CORRESPONDENCE
Pressure Vessels the Tube Sheet
- Let the Tubes Support
SIR: I have read with great interest the article on pressure vessels [G. D. Galletly, C. R. Garbett, IND.ENG.CHEM.50,1227 (1958)]. I n our office, we have calculated tube sheets by Miller’s method for 3 years, because we think that it gives more relief from stress phenomena than the TEMA method. Miller’s original paper does not emphasize enough the importance of stress due to thermal expansion. This is also an aspect not touched in this article, except in paragraph 4 of miscellaneous topics, where only the transient conditions are considered. Even the cases concerning permanent working conditions can lead to very important stresses of thermic origin, especially in the case of liquid-liquid exchangers where the coefficient of convection, outside the tubes, is often less than double the over-all heat transfer coefficient. I n these conditions, the temperature difference between tubes and shell can reach or exceed half of the mean temperature difference between fluids. When this variation reaches several tens of degrees centigrade, the thermal stresses are serious for box-type exchangers. Another case, even more severe, is when hot fluid is allowed to run through tubes before cold fluid circulates outside. The temperature difference between tubes and shell can then be very serious. The case of a n exchanger built with different metals for tubes and shell always raises problems of thermal expansion, even if tubes and shell are a t the same temperature. All the preceding remarks apply to exchangers with steady heads (box type) and without expansion bellows. The comparison between Miller’s and TEMA methods always leads to higher thicknesses with TEMA; this is normal
because Miller takes account of real stresses not considered by the TEMA method. As a trial of both methods, during the last months we have calculated scores of exchangers with steady heads using: (1) the TEMA method; (2) Miller’s method with thermal expansion and clamped tube sheet; and ( 3 ) Miller’s method without thermal expansion and clamped tube sheet. Plotting the results on a logarithmic diagram showed that the thicknesses given by Miller’s method without expansion are approximately the same as those given by the TEMA method, o r slightly less. If we take thermal expansions into account, Miller’s method leads to thicknesses about two or three times higher than those given by TEMA. However, there is experimental evidence that thicknesses calculated by the TEMA method are satisfactory and safe in industrial practice, and it is likely that the coefficients of safety could be reduced considerably without any danger, if Miller’s method is followed and thermal expansions are taken into account. We could thus agree with thicknessesgiven by TEMA, in case of exchangers submitted to thermal expansions, and probably be safe with thicknesses much less in the other cases. Besides, we are about to undertake, during the next year, a series of tests with a 26-channel strain gage apparatus. We agree on the variations of thicknesses given by Miller’s method, if the tube sheet is considered as clamped or simply supported. I n most cases, the hypothesis of a clamped edge leads to higher thicknesses. This is the result of a calculation supposing a perfectly clamped edge, while the shell turns slightly by effect of the bending moment distributed all around the sheet.
I n the case of Figure 3, where the tube sheet is fixed to the shell by one weld bead, this bead will bend to allow the rotation of the edge of the sheet, and we find it dangerous; in fact, the sheet itself behaves as simply supported, but concentrations of stresses will appear in the weld bead itself. I n such a case, Miller’s method can be employed, by taking the thickness of the tube sheet for calculating kD and functions G, and the thickness of the weld bead for calculating the maximum stresses. You get enormous stresses. I n spite of these few restrictions, we agree on the great interest of Miller’s method, which makes it possible to take into account most of the important physical variables involved in tube sheet calculations. We hope that this article, issued in a world known publication, will be read by more people than Miller’s article itself.
R. BAHOUT Socittt pour 1’Equipement des Industries Chimiques 14 Rue la Bottie Paris 8, France
SIR: Thermal expansion between tube and shell is included in the formula for p (given on p. 1228) in the form
p
=
na . . . . + YA- EL - C
The designer must use discretion in selecting the temperatures and pressures on which he bases his design. Naturally he must allow for all possible operating conditions that might be encounteredi.e., the loss of process pressure on tube or shell side, the stoppage of coolant flows, washing-out conditions, etc. FurVOL. 51, NO. 6
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JUNE 1959
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thermore, these conditions should be rebiewed as to whether they occur routinely (and hence call for conservative or code stress levels) or whether they rrpresent emergency conditions against which he wishes to guarantee the integrity of the structure. I t is entirely reasonable to expect that the inclusion of large temperature differences simultaneously with pressure loadings could lead to design thicknesses (based on a pre-determined stress level) which substantially exceed TEMA values. The question one must then face is whether the low stress levels specified are in reality justified. Mr. Bahout has thus indirectly raised a n important point for the philosophy of the designer. The ASME codes specify the design stress level; holvever, they do not give detailed stress distributions in their formulas. Rather, they give design formulas which have been proved successful, partly by analysis, partly by experience records. Are we then to penalize ourselves by insisting upon low stresses at every point in the structure, which arise from stress concentrations that become apparent only upon carrying out a detailed and sophis ticated analysis? Mr. Bahout’s suggestion is probably the compromise most palatable to the designer-use the design based upon detailed stress analysis when it gives a section thickness less than the code (provided the designer has assured himself that his analysis is fully valid), and use the code design when it gives the thinner section. Thereby he relies upon the plastic yielding of the code design (demonstrably safe through the experience with the code, one assumes) to take care of undetermined points of stress concentration. Figure 3 should have shown a weld bead on the underside of the tube sheet where it joins the shell. as well as the top (see sketch a ) . Alternative possibilities are also shown.
b
a
d
C
e
G. D. GALLETLY C. R. GARBETT Shell Development Co Emeryville, Calif.
SHELL TUBE
Correction Fermentation I n the “Fermentation” review [S. C. Beesch and F. W. Tanner, Jr., IND. ENG.CHEhf. 50, 1341 (September 1958)], Reference (66M) on page 1354 should be (66M) Takida, T., Tahara, K. (to Nippon Chemical D~~~ c0,), japan. patent 4435 (June 29,1955).
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Critical area in question i s the weld on top of the tube sheet. This is a type of tube sheet support which tends toward a simple support. Variations on the weld for support are shown at the top
INDUSTRIAL AND ENGINEERING CHEMISTRY
