Study of the thermal performance of multilayer insulation used in cryogenic transfer lines

Cryogenics 100 (2019) 114–122

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Research paper

Study of the thermal performance of multilayer insulation used in cryogenic transfer lines

T

⁎

Bicai Denga,b, Shaoqi Yanga, Xiujuan Xiea, , Yunlong Wanga, Xing Biana, Linghui Gonga, Qing Lia,b a

State Key Laboratory of Technologies in Space Cryogenic Propellants (Technical Institute of Physics and Chemistry, Chinese Academy of Sciences), 29 Zhongguancun East Rd., Beijing 100190, China b University of Chinese Academy of Sciences, No.19 (A) Yuquan Rd., Beijing 100190, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Multilayer insulation Thermal performance Cryogenic transfer line Test platform Large-scale helium refrigerator

We studied the relation between the thermal performance of multilayer insulation MLI used for cryogenic transfer lines and the layer density, number of layer and material of reflectors and spacers theoretically and experimentally. An optimum combination of layer density and number of layer of MLI is proposed. The heat flux and effective thermal conductivity of MLI are calculated using modified Lockheed Equation. Based on the theoretical studies, a horizontal cryogenic transfer lines test platform was built, thermal performance of MLI, including heat leakage per meter, heat flux and effective thermal conductivity were experimentally studied for layer density from 20 to 50 layers/cm and number of layer from 30 to 80 layers. Four MLI systems with different material of reflectors and spacers were tested. Both theoretical and experimental results show that heat flux decreases with the increases of number of layer and the decrease of layer density. The differences of heat flux between theoretical and experimental values when layer density is 20, 25 and 40 layers/cm are 23%, 20% and 39% for number of layer from 40 to 70, respectively. By comparing calculated and experimental results, optimum layer density and suitable number of layer are obtained for MLI used in cryogenic transfer lines at the temperature range for 293–77 K. In the four MLI systems constructed with different materials, the combination of Double-aluminized Mylar and Fiberglass paper (MP) has the best performance. Effective thermal conductivity and heat flux of MLI are 0.135 mW/(m·K) and 1.43 W/m2, respectively. And the heat leakage per meter of cryogenic transfer line is reduced to 0.49 W in suitable condition.

1. Introduction Cryogenic transfer lines are one of the key parts of large-scale refrigerators, which are used to transfer cryogenic fluid such as liquid helium or supercritical helium e.g. from the cold box to a liquid helium Dewar, to cryogenic control valve boxes or to heat loads. As the scientific facilities are large-scaled and complicated, the distances that cryogenic fluids produced by large-scale helium refrigerators need to be transferred vary from several meters to several kilometers. A highly efficient and reliable insulation of cryogenic transfer line would directly influence the stability of pipe and reduce the energy consumption of a large-scale helium refrigerator, especially for the long distance transmission. Multilayer insulation (MLI) is applied as a preferred thermal insulation. Its performance significantly influences the heat leak into the helium cryogenic transfer lines. In most cases, MLI systems used in cryogenic storage and tank have mainly investigated in the published

⁎

literatures [1–4]. Many of researches put forward different test apparatus to measure thermal performance of MLI consisting of heat flux and effective thermal conductivity ke in the laboratory using vertical cylinder calorimeter [5,6]. Influence issues of MLI included material [7], perforated rate [8], sudden loss of vacuum [9], variable density [1] are studied based on a calorimeter. As for the ideal thermal performance of MLI in laboratory, previous studies [7] demonstrate that heat flux of MLI are below about 1 W/m2 and effective thermal conductivity values are below about 0.1 mW/(m·K) at high vacuum. Some examples of ideal MLI system with ke even in the range of 0.05 mW/(m·K) are proposed in [10]. The thermal performance of MLI largely determines the performance of cryogenic transfer lines. S. A. Dye concluded that MLI for cryogenic propellant feedlines with diameter about 1 in. is much less effective than MLI tank insulation, with heat leak into spiral wrapped MLI on pipes 3–10 times higher than conventional tank MLI [11]. Typically a heat leakage value of 0.97 W/m for rigid transfer line can be

Corresponding author. E-mail address: [email protected] (X. Xie).

https://doi.org/10.1016/j.cryogenics.2019.01.005 Received 30 August 2018; Received in revised form 21 January 2019; Accepted 24 January 2019 Available online 24 January 2019 0011-2275/ © 2019 Elsevier Ltd. All rights reserved.

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ε f

Nomenclature T k Q P* q Do l δ Gv ρ hfg N n P α σ

absolute temperature (K) thermal conductivity, mW/(m·K) heat leakage, W non-dimensional contact pressure parameter heat flux of MLI, W/m2 inner diameters of test pipe, m length of test pipe, m thickness of MLI, m flow rate of evaporated gas density, kg/m3 latent heat of vaporization number of layer, layers layer density, layers/cm residual gas pressure, torr accommodation coefficient Stefan-Boltzmann constant (5.67 × 10−8), W/(m2·K4)

effective emissivity relative density of the separator compared to solid material circumference of length, m

L Subscripts e i s h c sc gc rc a r

effective MLI support warm boundary cold boundary solid conduction gas conduction radiation average value room temperature

with different number of layer. And four MLI systems composed of different material of reflectors and spacers were tested and analyzed.

accomplished without active shield cooling [12]. If greater effort is reasonable the heat leakage can be reduced to 0.73 W/m to 0.04 W/m [13,14]. A flexible transfer line has a typical heat leak of 1.2 W/m [15]. The cryogenic transfer lines are usually used to transfer cryogenic fluids in horizontal direction. Ohmori et al. [16–18] studied experimentally degradation of thermal performance of MLI by increasing the contact pressure between the adjacent layers due to the weight of the MLI itself and becomes higher at the upper part of the horizontal cylinder. Because of inherent insulation compression and its effect on conventional netting spacer, the performances on pipeline and tube are worse than MLI on a cryogenic tank or flat surface [19]. And significant degradation in the thermal performance of a given MLI system is greater than 50% because of heat leakage due to spacer and bending of cryogenic transfer lines [20]. In addition, it is difficult to insulate in cryogenic transfer lines with limited space and difficultly in outgassing. However, there is few literatures analyzed and measured heat leakage of MLI in cryogenic transfer lines, which used to optimize the performance of MLI. The heat leakages of multilayer insulation, a support and the overall leakage are 1.02 W/m, 0.44 W and 1.46 W/m from experimental data, respectively [21], in which lacking of experimental measurement and further optimization of MLI used in cryogenic transfer line. Therefore, theoretical and experimental researches of thermal performance of MLI in cryogenic transfer line are presented in this paper. Considering the complexity of MLI, heat transfer consisting of residual gas conduction, solid spacer conduction and radiation are existed in MLI. The thermal analysis including heat leakage per meter, heat flux and effective thermal conductivity of MLI for different layer density and number of layer used classical theory was discussed. In addition, a horizontal test platform of cryogenic transfer lines at temperature range for 293–77 K used to evaluate thermal performance of MLI has been built. Heat leakages per meter, heat flux and effective thermal conductivity have been experimentally analyzed for different layer density

2. Thermal analysis of MLI used in cryogenic transfer lines 2.1. Structure of cryogenic transfer lines The basic structure of liquid helium cryogenic transfer lines is shown in Fig. 1. A three-channel coaxial liquid helium pipe is proposed in Fig. 1(a), the details of which were presented in Ref. [21]. The liquid helium goes through the inner pipe and the gaseous helium returns through the space between inner pipe and middle pipe. Reflection shields separated by spacers are wrapped around the outer surface of middle pipe to reduce the heat leak of radiation, forming a MLI. It would have a chamber as a vacuum jacket between the MLI and outer pipe, which is evacuated to less than 5 × 10−5 torr [22] to reduce the heat leak caused by convection and conduction of the residual gas. In this paper, gas of nitrogen is selected as residual gas. In addition, G10 supports are mounted between middle and outer pipe to avoid the thermal bridge caused by contact. Generally, the temperature of the gaseous helium return through the inner pipe equals to that of the liquid helium going through the middle pipe. To simplify the model and increase the efficiency of thermal analysis, the liquid helium pipes can be seen as single cryogenic transfer lines, as shown in Fig. 1(b). Fig. 2 shows schematic drawings of test pipe used to test the thermal performance of MLI of liquid helium cryogenic transfer lines. A 2-meter test pipe without any supports is shown in Fig. 2(a). MLI consist of reflectors and spacers were wrapped on cold boundary (shown in Fig. 2(b)), and temperature sensors are attached on the surfaces of Aluminized Mylar every 10 layers seen in Fig. 2(c). It assumes room temperature Tr as warm boundary temperature, which means heat

(a) liquid helium cryogenic transfer lines

(b) simplified cryogenic transfer lines

Fig. 1. Schematic drawings of (a) three-channel coaxial liquid helium cryogenic transfer lines and (b) simplified liquid helium cryogenic transfer lines. 115

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(a) 2-meter test pipe

(b) arrangement of MLI

(c) test of layer temperatures of MLI Fig. 2. Schematic drawings of (a) 2-meter test pipe, (b) arrangement of MLI and (c) test of layer temperatures of MLI.

leakage into test pipe is from the ambient environment. The temperature at T1, T2, …, and TN are studied at every 10 layers of MLI. The heat leakage of MLI, caused by solid conduction, gas conduction, gaseous convection in the spacer and radiation between the reflectors, is main part directly influence total heat leakage of cryogenic transfer line. There are several factors that affect the performance of MLI systems, including reflector materials (such as Double-aluminized Mylar and aluminized), spacer materials (such as Fiberglass paper, Dacron net, Fabric), number of layers (1–70 layers), layer densities (20–50 layers/ cm) and methods of installation, such as layer-by-layer, blankets (multilayer assemblies), sub-blankets, seaming, butt-joining, spiral wrapping and roll-wrapping [5]. In next section, materials, number of layer and layer density of MLI are studied.

q=

(2) where

n=

Theoretical calculation of heat transfer of MLI is an important part of our research. There are two well-known methods to calculate the heat transfer of MLI [1]. The first method is a physics-based equation proposed by McIntosh [23]. The total heat flux through the MLI is given by

C2 fksp (Th − Tc ) σ (Th4 − Tc4 ) + C1 Pα (Th − Tc ) + 1/ εh + 1/ εc − 1 δ

N Δδ

(3)

The three terms of Eq. (2) corresponding to the models of solid conduction, radiation and gaseous conduction, respectively. From the Lockheed Equations, the coefficient A is the solid conduction, which is a function of the contact resistance between spacers and reflector shields. The coefficient B is radiation, which is a function of reflector material and its perforation rate. The coefficient C is gaseous conduction, which is a function of residual gas pressure between the layers of reflectors and spacers. According to Eq. (2), material, number of layer and layer density of MLI are considered in the calculation of heat flux. It should be noted that the McIntosh Equation is must be solved on every layer, whereas the Lockheed Equation is solved for the bulk system. Therefore, we use Eq. (2) to analysis the effect of number of layer and layer density for performance of total MLI system. Using Fourier’s law and assuming that the number of layer is sufficiently large (that means N≈N + 1). So the effective thermal conductivity from Eq. (2) is:

2.2. Theoretical calculation of MLI

q=

Bε (Th4.67 − Tc4.67) CP (Th0.52 − Tc0.52) A (n)2.63 (Th − Tc )(Th + Tc ) + + 2(N + 1) N N

(1)

In Eq. (1), the first term is the heat transfer caused by radiation of reflector, the radiation term includes the Setfan-Boltzman constant and the effective emissivity of the hot and cold surface, the second term is the heat transfer caused by the conduction and convection of residual gas, where P (units in Pa) is the pressure of residual gas and C1 is a coefficient about category and temperature of residual gas, the third term is the heat transfer caused by solid conduction through the spacer material and reflector, where f is the relative density of the separator with respect to solid material. C2 is an empirical constant (C2 = 0.008 for Dacron netting). ksp is spacer material conductivity. Another method is the generalized form of Lockheed Equations [24], which gives an empirical form of heat flux:

ke = q

Δδ ΔT

(4)

and can be written as

ke =

Bε (Th4.67 − Tc4.67) CP (Th0.52 − Tc0.52) A (n)2.63 (Th + Tc ) + + 2n n (Th − Tc ) n (Th − Tc )

(5)

From Eq. (5), we can obtain the thermal conductivity of solid conduction, radiation and gaseous conduction:

ks c = 116

A (n)2.63 (Th + Tc ) 2n

(6)

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krc =

k gc =

Bε (Th4.67 − Tc4.67) n (Th − Tc )

CP (Th0.52

(7) 2.3. Multilayer insulation material

Tc0.52)

− n (Th − Tc )

(8)

The typical reflector materials and spacers used in cryogenic transfer lines are listed in Table 1. The reflector materials tested include Double-aluminized Mylar of 6.5 μm thickness and Aluminum foil of 12 μm thickness. The spacer materials included Dacron netting and Fiberglass paper. The weight of Dacron netting and Fiberglass paper is 10 g/m2 and 14 g/m2, respectively. Four different MLI systems (Doublealuminized Mylar & Fiberglass paper, Double-aluminized Mylar & Dacron netting, Aluminum foil & Fiberglass paper, Aluminum foil & Dacron netting) could be used in cryogenic transfer line by combining two different reflectors and spacers. To improve the efficiency of MLI system, spacers are made of low conductivity material to reduce solid conduction, and the surfaces of reflectors are made clean and polished to increase reflectivity. MLI system is installed in high vacuum jacket to reduce the heat leakage caused by conduction and convection of gas. In order to reduce radiation, more reflector shields mean less distance between the layers of reflector, which will lead to more conduction between the shields through spacers and reflectors. As discussed in Refs. [25,26], there is a layer density where heat transfer is minimized when number of layer, boundary conditions and material stay the same. From the Eq. (2), coefficients A, B and C are derived from the particular multilayer insulation system and residual gas. In the final report of Lockheed Equation [27], Lockheed coefficient of MLI are shown as following: A = 7.30 × 10−8, B = 7.07 × 10−10, C = 1.46 × 104, which is from the test data for specimens through 9 composed of 80 layers of perforated Double-aluminized Mylar with Silk net spacers. In Ref. [1], the empirical coefficients A and B had been adjusted to accommodate multipurpose hydrogen test bed tank (MHTB) insulation. It is important note that the perforation rate of reflector and spacer material in Lockheed Equation were different than those of the cylindrical and slender-form cryogenic transfer lines. Therefore, the empirical coefficients A and B should be adjusted to fit cryogenic transfer lines insulation. And empirical coefficient C is determined by the interstitial gas. For nitrogen gas as residual gas, coefficient C is 1.46 × 104. In order to obtain coefficient of the conduction term A and coefficient of the radiation term B, the heat flux in terms of number of layer was formulated form the experimental data in Fig. 3. Firstly, the modified coefficient A and B is derived from perforated Double-aluminized Mylar for perforation rate 0.16% with Fiberglass paper at the layer density 25 layers/cm under 293–77 K using horizontal pipe with dimeter 88.9 mm in Fig. 3. From Fig. 3, Lockheed equation Eq. (2) with modified empirical coefficients of A and B yields a better fit to the experimental data. Therefore, these modified coefficients A, B and C were adjusted for cryogenic transfer lines using perforated Doublealuminized Mylar for perforation rate 0.16% with Fiberglass paper at the layer density 25 layers/cm and 293–77 K as following: A = 2.26 × 10−7, B = 2.90 × 10−9, C = 1.46 × 104 according to Lockheed approach in Fig. 3. After that, the theoretical results using modified empirical coefficients would be compared and validated with experimental data using the same materials and perforation rate for different layer density in later section.

According to Eqs. (2) and (5), it’s apparent that heat flux and effective thermal conductivity of MLI are related to temperature of warm and cold boundary, the layer density (n), number of layer (N) and coefficients A, B and C. Coefficients A, B and C are derived from the particular multilayer insulation system and residual gas. When the category and pressure of residual gas is decided, coefficient A, B and C are related to multilayer insulation system. As shown in Eq. (2), heat flux of solid conduction is affected by number of layer and layer density, while heat flux of radiation and gas conduction are only related to number of layer. Total heat flux (q) is proportional to layer density and inversely proportional to number of layer. Thermal conductivity of solid, radiation and gaseous conduction is only related to layer density in theoretical analysis. The thermal conductivity of solid conduction is proportional to layer density and thermal conductivity of radiation and gaseous conduction are inversely proportional to layer density. According to the analysis of thermal conductivity of solid, radiation and gaseous conduction, effective thermal conductivity (ke) in Eq. (5) can be minimized with an optimum layer density. Ohmor et al. [16,18] studied the contact pressure that is generated between the horizontal cylinder and a single thin film loosely wound around the cylinder. The non-dimensional contact pressure parameter P* is described by the next Eq. (9).

P * = 2 cos θ − cos θd −

tan θd ln{ −tan θd +

tan2 θd + 1 }

(9)

From the above equations, θ is the azimuthal angle measure from the top of the cylinder, θd is departure angle of MLI film departing from the surface of the cylinder, which is determined by the circumferential length of the MLI. The non-dimensional contact pressure parameter P* is related with the layer density of MLI as following Eq. (10) [16]. Heat fluxes of MLI in different regions around the horizontal cylinder have been obtained. It must be note the experimental heat flux data with different P* of MLI samples were fabricated in the vertical calorimeter to have homogeneous compressive pressure in every layers. A typical heat flux for the MLI is estimated to be 0.743 W/m2 for 40 layers. While the average non-dimensional contact pressure (Pa*) is estimated to be 82 for all layers around the horizontal cylinder [17].

n=

(P ∗ + 1)(1 − c ) bc

(10)

Therefore, in this paper, the average layer density (na) is used to signify the average contact pressure around horizontal cryogenic transfer lines. The circumferential length of the MLI (L) around horizontal pipe is used to indicate average layer density shown in Eq. (11), which is derived from Eq. (3). The heat flux analysis of total MLI system is researched through Eqs. (2) and (11).

na =

N L 2π

−

Do 2

(11)

Table 1 Typical reflector materials and spacer used in cryogenic transfer line. Category

Material

Thickness (mm)

Hole diameter (cm)

Perforation rate (%)

Basic weight (g/m2)

Reflector

Double-aluminized Mylar Aluminum foil

0.012 0.0065

0.187 0.187

0.61 0.61

17.5 ± 1.0 17.6 ± 1.0

Spacer

Dacron netting Fiberglass paper

≤0.06 ≤0.07

/ /

/ /

10.0 ± 2.0 14.0 ± 2.0

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pipe platform of six-meter cryogenic transfer lines with changeable MLI has been built and discussed in detail in Ref. [21]. Test platform of cryogenic transfer line and arrangement of MLI were shown in Fig. 6. Two guarded pipes were installed into both ends of 2-meter test pipe to be filled with liquid nitrogen to maintain 77 K cold boundary condition (Fig. 6(a)). Consequently, the heat leakage from both ends of test pipe could be nearly eliminated due to two guarded pipes. With disassemble outer pipe, different MLI materials can be replaced on the test platform. Before wrapping MLI on the cryogenic transfer lines, test specimens of MLI were evacuated and heated to release the absorbed gas, which for MLI systems includes five purge cycles from 5 Pa to 1 × 105 Pa at a temperature up to 393 K. Then, the cold vacuum pressure in the vacuum jacket should be in the range of 10−3 Pa with vacuum pumping. The temperature sensors are attached to Double-aluminized Mylar surface of MLI every 10 layers (seen in Fig. 2(a)). In addition, composite materials of shields and spacers, with a single Aluminized Mylar outer layer, were installed on the inner test pipe. After that, the outer surface of MLI is bundled with aluminized tape to fasten the joint of MLI. The principle of test platform is based on liquid nitrogen boil-off calorimetry, so the heat leakage through MLI into the test pipe is proportional to the liquid nitrogen boil-off rate Gv. The heat leakage is the basis for calculating the thermal performance of cryogenic transfer line, which includes effective thermal conductivity (ke), heat flux (q) of MLI. Therefore, the steady-state heat leakage (Q), heat flux (q) and effective thermal conductivity (ke) of MLI can be obtained:

Fig. 3. Heat flux as a function of number of layer for 25 layers/cm under 293–77 K.

2.4. Optimum layer density and layer number The optimum layer density n* can be obtained from the derivation of Eq. (5): 4.67

Bε (Th n∗ = ⎡ ⎢ ⎣

1

− Tc4.67) + CP (Th0.52 − Tc0.52) ⎤2.63 ⎥ 0.815A (Th2 − Tc2) ⎦

Q = Gv ρg hfg (12)

q=

In Ref. [28], the optimized layer density is derived from Lockheed Equation based on perforated Doubled-aluminized Mylar and Dacron net MLI configurations. In Ref. [1], a modified Lockheed Equation is proposed suited to MHTB insulation. According to Eq. (12), optimum layer density as well as coefficient A, B and C are derived from the particular multilayer insulation materials, interstitial gas and boundary temperature. In our research, the MLI system wrapped in slender-form cryogenic transfer line that is different from flat plate and Hydrogen Testbed. So it is necessary to find an optimum layer density and number of layer of MLI suitable for cryogenic transfer lines. With Eq. (2) and empirical parameters for cryogenic transfer line, the influences of number of layer and layer density on heat flux of MLI system are calculated, and the results are shown in Fig. 4 for cold boundary 77 K and warm boundary 293 K. By increasing the number of layer from 10 to 50 layers, the calculated heat flux reduces significantly, and becomes smooth after 50 layers. The heat flux increases with the increasing of layer density, implying that the wrapping MLI tightly would bring much more solid conduction and make it difficult to outgas. So an optimum layer density is existed and helpful to reduce heat flux. However, when the layer density is less than 40 layers/cm, the difference between the calculated heat fluxes for different layer density is very small from Fig. 4. Thus, we need to find suitable layer density and number of layer to easily install MLI material. According to Eqs. (5)–(8), calculated results of effective thermal conductivity with different layer densities, for absolute pressure 10−5 torr are plotted in Fig. 5. The thermal conductivity due to radiation krc and gas conduction kgc decrease with the layer density, and the thermal conductivity due to solid conduction ksc increases with the layer density. The minimum total effective thermal conductivity ke can be obtained when the layer density is between 20 and 25 layers/cm.

Q πl (D0 + δ ) Q ln

ke =

(13)

(14)

D0 + 2δ D0

2πl (Th − Tc )

(15)

From Eqs. (14) and (15), the calculation of heat flux and effective thermal conductivity are highly affected by measurement of MLI thickness. Thus, the outer layers circumference of MLI in the test pipe was measured and averaged shown in Fig. 6(b). The installation techniques of MLI wrapped on continuous spiral fashion in layer-pairs used in cryogenic transfer line. That is, MLI materials spiral are wrapped overlap almost 50% of the prior spiral reflector material according to the axle wire of reflectors. Finally, in order to make the MLI outgas quickly and reduce the conduction and convention of residual gas, the perforated MLI is used in Fig. 6(c). In the experiments procedure, test pipe, first guarded pipe and second guarded pipe were filled with high purity nitrogen gas to flush

3. Experimental test platform of cryogenic transfer lines Fig. 4. The number of layer and layer density influencing on theoretical heat flux of MLI system for P = 10−5 torr.

In real system, the horizontal and slender-form cryogenic transfer lines are more suitable for practical application. Thus, a horizontal test 118

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Fig. 7. Test measurements for layer temperature distribution of MLI.

Fig. 5. Layer density variations of theoretical effective thermal conductivity for P = 10−5 torr for 293–77 K.

errors in results. So a heavy wall slab and construction can improve thermal stability and repeatability of the test platform. The test pipes are cooled down and the temperatures are stabilized. For all tests, the cold boundary temperature of test pipe is approximately 77 K. As discussed above, reflector temperatures are measured every 10 layers, and the results are shown in Fig. 7. The temperatures of all measurement points become stable after 13 h. The room temperature curve is almost stable for 26 h. And the temperatures of different layers from T1 to T5 are fluctuating with room temperature. And the fine equilibrium for more than 26 h has been obtained from Fig. 7. Moreover, the reliability of test platform has been validated in Ref. [21]. As shown in Ref. [21], the test platform has three advantages.

other gases such as oxygen. Each of the three pipes is filled and vented through a single small pipe for easy operation and minimum overall heat leakage. Firstly, both guarded pipes are fully filled with liquid nitrogen. Then the 2-meter test pipe is fully filled through the filling pipe until liquid nitrogen in the vent pipe could come out slowly for a moment. So, liquid nitrogen in the test pipe is 100% full. A heavy wall slab between the guarded pipe and test pipe is used to reduce direct solid conduction heat transfer from one liquid chamber to another, which is important to achieve very low heat measurements. Slightly different liquid temperatures between the pipes can produce dramatic

(a) test platform of cryogenic transfer line

(c) picture of perforated multilayer insulation

(b) picture of arrangement of MLI

Fig. 6. Test platform of cryogenic transfer line and arrangement of MLI. 119

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When the layer density is 20, 25 and 40 layers/cm, the differences of heat flux between the calculated values from Lockheed equation Eq. (2) with modified empirical coefficients and experimental values are less than 23%, 20% and 39% for number of layer from 40 to 70, respectively. In addition, when the thickness of MLI is constant of 20 mm, experimental heat flux for layer density of 25 layers/cm is less than 20 layers/cm from Fig. 9. In addition, we measured the experimental effective thermal conductivity and heat flux versus layer density the results are shown in Fig. 10. We can see that the heat flux for 50 layers decreases when the layer density decreases, and the effective thermal conductivity has a minimal value when layer density changes, which agree with variation trend reported by Ref. [29]. So the minimum experimental effective thermal conductivity can be obtained when the layer density around 25 layers/cm from Fig. 10. In contrast to Fig. 5, the calculated optimum layer density is about 20–25 layers/cm for minimum effective thermal conductivity. From the experimental results of effective thermal conductivity for 40, 50 and 60 layers versus layer density, the deviation of ke is less than 12% with 40, 50 and 60 layers for layers density less than 25 layers/cm. However, the deviation of ke between 40 and 50 layers is larger than 24% for 40 layers/cm. Moreover, the variation trend of heat flux is relatively smooth with the decreasing of layer density when layer density less than 25 layers/ cm. The heat flux at 20 layers/cm reduces by less than 17% comparing to 25 layers/cm from Fig. 10. However, when the thickness of MLI is 20 mm, the experimental heat flux of 25 layers/cm is less than 20 layers/cm. There is a minimum experimental ke in 25 layers/cm. Therefore, the optimum layer density is selected about 25 layers/cm, and a suitable number of layer is 50 for MLI used in cryogenic transfer line between 293 K and 77 K.

Firstly, measurement error is reduced by using two guarded pipes to maintain the same boundary condition with test pipe. Secondly, through disassemble outer pipe, the main heat leakage parts of MLI can be analyzed and optimized easily. Finally, vent pipe is installed on the top of horizontal test pipe to vent gas easily so as to vapor bubbles cannot be get trapped. There are two key parameters, the flow rate of evaporated nitrogen gas and the temperature of MLI, which need to be measured accurately within the scope of the testing accuracy. The volumetric flow rate of evaporated nitrogen gas, which is proportional to the energy transmitted through the liquid nitrogen (hfg), was measured by a gas flow meter. The accuracy of the flow meter is 0.8% of the reading plus 0.2% of full scale value in the range of 0–2 L/min. The temperature of MLI is used to verify the efficiency of a cryogenic transfer line. All temperatures are measured with four-wire platinum RTDs of which the accuracy is ± 0.1 K. According to the measurement devices, the theoretical uncertainly of the test platform is less than 4.2%. Further optimum research of MLI would be measured and discussed based on the test platform in the next parts. 4. Result and discussion As discussed above, heat leakage through MLI is the main source of heat loss in cryogenic transfer line. And the optimized layer density and number of layer are important to improve the insulting performance of MLI. Besides previous two factors, materials used in MLI system also influence the performance of MLI. Therefore, through this test platform, the influences of layer density, number of layer and different reflectors and spacers are studied in following. 4.1. Influence of MLI layer density and number of layer Firstly, MLI system including Mylar & Paper used to test and analysis the influence of layer density and number of layer at the vacuum absolute pressure 10−5 torr from 293 K to 77 K. And main installation data are measured in Table 2 according to Fig. 6(b). According to outer layers circumference of MLI, the thickness and mean area of MLI can be obtained. The number of layer is varied with the intervals of 10 layers, whereas a minimal layer density is exist between 20 and 30 layers/cm according to theoretical calculation in Fig. 4. In addition, the measured results of warm boundary temperature were obtained in Table 2. Fig. 8 shows the measured heat leakage per meter and effective thermal conductivity of MLI for different layer density and number of layer. As shown in Figs. 8(a) and 9, both heat leakage and heat flux decrease significantly with the number of layer from 30 to 50. However, the decrease in both of them become very small when the number of layer is more than 50 with layer density 20, 25 and 40 for both of experimental and theoretical results. So increasing the number of layer will not reduce heat leakage and heat flux significantly when number of layer is more than 50. And Fig. 8(b) shows that the experimental effective thermal conductivity is the minimized when the number of layer is 50. Since increasing the number of layer will result in higher material cost, longer evacuation time, insufficient degassing of inner layers and longer cool-down times, we use 50 layers of reflectors and spacers as a suitable number of layer in the MLI used in cryogenic transfer line. On the other hand, the experimental heat leakage and heat flux decrease slowly when layer density less than 25 layers/cm from Figs. 8(a) and 9, which agrees well with our calculation (Fig. 3). As shown in Fig. 8(b), experimental effective thermal conductivity firstly decreases and then increases with number of layer. And experimental effective thermal conductivity can be minimized when the layer density is 25 layers/cm for number of layer from 30 to 80. The theoretical results using Lockheed equation Eq. (2) with modified empirical coefficients at 25 layers/cm have been compared with experimental results using the same materials and perforation rate for 20 and 40 layers/cm in Fig. 9. As shown in Fig. 9, the variation trend of q obtained from calculation and measurement shows good consistency.

4.2. Influence of different MLI materials Based on the study in Section 4.1, we tested four MLI systems with different materials of reflector and spacer under same condition of layer density 25 layers/cm and 50 layers. The other test boundary temperature (293–77 K) and test procedure are the same for different MLI materials. The same hole dimeter and perforation rate for four materials are listed in Table 1. For different materials used in cryogenic transfer line, the heat leakage per meter for diameter of 88.9 mm pipe is various from 0.49 W to 1.55 W. So the materials of MLI system have a great influence on the thermal performance of cryogenic transfer lines. The experimental Table 2 Guide to different layer density and number of layer for Mylar and Paper for 2meter test pipe.

120

Layer density-n (layers/ cm)

N (layers)

Outer layers circumference of MLI (mm)

δ (mm)

Mean area (m2)

Th (K)

Q (W)

20

40 50 70

404.75 436.15 498.95

20.00 25.00 35.00

0.68 0.72 0.78

293 292 293

0.540 0.436 0.446

25

30 40 50 60 70 80

354.51 379.63 404.75 429.87 454.99 480.11

12.00 16.00 20.00 24.00 28.00 32.00

0.63 0.66 0.68 0.71 0.73 0.76

293 293 294 292 295 290

0.770 0.620 0.488 0.467 0.488 0.477

30

50

383.81

16.67

0.66

293

0.571

40

40 50 70

341.95 341.95 404.75

10.00 10.00 20.00

0.62 0.62 0.68

293 292 295

1.260 0.840 0.802

50

50

436.15

25.00

0.72

291

1.515

Cryogenics 100 (2019) 114–122

B. Deng, et al.

Fig. 8. Experimental value for different layer density and number of layer of MLI (a) heat leakage per meter-Q; (b) effective thermal conductivity- ke for absolute pressure 10−5 torr.

cryogenic transfer line decreases to 0.49 W by more than 52% compare to Ref. [21] when choose the suitable number of layer and optimum layer density. 5. Conclusions Theoretical and experimental investigations on the performance of multilayer insulation (MLI) including different layer density, number of layer and materials used in cryogenic transfer lines are presented in this paper. An optimum configuration consisting of layer density and number of layer of MLI is proposed. Thermal analysis of MLI using theoretical approach is studied about heat flux and effective thermal conductivity. Test platform of horizontal cryogenic transfer lines for diameter 89 mm used to analysis and optimize performance of MLI has been built. Heat leakage, heat flux and effective thermal conductivity have been experimentally analyzed for different layer density with different number of layer. Fig. 9. Comparison heat flux between theoretical values and experimental values for absolute pressure 10−5 torr.

(1) The theoretical and experimental results show that heat flux decreases with increasing of number of layer and decreasing of layer density. The differences of heat flux between theoretical values and experimental values in layer density of 20, 25 and 40 layers/cm are within 23%, 20% and 39% for number of layer from 40 to 70, respectively. (2) The optimum layer density is about 25 layers/cm, and a suitable number of layer is 50 for MLI system used in cryogenic transfer line between 293 K and 77 K. (3) Four different MLI systems with different reflectors and spacers have been measured and analyzed. Effective thermal conductivity and heat flux of MLI are 0.135 mW/(m·K) and 1.43 W/m2 under the suitable MLI system with Double-aluminized Mylar and Fiberglass paper, respectively. (4) The heat leakage per meter of cryogenic transfer line decreases to 0.49 W in suitable condition.

5 0.24

q for 50 layers ke for 50 layers

4

ke for 40 layers

0.20

ke for 60 layers

3

0.18 2

q (W/m2)

ke (mW/(m·K))

0.22

0.16 1

0.14 0.12

0 20

25

30

35

40

45

50

layer density (layers/cm)

Acknowledgement

Fig. 10. Experimental effective thermal conductivity and heat flux varying with layer density.

This work was supported by the fund of the State Key Laboratory of Technologies in Space Cryogenic Propellants, SKLTSCP1801 and the fund of National Research and Development Project for Key Scientific Instruments (ZDYZ2014-1).

results of heat flux and effective thermal conductivity for FP and FN shown in Table 3 are larger than one for MP and MN. Thus, the thermal performance of MLI consisting of MP used in cryogenic transfer line is better than others, whose heat flux is 1.43 W/m2 and effective thermal conductivity is 0.135 mW/(m·K). The heat leakage per meter of

Appendix A. Supplementary material Supplementary data to this article can be found online at https:// 121

Cryogenics 100 (2019) 114–122

B. Deng, et al.

Table 3 Experimental thermal performance data of MLI system for different MLI materials. Category

Code

Reflector

Spacer

Q (W)

Mylar& Paper Mylar& Net Foil& Paper Foil& Net

MP MN FP FN

Double-aluminized Mylar Double-aluminized Mylar Aluminum foil Aluminum foil

Fiberglass paper Dacron netting Fiberglass paper Dacron netting

0.49 0.74 1.55 1.52

doi.org/10.1016/j.cryogenics.2019.01.005. [15]

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