Ind. Eng. Chem. Fundam. 1986, 25, 425-433
molecule (Pedram and Hines, 1983; Gupta and Bhatia, 1969), we estimated the surface are for adsorption to be 170 m2/g of corn grits. This estimate is comparable to the values of 210 m2/g reported for starch (Gupta and Bhatia, 1969) and 263 m2/g for shelled corn (Hall and Rodriguez-Arias, 1958),which were also obtained by using water adsorption data. Conclusions Corn grits adsorb water in the range of 323-373 K. Experimental adsorption data were fitted to a modified Henderson's equilibrium equation. The equation was modified by assuming that one of ita parameters, n, was temperature independent. The second parameter, K, was found to have an Arrhenius-type dependence on temperature. The modified equation may be useful for extrapolations to lower temperatures as well. The calculated heats of adsorption (10.8-14.6 kcal/g-mol) are close to the latent heats of condensation (9.7-10 kcal/g-mol), thus indicating a physical adsorption phenomenon. Acknowledgment This work was supported by USDA Contracts 901-15112 and 80-CRCR-2-0596. We acknowledge helpful discussions during the course of this work with Dr. George T. Tsao, Director of LORRE. Nomenclature a = constant in eq 3 b = constant in eq 4
C = constant in the BET eq 1, dimensionless
d = constant in eq 3 e = constant in eq 4
E = constant characteristic energy, kcal/g-mol -H = heat of adsorption, kcal/g-mol K = constant in eq 2, K-'
425
KO = preexponential constant in eq 5, K-I M = % moisture (dry basis), g of water/100 g of adsorbent n = constant in eq 2, dimensionless p* = partial pressure of water, kPa P = vapor pressure of water, kPa R = gas constant, kcal/(g-mol K) T = absolute temperature, K V = volume of adsorbate adsorbed, cm3of liquid water/g of adsorbent V , = volume of the monolayer, cm3 of liquid water/g of adsorbent X = mass of adsorbate adsorbed, g of water/g of adsorbent y = latent heat of condensation, kcal/g-mol Registry No. HzO, 7732-18-5. Literature Cited Brunauer, S. The Adsorptkm of Gases and Vapors; Princeton University Press: Princeton, NJ, 1945; Vol. I, pp 151-162. Brunauer, S.; Emmett, P. H.; Teller, E. J . Am. Chem. SOC. 1938, 60, 309. Bushuk, W.; Winkier, C. A. CerealChem. 1957, 34, 87. Chung, D.-S.; Pfost, H. B. Trans. ASAE 1967a, 10, 549. Chung, D.-S.; Pfost. H. B. Trans. ASAE 1867b, 10, 552. Day, D. L.; Nelson, G. L. Trans. ASAE 1965, 8, 293. Duprat, F.; Guilbot, A. Water Relations of Foods; Duckwork, R. B., Ed.; Academic: London, 1974; Chapter 9. Gupta, S. L.; Bhatla, R. K. S. I n d k n J . Chem. 1869, 7, 1231. Hall, C. W.; Rodriguez-Arias, J. H. Agric. Eng. 1958, 39, 446. Henderson, S . M. Agric. Eng. 1952, 33, 29. Hong, J.; Voloch, M.; Ladisch, M. R.; Tsao, G. T. Biotechnol. Bloeng. 1982, 24, 725. Jury, S. H.; Edwards, H. R. Can. J . Chem. Eng. 1971, 49, 663. Ladisch, M.; Voloch, M.; Hong, J.; Bienkowski, P.; Tsao, G. T. Ind. Eng. Chem. Process Des. D e v . 1984, 2 3 , 437. Nelson, L. F. Trans. ASAE 1967, 10, 28. Pedram, E. 0.;Hlnes, A. L. J . Chem. Eng. Data 1983, 28, 11. Rodriguez-Arias, J.; Hall. W. W.; Bakker-Arkema, F. W. Cereal Chem. 1963, 40, 676. Strohman, R. D.; Yoerger, L. L. Trans. ASAE 1967, 1 0 , 685. Treybal, R. E. Mass Transfer Operations; McGraw-Hill: New York, 1968; pp 499-500. Voloch, M.; Ladisch, M.; Bienkowski, P.; Tsao, G. T. In Cereal PolysaccharMes in Technology 0nd Nutrition; Rasper, V. F., Ed.; American Association of Cereal Chemists Publications: St. Paul, MN, 1984; p 103.
Received for review October 25, 1984 Accepted October 15, 1985
Velocity and Temperature Fields in Turbulent Jets Issuing from Sharp-Edged Inlet Round Nozzles Nslma 1. Obot," Thomas A. Trabold, Michael L. Graska,+ and Faroukh Gandhl Department of Chemical Engineering, Clarkson University, Potsdam, New York 13676
An experimental study of the mean velocity and temperature fields in round turbulent jets, including the effect of entrainment on heat transfer, was carried out with various initial temperatures. For isothermal and nonisothermal jets, it has been established that the rate of fluid entrainment by the jet is a strong function of nozzle design. A s to the effect of entrainment on heat transfer, it has been shown that, for a given nozzle exit temperature and Reynolds number, the larger the mass flow rate of ambient fluid entrained by a jet, the lower the jet temperature and enthalpy at locations downstream from the nozzle exit. For purposes of localized impingement evaporation and drying, the results suggest that, in view of the marked decrease in the jet's temperature and enthalpy with increasing axial distance, significant savings in energy can be realized by maintaining the narrowest standoff spacing possible, whether the jet is generated with short or long nozzles.
Introduction Heated air jets are widely used for heating of solid Surfaces, for evaporation from free liquid surfaces, and for drying of various materials. Effective design of impinge-
* To whom correspondence should be addressed.
'Department of Chemical Engineering, University of Illinois, Urbana, IL 61801. 0196-4313/86/ 1025-0425$01.50/0
ment equipment for evaporation or drying is much more involved than that for cooling of solid surfaces and requires a good knowledge of the velocity and temperature fields in various turbulent jet configurations. For the latter situation which usually involves use of room-temperature jets, since a jet must entrain some of the surrounding fluid 80 that its mass flow rate increases with axial distance from the nozzle, this entrainment often results in hardly any 0 1986 American Chemical Society
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Ind. Eng. Chsm. Fundam., Vol. 25, No. 3, 1986
change in the jet temperature until impingement. For this simple case, convective heat transfer rate is essentially proportional to the temperature difference between the target surface and the jet a t the nozzle exit. However, when a jet is discharged at a temperature different from that of the surroundings, its temperature will decrease or increase according to whether the entrained fluid is colder or warmer. Here, depending on the separation distance between the surface and the nozzle exit, the jet may approach the surface at a temperature that can be significantly different from its nozzle exit value; the value which determines heat and mass transfer at the product surface is that approaching the target, and for a given nozzle exit condition, this arrival temperature may depend on the nozzle design, as does the arrival velocity. The magnitude of the effect entrainment has on heat transfer in turbulent jets can be quite pronounced and, in view of the strong dependence of entrainment rate on nozzle configuration (Obot et al., 1984), must also be expected to depend on the details of the nozzle. But this cannot be established from the available literature. Although numerous studies (Corrsin, 1943; Corrsin and Uberoi, 1949; Baron and Alexander, 1951; Wilson and Danckwerts, 1964; to mention but a few) have been carried out with turbulent heated jets discharging into still surroundings, virtually all of the published literature pertains to nearly turbulence-free uniform jets generated with well-rounded convergent nozzles. However, in many industrial applications, the square-edged nozzle configuration is preferred primarily because of ease of fabrication and installation, especially when working with multiple-jet systems. In fact, the only experimental investigation with heated jets issuing from sharp-edged inlet nozzles (Hollworth and Wilson, 1984) considered excess temperatures between 0 and 62 OC, and data on entrainment or heat content were not provided. Also, in many of these previous studies, data were obtained for relatively large distances from the nozzle which are, by virtue of the increase in mass flow rate and the corresponding decrease in jet temperature with axial distance, well outside the range of interest in many industrial situations, especially those involving evaporation and drying. Another relevant investigation (Sforza and Mons, 1978) considered mass, momentum, and energy transport in turbulent-free jets. Although their precise nozzle configuration was not specified, it may be inferred from the sketch of the binary jet experimental facility and the excellent agreement between their results and those of previous investigators who used convergent nozzles that the nozzle entrance configuration was also well-rounded. The authors found that, whereas mass and energy transport were identical processes, the diffusion of momentum was quite distinct, in agreement with findings of other investigators. The ultimate objective of our research program is to determine evaporation rates from surfaces exposed to heated jets. In view of the lack of experimental data on heat transfer in jets generated with the more practical squared-edged inlet nozzles, it was considered worthwhile to begin the research by studying the near field behavior of such jets. The results for nonisothermal jets which are covered in this paper complement those for isothermal jets detailed in a recent publication (Obot et al., 1984). In the present investigation, the jet excesa temperature was varied between 15 and 180 O C . Two values of the jet Reynolds number, Re = 13000 and 22000, were tested. Experimental Apparatus and Procedures The experimental apparatus and test procedures were
ldt305mmd
llzl
I
L
Figure 1. Geometric details of the nozzle plates.
the same as those described in sufficient detail elsewhere (Obot et al., 1984);hence, the following presentation will not contain exhaustive details. The test facility consisted of a blower which delivered room-temperature air through a calibrated orifice meter, a box containing electric heating elements, a 254-mm square plenum chamber fitted with honeycomb and fine mesh screens, and a nozzle attached to the downstream end of the plenum. The geometric confiiations of the two interchangeable nozzle plates are shown in Figure 1. The internal diameter of the L l d = 1nozzle was 12.7 mm while that for Lld = 12 was 12.0 mm. The inlet and exit sections were square-edged, the use of this nozzle inlet geometry being one of the main differences between the present investigation and virtually all of the previous heated-jet studies. A large flanged section, structurally an extension of each nozzle plate, was provided at the square-edged exit (Figure 1). It should perhaps be noted that the presence of such a flanged section can lower the rate of fluid entrainment into the jets, especially for the initial region which extends from the nozzle exit to about 10 jet hole diameters downstream (Trabold et al., 1985). It should also be emphasized that, since the distance between the nozzle exit and the laboratory floor was about 1 m, as was also the distance to the nearest wall, the results shown subsequently are for free jets. For nonisothermal jets, it was necessary to obtain data for total temperature as well as total and static pressures at the same point in the jet flow. This was accomplished by using a 3.2-mm-diameter Pitot static probe equipped with a built-in chromel-constantan thermocouple. A temperature probe of similar design and thermocouple material (1.7-mm 0.d.) was used to check the reliability of the data obtained with the dual-capability probe, and the degree of agreement between the two sets of data was generally within 1% From calculations using the methods outlined in Abramovich (1963), it was concluded that the upward deflection of the hot jet center line due to buoyancy was unimportant for the range of axial locations considered here. It is of some interest to note that, for the same range of excess temperatures as considered here, Wilson and Danckwerts (1964) reported that such a de-
.
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986
1 60
30 1
I .o
40
2u
427
Re
22,000
0
3
LEFT A X I S
cE
1
\
0
RIGHT A X I S L/d
20
0
=
I
Y
0.5
3
0
5
10
15
20
25
15
20
25
Z/d IO0
Figure 3. Center line velocity decay.
30
20 50
0
0.I
0.2
0.3
0.4
0.5
X = r/d Figure 2. Typical velocity and temperature profiles at nozzle exit. 0
flection is less than 1 nozzle diameter at 100 diameters downstream. One of the primary interests in this study was to examine the role of entrainment in determining heat-transfer characteristics in nonisothermal jets. At any axial location z from the nozzle, the mass flow rate is given by an integral over the axial component of mean velocity: M(z) = lm 0 p ( r , z )U(r,z) 27rr dr
(1)
The mass flow rate of entrained flow is given by
M&) = M ( z ) - Mo
(2)
where Mo is the corresponding value at the nozzle exit. For heat transfer, if the nozzle exit profiles for velocity and temperature are uniform, then the exit heat content, H,, is given by Ho= MoCp6 ,where e,, is the excess temperature above ambient. gowever , for nonuniform velocity and temperature distributions, nozzle exit heat content, as well as the value at any downstream location, is given by
H ( z ) = xmCpp(r,z)U(r,z) B(r,z) 27rr dr
(3)
The integrals which are given by eq 1 and 3 were evaluated numerically. The velocity and temperature trends, some of which will become quite evident from the subsequent presentation of results, made adoption of an arbitrary method of evaluating the integrals a necessity. The approach used here wa8 to fix the range of interest as that bounded by r = 0 and r = ro.l, where U(r0.J = O.lUo and O(ro.l) = 0.16,. It is of interest to note that, for either nozzle, fairing the velocity or velocity and temperature profiles to zero before integration gives results that are not significantly different from those obtained by the present method.
5
10
2 /d
Figure 4. Distribution curves for center line temperature.
Results and Discussion To begin discussion of results, attention may be turned to Figures 2-6, the first of which shows typical nozzle exit velocity and temperature profiles for Re = 13OOO and two values of Oj0. It should be mentioned that, in order to ascertain that the jet flow was symmetric, measurements of nozzle exit profiles, as well as the radial profiles at all downstream locations, covered both halves of the jet. However, owing to space limitations, half of the jet is given in Figure 2 and in all radial patterns shown subsequently. The variations of maximum values for velocity and temperature, expressed in terms of the corresponding values at the nozzle exit, with distance along the jet axis are given in Figures 3 and 4. An attempt to generalize the heated jet velocity decay data (Figure 3) in terms of our previous results for isothermal jets (Obot et al., 1984) is shown in Figure 5, while correlation of the center line temperature is illustrated graphically in Figure 6. Two important features associated with the exit profiles are crossing of the velocity profiles for both nozzles, an expected trend from continuity and one that is equally applicable to isothermal jets of the same Re, and the fact that the profiles for temperature are somewhat narrower than for velocity. This may be due to conduction through the nozzle plates. The few available nozzle exit profiles (Corrsin, 1943; Corrsin and Uberoi, 1949) appear to suggest that, even when the exit velocity distributions are reasonably flat, there is a tendency toward slightly peaked profiles for temperature. However, as shown subsequently, after the jet leaves the nozzle, the above trend is reversed due to more intense diffusion of the temperature field. Both center line variables (Figures 3 and 4) decrease markedly with axial distance, and the higher the nozzle exit center line excess temperature, the shorter the lengths of both the dynamic and thermal cores. Consequently,
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428
I.
I
6
Table I. Summary of Predictive Equations UjolUo = a$, ojo/oo = bJ Lld
a0
bo
range
3
Lld
0
3
L/d * I
\
1
R e * 22,000
$ 0
12
8
0
z
16
24
32
Figure 5. Correlation of center line velocity data.
II8
I
:17:"
3
I7 0
L/d . I 2
Re
8
16
-
22,00(
24
2
"1 32
Figure 6. Correlation of center line temperature data.
after elimination of the core region, center line variables decrease more rapidly with increasing exit temperature, in line with the trends already established by Corrsin and Uberoi (1949). The only exception to this consistent trend can be seen in Figure 4 for the L/d = 1distribution curves for temperature. Here, the results show hardly any effect of exit temperature or Reynolds number. The results of Hollworth and Wilson (1984) for nozzles of similar design and 0, I 65 OC exhibited the same trends as noted here. In this regard, it will be noticed that, even for isothermal jets, the L l d = 1 nozzle dynamic core is only about two jet hole diameters and that the effect of exit temperature on it is unusually small (Figure 3)) as is also the influence of exit temperature or Re on the thermal core. It would seem then that, in order to bring about any measurable effect of 0, on center line temperature for locations farther from the core, the thermal core must be reduced. However, since the thermal core region extends to no more than one jet hole diameter, in sharp contrast with the 3d to 4d for L l d = 12, the result is a set of distribution curves that are almost coincident for both Re and all Ojo. The trends in Figures 3 and 4 imply three things. First, the rate of entrainment is different for the two nozzles.
Cn
do
ranee
0.097 0.077
0.122
zld 2 6 z/d 2 8
0.103
This has already been verified by our results for isothermal jets which indicated differences of as much as 3 times, the L l d = 1results being the higher set. So, the differences between the temperature trends for both nozzles (Figure 4) can be attributed to entrainment. Second, since the decrease of center line temperature with z l d is more rapid than for velocity, it must be expected that in a turbulent heated jet the diffusion of the temperature field is more appreciable than for momentum. This expectation will be verified by results presented subsequently for velocity and temperature distributions across the jets and the corresponding half-widths. Third, the fact that each Uo/Ujo distribution curve is associated with a particular value for Ojo is important because it suggests that the rate of entrainment by a jet may be a function of the nozzle exit temperature. This will be examined in detail later. For the purposes of comparison of the heated jet center line velocity data with those for isothermal jets, as well as generalization of the velocity and temperature data, the density difference between the jet and the room-temperature air has been incorporated in the definition of the nondimensional axial distance. The results are shown in Figures 5 and 6. The solid lines in Figure 5 represented our isothermal jet data within 5 % , while those in Figure 6 correspond to a least-squares estimated inclination of straight lines through the data points. In both figures the lines have been faired to pass through the origin. According to the results in Figure 5, the isothermal jet relations hold within 5-10%, the L l d = 12 data for Re = 22 000 and Ojo = 174 O C being the only exception for 2 I 20. Also, the jet center line temperature for either nozzle can be closely approximated by a single equation, with an average error of no more than 10% even at the lowest temperature. The predictive equations for center line velocity and temperature are given in Table I. Extensive measurements of velocity and temperature distributions were made for the region extending from the nozzle exit to 25 jet hole diameters downstream. These results are too numerous to include here, but typical profiles are presented differently in Figures 7-10. Dimensional plots of velocities and temperatures are shown in Figure 7, while plots of VIVOand O / O o vs. X are illustrated in Figures 8 and 9. In Figure 10 dimensionless plots of velocities and temperatures obtained at several locations are shown for Re = 13000. The horizontal axis indicates the distance from the jet axis measured in terms of r l j 2and tl12,where U(rl12)= 0.5U0 and O(tl12)= O.5Oo. The dependence of these normalizing factors, r l I 2and tl12,for r on axial location is illustrated in Figure 11. The fact that the diffusion of heat is more intense than for momentum, as inferred from the results in Figures 3 and 4, is verified by the results in Figures 7-9 which show wider profiles for temperature than for velocity, in agreement with the findings of other investigators. Figure 7 shows a crossing of the velocity profiles for both nozzles, as was the case for isothermal jets, as well as much higher temperatures with L/d = 12 than with L / d = 1,features which can only be expected when the rates of entrainment
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429
I .o 174.8 o 175.6
0.8
0
100
0.6
12 I
Re = 13,000
0.4
50
40 0.2
Y
-a-
ZId.6
To1:.
20
0
(a)
75
a3
s-
0.8
c
O
E 0.6
3
50
20
0.4 0.2
25
IO
0
0.5
I.o
I .5
2.0
2.5
x = r/d 0
0.5
1.5
1.0
2.0
Figure 9. Typical effed of nozzle length on temperature distributions.
X = r/d
Figure 7. Velocity and temperature distributions across the jets. I .o
1.0
I
0.8
12
5 0.5
1.0
&
Z/d = I 2 R e = 13,000
\
3
\
ln
3 \
3
(a)
0.8
0.6
0 1.0
0.4
0.2
mo
&
0.5
I 0
5
I.o
0.5
7”
3
= r’rv2
1
TT
1.5 =
2.0
r”ll2
Figure 10. Nondimensional profiles for velocity and temperature.
I
(b)
0
0.5
1.0
1.5
2.0
2.5
X = r/d Figure 8. Normalized velocity and temperature profiles at z / d = 12.
into the jets are different. In Figures 7-9 it can also be seen that the L l d = 12 radial profiles for velocity and temperature are generally narrower than for L / d = 1. In other words, for jets issuing from long nozzles, momentum or energy transport occurs over a region that is much smaller than that for relatively short nozzles. A further indication of the difference in development between the velocity and temperature fields in turbulent jets will be observed by noting the deviation between the experimental data and the Gaussian profiles in Figure 10.
Here, it appears that a close approximation of the temperature data is provided by the Gaussian function even for relatively short distances from the nozzle exit, especially for the jet emerging from the Lld = 1 nozzle and which is characterized by a rela$ively short thermal core. As has been noted already for isothermal jets (Obot et al., 1984) and also confirmed here for heated jets, a similar approximation for mean velocity is realized after elimination of the dynamic potential core and the establishment of developed jet, and the numerical constant, quoted here as 0.693, is dependent on nozzle details and axial location. Although these residual effects of nozzle geometry and location are also discernible in plots for temperature, their magnitudes are generally smaller than for velocity. It is of interest to note that the usual practice has been to reduce velocity and temperature data by using the format
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986
430
I
1
3 A
A
\ " 2
A
Bjo
3
96T
(Y
z
L
I
0 3
0
c
4
8
16
24
Z /d Figure 11. Velocity and temperature half-widths.
adopted here in Figure 10. Although this approach does highlight the similarity in jet development for a range of parameters, it clearly obscures very important effects already established in Figures 7-9. Concerning the typical plots for half-widths, it may be noted that the solid lines in Figure l l a were found to hold for isothermal jets within 4%. Consistent with an earlier observation of wider profiles for temperature than for velocity, it can be seen here that t1Izis always larger than r1/2,as has been documented by virtually all previous investigators. For either nozzle, the velocity and temperature half-widths were found to be essentially independent of nozzle exit temperature. In the case of t , / z ,this finding agrees with the results of Wilson and Danckwerts (1964) for 50 OC I0,s 200 "C. However, it will be observed that values of rl for the L l d = 12 nozzle are generally lower than for L / d = 1,regardless of whether the jet is heated or not, as are also the values of tllz. These results are also summarized in Table I. As stated in connection with the discussion of Figures 3 and 4, the implication was that entrainment into the jets might be a function of nozzle exit temperature. For the lower Re of 13000, data for mass flow rate of fluid entrained by the jets, as calculated via eq 1and 2, are shown in Figure 12. To permit comparison of the present results with those in the literature which were usually given in nondimensional form, the corresponding M ovalues for Oj0 = 0,55, and 96 "C could be stated successively as 0.002 57, 0.00247, and 0.00231 kg/s for L l d = 1 and as 0.00250, 0.0024, and 0.00253 kg/s for L l d = 12. These values, determined from integration of the exit profiles, are about 4-9% lower than those deduced from the orifice calibration from which the Reynolds number was computed. The data for 0, = 0 "C,which are included in this figure, represent separate measurements, and it can be readily established, by dividing the values on this plot by the appropriate Mo, that the results in our recent publication (Obot et al., 1984) are reproducible within 5%. According to the results in Figure 12, there is a detectable trend toward slightly higher mass flow rates when the jet temperature is higher than that of the surrounding fluid, the absolute effect of exit temperature being more pronounced for L l d = 1 2 than L / d = 1. For the latter, the lack of a strong effect of nozzle exit temperature or Reynolds number on entrainment rate is also suggested by the results in Figures 3 and 4. I t is also especially
0
16
8
24
Z/d (,om@'''
Figure 12. Mass flow rate of surrounding fluid entrained by the jets.
noticeable that the shorter nozzle jet which decays and spreads at faster rates continues to entrain comparatively more surrounding fluid than the jet issuing from the L l d = 12 nozzle. It should also be mentioned that, although results are shown here for Re = 13000, calculations were made for the few traverses with Re = 22000. These results do not modify our previous finding; that is, for the z l d C 10 region entrainment rate for either nozzle is essentially the same for both Re but with lower rates for Re = 13OOO and z l d > 10, the largest Re effect being associated with the L / d = 12 nozzle as expected. Comparisons of the isothermal jet entrainment data with published results were presented graphically and discussed in detail in our recent paper; hence, such information will not be duplicated here. The interested reader may wish to refer to a more comprehensive presentation dealing with the entrainment characteristics of turbulent jets (Trabold et al., 1985). Having established the influence of nozzle length on entrainment, it is necessary to carry the discussion a stage further by considering the effect on heat content in the jet, typical results of which are presented in Figures 13 and 14 for Re = 13OOO. It is useful to recall that, for the results in Figure 13,the upper limit of integration was for both velocity and temperature. Also, alternative representations of the data in Figure 13a,b are given in Figure 13c,d where the normalizing factor for H is the value at the nozzle exit. The results of Sforza and Mons (19781, though probably obtained for experimental conditions and nozzle details that were different from those for the present study, are included in Figure 13c,d for qualitative comparison of the trend established here for variation of heat content with axial location. It might appear at first, from the trends in Figure 13, that there is neither a systematic dependence on nozzle length nor a strong effect of axial location similar to that already established for center l i e temperature. For either nozzle, the trend with increasing axial location is expected from consideration of the requirement of constancy of heat flow at consecutive cross sections. However, it should be
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986
A
l2
5
0
10
15
20
cE
25
Y
Z/d (p&)1'2
-= I .5
0
5
IO
20
15
25
IO0
75
50
25
v)
$
0
I
150
IO0
50
0
0
16
:10
ri
t
11
4M 0 25
0.50
X =r/d Figure 15. Typical effect of nozzle geometry on exit velocity and turbulence.
f/d Figure 13. Variation of heat content with axial distance.
+ -
:I
8 1
0
810 = 55.C
A - Sfwra and Mons
L/d L/d
431
24
Z/d(p,/,5)"2
Figure 14. Jet heat content for the X 5 1 region.
kept in mind that, since the shorter nozzle jet entrains appreciably more fluid and is also associated with wider radial profiles for both velocity and temperature (Figures 7-91, use of the ro.larbitrary limit results in areas that are different for the two nozzles. It seems more logical, at least from the standpoint of examining the influence on localized heat- and/or mass-transfer characteristics, to consider a fixed area in the evaluation of the heat content in the jet. The results of such calculations are presented in Figure
14 for hemispherical regions of radii one-half and one jet hole diameter. It can be seen that, in sharp contrast with the trend in Figure 13, the L/d = 1 nozzle yields consistently lower H values for some distance from the nozzle exit when the integral mean values are evaluated for the 0 IX I0.5 or 0 I X I 1 region. This trend is, of course, consistent with the fact that the short nozzle is characterized by lower velocities and temperatures for the region of interest (Figures 7-9). It is also strikingly apparent that the distribution curves in Figure 14 decrease more rapidly with axial location from the nozzle, paralleling the trends already charted for both velocity and temperature along the jet axis. It will also be observed that the magnitudes of the differences between the results for both nozzles do vary with exit temperature. From the results so far presented, it is clear that, for a given entrance configuration,varying the nozzle length can produce orderly changes in the mean velocity and temperature fields in turbulent jets. It remains, however, to try to provide some explanation for the origin of these differences. Such an explanation obviously requires detailed information on the mean flow and turbulence characteristics for the near field region, including the nozzle exit. Although there is no detailed study of turbulence for jets generated with sharp-edged inlet nozzles, the fact that these differences in flow development originate from the initial flow conditions at the nozzle will be examined here with the help of Figure 15, reproduced from an earlier paper (Obot et al., 1979). In Figure 15, profiles for initial mean velocity and axial turbulent velocity fluctuation are shown for two squareedged inlet nozzles, L / d = 1 and 10, and for a wellrounded, convergent short nozzle of L/d = 1(open circles). The latter is similar in design to those used by most previous investigators, and its profiles are included simply to be contrasted with those for the square-edged inlet. The exit turbulence profile for L/d = 1 2 should not be significantly different from that for L l d = 10, as can be established from the results in the work cited above. The jet Reynolds number for the results in Figure 15 was 60000. Although the exit turbulence profiles can be expected to exhibit residual effects of the Reynolds number, especially near the wall, the radial patterns should be almost independent of Re, as has been documented by previous investigators. Thus, every feature on this figure must be expected to occur for Re = 13OOO or 22 OOO, a fact that can be established, even in the case of mean velocity,
432
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986
from comparison between Figures 2 and 15. With a square-edged entry, the dominant feature is the strong capability for turbulence generation. However, as is evident from Figure 15, the transport of much of the turbulence generated at the sharp-edged inlet to the center line is so rapid that, at 10d downstream, the turbulence levels for the X > 0.3 region are significantly lower than for L l d = 1. At the moment of discharge, since the axial momentum for the region nearest to the wall is not significantly different for the two nozzles, the stronger and more immediate interaction between the L l d = 1 nozzle jet and the surrounding fluid, than is the case for L/d = 12, appears to be largely the result of the high turbulence generated near the X = 0.5 region. It is of interest to note that, downstream from the nozzle, turbulence in the developing jet is generally found to be greatest in the center of the mixing region which is also located around X = 0.5. Consequences of this unusually high degree of mixing and interaction of the jet with the ambient fluid include reductions in the core lengths, higher rates of entrainment and of spread, and faster rate of decay of center line velocity. Also, the turbulent velocity fluctuation along the jet’s axis attains its maximum value around z/d = 5, in sharp contrast with the z / d range of between 8 and 10 for long and convergent nozzles (Obot et al., 1979). In our recent paper, it was noted that the mean flow properties for the z l d 5 10 region (i.e., rates for decay, spread, and entrainment) were highest for the L/d = 1 sharp-edged inlet nozzle and lowest for L/d = 12, with intermediate values for a convergent nozzle which is associated with flat exit velocity profile. For the latter, it can be seen from Figure 15 that the turbulence intensities are by far the lowest. However, to counter this, it will also be observed that the mean velocity gradient near X = 0.5 is clearly the highest. Since the axial momentum for the X = 0.5 region is significantly greater than for jets discharged from long or square-edged inlet nozzles, the jet diffuses more readily into the surrounding fluid, the degree of mixing being more intense than for the long nozzles but less than that associated with the relatively short square-edged inlet nozzle. So, as to the variables which determine entrainment rate by jets, it appears that the important ones are the velocity gradient near the nozzle walls and the turbulence generated near the X = 0.5 region. Finally, as the primary interest in this study has been to develop knowledge of the velocity and temperature fields that is relevant to better understanding of the different external factors which affect impingement evaporation or drying, the present results will now be briefly discussed from this viewpoint. In many situations involving localized evaporation, the area of interest is usually comparable to that of the nozzle. Thus,the present results, in particular those in Figures 4 and 14, can be used to provide good insight on the role of some of the external variables. A further justification for such a parametric evaluation stems from the results of a recent study (Hollworth and Wilson, 1984) which showed that trends in recovery temperature measured along an adiabatic impingement surface parallel those in the free jets. For adiabatic evaporation, it is reasonable to assume that the rate of mass transfer from the surface will exactly balance the rate of heat transfer from the air jets and that the heat content in the jet will supply the heat of vaporization of the liquid. Now, several important observations can be made, the first of which concerns the effect of jet-to-surface separation. The results show conclusively that, in view of the
marked decrease in temperature and heat content with distance, some benefit can be obtained by maintaining relatively short spacing between the nozzle exit and the surface for any particular nozzle configuration. Second, any factor that gives rise to an increase in entrainment by a jet can be expected to bring about reductions in jet temperature and heat content which, in turn, may lower the rate of evaporation from a surface. Also, a generally expected observation is that, for a constant absolute air humidity and flow Reynolds number, the rate of evaporation should increase with increasing nozzle exit temperature for a fixed jet-to-surface separation, this being a natural consequence of the corresponding effect of exit temperature on heat content. Finally, the results indicate that the nozzle configuration is an important design parameter, especially since it affects not only the fan power but also momentum and energy transport after the jet leaves the nozzle.
Conclusion Measurements of mean velocity and temperature in round turbulent air jets, issuing from two square-edged inlet nozzles of length 1 and 12 jet hole diameters, have been made for various initial temperatures. Results of detailed calculations for mass flow rate of surrounding fluid entrained by the jets and for jet heat content have been provided. The jet generated with the short square-edged inlet nozzle constitutes a special case in that it is characterized by relatively short lengths for the dynamic and thermal cores and by rates of decay and spread that are different from those for jets emerging from long tubes. The mass flow rate of surrounding fluid entrained by the L l d = 1 nozzle jet is also more than double that for L/d = 12, especially for the region extending from the nozzle exit to about 10 jet hole diameters downstream. Consequently, the L l d = 1distribution curves for temperature and heat content averaged over the X I1 region drop off more rapidly with distance from the nozzle than do profiles for L/d = 12. For either nozzle, the diffusion of heat was found to be more appreciable than that for momentum, as has been documented by virtually all previous investigators. For the purposes of evaporation and drying with heated jets, the results clearly suggest that, since the heat of vaporization is provided by the heat content in the jet, substantial savings in energy can be realized by maintaining the narrowest standoff distance possible, regardless of whether the jet is generated with short or long nozzles.
Acknow Iedgment This work was supported by the Chemical Research and Development Center of the US.Army under ARRADCOM Contract DAAKll-82-K-0001. Technical liason for this project was provided by Paul Grasso, Operational Sciences Section, Physics Branch, CRDC, Aberdeen, MD. Nomenclature A = nozzle area, m2 C, I= specific heat, J/(kg K) d = nozzle diameter, m H = heat content, W L = nozzle length, m M = mass flow rate, kg/s Re = Reynolds number = M,-,d/Ap r = radial distance from jet axis, m ro,l= distance from jet axis to location where U = O.lUo and 0 = O.1B0, m rIl2 = distance from jet axis to location where U = 0.5U0,m
Ind. Eng. Chem. Fundam. 1986, 25, 433-443
= distance from jet axis to location where 0 = o.580, m = local mean velocity, m/s u' = rms value of fluctuating component of velocity, m/s X = nondimensional distance = r / d z_ = axial distance from nozzle, m = z/d(pm/po)'/2 3 2
Greek Symbols qv = nondimensional distance = r/rl12 qt = nondimensional distance = r / t l f z
0 = excess temperature above ambient, p = fluid viscosity, Pa s p = fluid density, kg/m3
"C
433
Superscript - = mean value
Literature Cited Abramovich, G. N. The Theory of Turbulent Jets; M.I.T. Press: Cambridge, MA, 1983. Baron, T.; Alexander, L. G. Chem. Eng. Prog. 1951, 47, 181-189. Corrsin, S. Report No. WR-94, 1943; National Advisory Committee for Aeronautics, Washington, DC. Corrsin, S.; Uberoi, S.M. Report No. TN 1885, 1949; National Advisoly C o m mittee for Aeronautics, Washington, DC. Hollworth, B. R.; Wilson, S. I . J . Heat Transfer 1984, 106, 797-803. Obot, N. T.: Graska, M. L.; TrabW, T. A. Cen. J. Chem. Eng. 1984, 6 2 , 587-5 93. Obot, N. T.; Mujumdar, A. S.;Douglas, W. J. M. Paper No. 79-WA/HT-53, 1979; American Society of Mechanical Engineers, New York. Sforza, P. M.; Mons, R. F. Int. J . Heat Mess Transfer 1978, 21, 371-384. Trabokl. T. A.; Esen, E. 8.; Obot, N. T. I n Proceedhgs, Internatbnal Symposium on Jets and Cavities, Mhmi Beach, Nov 1985; American Society of Mechanical Engineers: New York. 1985; pp 101-109. Wilson, R. A. M.; Danckwerts, P. V. Chem. Eng. Sci. 1964, 19, 885-895.
.
Subscripts j0 = center line value at nozzle exit 0 = center line value downstream from nozzle = value at ambient condition
Receiued for reuiew November 8, 1984 Accepted August 22,1985
n-Decane Pyrolysis at High Temperature in a Flow Reactor Francls Blllaud Dgpartement de Chimie-Physique des RiSactions, L.A. No. 328 CNRS, INPL-ENSIC. 54042 Nancy Cedex, France
Edouard Freund Dgpartement de Physique et Analyse, Instifut Franqis du Pgtrole, BP 3 11, 92506 RueiMWnaison Cedex, France
Thermal decomposition of ndecane is studied in a flow reactor heated by high-frequency induction around 810 O C (1083 K). The main products, determined by gas-phase chromatography, are hydrogen, methane, ethylene, and C3to Cg a-olefins. A theoretical chain radical mechanism indicates that these compounds shouM be primary products. We estimate the importance of intramolecular isomerizations by 1,4- and 1,541ydrogentransfer (transition states with five and six centers, including H) with respect to other elementary processes for bond breaking. Nine theoretical and independent main primary stoichiometries can be deduced from this radical mechanism. Secondary products are also formed. The main secondary products are benzene, toluene, and 1,3-butadiene. To qualitatively interpret the formation of these products (initial rate zero), elementary processes, including the main primary products, are proposed.
Introduction Many experimental and theoretical works have been carried out to analyze the mechanisms and kinetics of hydrocarbon cracking since the pioneering papers of Rice (1931, 1933, 1934, 1943). Formerly, such studies had practical importance because of the need of developing a cracking process to produce petrol from various petroleum products. Now, understanding the mechanism and kinetics of hydrocarbon cracking still represents an important practical interest because of the development of steam-cracking processes (pyrolysis in the presence of steam) to produce light olefins from feeds as different as petroleum gases (LPG) and vacuum gas-oils (VGO), either virgin or hydrotreated. Even though the technology of LPG steam cracking may be satisfactorily mastered, this is not true for gas-oil steam cracking, particularly vacuum gas-oil cracking. This has prompted fundamental studies to elucidate the a priori very complex mechanisms operating 0196-4313/86/1025-0433$01.50/0
in the case of heavy feeds (Hirato et al., 1971). Studies have been conducted using model compounds (e.g., Woinsky, 1968;Illes et al., 1973,1974;Doue and Guiochon, 1968; Blouri et al., 1981). Our studies of the pyrolysis of n-decane in the presence of steam at temperatures around 810 "C (1083 K)are part of a larger project and will be used subsequently as a reference for studies of coreactions of n-decane-gas-oil components. After recalling the possible mechanisms and briefly describing the experimental apparatus, we give our results on the pyrolysis of n-decane in our high-temperature flow reactor. The results are then discussed, commented upon, and interpreted on the basis of free radical mechanisms.
Recall of Possible Mechanisms for Hydrocarbon Decomposition It is well-known that the distribution of products obtained from thermal cracking of light alkanes can be in@ 1986 American Chemical Society
