Theory and experiment of the hottest resistance ty

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Theory and experiment of resistance type low temperature heat exchanger Abstract: by analyzing the thermodynamic characteristics of the last stage heat exchanger of helium liquefier, this paper expounds the theory that using distributed resistance can improve the heat transfer performance and increase the output of liquid helium. At the same time, a distributed resistance heat exchanger is designed and manufactured, and a comparative experiment is carried out on a 4.2K small refrigerator to verify the above theory. Fig. 4, ref. 6

key words: low temperature heat exchanger flow resistance helium liquefier

1 preface

it is well known that the flow resistance of general heat exchangers is a kind of system energy loss. In this regard, the smaller the better. However, under special conditions, it is possible to use flow resistance to improve the performance of low-temperature heat exchanger, so as to improve the efficiency of liquefaction cycle. Scott proposed to use the distributed resistance (along the way resistance) of the last stage heat exchanger of the helium liquefier to increase the liquid helium production [1]

in addition to the helium liquefaction cycle using a two-phase expander, the general helium liquefier, regardless of the precooling method, finally reaches the liquid helium temperature region by throttling. The last stage heat exchanger refers to the counter flow heat exchanger in front of the throttle valve, as shown in Figure 1. The heat transfer process of the final stage heat exchanger is usually carried out at very low temperature (4~14k) and very small temperature difference (0.5~2.5k). Its performance has a great impact on the cycle, and has always been paid attention to. On the basis of analyzing the thermodynamic characteristics of the last stage heat exchanger of the helium liquefier, the author expounds the theoretical basis for using resistance to increase the output or cooling capacity of liquid helium, and has designed and manufactured a distributed resistance heat exchanger. The above theory is verified by comparing the 4.2K small refrigerator [3] with the non resistance heat exchanger

2 thermodynamic characteristics of the last stage heat exchanger of helium liquefier

the characteristics of the last stage heat exchanger are related to the thermophysical properties and working conditions of the working medium. Its temperature and pressure conditions can usually be set according to the precooling mode of helium liquefaction cycle and practical experience. The helium inlet temperature T3 (corresponding to point 3 in Figure 1) of the low-pressure channel of the final stage heat exchanger is determined by the saturated pressure of liquid helium, and the general range is 3.7~4.5k. The inlet temperature T1 of helium in the high-pressure channel (corresponding to point 1 in Figure 1) depends on the precooling mode of the previous stage. Since the throttling refrigerating capacity is approximately equal to the isothermal throttling effect, the lower T1, the greater the refrigerating capacity or liquefaction rate. In order to ensure a certain refrigerating capacity or liquefaction rate, T1 is usually designed at 10 ~ 14K. The outlet temperature T2 of the high-pressure channel (corresponding to point 2 of figure L), that is, the temperature before throttling, has a direct impact on the refrigerating capacity or liquefaction rate. From the temperature entropy diagram [4] of helium, the saturated gas line within the range of 3.7~4.5k almost coincides with the isoenthalpy line of 30.9j/g, and the conversion point of the isoenthalpy line [differential throttling effect( э T/ э P) H=0] is 7.8k. Therefore, T2 must be lower than 7.8k to liquefy helium. In fact, T2 is usually lower than 6K. The outlet temperature T4 of the low-pressure channel (corresponding to point 4 in Figure 1) depends on the temperature difference at the hot end of the final stage heat exchanger. In order to improve the heat exchange efficiency, this temperature difference is generally chosen to be very small, usually below LK, or even only 0.3k. It can be seen that the remarkable characteristics of the last stage heat exchanger of helium liquefier are very low operating temperature and very small heat transfer temperature difference

as for the working pressure of the final stage heat exchanger, the flow resistance of the low-pressure channel is generally very small. If omitted, the low-pressure side pressure PL is equal to the saturation pressure of liquid helium. It is usually about 0.1MPa. The high-pressure side pressure pH can be designed according to the inlet temperature T of the high-pressure channel, that is, the conversion pressure when the conversion temperature is equal to T1. In this way, the high-pressure helium inlet state points (T1, pH) will be located on the conversion curve of the temperature pressure diagram. For example, if t1=9.5k, the value is 18.5mpa. See point a in Figure 2. The enthalpy value of point a should be the minimum value under T1 temperature, and the corresponding isothermal throttling effect is the largest. Hainan will build a comprehensive shipping test area and a bulk commodity trading base, which can be called the best pressure. For the conventional non resistance type final stage heat exchanger, since the flow resistance of the high-pressure channel is also small, the optimal pressure selected according to T1 cannot also be the optimal pressure corresponding to the outlet temperature T2

in the example, if the flow resistance in the high pressure channel is omitted, when t2=6k, the outlet state point B will fall on the 24.0j/g isoenthalpy line at the lower right of the conversion curve. A problem worth studying is that if the distributed resistance can be set in the high pressure channel, the outlet pressure can be reduced to 6K; The optimum pressure of F should be 0.75mpa, then point C at the outlet state will fall on the isoenthalpy line of 20.4j/g, reducing the enthalpy value before throttling by 3.6j/g, which means that the unit refrigerating capacity will increase by 3.6j/g after throttling. From another point of view, assuming that the exothermic heat of high-pressure helium remains unchanged, the outlet enthalpy remains at 24.0j/g, while the distributed resistance reduces the outlet pressure to 1.0MPa, still making it on the conversion curve. In that case, the outlet temperature T: will be equal to 6.6k, which will increase the outlet heat transfer temperature difference by 0.6k (this can protect the sensor collision heat exchanger, which has been considerable), so the heat transfer area can be reduced

the above analysis does not cover the change of heat transfer coefficient caused by setting distributed resistance. In fact, without the distributed resistance, the increase of air velocity and disturbance is conducive to the improvement of heat transfer coefficient, so it will not have a negative impact. In short, as long as the reasonable distributed resistance is set in the high-pressure channel of the final heat exchanger of the helium liquefier, the liquefaction rate or refrigeration capacity may be improved. This does not violate the second law of thermodynamics. Because from a local point of view. Setting the distributed resistance will cause entropy increase and increase the irreversible loss, but at the same time, the throttling degree of the throttle valve behind the non stage heat exchanger must be greatly reduced, otherwise the pressure PL after throttling cannot be kept unchanged, so the entropy increase of the throttle valve is reduced. In general, the total entropy increase of the two parts is not increased, but decreased [5]

3 thermodynamic parameter relationship

high pressure helium in the channel of heat exchanger with distributed resistance experiences the process of heat release and throttling, so the relationship between state parameters is complex. Through a series of equations such as energy balance equation and continuity equation, the following relationship of pressure, temperature and entropy along the distributed resistance pipeline can be derived [5]

p -- pressure, pa

t -- temperature, k

s -- entropy, J/kg · k

x -- resistance tube length, m

q -- heat flow, w/m2

u -- resistance tube cross-sectional perimeter, m

a -- resistance tube cross-sectional area, m2

t -- time for helium to pass through DX tube length,

ρ—— Density, kg/m3

β— This action loosens the cylindrical storage tank - constant pressure expansion coefficient, 1/k

k - constant temperature compression coefficient, 1/pa

w - flow rate, M/s

d - equivalent diameter of resistance pipe, m

f - friction coefficient of resistance pipe

cp - constant pressure specific heat, J/kg · k

α H-differential throttling effect, K/pa

4 comparative experiment

in order to verify the theory of resistance heat exchanger, the author carried out comparative experiment on a 4.2K small refrigerator

4.1 experimental device

4.2 K small refrigerator is shown in Figure 3. It is a closed cycle helium refrigerator that can continuously provide cooling capacity at 4.2K temperature. It consists of a compression system and a refrigeration system. The latter consists of a GM refrigerator (precooling source) and a throttling circuit. In the figure, 11 is the component that outputs cooling capacity at the temperature of 4.2K (equivalent to liquid helium tank). Figure 9 shows the final stage heat exchanger

1. throttling compressor 2. primary compressor 3. secondary compressor 4. GM refrigerator 5. primary heat exchanger 6. primary cold head heat exchanger

7. secondary heat exchanger 8. secondary cold head heat exchanger 9. final heat exchanger 10. throttle valve 11. tertiary cold head 12. neon heat pipe

the distributed resistance and non resistance heat exchangers in the comparative experiment are counter flow sleeve type, and the pipes, pipe diameters and pipe lengths used by the two final heat exchangers are the same. Outer tube is Φ five × 0.5mm, inner pipe is Φ two × 0.1mm, the pipe is 1Crl8Ni9Ti stainless steel, the pipe length is 2.5m, and the coiled spiral pipe with a diameter of 130mm creates a new opportunity for manufacturing parts with enhanced mechanical properties. Whether the resistance setting in the high pressure channel of distributed resistance heat exchanger is reasonable or not is the key to the success of the experiment. Ideally, the distributed resistance should make the helium state change along the transformation curve. In order to facilitate processing, the method of adding resistance to the tube core is not adopted, but the method of appropriately flattening the inner tube with high-pressure helium. After preliminary calculation and practical test, it is finally decided to roll the pipe section in the distributed resistance section into approximately 3 × 0.4mm rectangle. Since the inlet temperature of the high-pressure helium of the final stage heat exchanger of the 4.2K small refrigerator is about 14K and the pressure is about 2.0MPa, in order to make the differential throttling effect less than zero, the distributed resistance is only set in the pipe section 480mm long from the outlet

4.2 experimental results

a large number of experiments have been done for different high pressure pH and different throttling circuit flow, and the results can verify the above theory. Figure 4 shows the results of a group of comparative experiments, which reflects the relationship between the refrigerating capacity and the helium flow under the conditions of high pressure ph=2.01mh and throttled temperature of 4.15 ± 0.15k. Comparative experiments show that the cooling capacity of distributed resistance type is larger than that of non resistance type under the same conditions. For each type of heat exchanger, there is an optimal flow rate with the maximum cooling capacity

5 conclusion

(1) adding reasonable resistance in the high pressure channel of the last stage heat exchanger can improve the refrigerating capacity or liquefaction rate; If the refrigerating capacity or liquefaction rate remains unchanged, the heat transfer area can be reduced

(2) the applied resistance must be in the section where the differential throttling effect of helium is less than zero, so that compared with the non resistance type, it has higher temperature and larger heat transfer temperature difference under the condition of equal heat release

(3) it should be better to set the distributed resistance by adding resistance to the tube core than by flattening the inner tube: the ideal distributed resistance is to change the state of helium to the transformation curve, although it is difficult to achieve. However, the state change process line should also be close to the transformation curve as much as possible


1 Scott R B, translated by Shu Quansheng, et al. Cryogenic engineering Beijing: Science Press, 1977.

2 Mann D B, et, and performance of a laboratory size helium liquid. Advances in Cryo eng, 1959 (5)

3 Zhao Kaitao, Ji Shiliang, et al. Development and test of 1W/4, 2K small refrigerator. Low temperature and superconductivity, 1988 (4)

4 the fourth Design Institute of chemical industry. Cryogenic manual (Volume I). Beijing: Fuel Chemical Industry Press, 1973.

5 Jin Sumin. Research on the final stage heat exchanger of 4.2K micro refrigerator. Master's degree thesis of Nanjing Institute of technology, 1988.

6 Zhang Zhiku, et al. Refrigeration and cryogenic technology (Volume I). Beijing: Machinery Industry Press, 1981

* zhaokaitao, male, born in July 1939, graduated from the power department of Nanjing Institute of technology in 1964. He is now an associate professor of the refrigeration teaching and Research Office of the power department of Southeast University, engaged in teaching and scientific research. (end)

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