AIAA-46701-309

JOURNAL OF AIRCRAFT Vol. 32, No. 1, January-February 1995 Study of the Droplet Spray Characteristics of a Subsonic Wind Tunnel Michael B. Bragg* and Abdollah Khodadoustt University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 A finite difference, two-dimensional potential flow solver, and a three-dimensional particle trajectory code have been written to compute water droplet trajectories in a subsonic incompressible flow wind tunnel. This method was used to study the spray cloud in the test section of a two-dimensional wind tunnel resulting from the injection of a distribution of water droplets in the settling chamber ahead of the inlet. The results of this computational study showed that the trajectories of the larger water droplets were affected by the droplet inertia and gravity more dramatically than that for the smaller particles. The calculated liquid water content across the test section indicated a high concentration near the tunnel centerline. The largest droplets were present at the test section only in the center one-third of the wind tunnel, whereas the smaller droplets spanned almost the entire test section width. This resulted in a computed droplet size distribution skewed toward the larger droplets in comparison with the initial Langmuir-D distribution. The distribution of particle sizes and concen- trations required at the droplet injection point in the settling chamber for a Langmuir-D distribution of uniform liquid water content in the center third of the test section was computed. A CD CR Fr 8 H Hs K S t u u v P a T 0) Nomenclature droplet trajectory stream tube area droplet drag coefficient tunnel contraction ratio, Hf/HTS Froude number, £/TS/V//,-g gravitational acceleration constant tunnel width flowfield total head, Ptotal/p droplet inertia parameter, z = Subscripts TS = droplet freestream Reynolds number, stream function time average flow speed at an x location local flow speed in x direction local flow speed in y direction tunnel Cartesian coordinate system droplet diameter droplet nondimensional position air density droplet density nondimensional time, Ut/H, flow vorticity = tunnel inlet value = tunnel test section value Superscripts = vector quantity = first derivative with respect to r = second derivative with respect to T Received Feb. 23, 1994; revision received May 28, 1994; accepted for publication May 30, 1994. Copyright © 1994 by M. B. Bragg and A. Khodadoust. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. *Associate Professor, Department of Aeronautical and Astro- nautical Engineering. Associate Fellow AIAA. tPostdoctoral Research Associate, Department of Aeronautical and Astronautical Engineering. Student Member AIAA. Introduction D URING flight in adverse weather conditions, an aircraftis subjected to water droplet impingement. Given the proper conditions, the impinging water may freeze on the flight surfaces, reducing their aerodynamic efficiency. To pro- vide the aircraft all-weather capability, anti-icing and de-icing systems are used on the leading edge of the most flight-critical surfaces. In order to determine the extent of the surface that is to be protected by the anti- or de-icing equipment, and the amount of protection needed, it is necessary to know the details of the water droplet impingement on the surface. Computational methods have been developed to calculate water droplet impingement on airfoils and wings. 1 ~ 6 Wind- tunnel tests have been conducted in icing tunnels to measure impingement characteristics for code validation.7"9 While the existing codes calculate the impingement efficiency in free air, the validation studies are performed in wind tunnels where the tunnel walls can affect the droplet trajectories. The wall effects have been found to be small and within the limits of experimental error for most two-dimensional airfoil testing in a typical subsonic wind-tunnel test section, without accounting for the upstream inlet contraction effects on the water droplet trajectories.10 Effects of the wind-tunnel walls on the com- puted trajectories in a three-dimensional flowfield with a re- flection-plane mounted rectangular wing are currently under investigation.11 These early three-dimensional results show trends similar to the two-dimensional wall effects. The previous wall-effects studies10-11 assumed that the wind- tunnel spray system had been adjusted to provide a uniform cloud in the test section with regards to both droplet size and liquid water content. These studies then examined the effect of the wind-tunnel walls on the aerodynamics of the airfoil or wing and how this affected its droplet impingement char- acteristics. This study is intended to provide insight into how the wind-tunnel contraction affects the water droplet cloud in the test section, and how the initial spray cloud can be modified to provide a uniform test section cloud. Numerical Formulation Flowfield The flowfield solution technique employed here was used by Coirier12-13 to study the effect of screens on two-dimen- sional inlets using a finite difference method for subsonic 199 200 BRAGG AND KHODADOUST: DROPLET SPRAY CHARACTERISTICS 201 x51 grid x/H. Fig. 1 Computational grid in the physical domain. inviscid incompressible flow. The stream function S satisfying the continuity equation is defined such that the velocity field is given by dS dS ' dx (1) Substitution into the momentum equation leads to the fol- lowing Poisson equation: (2) where 3Hs/dS is defined as the source term P(S). Introducing a Laplace equation of a different variable TV as Nxx + NVY = 0 (3) and inverting the Poisson system of Eqs. (2) and (3) yields the following elliptic partial differential equations that are solved in the rectangular computational domain: AXSS - 2BXsn + CXnn = -J2(PXS) (4) AYSS - 2BYsn + CYnn = -J2(PYS) (5) A = XI + Yl (6) B = YsYn C = X* + Y2S J = XsYn - XnYs (7) (8) (9) These equations determine the X and Y locations of the constant S (streamlines) and constant N lines in the physical domain. The transformation yields the flow streamlines, thus, the generation of the elliptic grid yields the velocity field using Eq. (1). Figure 1 shows the computational grid in the physical domain with the inflow and outflow planes set one inlet length upstream and downstream of the inlet and exit planes, re- spectively. This boundary placement will allow the flow angle distribution to smoothly approach zero at the inflow and out- flow planes. Equations (4) and (5) were solved using second-order cen- tral and one-sided finite differences in a successive line-re- laxation method. The value of the S on the upper and lower boundaries and the flow angle at the inflow and outflow planes served as the boundary conditions on the rectangular com- putational domain. The value of the total head gradient or P(S) was set to zero for this study, except for the special case described in the Code Verification section. Particle Trajectory Assuming a low concentration of spherical droplets of con- stant mass, Newton's second law of motion in nondimensional form yields2 14 CDR 24 Fr2. where the droplet Reynolds number is R = (11) The velocity u/U in Eqs. (10) and (11) are determined by interpolation of velocities obtained from the finite difference solution of the flowfield. The particle drag is calculated by the method of Langmuir and Blodgett,15 which yields the following form in the trajectory equation above: 24 = 1.0 + 0.197/? (1 2.6 x 10"4/?1 (12) Given the droplet initial conditions in addition to the free- stream and droplet size data, the trajectory equation is nu- merically solved by a predictor-corrector scheme due to Gear.16 In two dimensions, the droplet stream tube areas A,- and AIS at the inlet and test section, respectively, are obtained from adjacent droplet trajectories. Then, through the prin- ciple of mass conservation LWC,, = LWC, - - (13) relates the liquid water content (LWC) in the wind-tunnel inlet LWC,, and test section LWCIS, where droplet evapo- ration is ignored. The droplet velocity at the inlet plane and the test section plane are assumed equal to the corresponding x components of the tunnel velocity. Assuming uniform flow at the inlet and test section planes, the velocity ratio is 17,7 (7TS, and is equal to the wind-tunnel contraction ratio CR. Code Verification The verification of the code was carried out in two steps. First, the flowfield calculations were verified, and in the sec- ond step, trajectory computations were verified. An initial check was performed using a 161 by 31 grid to ensure that mass was conserved within the tunnel. In an incompressible flow, the increased velocity in the test section is proportional to the contraction ratio of the tunnel inlet. The average u component of velocity, nondimensional with respect to the test section velocity, should be l/CR at the wind-tunnel inlet. The average velocities at the inflow plane were within 0.047% , proving that mass within the wind tunnel was indeed being conserved. A second test of the flowfield was also performed. For an arbitrary two-dimensional contraction with constant vorticity everywhere in the flowfield, the analytical solution for the u- velocity profile may be obtained at the inflow plane by12 M, = -< + (o)Hf/2) + (l/CR) and at the outflow plane by u2 = -, fjim 6.31 10.58 14.46 20.36 27.89 35.42 45.19 Mass % 5 10 20 30 20 10 5 droplet diameter = 10.58 microns Fig. 4 Droplet trajectories for the 10.58-/nm droplet. 0.5 0.4 0.3 0.2 0.1 0.0 droplet diameter = 45.19 microns Fig. 5 Droplet trajectories for the 45.19-/*m droplet. velocity was set equal to the tunnel velocity at the injection point. Droplet trajectories were terminated when the test section location xlH, = 2.5 was reached. Figure 4 shows the computed trajectories for the 10.58-/mi droplets. These droplets follow the flowfield streamlines more closely than the larger droplets whose trajectories are shown in Fig. 5. Due to the larger droplet size and mass, the droplets do not negotiate the turn in the tunnel contraction just prior to the test section. The droplets' inertia carry them near the tunnel centerline downstream of the contraction. The larger droplets have more inertia, and as a result, their ability to follow the flowfield in regions of high-velocity gradients were reduced in comparison with smaller droplets. Since the droplets have size and mass, it is anticipated that their motion will be affected by gravity. Droplet fallout, de- fined as the 2 distance traveled by the droplet, is shown in Fig. 6. The 10.58- and 45.19-jiun droplets were released at the same x and z, but at different y locations. The droplets released at y/H,- = 0.40 take more time to reach the test section than the droplets released at y/Hi = 0.05. Conse- quently, the fallout for the droplet trajectories originating at y/H,- = 0.40 was larger. The maximum fallout is computed to be 0.165 in. for the 45.19-jnm droplet over the 8 ft distance 202 BRAGG AND KHODADOUST: DROPLET SPRAY CHARACTERISTICS 0.0000 -0.0005 -0.0010 -0.0015 -0.0020 -0.0025 -0.0030 8=10.58 Jim y0=0.05 ——— - y0=0.40 8=45.19 M-m 2 x/Hj Fig. 6 Comparison of the computed fallout for the 10.58- and 45.19- fjLm droplets. -•— 8=6.3 ln-m o 8=10.58fim - •- S=14.45|im - - - & - - 8=20.36|im -^- 6=27.89nm - — * - • • • 5=35.42^im V* 0.0 0.1 0.2 0.3 y/HTS 0.4 0.5 Fig. 7 LWCs across the tunnel test section for monodisperse sprays with the inlet LWC = 1. from the nozzle location in the inlet to the test section. The maximum fallout for the smaller droplet is computed to be 0.0133 in. Neither of these fallout distances is considered significant, particularly since fallout for this two-dimensional tunnel is in the direction perpendicular to the plane of the contraction. In order to investigate the mass distribution across the test section, the LWC in the test section must be estimated. The trajectories for seven droplet sizes based on the Langmuir-D distribution were computed. The LWC in the test section for the seven droplet sizes are shown in Fig. 7. The distributions shown are not weighted by the Langmuir-D distribution. They show the LWC for each droplet size as if a separate mono- disperse cloud was tested at each droplet size. The results reflect the trend seen in the individual particle trajectories shown in Figs. 4 and 5. The smaller droplets are able to follow the flowfield closely and, therefore, their LWC across the test section is nearly uniform. The smallest droplet at a diameter of 6.31 fjim has a LWC near 1 at the centerline increasing slightly as the tunnel wall is approached. The LWC goes to zero beyond approximately y/Hls = 0.43, where even this small droplet cannot follow the flow due to the high gradients in the vicinity of the rapid contraction coming into the test section. As the droplet size is increased (Fig. 7), the LWC at the centerline increases and the reduction in LWC to zero occurs closer to the tunnel centerline. This is of course due to the increasing inertia of the droplets. For the largest droplet tested at 45.19 jam, the LWC predicted was 2.27 at the cen- terline with a rapid increase to 4.73 before dropping to zero aty/Hls = 0.172. Test Section Cloud Resulting from a Uniform Inlet Cloud Now consider a uniform initial cloud at the nozzle plane that has a Langmuir-D distribution and LWC = 1. Table 1 gives the droplet sizes for a Langmuir-D distribution for a MVD = 20.36 /xm and the corresponding percentage of the total mass represented by each droplet. If the tunnel walls had no effect on the droplet trajectories, a Langmuir-D dis- tribution with LWC = 1 would be expected across the entire test section. However, due to the tunnel wall effects in the inlet, the LWC and droplet size distribution will vary across the test section. The effect of the tunnel walls on the total LWC across the test section is plotted in Fig. 8. The curve is not as smooth as might be expected since only seven droplets were chosen to represent the distribution, as is typically done in icing calculations. The LWC is greater than one in the center of the tunnel due to the increased concentration of large droplets, and is fairly constant at a LWC ~ 1.35 until y/H-Ys ~ 0.20. From this location out towards the tunnel wall the LWC drops rapidly due to the absence of the larger drop- lets. An LWC = 1.0 is reached at approximately y/HTS = 0.30, and no mass is predicted in the tunnel beyond y/Hls = 0.430. In an experimental study measuring ice accretion or droplet impingement, the test section LWC is measured using a ref- erence collector or other device. During the facility calibra- tion, the placement of the nozzles in the inlet is adjusted to provide uniform LWC or ice accretion over as large a portion of the test section as possible. Thus, a usable cloud of uniform LWC in the center of the tunnel is available for testing, with the effect of the tunnel walls on LWC essentially removed. However, the effect of the tunnel walls on the droplet size distribution is not so easily measured or corrected. Figure 9 shows the mass, made nondimensional with respect to the total mass, for each of the seven droplet sizes at nine locations across the tunnel test section. Also shown is the initial Langmuir-D droplet distribution at the inlet from Table 1. The droplet size distributions at the tunnel centerline and U 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 • — • — UIUC 5x1 test section > ——— -*— ———— ^ -*_^ No wall effect \\ \ \ \ 0 0.1 0.2 0.3 0.4 0. y/HTS Fig. 8 LWC across the test section with the inlet LWC = 1 and a Langmuir-D distribution. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -•— Langmuir-D --o- y/HTS=0 --v-- y/HTS=.06 -•- y/HTS=.12 -B— y/HTS=.18 -*- y/HTS=.24 -*•••• y/HTS=.30 --A- y/HTS=.36 0 10 50 6020 30 40 droplet size (microns) Fig. 9 Droplet size distributions at several locations across the test section with the inlet LWC = 1 and a Langmuir-D distribution. BRAGG AND KHODADOUST: DROPLET SPRAY CHARACTERISTICS 203 a Q y/HTS Fig. 10 Effective MVD across the test section with the inlet LWC = 1 and a Langmuir-D distribution. the next three stations are very similar. Although shifted to the right due to the presence of more large droplets than that found in the Langmuir-D distribution, only a small variation with tunnel location is seen in this center area of the tunnel. This region corresponds roughly to the region of constant LWC in Fig. 8. As would be expected from the results