Educated Spray A Geometry
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Transcript of Educated Spray A Geometry
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