VISCOSITY OF HYDROGEN IN T H E G A S E O U S A N D LIQUID S T A T E S FOR T E M P E R A T U R E S U P TO 5000" K. LEONARD I . S T I E L ' A N D
GEORGE THODOS
.l'orthwestern Cj2wersity, Ecanston, Ill.
A viscosity correlation for hydrogen has been developed for reduced temperatures up to T R = 75 and reduced pressures up to P R = 100. Experimental viscosities available in the literature for hydrogen at moderate pressures were utilized to establish the atmospheric viscosity behavior of this substance. For each experimental high density va!ue, the residual viscosity, p - p * , was determined from the atmospheric pressure relcitionship and plotted against reduced density to produce a continuous curve for both the gaseous and liquid regions. This information enabled a plot of viscosity against reduced temperature and reduced pressure to b e developed for this substance. Viscosity values of dissociating hydrogen for temperatures up to 5000" K. were obtained from reported theoretical calculations and were plotted against temperature for constant pressures.
HE increased importance of hydrogen in design applications Tnecessitates the development of a n accurate correlation for the prediction of the viscosity of this substance. Thodos and coivorkers (d, 23, 28, 34, 36) have developed reduced state correlations for the es1:imation of the transport properties of individual substances, which have proved to be highly accurate. For hydrogen! Schaefer and Thodos (33>35) have developed reduced state density and thermal conductivity correlations from the experimental values of these properties available in the literature. In the present study, the approach used b>-the previous investigators has been employed to develop a correlation for the viscosity of hydrogen in the gaseous and liquid states for pressures u p to 1280 atm. and temperatures up to 5000O K. Rogers. Zeigler, and Mcil'illiams (37) have recently developed equations relating the viscosity of hydrogen in the gaseous and liquid states to the corresponding density for a wide range of temperatures and pressures. from experimental values available in the literature through a n approach similar to that utilized in the present investigation. However, their results are not presented in a form which permits this property to be readily established a t any remperature and pressure, since the density of hydrogen must be known a t these conditions. Also, in this investigation the high pressure viscosity data are analyzed differently from those in the study of Rogers. Zeigler, and Mcil'illiams (,37), and new theoretical calculations of the transport properties of hydrogen at temperatures where dissociation is prevalent (52) now permit the viscosity behavior of the substance in the high temperature region to be re-examined.
Viscosity Behavior at Normal Pressures
Experimental values of the viscosity a t atmospheric pressure. reported by 43 investigators ( 7 > 1. 5-7, 9. 7 7 . 73: 75, 76, 78. 10-21, 24-17. 2 3 , 30: 37, 38-57. 53-55, 57-67) for hydrogen lvere obtaiimd from the literature and plotted against the corresponding temperature. The data for most of these references were found to be consistent with each other and permitted the moderate pressure viscosity behavior of hydrogen to be established with a high degree of accuracy for temperap*.
Present address, Syracuse University, Syracuse, N. Y .
rures up to llOOo K. In Figure 1 rhe resulting relationship bet\veen viscosiT and reduced temperature is presented: along mith the experimental points of the most significant references (7, 7 7 , 78, 30, 57). Below T , = 1.00: the dependence of viscosity on reduced temperature is linear on log-log coordinates and can be expressed analytically as follows : p*
= 175 X
(1)
1O-57$.gM
The relationship of Figure 1 has been exrended to T , = 75, at which point dissociation becomes noticeable. For 5 6 T, 75, the viscosity dependence on temperature is again linear and can be expressed as
was calculated by the use of the atmospheric viscosit): value at the same temperature obtained from the relationship of Figure 1. These residual viscosities were plotted against the corresponding reduced density values obtained from the reduced state density correlation of Schaefer and Thodos (33),as shown in Figure 2. It can be seen in Figure 2 that the dara of most of the investigators for the low density region are consistent and fall on a single curve. The data of Michels, Schipper, and Rintoul (27) for isotherms of 25'; 50°, 75', loo', and 125' C. were found to lie on this curve u p to reduced densities of p R = 1.50. However, the data of these investigators for the 25' C. isotherm in the dense gaseous region for pressures between 905 and 1900 atm. deviated from the relationship obtained by extending the low density curve through the liquid points in a continuous VOL. 2
NO. 3
AUGUST
1963
233
Reduced Temperature, T =-T Tc Figure 1 .
Relationship between viscosity and temperature at moderate pressures
fashion. Continuous relationships between the residual transport properties and density exist for all of the other substances investigated (4, 23, 28, 34, 36) and therefore it is felt that the high density values of Michels et al. for the 25' C. isotherm d o not accurately represent the viscosity behavior of hydrogen in this region, possibly because of diffusional effects a t these extreme pressures. Jossi, Stiel, and Thodos (79) have shown that for nonpolar gases, with the exception of hydrogen and helium? a unique relationship exists between the group ( p - @*)E and pR where = T c ~ / 6 / M ~ ~ 2 P , 2By ~ 3the . use of viscosity values for deuterium in the dense gaseous region to 2150 atm. reported by Michels, Schipper, and Rintoul (27) and for the liquid region reported by van Itterbeek and van Paemel (56), the group ( p - p*)E for this substance was plotted against p R along with values of this quantity for hydrogen. Atmospheric viscosities for deuterium were obtained from Coremans et al. (7) and Golubev and Petrov (77). Essentially a single curve resulted for both substances; however, a t high pressures in the dense gaseous region, the data for deuterium began to curve upward from the corresponding values for hydrogen, and the curve through these points when extended appeared to coincide properly with the liquid points. This behavior indicated that a single continuous relationship should also exist for hydrogen in the dense gaseous and liquid regions. 234
ILEC FUNDAMENTALS
Rogers, Zeigler, and McWilliams (37) have accepted the high density values of Michels e t al. and have presented qep arate relationships for the viscosity of gaseous and liquid hydrogen. However, if the viscosity behavior of hydrogen is not continuous in the dense gaseous and liquid region, a plot of viscosity against temperature for different pressures would exhibit discontinuities which should not exist. Therefore, the low density curve of Figure 2 was extended through the dense gaseous and liquid region to include the liquid points, by plotting log ( p - p * ) us. 1/ p R and interpolating through this region. The relationship of Figure 2 should be more dependable than the similar relationship presented by Brebach and Thodos ( d ) for hydrogen because of the inclusion of the additional data of Golubev and Petrov ( 7 7) in the present study. A further experimental study is required to verify the viscosity behavior of hydrogen established in this study for reduced densities in the range 1.5 6 pR 2.2.
