Quality Assurance Plan

For the Project

Measurements and Modeling of Size Distributions, Settling and Dispersions (turbulent diffusion) Rates of Oil Droplets in Turbulent Flows.

Principal Investigator: Professor Joseph Katz

Department of Mechanical Engineering The Johns Hopkins University 3400 N. Charles St. Baltimore MD 21218

Additional Investigators: Balaji Gopalan (PhD candidate)

Department of Mechanical Engineering The Johns Hopkins University 3400 N. Charles St. Baltimore MD 21218

December 19, 2006

Funded By

The Coastal Response Research Center (January, 2006 – December, 2007)

1. Project Description 1.1 Introduction and Objectives: Application of dispersants to patches of oil spills in the ocean breaks the large slicks to droplets that are transported and dispersed by currents and turbulence. Dispersion increases the surface area of the droplet, and consequetly increases their rate of evaporation and chemical decomposition. Since it is not practical (and not desirable) to compute the detailed flow around each individual droplet transported by oceanic flows, prediction and/or computational modeling of droplet transport, dispersion and settling (due to gravity/buoyancy) require quantitative data on their size distributions and hydrodynamic interactions with the local flow. Hydrodynamic interactions between droplets and the surrounding turbulent flow are affected by: (a) Droplet properties, such as size, viscosity, specific gravity, and surface tension; (b) Characteristics of the surrounding flow, turbulence intensity and length scales; (c) Water properties, including salinity that affects the effectiveness of dispersants. Very limited research has been performed in measuring and modeling size, rise/settling rate and turbulent diffusion of liquid droplets whose densities are close to that of water, e.g. oil droplets, unlike the extensive work done with heavy (e.g. sediment) particles and bubbles. Consequently, we lack the fundamental information needed for developing reliable models for breakup of spills and subsequent dynamics of dispersing droplet in oceanic turbulence. The objective of this project is to obtain the required database on transport of oil droplets in carefully characterized turbulent flows, and then use it to develop reliable predictive models. Specifically, we propose to (a) Measure and models the dispersion (turbulent diffusion) and mean rise/settling rates of oil droplets in a turbulent flow. For the data to be meaningful, the turbulence levels and scales must be fully characterized, while spanning and representing relevant conditions that exist in oceanic flows. These measurements must involve relevant crude oil properties and droplet sizes, and include effects of typically used dispersant. (b) Introduce relatively large droplets and/or small patches to varying but known turbulence, observe their breakup and measure the resulting size distributions of droplets. These tests will also quantify the effect of dispersants on the breakup process and resulting size of droplets. Since the range of turbulence levels covers conditions occurring in swirling and baffle flask tests, which are used by EPA as standards for effectiveness of dispersants, data will enable us to relate between results of these tests to droplets sizes in treated oceanic oil spills. Measuring transport of small droplets in turbulent flows requires means to track their 3D trajectories for extended periods. The turbulent diffusivity can then be calculated directly from the Lagrangian autocorrelation function of droplet velocity. To perform this task, we have adapted high-speed digital holographic cinematography, and developed the required acquisition and analysis tools. The unique facility for generating controlled turbulence, and the optics, procedures and software needed for completing the study in two years are already available. To provide meaningful insight and support computational modeling, trends of the measured dispersion rate, settling/rise velocity and size distributions must be expressed in terms of relationships among dimensionless parameters, e.g. Weber number, Reynolds number, viscosity and density ratios as well as Stokes number. Specific formats should be coordinated with people performing spill simulations to accommodate specific modeling needs. 1.2 Droplet Dynamics:

When droplets are exposed to turbulence:

a. They breakup, a process dominated by a balance between surface tension and turbulence induced shear (characterized by a turbulent Weber No. – see below), but viscosity and density

ratios also affect the characteristic droplet size (Campbell 1985, Rayleigh 1879, Taylor 1934, Hinze 1955, Collins and Knudsen 1970, Delvigne and Sweeney 1988, Lunel 1993, Bouwmeester and Wallace 1986 Crowe et al. 1998, Adamson and Gast 1997). Previously measured droplet sizes range from 10 to 2000 µm, but the typical size is close to 50µm. Delvigne and Sweeney (1988) conclude that droplet sizes is proportional to ν0.34 (ν is oil viscosity) and to ε-0.5 at high turbulence level (ε is the dissipation rate). The shape of their droplet size distribution is independent of salinity, and has the form N(d)~ d-2.30. Below an oil slick and for a premixed variety of oil and dispersant combinations, the are in the 3-70 µm range, with median of 20 µm (Lunel 1993), Consequently, droplets smaller than 70 µm are considered as dispersed, while larger droplets are defined as suspended, i.e. they are not expected to remain suspended due to gravity (buoyancy). In our previous experiments, we measured the size distributions of diesel fuel and SAE10W oil droplets generated as a water jet impinges on a fuel-water interface (Friedman and Katz, 2001), and at the interface of a water-fuel stratified shear layers (Wu, 2002). In both cases, the size distributions of droplets are log normal with a mode of about 0.6-0.8 mm, mean value in the 1-2.5 mm range and standard deviation of 0.6-0.8 mm. Increasing viscosity ratio has a weak effect on the mode of the distribution, but broadens it.

Until recently, for a dispersant to be listed on the National Contingency plan (NCP) as a viable dispersant, it had to pass an effectiveness test using the so-called “swirling flask” (SF) test (Fingas 1987). During this test, the dispersant is premixed with the oil in a flask, and the mixture is placed on an orbital shaker. To pass the test, at least 45 % of the oil (Prudhoe Bay or South Louisiana crude oils) has to remain suspended as small droplets ten minutes after the shaker is turned off. This method has come under the scrutiny of the EPA recently due to irreproducibility in the hands of different analyst (Venosa et al., 2002), and because the conditions within the flask do not represent oceanic dispersion. As a replacement, the “baffle flask” (BF) test was introduced (Venosa et al., 2002; Sorial et al., 2004; Kaku et al. 2006). Recent measurements (Kaku et al. 2006) provide statistics on turbulence within both flasks. The BF turbulence is substantially higher than that in SF, and both fall within the range available in our isotropic, homogeneous turbulence facility.

b. Their mean gravity/buoyancy-induced settling/rise velocities changes substantially. Dynamics of particles in a turbulent flow is affected by buoyancy, pressure gradients, inertia (including virtual mass), Basset history force, drag and lift (e.g. Maxey & Riley 1983, Michaelides & Feng 1996, Magnaudet & Eames 2000, Michaelides 2003). For a droplet with diameter, d, dimensional analysis of parameters contributing to rise or settling velocities - Uslip (Friedman & Katz 2002) leads to:

Uslip/Uq=f(Red,u’/Uq,St,ρd/ρc,WeT).

Here, Uq is the quiescent rise velocity, u’ is the rms value of velocity fluctuations, ρd and ρc are the droplet and water (continuous phase) densities, respectively, Red= ρcu’d/µc is a Reynolds number defined based on the turbulence level, droplet diameter and water properties, WeT= ρdu’2d/σ is the turbulent Weber number, where σ is the interfacial tension between water and fuel, and St is the Stokes number, i.e. it is the ratio of droplet response time to the turbulence time scale, St=! d /! c . Typically, ! d = "pd 2 18#"c (Crowe et al. 1998) and ! c = (" / #)1/2 is the Kolmogorov time scale, ε being the dissipation rate.

It is well established that turbulence enhances the settling velocity of small dense particles but suppresses the rise velocity of bubbles. In the case of slightly positively or negatively buoyant particles, such as oil droplets, trends vary (Ruiz et al 2004, Friedman & Katz 2002). Several phenomena are involved including: i. Trajectory biasing (Maxey 1987; Wang & Maxey 1993), ii. Nonlinear drag and effect of turbulence on drag coefficient: (Hwang 1985Tunstall & Houghton

1968; Fung 1993; Mei 1994; Stout et al. 1995; Maxey & Corrsin 1986, Clift et al. 1978; Temkin & Mehta 1982; Brucato et al. 1998; Chang & Yang 1996, Cheng 1997 Hoyal et al. 1995), iii. Lift forces (Michaelides 2003; Magnaudet & Eames 2000; Sridhar & Katz 1995 1999; Bagchi & Balachandar 2003 Spelt & Biesheuvel, 1997, 1998)). Measurements of the mean rise rate of small diesel fuel droplets (specific gravity 0.85) in varying, carefully-characterized turbulent domain (Friedman and Katz, 2002) have shown that Uslip depends on the turbulence level scaled with the quiescent rise velocity (u’/Uq), and on the Stokes number. Uslip is greater than quiescent rise rate (Uslip/Uq>1) at high turbulence levels, approaching Uslip=0.25u’ when u’/Uq>5, regardless of St. At high turbulence levels, this trend imply a rise rate of five times the quiescent rate. Thus, under high turbulence levels the behavior of the fuel droplets is more consistent with the heavy particles than with the bubbles. At very low turbulence levels, Uslip=Uq, while at intermediate u’/Uq, the data bifurcate and are strongly dependent on Stokes number. These trends may seem to be puzzling, but they can be explained by combining effects of inertia, non-linear drag, trajectory biasing and lift. Yet, short of performing experiments, it is extremely difficult to predict rise rate of droplets with different specific gravity and different surface tension, which in turn, affects the shape and drag force on droplets. Consequently, as part of the presently proposed effort, we will measure the rise rate of droplets over range of properties that are relevant to oil spills, including effects of dispersants.

c. They disperse due to turbulence-induced diffusion.

There are many unsettled issues in prediction and modeling of turbulent diffusion, which include even disagreements on the use of Fickian diffusion models, although this approach has been popular (Snyder & Lumley 1971, Lilly 1973, Batchelor 1952; Kraichnan 1970, Shlien & Corrsin 1974, Kaneda & Gotoh 1991). Numerical studies of turbulent particle diffusion with varying degrees of complexity (e.g. Reeks 1977, Nir & Pismen 1979, Squires & Eaton 1991, Elghobashi & Truesdell 1992, Mei & Adrian 1995) show various effects, e.g. increased eddy diffusivity caused by inertia, and reduced horizontal diffusion due to trajectory biasing and nonlinear drag. We have confirmed the latter trends recently using high-speed digital holographic cinematography to measure 3D droplet trajectories (Gopalan et al 2005, 2006).

Morales et al. (1997) report on Field dispersion experiments performed in the North Sea, which follow the spreading rate of neutrally buoyant dye. Inherently to field-tests, it is virtually impossible to obtain data on all the relevant parameters (wind, waves, tidal currents, turbulence). Nonetheless, they introduce a linear model for relation between diffusivities tidal current and wind speed. Their horizontal diffusivities are in the 100-300 cm2/s range in horizontal direction, and 10-100 cm2/s in the vertical direction. These very large values most likely include (are contaminated by) contributions of advection by mean flow. In comparison, our measured diffusivity of fuel droplets at intermediate turbulence levels falls in the 3-6 cm2/s range, a result consistent with typical order of magnitude of eddy viscosities. Subsequent studies (e.g. Varlamov et al., 1999) use the Morales et al. (1997) data as input for modeling of oil dispersion, and Stokes flow model (i.e. quiescent) for the mean rise rate of droplets. We believe that both assumptions are substantially off the correct values. It is also worth noting that Proctor et al. (1992) simulate tides in the Arabian Gulf, and couple them with particle tracking that include a diffusion coefficient as a parameter.

2. Techniques and Procedures 2.1 Theoretical Background to Measurement of dispersion Extension of Taylor’s (1921) pioneering work on turbulent dispersion shows that the mean square displacement or dispersion, Y2(T), in time T of a particle/droplet in turbulent flow could be calculated from

Yi2 (T ) = 2(Ui

2 )av Rii (! )d!dt""

where Ui (t) is the droplet velocity (i indicates direction),

Rii (t) = Ui (t)! Ui (t + " )dt / Ui2 (t)! dt

is the Lagrangian autocorrelation function, and the subscript “av” indicates a time average. Assuming Fickian diffusion, i.e. that dispersion is proportional to concentration gradients, the diffusion coefficient becomes

Dii (t) = (Ui2 )av Rii (t)dt!

Thus, direct measurement of droplet dispersion requires data on the time history of its velocity along its 3-D trajectory, which can then be integrated and averaged over many droplets to obtain the dispersion rate and diffusion coefficient. By varying the droplet properties, the results can be expressed non-dimensionally as

Yi2 /!2 = g(Red ,u '/Uq ,St,"d / "c ,WeT )

where η is the Kolmogorov scale of turbulence. Due to effect of gravity, vertical and horizontal dispersion rates differ. Data on dispersion of solid particles in air can be found in Snyder and Lumley (1971), but there is not parallel data for liquid droplets suspended in another liquid. Lack of means to track 3D motions of droplets in well-characterized turbulence has been the primary obstacle to obtaining the required data. We have developed the required technology over the past several years, and propose to implement it, facilities, and data analysis procedures to generate and extensive database on the dispersion rate of fuel droplets in turbulent flows as a function of droplet properties (size, density, surface tension), turbulence level and scales. The results will be expressed in terms of dimensionless parameters, such as those shown above, that can be incorporated into computational models that simulate various types of oceanic flows.

2.2 Proposed Measurements: Using the fuels, dispersants salinities and temperatures listed below, we will measure and develop functional relationships for:

a. Settling/rise rates b. Diffusion (dispersion rate), and c. Size distribution of oil droplets in turbulent flows.

To be relevant to predictions of oil spills, we will perform measurements using the oils listed in Table 1. Relevant information has been obtained from http://www.etc-cte.ec.gc.ca/databases/OilProperties/OCPOSM-Data%20Report-Draft.pdf http://www.mms.gov/tarprojects/506/506AA.pdf http://www.mms.gov/tarprojects/506/506AB.pdf

• For one of the selected oils, e.g. Arabian Heavy, tests will be repeated after evaporative mass loss increases the oil viscosity substantially (up to 2416.7 (mPa-s) after 23.3% mass loss).

• Since salinity increases the effectiveness of the dispersant (Fingas et al., 2003), presumably due to sensitivity of the hydrophilic portion of the surfactant to presence of salt, the proposed measurements will be performed at salinities of 0%, 2% and 4% ( 0, 20 and 40 ppt).

• Tests will be repeated with and without the common dispersant, Corexit 9500 and 9527 (Clark, 2005 http://newton.nap.edu/openbook/030909562X/html/54.html, www.pwsrcac.org/docs/d0002700.pdf)

• Observations and measurements will be performed using oil mixed with particles, which presumably increases their effective density above that of water, causing settling of droplets.

• The turbulent diffusion and rise rate of droplets will be performed for droplets diameters ranging between 20 – 2000 µm.

• The large variability in viscosity of the selected fuels, and changes to surface tension when dispersants are introduced, will enable us to quantify and model droplet size distribution as functions of Weber number and viscosity ratio. Of particular interest is the critical Weber number for which droplets stabilize and stop breaking due to turbulence-induced shear. Consequently, we also propose to introduce large droplets of the order of 1 cm, or small patches with varying properties (density, viscosity, surface tension) into our turbulent flow facility, observe their breakup process, and measure the characteristic stable size distributions resulting from exposure to the turbulence. These measurements will provide the critical Weber number as a function of viscosity ratio and turbulence level for which surface tension is sufficient to prevent further breakup.

2.3. Facilities and Techniques Facility: The measurements will be performed in a specially constructed laboratory facility that generates carefully controlled turbulence with known scales and intensity. As illustrated Figure 1, nearly isotropic turbulence with very weak mean flow is generated by four symmetrically located, independently controlled, spinning grids, which are positioned in the corners of a 120x45x22 cm, transparent tank. The sample volume is located at the center of this tank, and has equal distance from each grid. By counter-rotating neighboring grids, and due to the geometric symmetry, we obtain very high turbulence level but very low mean velocity at the center of this tank. Each is attached to a motor, which is independently powered by variable frequency inverters. Varying the rotation speed and grid sizes enable control of turbulence intensity and length scales. Unlike the experiments of Delvigne and Sweeney (1988), where there is direct interaction of the grids with the oil being tested, and there is spatial non-uniformity in turbulence levels, in the system depicted in Figure 1, the grids are located far from the sample volume, preventing direct contact with the relevant oil droplets being studied. The turbulence in this sample volume is also nearly isotropic, spatially uniform and fully characterized (Friedman & Katz, 2002).

Oil Type Density (g/mL) Dynamic Viscosity (mPa-s)

Interfacial Tension (Sea water) (mN/m)

Prudhoe Bay 0.895 38.9 28.1 South Louisiana 0.839 7.1 22.0 Arabian Heavy 0.8923 49.7 26.5 IFO 180 0.96 2471 21.1 IFO 380 0.979 9399 22.1 Diesel Fuel (measurements are in progress)

0.85 5.5 13 (fresh water)

Table 1: Oils to be tested during the presently proposed study. Properties are at 150C

Characterization of the Turbulence: The turbulence is characterized prior to introduction of droplets, based on extensive Particle Image Velocimetry (PIV) measurements (Friedman and Katz, 2002, Liu et al., 1999, Chen et al., 2005, 2006, Gopalan et al., 2005, 2006). They provide the distributions of mean velocity, turbulence intensity (rms values of velocity fluctuations), Reynolds stresses, and associated length scales. The dissipation rate can either be estimated directly from local velocity gradients, or by plotting the kinetic energy spectra and fitting -5/3 slope line to the inertial part of the spectra. For isotropic turbulence, Eii (k) = 18 55Ck! 2 3ki"5 3 where ! is the dissipation rate, ki is the wave number and

�

Ck = 1.6 . Curve fitting to spatial energy spectra computed from the PIV data can be

used for estimating ! . Based on ! , one obtains the Kolmogorov scale ! = " 3 #( )1 4 (! is the

kinematic viscosity), Taylor micro scales ( ! = u ' 15" #( )1/2 ), and integral scale ( L ! "u 3 / # )

(Monin & Yaglom, 1971; Tennekes & Lumley, 1972, Pope, 2000, Liu et al., 1994, Friedman and Katz, 2002). Characteristic values, provided in Table 2, show that we can obtain a wide range of turbulence scales, and can cover typical conditions that one expects to find in the ocean. In coastal waters, η in the free stream can reach 1 mm (Gargett al., 1984), whereas near interfaces, such as near the bottom, our own measurements indicate η in the 0.5-1 mm range (Nimmo-Smith et al., 2005; Luznik et al., 2006). At the free surface, where waves break, the Kolmogorov scale decreases to ~0.1 mm or lower (Gargett, 1989; Thorpe, 2005). We can further increase the turbulence level by operating the system at higher rpm, by increasing the size of spinning grids, or by reducing the distance between grids and sample volume. The data in Table 2 represent conditions tested to-date. The mean velocity is only 10-20% of the rms values of velocity fluctuations, and its value is accounted for while calculating settling and diffusion rates.

Table 2: characteristic length scales of the turbulence in the rotating grid facility.

Mixer rpm 24 60 150 225 337.5 506.25 RMS Velocity (cm/s) 3.0 4.55

(4.04, 4.7, 4.91)*

6.6 9.4

Average Absolute Mean Velocity (cm/s)

0.6 0.65 1.5 2.0

Dissipation ε (m2/s3) 8.2E-7 2.9E-5 0.00055 0.0017 0.0086 0.02 Taylor Microscale, λ (mm)

4.5 4.3 2.5 1.9

Kolmogorov Length Scale, η (mm)

1.05 0.43 0.18 0.156 0.088 0.065

Integral Length Scale, L (mm)

49 55 33 28

Taylor Scale Reynolds Number Reλ

167 194 203 223

120 cm

22 cm

45 cm y

z x

Sample volume

Figure 1: Isotropic turbulence generation facility.

Obviously, the integral scale of oceanic turbulence is much higher than conditions that one can obtain in the laboratory. However, the critical scales are those that shear droplets or generate hydrodynamic forces that cause transport relative to the local flow (“slip”). These effects are dominated by scales that are at most 1-2 orders of magnitude larger than the droplet. Thus, integral scales in the 3-5 cm range are sufficient for studying behavior of droplets whose sizes are in the 0.03-2 mm range. However, we will repeat selected measurements, e.g. those at 337 rpm, using rotating grids with twice the present diameter. This change should a least double the integral scale.

Introducing Oil Droplets: The droplets are injected/introduced into the center of this tank through injectors, and then followed as they diffuse due to the turbulence. Use of fine metering valves and varying the injector diameters enable us to control the size of droplets, but they are individually measured. Droplets in the 0.2-2 mm range are introduced, as we have done to-date, by controlled injection through a syringe with varying size, and controlling the flow rate by a fine metering valve. To generate small droplets (<100 µm diameter), we may use small capillary glass injectors, controlled by fine metering valves (Ran and Katz, 1991; Gopalan et al., 1999). In cases with oil premixed with surfactants, injection (forcing by pressure difference) of oil through a fine porous surface (or tube) may also be effective, and simpler to implement. In all cases, size of each droplet must be measured.

In the case of very large droplets (or patches), introduced to observe breakup, the holographic measurements will provide detailed images on the breakup process, and on the ultimate stable size distribution of droplets. Results will be expressed (e.g.) as a critical Weber number as a function of oil to water viscosity and density ratios as well as Reynolds number (maybe even Stoked number and normalized turbulence level). The small patches or large droplets of oil will be introduced into the region with well-characterized turbulence, either by injection or by installing a small reservoir containing oil with its open-surface facing the sample volume. We will then observe and perform measurements associated with the process of droplet entrainment, as we have done before for various types of shear flows (Friedman et al., 2002). The new data will be combined with results of previous shear flow measurements (some unpublished yet) to obtain an extended picture on the effect of turbulence, surface tension and viscosity ratio on droplet size distributions.

The density ratio of droplets will vary from 0.85 to 0.98, but we will also attempt to study droplets mixed with particles that have specific gravity grater than that of water. The oil viscosity will vary from 7.1 to almost 10,000 mPa-s. The surface tension will be varied by adding dispersants, Corexit 9500 and 9527. Standard tools for measuring surface tension and viscosity are available.

Measurements of Droplet Size and Trajectories: To measure the time history of droplet velocity in three dimensions, we use high speed, digital holographic particle image velocimetry (digital HPIV), a technology that we have developed over the past several years. Small droplets moving in 3D trajectories cannot be followed for extended periods using conventional photography since the images get out of focus. Conversely, holography, including digital holography, maintains the same lateral resolution over substantial depth, enabling measurements of shape, 3D location and velocity over an entire sample volume. Furthermore, digital holographic particle image velocimetry is the only technique to-date that can measure 3-D trajectory and shape of thousands of particles over a sample volume with an extended depth without loss of resolution (Malkiel et al., 2003; Pu and Meng, 2000; Sheng et al., 2006). The optical setup is illustrated in Figure 2. In most of experiments performed to-date, we have recorded two perpendicular in-line digital holograms in order to maintain the same spatial resolution in all the directions (The resolution is lower in the direction aligned with the optical axis of laser beam, Tao et al., 2002). However, one digital hologram is sufficient for most experiments, since it still enables 3D tracking of droplets,

but provides accurate time history of two velocity components, e.g. vertical and one of the horizontal components), which provides data needed for calculating the horizontal and vertical diffusion. In early experiments, it has been important to verify that both horizontal diffusion components are the same, as the data confirms (see below). The Light source is a Q switched Nd:Ylf diode pumped laser. The laser beam is passed through a spatial filter, a collimating lens and a beam splitter before illuminating the sample volume from two perpendicular directions. The lenses marked as L1 and L2 de-magnify the beam to cover the desired volume. Based on our experience to-date, our sample volume in proposed experiments will nominally be 5x5x5 cm, but it will be increased during some tests. The images are acquired by two Photron 1k x 1k cameras that have pixel resolution of 17-µm. The acquisition rate for the 225 rpm set is 250 frames/sec. At 500 rpm, the rate is increased to 2000 frames/sec.

The digital holograms are reconstructed numerically using the Fresnel approximation by convolving the intensity distribution with a source function (Malkiel et al., 2003). During subsequent data analysis, we first track the 2-D projection of tracks separately and then match them to obtain 3-D coordinates of the droplets. Multiple thresholding and a circularity filter are used for measuring the droplet location. In each view we determine the location in the laser beam axial direction to within ~5 mm based on maximum edge intensity. Matching of tracks in successive frames is based on several criteria, including: (i) Closest point in the next time step, (ii) Radius within prescribed tolerance range, (iii) Depth within a certain tolerance range, (iv) Maximum allowed acceleration, (v) Avoiding very sharp unnatural jitter, and (vi) Linear regression for crossing of tracks. Substantial effort has been invested in development of an automated code to track the droplets based on these criteria, which presently enables us to track thousands of droplets and obtain converged statistics. The 2-D tracks are matched by finding the one with the least square difference between the common axes (vertical). Cross correlation analysis is then used for determining the velocity in order to get sub pixel accuracy. The velocity time series is low pass filtered to remove high frequency jitter.

In all cases, size of each droplet must be measured. In optical setups covering large volumes, the spatial resolution may not be sufficient for measuring the size of small droplets. For example, covering 5x5x5 cm using the 1000x1000 pixels, high speed digital camera implies that the camera resolution is 50 µm/pixel. It will be sufficient for racking a droplet (which will appear as 1-2 pixels dot), but obviously not sufficient for measuring its size. Thus, an independent (but simultaneous) size measurement is essential, e.g. by using another (available) 2048x2048 pixels digital camera focusing on the immediate vicinity of the injector, and covering a volume of 1x1x1 cm. The resolution of this camera is 5 µm/pixel, which is sufficient for the present objectives.

The mean fluid velocity in the volume, obtained from previous PIV measurements, is subtracted from each instantaneous velocity to obtain time history of droplet velocity fluctuations. The mean rise/settling velocity is obtained by averaging trajectories of thousands of droplets within a certain

Figure 2: Optical setup for in-line, high-speed, digital Holographic PIV measurements.

size bin. To measure dispersion, the mean correlation function (Rii) is determined by averaging individual correlations of the velocity of thousands of droplets. The mean values of Rii are then integrated to obtain the mean dispersion rate, Y2(T), and diffusion coefficient, Dii. For further details and sample results, see Gopalan et al. (2006). Additional, recently obtained data that extends to a larger volume is presently being processed.

3. Project Organization and Responsibilities

The project team consists of: (a) Principal Investigator (J. Katz) that will act as a supervisor, will be involved in data analysis and decision-making process as test conditions are selected, (b) Two full-time graduate (PhD) students that will perform the experiments and subsequent data analysis. One of them (Balaji Gopalan) is already in advanced stages of his graduate studies, and has developed many of the tools described in this proposal. The second (younger) student will work with him, assuming increasing role in time, since processing and analyzing the proposed large database requires two people (at least), and (c) A 5% of support for a mechanical and/or electronic engineer that assist the students in maintaining, operating and modifying the facility and associated instruments.

4. Quality Assurance 4.1 Accuracy Velocity and Turbulence Characterization – PIV data. The acquisition and data analysis hardware and software have been developed and calibrated extensively for a variety of flows (e.g. Sridhar and Katz, 1995, Roth et al. 1999, 2001, Chen et al. 2005). These procedures and tools have been implemented extensively both in the laboratory and in oceanic field studies (e.g. Nimmo Smith et al. 2006, Luznik et al. 2006). In Chen et al. (2005) we also introduce an accurate analysis approach that overcomes inherent bias problems in typical/commercial data analysis procedures. These procedures have been tested and calibrated extensively. This paper received the Best Paper in Fluid Mechanics Award by Measurement Science and Technology Journal (for 2005), and we are presently in the process of negotiating agreement to commercialize this technique. The PIV measurements of turbulence characteristics were also compared to and agreed very well with hot-wire measurements of turbulence in a wind tunnel (Zhu etal. 2006) Typically, the (realistic) uncertainty of instantaneous PIV measurement is about 0.1-0.2 pixel, provided the sample volume contains at least 5-10 particles. This level accounts for optical distortion, non-uniform particle distribution, inherent limitations, non-uniform background, etc. For a typical displacement of 10-20 pixels, the uncertainty in instantaneous velocity is 1%. In calculating the mean statistics, the uncertainty in mean velocity is reduced by 1 / N , where N is the number of instantaneous values being averaged. For N=1000, the uncertainty in mean velocity is about 0.03%. To estimate the uncertainty in Reynolds stresses, we use (Benedict & Gould 1996)

( )1 2

2 2 21 96 1! "# # # #$ = +

% &

/

i j ij i ju u . R u u / N , R

ij= !u

i!uj

/ !ui

2 !uj

2"#$

%&'

1/ 2

Typical values are about 1% when the sample size exceeds 1000 realizations – a typical value. The uncertainty in dissipation rate, estimated from spectra is an order of magnitude higher, i.e. in the order of 10% (Luznik et al. 2006). Considering that typical dissipation rates in oceanic flows

vary by 5 orders of magnitude, this level of accuracy is more than adequate for characterizing the turbulence in the test facility. The flow/turbulence conditions in the test facility have already been measured independently several times (by different students – Friedman and Katz 2002, Chen et al. 2005, 2006, Gopalan et al. 2005, 2006) and results have been repeatable. Nevertheless, we will repeat the turbulence characterization tests prior to each series of new measurements (with different rpm or grid), at least to the level that they show/confirm results of previous tests. 4.2 Accuracy of Holographic Measurements of Trajectories and Velocity Detail analyses of uncertainty in 3D holographic velocity and trajectory measurements have been discussed in several recent studies (Zhang et al. 1997, Tao et al. 2002, Sheng et al. 2003, 2006a, b, Malkiel et al., 2003). When all three velocity-components are available, we estimate the uncertainty by evaluating how well data satisfy the continuity equation. As discussed in the abovementioned references, the uncertainty in holographic measurements is better than that obtained from planar PIV measurements. While analyzing the trajectory of individual particles, we compare the correlation-based automated analysis that involves also smoothing of high frequency jitter (Gopalan at al. 2005, 2006) to direct measurement of displacement of the particle centroid. Typical uncertainty in individual particle displacement is about 0.2 pixels, provided the particle image size occupies at least 10 (~3x3) pixels. For a typical displacement between exposures of 10 pixels, the uncertainty is 2%. Since the Lagrangian Correlation function used for calculating the dispersion (Section 2.1) is an average of at least several hundred individual trajectories, the uncertainty in the correlation and dispersion rate can be estimated conservatively at about 1%. As part of this project, these values will be (and must be) verified by:

a. Theoretical analysis of error propagation, including uncertainty and sensitivity of results to specific contributors.

b. Examining the convergence of dispersion and settling velocity for each condition being tested, i.e. by measuring how much does adding data affect the results. The number of samples is sufficient when adding data does not alter the result by more than the desired/target uncertainty of 1%.

4.3 Repeatability of Measured and Modeled Dispersion and rise Rates Measurements involving crude oil are susceptible to variability in properties of the fuel, e.g. surface tension, viscosity and specific gravity, even when it comes form the same source. Thus, measurements of the fuel properties are essential for each series of tests. In addition, selected tests under identical conditions (oil, turbulence and dispersant) must be repeated using different samples of the same or similar (but quantified) oil properties to insure that the measured statistics are repeatable, and if not, we must quantify the variability and causes for it (e.g. difference in viscosity). The final analysis phase will also examine and evaluate the uncertainty of empirical models that will be developed based on the measured data. Specific test conditions will be specifically selected and performed to test the validity of the model. These evaluations will be coordinated with the modeling group headed by Bill Lehr in order to insure that the models are formulated in term of parameters that are available in their simulations.

5. References

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