Educated Spray A Geometry Thomas Furlong Prof. Caroline Genzale August 2012

2 Notes for geometry use: The following presentation outlines the method utilized to smooth the STL file created from x-ray tomography measurements of nozzles and Due to the low resolution of the x-ray tomography measurements (~4 microns), there is still uncertainty in the ability to capture real features and asymmetry –Nozzle has a convergence near the outlet on the order of the measurement resolution and is not captured in the smoothed geometry –Nozzle features a more significant convergence, which is captured in the smoothed geometry This presentation is intended to be the first step towards the ultimate goal of fully understanding the geometry of Spray A and Spray B nozzles and the implications of these geometries

3 The Starting STL File The STL file is oriented such that the Z-axis is oriented along the orifice center and centered at the (0,0) X and Y coordinates

4 The STL file is cut into discrete theta regions of size π /150 to stipulate 300 splines to define the geometry –The x-ray tomography STL file contains a limited number of data points –A larger discrete theta region of size π /10 is then necessary to produce each spline fit –A vertical spline curve is created at each one of these locations with ~12 nodes per 0.1 micron Step 1- Theta Slices Y X

5 All STL points within the bounds are utilized in obtaining the spline fit Step 1- Theta Slices Lower Bound Spline Location Upper Bound Y X

6 Step 1- Theta Slices Additional splines utilize partially overlapping regions The rotation between the two upper bounds is equivalent to the rotation between the spline points ( π /150) Y X Neighboring Spline Overlapping region Non-overlapping region

7 For each theta slice, the minimum diameter in the outlet region is found and defined as the local outlet location –The local outlet locations do not occur at a consistent vertical location (Z-axis) Step 2 – Outlet Identification Outlet Vertical Location (mm) Min= Mean=0.101 Max=0.175

8 Step 2 – Outlet Identification The global outlet location is defined as the mean local outlet location (along the Z-axis) Z X Minimum Mean Maximum

9 Vertical spline creation via theta slices Nozzle, orifice, and sac splines are generated separately using the function spap2 Knots are first defined utilizing the matlab splinetool and hardcoded The knot locations are iterated using the ‘newknt’ function to minimize spline fit errors with the current theta slice Step 3 – Spline Fit knots=augknt([min(R_orf(:,2)),0.7966,1.0702,1.1137,1.1495],3); f1_orf=spap2(knots,3,R_orf(:,2),R_orf(:,1)); for k=1:10 f1_orf=spap2(newknt(f1_orf),3,R_orf(:,2),R_orf(:,1)); end

10 The outlet region Step 3 – Spline Fit Note: No convergence trend in tomography points for 675

11 The turning region Step 3 – Spline Fit

12 Turning Angle Calculation The turning angle is defined from Kastengren et al. (2012) using two lines, one within the sac and one within the orifice

13 The inlet turning angles derived from the first spline smoothed are not significantly altered –The inlet turning angle is determined utilizing the inletTurn675.m matlab code provided by Dr. Pickett Resulting STL File

14 Resulting STL File However it is insufficient for meshing without connectivity between the splines Figure shows the interior of the STL file near the sac/orifice turning junction Inconsistencies

15 Step 4 – Establish Connectivity Between Splines The second geometry fit is done utilizing vertical slices (instead of theta slices) to generate connectivity points at consistent Z locations ΔZΔZ Select a region of data of size ΔZ (0.1 micron) Create a spline fit around the data (200 nodes) –Utilizes two splines, one on the top and a second on the bottom (see next slide) Each ΔZ contains ~12 nodes as stated before (defined via first spline)

16 Step 4 – Establish Connectivity Between Splines Consistent connectivity is established without altering geometry significantly

17 Step 4 – Establish Connectivity Between Splines Turning angle retains trends seen from original data

18 A semisphere is added to the outlet to enable proper meshing Step 5 – Add an Outlet Semisphere

19 Step 5 – Resulting STL The resulting STL file is smooth, capable of being meshed well, and represents the outlet diameter and turning angle of the tomography measurements

20 Outlet Diameter Comparison Using a circle fit function (assumes circular orifice) we can compare the representative outlet diameters* *Utilizes the mean z location as the outlet Optical microscopy –89.4 μm Tomography –86.74 μm Smoothed geometry –89.11 μm

21 Axial Diameter Comparison The axial diameter of the smoothed geometry predominately captures the tomography data Utilizing the mean z location as the outlet This 2-dimensional representation assumes a circular orifice Z-axis

22 The current method does not capture an outlet convergence due to the inability of the splines to capture some fluctuations and not others 3 μm Discussion of Outlet Convergence The spline method cannot distinguish between: –Fluctuations due to noise –Real fluctuations of the same magnitude

23 Nominal Mesh Comparison Spray A Mesh on ECN website

Conclusions The STL file generated utilizing x-ray tomagraphy was smoothed while retaining the inlet turning angle trends The outlet diameter produced matches well with the optical microscopy measurements The outlet region does not capture the convergence effects seen in phase contrast since the convergence is on the order of the tomography resolution (Kastengren et al. (2012))

Smoothing A similar process was implemented for nozzle A more distinct convergence section allowed for the nozzle to be split into 3 sections to create a spline (sac, orifice, and outlet)

Outlet Diameter The outlet diameter provides a reasonable comparison to the optical microscopy Optical microscopy –83.61 μm Tomography –83 μm Phase contrast –84.13 μm Smoothed geometry –84.53 μm

Axial Diameter The axial diameter matches well with respect to the original STL file with some offsets with experiments

Turning Angle The smoothing process maintains the original turning angle well

29 Axial Diameter 675/677 Comparison

30 Turning Angle 675/677 Comparison