Viscosity Measurement of Endothermic Fuels at Temperatures from

Article pubs.acs.org/jced

Viscosity Measurement of Endothermic Fuels at Temperatures from 303 K to 673 K and Pressures up to 5.00 MPa Zhuqiang Yang,† Qincheng Bi,*,‡ and Song Feng‡ †

School of Energy and Power Engineering, Dalian University of Technology, Dalian, Liaoning 116023, People’s Republic of China State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China

‡

ABSTRACT: To meet the requirement of hydrocarbons online viscosity measurement at high temperatures and high pressures, two different methods are proposed in a two-capillary viscometer based on the Hagen−Poiseuille theory. Referenced flow method (RFM) measures the pressure drop, mass flux, and density ratios of the test and referenced fluid in a two-capillary system, and then calculates the test viscosity from the ratio relations regardless of the tube parameters. In another thermal expansion method (TEM), the fluid viscosity is obtained in a two-capillary process by measuring the pressure drop ratio, density ratio, and thermal expansion of a capillary tube. Note that mass flux and referenced fluid are no longer required in TEM. Pure n-dodecane and a binary mixture of n-heptane and n-octane were adopted respectively to validate the reliability and accuracy of the two methods. Results showed that the average absolute deviation (AAD) was lower than 0.75% and the maximum absolute deviation (MAD) was within 2.2%. Finally, viscosities of two endothermic fuels were obtained using the two-capillary viscometer at temperatures from (303.2 to 673.2) K and pressures up to 5.00 MPa. Accordingly, a viscosity relation formula as a function of temperature for two fuels was given within 4.2% deviation.

1. INTRODUCTION The thermal management of high-temperature propulsion components of scramjet engines has become a crucial issue.1,2 In all emerging cooling technologies, the regenerative cooling system using the “endothermic fuel”3 onboard to meet the cooling requirements attracts significant research interests. Endothermic fuel is used not only as propellant for the scramjet with a high heat sink, high density, and excellent stability, but also as a primary coolant absorbing excessive aerodynamic heat by its endothermic cracking reactions.4−6 Properties of these endothermic fuels such as heat sink capacity,7,8 thermochemical and physical properties,9−14 combustion process,15,16 and heat transfer characteristics17,18 have been under study. As an important thermophysical parameter, the viscosity of the fuel was valued in the flow Reynolds number and kinetic modeling in the cooling process. It was an indispensable part in the theoretical analysis and numerical simulation for the endothermic fuels. Boned et al.19 investigated the viscosities of two synthetic hydrocarbons made of heavy petroleum distillations at (293.15 to 343.15) K and pressure up to 100 MPa by a falling-body viscometer. Bruno et al.20,21 successively investigated the viscosities of Jet Propellant-10 (JP-10) fuel and aviation fuel mixtures of Jet-A using a commercial viscometer SVM3000 at temperatures from (233.15 to 373.15) K and pressure of (0.083−0.084) MPa. A viscosity calculation model was then established for the fuels based on their experimental data. Tate et al.22 modified the Saybolt viscometer and measured three biodiesel fuels at temperature up to 573 K. Outcalt et al.23 studied the viscosities of Jet Propellant fuels RP-1 and RP-2 with a gravity-type capillary viscometer, in © XXXX American Chemical Society

which the test temperature was (293.15−373.15) K and test pressure was technical atmosphere. More recently, Gascoin et al.12 realized the kinematic viscosity measurement of pure and multispecies hydrocarbons based on the fluid permeation through characterized porous media. The designed viscometer could be applied under pyrolysis reactions. On the basis of these experimental works, many test technology and viscosity data of hydrocarbons were obtained. However, few data for representative fuels could be available above 400 K. Accordingly, the present work proposed a modified two-capillary viscometer to obtain the viscosities of endothermic fuels at higher temperatures and pressures. The two-capillary viscometer was first proposed by Berg et al.24,25 for measurements on gas samples. Further optimization research for the connecting tubing in a two-capillary viscometer was conducted by Zhang et al.,26 who found that the systematic error of viscometer would diminish with a decrease in Dean Number. Then the two-capillary viscosity methodology was developed for the liquids viscosity measurement.13,27 In our previous work,13 a novel two-capillary viscosity system was established, and the viscosity of kerosene-type hydrocarbon fuel was measured at a temperature from (303.2 to 513.2) K and supercritical pressures. In the present paper, the two-capillary viscometer system was upgraded, in which the measurement temperature further increased to 673.2 K. Two different methods were proposed Received: May 13, 2016 Accepted: September 15, 2016

A

DOI: 10.1021/acs.jced.6b00391 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

for the liquid and supercritical fluid viscosity measurement. After calibration, the viscosities of two endothermic fuels were measured through the two methods at a temperature from (303.2 to 673.2) K and pressures up to 5.00 MPa. Eventually, a nonlinear regression method was used to fit the experimental data of two fuels to Yaws’ viscosity equation.28

Table 1. Description of Samples chemical name n-dodacane n-heptane n-octane

2. EXPERIMENTAL SECTION 2.1. Methodology and Procedure. Prior to each test, the reservoir and the capillaries were cleaned with acetone and dried with nitrogen. Test sample was then pumped into the system and flowed stably for 20 min. Two different methodologies were proposed to calculate the viscosity of hydrocarbons in a wide temperature range and at high pressures. 2.1.1. Referenced Fluid Method. On the basis of the Hagen− Poiseuille’s Law of a laminar flow in two capillary tubes, the pressure drop of test and referenced fluids was measured. The calculating process was described in detail in ref 13 and the viscosity formula of test fluid was expressed as mea ηdown, T

=

ref ηdown, T

RP-3 EHF-1

initial mole fraction purity

purification method

0.995

distillation

0.995

distillation

0.995

distillation

Sinopharm Chemical Reagent Company Sinopharm Chemical Reagent Company Sinopharm Chemical Reagent Company Liming Research Institute of Chemical Industry kerosene fuel

distillation distillation

Table 2. Detailed Compositions of Jet Fuel RP-3

ref mea mTref0 Δpdown, T Δpup, T0 ρTmea mea ref ref mTmea Δpup, T0 Δpdown, T ρT 0

source

(1)

ref where ηmea down,T and ηdown,T stand for the viscosity of test and referenced fluid in downstream capillary at a test temperature T, ref ηmea up,T0 and ηup,T0 represent the viscosity of test and referenced fluid ref in upstream capillary at a reference temperature T0, mmea T0 and mT0 ref are the mass flux of test and referenced fluid at T0, ρmea and ρ T T are the density of test and referenced fluid at T. In the experiments, the obtained pressure drops of capillaries were ref mea ref presented by Δpmea down,T, Δpdown,T, Δpup,T0 and Δpup,T0 respectively. In viscosity measurements, the test and referenced fluid viscosity ratio can be obtained from the ratios of pressure drops at different temperatures, density at the test temperature, and mass flux at the reference temperature. Toluene with a purity higher than 99.5% was selected as the reference fluid because of its good stability and economy in experiments. The reference temperature of the upstream thermostat was designed and kept nearly constant at 303.2 K, while the test temperature was varied in steps of 10 K between 303.2 and 673.2 K with a digital temperature control system on th edownstream thermostat. In the calculation, some corrections were considered for the modified two-capillary viscometer, such as compression factor, kinetic energy, centrifugal factor, slip, and thermal corrections.29,30 Finally a relative expansion uncertainty of viscosity in RFM ur(ηmea down,T) was calculated as eq 213 and identified to be (2.22 to 5.28) % (coverage factor k = 2).

mea ref ref 2 mea ur2(ηdown, ) = ur2(ηdown, ) + ur2(m up, T0 ) + ur (m up, T0 ) T T mea mea + ur2(Δpdown, ) + ur2(Δpup, ) T T

no.

composition

mass fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

n-nonane n-decane n-undecane n-dodecane n-tridecane n-tetradecane n-pentadecane n-hexadecane n-heptadecane 2-methyloctane 3-methyloctane 4-methyloctane 2-methylnonane 3-methylnonane 4-methylnonane 2-methyldecane 3-methyldecane 4-methyldecane 2-methylundecane 3-methylundecane 4-methylundecane 1,2,3-trimethylbenzene 1,3,5-trimethylbenzene 1-ethyl-3-methylbenzene 2-ethenyl-1,3-dimethylbenzene cyclododecane 1-hexylcyclopentane 1-butyl-2-ethyl cyclopentane 1,1,3-trimethyl cyclohexane 1-butylcyclohexane 1-heptylcyclohexane 1-ethyl-4-methylcyclohexane decahydro-naphthalene 1-methyl-naphthalene 2-methyl-naphthalene 2-methylpentalene others

0.0252 0.0578 0.0439 0.0384 0.0321 0.0165 0.0057 0.0059 0.0308 0.0108 0.0153 0.0172 0.0093 0.0105 0.0128 0.0124 0.0155 0.0178 0.0118 0.0166 0.0170 0.0607 0.0527 0.0781 0.0490 0.0200 0.0503 0.0217 0.0294 0.0511 0.0139 0.0270 0.0379 0.0245 0.0194 0.0259 0.0151

0

ref ref + ur2(Δpup, ) + ur2(Δpdown, ) + ur2(ρTref ) T T

2.1.2. Thermal Expansion Method. The thermal expansion method was proposed by integrating the thermal expansion of capillary material into a two-capillary system. The volume flow rate of a laminar flow in a capillary tube could be denoted as

0

⎡ ∂η mea ⎤ down, T u(T ) ⎥ + ur2(ρTmea ) + ⎢ mea ⎢⎣ ∂T ηdown, ⎥ T⎦

2

⎡ ∂η mea u(T ) ⎤2 ⎡ ∂η mea ⎤2 down, T down, T u(P) 0 ⎥ ⎢ ⎢ ⎥ + + mea mea ⎢⎣ ∂T0 ηdown, ⎥ ⎢ ⎥ η P ∂ ⎦ ⎣ down, T ⎦ T

Q=

πR4 Δp 1 Δp = 8η L Z η

(3)

where Q, R, L, η, and Δp stand for the volume flow rate, internal radius, tube length, fluid viscosity, and pressure drop in the capillary,

(2) B



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Table 3. Detailed Compositions of Hydrocarbon Fuel EHF-113

ηT ηT

no.

composition

mass fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

decahydronaphthalene 2-methyl-bicyclo[2.2.2]octane 5-undecene 2-methyl-trans-Decalin 2-syn-methyl-cis-Decalin decahydro-2,6-dimethyl-naphthalene 1,2,3,4-tetrahydro-1,4-dimethyl-naphthalene trans,cis-1,8-dimethylspiro[4.5]decane 7-pentyl-bicyclo[4.1.0]heptane 1-(1-methylethenyl)-2-(1-methylethyl)-benzene 4-(2-butenyl)-1,2-dimethyl-,(E)-benzene, 1-methyl-4-(1-methylbutyl)-cyclohexane 2-butyl-1,1,3-trimethyl-cyclohexane 2,6-dimethyl-undecane, cis,trans-1,9-dimethylspiro[5.5]undecane 3-methyl-7-pentyl-bicyclo[4.1.0]heptane 2-methyl-7-pentyl-bicyclo[4.1.0]heptane 2-hexyl-bicyclo[2.2.1]heptane 1-nonadecene 7-methyl-6-tridecene others

0.0181 0.0290 0.0133 0.1621 0.0870 0.1291 0.0123 0.0551 0.0162 0.0290 0.0039 0.0225 0.0493 0.0450 0.0444 0.0943 0.0590 0.0291 0.0052 0.0303 0.0658

Δpdown, T

0

=

0

0

(5)

where the ratio of structure coefficients of downstream capillary tube at different temperatures could be simplified as a formula on length variation. Zdown, T0

=

Zdown, T

3 LT0 RT 4 ⎛ ΔL ⎞⎟ ΔL ⎜1 + = ≈1+3 4 ⎝ ⎠ L L R T0 LT

(6)

In the present work, ΔL/L presents the thermal expansion of test 316L stainless steel capillary supplied by VICI Company. Thus, the measured viscosity of test fluid was calculated as Δpdown, T Zup, T ⎛ ΔL ⎞⎟ ρT 0 ⎜1 + 3 0 Δp ⎝ Zdown, T0 L ⎠ ρT up , T

ηT = ηT

0

0

Δpdown, T ⎛ ΔL ⎞⎟ ρT ⎜1 + 3 ≈ ηT 0 Δp ⎝ L ⎠ ρT down, T 0

(7)

0

According to eq 7, the combined relative standard uncertainty of measured viscosity in TEM is derived as ur2(ηT ) = ur2(ηT ) + ur2(Δpdown, T ) + ur2(Δpup, T ) + ur2(ρT ) 0

+

ur2(ρT ) 0

0

9 + uc2(ΔL /L) (1 + 3ΔL /L)

(8)

where ur(η), ur(Δp), and ur(ρ) stand for the relative standard uncertainty of viscosity, pressure drop, and density of fluid. The uc(ΔL/L) presents the standard uncertainty of thermal expansion of a capillary tube. Thus, the combined relative expansion uncertainty of viscosity in TEM was finally determined as (0.90 to 2.42) % (coverage factor k = 2). In short, the above two designed approaches for viscosity measurement have their advantages and disadvantages. The referenced fluid method does not require knowledge of tube parameters, but its application range and accuracy are both restricted by a referenced fluid. The thermal expansion method

Zup, T0 Zdown, T0

Δpup, T Zdown, T ρT

Δpdown, T ⎛ Zup, T Zdown, T ⎞ ρ 0 0 ⎜ ⎟ T · = Δpup, T ⎜⎝ Zdown, T0 Zdown, T ⎟⎠ ρT 0 0

respectively. Z = was defined as a structure coefficient of capillary tube with R and L for convenience in the following calculation. In the experiments, constant mass flux of test fluid first flows through the upstream and downstream capillaries at reference temperature T0. Comparing two pressure drops of the capillaries, the formula was obtained as 0

Δpdown, T Zup, T ρ 0 T

0

8L πR 4

Δpup, T

=

(4)

Then, the temperature of the downstream thermostat is elevated to a design value T, and the viscosity ratio of fluid at T0 and T can be expressed as

Figure 1. Schematic diagram of viscosity measurement system. C



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Test capillary tubes (1/32 in. o.d. and 0.25 mm i.d.) with 3000 mm length were immersed in a liquid thermostat upstream and downstream, respectively (detailed structure of equipment was shown in Figure 2). Note that the upstream temperature of thermostat throughout remained at a fixed 303.2 K with a water bath. And the downstream thermostat was processed in a two-stage, thermal oil (Therminol 55) bath at temperatures from (303.2 to 513.2) K and a molten salt bath (60 wt % NaNO3 + 40 wt % KNO3) between 513.2 and 673.2 K. Each thermostat was automatically adjusted by a PID regulator (SHIMADEN FP23) and a direct current stabilized power supply (HCP20-30). The pressures inside two capillary tubes were measured by pressure transducers (Rosemount 3051) with an uncertainty of

has the potential to be applied at higher temperature conditions without a specified mass flux. However, the thermal expansion coefficient of the capillary tube should be known in advance. In application, different methods could be adopted respectively according to the actual situation. 2.2. Materials and Characterization. Pure hydrocarbon n-dodecane, n-heptane, and n-octane were all supplied by Sinopharm Chemical Reagent Company, and selected with purities higher than 99.5% to calibrate the designed viscometer. Two representative samples of endothermic fuels were chosen and tested, a typical jet fuel RP-3 purchased from Liming Research Institute of Chemical Industry and a kerosene-type of endothermic hydrocarbon fuel (EHF-1) distilled from petroleum. The detailed descriptions of all samples could be found in Table 1. Jet fuel RP-3 is made of 42.33% alkanes, 24.05% benzenes, 21.35% cycloalkanes, 8.18% naphthalenes, and 4.09% other hydrocarbons, consisting of an average molecular formula C10.62H19.69 with a molecular weight of 147.1 g·mol−1, and the density of RP-3 at ambient temperature is 769.2 kg·m−3 measured using a gamma densitometer. Another EHF-1 fuel consists of 81.40% cycloalkanes, 4.75% alkanes, 4.88% alkenes, and 4.00% aromatics, with minor amounts of olefins, naphthalenes, and other hydrocarbons.13 The average molecular formula is C12.65H24.13 and the molecular weight is 175.9 g·mol−1. The density of EHF-1 is 820.4 kg·m−3 at ambient test temperature. The detailed compositions of two fuels were described respectively in Tables 2 and 3. As determined by the critical opalescence phenomenon in a visualization apparatus,31 critical parameters of two fuels were obtained with Tc = 645.5 K, pc = 2.39 MPa for RP-3 and Tc = 694.1 K, pc = 2.35 MPa for EHF-1. Meanwhile, both fuels remained in a liquid state for a laminar flow of an incompressible Newtonian fluid, and no thermal decomposition occurred under the test temperatures. 2.3. Apparatus and Measurement. On the basis of a pressure drop ratio of the referenced and measured fluid medium, kinematic viscosity of a liquid fluid could be deduced by a two-capillary viscometer, which was verified as an online apparatus for hydrocarbons at moderate temperatures and pressures. The structure and operation of the apparatus has been described in detail previously.13 The schematic diagram of the two-capillary viscosity measurement system was shown in Figure 1. Test hydrocarbons were pumped into the capillary tubes at a constant flow rate by a liquid chromatography pump (P230II).

Table 4. Experimental Viscosity ηRFM in RFM and ηTEM in TEM of n-Dodecane at Test Pressure p = 5.00 MPa and Temperature T with a Modified Two-Capillary Viscometer T

ηRFM

ηTEM

T

ηRFM

ηTEM

K

μPa·s

μPa·s

K

μPa·s

μPa·s

303.2 313.2 323.0 333.1 343.3 353.3 363.2 373.3 383.2 393.2 403.2 413.2 423.2 433.2 443.4 453.1 463.2 473.2 483.1 483.1

1333.5 1122.1 970.0 851.9 744.2 673.6 607.5 546.7 490.2 447.2 411.2 378.5 350.8 327.7 297.4 282.2 260.4 244.0 225.0 225.0

1314.4 1116.3 962.6 843.4 744.5 666.1 596.9 539.7 491.3 448.0 411.8 379.9 351.6 325.9 304.1 282.7 261.9 244.0 225.9 225.9

493.2 503.2 513.1 523.2 533.1 543.2 553.2 563.2 573.2 583.3 593.2 603.2 613.2 623.1 633.2 643.1 653.2 663.2 673.2 673.2

207.6 196.4 184.6 172.2 160.8 148.9 137.5 129.7 120.1 112.6 103.1 97.4 91.3 83.9 76.7 69.4 65.7 60.5 55.1 55.1

207.2 196.9 183.5 169.8 159.1 148.7 139.1 130.5 122.1 114.1 106.4 98.7 91.5 84.9 78.6 71.4 65.0 60.5 54.8 54.8

a

Standard uncertainties u are u(T) = 0.27 K, u(p) = 0.008 MPa and the combined expanded uncertainty Uc is Uc,RFM (η) = 10.66 μPa·s, Uc,TEM (η) = 5.59 μPa·s (0.95 level of confidence).

Figure 2. Schematic diagram of each thermostat. D



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Table 6. Experimental Viscosity ηRFM in RFM and ηTEM in TEM of Binary Mixture (x1n-heptane + (1 − x1)n-octane) at Different Mass Ratios x1, Pressure p and Temperature T Compared with Reference Viscosity ηref measured by Abdulagatov et al.36 x1

p/MPa

T/K

ηRFM/μPa·s

ηTEM/μPa·s

ηref

0.255

0.10 0.10 0.10 5.00 5.00 5.00 5.00 0.10 0.10 0.10 5.00 5.00 5.00 5.00 0.10 0.10 0.10 5.00 5.00 5.00 5.00

303.5 333.8 363.4 303.9 373.2 413.9 473.5 303.5 333.5 363.4 303.5 373.6 413.7 473.4 305.7 335.6 364.6 305.7 373.2 424.4 472.5

442.2 323.4 244.7 466.3 241.5 179.2 118.6 414.9 301.1 232.9 436.2 227.7 170.2 112.4 379.8 281.5 216.4 403.2 218.1 149.7 107.1

441.7 322.8 246.4 465.8 240.2 180.1 118.4 413.0 302.6 232.3 435.7 227.5 169.8 112.5 378.4 280.6 216.9 402.9 217.5 149.3 107.5

441 322 245 465 241 178 118 414 300 232 435 227 167 112 379 281 216 402 217 149 107

0.510

Figure 3. Deviation of experimental and literature viscosities34 of n-dodecane at p = 5.00 MPa and T = (303 to 673) K. ■, this work, RFM; ○, this work, TEM.

0.759

a Standard uncertainties u are u(T) = 0.27 K, u(p) = 0.008 MPa and the combined expanded uncertainty Uc is Uc,RFM(η) = 10.12 μPa·s, Uc,TEM(η) = 4.48 μPa·s (0.95 level of confidence).

Table 7. Experimental Viscosity ηTEM in TEM of RP-3 at Test Pressure p = 5.00 MPa and Temperature T with a Modified Two-Capillary Viscometer

Figure 4. Deviation of experimental and literature viscosities34 of n-octane at p = 3.10 MPa and T = (303.2 to 583.2) K. ■, this work, RFM; ○, this work, TEM.

Table 5. Experimental Viscosity ηRFM in RFM and ηTEM in TEM of n-Octane at Test Pressure p = 3.10 MPa and Temperature T with a Modified Two-Capillary Viscometer T

ηRFM

ηTEM

T

ηRFM

ηTEM

K

μPa·s

μPa·s

K

μPa·s

μPa·s

303.2 313.3 323.2 333.2 343.2 353.1 363.2 373.3 383.0 393.1 403.2 413.2 423.2 433.1 443.2

491.3 442.6 396.1 363.4 331.1 301.3 276.5 254.0 234.0 220.5 201.9 190.5 176.1 164.3 152.6

494.8 443.1 397.9 361.7 330.8 303.2 277.5 258.0 237.9 220.2 204.0 190.2 177.5 164.2 151.4

453.1 463.2 473.1 483.1 493.1 503.0 513.2 523.3 533.4 543.4 553.4 563.3 573.3 583.1

141.7 132.1 122.8 113.8 106.8 99.3 90.1 82.5 75.3 67.8 60.7 53.2 44.4 32.5

142.8 131.8 124.1 115.2 107.2 98.3 90.4 82.6 75.1 67.8 60.9 53.4 44.6 32.3

T/K

ηTEM/μPa·s

T/K

ηTEM/μPa·s

306.6 314.5 323.9 333.9 343.5 353.6 363.5 373.6 383.5 394.1 403.7 414.1 424.3 434.1 444.0 453.8 464.0 473.9 483.5

950.1 841.7 740.7 651.1 582.6 522.0 471.6 428.1 390.9 356.5 329.3 303.2 279.6 259.4 240.7 223.5 207.2 192.5 179.7

493.5 502.7 513.4 523.7 533.7 543.9 553.7 563.9 573.8 583.5 593.8 603.8 613.9 623.7 634.0 643.8 654.0 664.0 673.4

167.4 158.1 145.9 136.4 126.6 117.1 108.6 100.5 93.4 87.4 81.6 76.2 71.1 65.3 59.7 55.0 51.3 47.2 42.5

a

Standard uncertainties u are u(T) = 0.27 K, u(p) = 0.008 MPa and the combined expanded uncertainty Uc is Uc,TEM(η) = 4.34 μPa·s (0.95 level of confidence).

a

Standard uncertainties u are u(T) = 0.27 K, u(p) = 0.008 MPa and the combined expanded uncertainty Uc is Uc,RFM(η) = 3.98 μPa·s, Uc,TEM(η) = 2.10 μPa·s (0.95 level of confidence).

of 0.248 MPa. Fluid temperature was measured with four standard exposed thermocouples (Omega GG-K) with an uncertainty of ±0.25 K. The qualitative temperature was then calculated

0.075%, and the pressure drops of capillaries were monitored by transducers with an uncertainty of ±1.9 × 10−4 MPa in a full scale E



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Table 8. Experimental Viscosity ηRFM in RFM of EHF-1 at Test Pressure p = 3.00, 4.01, and 5.00 MPa and Temperature T with a Modified Two-Capillary Viscometer T/K 303.1 313.2 323.2 333.1 343.1 353.1 363.2 373.2 383.2 393.2 403.2 413.1 423.2 433.2 443.2 453.1 463.1 473.2 483.1 303.1 313.2 323.2 333.1 343.1 353.1 363.2 373.2 383.2 393.2

ηRFM/μPa·s

T/K

p = 3.00 MPa 1780.4 493.1 1490.2 503.1 1295.8 513.1 1130.6 523.2 988.6 533.2 875.0 543.2 778.9 553.2 698.0 563.2 623.1 573.2 572.3 583.3 519.7 593.1 475.4 603.1 438.4 613.1 400.9 623.1 371.5 633.1 345.7 643.1 317.2 653.1 293.2 663.1 270.4 p = 4.01 MPa 1815.9 493.1 1576.6 503.1 1336.7 513.1 1159.7 523.2 1009.5 533.1 889.5 543.2 793.4 553.2 710.7 563.2 642.5 573.2 581.6 583.3

ηRFM/μPa·s

T/K

247.4 225.7 209.1 193.8 180.4 168 157.1 145.9 135.8 127.3 118.5 109.7 102.3 93.8 87.3 80.0 71.1 64.4

403.2 413.1 423.2 433.2 443.2 453.1 463.1 473.2 483.2 303.1 313.2 323.2 333.1 343.1 353.1 363.2 373.2 383.2 393.2 403.2 413.1 423.2 433.2 443.2 453.1 463.1 473.2 483.1

255.9 236.6 216.1 199.4 186.0 173.8 161.5 150.2 140.0 131.5

ηRFM/μPa·s

T/K

p = 4.01 MPa 529.4 593.1 485.9 603.1 444.8 613.1 408.3 623.1 376.6 633.1 351.3 643.1 323.8 653.1 299.8 663.1 278.1 673.1 p = 5.00 MPa 1853.2 493.1 1562.5 503.1 1344.0 513.1 1166.5 523.2 1024.2 533.2 903.0 543.3 806.6 553.2 726.1 563.2 655.8 573.2 592.4 583.3 543.4 593.1 497.3 603.1 455.6 613.1 419.8 623.1 387.4 633.1 357.3 643.1 331.2 653.1 307.3 663.1 285.2 673.1

ηRFM/μPa·s 122.8 113.7 105.9 98.0 91.9 84.5 75.3 71.1 64.7 265.1 244.3 226.4 207.1 193.6 181.4 168.8 157.8 147.3 138.7 129.0 119.9 111.8 103.6 97.9 90.3 81.1 77.1 69.8

Standard uncertainties u are u(T) = 0.27 K, u(p) = 0.008 MPa, and the combined expanded uncertainty Uc is Uc,RFM(η) = 9.71 μPa·s (0.95 level of confidence).

a

Figure 5. Comparison of fitted curve and experimental data for the viscosity measurement of RP-3 at p = 5.00 MPa and T = (303 to 673) K. □, this work, RFM; bold , fitted curve; ■, relative deviations Δη/η = (ηfit − ηexp)/ηexp of experimental viscosities from values obtained with the correlation of Yaws et al.28 as a function of temperature T.

3. RESULTS AND DISCUSSION The viscosity measurements of pure fluids and the binary mixture were implemented to support two developed methods in a twocapillary viscometer. The measurement accuracy of the methods was then determined. Subsequent to this section, the viscosities of two endothermic fuels (RP-3 and EHF-1) were measured with a two-capillary viscometer, and viscosity formula on the fuels was established thereafter.

by the mathematic average of the inlet and outlet temperatures. As a result, a combined uncertainty in pressure drop was estimated to be ±1.34 × 10−4 MPa with contributions from pressure drop transducers, a pressure control system, and a pressure acquirement system. The combined uncertainty of fluid temperature was ±0.27 K based on the uncertainties from the thermocouple and temperature fluctuation of the thermostat and temperature acquirement system. F



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compared with the calculated data34 in RFM and TEM, respectively. The results were given in Figure 4 and Table 5, in which the AAD was just 0.48% in RFM and 0.42% in TEM. MAD was 1.28% at 503 K and 1.13% at 493 K, and RMS was calculated as 0.24 and 0.18 accordingly. Moreover, the binary mixtures of {x1n-heptane + (1 − x1)n-octane} mixtures at mass ratio x1 = (0.255, 0.510, 0.759) were reported and compared with ref 36 in Table 6. This contributes to prove the applicability of the designed viscometer for hydrocarbon mixtures. Though the measured viscosities in RFM and TEM are higher than those in literature, the maximum relative deviation was lower than 2.0% in the whole tests. 3.2. Viscosity Measurement of Fuels. With a modified viscometer, the viscosities of two endothermic fuels were measured. The viscosity of jet fuel RP-3 was measured in TEM at temperatures from (303 to 673) K and a supercritical pressure of 5.00 MPa. Another endothermic fuel EHF-1 was measured in RFM between (303 and 663) K from 3.00 to 5.00 MPa. The results are shown in Table 7 and Table 8, respectively. Though the working pressures were both higher than the critical pressure of the two fuels, the test temperatures were lower than their pseudocritical temperatures. The fuels were under a supercritical liquid state. The fuels’ viscosity as a function of temperature was fitted by a formula proposed by Yaws28

Table 9. Fitting Coefficients of Calculated Viscosities for EHF-1 at Test Pressure p = 3.00, 4.01, and 5.00 MPa parameter

p = 3.00 MPa

p = 4.01 MPa

p = 5.00 MPa

A B C D MAD

−4.6072 974.6308 0.007484 −6.8426 × 10−6 3.01%

−4.1295 917.5538 0.006254 −5.8010 × 10−6 2.09%

−3.9396 889.8626 0.005815 −5.4024 × 10−6 2.03%

3.1. Calibration. Viscosities of n-dodecane were measured at temperatures from (303 to 673) K and a pressure of 5.00 MPa by our modified viscometer. The experimental results are listed in Table 4, where the viscosities decrease with test temperature increases and the fluid transforms from a liquid state to a supercritical condition. To assess the accuracy of the referenced fluid method (RFM) and thermal expansion method (TEM), the experimental viscosities were compared to the literature data32,33 calculated by the NIST-REFPROP software.34 The relative deviations (RDs), average absolute deviation (AAD), maximum absolute deviation (MAD), and root-mean-square (RMS) deviation35 were calculated, and good agreement was obtained as shown in Figure 3. ηexp − ηref i i RD(%) = 100 ηref (9)

log10 η = A +

i

AAD =

100 n

n

∑ abs(RDi)

MAD = max(abs(RDi )) n ⎡ 100 100 RMS = [∑ RDi2 ] − ⎢ n i=1 ⎣⎢ n 2

(11)

⎤2 ∑ RDi⎥ ⎥⎦ i=1

(13)

where η is the dynamic viscosity in Pa·s, T is the absolute temperature in K and A, B, C, and D are constants specific to test fluid. For RP-3, the values of −7.3716, 866.7354, 0.006949, and −6.5300 × 10−6 were obtained for A, B, C, and D, respectively. Figure 5 shows that the high correlation coefficient of the fitted curve is greater than 0.99 and the overall relative deviations between the viscosities calculated fitted curve and experimental data are lower than 4.2%. In the same way, the viscosity of EHF-1 was predicted with parameters as shown in Table 9 at different pressures. The fitted curve and deviation between the calculated viscosities and experimental data were shown in Figure 6, where the overall relative deviations were within 3.01%. All the above results fully verified that the fitted formula could accurately predict the viscosity of two endothermic fuels in the liquid state.

(10)

i=1

B + CT + DT 2 T

n

(12)

As shown in Figure 3, the AAD of n-dodecane in RFM and TEM were 0.74% and 0.75%, respectively, and the MAD was around 2.18% at 643 K and 1.90% at 633 K. The RMS deviation was calculated as eq 12 with 0.81 for RFM and 0.77 for TEM. For further validation, the viscometer was also used for pure fluid of n-octane at constant pressure p = 3.10 MPa and varied temperature from 303.2 to 583.2 K. The test viscosities were

Figure 6. Comparison of fitted values obtained with the correlation of Yaws et al.28 and experimental data in TEM measurement of EHF-1 at p = 3.00, 4.01, and 5.00 MPa and T = (303 to 663) K. ■, this work, p = 3.00 MPa; ●, this work, p = 4.01 MPa; ▲, this work, p = 5.00 MPa; bold , fitted curve; □, relative deviations Δη/η = (ηfit − ηexp)/ηexp at p = 3.00 MPa; ○, relative deviations Δη/η = (ηfit − ηexp)/ηexp at p = 4.01 MPa; △, relative deviations Δη/η = (ηfit − ηexp)/ηexp at p = 5.00 MPa. G



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(13) Yang, Z. Q.; Liu, Z. H.; Bi, Q. C.; 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. (14) Yang, Z. Q.; Bi, Q. C.; Guo, Y.; Yan, J. G.; Zhang, Q.; Liu, Z. Design of a gamma densitometer for hydrocarbon fuel at high temperature and supercritical pressure. J. Chem. Eng. Data 2014, 59, 3335−3343. (15) Powell, O. A.; Edwards, J. T.; Norris, R. B.; Numbers, K. E.; Pearce, J. A. Development of Hydrocarbon-Fueled Scramjet Engines: The Hypersonic Technology (HyTech) Program. J. Propul. Power 2001, 17, 1170−1176. (16) Gascoin, N.; Abraham, G.; Gillard, P. Synthetic and jet fuels pyrolysis for cooling and combustion applications. J. Anal. Appl. Pyrolysis 2010, 89, 294−306. (17) Derevich, I. V. Thermodynamic model of viscosity of hydrocarbons and their mixtures. Int. J. Heat Mass Transfer 2010, 53, 3823− 3830. (18) Liu, Z. H.; Bi, Q. C.; Guo, Y.; Su, Q. H. Heat transfer characteristics during subcooled flow boiling of a kerosene kind hydrocarbon fuel in a 1mm diameter channel. Int. J. Heat Mass Transfer 2012, 55, 4987−4995. (19) Boned, C.; Zéberg-Mikkelsen, C. K.; Baylaucq, A.; Daugé, P. High-pressure dynamic viscosity and density of two synthetic hydrocarbon mixtures representative of some heavy petroleum distillation cuts. Fluid Phase Equilib. 2003, 212, 143−164. (20) Bruno, T. J.; Huber, M. L.; Laesecke, A.; Lemmon, E. W.; Perkins, R. A. Thermochemical and thermophysical properties of JP-10; NISTIR 6640; NIST, 2006. (21) Bruno, T. J.; Laesecke, A.; Outcalt, S. L.; Seelig, H. D.; Smith, B. L. Properties of a 50/50 Mixture of Jet-A + S-8; NISTIR 6647; NIST, 2007. (22) Tate, R. E.; Watts, K. C.; Allen, C. A. W.; Wilkie, K. I. The Viscosity of Three Biodiesel Fuels at Temperatures up to 300°C. Fuel 2006, 85, 1010−1015. (23) Outcalt, S. L.; Laesecke, A.; Brumback, K. J. Thermophysical properties measurements of rocket propellants RP-1 and RP-2. J. Propul. Power 2009, 25, 1032−1040. (24) May, E. F.; Moldover, M. R.; Berg, R. F.; Hurly, J. J. Transport properties of argon at zero density from viscosity-ratio measurements. Metrologia 2006, 43, 247−258. (25) Berg, R. F.; May, E. F.; Moldover, M. R. Viscosity Ratio Measurements with Capillary Viscometers. J. Chem. Eng. Data 2014, 59, 116−124. (26) Zhang, J. T.; Lin, H.; Che, J. Effect of Connecting Tubing on a Two-Capillary Viscometer. Metrologia 2013, 50, 377−384. (27) Liu, Z. H.; Trusler, J. P. M.; Bi, Q. C. Viscosities of liquid Cyclohexane and Decane at Temperatures between (303 and 598)K and Pressures up to 4 MPa Measured in a Dual-Capillary Viscometer. J. Chem. Eng. Data 2015, 60, 2363−2370. (28) Yaws, C. L.; Lan, L. X. D. Transport Properties of Chemicals & Hydrocarbons; Wlliam Andrew, 2009. (29) Berg, R. F. Simple flow meter and viscometer of high accuracy for gases. Metrologia 2005, 42, 11−23. (30) Berg, R. F. Quartz capillary flow meter for gases. Rev. Sci. Instrum. 2004, 75, 772−779. (31) He, M. G.; Xin, N.; Liu, Y.; Zhang, Y. Determination of critical properties for binary and ternary mixtures of short chain alcohols and alkanes using a flow apparatus. J. Supercrit. Fluids 2015, 104, 19−28. (32) Knapstad, B.; Skjoelsvik, P. A.; Oeye, H. A. Viscosity of pure hydrocarbons. J. Chem. Eng. Data 1989, 34 (1), 37−43. (33) Huber, M. L.; Laesecke, A.; Perkins, R. A. Transport properties of n-dodecane. Energy Fuels 2004, 18 (4), 968−975. (34) 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. (35) Huber, M. L.; Laesecke, A.; Perkins, R. A. Transport Properties of n-Dodecane. Energy Fuels 2004, 18, 968−975.

4. CONCLUSION This paper proposed two methods for viscosity measurement of hydrocarbons using a two-capillary viscometer, which could be used in a wide temperature range and at supercritical pressures. The referenced fluid method was based on the pressure drop of the test and referenced fluids, and the thermal expansion method was proposed by integrating the thermal expansion of a capillary material into a two-capillary system. For validation, the viscosities of pure n-dodecane and a binary mixture hydrocarbons were measured and compared with literature data obtained in a respective method. The two methods both show good feasibility and accuracy in the viscosity measurement of hydrocarbons. Using the two-capillary viscometer, viscosities of two endothermic fuels (RP-3 and EHF-1) were tested from (303 to 673) K at different supercritical pressures. Finally, a relation formula with high correlation coefficients was fitted based on the experimental data.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The authors gratefully acknowledge funding support from the Fundamental Research Funds for the Central Universities. Notes

The authors declare no competing financial interest.

■

REFERENCES

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(36) Abdulagatov, I. M.; Azizov, N. D. p,ρ,T,x) and viscosity measurements of {x1n-heptane+(1-x1)n-octane} mixtures at high temperatures and high pressures. J. Chem. Thermodyn. 2006, 38, 1402−1415.

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Viscosity Measurement of Endothermic Fuels at Temperatures from

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