Quick method for
Measuring Drop Size of Hollow Cone Sprays
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Can Analyze and Evaluate Spray Systems for evaporation drying combustion
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size and drop size distribution are important variables controlling such processes as spray evaporation, spray drying, and fuel spray combustion. While it is desirable to know drop size, it is a most difficult task to make such measurements. However. for a conical spray from a single fluid nozzle, drop size can be measured by a simple test method. Basis for Test Method
.%ir is induced to enter a conical spray a t right angles to the surface of the cone (Figure 1). pass through the spray while changing direction, and take a final direction parallel to the nozzle axis ( 7 ) . The inside of the cone is filled nith spray particles entrained when the air passes through the spray sheet. Air velocity outside and inside the spray cone is set by continuity requirements. At the spray cone boundary it is related to the momentum change of the spray passing across the flow cross section. This. in turn, is a function of the sum of changes in momentum of spia) drops decelerating as they pass across the flon. cross section. In the spray sheet the drop encounters 1
HIKMET BINARK' and W. E. RANZ2 The Pennsylvania State University, University Park, Pa.
Relation between Stopping Distance and Drop Size
an induced air motion a t nearly right angles to its path. The motion of the drop along the spray cone is essentially a decelerating motion similar to that occurring in still air. An individual drop travels along the cone nearly as far as its stopping distance by which time it has assumed the motion of the air and goes inside the cone: moving parallel to the nozzle axis. Smaller drops with shorter stopping distances move near the axis. Larger drops with larger stopping distances move farther from the axis. This separation of drop sizes according to stopping distances is the basis for the test method. As it travels along the spray cone, a drop is continuously subjected to lateral aerodynamic force, actually following a curved path. At high liquid issue velocities the spray sheet bends toward the nozzle axis. Because lateral air velocity is less than about 10% of relative velocity of the drop, sideways force is only a small percentage of the decelerating force during that part of the motion which causes a separation of drop sizes. For the test method it is assumed that drop motion can be simplified to a onedimensional deceleration along the visible spray cone for a distance equal to the stopping distance. Here the drop turns and moves a t induced air velocity along a line parallel to the nozzle axis. Effects of curving trajectories and gravity are alleviated by measuring liquid flux at sorne distance below the spray sheet.
I n the absence of all forces except aerodynamic forces. the equation of motion of a spherical drop in a still gas is - ( ~ P , , C D / ~ P ~ D=) du/dt U~
(I)
Equation 1 can be rewritten in terms of a variable Reynolds number, .VRa = D p , u / p , , and, by substituting dt = dx,'u, a dimensionless distance. x' = (18 p , / D p r ) x . Boundary conditions for the motion are .\'E, = -TReo = D p ~ ~ o / p ~ when x ' = 0, and ' V R e = 0 when x' = s', the dimensionless stopping distance. These changes in variables and solution of Equation 1 for the given boundary conditions result in the following expression for stopping distance : S' =
Figure 2 . a graphical form of Equation 2. is based on experimental values of 24,'CDaTRe US. I T R ~( 2 ) . L\-R,, = DP&O @ g , interpreted as a dimensionless drop size, is plotted us. S'.\g,, = ( 1 8 p Q 2 u ~ / p l p , ) S , interpreted as a dimensionless stopping distance independent of drop size. Experimental Procedure
If the assumptions of the test method are correct, the percentage of total liquid flux moving along the nozzle
Present address, Technical University
of Istanbul, Istanbul, Turkey.
* Present
address, University of Minne-
sota, Minneapolis, Minn.
Figure 1. Air flow and drop trajectories in a hollow cone spray Drops are formed near the nozzle orifice and projected in a narrow band at nominal spray cone angle 8. Induced air flow bends cone surface inward
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b Figure 2. This graphical form of Equation 2, showing drop size vs. stopping distance, is based on experimental values of drag coefficient
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Figure 3. Drops with stopping distances less than B were carried through chimney by induced air flow. All other drops were collected in Pan
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axis within a certain radius is the cumulative mass percentage of drops with sizes smaller than the drop with a stopping distance corresponding to that radius. Thus, the procedure should measure liquid flux without seriously altering air or liquid flow patterns. Several methods were employed to measure liquid flux distribution. I n the simplest and most successful, a series of “cake pans” with central chimneys of varying diameters (1.3-, 2.5-, 3.5-, 5.2-, 8-, and 12-inch inside diameter) were held concentrically under the spray so that the spray cone hit the outer wall of the pan but not the chimney (Figure 3). Spray liquid carried by induced air flow a t radii less than the chimney radius was allowed to pass down through the open chimney. Remaining liquid was collected in the pan. Flux measurements (Figure 4 ) were plotted in terms of radial distance from the spray cone axis and the corresponding stopping distances. Figure 4 also shows a data point for the longest stopping distance observed, representing ‘‘maximum drop size.” This was obtained by holding the nozzle upward, its axis at an angle equal to one half the nominal cone angle, such that the lower surface of the cone was horizontal. The longest horizontal distance the
Figure 4. This example of flux data for an 80’ nozzle (Delavan Mfg. Co.), spraying fuel oil at 12.2 gallons per hour, was obtained with equipment shown in Figure 3. Air density was 1.15 X gram/cc. and air viscosity was 1.85 X poise
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Figure 5. Drop size distribution of fuel oil spray was plotted from data in Figure 4 using Figure 2
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spray traveled was taken as maximum stopping distance. T o interpret Figure 4 in terms of drop sizes it is also necessary to measure uo. This was accomplished by orienting a miniature impact tube at the nominal spray cone angle facing the liquid flow. The tube was traversed across the orifice at a distance of about 0.01 inch from the orifice, and the maximum reading was used to calculate liquid issue velocity. For the given test conditions each stopping distance in Figure 4 represents a particular drop size and is replotted in Figure 5 as drop size us. a cumulative mass percentage. Included are three data points obtained by an entirely different test method ( 3 ) . Agreement is apparently excellent. The present method, however, establishes cumulative percentage over a wider range of drop sizes and requires much simpler equipment. Nominal stopping distance and stopping distance along the cone surface (Figure 4 ) are nearly identical for the
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first 4 inches (and first four points on the cumulative size distribution curve in Figure 5). T o have used nominal stopping distance for distances larger than about 5 inches would have resulted in a “drooping” size distribution curve with 807, cumulative mass at a drop size about 15% lower. The spray cone can be mapped photographically or measured directly. It can also be established by varying the distance of the “cake pans” from the nozzle. When the distance is too short, spray hits the wall inside the chimney (Figure 3 ) ; when the distance is too large, spray splashes on the edge cover. Maximum collection indicates optimum distance. Nomenclature
D = drag coefficient; for drop, CD = CI, (drag force)/ (pou2/2) ( a D 2 , / 4 ) = drop diameter -vRe = D P g u ! p ~ ; *VReo = D P & O ’ f i ~ S = stopping distance t = time u = drop velocity with respect to air = liquid velocity at nozzle orifice uo x = distance f i 0 = air viscosity pg = air density p L = density of spray liquid literature Cited
(l),Binark, Hikmet, Ranz, W. E., National Meeting, Am. SOC.Mech. Engrs., New York, December 1958. (2) “Chemical Engineers’ Handbook” [J. H. Perry, ed.), 3rd ed., p. 1018, Table 4, McGraw-Hill, New York, 1950. (3) Ranz, W. E., Hofelt, Clarence, Jr., IND.ENG.CHEM.49, 288 (1957). RECEIVED for review .4UgUSt 8, 1958 ACCEPTED November 24, 1958 Work sponsored by Project Squid, supported by Office of hTavalResearch under contract Nonr 1858 (25) NR-098-038.
