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Measurement of local rates of mass transfer from solid bodies of revolution
Chemical Engineering Science, 1968, Vol. 23, pp. I 157-l 158.
Measurement
Pergamon Press.
Printed in Great Britain.
of local rates of mass transfer from solid bodies of revolution
(First received
16 October
1967; in revisedform 2 February
IN A RECENT study[l] of the influence of particle shape on mass transfer processes a theoretical analysis was developed for the prediction of local rates of mass transfer from the oblate spheroidal shapes frequently assumed by drops. To test the analysis it was necessary to measure accurately local rates of mass transfer from solid models supported in a wind tunnel. Changes in the dimensions of a model alter its transfer area as well as its size and shape so that it is essential that only a small dimensional change should occur between measurements. In the method of measurement which has been most frequently used for bodies of revolution the bodies are photographed on separate films before and after an experiment [2-71. The two negatives are later superimposed in their correct relative position and enlarged sufficiently for precise measurements to be made. A small displacement in the relative position of the two negatives gives rise to large errors. For cylinders, measurements have generally been made with the aid of feeler gauges, micrometer dial indicators, etc.[8-lo]. Such methods cannot easily be adapted for use with bodies of revolution and there is the possibility of damage occurring to the specimens. To prevent such damage Macleod and Stewart[ll] used a free air jet to measure dimensional changes of acenaphthene cylinders. With their method there is the risk of incurring errors due to sublimation; also it may be unsuitable when surface curvature varies rapidly with position. Various workers have studied rates of evaporation or sublimation from sample areas of bodies[l2-141. The models were difficult to construct and the zones from which transfer was measured were relatively large. Danckwerts and Anolick[lS] coated metal slats with a thin film of naphthalene of known uniform thickness. From photographs taken at fixed time intervals they were able to construct contour maps of the mass transfer coefficient. Their method was not used in the present work as a means could not be devised for the deposition of a uniform film on bodies of revolution. Electra-chemical methods in which reaction rate is diffusion controlled have been used to obtain local and overall rates of transfer in both free and forced convection[ 16-181. To measure local rates an insulated electrode is incorporated in the model surface. For bodies such as the sphere or cylinder only one test model is required as the body may be rotated in order to obtain additional point measurements. This is not usually possible, however, for other body shapes. Of the methods considered the photographic one seemed to be the most suitable for bodies of revolution provided that
1968)
the problem of superimposing the two images correctly could be overcome. The obvious solution seemed to be to obtain both images on the same photographic plate by double exposure of the plate. In preliminary experiments shadow-grams were produced by means of a parallel beam of light projected past the body into the camera. The double images obtained were not, however, sufficiently well defined for accurate measurements to be made. Direct photography was tried as an alternative and, at first, in order to avoid fogging of the first image, rear lighting was used for the first exposure and frontal illumination for the second[l9]. Satisfactory results could not be obtained for the second exposure as adequate frontal illumination could not be provided. An alternative procedure using rear lighting for both exposures was used. This technique has the disadvantage that the second exposure causes the first image to be partially fogged so that the accuracy with which the edge of the first image may be identified is reduced. To minimise this effect the light intensities of both exposures should be. restricted to relatively low levels. On the other hand it is difficult to obtain satisfactory contrast in the negative at low image densities. Trial photographs were taken using different combinations of light intensities until optimum results were obtained. A long focal length lens was necessary as the camera lens had to be sufficiently far from the object to make parallax errors neglible. A variety of lenses were compared and the most suitable found to be an 8.25 in. focal length TaylorHobson ‘Ental II’ used at a stop number of f/8 and with an image to object magnification of two and onehalf. The lens was mounted in the reverse direction inside the lens panel of a monorail camera mounted on the same optical bench as that used to support the test specimens in the wind tunnel. By this means relative movement of the camera and test specimen was minimised. To eliminate blurring of the image, flash illumination was employed. The equipment layout is shown in Fig. 1. When photographs were taken the plug shown in the tunnel wall was removed. The use of photographic plates rather than film was necessary to prevent dimensional changes occurring during processing. Ilford ‘High Resolution’ plates, developed in a high contrast developer, were completely satisfactory. Figure 2 shows a positive print of a double exposure photograph of a composite spheroid. The outer boundary represents the original shape, the dark portion the final shape, and the grey portion between the two boundaries the mass transferred. It is interesting to note that, in agreement with the theoretical analysis, the maximum rate of transfer occurred
1157
Shorter Communications
Wind Slnar
Tunnel
TE
Monorail
Ji_ _-Spheroid
d?++-
Support /-OptIcal Bench (Supported by
Rlgld
Structure)
Fig. I. Photographic equipment. not at the front stagnation point, but at a region not too far removed from the separation zone. Measurements of dimensional changes were made from images of the spheroids enlarged to a size twenty times the original. The definition of the enlarged images was very good and no difficulty was experienced in measuring the diminutions with an accuracy that corresponds to an actual dimensional change of 0.0 1 mm. Local mass transfer rates were calculated from the diminutions measured at successive intervals of ten degrees around the peripheries of thirteen spheroidal shapes. The total amounts of mass transferred were calculated and compared with amounts determined from direct weighings. The maximum and mean differences between the calculated and weighed amounts transferred were 5.8 per cent and 3.0 per cent of the weighed amounts, respectively. However, to make these comparisons it was necessary to determine the
density of cast naphthalene. Several measurements were made and the density was found to vary by plus and minus 3.0 per cent about a mean value. Acknowledgment-The photographic equipment described was purchased from a grant kindly given by Imperial Chemical Industries Ltd. The award of an Attack Oil Company fellowship to S. A. Beg is gratefully acknowledged. Department of Chemical Engineering S. A. BEG and Chemical Technology N. DOMBROWSKIt Imperial College A. R. H. CORNISH London, S. W.7 tPresent address: Department of Chemical Engineering, Houldsworth School of Applied Science, The University, Leeds.
REFERENCES [l] BEG S. A., Ph.D. Thesis, University of London 1966. 121 FROSSLING N., Beitr. Geophys. 1938 52 170 (AERE Harwell Translation, August 1963). [3] GARNER F. H. and GRAFTON R. W., Proc. R. Sot. 1954 224A 64. [4] GARNER F. H. and SUCKLING R. D.,A.Z.Ch.E.JI 1958 4 114. [5] GARNER F. H. and KEEY R. B., Chem. Engng Sci. 1958 9 218. 161 GARNER F. H. and HOFFMAN J. M.,A.I.Ch.E. Jl 19606 579. [7] SKELLAND A. H. P. and CORNISH A. R. H.,A.Z.Ch.E. Jl 1963 9 73. IS] WINDING C. C. and CHENEY A. J., Ind. Engng Chem. 1948 40 1087. [9] SHERWOOD T. K. and BRYANT H. S., Can. J. Chem. Engng 1957 35 51. lo] CHRISTIAN W. J. and KEZIOS S. P.,A.I.Ch.E3119595 61. 111 MACLEOD N. and STEWART G., Chem. Engng Sci. 1960 12 142. 121 POWELL R. W. and GRIFFITHS E., Trans. Instn Chem. Engrs 1935 13 175. 131 POWELL R. W., Trans. Instn Chem. Engrs 1940 18 36, 141 MAISEL D. S. and SHERWOOD T. K.,Chem. Engng Prog. 195046 131,172. IS] DANCKWERTS P. V. and ANOLICK C., Trans. Znstn Chem. Engrs 1962 40 203. 1161GRASSMANN P., IBL N. and TRUBT., Chemie-Zngr-Techn. 196133 529. 171 SCHUTZG.,Znt. J. HeatMuss Transfer 19636873. 181 GLEN J. B. and KEEY R. B., Chem. Engng Sci. 1965 20 444. 191 DOMBROWSKI N. and LEVY A., Nature 1964 202 521.
1158
Support
Direction of F l o w
i
R e g i o n of M a x i m u m Mass Transfer Rate Fig. 2.
Facing page 1158
Measurement
Pergamon Press.
Printed in Great Britain.
of local rates of mass transfer from solid bodies of revolution
(First received
16 October
1967; in revisedform 2 February
IN A RECENT study[l] of the influence of particle shape on mass transfer processes a theoretical analysis was developed for the prediction of local rates of mass transfer from the oblate spheroidal shapes frequently assumed by drops. To test the analysis it was necessary to measure accurately local rates of mass transfer from solid models supported in a wind tunnel. Changes in the dimensions of a model alter its transfer area as well as its size and shape so that it is essential that only a small dimensional change should occur between measurements. In the method of measurement which has been most frequently used for bodies of revolution the bodies are photographed on separate films before and after an experiment [2-71. The two negatives are later superimposed in their correct relative position and enlarged sufficiently for precise measurements to be made. A small displacement in the relative position of the two negatives gives rise to large errors. For cylinders, measurements have generally been made with the aid of feeler gauges, micrometer dial indicators, etc.[8-lo]. Such methods cannot easily be adapted for use with bodies of revolution and there is the possibility of damage occurring to the specimens. To prevent such damage Macleod and Stewart[ll] used a free air jet to measure dimensional changes of acenaphthene cylinders. With their method there is the risk of incurring errors due to sublimation; also it may be unsuitable when surface curvature varies rapidly with position. Various workers have studied rates of evaporation or sublimation from sample areas of bodies[l2-141. The models were difficult to construct and the zones from which transfer was measured were relatively large. Danckwerts and Anolick[lS] coated metal slats with a thin film of naphthalene of known uniform thickness. From photographs taken at fixed time intervals they were able to construct contour maps of the mass transfer coefficient. Their method was not used in the present work as a means could not be devised for the deposition of a uniform film on bodies of revolution. Electra-chemical methods in which reaction rate is diffusion controlled have been used to obtain local and overall rates of transfer in both free and forced convection[ 16-181. To measure local rates an insulated electrode is incorporated in the model surface. For bodies such as the sphere or cylinder only one test model is required as the body may be rotated in order to obtain additional point measurements. This is not usually possible, however, for other body shapes. Of the methods considered the photographic one seemed to be the most suitable for bodies of revolution provided that
1968)
the problem of superimposing the two images correctly could be overcome. The obvious solution seemed to be to obtain both images on the same photographic plate by double exposure of the plate. In preliminary experiments shadow-grams were produced by means of a parallel beam of light projected past the body into the camera. The double images obtained were not, however, sufficiently well defined for accurate measurements to be made. Direct photography was tried as an alternative and, at first, in order to avoid fogging of the first image, rear lighting was used for the first exposure and frontal illumination for the second[l9]. Satisfactory results could not be obtained for the second exposure as adequate frontal illumination could not be provided. An alternative procedure using rear lighting for both exposures was used. This technique has the disadvantage that the second exposure causes the first image to be partially fogged so that the accuracy with which the edge of the first image may be identified is reduced. To minimise this effect the light intensities of both exposures should be. restricted to relatively low levels. On the other hand it is difficult to obtain satisfactory contrast in the negative at low image densities. Trial photographs were taken using different combinations of light intensities until optimum results were obtained. A long focal length lens was necessary as the camera lens had to be sufficiently far from the object to make parallax errors neglible. A variety of lenses were compared and the most suitable found to be an 8.25 in. focal length TaylorHobson ‘Ental II’ used at a stop number of f/8 and with an image to object magnification of two and onehalf. The lens was mounted in the reverse direction inside the lens panel of a monorail camera mounted on the same optical bench as that used to support the test specimens in the wind tunnel. By this means relative movement of the camera and test specimen was minimised. To eliminate blurring of the image, flash illumination was employed. The equipment layout is shown in Fig. 1. When photographs were taken the plug shown in the tunnel wall was removed. The use of photographic plates rather than film was necessary to prevent dimensional changes occurring during processing. Ilford ‘High Resolution’ plates, developed in a high contrast developer, were completely satisfactory. Figure 2 shows a positive print of a double exposure photograph of a composite spheroid. The outer boundary represents the original shape, the dark portion the final shape, and the grey portion between the two boundaries the mass transferred. It is interesting to note that, in agreement with the theoretical analysis, the maximum rate of transfer occurred
1157
Shorter Communications
Wind Slnar
Tunnel
TE
Monorail
Ji_ _-Spheroid
d?++-
Support /-OptIcal Bench (Supported by
Rlgld
Structure)
Fig. I. Photographic equipment. not at the front stagnation point, but at a region not too far removed from the separation zone. Measurements of dimensional changes were made from images of the spheroids enlarged to a size twenty times the original. The definition of the enlarged images was very good and no difficulty was experienced in measuring the diminutions with an accuracy that corresponds to an actual dimensional change of 0.0 1 mm. Local mass transfer rates were calculated from the diminutions measured at successive intervals of ten degrees around the peripheries of thirteen spheroidal shapes. The total amounts of mass transferred were calculated and compared with amounts determined from direct weighings. The maximum and mean differences between the calculated and weighed amounts transferred were 5.8 per cent and 3.0 per cent of the weighed amounts, respectively. However, to make these comparisons it was necessary to determine the
density of cast naphthalene. Several measurements were made and the density was found to vary by plus and minus 3.0 per cent about a mean value. Acknowledgment-The photographic equipment described was purchased from a grant kindly given by Imperial Chemical Industries Ltd. The award of an Attack Oil Company fellowship to S. A. Beg is gratefully acknowledged. Department of Chemical Engineering S. A. BEG and Chemical Technology N. DOMBROWSKIt Imperial College A. R. H. CORNISH London, S. W.7 tPresent address: Department of Chemical Engineering, Houldsworth School of Applied Science, The University, Leeds.
REFERENCES [l] BEG S. A., Ph.D. Thesis, University of London 1966. 121 FROSSLING N., Beitr. Geophys. 1938 52 170 (AERE Harwell Translation, August 1963). [3] GARNER F. H. and GRAFTON R. W., Proc. R. Sot. 1954 224A 64. [4] GARNER F. H. and SUCKLING R. D.,A.Z.Ch.E.JI 1958 4 114. [5] GARNER F. H. and KEEY R. B., Chem. Engng Sci. 1958 9 218. 161 GARNER F. H. and HOFFMAN J. M.,A.I.Ch.E. Jl 19606 579. [7] SKELLAND A. H. P. and CORNISH A. R. H.,A.Z.Ch.E. Jl 1963 9 73. IS] WINDING C. C. and CHENEY A. J., Ind. Engng Chem. 1948 40 1087. [9] SHERWOOD T. K. and BRYANT H. S., Can. J. Chem. Engng 1957 35 51. lo] CHRISTIAN W. J. and KEZIOS S. P.,A.I.Ch.E3119595 61. 111 MACLEOD N. and STEWART G., Chem. Engng Sci. 1960 12 142. 121 POWELL R. W. and GRIFFITHS E., Trans. Instn Chem. Engrs 1935 13 175. 131 POWELL R. W., Trans. Instn Chem. Engrs 1940 18 36, 141 MAISEL D. S. and SHERWOOD T. K.,Chem. Engng Prog. 195046 131,172. IS] DANCKWERTS P. V. and ANOLICK C., Trans. Znstn Chem. Engrs 1962 40 203. 1161GRASSMANN P., IBL N. and TRUBT., Chemie-Zngr-Techn. 196133 529. 171 SCHUTZG.,Znt. J. HeatMuss Transfer 19636873. 181 GLEN J. B. and KEEY R. B., Chem. Engng Sci. 1965 20 444. 191 DOMBROWSKI N. and LEVY A., Nature 1964 202 521.
1158
Support
Direction of F l o w
i
R e g i o n of M a x i m u m Mass Transfer Rate Fig. 2.
Facing page 1158