Ind. Eng. Chem. Process Des. Dev. 1082, 27, 646-650
646
textile, pulp, refinery, petrochemical, glass, and rubber industries, 5-10 (ton/h)/MW; sugar and food industries, 10 (ton/h)/MW. Accordingly, it can be helpful to choose suitable energy conservation technologies according to steam-dominant or power-dominant cases in steam and power demands. Above all, an idea of energy-oriented industry complex might become promising when common utility facilities are built for different types of process industries.
+
Conclusion
Two different types of demand case of steam and power were defined, namely, steam-dominant and power-dominant cases. Major energy conservation technologies were classified in accordance with whether the case of steampower demand is power-dominant or steam-dominant. A strategy to determine the steam-power balance for energy conservation at the preliminary design stage was proposed from an overall viewpoint based on the available energy analysis. Acknowledgment
The authors wish to express their thanks to Chiyoda Chemical Engineering and Construction Company for supporting the present study and for permitting ita publication. They also express their appreciation to Mr. J. Itoh for his valuable suggestions in the early stages of this work. Nomenclature AL1 AL2
= loss of available energy in the process systems, kcallh
= loss of available energy in the steam-power system, kcal/h A L = loss of available energy in the power generation section, gcal/h a = specific available energy of a stream, kcallkg b = boiler D 1= decision vector in the process systems D 2 = decision vector in the steam-power system h = specific enthalpy of a stream, kcallkg
h* = specific enthalpy of steam at isentropic expansion, kcallkg f i = equation representing the relation between X iand D 2 f k = equation representing the relation between Xk and D g = equation representing the relation between W and D 1 Pb = boiler pressure, kg/cm2 P,, = allowable maximum boiler pressure, kg/cm2 Q1 = waste heat in the process systems, kcallh Q2 = waste heat in the steam-power system, kcal/h S = entropy of a stream, kcal/(kg K) ST = entropy at the temperature of kth steam required, kcal/(kg K) T = absohte temperature of a stream, K To= environment temperature, K W = power demand, kcal/ h XI., = steam flowrate to be generated at a boiler, ton/h X , = steam flowrate to condensing turbines, ton/h Xi = mass flowrate to the energy supply system, ton/h Xj = mass flowrate of exhausts in the steam-power system, ton/h Xk = mass flowrate of kth steam required X, = mass flowrate of pth product in the process systems, ton/h X,= mass flowrate of rth raw material in the process systems, ton/h X , = mass flowrak of exhausts in the process systems, ton/h 7M = adiabatic efficiency of turbine 7~ = effectiveness of turbine (work/available energy change) L i t e r a t u r e Cited Gaggioii, R. A.; Petit, P.J. CMM7ECH 1977, 496. Nishio, M.; Itoh, J.; Shiroko, K.; Umeda, T. Ind. Eng. Chem. Process Des. D e v . 1980, 19, 306. Shiroko, K.; Umeda, T. J . Jpn. Pet. Inst. 1980, 23(5),348. Umeda, 1.;Itoh, J.; Shlroko, K. Chem. Eng. f r o g . 1978, 74(7), 70. Umeda, 1.;Niida, K.; Shiroko, K. A I C M J. 1979, 25(3),423. Umeda, T.; Shiroko, K. I n "Energy Utilization Engineering" (in Japanese), Ohm Press: Tokyo, 1980; Chapter 5.
Received far review May 26, 1981 Accepted April 20, 1982
Work was presented at the AIChE 90th National Meeting, Houston, April, 1981.
Turbulent Forced Convection Heat Transfer Enhancement Using Pall Rings in a Circular Duct Dean Burfoot' and Peter Rlce Department of Chemical Englneering, Loughborough University of Technology, Loughborough LE 1 1 3TU, England
This paper reports the results of an experimental investigatlon of turbulent heat transfer and flow resistance in a circular duct containing stalnless steel pall rings in various collflgurations. The increase in heat transfer over an empty duct (60% maximum) is shown to be less than that obtained by using optimum integrally roughened ducts. The flow resistance increases considerably more rapidly than the heat transfer enhancement. The degree of mixing, of the stream entering each pall ring, is shown to have an effect on the pressure drop and heat transfer characteristics.
Introduction
The increase of heat transfer using inserts of various shapes, and by f i i e d tubing, has been reviewed by Bergles (1969). In-line mixers have been suggested for this purpose (see Pahl and Muschelknautz, 1980). Many in-line mixers 0196-4305/82/1121-0646$01.25/0
have been developed from column packings, while Colburn and King (1931) investigated the heat transfer enhancement in randomly packed tubes. In the present work, we used stainless steel pall rings adapted for insertion into a copper tube of 20 mm inside @ 1982 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982 647
Table I. Details o f Experimental Pressure Drop Analyses (Results Apply to Figure 3 )
SP. 0
N
46 16 10 7 4 2 0
2 4 6 12 36
no.
A.A.D.
R.A.D.
M.A.D.
R2
S
E
28 24 21 21 21 24 75
1.37 2.55 2.43 1.94 1.20 0.91 1.55
1.59 2.99 2.71 2.08 1.39 1.01 1.87
3.04 5.06 4.34 3.11 2.45 1.63 4.44
0.980 0.965 0.970 0.981 0.992 0.996 0.986
-0.20 -0.25 -0.23 -0.23 -0.25 -0.28 -0.27
0.02 0.03 0.02 0.02 0.02 0.01 0.01
Table 11. Details of Experimental Heat Transfer Analyses (Results Apply to Figure 4 )
N -
SP.
no.
A.A.D.
R.A.D.
M.A.D.
42 14 8 6 4 2 0 0 0
0 2 4 6 12 36
22 27 27 27 27 27 27 27 27
5.47 2.31 3.75 2.62 1.88 2.92 6.01 4.30 3.77
6.26 3.14 4.58 3.17 2.41 3.49 7.21 4.87 4.49
9.87 10.2 9.86 7.25 6.33 6.87 12.7 7.80 8.85
,
51+m
965
~
JQL
R2 0.977 0.995 0.990 0.996 0.997 0.995 0.977 0.990 0.991
S
E
0.74 0.75 0.76 0.79 0.78 0.80 0.80 0.80 0.80
0.06 0.03 0.04 0.03 0.02 0.03 0.05 0.04 0.03
12 9
d
bdlrqHbtU
bdU
-=7--'
Figure 1. Experimental layout: test section i.d., 20; test section o.d., 22; calming section i.d., 20; annulus i.d., 38;all dimensions in millimeters.
diameter. The pall rings were easily inserted into the tube and acted as a roughness a t the tube wall. The increase in heat transfer over an empty tube (60% maximum) was found to be considerably below that obtained using integrally roughened surfaces (see Norris, 1970).
Experimental Apparatus and Procedure Figure 1shows a schematic diagram of the experimental apparatus. Water was passed countercurrently through the concentric tube heat exchanger. The test section, calming section, mixing mesh, M1, and adiabatic mixing chambers, M2 and M3, were lagged using asbestos rope and asbestos blocks. The test section was initially packed with a material of low thermal conductivity, and heat losses to the ambient air were found by passing the hot fluid, heated by steam injection using S1, through the annulus; the heat loss never exceeded 1% of the total heat input. The volumetric flowrate of each stream was measured using the rotameters, R1 and R2, which had been calibrated in situ with orifice plates to BS1042. Chromelalumel thermocouples and a Schlumberger Solartron data transfer unit and digital voltmeter were used to measure and record the inlet and outlet fluid temperatures, T1-4, and the tube wall temperatures, T5-10. Four circumferentially equidistant tappings were present a t each of the positions P1, P2, and P3. Valves were in each of the lines connecting the pressure tappings to the manometers which were of 95 cm length, one containing a carbon tetrachloride/iodine mixture (S.G. = 1.6); the other contained mercury. In the present work, only the tappings a t points P2 and P3 were used. For the heating tests all of the
Figure 2. Photograph of adapted pall rings.
pressure tapping valves were open; for the isothermal tests each of the valves a t P 3 was opened individually and readings were recorded; and finally all of the valves were opened. After attaining steady-state conditions a t each flowrate, the temperatures, rotameter readings, and manometer levels were recorded at approximately 20-min intervals over a 40-min period. Heat balances for the two streams never exceeded h5.5%. The pall rings were centrally fitted within the test section. The number of rings used, and the respective spacings, are given in Tables I and 11; Figure 2 shows individual pall rings. One-inch pall rings were adapted for insertion into a tube of 20 mm inside diameter by hand cutting away one-fifth of the circumference of the original pall rings. The rings, manufactured from 304 stainless steel, were easily re-formed and when placed in the tube remained a t their required locations even when subjected to fluid pressures of almost 100 psi. Intimate contact of the rings on all of the tube circumference was not obtained.
Calculation Procedure Friction factors, Reynolds numbers, and Nusselt numbers are based on the tube inside diameter. Fluid properties were calculated using the mean of the inlet and outlet fluid temperatures corrected for end losses due to conduction. These losses were based on the measured longitudinal tube wall temperature distribution outside the heated section; the losses never exceeded 0.3% of the total heat transferred.
648
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
I
I
10
1 b
Reynolds N i m o e r Re
10'
Figure 3. Experimental and calculated pressure drop characteristics of stainless steel pall rings obtained under heating conditions.
Figure 4. Experimentally determined heat transfer characteristics
Friction Factor. Measured pressure drops were corrected to allow for the inlet and outlet unpacked lengths of the test section; the Blasius equation (1)was used for this calculation.
a constant average inside fluid temperature (35 "C in this work), eq 4 may be written as
$ST
= 0.0396Re-0.25
(1)
of stainless steel pall rings obtained under heating conditions.
=U1 = c + dihi -do Using the common form
-Nu-
The friction factor is defined by 1 Ap = 44-pu2 d
(2)
The differential head in the manometer always exceeded 4.5 cm of manometer fluid. When we used the leastsquares log-log fitting equations of the heating and isothermal friction factors, evaluating the mean percentage difference between the two seta of equations for Re = 15000 and 80000, we found that this percentage difference never exceeded 5%. For this reason the isothermal results are not shown here. Pertinent details are given in Table I. Figure 3 shows the friction factor results obtained under heating conditions. Also shown in this figure are results calculated by considering that the effect of each insert is limited to the pipe length in which it is situated. On this basis, each arrangement consists of a packed length and an empty tube length. Hence we may write 4calcd
=
~ST + (1ST~ S+TZSM)
~SM~SM (/ST +ISM)
(3)
Heat Transfer. The overall heat transfer coefficient is given by the relation 1
-
U
= -1+ - xd, h,
k,dM
do ++ Ri + R , dihi
(4)
Wilson (1915) suggested that
-U1= c + -V0.82 t
Over a limited period of time, if we use a constant average outside fluid temperature (80 "C in this work) and
(6)
-@Rea
(7)
we obtain (1/P)d, U kReaPr0.4 The data of Dittus and Boelter (1930) were represented by McAdams in the form
-1= c +
Nu = 0.023Re0.8Pr0.4 (9) If we use experimental data for an empty tube, and a = 0.8, a least-squares fit of eq 8 will provide the constant C, from which hi and Nu may be calculated. The values of Nu thereby obtained may thus be used in eq 7; however, performing a least-squares log-log analysis will not show a to be 0.8 unless all of the experimental data lie on the least-squares fit of eq 8. Combining eq 6 and 7 we obtain
In
[
d0
] = l n PrO.4 [ ~ ]
[ ( l / U ) - C]kPr0.4
= In [P] + a In [Re] (10) Using the empty tube experimental data, with a = 0.8, we may use the sequential simplex method of Nelder and Mead (1965) to find C and @ which produce a least-squares fit of eq 10. Alternatively, the value of C may be changed iteratively until a least-squares fit to (lo), which gives a = 0.8, is obtained. In analyzing the results with pall rings, the value of C was found by using the empty tube results obtained prior to, and after, the pall ring tests. Three sets of empty tube data were obtained in this work; each of the two values of C used were based on 54 experimental results. The least-squares lines are given as Figure 4; the pertinent details are listed in Table 11. As performed with the
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982 649
OOL
'h
10 20 30 4'0 i6 Number o l Poll Rings in the Section, N
Figure 6.' The effect of the pall ring arrangement on the pressure drop characteristics.
I
I
1
10 10'
,
,,,,I
~
105 R e y n o l d s YumSer,Re
Calculated heat transfer charadenstics obtained using t. 3 experimentally determined fully packed and empty tube results and the respective lengths.
Figure
friction factor data, the effect of an insert may be considered to be limited to the pipe length in which it is situated; hence
Re:l5500
10 Number of Pall R i n g s in the H e a l e d Section . N
Figure 7. The effect of the pall ring arrangement on the heat transfer characteristics.
The results of these calculations are shown as Figure 5.
Results and Conclusions Table I1 shows that, for all except one set of results, the 95% confidence interval on the slopes of the lines of Figure 4 lie within the range of the Wilson assumption (11= 0.8. No significant curvature of these curves can be noted. The empty tube data refers to an "unmixed" stream, while for the data with no spacings the stream may be considered almost fully "mixed". From Figure 3 we can see that the calculated friction factors are smaller than the experimental results; this is presumably because the empty tube lengths contain a stream which is partly "mixed", thereby increasing the pressure drop. It may be further postulated that for small ring spacings the fluid will rapidly become mixed upon entering the packed length; thus only small increases in the heat transfer coefficient are to be expected as the spacing is decreased. However, the friction factor will continue to increase as the number of rings increases since each ring will produce form drag, though not necessarily any further "mixing" of the stream. For large ring spacings it is expected that the Nusselt number will rise more rapidly than in the above case since the fluid never becomes fully mixed, but instead each insert added will increase the mixing. Furthermore the increase in "mixing" willicause the friction factor to rise rapidly. The above considerations are in agreement with the data shown in Figures 6 and 7. Figure 8 shows a sample of the data presented by Norris (1970). These data represent the results of tests using optimum forms of integral roughness; Norris noted no significant Reynolds number effect. It can be seen that the heat transfer enhancement obtained using pall ring inserts is significantly less than that obtained using an
Figure 8. Comparison of the heat transfer and flow resistance obtainable with stainless steel pall rings and with integrally roughened tubes. The experimental points are the average of the ratios obtained using pall rings at Reynolds numbers of 15 500 and 86 500: The short lines through these points indicate the effect of Reynolds number. The numbers, which refer to the data of Norris (1970),are detailed below: square ribs, large spacing, Pr = 0.7 (1); sand grain roughness, Pr = 4 (2); Pr = 6 (3);Pr = 0.7 (6); wire type ribs, Pr = 0.7 (4); rectangular ribs, large spacing, A. = 0.7 (5);square ribs and V-shaped grooves, small spacing, Pr = 0.7 (7).
optimum integral roughness. The pall rings will provide little, or no, fin effect, while portions of the inserts project into the bulk flow thereby leading to form drag. The use of stainless steel pall rings has the advantage that they may be inserted easily into existing equipment; it is difficult to produce integral roughness inside circular tubing, with the exception of knurled roughness. Acknowledgment The authors wish to thank Mr. K. Robinson of Norton Chemical Process Products (Europe) Ltd. for supplying the pall rings used. One of us (D.B.) acknowledges the financial support of the Science Research Council (Great Britain).
650
Ind. Eng. Chem. Process Des. Dev. 1882, 21, 650-653
Nomenclature A.A.D. = average absolute percentage deviation from the least-squares line C = tube wall and outside film resistance to heat transfer d = tube diameter E = 95% confidence interval, on the slope of the least-squares line, obtained using Student's t distribution h = film heat transfer coefficient k = fluid thermal conductivity k , = tube wall thermal conductivity 1 = packed length of tube (including spacings) lSM = total length of the inserts only in the packed length lST = total length of the inserts only in the heated length M.A.D. = maximum absolute percentage deviation from the least-squares line N = number of pall rings in the packed or heated section no. = number of experimental data points used to obtain the least-squares line Nu = Nusselt number based on the tube inside diameter Pr = Prandtl number R = scale resistance to heat transfer R2 = correlation coefficient R.A.D. = root mean square absolute percentage deviation from the least-squares line Re = Reynolds number S = slope of least-squares log-log line Sp = spacing between pall rings u = fluid velocity U = overall heat transfer coefficient
V = fluid velocity corrected to a reference temperature of 60 O F
x =
tube wall thickness
A p = pressure drop CY = Reynolds number exponent /3 = a parameter in eq 6 e = a parameter in eq 4 p = fluid density 4 = friction factor
Subscripts
calcd = calculated result i = inside m = hydraulic mean o = outside SM = based on the experimental result with zero insert spacing ST = based on the empty tube result Literature Cited Bergles, A. E. Int. J . Heat Mess Transfer 1969, 1 . 331-424. Colburn, A. P.; King, W. J. Trans. AIChE 1931, 26, 196-207. Dittus, F. W.; Boelter. L. M. K. Univ. &/if. Pubi. Eng. 1990, 2 , 443-461. Nelder, J. A.; Mead, R. Comput. J. 1965. 7, 308-313. Norris, R. ii. I n "Augmentation of Convective Heat and Mess Transfer"; Bergles, A. E.: Webb, R. L., Ed.; ASME: New York, 1970. Pahl, M. H.; Muschelknautz, E. Chem. Ing. Tech. 1980, 52, 285-291, Wilson, E. E. Trans. ASME 1915, 3 7 , 47-71.
Received for review June 5, 1981 Accepted March 30, 1982
Comparative Assessment of the Performance of the Three Designs for Liquid Jet Mixing Ashley 0. C. Lane and Peter Rlce' Department of Chemlcal Englnwrlng, Loughborough University of Technology, Loughborough, Leicestershire LE 1 1 3TU, Engknd
The three designs proposed for batchwise liquid jet mixing, in a tank, have been studied experimentaliy and a mixing time expression has been formulated for each design which is applicable to both the laminar and turbulent Let regimes. These expressions have allowed a comparative assessment to be made of the mixing performance of all the designs. This has shown that for the shortest mixing time, ail other conditions being the same, a design incorporating an axial vertical jet in a hemispherical base cylindrical tank should be used.
Introduction As a result of rapidly rising energy costs, batchwise liquid jet mixing in a tank has become increasingly important because as King (1980) has shown, it can be a faster and more energy effective mixing technique than using conventional mechanical agitators. Jet mixing of miscible liquids was originally proposed by Fossett and Prosser (1949) for the blending of tetraethyllead into petrol. These investigators published a design which is widely in use today (Fossett and Prosser, 1949, 1951, 1973). Figure l a liquid level 1 illustrates this design, which has an inclined side-entry jet near the base of a flat bottom cylindrical tank. Following the work of Fossett and Prosser (1949, 1951) little attention was shown in developing the design of jet mixing systems. It was not until nearly 30 years later that Hiby and Modigell(l978) proposed an alternative design. This uses an axial vertical jet in a flat base cylindrical tank; see Figure lb. A modification to Fossett and Prosser's design was suggested by Coldrey (1978). To increase the effectiveness of this design, Coldrey proposed that the 0196-4305/82/1121-0650$01.25/0
height of liquid in a tank should allow the longest possible length of a jet to be utilized; see Figure l a liquid level 2. Recently, Lane and Rice (1981) have published a third design. This consists of an axial vertical jet in a hemispherical base cylindrical tank; see Figure IC. Further designs for jet mixing systems have been proposed, but all of these are modifications to the three designs already mentioned. Many mixing time correlations (Fossett and Prosser, 1949,1951,1973;Lane and Rice, 1981;Van de Vusse, 1959; Okita and Oyama, 1963; Racz and Groot Wassink, 1974) have been proposed for jet mixing. However, all of these have been formulated by investigations in different experimental environments using various techniques to monitor and measure mixing times. It was not until the recent investigations by Hiby and Modigell (1978) and Lane and Rice (1981) that a specified degree of mixing was used to define their respective mixing time correlations. Any attempt to compare mixing times from the published correlations can lead to widespread discrepancies in the results obtained. This is as a result of the variety 0 1982 American Chemical Society
