Educated Spray A Geometry

Educated Spray A Geometry

Thomas FurlongProf. Caroline Genzale

August 2012

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Notes for geometry use:Notes for geometry use:

• The following presentation outlines the method utilized to smooth the STL file created from x-ray tomography measurements of nozzles 210675 and 210677

• 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 210675 has a convergence near the outlet on the order of the

measurement resolution and is not captured in the smoothed geometry– Nozzle 210677 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

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The Starting STL FileThe 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

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• 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 SlicesStep 1- Theta Slices

Y

X

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• All STL points within the bounds are utilized in obtaining the spline fit

Step 1- Theta SlicesStep 1- Theta Slices

Lower Bound

Spline Location

Upper Bound

Y

X

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Step 1- Theta SlicesStep 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

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• 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 IdentificationStep 2 – Outlet Identification

OutletVerticalLocation(mm)

Min=0.0857

Mean=0.101

Max=0.175

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Step 2 – Outlet IdentificationStep 2 – Outlet Identification

• The global outlet location is defined as the mean local outlet location (along the Z-axis)

Z

X

Minimum Mean Maximum

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• 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 FitStep 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

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• The outlet region

Step 3 – Spline FitStep 3 – Spline Fit

Note: No convergence trend in tomography points for 675

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• The turning region

Step 3 – Spline FitStep 3 – Spline Fit

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Turning Angle CalculationTurning Angle Calculation

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

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• 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 FileResulting STL File

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Resulting STL FileResulting 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

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Step 4 – Establish Connectivity Between SplinesStep 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

ΔZ

• 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)

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Step 4 – Establish Connectivity Between SplinesStep 4 – Establish Connectivity Between Splines

• Consistent connectivity is established without altering geometry significantly

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Step 4 – Establish Connectivity Between SplinesStep 4 – Establish Connectivity Between Splines

• Turning angle retains trends seen from original data

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• A semisphere is added to the outlet to enable proper meshing

Step 5 – Add an Outlet SemisphereStep 5 – Add an Outlet Semisphere

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Step 5 – Resulting STLStep 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

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Outlet Diameter ComparisonOutlet 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

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Axial Diameter ComparisonAxial 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

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• 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 ConvergenceDiscussion of Outlet Convergence

• The spline method cannot distinguish between:– Fluctuations due to noise

– Real fluctuations of the same magnitude

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Nominal Mesh ComparisonNominal Mesh Comparison

• Spray A Mesh on ECN website

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210675 Conclusions210675 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))

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210677 Smoothing210677 Smoothing

• A similar process was implemented for nozzle 210677

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

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210677 Outlet Diameter210677 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

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210677 Axial Diameter210677 Axial Diameter

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

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210677 Turning Angle210677 Turning Angle

• The smoothing process maintains the original turning angle well

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Axial Diameter 675/677 ComparisonAxial Diameter 675/677 Comparison

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Turning Angle 675/677 ComparisonTurning Angle 675/677 Comparison