Treatments of thermodynamics

D. Chisholm

Conclusions E q u a t i o n s for use in the d e s i g n of air-lift p u m p s h a v e b e e n d e v e l o p e d . E q (15) for p r e d i c t i n g m a s s flow rates, g i v e n the m a s s d r y n e s s fraction, has b e e n s h o w n to give values w i t h i n 15% of e x p e r i m e n t . A p p r o x i m a t e e q u a t i o n s h a v e also b e e n d e v e l o p e d for use at the ' m a x i m u m flow rate c o n d i t i o n ' . E q s (23) a n d (25) a l l o w r a p i d p r e d i c t i o n of the m a s s d r y n e s s fraction at that c o n d i t i o n , w h i l e E q (27) allows a p p r o x i m a t e e s t i m a t e s of the a s s o c i a t e d flow rate.

h e n c e the m a s s d r y n e s s fraction is o b t a i n e d f r o m E q (25) 3.282 e - 1 x = =0.0134 1000/1.368 - 1 T h e flow cross-section is 7r

2

A = ~- x 0.0267 = 5.6 x 10 -4 m e T h e liquid m a s s flow rate is t h e n ML = (1 - 0.0134) x 362 x 5.6 x 10 -4 = 200 g / s a n d the c o r r e s p o n d i n g air m a s s flow rate

Appendix

M c = 0.0134 x 362 x 5.6 x 10 -4 = 2.7 g / s

Numerical example F o r an air-lift p u m p of 26,7 m m b o r e a n d 8.14 m in length, m a k e an a p p r o x i m a t e e s t i m a t e of the maxim u m liquid flow rate, w h e r e the m i x e r is 3.07 m b e l o w the l i q u i d s u m p level. VL = l X 10 -3 m 3 / k g ; tzL = 1.002 x 10-3N s / m e. U s i n g E q (12) 3.07 S = =0.3771 8.14

T h e m a s s flow rates in T a b l e 2 w e r e o b t a i n e d u s i n g E q (15) rather t h a n E q (26).

References 1.

A.S.M.E., Journal of Engineering for Power, 1968, 106-110 2.

Multiphase Flow, 1979, 5, 225-228

G = [27 8 x 9 " 8 x 0 " 3 7 7 1 3 x 0 ' 0 2 6 7 1 ' e 5

]1/1.75

3. 4.

T h e c o r r e s p o n d i n g m a s s d r y n e s s fraction is evaluated as follows. F r o m E q (24) 1 = 2.977

Fluids in Motion, Principles and Design Practices. Gupta A. and Cheremesinoff N. P. (Editors). Ann Arbor Sciences/Butterworth (in press)

7.

9.

2

T h e specific v o l u m e of the air is e v a l u a t e d u s i n g E q (16) 9.8 x 8.14 x 0.3771] ~ J = 1.368 k g / m 3

Letter to the Editors Treatments of thermodynamics I n y o u r M a r c h 1982 issue (Vol 3, N o 1), Dr T. J. Kotas r e v i e w e d m y b o o k T h e r m o d y n a m i c P r i n c i p l e s of E n e r g y d e g r a d i n g . M a n y of his criticisms are, I believe, u n f o u n d e d . T o b e q u i t e specific, a h o r d e of text-books h a v e a p p e a r e d in the last f e w d e c a d e s p u r p o r t i n g to treat the S e c o n d L a w in d e p t h , yet a l m o s t all of t h e m c o p y b l i n d l y the c o n c e p t s p r e s e n t e d in others, w i t h o u t seeking either to a d o p t a n e w a p p r o a c h or s i m p l i f y the subject for the benefit of p r a c t i s i n g e n g i n e e r s a n d scientists. T h e b o o k is not i n t e n d e d to t h r e a t e n the n a r r o w w o r l d of a c a d e m i c s s u c h as Dr Kotas,

152

Chisholm D. Gas-liquid flow in pipeline systems. In:

Andeen G. B. and Griffith P. Momentum flux in two-phase flow. A.S.M.E. Preprint No 67-HT-32, August 1967 Wiafe F. Two-phase flow in rough tubes. Ph.D. Thesis, The University of Strathclyde, Glasgow, 1970

2.977 + (2.9772 + 4) 1/e _ 3.282

1 = 1.19 1+

6.

8.

t h e n f r o m E q (23)

-

Chisholm D. Void fraction during two-phase flow. J. Mech. Eng. Sci., 1973, 15(3), 235-236

= 362 kg m -e s -1

VH" 1/2

Hussain L. A. and Spedding P. L. The theory of the gas-lift pump. Int. ]. Multiphase Flow, 1976, 1, 83-87 Collier J. G. Convective boiling and condensation. McGraw-Hill (Publishers) Ltd, London, 1972

5.

3 2 x 0.3771

Jeelani S. A. K., Kasipati Rao K. V. and Balasubramanian

G. R. The theory of the gas-lift pump: a rejoinder. Int. ].

t h e n f r o m E q (27) the m a x i m u m m i x t u r e m a s s velocity is o b t a i n e d ,

E -

Stennlng A. H. and Martin C. B. An analytical and experimental study of air-lift pump performance. Trans.

10.

Gosline ]. E. Experiments on the vertical flow of gas-liquid mixtures in glass pipes. Trans. Am. Min. Metall. Engs, 1936, 118, 56-70 Chisholm D. The anti-gravity thermosiphon. I. Chem. E. Symp. Set. No 38. L Chem. E./L Mech. E. Joint Syrup. on Multi-phase Flow Systems, University of Strathclyde, Glasgow, 2-4 April 1974, 2 Paper F3. The Institution of Chemical Engineers, London, 1974

w h o I a m sure is a u f a i t w i t h the latest esoteric t r e a t m e n t of the subject. F r a n k l y , I a m not at all interested in the diverse a n d often c o n f u s i n g treatm e n t s of this very i m p o r t a n t subject w h i c h are e v i d e n t in the literature. M y p u r p o s e has b e e n to p r o d u c e a simplified a n d reliable a c c o u n t of First a n d S e c o n d L a w influences, a n d in d o i n g so I feel I h a v e s u c c e e d e d in a p p e a l i n g to a large n u m b e r of p r a c t i s i n g scientists a n d r e s e a r c h - a n d - d e v e l o p m e n t e n g i n e e r s w h o earn their k e e p b y p r o d u c t i v e e n d e a v o u r s in industry. It is also o b v i o u s that the n e w definitions a n d s i m p l i s t i c a p p r o a c h h a v e b e e n too t h r e a t e n i n g for Dr Kotas. Because of the existence of m a n y different definitions, it has b e e n n e c e s s a r y to use s y n o n y m o u s terms. I f u n c o m m o n m e a n i n g has b e e n g i v e n to the t e r m 'external irreversibility', I a m curious to k n o w

Vol 3, No 3, September 1982

Letter to the editor what other meaning Dr Kotas offers. The comment that 'this relationship (between energy degrading and both internal irreversibility and changes in unavailable energy) is never put to the t e s t . . . ' is ludicrous. Any engineer will tell you that if two separate effects are identifiable in a process, they can be combined additively; it is not necessary to test anything but simply to use one's God-given common sense. I also refute most emphatically the statement 'The fallacy of this treatment...', since it is not at all necessary for the temperatures at which heat is transferred to be the same. Quite simply, a process with combined heat and work interactions is divided into two composite processes, one with work interactions only (including friction), and the second with heat transfer only. This heat transfer can be thought of as occurring very rapidly after the work interaction (and therefore under entirely different conditions compared with the real combined process) provided that the same end state is reached. There is no mystery about this; the procedure is well-explained in the text. By adopting such a simple technique, this complex subject becomes at last amenable to simple mathematical treatment. Dr Kotas seems to have missed this important point.

D. F. Moore Department of Mechanical Engineering University College, Dublin Reviewer' s reply I will, for once, agree with Dr Moore that there is no satisfactory English language book available currently that would deal in a comprehensive way with the practical applications of the Second Law to thermal plant analysis. Unfortunately, I do not believe that his book fills this gap. The treatment of this important subject which he has presented, in spite of his claims, is neither simplified nor reliable. My impression of this book is that it is more likely to confuse than inform those potential readers who are new to this subject. The point of criticism in my review of his book to which Dr Moore takes particular umbrage is that concerning his technique of replacement of an actual process with two component processes. To answer his rhetorical arguments may I be permitted to prove my point by applying his technique to a special case for which the answer is simple and well-known. Fig 1 shows the analysis of an isothermal expansion process presented in exactly the same 2

o

Ou~v

d ASINTq t"--Z~SEX T "I Combined work and heat transfer (i)

!-Work transfer only (ii)

ASExT "1 Heot tronsfer only

S

(iii)

Fig 1 Analysis of an isothermal expansion process following Moore's presentation and nomenclature

Int. J. Heat & Fluid Flow

way as that of a more general expansion process shown in Figure 6.4 in Dr Moore's book. Both the symbols and nomenclature used are his. Let us assume that the heat transfer to the expanding fluid occurs at a temperature, TR, only marginally higher than that of the fluid so that the irreversibility associated with the heat transfer is negligible. The process will be assumed to suffer some irreversibility due to internal fluid friction. According to Dr Moore, the actual process 1-2 can be split up into two component processes 1-a and a-2 and the irreversibility, or the energy degrading as he prefers to call it, of the actual process is equal to the sum of the internal irreversibility lint Of the adiabatic work transfer process and the irreversibility of the isobaric heat transfer process which, again, he calls by his own name of increase in unavailable energy and denotes by AQ ..... This relationship can be written as (expression (6.5) in Dr Moore's book) follows:

E.D . . . .

bined = l i n t q- A ~ ) . . . .

(1)

A reference to Fig 1 (iii) will show that even with reversible heat transfer (ie TSVSTEM= TR), Dr Moore's technique will give AQ . . . . > 0, which is obviously wrong. If, further, the frictional dissipation is reduced so that, in the limit, llnt = 0, the total 'energy degrading' in such an obviously fully reversible process will still be found to be greater than zero according to this technique. It is obvious that we cannot assume as Dr Moore does, 'that if two separate effects are identifiable in a process, they can be combined additively'. The arguments which Dr Moore is offering in support of his technique such as 'Any engineer will tell y o u ' . . . , do not carry much weight in a properly conducted scientific debate, a view with which I am sure most engineers and scientists would agree. With regard to 'external irreversibility', my definition of it is that it is that part of the total irreversibility associated with a given process, which occurs outside the system. The quantity which Dr Moore calls external irreversibility is shown in Fig. 1(i) as Iext. This quantity will be seen to be neither external nor any kind of irreversibility. And, incidentally, on the question of arbitrary nomenclature, another concept which Dr Moore 'invented' and to which he gave his own special name is gross irreversibility, defined on page 135 in his book. This will be found to be nothing else but the old familiar concept of reheat, which 'as any engineer will tell you', is not wholly an irreversibility and the qualifying word 'gross' will not change this fact. The lesson, which in my view, is to be learnt from this case is that new, untried ideas should not be put directly into a book, but the author should try to publish them first so that he gets the benefit of the associated process of refereeing and criticism.

T. d. Kotas Department of Mechanical Engineering Queen Mary College, University of London Note added in proof: Dr Moore contends that the example given above is flawed, not his combination technique. Further discussion will appear in the next issue.

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