Density determination of slush nitrogen by the improved capacitance-type densimeter

Experimental Thermal and Fluid Science 35 (2011) 328–337

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Density determination of slush nitrogen by the improved capacitance-type densimeter Y.Y. Jiang, P. Zhang ⇑ Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e

i n f o

Article history: Received 6 November 2009 Received in revised form 30 September 2010 Accepted 5 October 2010

Keywords: Densimeter Slush nitrogen Multiphase flow Capacitance Phase change Measurement

a b s t r a c t Slush nitrogen is considered to be a better coolant than subcooled liquid nitrogen for the high-temperature superconducting cable cooling because of its greater density and cooling capacity. The capacitancetype densimeter is utilized to determine the density of slush nitrogen in this paper. In order to improve the densimeter performance, the bulk shielding method, based on the application of the double-shielded cables, is introduced, and the influence of the frequency of the applied voltage is investigated. The parasitic capacitance of the densimeter system is significantly reduced, and the fluctuation of the capacitance is depressed within ±2.0  104 pF at a frequency of 1.0 MHz, and the typical sensitivity of the differential type densimeter is 3.718 pF and the high accuracy of within ±0.25% for density measurement is obtained. In process of producing slush nitrogen by the freeze–thaw method, the discharge rate is 4 l/s and the time of the freeze and thaw cycles is 10 s and 5 s respectively to obtain slush nitrogen with fine solid particles, and slush density is measured by the densimeter system. According to the experimental results, the rotating speed, higher than 50 rpm in this study, is necessary to homogenize slush nitrogen for the high accuracy of the density measurement. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction Slush nitrogen is a two-phase cryogenic fluid which contains fine solid nitrogen particles in liquid nitrogen. The cooling capacity of slush nitrogen is enhanced because the latent heat of fusion is utilized for cooling, and the temperature is kept at the triple point until solid particles melt completely, as a result, the coolant consumption and the volume of cooling system are reduced, and the stability of cooling system is improved. Therefore, slush nitrogen is expected to be a better coolant than subcooled liquid nitrogen for the high-temperature superconducting cable cooling. There are several slush fluid production techniques, such as the freeze–thaw method [1] and the Auger method [2], and the former is commonly used in the laboratory due to its simplicity. In the freeze–thaw method, solid layers are created on the liquid/vapor interface by evacuating the vapor during the freeze cycle, then are submerged into the liquid during the thaw cycle and finally are broken into solid particles by the agitator. The thaw cycle is generally accomplished in two ways. One is by pressurizing gaseous helium. Haberbusch and McNelis [3] compared the production rate of slush hydrogen with different freeze and thaw cycle times by this method. Under certain conditions the dense solid layers, which are difficult to be broken, are probably created on the ⇑ Corresponding author. Tel.: +86 21 34205505; fax: +86 21 34206814. E-mail address: [email protected] (P. Zhang). 0894-1777/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2010.10.002

liquid/vapor interface, decreasing the production rate, and these solid layers can be eliminated by adjusting the pressure variation between the two cycles, known as pressure swing, inside the dewar. However, an extra helium system is demanded, making it not suitable for laboratories to produce small quantities of slush fluid. The other is by evaporating liquid [4], namely the self-pressurized method. While the evacuation is stopped, the pressure will be increased a little and the solid near the wall melts because of heat leakage from outside of the dewar, resulting in solid layers being submerged into the liquid. The problem that the dense solid layers hinder the liquid evaporation can be well solved by adjusting the time of the freeze and thaw cycles. Experimental apparatus of this method is simpler than that of the former, and therefore it is often used in the laboratory to produce slush fluid [5,6]. One of the most important properties which affect the flow and heat transfer characteristics of cryogenic slush fluid is solid volume fraction, which is often obtained by measuring the slush density. So far, various techniques have been developed to determine the densities of slush fluids, mainly including microwave method, gammaray method and capacitance method. Ellerbruch [7] used microwave instruments to measure the density of slush hydrogen and obtained the uncertainty of less than ±2%. Due to the reflection of microwave by the inner wall of dewar, the wave-absorbent material is required to improve the measurement accuracy. Carapelle and Collette [8] developed a densimeter using gamma-ray attenuation to measure the densities of cryogenic slush fluids for space

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329

Nomenclature C Cd D d dp f L l M Ro Re r Sn T U Z

capacitance (pF) reactive capacitance (pF) diameter of agitator shaft (mm) distance between electrodes (mm) diameter of solid particles (mm) frequency of voltage (Hz) inductance (H) length of cylindrical electrode (mm) polarizability (m3/kg) resistance (X) Reynolds number (ql dp up =gl ) radius of cylindrical electrodes (mm) sensitivity of densimeter (pF) temperature (K) voltage (V) complex impedance (X)

Greek symbols D absolute error d relative error

application, and the relative error for slush nitrogen density is within ±5.8%. However, it is not suitable for the radioactive substances and not very safe because of the radioactivity. Among the three methods mentioned above, the capacitance method is the most widely utilized to determine the densities of two-phase fluids for its simple configuration, fast response and high accuracy. A threedimensional, wire matrix, capacitance-type densimeter was developed by Turney and Snyder [9] to measure the densities of gas–liquid two-phase and liquid hydrogen, and most of the calculated and measured density values differed by less than ±15% of the full-scale (liquid hydrogen) density. When the capacitance method is used to measure the density of slush fluid, the influence of solid particles should be taken into consideration, and a densimeter with a simple configuration is preferred. Ohira and Nakamichi [10] compared three simple configurations of the capacitance-type densimeter for slush fluid and the accuracy of ±0.5% for the density measurement was obtained. However, capacitive sensors are usually subjected to the influence of large parasitic capacitance and the low anti-interference ability, especially when the capacitancetype densimeters are applied to cryogenic slush fluids. Because the LCR meter is not able to work at the very low temperature, the cables, which connect the densimeter to the LCR meter, are generally very long, resulting in that the parasitic capacitances of the cables are large and unstable, seriously deteriorating the performance of the densimeter. Since the technique of reducing the influence of parasitic capacitance and improve the measuring stability was not provided, the capacitance-type densimeter is difficult to be applied by other researchers, even if the densimeter with the optimal configuration is utilized. The objective of this study is to investigate the density determination of slush nitrogen by a capacitance-type densimeter system. The bulk shielding method, which is based on the application of the double-shielded cables, is introduced to improve the performance of the densimeter system. The effect of the frequency of the applied voltage on the density measurement is investigated from both experimental and theoretical aspects in order to determine an optimal frequency for the densimeter system. The performance of the densimeter system, including the sensitivity and the resolution, is validated in the experiments and the measuring accuracy is analyzed theoretically. Before the application of the densimeter system, the technique for producing slush nitrogen

e e0 q us xm xp

specific dielectric constant dielectric constant in vacuum (8.854  1012 F/m) density (kg/m3) solid volume fraction rotating speed of the agitator for density measurement (rpm) rotating speed of the agitator for slush production (rpm)

Subscripts A, B core wire of double-shielded cable A0 , B0 uncovered part of core wire e effective value G ground point I, O inner and outer shielding layers K interference source l liquid phase N normal cable s solid phase sl slush fluid X load capacitance

by the self-pressurized freeze–thaw method is studied in the experiments in order to obtain slush nitrogen containing fine solid particles. The improved capacitance-type densimeter system is utilized to determine the density variation of slush nitrogen, and the minimal agitator rotating speed necessary to keep slush nitrogen homogeneous is investigated.

2. Experimental apparatus 2.1. Experimental apparatus The self-pressurized freeze–thaw method is employed to produce slush nitrogen [3], and the schematic illustration of the experimental apparatus in this study is shown in Fig. 1. A dewar with an inner diameter of about 300 mm and a height of about 1000 mm, is used as the slush container, and three thermal shields are set in the inner tank to minimize the heat leakage from the top flange. There are four observation windows, one of which is on the top flange (top window), and the other three are at 200 mm from the bottom of the inner tank (side windows). A vacuum pump with the maximal discharge rate of 4L/s is connected to the inner tank to evacuate the vapor nitrogen in order to reduce the pressure and to form solid layers. The pressure and the discharge rate are controlled by the pressure controlling system composed of pressure gauge, pressure controller and exhaust throttle valve. An agitator driven by an electric motor is utilized for obtaining homogeneous slush nitrogen. The agitator with a diameter of 160 mm, has two parts: the helix part with a height of 460 mm to break the solid nitrogen layers created on the liquid/vapor interface, and five blades installed at the lower part to enhance the agitating intensity. The space between two parts is used for visualization through the observation windows. And the agitator is installed off center for higher agitating intensity. The pressure is measured by a pressure sensor located on the top flange and the temperature is measured by three Rh-Fe resistance thermometers which are placed at 50 mm, 200 mm, 400 mm from the bottom of the inner tank, respectively. The capacitance-type densimeter system, consisting of a densimeter and a LCR meter, is used to measure the density of slush nitrogen in the dewar. The signals of temperature and pressure are both

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3

13

4 5 10

6

14

1 8

15 11 7 16 2

9

12

1. Dewar

7. Temperature sensors

12. Vacuum pump

2. Observation windows

8. Agitator

13. LCR meter

3. Pressure sensor

9. Densimeter

14. Data acquisition device

4. Electric motor

10. Valve

15. Pressure controller

5. Magnetic fluid seal

11. Exhaust throttle valve

16. Computer

6. Thermal shields Fig. 1. Experimental apparatus for slush nitrogen production and density measurement.

collected by the data acquisition device and then saved in the computer together with the capacitance measured by the LCR meter. 2.2. The capacitance-type densimeter 2.2.1. Working principle The capacitance-type densimeter for two-phase fluids works based on the Clausius–Mossotti equation, as shown by Eq. (1), which relates the density q to the specific dielectric constant e and the polarizability M of the fluid.

M¼

e  1 1 q eþ2

ð1Þ

Simple theory states that the polarizability is approximately a constant for nonpolar fluids, such as hydrogen and nitrogen [11], indicating that the fluid density is a unique function of the specific dielectric constant. Since the density and the specific dielectric constant of the liquid have already been known, the slush density will be determined from the specific dielectric constant of slush fluid. In addition, the capacitance C of the densimeter and the specific dielectric constant e of the fluid between the electrodes have the relationship expressed by

C ¼ Sn e þ C d

ð2Þ

The sensitivity Sn and the reactive capacitance C d of the densimeter are both considered to be constant for a specified densimeter because they are determined by the configuration of the densimeter. Therefore, if both Sn and C d are known, the specific dielectric constant of the two-phase fluid can be obtained by measuring the capacitance of the densimeter, and consequently the density of two-phase fluid can be determined by the capacitance-type densimeter system. For the investigation of slush fluids, the solid volume fraction is more commonly used than the density, and therefore, the measured results are usually presented with the solid volume fraction us , which is calculated by

us ¼

qsl  ql qs  ql

ð3Þ

2.2.2. Configuration of the densimeter While designing the configuration of the densimeter, the properties of slush nitrogen containing solid particles, must be taken into consideration. On the one hand, a densimeter with high sensitivity and high resolution is desirable because of the very small variation of the specific dielectric constant e of the fluid. Taking nitrogen as an example, when the state of liquid nitrogen change from the normal boiling point to the triple point, the specific

Y.Y. Jiang, P. Zhang / Experimental Thermal and Fluid Science 35 (2011) 328–337

1.48

Sn ¼

Specific dielectric constant (-)

Liquid

ln½ðd þ

4p=e0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 d  r 2 Þ=r

331

ð4Þ

Then the theoretical value of Sn for the differential type densimeter in this study is 3.156 pF. However, serious errors may be caused if the theoretical sensitivity is used in Eq. (2) directly, and the main reason for this is explained as follows. In general, a real electronic component has three physical properties: resistance R, capacitance C and inductance L, and its complex impedance Z in a sine AC circuit is

1.46

1.44

 Z ¼ R þ j 2pfL 

1.42 80

For the capacitance-type densimeter system, the inductance, which includes that of the cables and the densimeter, is normally ignored. If the inductance is considered, the total capacitance of the densimeter and the cables, namely the effective capacitance C e of the densimeter system, can be expressed as

76

72

68

64

60

Temperature (K) Fig. 2. Variation of the specific dielectric constant of liquid nitrogen with the temperature.

dielectric constant changes from 1.4345 to 1.46867, as shown in Fig. 2. The specific dielectric constant of solid nitrogen is 1.520 at the triple point. If the maximal solid volume fraction of slush nitrogen is 50%, the variation of specific dielectric constant during the whole experiment is only 0.0598. On the other hand, different from the single phase fluid, slush fluid contains solid particles, which are easily blocked by the electrodes if the distance between electrodes is not big enough, leading to the decrease of measurement accuracy. So a densimeter with a simple configuration is more suitable to ensure solid particles to pass it smoothly. Therefore, the densimeter as shown in Fig. 3 [10] is applied in this study, which is comprised of one square flat-plate electrode with a side length of l = 50 mm and two cylindrical electrodes with a radius of r = 1.5 mm and a length of l = 50 mm. The cylindrical electrodes are symmetrically placed on both sides of the flat-plate electrode, and the distance between the cylindrical and flat-plate electrodes is d = 3 mm. The electrodes are made of copper, and the support of the electrodes is made of Teflon to ensure the insulativity between the electrodes at the low temperature. The densimeter can be utilized in two ways, differential and nondifferential, and the former is more commonly used because its sensitivity, which is approximately calculated by Eq. (4) [10], is theoretically four times as high as that of the latter.

l

d r

Cylindrical electrodes

Square flat-plate electrode

Fig. 3. Configuration of the capacitance-type densimeter.

Ce ¼

1 2pfC

C 1  ð2pf Þ2 LC

 ð5Þ

ð6Þ

The inductance L is usually regarded as a constant for a specified densimeter, and then the relationship between the effective sensitivity Sne of the densimeter system and the theoretical sensitivity Sn is

Sne ¼

Sn ½1  ð2pf Þ2 LC2

ð7Þ

Since the variation of the capacitance is very small in the experiments, it is reasonable to consider Sne as a constant for a certain frequency, indicating that the densimeter still has a high linearity even when the inductance is taken into consideration. Eq. (7) also shows that the effective sensitivity is higher than the theoretical value calculated by Eq. (4) and increases with the frequency for a specified densimeter. Additionally, the measured capacitance of the densimeter system varies randomly in different experiment runs even when the densimeter is located in the liquid nitrogen with the same pressure and temperature due to the installation error and the complex parabolic capacitance. Therefore it is quite difficult to calculate Sn and C d accurately, and calibration of the densimeter system before each experiment run is therefore indispensable for improving the measurement accuracy. 2.2.3. Performance improvement of the densimeter system Similar to other capacitive sensors, the capacitance-type densimeter has two obvious shortcomings. One is the influence of parasitic capacitance. The cables connecting the densimeter to the LCR meter are about 2 m each, because the densimeter is placed near the bottom of the inner tank and the LCR meter is outside, which results in that the parasitic capacitance is much larger than the densimeter capacitance. Additionally, the parasitic capacitance usually changes randomly in the complex experimental environment, seriously decreasing the resolution of the densimeter system. And the other is the low anti-interference ability. The densimeter capacitance is generally less than 5 pF for differential type and about 1 pF for non-differential type, so the output impedance of the densimeter is as high as several MX, which results in the capacitance measurement being easily interfered. Moreover, the measurement signal is very weak so that even small interference is considerable for the densimeter. And small variation of the measured capacitance requires high resolution of the densimeter, too. In order to solve the problems mentioned above and to improve the performance of the densimeter system, the bulk shielding method based on the application of the double-shielded

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Core wire Inner shielding layer Outer shielding layer Insulating layers

Fig. 4. Schematic diagram of the double-shielded cable.

cables is introduced to the capacitance-type densimeter to reduce the parasitic capacitance and to improve the anti-interference ability of the densimeter system. Fig. 4 illustrates the double-shielded cable used in this study, which is composed of a core wire, inner and outer shielding layers and three insulating layers. The core wire is the Ag-coated copper wire with a diameter of about 0.3 mm, and the inner shielding layer is the Ag-coated copper braid. The outer shielding layer is made of aluminum foil for a small diameter of the cable, because the cable dimension is restricted by the size of the feedthrough on the top flange, through which the cables are led out of the dewar. The insulating layers are placed between the core wire and the inner shielding layer, the inner and outer shielding layers, and outside the outer shielding layer. Completed cables, which connect the densimeter to the LCR meter directly, are preferred to ensure the integrity of the shielding layers and to reduce the influence introduced by the cable connector. The connection mode and the simplified equivalent circuit of the bulk shielding method are presented in Fig. 5. The outer shielding layers of two cables are connected to one end, and the inner shielding layers are connected as well and then grounded together with the LCR meter. It is worth noting that the wire which connects the shielding layers to the ground point of the LCR meter should be as short as possible to ensure they are at the same zero potential. And the grounding wire of the densimeter system is preferred to be separated from those of other instruments to reduce the common impedance coupling caused by the common grounding wire. And the performance of the densimeter system with the bulk shield is analyzed as follows.

Core wire

2.2.3.1. Reduction of the parasitic capacitance. The influence of the parasitic capacitance is estimated from the diagram of the equivalent circuit, as shown in Fig. 5b, where the resistances and the inductances of the densimeter system are both ignored compared with the capacitive reactance. The output is the capacitance measured by the LCR meter, and C X is the densimeter capacitance. Since the parts of the core wires, which is not covered by the shielding layers, is usually less than 5 cm in length, C A0 B0 is much smaller than the capacitance between two normal cables with a length of 2 m. Furthermore, the capacitances between the core wires and the inner shielding layers, CAI and CBI, and those between the inner and the outer shielding layers, CAIO and CBIO, the capacitances between the inner and outer shielding layers of two cables, are connected in series before they work on the densimeter capacitance CX, and therefore, the effective parasitic capacitance is significantly reduced. Moreover, the bulk shielding method is capable of keeping the parasitic capacitance of a specified densimeter system constant in the complex electric environment, and the measurement fluctuation caused by the variation of the parasitic capacitance is effectively suppressed. 2.2.3.2. Improvement of the anti-interference ability. The anti-interference ability of the densimeter is examined by comparing the interference with the normal cable and the double-shielded cable under the same condition, and only one cable of the densimeter system with a length of 2 m is considered for simplicity. The interference source K with a voltage of UK works on the normal cable and the double-shielded cable, respectively, and the diagrams of the equivalent circuits are shown in Fig. 6 [12]. Thus, the interference voltages UXN and UXB of the load capacitance CX in these two cases are obtained by

U XN ¼

C KN UK C KN þ C NG þ C X

ð8Þ

U XB ¼

C KB0 UK C KB0 þ C BI þ C B0 G þ C X

ð9Þ

Since the accurate values of the capacitances in Eqs. (8) and (9) are impossible to be obtained, the method of magnitude analysis is employed here to evaluate the interference voltages, and the magnitudes of the capacitances are determined by measuring with the LCR meter. The load capacitance CX, namely the capacitance of the densimeter, is generally about 1 pF for the non-differential type, and less than 5 pF for the differential type, while CKN and CNG are usually larger than 30 pF, much larger than CX. CKB0 and CB0 G are usually smaller than 0.01 pF because the uncovered part of the double-shielded cable is very short. And CBI is estimated to be more

Inner shielding layer

Output CX

Densimeter

CP

LCR Meter

C A'B' C AI

C AIO

C A'G

C BIO

C BI

C OG

C B'G

Outer shielding layer

(a)

(b)

Fig. 5. Schematic diagram of the bulk shielding method. (a) The connection mode and (b) the simplified equivalent circuit.

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K

C KB'

N

C KN

B C BI

K C KO U0

C NG

C KG

CX

C IO

U XN

U0

C KG

C B'G

C OG

(a)

CX

U XB

(b)

Fig. 6. The equivalent circuits when the cables are affected by an interference source K. (a) The normal cable and (b) the double-shielded cable with the inner shielding layer grounded.

Table 1 The magnitudes of the load capacitance and the parasitic capacitances. Parameters

CX

CKN

CNG

CKB0

CB0 G

CBI

Magnitude

d

1

1

d2

d2

1

than 65 pF, also much larger than CX. The magnitudes of the larger capacitances are defined to be 1, and the smaller capacitance CX is represented by d(d  0.1), CKB0 and CB0 G, which are much smaller than CX, are represented by d2(d2  0.01). The magnitudes of various capacitances are shown in Table 1. Hence, the interference voltage of two cables is approximately represented as

U XN ¼

U XB ¼

1 1 UK  UK 2þd 2 d2 1 þ d þ 2d2

ð10Þ

U K  d2 U K

ð11Þ

It is understood from Eqs. (10) and (11) that the interference voltage of the load capacitance for the double-shielded cable is much smaller than that for the normal cable, indicating that the anti-interference ability of the densimeter is significantly improved by the application of the double-shielded cables and the bulk shielding method. 2.2.4. Selection of the frequency of applied voltage The Clausius–Mossotti equation indicates that the specific dielectric constant of the fluid like nitrogen is independent of the frequency. However, the frequency actually plays an important role on the density measurement. It is shown in Eq. (7) that the effective sensitivity of the densimeter increases with the frequency, but the relationship between the fluctuation of the measured capacitance and the frequency is not clear, and in addition, the appropriate frequency for the densimeter is also related to the system inherent resonance frequency, the value of which is difficult to be determined. Although the frequency of 1.0 MHz is suggested to be applied to measure the capacitance by Ohira and Nakamichi [10], the detail information, such as the influence of the frequency on the sensitivity and the resolution of the densim-

eter, is still not clear. Hence, it is indispensable to determine the optimal frequency for the densimeter system by the experiments in order to further improve the performance of the densimeter system.

3. Experimental results and discussion 3.1. The performance of the densimeter system The performance of the densimeter system with the bulk shield is examined in the experiment. Liquid nitrogen is firstly filled into the dewar, and the vacuum pump is turned onto evacuate vapor nitrogen to reduce the pressure and temperature, and then the pressure in the dewar is kept at 80 kPa by the pressure controlling system. Three non-differential type densimeter systems, using the normal cables, the double-shielded cables and the double-shielded cables with the bulk shield, are installed in the liquid nitrogen, respectively, and the capacitances of the densimeters are measured with the LCR meter, and the measuring voltage is 1.0 V with the frequency of 500 kHz. In the experiment, the agitator is running along to reduce the vertical temperature stratification caused by the small thermal conductivity of liquid nitrogen. The measured results are presented in Table 2, where the capacitance is the total value of the densimeter capacitance and the parabolic capacitance. When the normal cables are used, the measured capacitance is about 36–37 pF, and the stable and accurate results cannot be obtained because the measurement is seriously interfered by the signals of other instruments. The measured capacitances and the fluctuations of the densimeters using the double-shielded cables without and with the bulk shield are show in Fig. 7. When the bulk shield is not utilized, the measured capacitance is 13.148 pF with a fluctuation less than ±0.02 pF, indicating that the performance of the densimeter is improved compared with the densimeter using normal cables. However, as compared to the densimeter capacitance of about 1 pF, the parasitic capacitance is still the main part of the measured result, and the resolution of the densimeter is not high enough for the density measurement of slush nitrogen. In the case that the bulk shielding method is applied, the measured capacitance is

Table 2 Experimental results of the performance of the non-differential densimeters using different cables.

Capacitance (pF) Fluctuation (pF)

Normal cables

Double-shielded cables

Double-shielded cables with bulk shield

36–37 –

13.148 ±0.02

0.543 ±0.001

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13.20

double-shielded cable

C (pF)

13.15

13.10

double-shielded cable with bulk shield

0.60

0.55

0.50 0

5

10

15

Time (min) Fig. 7. Capacitance measurement of the densimeter system using the doubleshielded cable and using the double-shielded cable with bulk shield.

0.543 pF, near the capacitance of the densimeter itself. Meanwhile the fluctuation is reduced to around ±0.001 pF. The experimental results show that the parasitic capacitance is significantly reduced and the anti-interference ability of the densimeter is effectively increased by the application of the bulk shield. Since the performance of the densimeter systems before the improvement with the bulk shield is not high enough for the density measurement, only the densimeter system with the bulk shield is discussed in the following context. 3.2. Determination of the optimal frequency for the densimeter system The improved densimeter systems with the bulk shield, including the non-differential type and the differential type, are utilized here, to investigate the influence of the frequency on the density measurement, and then to determine the optimal frequency for the densimeter system. 3.2.1. Influence of the frequency on the densimeter resolution Firstly, the influence of the frequency on the resolution of the densimeter system is investigated. The pressure in the dewar con-

0.002

500kHz 0.526pF

0.001 0.000 -0.001

Δ C (pF)

-0.002 0.002

800kHz 0.497pF

0.001 0.000 -0.001 -0.002 0.002

1.0MHz 0.464pF

0.001 0.000 -0.001 -0.002 0

2

4

6

8

10

Time (min) Fig. 8. Capacitance measurement of the non-differential type densimeter located in the stable liquid nitrogen at the various frequencies.

taining liquid nitrogen is kept at 80 kPa in the same way as Section 3.1. Several frequencies of the applied voltage (1.0 V), including 200 kHz, 500 kHz, 800 kHz, 1.0 MHz and 5.0 MHz, are utilized to measure the capacitance o f the non-differential type densimeter located in liquid nitrogen. It is found in the experiment that no stable measurement results can be obtained at 200 kHz and 5.0 MHz, which is mainly because when the frequency is 200 kHz, the capacitive reactance is too large and the measurement is seriously interfered; while 5.0 MHz might be too close to the inherent resonance frequency of the densimeter system, resulting in that the densimeter cannot work normally [13]. Therefore only three other frequencies will be discussed in the following context. The control experimental results are presented in Fig. 8. As the bulk shielding method is applied, the fluctuations are all within ±0.001 pF as shown in Fig. 8, i.e. ±1.0  103 pF at 500 kHz, ±0.3  103 pF at 800 kHz and ±0.2  103 pF at 1.0 MHz, respectively. The resolution of the densimeter increases with the frequency, because the low capacitive reactance at high frequency increases the anti-interference ability of the densimeter. The measured capacitances are 0.526 pF, 0.497 pF and 0.464 pF at the three frequencies, respectively, and this difference mainly results from the influence of the frequency and the parasitic capacitance. Theoretically, the effective capacitance, which is measured by the LCR meter, is related to the inductance and the frequency in addition to the capacitance of the densimeter system according to Eq. (6). The inductance of a specified densimeter system is usually considered to be a constant, so when the capacitance of the densimeter itself remains constant, the effective capacitance will increase with the frequency. However, the capacitance of the densimeter system includes not only the capacitance of the densimeter itself but also the parasitic capacitance of the densimeter system, which is constant during each experiment run but varies randomly in different experiment runs, so that the measured capacitances in various experiment runs normally differ even when liquid nitrogen, in which the densimeter is located, is at the same state. Thus, the change of the measured capacitance with the frequency is almost impossible to be predicted. 3.2.2. Influence of the frequency on the densimeter sensitivity According to Eq. (7), the effective sensitivity of the densimeter system is affected by the frequency of the applied voltage, and the influence of the frequency on the sensitivity is validated in the experiment. The non-differential type densimeter is calibrated at 500 kHz and 1.0 MHz, and the differential type at 1.0 MHz, respectively. When the state of liquid nitrogen in the dewar changes from the normal boiling point to the triple point by evacuating vapor nitrogen, 4–5 calibration points are used as references. At each calibration point, the pressure inside the dewar is kept constant for about 10 min to measure the pressure, the temperature and the capacitance, and then the pressure is decreased to the next calibration point. This procedure is repeated until the calibration of the densimeter system is finished. The agitator is running during the entire experiment to reduce the temperature stratification. According to the Clausius–Mossotti equation, as shown by Eq. (1), the specific dielectric constant of liquid nitrogen is related to its density, namely the state of liquid nitrogen, and therefore, the specific dielectric constant of liquid nitrogen at the calibration points can be obtained from the pressure and the temperature measured in the experiment. Then the sensitivities Sn and the reactive capacitances Cd of the densimeters in Eq. (2) at different frequencies are calculated by the lease squares method. The typical calibration process of the differential type densimeter system at the frequency of 1.0 MHz in liquid nitrogen is shown in Fig. 9. The measured capacitance increases with the decrease of the temperature as expected, and the resolution is high enough for the density measurement. The calibration results under varies

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80

6.00

Capacitance Temperature 76

C (pF)

72

68

5.90

Temperature (K)

5.95

64 5.85

0

50

100

150

Time (min) Fig. 9. Capacitance and temperature variations in the process of calibrating the differential type densimeter system at the frequency of 1.0 MHz.

5.5

1.0MHz, differential 1.0MHz, non-differential 500kHz, non-differential

5.4

C (pF)

C=3.718ε

measurement and the capacitance measurement accuracy of the LCR meter. The capacitance measured by the LCR meter is the total value of the capacitance of the densimeter itself and the parasitic capacitance. Because the densimeter is installed close to the agitator due to the dimension limitation of the dewar, the parasitic capacitance, furthermore the measured capacitance of the densimeter, will vary with the relative position of the densimeter and the agitator. It is found in the experiments that when the blades of the agitator stop at the different angles, the discrepancies of the measured capacitance are usually as high as 0.005 pF, which is quite large compared with the capacitance change in the experiments, resulting in serious errors of density measurement. If the agitator is running during the capacitance measurement, the discrepancies can be eliminated by averaging the measuring results. Furthermore, when the rotating speed of the agitator is lower than 75 rpm, most of solid particles in liquid nitrogen will deposit within less than one minute after the agitator stops, and serious errors will be caused by the uneven distribution of solid particles. Therefore, the agitator is kept working during the entire experiment, and its effect on the accuracy of density measurement can be ignored by averaging the measuring results. The capacitance measurement accuracy of the LCR meter used to measure the capacitance in this study is ±0.08%, which indicates that the relative error dC of the capacitance C in Eq. (2) is ±0.08%. The absolute error De of the specific dielectric constant calculated by Eq. (2) is expressed by

5.3

De ¼ 

ðC  C d ÞDSn þ Sn ðC  dC  DC d Þ

C=0.414ε

Therefore, in the case that De is known, the errors of the measured density and the measured solid volume fraction of slush nitrogen, dq and dus , can be calculated by

C=0.284ε 0.4

dq ¼  1.435

1.440

1.445

1.450

1.455

1.460

1.465

Specific Dielectric Constant ε 78

76

74

72

70

ð12Þ

S2n

0.6

68

qs  ql D ql es  qs el þ ðqs  ql Þe e

dus ¼  66

1

e  el

ð13Þ

ð14Þ

De

64

Temperature (K) Fig. 10. Calibration of the non-differential and differential type densimeters at the various frequencies.

conditions are presented in Fig. 10. For the non-differential type densimeter, the sensitivities are 0.284 pF at 500 kHz and 0.414 pF at 1.0 MHz respectively, indicating that the densimeter sensitivity increases with the frequency, corresponding to the theoretical analysis shown by in Eq. (7). The sensitivity of the differential type densimeter is 3.718 pF at 1.0 MHz, which is much higher than that of the non-differential type and slightly higher than the theoretical value of 3.156 pF, calculated by Eq. (4). Experimental results show that the capacitance-type densimeter system works normally when the frequency is in the range of 500 kHz–1.0 MHz, and the densimeter resolution and sensitivity both increases with the frequency. Consequently, the frequency of 1.0 MHz is applied to the capacitance-type densimeter system for higher sensitivity and higher resolution.

Only the differential type densimeter system improved with the bulk shield is considered here, and the frequency of the applied voltage (1.0 V) is 1.0 MHz. As the capacitance and the sensitivity of the densimeter system usually vary in different experiment runs because of the installation error, the average values from several experiments, presented in Table 3, are used for the uncertainty analysis. Consequently, the relative errors of the measured density and the measured solid volume fraction of slush nitrogen are ±0.25% and ±13.53%, respectively. That is to say, the capacitancetype densimeter system has a high accuracy. 3.4. Application of the capacitance-type densimeter system to slush nitrogen 3.4.1. Slush nitrogen generation Before the application of the capacitance-type densimeter system to slush nitrogen, the technique for producing homogeneous slush nitrogen by the self-pressurized freeze–thaw method is firstly investigated by taking the photographs of solid layers created on the liquid/vapor interface from the side observation

3.3. Uncertainty analysis of the densimeter system Since the performance of the densimeter system, including the resolution and the sensitivity, has been highly improved by the bulk shield, the accuracy of the densimeter system mainly depends on two different aspects, the effect of the agitator on the density

Table 3 The average vales used in the accuracy analysis. C

Sn

Cd

e

dC

DSn

DC d

5.965 pF

3.840 pF

0.396 pF

1.4587

±0.080%

±0.0256 pF

±0.0367 pF

Y.Y. Jiang, P. Zhang / Experimental Thermal and Fluid Science 35 (2011) 328–337

3.4.2. Application of the densimeter system to slush nitrogen According to the experimental result, slush nitrogen is produced at the discharge rate of 4L/s, and the time of the freeze and thaw cycles is 10 s and 5 s, and the agitator rotating speed is 30 rpm. The typical variation of the density of slush nitrogen in the production process, measured by the improved densimeter system with the bulk shield, is presented in Fig. 12 with both the density and the solid volume fraction of slush nitrogen. As can be clearly seen from Fig. 12, the solid volume fraction increases very slowly during the first 10 min of the production, and then it increases quickly. It is understood that the deposition of solid particles is considered to be the main reason for this. When the slush production has been proceeding continuously for more than 10 min, only a few solid particles are seen through the side observation windows. However, if the rotating speed of the agitator is

10mm

30 890 3

885

Discharge rate: 4L/s Freeze/Thaw time: 10/5s Agitator rotating speed: 30rpm LCR meter: 1.0MHz, 1.0V

25 20

880

15

875

10

Slush production

5

870 0 865 0

10

20

30

40

50

Solid volumetric fraction of SLN2 (%)

windows under various conditions. The agitator is stopped to avoid the created solid layers being broken, and the discharge rate and the time of the freeze and thaw cycles proper for this study are briefly discussed here. In addition to the production rate, the discharge rate plays an important role on the property of solid layers created on the liquid/vapor interface [14]. Fig. 11a is the solid layer created by evacuating the vapor continuously for 30 s at the discharge rate of 1L/s. The solid layer is about 10 mm in thickness, and its dense texture makes it difficult to be broken into solid particles. When the discharge rate is increased to 4L/s, it only takes 5 s to create a 25 mm thickness solid layer, as shown in Fig. 11b, which is porous and soft, and is easily broken into fine solid particles. Therefore, high discharge rate is usually applied in order to increase the production rate and to obtain homogeneous slush nitrogen. The morphology of solid layers depends strongly on the time of the freeze and thaw cycles as well, especially in the case of the high discharge rate. As previously stated, porous solid layers can be created at the high discharge rate. However, if the evacuation continues at this time, newly created solid nitrogen will fill in the lacunae of the solid layer, decreasing the porosity of the solid layer and changing its morphology into dense. On the other hand, if the thaw cycle is too short, solid nitrogen near the wall cannot melt enough and be submerged into the liquid in one freeze/thaw cycle. These solid layers will be refrozen in the next cycle, resulting in the texture of solid layers is changed from porous into dense. Actually, the proper time of the freeze and thaw cycles quite depends on the operating condition in the experiment. In this study, short time, such as 10 s for the freeze cycle and 5 s for the thaw cycle according to the experimental results is more appropriate for producing homogeneous slush nitrogen.

Measured density of SLN2 (kg/m )

336

-5

Time (min) Fig. 12. Variation of the measured density and solid volumetric fraction of slush nitrogen at the agitator rotating speed of 30 rpm during the production of slush nitrogen.

increased high enough at this time, it is observed that many solid particles are picked up by liquid nitrogen, which indicates that a lot of solid particles are deposited on the bottom of the dewar. In order to obtain the accurate density of slush nitrogen, the minimal agitator rotating speed necessary to keep slush nitrogen homogeneous must to be estimated. It is observed through the side windows that slush nitrogen is almost homogeneous when the agitator rotating speed is 75 rpm, so the measured results at 75 rpm is considered the average density of slush nitrogen. The minimal agitator rotating speed is determined in the following experiments, and the production of slush nitrogen at 30 rpm is taken for example here to elucidate the experimental procedure, which is divided into two parts, the production and the density measurement, and the agitator speeds are presented by xp and xm, respectively. After the state of liquid nitrogen reaches the triple point, slush nitrogen is produced at xp = 30 rpm firstly for a few minutes. Then the production is stopped and the density of slush nitrogen is measured by the densimeter system at xm = 30 rpm and xm = 75 rpm, respectively. After the measurement is finished, the rotating speed is decreased to xp = 30 rpm and the production of slush nitrogen is continued. This procedure is repeated until the density of slush nitrogen reaches the prescribed value. Since the heat leakage to slush nitrogen is small, it is reasonable to ignore the melting of solid nitrogen in the process of the density measurement. The measurement results are organized into two groups, xp = 30 rpm,

Liquid/vapor interface 25mm

Liquid/vapor interface

(a)

(b)

Fig. 11. Photographs of the solid layers taken through the side observation window: (a) solid layer created by evacuating the vapor for 30 s at the discharge rate of 1L/s and (b) solid layer created by evacuating the vapor for 5 s at the discharge rate of 4L/s.

Y.Y. Jiang, P. Zhang / Experimental Thermal and Fluid Science 35 (2011) 328–337

337

4. Conclusions

30

Solid volume fraction of SLN 2 (%)

Agitator Rotating Speed: ωp=30rpm, ωm=30rpm

25

ωp=30rpm, ωm=75rpm ωp=50rpm, ωm=50rpm ωp=50rpm, ωm=75rpm

20

ωp=75rpm, ωm=75rpm

15 10

LN2

SLN2-I

SLN2-II

5

±0.25% in density

0

Freeze/Thaw Time: 10/5s LCR Meter: 1.0MHz, 1.0V

-5 0

10

20

30

40

50

60

Time (min) Fig. 13. Variation of the solid volume fraction of slush nitrogen with time at different agitator rotating speed.

xm = 30 rpm and xp = 30 rpm, xm = 75 rpm, which are plotted in Fig. 13, respectively. The time spent on the density measurement has been subtracted from the total production time for the clear comparison. Slush nitrogen is produced and the density is measured in the same way when xp = 50 rpm. Based on the measurement results, the variation of the solid volume fraction with time can be separated into three periods, the period of liquid nitrogen at the triple point (LN2), the initial period of slush nitrogen production (SLN2-I) and the latter period of slush nitrogen production (SLN2-II), as shown in Fig. 13. When the state of liquid nitrogen is kept at the triple point, namely the LN2 period, the solid volume fractions measured under various conditions are all about zero, and the reliability and repeatability of the densimeter system are confirmed. In the case of xp = 30 rpm, the measured solid volume fraction at xm = 30 rpm is evidently lower than that at xm = 75 rpm and increases very slowly even when slush nitrogen is produced continuously in the SLN2-I period. And in the SLN2-II period, the solid volume fraction measured at xm = 30 rpm increases quickly and is finally larger than the results measured at xm = 75 rpm, and the discrepancy between them becomes larger with time. That is because during the initial period of slush nitrogen production, most of the solid particles are deposited in the region below the densimeter, and the measured result is less than the average solid volume fraction of slush nitrogen, namely the result measured at xm = 75 rpm. And when slush nitrogen is continuously produced, the region where solid particles are deposited expands in the vertical direction and submerges the densimeter, so the measured result is much higher than the average solid volume fraction. When slush nitrogen is produced at xp = 50 rpm, the measured results at xm = 50 rpm and xm = 75 rpm are almost the same, and is also constant with the results measured at xp = 75 rpm and xm = 75 rpm within the error range, indicating that slush nitrogen can be considered to be homogeneous at 50 rpm. It is also shown in Fig. 13 that under different agitator rotating speeds xp, the discrepancies between the measured results at xm = 75 rpm are less than ±0.25%. Therefore, the slush production rate is not evidently affected by the rotating speed of the agitator. Consequently, the relatively high rotating speed of the agitator, higher than 50 rpm in this study, is usually used to keep slush nitrogen homogeneous, and furthermore, to reduce the error of the density measurement caused by the deposition of solid particles.

The bulk shielding method based on the application of the double-shielded cables is employed to improve the performance of the capacitance-type densimeter system. By grounding the shielding layers of the double-shielded cables properly, the parasitic capacitance mainly caused by the cables is significantly reduced and the anti-interference ability is increased. The frequencies in the range from 500 kHz to 1.0 MHz can be applied to the densimeter system, and the sensitivity increases and the measuring fluctuation decreases with the increase of the frequency. The results of validation experiment show that the total capacitance of the densimeter and the cable is close to the capacitance of the densimeter itself, and the fluctuation of the capacitance measurement is within ±2.0  104 pF at the frequency of 1.0 MHz, and the typical sensitivity of the differential type densimeter is about 3.718 pF. The improved capacitance-type densimeter system with the bulk shield has a high accuracy of within ±0.25% for the density, and its reliability and repeatability are validated in the experiments. Slush nitrogen is produced by the self-pressurized freeze–thaw method at a discharge rate of 4L/s and the freeze and thaw cycle time of 10 s and 5 s, respectively, in order to obtain slush nitrogen containing fine solid particles. And in this process, the differential type densimeter system is applied to determining the density of slush nitrogen. Large error of slush density measurement is caused by the deposition of solid particles at the agitator rotating speed of 30 rpm, and therefore the rotating speed higher than 50 rpm is usually applied for high-accurate density measurement according to the experimental results. Acknowledgment This research is supported by the Fok Ying-Tong Education Foundation of China under the Contract No. 121056. References [1] D.B. Mann, P.R. Ludtke, C.F. Sindt, D.B. Chelton, Liquid–solid mixtures of hydrogen near the triple point, Advances in Cryogenic Engineering 11 (1966) 207–227. [2] R.O. Voth, Producing liquid–solid mixtures of hydrogen using an Auger, Cryogenics 25 (1985) 511–517. [3] M.S. Haberbusch, N.B. McNelis, Comparison of the Continuous Freeze Slush Hydrogen Production Technique to the Freeze/Thaw Technique, NASA, Glenn Research Center, 1996 (NASA/TM-107324). [4] K. Ohira, Study of production technology for slush hydrogen, Advances in Cryogenic Engineering 49 (2004) 56–63. [5] T. Takakoshi, M. Murakami, M. Ikeuchi, K. Matsuo, et al., PIV measurement of slush nitrogen flow in a pipe, Advances in Cryogenic Engineering 51 (2006) 1025–1032. [6] K. Matsuo, M. Ikeuchi, A. Machida, K. Yasuda, Fundamental study of pipe flow and heat transfer characteristics of slush nitrogen, Advances in Cryogenic Engineering 51 (2005) 1025–1032. [7] D.A. Ellerbruch, Microwave methods for cryogenic liquid and slush instrumentation, Advances in Cryogenic Engineering 16 (1971) 241–250. [8] A. Carapelle, J.P. Collette, Gamma-ray attenuation for measuring cryogenic slush mixture density, Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms 229 (1) (2005) 111– 116. [9] G.E. Turney, R.W. Snyder, Measurement of Liquid and Two-phase Hydrogen Densities with a Capacitance Density Meter, NASA, Glenn Research Center, 1969 (NASA-TN-D-5015). [10] K. Ohira, K. Nakamichi, Development of a high-accuracy capacitance-type densimeter for slush hydrogen, JSME International Journal, Series B 43 (2) (2000) 162–170. [11] J.W. Stewart, Dielectric polarizability of fluid para-hydrogen, Journal of Chemical Physics 40 (1964) 3297–3306. [12] H.W. Ott, Noise Reduction Techniques in Electronic Systems, second ed., John Wiley & Sons, New York, 1998. [13] L.K. Baxter, Capacitive Sensors: Design and Applications, Wiley-IEEE Press, New York, 1996. [14] C.F. Sindt, A summary of the characterization study of slush hydrogen, Cryogenics 10 (5) (1970) 372–380.