NONDISTURBING TRACER TECHNIQUE FOR QUANTITATIVE MEASUREMENTS IN TURBULENT FLOW F. F R A N T I S A K , l A . P A L A D E D E I R I B A R N E , J . W. S M I T H , A N D R . L . H U M M E L Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Canada
A new nondisturbing flow visualization technique, in which a photochromic dye is dissolved in the test fluid and irradiated with ultraviolet light to produce a colored trace, has been extended to make quantitative measurements in the entire cross section of a tube in both laminar and turbulent flow. A giant-pulse ruby laser with frequency doubler was used to induce the tautomeric reaction in the dye, and quantitative measurements were made from high-speed movies. The technique and experimental conditions required to produce a long, thin trace are described. Mean velocity profiles proposed by Spalding and others have been confirmed; mean shear stresses a t the wall agree very well with those calculated from the friction factor relation of Blasius.
visualization is one of a number of methods (Dance, 1960, 1967) for studying velocity fields in flow systems. Two general methods have been used for flow visualization studies: observation of physical changes occurring in the field, and addition of substances to the stream of fluid which follows the streamlines of the velocity field and is visible to the eye or camera. Examples of the first group include shadowgraphs and interference and holographic techniques which may be used to detect refractive index variations resulting from pressure, temperature, or density changes. Tracer techniques are members of the second group. Smoke, dust, titanium tetrachloride, etc., are usually used for visualizing the flow of gases. Malachite green, Durazol, and brilliant red can be used for visualizing the flow of liquids in combination with an effective illumination. Aqueous solutions of fluorescein-sodium are strongly fluorescent when irradiated with ultraviolet light. These liquid tracers are injected into the flow stream through the tube upstream of the points of interest in the flow field. Very effective visualization of water flow has been achieved by injecting streams of air or oxygen bubbles through probes. This method has been refined by generating hydrogen bubbles electrolytically a t electrodes (Kline and Schraub, 1965). Larger solid objects, such as spherical polystyrene beads and paraffin wax particles, have also been used for the visualization of fluid flows (Hettler et ai., 1964). All of these visualization techniques are subject to serious disadvantages : LOW
The tracer materials must be injected into the flow stream. They cannot have the same physical properties as the fluid. The flow stream must be disturbed by an injection tube or other probe, as in the case of the electrode probe. Solid particles, no matter how small, disturb the flow stream whenever used. These disturbances are very important a t phase boundaries, such as the wall of the pipe or a submerged object. Thus, conventional direct visualization of the velocity field and other fluid flow properties in the region very close to the wall cannot be reliable. These disadvantages make it impossible to obtain exact quantitative measurements of the velocity field. 1 Present address, Research Institute of Inorganic Chemistry, Usti nad Labem, Czechoslovakia.
160
l&EC FUNDAMENTALS
A technique without the above limitations was suggested by Goldish et al. (1965), who proposed that the blueprint reaction between ferro- and ferricyanide ions might be used for the study of velocity profiles in forced flow, but did not suggest how such measurements could be made quantitatively. A much more powerful technique of Popovich and Hummel (1967) utilized the fact that some dyes can be converted from colorless to colored form by light. The dye used was 2-(2’,4’dinitrobenzyl) pyridine dissolved in 95% alcohol. Tschitschibabin et al. (1925) first observed that when this dye (DNBP) is irradiated with ultraviolet light, a reversible photochromic reaction takes place in which the pale yellow darkens to deep blue in liquid solutions. The color change is believed to be due to the formation of the tautomeric aci-nitro structure (Mosher et al., 1960; Sousa and Weinstein, 1962):
N
// lo HO Popovich and Hummel irradiated the flowing dye solution in a rectangular channel with a photoflash and noted the deflection of the dye trace with a subsequent flash. They were able to make significant measurements of the thickness and fluctuating velocity of the viscous sublayer at a Reynolds number of 13,100. The present work describes a further refinement of the method, the light being introduced by means of a laser beam with a frequency doubler for the production of the dye trace, quantitative studies being made using a high speed camera with speeds u p to 10,000 frames per second. These advances permit the use of the technique for turbulent as well as viscous flows. Experimental Method
The dye material used, DNBP, responds with maximum absorbance in the ultraviolet region, corresponding to a wavelength of about 2500 A. (Hardwick et al., 1960). The ruby laser used in this work produces light with a wavelength of 6943 A. and could not be used directly for the production of the dye trace. The use of a sodium dihydrogen phosphate
frequency doubler permits the reduction of the wavelength by a factor of one half. The photochromic reaction is reversible, and the trace life is short, although it is lclng enough to be recorded by a camera for about 3 or 4 msec. The life of the trace depends on temperature, the coincentration of dye in the alcohol solution, and the amount of water present in the alcohol solution. Figure 1 is a schematic diagram of the apparatus used for calibration of the dye traces. The laser used was a giant-pulse ruby Model TRG-104A with an energy u p to 100 mw. and a wavelength of 6943 A. A second harmonic generator reduced the wavelength to 3471.5 A. and the energy efficiency to less than 20y0',. The pulse had a duration of about 30 X 10-9 second. The beam produced had a cross :section of about 2 X 3 mm., with a spread of about 5 milliradians. Under certain conditions, the diameter of the beaim could be reduced to about 1 to 0.25 mm. The laser head was adjusted from time to time with a n alignment telescope D-275 (supplied by Davidson Optronics) , Two converging quartz lenses with focal distances of 120 and 45 mm., respectively, were used in the optical system.
POWER SUPPLY
I I
focal length 5.5 cm.) with Kodak high contrast film. A 400-watt sodium lamp supplied by General Electric, Lucalox 400, was used for illumination of the system with a d.c. rectifier. The prints were made on Kodak E5 Kodabromide paper. Solutions of dye in alcohol were prepared on the same day as the measurements, using distilled alcohol to eliminate all influences such as age o f the solution and impurities in the alcohol. The DNBP was dissolved at temperatures less than 50' C. to avoid decomposition. Fluid properties of the solvent, such as density, viscosity, and surface tension were not affected by the low concentration. of DNBP used. The laser beam (Figure 1) was directed normally to one of the test section walls in order to avoid refraction. The lenses contracted the beam, the focus of the second lens falling into the liquid. The camera was placed a t 90" to the beam path and the light source (sodium lamp) was located behind the test section in the optical axis of the camera. The opening of the camera was synchronized with the triggering of the laser power supply. For every value of the variables, several pictures were taken. Generally, the pictures were read with a n accuracy of 1 0 . 1 mm., which corresponds to 1 1 0 to k 1 4 . 5 microns in the actual experiment, depending on the magnification. The variables studied to obtain the optimum trace (length maximized and diameter minimized) were : concentration of DNBP, concentration of ethyl alcohol (percentage water), energy of the laser beam, solvents other than ethyl alcohol, and focal length and type of lenses. The equipment used for measurements in forced flow is shown in Figure 2. The liquid flowed by gravity between two containers, each of 3-gallon capacity, through a vertical glass tube 135 cm. long, and with a cross section of 1.226 sq. cm. The pressure in the upper container was kept constant during each experiment. The average velocity of the flow for Reynolds numbers less
LASER POWER SUPPLY
for
TANK I. CONSTANT LIQUID
1
-i: TEST
II
I
I
HEAD
1IL
TANK 2
Figure 2. Schematic diagram of apparatus for measurements in forced flow
than 2 x IO4was determined by a previously calibrated orifice meter located a t the end of the vertical tube. Higher values of Reynolds number were obtained by increasing the pressure in the upper container. The average velocity was then computed by integration of the experimentally determined velocity profile. The laser beam was fired into the pipe 110 cm. downstream from the inlet to ensure a fully developed velocity profile. Optical distortion caused by the round tube was reduced by a square Plexiglas box (IO X 5 X 5 cm.) filled with ethyl alcohol. The trace formed by the light beam was followed with a high speed camera (Hycam 400-foot model) employing Eastman XX negative film. The camera speed was controlled with a timing light generator (TLG-SDC), previously calibrated with an oscilloscope, which gave 100 signals per second on the film. Instantaneous velocities were measured from prints made from 35-mm. copies of the original 16-mm. film. Readings were then made either directly or with the aid of an X Y coordinate digital converter (Coordicon T M ) The laser head, optical lenses, camera, and sodium lamp were arranged in the same way as for the measurements in the static liquid. I n these experiments, the concentration of DNBP was varied from 0.025 to 0.05% (by weight) in 9570 ethyl alcohol. For each run the lenses were located a t the optimal distances from the tube to obtain a thin long trace. The camera was
.
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161
Table 1.
Influence of Concentration of DNBP in 95% Ethyl Alcohol
Input Energy 900 Joules
x
Ao, mole/liter
1
cm. leaptl, cm. Diameter tracer, cm:
Not’vkble
lcalcd,
1.22
10-6
x
10-4
...
lexpti, cm. Diameter tracer, cm;
Not visible
3 . 1 x 104 9 . 3 2 x 10-4 12.7 4.42 2.47 0.08
1 . 5 5 x 10-3 2.73
Input Energy 600 Joules 2.07 0.029
2.31
x
10-3
2.07 0.116
1.68 0.030
3 . 1 x 10-3 1.4 1.4 0.104
6 . 1 x 10-3 0.74 1.01 0.108
1.04 0.036
0.78 0.058
Table II. Influence of Varying the Ethyl Alcohol in the Solution
Input Energy 600 Joules. Ethyl alc. concn., wt. % leXptl, cm. Tracer diam., cm.
DNBP Conen.,
wt.%
Set No:
95 1.04 0,030
80 0.93 0.039
10-aM
95
20
1.756
I1
0.040
95
23.5
1.638
95
25.5
1.588
loaded and synchronized with the laser apparatus and the timing light generator. The illumination of all the systems and the focusing of the camera were carefully controlled to obtain an accurate and well defined position of the inner wall of the tubing, and the laser beam was directed perpendicularly through the axis of the tube. The laser was triggered after the camera reached a constant speed.
7.22 11.9
Effect of DNBP Concentration on Length of Trace. Hummel (1767) has derived a theoretical relationship for the depth of penetration of trace I in centimeters as a function of indicator concentration A in moles per liter. 1 2.303 CY
where
CY
A0
In
rq)
1
-t 2.303 CY A0 ln(eu
- 1)
Time per Frame, X lo4,Sec.
Magnijieation
17.3 17.3
10.42 10.42
580 580
175.0
13,380 16,340
298.0
22,650
370,O 382.0
28.200 291100
5.76 5.80 3.80 3.74 3.80 3.37 2.71 2.61
6.65
214.5
1734 1723 2632 2671 2630 2970 3700 3775
137.5
10,820 13,800
214.5 371 .O
16,900 29,200
417.0
32,800
5.85 5.82 5.89 5.74 4.52 2.17 2.14 2.14 2.18
9.91
175.0
1710 1720 1695 1740 2215 4620 4665 4670 4590
6.65 6.65 6.65 6.65
9.91 9.91 9.91 9.91
From the measurements, Bo = mole per liter. CY = 2.66 X lo3 for X = 3500 A. was calculated using the BeerLambert law. Parameter y is related to the efficiency of light energy in converting the dye material from colorless to the blue form and was calculated to be about 20.9.
----- THEORY - EXPERIMENTAL
\ \
3.0
(1)
= extinction coefficient for indicator (colorless form),
liters/cm. mole A0 = initial indicator concentration, moles/liter Bo = dye (blue form) concentration, moles/liter y = 2.303 CYSI 6 = conversion factor = 8.36 l O 7 X q X = light wavelength, A. q = quantum yield Z = total incident light, joules/sq. cm. 162
10 0.91 0.0314
514 847
Experimental Results
I =
20 0.94 0.031
40 0.80 0.036
wt.
0.025 0.075
0.05
x
60 0.95 0.036
Table 111. Experimental Conditions and Properties of Solutions Ethyl Ale. Solution Camera Concn., Temp., v X loz, U,,, Sq. Speed, % O C. Sq. Cm./See. Cm./Sec. Re FrameslSec.
I
I11
DNBP Concn. 3.1
l&EC FUNDAMENTALS
/I 0
31XIO~‘
Figure 3.
j
CONC DNBP, moles/iiter
L
r
r
155x10’’
31x10’’
I
I
1
6 I x IO” M
Effect of DNBP concentration on length of tracer
The experimental and calculated measurements of I as a function of concentration of DNBP in 95% alcohol for a given power input are given in Table I and Figure 3, all other conditions being constant. There is good agreement between the data and the theory above dye concentrations A0 = 1.55 X mole per liter. For lower concentrations of dye, the experimental data and the theory differ, probably because of the simplifying assumptions involved in the theory. The theoretical curve shows, however, the general trend of the dependence of the visible length of the tracer as a function of the concentration. T h e numerical results of pho tographic sequences are shown in Table 11. The length of the tracer beam and its diameter are only slightly affected by the reduction in the proportion of alcohol down to 10% (Table 11). However, the proportion of alcohol has a large influence on the lifetime of the trace. Lower concentrations of alcohol resulted in shorter life, but for all cases, even of a concentration of 10% alcohol, the life of the tracer is longer than 6 msec. The reduction in the life of the trace a t lower concentrations of alcohol can be explained by the fact that water accelerates the reverse reaction of the photochromic change from blue to yellow. T h e solubility of DNBP is decreased as the proportion of water increases. Even 0.1% DNBP in 2070 alcohol is only partially soluble, a part of the DNBP being present in solid form in needle-like crystals a t 20' C. Influence of Beam Energy. T h e energy of the beam is a function of the input energy. This was varied over the range of 600 to 900 joules, as shown in Table I. T h e qualitative resultis of higher input energy are: Higher input energy results in darker traces. This means, as expected, that the higher energy available results in a greater conversion to the tautomeric aci-nitro structure. Higher energies for a constant pulse time result in longer trace life. Higher energy input results in greater diameters of the trace. Choice of Solvent. For the present experiments, 95% ethyl alcohol was chosen, because the dye fades slower (Sousa and Weinstein, 1962) in ethyl alcohol than in other solvents such as isobutyl alcohol, sec-butyl alcohol, and benzene. Results of Measuremen'ts in Forced Flows
T h e new nondisturbing tracer technique has been used in the present study for the measurement of fluid flow in smooth pipes in the turbulent region for comparison with other previously determined experimental data. T h e large number of both theoretical and experimental measurements possible in this system commend its use for calibration. T h e theories and limitations of experimental techniques such as the hot-wire technique and Pitot tube are thoroughly discussed by Hinze (1959) and others. Because the flash photolysis method is nondisturbing, it should be possible to use it as a n absolute standard for all other techniques which may be less time-consuming. T h e flash photolysis method should be especially useful for both experimental and calibration methods very close to solid boundaries. A limitation of the method lies in the fact that a t the present state of development, errors due to radial velocity components of individual fluid elements are not taken into account. However, intensive measurements of turbulence properties agree very well with the most reliable data available. This problem can be overcome by the use of stereophotography and modulated beams.
Experimental conditions and the properties of the solutions are summarized in Table 111. T h e diameter of the trace obtained in these experiments was between 0.024 and 0.07 cm., depending on the working conditions. The trace could be followed an axial distance of 3 cm. downstream in the vertical tube before it left the field of view of the camera. From a fixed axial position, x = 0, the vertical distances traveled by the tracer in successive frames XI, XL . . . x , were measured for different fixed values yl, y 2 . . of the distance from the wall ( j = 0). The velocities were then coniputed from ( x ~ +-~ .$)/At, where 4t is the time interval between two frames, and the average values of instantaneous velocity a, for each value of y were obtained. This value was checked by computing x n / t n for the last frame ( t = 0 a t the time of appearance of the trace). Dimensionless distances y + = y u * / v were also calculated, where u* = friction velocity = ( ? w / p ) l / z , v = kinematic viscosity, 7, = average shear stress a t the wall, and p = density. For dimensionless distances y + smaller than 5 , our measurements are in doubt, because of the optical distortion of the round vertical tube. Laminar flow measurements were made initially to check the effect of optical distortion. Simple optical laws will show that small deviations from 90' between the direction of the light flash and the axis of the tube, the dimensions of the box, the slope of the front wall of the box, the position of the camera, etc., can lead to errors. Extreme care is necessary, therefore, to maintain these variables constant during the whole series of measurements. The exact solution of the Navier-Stokes equations for fully developed flow in a smooth pipe is:
.
UZis the point velocity a t a position y from the wall and U, max is the maximum value of U, in the pipe center; r is the
where
radial distance from center = ro - y ; and ro is the radius of the tube. This equation was proved experimentally by Hagen (1839), Poiseuille (1840), and more recently by Nikuradse (1932) and other workers. Typical frames of the laminar flow profiles are shown in Figure 4. T h e calculated and measured velocity profiles taken from the frames are shown in Figure 5. Equation 2 is known to be correct for fully developed laminar flow with dimensionless entry length L I D greater than 0.03 R e (Schlichting, 1960). Therefore, these measurements may be used to obtain a calibration of the effect of optical distortion. The calibration curve obtained by comparison of the laminar profiles with the known solutions of the Navier-Stokes equations (Figure 6) is used to correct for the effect of distortion in the turbulent measurements. T h e measurements in the laminar regime were also used to obtain the maximum error in reading from the prints. For 20 readings from the same frame the maximum deviation is less than 1% of U.
Velocity Profile in Turbulent Flow
Preliminary experimental work has been carried out to check the experimental technique against established techniques in the region where the limitations of the established techniques, primarily due to the influence of the wall, are negligible. A typical sequence of frames for Reynolds number 13,800 VOL. 8
NO. 1
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163
164
l&EC FUNDAMENTALS
30
i!8 216 1'c
25 20
18
UX
16 I' G 12
10 8 6
2 0
,
1
1
0.1
0
1
0.2
1
1
0.3
1
1
1
0.4
y.
1
1
0.5
1
1
0.6
1
1
0.7
1
0.8
1
1
0.9
1
1.0
r. Figure 5.
Measured and calculated velocity profiles for Re = 847
Spalding (1967) :
y+=u++A
1.15
x
1~10
(4) 1.05
1'00
0
0.2
04
0.6
0.8
1.0
Y 10
Figure 6. efficient, K
Measured .distortion co-
is shown in Figure 7. The time elapsed during the photographing of the frames was about 0.0083 second. It is obvious that the time-average velocity for a sequence does not result in a smooth, symmetrical curve, and that eddies are preserved for a t least the elapsed time. This result is interesting in view of Klebanoff's (1954) measurements, which suggest that a smaller time scale a t fixed reference points gives smooth symmetrical profiles. The results of measurements (sets I1 and 111) are plotted as u + against y + in Figure 8. Also plotted are the analytical expressions of: Reichardt (1951) : u+ = 2.5 ln(1
f 0 . 4 ~ ~+ ' ) 7.8 x
where A and B are constants in the law of the wall. Von Karman's (1939) expressions for the universal velocity profile may also be superimposed on the data without significant deviation. Equations 3 and 4 are valid over the whole range of y+. The results are in excellent agreement with all these equations. I t is not possible to say which equation fits the measurements best. For heat and mass transfer calculations, the simplest equations fitting the entire range ofy + should probably be used. Wall Shear Stress
T h e instantaneous values of wall shear stress can be calculated from the slope of the velocity gradient of the viscous sublayer, rYr= -.~(&q'3y)~, where p is the viscosity. The instantaneous wall stress was calculated from successive frames, and an over-all average value FUlcomputed for each trace sequence. The shear stress was also calculated from the empirical equausing f,the friction factor relationship tion rYrcal. = (f.p.USv2)/8 of the Blasius equation, and UaV,the average velocity of flow. Both these results are shown in Figure 9. There is excellent agreement between Fzocalculated and 7, experimental. The friction velocity u* was then calculated for determination of U +.
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165
30
I
A 0
25
rn A
0 v 0 0
20
I
I
1
1
1
Re 28,200 32,800 29.100 29.200 22.650 16.340 10,820 13,380
1
,
1
I
I
I
,
,
,
I
,
I
I
I
l
l
1
SPALDING
-----
REICHARDT
. *
/A -
J-
n
15
“t
IO 5 0
I
I
I
I
I
1
Figure 8.
I I I I ,
Io1
I
I
I
I
I
I
I l l
I
IOL
I
I
I
l
l
1
lo3
Y‘
Comparison of present measurements with Spalding and Reichardt equations literature Cited
IO‘
20.10~
30 i o 3
Re
Figure 9. Average wall shear stress as CI function of Re
T h e experimentally determined flow characteristics reported here are in excellent agreement with other, well established data. T h e temchnique presented here is simple, and may be readily adapted .to many fluid flow systems.
Dance, E. W. G., Znst. Gus Engrs. J . 4, 282 (1967); Symposium on Flow Visualization, A.S.M.E. Meeting, November 1960. Goldish, L. H., Koutsky, J. A., Adler, R. J., Chem. Eng. Sci. 20, 1011 (1965). Hagen, J., Pogg. Ann. 46,423 (1839). Hardwick, E. R., Mosher, H. S., Passailaique, P., Trans. Faraday SOC. 56, 44 (1960). Hettler, J. P., Muntzer, P., Scrivener, O., Compt. Rend. 258, 4207 (1964). Hinze, H. O., “Turbulence,” McGraw-Hill, New York, 1959. Hummel, R. L., unpublished manuscript, 1967. Karman, Th. von, Trans. ASME 61,705 (1939). Klebanoff, P. S., National Advisory Committee for Aeronautics, NACA TN3178 (1954). Kline, S. J., Schraub, R. A., Mech. Engr. Dept. Stanford University, Rept. MD-12 (1965). Mosher, H. S., Hardwick, E. R., BenHur, D., J. Chem. Phys. 37, 904 (1962). Mosher, H. S., Souer, C., Hardwick, E. R., J . Chem. Phys. 32, 1888 (1960). Nikuradse, J.; VD T-Forschungsh. 1, 356 (1932). Poiseuille, J., Compt. Rend. 11, 961 (1840). Popovich, A. T., Hummel, R. L., A.I.Ch.E. J . 13, 854 (1967). Reichardt, H., 2.Angew. Math. Mech. 31, 208 (1951). Schlichting, H., “Boundary Layer Theory,” McGraw-Hill, New York, 1960. Sousa, 3. A., Weinstein, J., J . Org. Chem. 27, 3155 (1962). Spalding, D. B., J . Appl. Mech. 28,455 (1967). Tschitschibabin, A. E., Kuindshsi, B. M., Benewolens Kaya, s.w., Ber. Deut. Chem. Ges. 58, 1580 (1925). RECEIVED for review March 11, 1968 ACCEPTEDSeptember 30, 1968
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