Measurement of mass diffusion coefficients of O2 in aviation fuel through digital holographic interferometry

Chaoyue LI,Weihua LIU,Xiaotian PENG,Lei SHAO,Shiyu FENG

Key Laboratory of Aircraft Environment Control and Life Support of Ministry of Industry and Information Technology,College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

KEYWORDS Aviation fuel;Diffusion coefficients;Digital holographic interferometry;Oxygen;Viscosity

Abstract The experimental apparatus to measure the mass diffusion coefficients of O2 in aviation fuel was constructed based on the digital holographic interferometry method.The theory of mass diffusion coefficient and interference image processing were introduced in detail.The accuracy of the experiment was verified by measuring the mass diffusion coefficient of 0.33 mol/L KCl in aqueous solution at 298.15 K.The mass diffusion coefficients of O2 in RP3 and RP5 aviation fuels were measured at temperature from 278.15 K to 333.15 K,and the Arrhenius equation was employed to fit the experimental data.In terms of the Stokes-Einstein equation,the viscosities of these two aviation fuels were tested to estimate the correlation among mass diffusion coefficient,viscosity and temperature.A uniform polynomial calculation correlation was proposed to predict the mass diffusion coefficients of O2 in both RP3 and RP5 aviation fuels,and its accuracy is considerably higher than that of the Stokes-Einstein equation.

1.Introduction

The knowledge of oxygen diffusion and the dissolving property of oxygen in aviation fuel are highly important for the safety of an aircraft fuel tank system.As the aircraft climbs and cruises,the release of the dissolved oxygen results in the increase of oxygen concentration on ullage of the fuel tank because of the decrease of both the ambient pressure and the temperature.During the descent,the oxygen concentration of the aviation fuel increases because of the increase of both the pressure and the temperature.1When the ullage oxygen concentration of the aircraft tank is above the limiting oxygen concentration,the fuel in the tank is prone to catch fire or explode if the tank is exposed to an external ignition source,such as lightning,static electricity and shell.2,3In addition,dissolved oxygen can react with aviation fuel to form gums and deposits,4and this phenomenon will block the engine nozzles,and degrade atomization.5As a result,such an understanding of the nature and behavior of O2in aviation fuel is essential for the simulation and design of decreasing the oxygen concentration in the aircraft fuel tank system.

During the dissolution and release of O2into aviation fuel,the Mass Diffusion Coefficients(MDC)is one of the most important parameters to evaluate the rate of possible mass transfer.Unfortunately,the study on MDC of O2in aviation fuel is relatively scarce.The MDC strongly depends on composition,temperature and viscosity,6,7and there is no universal model to calculate the MDC accurately.Thus,experimental measurements are necessary to obtain the MDC of O2in aviation fuel.

Currently, many experimental methods have been presented to measure the MDC of gas-liquid diffusion system primarily include the glass capillary method,8the Taylor dispersion method,9the pressure-decay method,10the constant-pressure method11and the holographic interferometry method.12Compared with the other methods,the holographic interferometry method has several advantages in terms of less time consumption, high accuracy and nondirect contact with the experimental material.13

In this paper,an experimental system is constructed to measure the MDC of O2in aviation fuel using the method of digital holographic interferometry.The verification experiment is conducted by measuring the MDC of 0.33 mol/L KCl in aqueous solution at 298.15 K.The MDC of O2in currently utilized RP3 and RP5 aviation fuels at 278.15 K to 333.15 K are measured.The pressure in the aircraft fuel tank is always less than atmospheric pressure and it varies within a narrow range so that the effect of the pressure can be neglected.In addition,the viscosities of the fuel are also measured for the analysis of the relationships among MDC,viscosity and temperature.A uniform polynomial function is proposed to calculate the MDC of O2in both RP3 and RP5 aviation fuels.

2.Theory

For an isothermal one-dimensional diffusion process, the MDC can be considered constant because the variation is small.Based on Fick's second law,the MDC can be expressed as14

where c is the concentration of the gas,mol/m3;t is time,s;D is the MDC,m2/s and z is the distance of the diffusion,m.

At the initial moment t0,the concentration distribution of the two components in the upper and lower parts is cuand cl,respectively.Therefore,the concentration at position z at time t along diffusion direction is

The concentration difference Δc of two different instances can be written as

In the diffusion process,the variation of concentration and concentration difference are shown in Fig.1.There exist two extreme points for the concentration difference along the diffusion vessel and the distance between the two points is Δz.The MDC can be obtained by solving equations above

The refractive index of the transparent liquid is a linear function of the concentration,and the phase of the object beam passing through the liquid is a linear function of the refractive index of the liquid.As a consequence,the phase difference of the object beam has the same extreme points.15Therefore,Δz can be extracted from the phase difference of the object beam determined by interference image processing.The diffusion time t1and t2are counted by computer.

3.Experiment

The digital holographic interferometry experimental setup for measuring the MDC is presented in Fig.2.The wavelength of the diode pump laser is 650 nm and the monochrome CCD has a 1280×960 resolution and a 4.65 μm pixel size.The diffusion cell is made of stainless steel with a diffusion volume of 20 mm×20 mm×200 mm and is sealed by quartz glass.To maintain the constant temperature during the measurement process,a thermostatic water bath is connected to the diffusion cell to keep the temperature variation within 0.1 K.The entire apparatus is placed on an optical shockproof table to remove the impact of vibrations on the experimental results.

The laser light emitted from the diode pump laser has the high frequency noise of the light filtered out by passing through the spatial filter,afterwards a parallel beam is formed by passing the laser beam through the beam expander.After passing through the beam splitter,the parallel beam is split into two coherent light beams,known as the object beam and the reference beam.The object beam passes through the diffusion system and then interferes with the reference beam after combining the beams using another beam splitter.The interference images containing the concentration information of the diffusion system are recorded by the CCD.During the diffusion process,the change in concentration of the liquid alters the optical path length traveled by the object beam passing through the solution which finally results in the phase difference of the object at different times.

Fig.1 Concentration and concentration difference in diffusion system.

Fig.2 Schematic of digital holographic interferometry experimental apparatus.

Via the method of double exposure digital holographic interferometry,the key to measure the MDC is obtaining the Δz by interference image processing.The processing flow chart of the interference fringe is shown in Fig.3.

The MDC of 0.33 mol/L KCl in aqueous at 298.15 K is measured to verify the accuracy of the system.The image processing is shown in Fig.4,and the results are listed in Table 1.The experimental average value of the MDC (Dave) of 0.33 mol/L KCl in aqueous is 1.812×10-9m2/s,with the relative deviation being 1.5%compared with the literature16value of 1.84×10-9m2/s.

4.Results and discussion

For the gas-liquid diffusion system,which is different from the liquid-liquid diffusion system,only interference fringes in the gas or liquid part can be obtained because of the huge difference in density between gas and liquid.Only one extreme point can be obtained,and considering the distance between the extreme point and the edge of the interference fringe as Δz/2,as shown in Fig.5,the MDC can be obtained by doubling the distance.17

Fig.3 Flow chart of interference image processing.

Fig.4 Interference image processing of KCl in aqueous.

Table 1 MDC of 0.33 mol/L KCl in aqueous at 298.15 K.

The measured MDC of O2in RP3 and RP5 aviation fuels at 278.15 K to 333.15 K are presented in Table 2 and Fig.6.The MDC increases with temperature rising and the MDC of O2in RP3 aviation fuel is higher than that in RP5 aviation fuel at the same temperature.

For engineering applications,the MDC can be expressed as a function of temperature, according to the Arrhenius equation18:

where A is a constant pre-exponential factor,m2s/K;E is the activation energy,J/mol;R is the molar gas constant,8.314 J/(kg·K);T is temperature,K.

The value of A and E can be obtained by fitting the experimental MDC results.The fitted curves are also plotted inFig.6,where A is 1.184×10-4m2·s/K and E is 22021 J/mol for the O2-RP3 aviation fuel diffusion system; A is 1.346×10-4m2·s/K and E is 23115 J/mol for the O2-RP5 diffusion system.

Table 2 MDC of O2 in RP3 and RP5 aviation fuels.

Fig.5 Interference image processing for O2-RP3 aviation fuel diffusion system.

There are numerous studies suggesting that the MDC for a given system is closely related to the viscosity.19,20Several models,such as the Stokes-Einstein equation,the Scheibel equation and the Wilke-Chang equation21have been proposed to estimate the MDC with temperature,viscosity and molecular characteristics.The Stokes-Einstein equation is the most commonly used model(the MDC calculated from this equation are accurate to only about 20%.Nonetheless,this equation remains the standard against which alternative correlations are judged21)and can be expressed as

where k is the Boltzmann constant,1.38×10-23J/K;μ is the solvent viscosity,Pa·s;and R0is the solute radius,m.

All of the models mentioned above implied that the quantity of Dμ/T is constant for a given diffusion system.To examine the accuracy of those models on the prediction of the MDC of O2in aviation fuel system,the viscosity of the experimental aviation fuel is measured by employing a commercial viscosimeter,as plotted in Fig.7.According to the experimental results,the viscosities of RP3 and RP5 aviation fuels decrease significantly with the increase of temperature,and are adequately fitted to the Arrhenius equation.For the viscosity of RP3 aviation fuel, A is 1.12×10-5m2·s/K and E is 11316 J/mol;for the viscosity of RP5,A is 7.36×10-6m2·s/K and E is 13411.73 J/mol.

The calculated results of Dμ/T for both O2-RP3 aviation fuel and O2-RP5 aviation fuel diffusion systems are plotted in Fig.8.The value of Dμ/T is not strict constant but strongly depends on the temperature,in agreement with the findings of Behzadfar and Hatzikiriakos20.The value of Dμ/T rises with the increase of temperature from 278.15 K to 333.15 K by 78.8%for the O2-RP3 aviation fuel diffusion system and by 67.1% for the O2-RP5 aviation fuel diffusion system.Although the two groups of data points for RP3 and RP5 aviation fuel clearly have different intercepts,the quantity of Dμ/T can be roughly expressed as linear function of temperature,as shown in Fig.8.Therefore,the MDC can be written as a uniform polynomial for O2in both RP3 and RP5 aviation fuels as follows:

Fig.6 Curves of MDC of O2 in RP3 and RP5 aviation fuels.

Fig.7 Viscosity of aviation fuel vs temperature.

Fig.8 Quantity of Dμ/T vs temperature.

Fig.9 Deviations between experimental and calculated results of MDC.

To examine the accuracy of the polynomial in calculating the MDC of O2in RP3 and RP5 aviation fuel,the deviations between the experimental results Delisted in Table 2 and calculated results Dcby Eq.(7)are plotted in Fig.9.The relative deviations between the experimental and calculated results are within 10%.The accuracy of Eq.(7)is higher than that of the Stokes-Einstein equation for the prediction of the MDC of O2in both RP3 aviation fuel and RP5 aviation fuel.

5.Conclusions

In this study,a digital holographic interferometry experimental apparatus for measuring the MDC is constructed and verified.The MDC of O2in RP3 aviation fuel and RP5 aviation fuel have been measured at 278.15 K to 333.15 K.To analyze the relationship among the MDC,viscosity and temperature based on the Stokes-Einstein equation,the viscosities of the RP3 and RP5 aviation fuels are also measured at the same temperature.

(1)The result of the diffusion coefficient of 0.33 mol/L KCl in aqueous solution at 298.15 K agrees well with the literature,confirming the reliability of the experimental apparatus.

(2)The MDC rises with the increase of temperature owing to the increase of molecular thermal motion and the decrease of viscosity,following the Arrhenius equation adequately.

(3)The value of Dμ/T is not constant but is a linear function of temperature.The MDC can be expressed as a uniform polynomial with viscosity and temperature for O2in both RP3 and RP5 aviation fuels within a 10%relative standard deviation.

Acknowledgements

This work was supported by the Aeronautical Science Foundation of China(No.20132852040),the Fundation of Graduate Innovation Center in NUAA(No.kfjj20170116),the Fundamental Research Funds for the Central Universities,the Priority Academic Program Development of Jiangsu Higher Education Institutions.