3776
Ind. Eng. Chem. Res. 1996, 35, 3776-3781
Flow Field of Practical Dual Rectangular Jets Anthony S. Harpham and Robert L. Shambaugh* Department of Chemical Engineering & Materials Science, University of Oklahoma, Norman, Oklahoma 73019
Velocity fields were measured below two parallel, rectangular air nozzles. Each rectangular nozzle had a large length-to-width ratio, the nozzles were closely spaced, and the air jets intersected at a 60° angle. For positions near the center of the nozzles, the flow field closely approximated that of a two-dimensional jet. Several slot widths were tested. Correlations were developed to predict the velocity at any position below the pair of nozzles. Introduction Several investigators have measured the flow fields of practical nozzles used in industry. Obot et al. (1984, 1986) examined the velocity and temperature distributions in the fields produced by air exiting from straight, sharp-edged entrance orifice plates. Uyttendaele and Shambaugh (1989) and Majumdar and Shambaugh (1991) examined the velocity and temperature fields below sharp-edged annular nozzles. Annular nozzles of this type are used industrially to produce polymeric fibers in the process known as melt blowing. [In melt blowing, high-velocity gas streams impinge upon molten strands of polymer and fine filaments result; see Shambaugh (1988) for additional details.] Knowledge of the gas flow field permits modeling of the fiber-formation process (Uyttendaele and Shambaugh, 1990; Rao and Shambaugh, 1993). The velocity and temperature distributions below large arrays of nozzles (165 orifices in three rows) were recently examined by Mohammed and Shambaugh (1993, 1994). Such arrays are used commercially to make melt blown fibers (Schwarz, 1983). Another very common type of industrial melt blowing die is the slot die (Shambaugh, 1988). In this die fibers are formed when high-velocity air impacts upon polymer that is extruded from a row of fine capillaries; see Figures 1 and 2. The air emits from a pair of slots, and the plane of each slot is at an acute angle relative to the face of the die. This paper involves the examination of the flow fields below such a jet arrangement. Though this paper confines itself to room temperature (ambient) air, the results can be extrapolated to the higher temperatures involved in melt blowing. Mohammed and Shambaugh (1993) reference past work on linear arrays of rectangular nozzles. For example, ventilated and unventilated dual jets were studied by Lund et al. (1986) and Lin and Sheu (1991). [The slot die of this study is unventilated since, other than the two air slots, there are no other openings in the die face to permit additional air flow via entrainment.] None of the previous work involved sharp-edged, dual jets in the angular arrangement shown in Figures 1 and 2. Single rectangular nozzles have been studied by a number of investigators, including Miller and Comings (1957), Van der Hegge Zijnen (1958), Heskestad (1965), Sforza et al. (1966), Trentacoste and Sforza (1967), Jenkins and Goldschmidt (1973), Kotsovinos (1976), and Sfier (1978). Sforza et al. (1966) described these three regions below a rectangular jet: (1) the potential core region, (2) the characteristic decay region, and (3) the axisymmetric region. Region 1 is a transition region between the die exit conditions and the well-developed S0888-5885(96)00074-7 CCC: $12.00
Figure 1. Experimental setup.
Figure 2. Side view of the air exit region of the die. A width setting of h ) 3.32 mm (the base setting) is shown.
velocity profiles of region 2. In region 2 the velocity profiles have the same functional form and change only in scale. In region 3, the velocity profiles approach those expected from a point source (i.e., the jet is independent of slot geometry). Experimental Equipment and Procedures The experimental setup is shown schematically in Figure 1. Air at 480 kPa (70 psig) was fed to a bank of flow meters. The melt blowing die had the configuration shown in Figures 2 and 3. The slot widths on the die were adjustable; as a base condition, a slot width of b ) 0.65 mm was used. Each slot had a length of l ) 74.6 mm (2.94 in.). The h is the distance between the outer edges of the slots. Gas velocities were measured with a Pitot (cylindrical impact) tube. This tube had an outer diameter of 0.71 mm, an inner diameter of 0.45 mm, and a conical nose shape with a cone angle of 25°. Because of the small dimensions of the Pitot tube, measurements could be taken in a very small space. This was an advantage because the slot die had fine dimensions. (A Pitot© 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3777
Figure 3. View of the face of the die. The z-axis (not shown) is perpendicular to the plane of this drawing. Positive z values are located above the plane of the drawing.
static tube is bulkier and was judged to be not suitable for the measurements of this study.) The Pitot tube was 6.35 cm long and was connected with 3.2 mm inner diameter tubing to an oil-filled manometer. The formula used to convert pressure to velocity is discussed by Uyttendaele and Shambaugh (1989). The Pitot tube pressure was referenced to ambient static pressure, and the tube was oriented vertically during the measurements. The Pitot tube was positioned with a Velmex 3-D traverse system which permitted x, y, and z motions in 0.01 mm increments. The coordinate system selected for the experiments is shown on Figure 3. The origin of the system is at the center of the face of the die. The y-direction is parallel to the major axes of the nosepiece and slots, the x-direction is transverse to major axes of the nosepiece and slots, and the z-direction is perpendicular to the plane of the drawing of Figure 3. The positive z-axis is directed vertically downward (see Figure 1). The air flow rate, at standard conditions of 21 °C and 1 atm pressure, was maintained at either 1.67 × 10-3 or 3.33 × 10-3 m3/s (100 or 200 L/min). The slot width settings were changed by moving the left and right air plates. Equal slot widths of b ) 0.44, 0.65, and 1.35 mm were used in the experiments. For a slot width of b ) 0.65 mm, the two air flows produced average discharge velocities of vj0 ) 17.3 and 34.6 m/s. The corresponding Reynolds numbers (based on a 0.65 mm slot width) are 3800 and 7600. For all runs, the air temperature was maintained at ambient (21 °C). Results and Discussion The l/b (length-to-width) ratio of the individual die slots ranged from 55 to 170, while the l/h ratio ranged from 16 to 26 (see Figure 2). Since these ratios are large, the die was assumed to approximate an infinitelength die for positions that were both near the center plane of the die and not at extremely large distances from the die. The verification of this assumption will be discussed later. Because of this assumption, a large number of experiments were run for positions in the bisecting plane (y ) 0; see Figure 3) of the die. Kotsovinos (1976) observed that, for single rectangular jets, an infinite length (2-D) jet assumption is good for a length-to-width ratio (l/w) > 20. (For the die of this study, the slot width b and the overall width h are as shown in Figure 2. The symbol w refers to the slot width of single rectangular jets used by others.) Over
Figure 4. Development of the velocity profile for positions near the die face. All values were measured at y ) 0 and with h ) 3.32 mm.
Figure 5. Nondimensional velocity profiles for intermediate positions below the die. Data for three different die settings (h values) are given.
5000 individual velocity measurements were made during this study. Profile Development. Figure 4 shows the development of the velocity profile for positions close to the die face. At z ) 0.25 mm, there are two distinct peakssan expected result because there are two slots. For increasing z values, the two peaks merge together. By z ) 5.00 mm, only a single peak remains. A Pitot tube gives an error of
