A ₅for the cross-sectional area of cool end heat exchanger 5, r ₅for flow resistance in cool end heat exchanger 5, for being the volume flow rate of x position with pulse tube 6 entrance distance in cool end heat exchanger 5, in expression formula (15) for the volume flow rate of cool end heat exchanger 5 porch, for pulse tube 6 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-5for being the dynamic pressure of x position with pulse tube 6 entrance distance in cool end heat exchanger 5, the Z in expression formula (16) ₅for the impedance of cool end heat exchanger 5 porch; Expression formula (17), expression formula (18) and expression formula (19) is utilized to calculate the dynamic pressure of regenerator 4 porch, volume flow rate and impedance:

$Z_4=p_4/{\stackrel{\·}{U}}_4---\left(19\right)$

P in expression formula (17) ₄for regenerator 4 porch dynamic pressure, p ₅for cool end heat exchanger 5 porch dynamic pressure, l ₄for the length of regenerator 4, ω is angular frequency, ρ ₄for the density of Working medium gas in regenerator 4, i is imaginary part, for the porosity of regenerator 4, A ₄for the cross-sectional area of regenerator 4, r ₄for flow resistance in regenerator 4, for being the volume flow rate of x position with cool end heat exchanger 5 entrance distance in regenerator 4, in expression formula (18) for the volume flow rate of regenerator 4 porch, for cool end heat exchanger 5 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-4for being the dynamic pressure of x position with cool end heat exchanger 5 entrance distance in regenerator 4, g is the control source item that thermograde causes, the Z in expression formula (19) ₄for the impedance of regenerator 4 porch; Utilize the dynamic pressure of expression formula (20), expression formula (21) and expression formula (22) calculation stage aftercooler 3 porch, volume flow rate and impedance:

$Z_3=p_3/{\stackrel{\·}{U}}_3---\left(22\right)$

P in expression formula (20) ₃for level aftercooler 3 porch dynamic pressure, p ₄for regenerator 4 porch dynamic pressure, l ₃for the length of level aftercooler 3, ω is angular frequency, ρ ₃for the density of Working medium gas in level aftercooler 3, i is imaginary part, for the porosity of level aftercooler 3, A ₃for the cross-sectional area of level aftercooler 3, r ₃for flow resistance in level aftercooler 3, for being the volume flow rate of x position with regenerator 4 entrance distance in level aftercooler 3, in expression formula (21) for the volume flow rate of level aftercooler 3 porch, for regenerator 4 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-3for being the dynamic pressure of x position with regenerator 4 entrance distance in level aftercooler 3, the Z in expression formula (22) ₃for the impedance of level aftercooler 3 porch; Expression formula (23), expression formula (24) and expression formula (25) is utilized to calculate the dynamic pressure of connecting leg 2 porch, volume flow rate and impedance:

$p_2=p_3+{\∫}_0^{l_2}(\frac{{\mathrm{\ω\ρ}}_{2}i}{A_2}+\frac{{\mathrm{\μS}}_2}{A_2^2{\mathrm{\δ}}_v}){\stackrel{\·}{U}}_{x-2}dx---\left(23\right)$

${\stackrel{\·}{U}}_2={\stackrel{\·}{U}}_3+{\∫}_0^{l_2}\frac{{\mathrm{\ωA}}_{2}i}{{\mathrm{\γP}}_m}{p}_{x-2}dx---\left(24\right)$

$Z_2=p_2/{\stackrel{\·}{U}}_2---\left(25\right)$

P in expression formula (23) ₂for connecting leg 2 porch dynamic pressure, p ₃for level aftercooler 3 porch dynamic pressure, l ₂for the length of connecting leg 2, ω is angular frequency, ρ ₂for the density of Working medium gas in connecting leg 2, i is imaginary part, A ₂for the cross-sectional area of connecting leg 2, μ is dynamic viscosity, S ₂for connecting leg 2 section girth, δ _vfor the viscous osmotic degree of depth, for being the volume flow rate of x position with level aftercooler 3 entrance distance in connecting leg 2, in expression formula (24) for the volume flow rate of connecting leg 2 porch, for level aftercooler 3 porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-2for being the dynamic pressure of x position with level aftercooler 3 entrance distance in connecting leg after level 2, the Z in expression formula (25) ₂for the impedance of connecting leg 2 porch;

Step 7: whether the volume flow rate of connecting leg 2 entrance calculated in contrast step 6 is equal with the volumetric flow rates that step 2 calculates, if equal, expression formula (26) and expression formula (27) is utilized to calculate refrigerating capacity and the refrigerating efficiency of pulse tube cold finger 10 respectively:

${\stackrel{\·}{Q}}_{cool}={\left(PV\right)}_5-(1-\mathrm{\ϵ})\left(C_p{P}_m\right({\stackrel{\·}{U}}_4-{\stackrel{\·}{U}}_5)/{\mathrm{\πR}}_g)---\left(26\right)$

$COP=\frac{Q_{cool}}{{\left(PV\right)}_2}---\left(27\right)$

In expression formula (26) for the refrigerating capacity of pulse tube cold finger 10, (PV) ₅for the sound merit of cool end heat exchanger 5 porch, ε is regenerator efficiency, C _pconstant pressure specific heat is held, P _mfor the blowing pressure, for regenerator 4 porch volume flow rate, for cool end heat exchanger 5 porch volume flow rate, π is pi, R _gfor gas constant, the COP in expression formula (27) is refrigerating efficiency, (PV) ₂for the sound merit of connecting leg 2 porch, then carry out step 8; If unequal, jump to step 5, the volume flow rate of adjustment air reservoir 9 porch initial value, and repeat step 6 and step 7;

Step 8: in comparison step six, the resistance value of connecting leg 2 entrance of gained and step one calculate the optimum pulse tube cold finger resistance value of gained, and the target refrigerating capacity simultaneously calculated in comparison step seven in the refrigerating capacity of gained and refrigerating efficiency and step 3 and refrigerating efficiency, if all equal, so designed, now the size of each parts of pulse tube cold finger 10 can realize the Optimum Matching with linear compressor 1.If have one not identical or all unequal, return step 6, the size value of adjustment pulse tube cold finger 10 all parts, then repeat step 6 to step 8.

Claims (1)

1., with the method for designing of the inertia cast pulse tube cold finger of linear compressor Optimum Matching, it is characterized in that, described method for designing comprises the following steps:

Step one: inertia cast high frequency pulse tube cooler comprises linear compressor (1), connecting leg (2), level aftercooler (3), regenerator (4), cool end heat exchanger (5), pulse tube (6), hot end heat exchanger (7), inertia tube (8), air reservoir (9); Wherein connecting leg (2), level aftercooler (3), regenerator (4), cool end heat exchanger (5), pulse tube (6), hot end heat exchanger (7), inertia tube (8) and air reservoir (9) constitute pulse tube cold finger (10), and linear compressor (1) is connected by connecting leg (2) with pulse tube cold finger (10); According to circuit analog model, the pressure in high frequency pulse tube cooler is equivalent to electromotive force, and volume flow rate is equivalent to electric current, flow resistance, fluid capacitance and inertia by the resistance be equivalent to respectively in circuit, electric capacity and inductance, whole high frequency pulse tube cooler cold finger equivalence can become alternating current circuit;

Step 2: the magnetic field intensity measuring magnet in given linear compressor (1), the area of piston, the mechanical damping of piston, the length of coil, the resistance of coil, the axial rigidity of flat spring and the size of mover quality, the expression formula of the electric efficiency after linear compressor (1) mates with pulse tube cold finger (10) is:

η in expression formula (1) is the conversion efficiency that the input electric work of linear compressor (1) is converted to pulse tube cold finger (10) porch sound merit; | Z _a| be the amplitude of pulse tube cold finger (10) impedance, θ is the phase angle of pulse tube cold finger (10) impedance, and B is the magnetic field intensity of magnet in linear compressor (1); L is loop length; A _pfor piston area; B is piston machine damping; R _efor coil resistance; M is mover quality, and ω is angular frequency; k _xfor flat spring axial rigidity; Based on the expression formula (1) of compressor electric motor efficiency, the amplitude of pulse tube cold finger (10) impedance under accomplished Optimum Matching, phase angle and running frequency;

Step 3: according to the maximum piston the run stroke of linear compressor (1), set suitable compressor piston stroke, and draw the volume flow rate size in linear compressor (1) exit according to the calculation expression (2) of piston face volume flow rate:

In expression formula (2) for linear compressor (1) exit volume flow rate, A _pfor piston area, ω is angular frequency, and X is piston stroke;

Step 4: according to the application demand of reality, arranges the target cryogenic temperature of rational pulse tube cold finger (10), refrigerating capacity and refrigerating efficiency;

Step 5: give initial value to all parts of pulse tube cold finger (10), comprise cross-sectional area and the length of connecting leg (2), the cross-sectional area of level aftercooler (3), length and porosity, the cross-sectional area of regenerator (4), length, wire diameter sizes and porosity, the cross-sectional area of cool end heat exchanger (5), length and porosity, the cross-sectional area of pulse tube (6) and length, the cross-sectional area of hot end heat exchanger (7), length and porosity, the cross-sectional area of inertia tube (8) and length, and the volume of air reservoir (9),

Step 6: the volume flow rate of giving the blowing pressure and air reservoir (9) porch initial value, utilizes expression formula (3) and expression formula (4) to calculate dynamic pressure and the resistance value of air reservoir (9) entrance:

P in expression formula (3) ₉for air reservoir (9) porch dynamic pressure, γ is adiabatic coefficent, P _mfor the blowing pressure, ω is angular frequency, V ₉for the volume of air reservoir (9), i is imaginary part, for air reservoir (9) inlet volumetric flow rate, Z in expression formula (4) ₉for the impedance of air reservoir (9); Expression formula (5), expression formula (6) and expression formula (7) is utilized to calculate the dynamic pressure of inertia tube (8) porch, volume flow rate and impedance:

P in expression formula (5) ₈for inertia tube (8) porch dynamic pressure, p ₉for air reservoir (9) porch dynamic pressure, l ₈for the length of inertia tube (8), ω is angular frequency, ρ ₈for the density of Working medium gas in inertia tube (8), i is imaginary part, A ₈for the cross-sectional area of inertia tube (8), μ is dynamic viscosity, S ₈for the section girth of inertia tube (8), δ _vfor the viscous osmotic degree of depth, for being the volume flow rate of x position with air reservoir (9) entrance distance in inertia tube (8), in expression formula (6) for the volume flow rate of inertia tube (8) porch, for air reservoir (9) porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-8for being the dynamic pressure of x position with air reservoir (9) entrance distance in inertia tube (8), the Z in expression formula (7) ₈for the impedance of inertia tube (8) porch; Expression formula (8), expression formula (9) and expression formula (10) is utilized to calculate the dynamic pressure of hot end heat exchanger (7) porch, volume flow rate and impedance:

P in expression formula (8) ₇for hot end heat exchanger (7) porch dynamic pressure, p ₈for inertia tube (8) porch dynamic pressure, l ₇for the length of hot end heat exchanger (7), ω is angular frequency, ρ ₇for the density of Working medium gas in hot end heat exchanger (7), i is imaginary part, for the porosity of hot end heat exchanger (7), A ₇for the cross-sectional area of hot end heat exchanger (7), r ₇for flow resistance in hot end heat exchanger (7), for being the volume flow rate of x position with inertia tube (8) entrance distance in hot end heat exchanger (7), in expression formula (9) for the volume flow rate of hot end heat exchanger (7) porch, for inertia tube (8) porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-7for being the dynamic pressure of x position with inertia tube (8) entrance distance in hot end heat exchanger (7), the Z in expression formula (10) ₇for the impedance of hot end heat exchanger (7) porch; Expression formula (11), expression formula (12) and expression formula (13) is utilized to calculate the dynamic pressure of pulse tube (6) porch, volume flow rate and impedance:

p ₆＝p ₇(11)

P in expression formula (11) ₆for pulse tube (6) porch dynamic pressure, p ₇for hot end heat exchanger (7) porch dynamic pressure, in expression formula (12) for the volume flow rate of pulse tube (6) porch, for hot end heat exchanger (7) porch volume flow rate, l ₆for the length of pulse tube (6), ω is angular frequency, A ₆for the cross-sectional area of pulse tube (6), i is imaginary part, and γ is adiabatic coefficent, P _mfor the blowing pressure, the Z in expression formula (13) ₆for the impedance of pulse tube (6) porch; Expression formula (14), expression formula (15) and expression formula (16) is utilized to calculate the dynamic pressure of cool end heat exchanger (5) porch, volume flow rate and impedance:

P in expression formula (14) ₅for cool end heat exchanger (5) porch dynamic pressure, p ₆for pulse tube (6) porch dynamic pressure, l ₅for the length of cool end heat exchanger (5), ω is angular frequency, ρ ₅for the density of Working medium gas in cool end heat exchanger (5), i is imaginary part, for the porosity of cool end heat exchanger (5), A ₅for the cross-sectional area of cool end heat exchanger (5), r ₅for flow resistance in cool end heat exchanger (5), for being the volume flow rate of x position with pulse tube (6) entrance distance in cool end heat exchanger (5), in expression formula (15) for the volume flow rate of cool end heat exchanger (5) porch, for pulse tube (6) porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-5for being the dynamic pressure of x position with pulse tube (6) entrance distance in cool end heat exchanger (5), the Z in expression formula (16) ₅for the impedance of cool end heat exchanger (5) porch; Expression formula (17), expression formula (18) and expression formula (19) is utilized to calculate the dynamic pressure of regenerator (4) porch, volume flow rate and impedance:

P in expression formula (17) ₄for regenerator (4) porch dynamic pressure, p ₅for cool end heat exchanger (5) porch dynamic pressure, l ₄for the length of regenerator (4), ω is angular frequency, ρ ₄for the density of Working medium gas in regenerator (4), i is imaginary part, for the porosity of regenerator (4), A ₄for the cross-sectional area of regenerator (4), r ₄for flow resistance in regenerator (4), for being the volume flow rate of x position with cool end heat exchanger (5) entrance distance in regenerator (4), in expression formula (18) for the volume flow rate of regenerator (4) porch, for cool end heat exchanger (5) porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-4for being the dynamic pressure of x position with cool end heat exchanger (5) entrance distance in regenerator (4), g is the control source item that thermograde causes, the Z in expression formula (19) ₄for the impedance of regenerator (4) porch; Utilize the dynamic pressure of expression formula (20), expression formula (21) and expression formula (22) calculation stage aftercooler (3) porch, volume flow rate and impedance:

P in expression formula (20) ₃for level aftercooler (3) porch dynamic pressure, p ₄for regenerator (4) porch dynamic pressure, l ₃for the length of level aftercooler (3), ω is angular frequency, ρ ₃for the density of Working medium gas in level aftercooler (3), i is imaginary part, for the porosity of level aftercooler (3), A ₃for the cross-sectional area of level aftercooler (3), r ₃for flow resistance in level aftercooler (3), for being the volume flow rate of x position with regenerator (4) entrance distance in level aftercooler (3), in expression formula (21) for the volume flow rate of level aftercooler (3) porch, for regenerator (4) porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-3for being the dynamic pressure of x position with regenerator (4) entrance distance in level aftercooler (3), the Z in expression formula (22) ₃for the impedance of level aftercooler (3) porch; Expression formula (23), expression formula (24) and expression formula (25) is utilized to calculate the dynamic pressure of connecting leg (2) porch, volume flow rate and impedance:

P in expression formula (23) ₂for connecting leg (2) porch dynamic pressure, p ₃for level aftercooler (3) porch dynamic pressure, l ₂for the length of connecting leg (2), ω is angular frequency, ρ ₂for the density of Working medium gas in connecting leg (2), i is imaginary part, A ₂for the cross-sectional area of connecting leg (2), μ is dynamic viscosity, S ₂for connecting leg (2) section girth, δ _vfor the viscous osmotic degree of depth, for being the volume flow rate of x position with level aftercooler (3) entrance distance in connecting leg (2), in expression formula (24) for the volume flow rate of connecting leg (2) porch, for level aftercooler (3) porch volume flow rate, γ is adiabatic coefficent, P _mfor the blowing pressure, p _x-2for being the dynamic pressure of x position with level aftercooler (3) entrance distance in connecting leg after level (2), the Z in expression formula (25) ₂for the impedance of connecting leg (2) porch;

Step 7: whether the volume flow rate of connecting leg (2) entrance calculated in contrast step 6 is equal with the volumetric flow rates that step 2 calculates, if equal, expression formula (26) and expression formula (27) is utilized to calculate refrigerating capacity and the refrigerating efficiency of pulse tube cold finger (10) respectively:

In expression formula (26) for the refrigerating capacity of pulse tube cold finger (10), (PV) ₅for the sound merit of cool end heat exchanger (5) porch, ε is regenerator efficiency, C _pconstant pressure specific heat is held, P _mfor the blowing pressure, for regenerator (4) porch volume flow rate, for cool end heat exchanger (5) porch volume flow rate, π is pi, R _gfor gas constant, the COP in expression formula (27) is refrigerating efficiency, (PV) ₂for the sound merit of connecting leg (2) porch, then carry out step 8; If unequal, jump to step 5, the volume flow rate of adjustment air reservoir (9) porch initial value, and repeat step 6 and step 7;

Step 8: in comparison step six, the resistance value of connecting leg (2) entrance of gained and step one calculate the optimum pulse tube cold finger resistance value of gained, and the target refrigerating capacity simultaneously calculated in comparison step seven in the refrigerating capacity of gained and refrigerating efficiency and step 3 and refrigerating efficiency, if all equal, so designed, now the size of pulse tube cold finger (10) each parts can realize the Optimum Matching with linear compressor (1).If have one not identical or all unequal, return step 6, the size value of adjustment pulse tube cold finger (10) all parts, then repeat step 6 to step 8.