Experimental Measurement of JP-10 Viscosity at ... - ACS Publications

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX-XXX

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Experimental Measurement of JP-10 Viscosity at 242.7−753.3 K under Pressures up to 6.00 MPa Siyuan Gong,† Xiangwen Zhang,†,‡ Qincheng Bi,§ Zhaohui Liu,§ and Guozhu Liu*,†,‡ †

Key Laboratory for Green Chemical Technology of Ministry of Education, School of Chemical Engineering and Technology, and Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin University, Tianjin 300072, China § State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shanxi 710049, China ‡

S Supporting Information *

ABSTRACT: Viscosity under high temperatures and pressures is one of the most important thermophysical properties related to the heat-transfer calculation for fuel-cooled thermal management technology. The viscosities of a high-density hydrocarbon fuel JP-10 were measured using a two-capillary method at 242.7−753.3 K under 0.69−6 MPa. After the viscosity data of pure n-octane was measured and compared with the literature data, the measurement system was calibrated, and the average absolute deviation (AAD) and the maximum absolute deviation (MAD) were found to be 0.71% and 1.35%. Yaws’ equation and Bruno’s equation are used to correlate the experimental data. The results are that the correlation AAD for Yaws’ equation and Bruno’s equation are within 4.04% and 4.25% under all the test conditions, respectively.

1. INTRODUCTION JP-10 (exo-tricyclo[5.2.1.02,6]decane, C10H16), derived from the hydrogenation and isomerization of dicyclopentadiene, is used as a pure-component aviation turbine fuel because of its high volumetric energy density, high specific impulse, and low freezing point.1−4 With the development of fuel-cooled thermal management technology used in supersonic and hypersonic aircrafts, JP-10 also becomes a promising endothermic fuel as coolants to absorb aerodynamic heating.2 Viscosity is one of the most important thermophysical properties of a hydrocarbon fuel,5 and has a great influence on the fuel atomization in the combustor and heat-transfer estimation for the diesel engines. A higher viscous fuel will cause poor fuel atomization leading to bad engine performance because of its tendency to form large droplets, while a lower viscous fuel is more easily prone to fuel leakage than a higher viscous fuel.6,7 To better comprehensively evaluate the cooling performance of JP-10 in the engine, the viscosity property of JP-10 needs to be understood. Some researchers had reported the viscosity measurement of JP-10 with different methods. Bruno et al.1 measured the viscosities of JP-10 under temperatures range from 233.15 to 373.15 K and pressure of 84 kPa by applying the Stabinger viscodensimeter SVM3000 in the measurement system. Yang et al.8 made the binary mixtures of JP-10 + n-octane and JP-10 + n-decane, then measured the densities and viscosities of the two binary mixtures from 293.15 to 313.15 K at atmospheric pressure over the entire composition range. In 2009, they further conducted detailed measurements on density and viscosity at 298.15 K of the binary mixtures of JP-10 and diethyl carbonate © XXXX American Chemical Society

(DEC) over the whole composition range and vapor pressure at various temperatures.9 Then the same group measured the bubble-point vapor pressure, density, and viscosity of binary mixtures of JP-10 and methylcyclohexane (MCH) at several temperatures.10 While some relevant viscosity data of JP-10 are available now, the current data of JP-10 are concentrated under low temperature and different pressures, less data is reported under high temperatures and high pressures. In this paper, the viscosity data of JP-10 was presented from 242.7 to 753.3 K with pressures up to 6 MPa using a two-capillary viscosity measurement system which was calibrated by a pure fluid in advance, and the experiments were conducted in the State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University. Two correlation methods were used to compare with the experimental data which proved to be wellmatched.

2. EXPERIMENTAL SECTION 2.1. Experimental System. Experiments were performed in a two-capillary viscosity measurement system to achieve hydrocarbon fuels online viscosity measurement. The highest pressure of the system was 10 MPa. Test fluids were driven by a liquid chromatography pump (P230II) at a constant volume flow rate, the range of which was 0.01−9.99 mL/min. A low temperature circulation device (LHDT800) was used to test pressure Received: April 29, 2017 Accepted: October 13, 2017

A

DOI: 10.1021/acs.jced.7b00396 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 3. Experimental Viscosity ηexp of JP-10 under Test Pressure p = 0.69 MPa and Temperature T = 242.7−753.3 K and Comparison to Two Correlation Methods

Table 1. Information of Two Samples chemical name n-octane JP-10

source Sinopharm Chemical Reagent Company kerosene fuel

initial mole fraction purity

purification method

0.995

distillation

Ta

ηexpb

0.995a

distillation

K

μPa·s

Table 2. Experimental and Reference Viscosity Data of n-Octane under Test Pressure p = 5.10 MPa, Temperature T = 303.2−553.4 K and Deviations for n-Octane Ta

ηexpb

ηlitb

K

μPa·s

μPa·s

ADc

%

303.2 353.1 403.2 453.1 503.0 553.4

501.4 307.8 207.0 146.5 104.9 69.2

506.2 308.7 208.8 147.1 103.5 69.5

4.8 0.9 1.8 0.6 −1.4 0.3

0.95 0.29 0.86 0.41 −1.35 0.43

RDc

a

Standard uncertainties u in temperature and pressure are u(T) = 0.27K, u(p) = 0.008 MPa, respectively, and the combined expanded uncertainty UC is UC(η) = 2.30 μPa·s (0.95 level of confidence). bηexp represents the experimental value and ηlit represents the literature value. cAD represents the absolute deviation and RD represents the relative deviation.

drop under a low temperature range while a molten salt thermostatic bath, made up of 60 wt % NaNO3 and 40 wt % KNO3, was used to achieve a high temperature test, and all the thermostats were automatically controlled by a PID regulator (SHIMADEN FP23) together with a DC power. The external diameter and nominal diameter of experimental capillaries, made of quartz, were 1/32 in. and 0.25 mm, respectively, and each capillary, with a length of 3000 mm, was coiled 17.5 times to form a helix, the height and curvature diameter of which were about 50 mm and 50.8 mm. In this viscosity measurement system, the data of pressure drop and fluid temperature were measured. On the basis of the Hagen-Poiseuille’s Law in a laminar flow, the viscosity of the test fluid could be calculated by combining the pressure drop of upstream and downstream, structure size of capillaries, and density of fluid.

10688.1 5780.2 2478.8 1996.3 1680.1 1141.7 886.8 706.5 526.7 417.2 360.5 312.3 225.5 205.4 160.2 130.9

573.4 593.2 613.6 633.4 653.3 673.3 692.5 713.8 734.0 753.3

30.4 32.4 28.8 33.8 27.7 26.5 31.1 27.6 30.3 32.4

RDYawsc

RDBrunoc

μPa·s

μPa·s

%

%

−2.87 4.62 1.66 5.86 −9.14 0.29 −0.69 −2.26 4.52 6.38 0.14 −5.71 6.92 −3.84 0.90 1.11

−2.61 4.07 0.98 5.23 −9.53 −0.01 −0.90 −2.44 4.30 6.08 −0.24 −6.15 6.32 −4.42 0.30 0.58

a

Standard uncertainties u in temperature and pressure are u(T) = 0.27 K, u(p) = 0.008 MPa, respectively, and the combined expanded uncertainties UC are UC(η) = 0.10η for liquid phase and UC(η) = 2.52 μPa·s for gas phase (0.95 level of confidence). bηexp represents the experimental values; ηcorr, Yaws and ηcorr, Bruno represent the correlation values by Yaws’ equation and Bruno’s equation, respectively. cRDYaws is the relative deviation calculated from Yaws’ equation and RDBruno is calculated from Bruno’s equation.

ηT ηT

=

Δpdown ρT Zup, T0 Δpup ρT Zdown, T

0

4

Δp 1 π Δp R = η= 8 L Q Q Z

242.7 262.4 303.2 313.1 333.2 353.1 373.1 393.2 413.2 433.2 453.1 473.2 493.2 513.2 533.2 552.9

ηcorr, Brunob

Liquid Phase; Pa/MPa = 0.69 10381.2 10409.4 6047.2 6015.2 2520.0 2503.0 2113.3 2100.6 1526.5 1520.0 1145.0 1141.6 880.7 878.8 690.6 689.3 550.5 549.3 443.8 442.6 361.0 359.6 294.5 293.1 241.1 239.8 197.5 196.3 161.6 160.7 132.4 131.7 Gas Phase; Pa/MPa = 0.69

a

The initial mole fraction purity of the sample of JP-10 is 0.995 which still contains adamantane (0.004 mole fraction) and the endoisomeric modification of JP-10 (0.001 mole fraction).

ηcorr, Yawsb

(2)

0

where ρ represents the density of test fluid, Δpup and Δpdown represents the pressure drop of the upstream and downstream capillaries. As the quartz capillary expansion coefficient is small, the influence of thermal expansion can be ignored. So eq 2 can be simplified as

(1)

where Q represents the volume flow rate, R represents the internal radius of the capillary tube, L represents length of the tube, Δp represents pressure drop of the length L, η represents fluid viscosity, Z represents structure coefficient of experimental capillary which is a function of internal radius R and length L. Two quartz capillaries of the same size were put in the upstream and downstream of the measurement system, the expansion coefficient of which was so small that it could be ignored. First, the both of the two capillaries were put in a thermostatic bath at constant reference temperature T0. Then the temperature of the downstream thermostatic bath was controlled to a design value T, while the upstream thermostatic bath temperature was still T0. With same mass flow rate and the viscosity formula being combined, the expression could be

Δpdown ρT ⎛ Zup, T0 Zdown, T0 ⎞ Δpdown ρT ⎟⎟ ≈ η ⎜⎜ T0 0 Δp ρT ⎝ Zdown, T0 Zdown, T ⎠ Δpup ρT up 0 0

ηT = ηT

(3)

Through this deduced equation, the viscosity data of the test fluid could be calculated, and the combined relative standard uncertainty of the experimental viscosity measurement of JP-10 could be ur2(ηT ) = ur2(ηT ) + ur2(Δpdown, T ) + ur2(Δpup, T ) + ur2(ρT ) 0

+ B

ur2(ρT ) 0

0

(4) DOI: 10.1021/acs.jced.7b00396 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Figure 1. Measured viscosity data of JP-10 varies with temperature from 242.7 to 753.3 K under 0.69 MPa.


Table 4. Experimental Viscosity ηexp of JP-10 under Test Pressure p = 1.70 MPa and Temperature T = 242.7−753.3K and Comparison to Two Correlation Methods


Ta

ηexpb

K

μPa·s

242.7 262.4 303.2 313.2 333.2 353.2 373.1 393.1 413.1 433.1 453.1 473.2 493.2 513.2 533.2 552.9 573.4

10728.3 5820.1 2482.9 2026.1 1700.8 1164.7 906.8 726.5 551.8 437.2 400.5 300.3 255.2 220.4 180.9 150.9 125.4

593.2 613.6 633.4 653.3 673.3 692.5 713.8 734.0 753.3

39.4 38.9 37.1 32.8 30.2 32.1 29.4 32.4 35.2

ηcorr, Yawsb

ηcorr, Brunob

RDYawsc

RDBrunoc

μPa·s

μPa·s

%

%

−3.25 4.58 2.84 5.61 −8.79 −0.01 −0.76 −2.32 3.15 5.78 −5.23 4.37 2.03 −1.55 0.12 0.46 0.36

−2.98 4.17 2.20 4.99 −9.22 −0.36 −1.02 −2.53 2.94 5.56 −5.48 4.04 1.63 −2.00 −0.41 −0.11 −0.23

Liquid Phase; Pa/MPa = 1.70 10380.0 10408.7 6086.8 6063.0 2553.4 2537.5 2139.7 2127.3 1551.3 1544.0 1164.6 1160.5 899.9 897.5 709.6 708.1 569.2 568.0 462.5 461.5 379.5 378.6 313.4 312.4 260.4 259.4 217.0 216.0 181.1 180.2 151.6 150.7 125.8 125.1 Gas Phase; Pa/MPa = 1.70

a

Standard uncertainties u in temperature and pressure are u(T) = 0.27 K, u(p) = 0.008 MPa, respectively, and the combined expanded uncertainties UC are UC(η) = 0.10η for liquid phase and UC(η) = 2.52 μPa·s for gas phase (0.95 level of confidence). bηexp represent the experimental values, ηcorr, Yaws and ηcorr, Bruno represent the correlation values by Yaws’ equation and Bruno’s equation, respectively. cRDYaws is the relative deviation calculated from Yaws’ equation and RDBruno is calculated from Bruno’s equation.

Figure 3. Measured viscosity data of JP-10 varies with temperature from 242.7 to 753.3 K under 3.00 MPa. C



Article

Table 5. Experimental Viscosity ηexp of JP-10 under Test Pressure p = 3.00 MPa and Temperature T = 242.7 to 753.3 K and Comparison to Two Correlation Methods Ta

ηexpb

K

μPa·s

242.7 262.5 303.1 313.2 333.1 353.1 373.2 393.0 412.9 433.1 453.2 473.2 493.2 513.2 533.4 553.5 573.4 593.3 613.0 633.3 653.4 672.3 692.5 713.8 734.0 753.3

10795.8 5827.6 2490.0 2146.3 1708.8 1233.7 946.7 736.5 581.1 477.6 390.3 320.4 275.2 226.4 183.7 150.2 135.4 115.4 101.6 97.7 89.8 80.4 76.8 68.9 64.5 62.8

phase liquid

↓

subcritical

ηcorr, Yawsb

ηcorr, Brunob

RDYawsc

RDBrunoc

μPa·s

μPa·s

%

%

9643.9 6172.9 2780.9 2329.2 1678.1 1238.9 935.0 723.5 569.8 455.1 369.8 305.2 255.2 216.2 184.9 160.0 140.0 123.6 110.3 98.8 89.4 81.8 75.0 68.9 64.0 60.0

−9.50 5.78 10.85 7.81 −2.15 0.41 −0.91 −1.17 −1.15 −3.84 −4.36 −3.89 −6.51 −3.91 1.11 6.80 3.49 7.08 8.34 0.91 −0.71 1.66 −2.26 0.45 0.14 −3.04

−10.67 5.93 11.68 8.52 −1.79 0.42 −1.24 −1.76 −1.94 −4.72 −5.26 −4.76 −7.25 −4.52 0.65 6.51 3.40 7.15 8.54 1.15 −0.50 1.77 −2.36 −0.01 −0.79 −4.51

Pa/MPa = 3.00 9770.2 6164.4 2760.1 2314.0 1672.1 1238.8 938.1 727.9 574.4 459.3 373.3 307.9 257.3 217.6 185.7 160.4 140.1 123.6 110.1 98.6 89.2 81.7 75.1 69.2 64.6 60.9

a Standard uncertainties u in temperature and pressure are u(T) = 0.27 K, u(p) = 0.008 MPa, respectively, and the combined expanded uncertainties UC are UC(η) = 0.10η (0.95 level of confidence). bηexp represent the experimental values, ηcorr, Yaws and ηcorr, Bruno represent the correlation values by Yaws’ equation and Bruno’s equation, respectively. cRDYaws is the relative deviation calculated from Yaws’ equation and RDBruno is calculated from Bruno’s equation.

conducted on a two-capillary viscometer. The experimental viscosity data were compared with the literature data from NIST database.13,14 To evaluate those data better, the absolute deviation (AD), the relative deviation (RD), the average absolute deviation (AAD), and the maximum absolute deviation (MAD) were defined and calculated. The detailed experimental and reference viscosity data and deviations for n-octane under 5.10 MPa and temperature from 303.2 to 553.4 K are shown in Table 2. The AAD and MAD for the measured viscosity data of n-octane are 0.71% and 1.35%, which shows a good accuracy of the viscosity measurement system.

In this work, the temperature was measured in the range of 242.7−753.3 K with a standard uncertainty of 0.27 K, and the operating pressure was from 0.69 to 6 MPa with a standard uncertainty of 0.008 MPa. The standard uncertainty of pressure drop was controlled to ±0.134 kPa under a total scale of 0.248 MPa. The viscosity and density data of reference fluid were referred to the NIST Standard Reference Database, and the standard uncertainty of density of the test fluid was 0.15%− 1.14%. Detailed density measurement information can be found in the Supporting Information. Then, the combined relative expansion uncertainty of viscosity measurements was calculated with eq 4 as 0.88 %−2.40 % (coverage factor k = 2). The detailed structure and operation of the experimental system and concrete theory deduction can be found in a previous work of Yang et al.11,12 2.2. Experimental Material. The calibration fluid pure n-octane with purity higher than 99.5% was supplied by Sinopharm Chemical Reagent Company, and the fluid viscosity data under different conditions can be easily obtained from the literature.13,14 Pure exo-tricyclo[5.2.1.02,6]decane is the detailed composition of JP-10, the critical pressure and temperature of which were measured to be 3.73 MPa and 698 K.1 The detailed information on the two samples is shown in Table 1. 2.3. Calibration. The viscosity measurement of pure n-octane under a pressure of 5.1 MPa and temperature from 303.2 to 553.4 K was used to verify the accuracy of the experiment

AD = ηexp − ηlit RD% =

AAD =

ηexp − ηlit ηlit 100 n

(5)

100 (6)

n

∑ abs(RDi) i=1

MAD = max(abs(RDi ))

(7) (8)

3. RESULTS AND DISCUSSION After measuring the viscosity of pure n-octane, the accuracy of the experimental system was verified and the viscosity data of D



Article

Table 6. Experimental Viscosity ηexp of JP-10 under Test Pressure p = 6.00 MPa and temperature T = 242.7−753.3 K and Comparison to Two Correlation Methods Ta

ηexpb

K

μPa·s

242.7 262.5 303.1 313.2 333.1 353.1 373.2 393.4 413.1 433.2 453.1 473.1 493.1 513.1 533.4 553.3 573.3 593.2 613.4 633.3 653.5 673.2 692.5 713.8 734.0 753.3

phase

10825.0 5887.6 2497.7 2186.2 1757.8 1267.7 978.9 766.1 602.8 499.2 432.1 367.5 305.5 296.4 213.9 189.9 155.4 145.3 131.6 117.7 99.1 95.6 92.7 88.9 84.4 82.8

liquid

↓ subcritical

ηcorr, Yawsb

ηcorr, Brunob

RDYawsc

RDBrunoc

μPa·s

μPa·s

%

%

10135.8 6195.7 2713.4 2277.6 1659.4 1247.1 962.3 759.3 614.4 503.5 419.4 353.4 300.9 258.6 223.5 195.1 171.1 150.9 133.4 118.5 105.5 94.3 84.7

−6.56 4.79 8.49 4.16 −5.42 −1.29 −1.28 −0.45 2.35 1.18 −2.75 −3.80 −1.61 −12.97 4.10 2.23 9.53 3.33 0.94 0.47 6.45 −0.95 −7.85

−6.37 5.23 8.63 4.18 −5.60 −1.62 −1.70 −0.89 1.93 0.86 −2.94 −3.84 −1.50 −12.75 4.50 2.72 10.10 3.85 1.35 0.70 6.41 −1.35 −8.63

Pa/MPa = 6.00 10115.1 6169.5 2709.7 2277.1 1662.5 1251.4 966.4 762.7 616.9 505.1 420.2 353.5 300.6 257.9 222.7 194.1 170.2 150.1 132.8 118.3 105.5 94.7 85.4

supercritical

a Standard uncertainties u in temperature and pressure are u(T) = 0.27 K, u(p) = 0.008 MPa, respectively, and the combined expanded uncertainties UC are UC(η) = 0.10η (0.95 level of confidence). bηexp represent the experimental values, ηcorr, Yaws and ηcorr, Bruno represent the correlation values by Yaws’ equation and Bruno’s equation, respectively. cRDYaws is the relative deviation calculated from Yaws’ equation and RDBruno is calculated from Bruno’s equation.

Table 7. Regression Values of Adjustable Parameters and the Correlation Coefficient of Yaws’ Equation under Different Pressures and the Deviations between the Experimental Data and Results Fitted by Yaws’ Equation parameter

P = 0.69 MPa

P = 1.70 MPa

P = 3.00 MPa

P = 6.00 MPa

A B (K) C (K−1) D (K−2) R2 AAD MAD

−1.3621 979.7237 0.00743 −7.8385 × 10−6 0.998 3.56% 9.14%

−0.8045 919.8118 0.0057 −5.9862 × 10−6 0.999 3.01% 8.79%

3.2546 425.3511 −0.0049 2.9191 × 10−6 0.999 3.78% 10.85%

1.3405 663.5607 −0.000155 −5.4124 × 10−7 0.998 4.04% 12.97%

573.4 K and between 573.4 and 592.5 K under pressures of 0.69 and 1.70 MPa, respectively. It could be speculated that phase changes happened and the boiling points of test fluid JP-10 were between the two periods. That the boiling point increases with increasing pressure is just consistent with the trend. From Figure 3 and Table 5, the data were found continuous under 3.00 MPa, so it could be guessed that when the pressure reaches 3.00 MPa, a pressure close to the critical pressure 3.73 MPa of JP-10, the boiling point Tb is so high that the test fluid JP-10 has become a subcritical state. And from Figure 4 and Table 6 under 6.00 MPa, beyond the critical pressure, the phase changes from liquid to supercritical fluid and the decrease of viscosity is a continuous gradual process. As ref 1 reported, Bruno et al. measured the viscosities of JP-10 under temperatures ranging from 233.15 to 373.15 K

JP-10 were determined by this system subsequently. To test and verify the validation of measured data, two correlation methods were used which proved to be well-matched. 3.1. Viscosity Data. The viscosity of JP-10 was measured by a modified two-capillary viscometer at temperature from 242.7 to 753.3 K under pressure from 0.69 to 6.00 MPa. The detailed data are shown in Tables 3−6, and the viscosity data varies with temperature under 0.69, 1.70, 3.00, and 6.00 MPa as shown in Figures 1, 2, 3, and 4, respectively. As the results indicate, the viscosity decreases with the increase of test temperature and the lower the temperature is, the faster the viscosity decreases. At the same temperature, the viscosity increases with the test pressure increasing. From Figures 1 and 2 and Tables 3 and 4, it can be seen that there are sharp decreases of the viscosity data between 552.9 and E



Article

Table 8. Regression Values of Adjustable Parameters and the Correlation Coefficient of Bruno’s Equation under Different Pressures and the Deviations between the Experimental Data and Results Fitted by Bruno’s Equation parameter

P = 0.69 MPa

P = 1.70 MPa

P = 3.00 MPa

P = 6.00 MPa

β1 β2 β3 β4 R2 AAD MAD

5.5510 −0.1277 3.1656 −1.0872 0.998 3.38% 9.53%

6.0173 −0.08702 2.7582 −0.8966 0.999 2.93% 9.22%

14.4343 0.6328 −0.4929 0.1573 0.999 4.15% 11.68%

8.7488 0.1581 1.2447 −0.3057 0.998 4.25% 12.75%

3.2. Viscosity Correlation. There are many correlation formulas about viscosity in the literature to describe it as a function of temperature, in which the most used expressions are two equations proposed by Vogel15 and Yaws,16 respectively. Bruno et al. found that the Vogel−Tammann−Fulcher (VTF) equation is inadequate to describe their data of JP-10 measured under 84 kPa from 233.15 to 373.15 K; therefore they combined the reduced absolute viscosity and the reduced absolute temperature to develop a new expression eq 10 which proved to fit well. To understand and verify the viscosity data of JP-10 under a larger range of conditions, the two following equations were adopted to correlate those data. B log10 η = A + + CT + DT 2 (9) T

Figure 5. Degree of agreement between measured viscosity data and regression data of JP-10 through Yaws’ equation under different pressures: ■, 0.69 MPa; ●, 1.70 MPa; ▲, 3.00 MPa; ▼, 6.00 MPa.

⎛ β ⎞ η 1 = exp⎜⎜ + β3Tr + β4 Tr ⎟⎟ η0 ⎝ Tr + β2 ⎠

(10)

where A, B, C, D and β1, β2, β3, β4 are the adjustable parameters, viscosity η is in mPa·s, and temperature T is in K. For the viscosity data of JP-10 measured under 0.69 MPa and temperature from 242.7 to 753.3 K, eq 9 (proposed by Yaws) is used and the regression values of four adjustable parameters A, B, C, and D are −1.3621, 979.7237, 0.00743, and −7.8385 × 10−6, respectively. The correlation coefficient R2 is 0.997, and the detailed correlating data and RD are shown in Table 3. The deviations described above between the experimental data and results fitted by eq 9 were calculated, among which the AAD is 3.56% and the MAD is 9.14%. The other correlating viscosity data under different pressures are shown in Tables 4−6. The detailed regression information and deviations are shown in Table 7. And the degree of agreements between measured viscosity data and regression data through Yaws’ equation under 0.69, 1.70, 3.00, 6.00 MPa are shown in Figure 5. Figure 6 shows deviations of the fitted viscosity data through Yaws’ equation and the experimental data. It can be seen that the majority of points under four different pressures are located in ±6% error band. The expression proposed by Bruno et al. was also used to do the correlation. For the same measured viscosity data of JP-10 under 0.69 MPa and temperature from 242.7 to 753.3 K, the regression values of the adjustable parameters β1, β2, β3, and β4 are 5.5510, −0.1277, 3.1656, and −1.0872, respectively, and the correlation coefficient R2 is 0.997, which shows a good agreement between the expression and the measured data. To compare the experimental data and results fitted by eq 10, those deviations were calculated and the AAD and MAD are 3.48% and 8.39%, respectively. The other correlating viscosity data by eq 10 under different pressures are shown in Tables 4−6. The detailed regression values of β1, β2, β3, and β4, the correlation coefficient R2,

Figure 6. Deviations (ηfit/ηexp − 1) of the measured viscosity data and regression data of JP-10 through Yaws’ equation: ■, 0.69 MPa; ●, 1.70 MPa; ▲, 3.00 MPa; ▼, 6.00 MPa.

and a pressure of 84 kPa using the Stabinger viscodensimeter SVM3000 in the measurement system. After the data measured by Bruno et al. and the present measurements were compared, the viscosity data under 84 kPa was found a little higher than that under 0.69 MPa which was contrary to the trend that the viscosity increases with the operating pressure increasing. The most possible reason is that the sample of JP-10 used by Bruno et al. contained JP-10 (0.965 mole fraction), adamantane (0.010 mole fraction), and the endoisomeric modification of JP-10 (0.025 mole fraction), but our sample contained a higher purity of JP-10 (0.995 mole fraction), adamantane (0.004 mole fraction) and the endoisomeric modification of JP-10 (0.001 mole fraction). And adamantane is a good synthetic raw material for lubricants and can be used to prepare advanced lubricants which has a higher viscosity than JP-10. Therefore, the higher mole fraction of adamantane may lead to the deviations. With the critical temperature 698 K of JP-10 further considered, the data range from 242.7 to 552.9 K under 0.69 MPa, 242.7 to 573.4 K under 1.70 MPa, 242.7 to 753.3 K under 3.00 MPa, and 242.7 to 692.5 K under 6.00 MPa were correlated. F



Article

0.69 to 6.00 MPa. The viscosity measurement system was calibrated by measuring the viscosity data of pure n-octane under a pressure of 5.1 MPa and temperature from 303.2 to 553.4 K, then compiled with the literature data. The AAD and MAD for the measured viscosity of n-octane are 0.71% and 1.35% which shows good accuracy of this system. Two correlation methods, Yaws’ equation and Bruno’s equation, were used to test the validation of measured data of JP-10. For the Yaws’ equation, the AADs between experimental viscosity data and fitted data under pressure of 0.69, 1.70, 3.00, and 6.00 MPa are 3.56%, 3.01%, 3.78%, and 4.04%, respectively, and for Bruno’s equation, the AADs are 3.38%, 2.93%, 4.15%, 4.25% between experimental viscosity data and fitted data, respectively.

and the deviations are shown in Table 8. Also the degree of agreements between measured viscosity data and regression data through Bruno’s equation under 0.69, 1.70, 3.00, and 6.00 MPa are shown in Figure 7. Deviations between the fitted viscosity

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00396.

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Example of experimental density of JP-10 (PDF)

AUTHOR INFORMATION

Corresponding Author

Figure 7. Degree of agreement between measured viscosity data and regression data of JP-10 through Bruno’s equation under different pressures: ■, 0.69 MPa; ●, 1.70 MPa; ▲, 3.00 MPa; ▼, 6.00 MPa.

*E-mail: [email protected]. Tel./Fax: +86-22-85356099. ORCID

Guozhu Liu: 0000-0003-2193-5289

data through Bruno’s equation and the experimental data are shown in Figure 8 where the majority of points are within ±6% of the error band.

Funding

The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (21522605). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Bruno, T. J.; Huber, M. L.; Laesecke, A.; Lemmon, E. W.; Perkins, R. A. Thermochemical and Thermophysical Properties of JP-10. NIST: Gaithersburg, MD, 2006. (2) Xing, Y.; Fang, W.; Xie, W.; Guo, Y.; Lin, R. Thermal Cracking of JP-10 under Pressure. Ind. Eng. Chem. Res. 2008, 47, 10034−10040. (3) Gao, C. W.; Vandeputte, A. G.; Yee, N. W.; Green, W. H.; Bonomi, R. E.; Magoon, G. R.; Wong, H.-W.; Oluwole, O. O.; Lewis, D. K.; Vandewiele, N. M.; Van Geem, K. M. JP-10 combustion studied with shock tube experiments and modeled with automatic reaction mechanism generation. Combust. Flame 2015, 162, 3115−3129. (4) Davidson, D.; Horning, D.; Oehlschlaeger, M.; Hanson, R. The decomposition products of JP-10. 37th Joint Propulsion Conference and Exhibit, Salt Lake City, Utah, 8−11 July, 2001. (5) Deng, H. W.; Zhang, C. B.; Xu, G. Q.; Zhang, B.; Tao, Z.; Zhu, K. Viscosity Measurements of Endothermic Hydrocarbon Fuel from (298 to 788) K under Supercritical Pressure Conditions. J. Chem. Eng. Data 2012, 57, 358−365. (6) Duncan, A. M.; Pavlicek, N.; Depcik, C. D.; Scurto, A. M.; Staggwilliams, S. M. High-Pressure Viscosity of Soybean-Oil-Based Biodiesel Blends with Ultra-Low-Sulfur Diesel Fuel. Energy Fuels 2012, 26, 7023−7036. (7) Freitas, S. V. D.; Segovia, J. J.; Martín, M. C.; Zambrano, J.; Oliveira, M. B.; Lima, Á . S.; Coutinho, J. A. P. Measurement and prediction of high-pressure viscosities of biodiesel fuels. Fuel 2014, 122, 223−228. (8) Yang, F.; Guo, Y.; Xing, Y.; Li, D.; Fang, W.; Lin, R. Densities and Viscosities of Binary Mixtures of JP-10 with n-Octane or n-Decane at Several Temperatures. J. Chem. Eng. Data 2008, 53, 2237−2240. (9) Xing, Y.; Fang, W.; Li, D.; Guo, Y.; Lin, R. Density, Viscosity, and Vapor Pressure for Binary Mixtures of Tricyclo [5.2.1.02.6] Decane and Diethyl Carbonate. J. Chem. Eng. Data 2009, 54, 1865−1870.

Figure 8. Deviations (ηfit/ηexp − 1) of the measured viscosity data and regression data of JP-10 through Bruno’s equation: ■, 0.69 MPa; ●, 1.70 MPa; ▲, 3.00 MPa; ▼, 6.00 MPa.

Both of the correlation methods have shown good accuracy on viscosity data of JP-10 and it can be seen that the figure plots by the two methods are very close, which just illustrates the validation of them. When the two formulas are compiled, the accuracy is similar under low pressures, but under high pressure, near and over critical pressure, the Yaws’ equation is a little better than Bruno’s equation.

4. CONCLUSION Using a modified two-capillary viscosity measurement system, the viscosities of a promising endothermic fuel JP-10 were measured at temperatures from 242.7 to 753.3 K under pressure from G



Article

(10) Xing, Y.; Yang, X.; Fang, W.; Guo, Y.; Lin, R. Measurement on vapor pressure, density and viscosity for binary mixtures of JP-10 and methylcyclohexane. Fluid Phase Equilib. 2011, 305, 192−196. (11) Yang, Z.; Bi, Q.; Feng, S. Viscosity Measurement of Endothermic Fuels at Temperatures from 303 to 673 K and Pressures up to 5.00 MPa. J. Chem. Eng. Data 2016, 61, 3472−3480. (12) Yang, Z.; Liu, Z.; Bi, Q.; Feng, S.; Pan, H.; Guo, Y. Viscosity measurements of hydrocarbon fuel at temperatures from (303.2 to 513.2)K and pressures up to 5.1 MPa using a two-capillary viscometer. Thermochim. Acta 2015, 617, 1−7. (13) Huber, M. L.; Laesecke, A.; Xiang, H. W. Viscosity correlations for minor constituent fluids in natural gas: n-octane, n-nonane and ndecane. Fluid Phase Equilib. 2005, 224, 263−270. (14) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23, NIST Reference Fluid Thermodynamic and Transport Properties, REFPROP, version 9.0; Standard Reference Data Program; National Institute of Standards and Technology: Gaithersburg, MD, 2010. (15) Seeton, C. J. Viscosity−temperature correlation for liquids. Tribol. Lett. 2006, 22, 67−78. (16) Yaws, C. L. Transport Properties of Chemicals and Hydrocarbons; Elsevier; Oxford, 2014.

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