A Photogrammetric Technique for Developing Boundary Equations for Flexible Sheath Waterless Trap Seals as Used in Building Drainage Systems
Abstract
:1. Introduction
1.1. The Trap Seal
1.2. Modelling Waterless Traps
2. Materials and Methods
2.1. Reference Devices
2.2. Laboratory Setup
2.3. Data Acquisition
2.3.1. Photographic Imaging (Camera and Lighting)
2.4. Analysis Methods—Image Analysis Procedure
- an executable program (*.exe);
- a text input file detailing the threshold parameter and instructions for conversion of images (*.txt);
- photograph input folder (storing all original images to be converted to black and white images in jpeg format);
- photograph output folder—gathering all converted black and white images (in jpeg format);
- the results (percentage, height and width) from each image in the output folder recorded in sequential order in comma separated valves format (*.csv);
- binary image processing.
2.5. Experimental Procedure
- set up physical experiment;
- set appropriate lighting;
- start data acquisition/camera;
- set system air pressure;
- increase air pressure every 10 s;
- end experiment.
- run C ++ program;
- codify images;
- process pressure data.
2.5.1. System Pressures
2.5.2. Image Types and Codification
2.5.3. Segmentation
2.5.4. Threshold and Averaging
3. Results
3.1. Laboratory Results
3.2. Measurements of Repeatable Patterns
- Sample 1 reduces most steadily in the length of a cycle as the pressure is increased on the valve;
- Sample 2 remains constantly open at low pressures but quickly mimics the pattern found in Sample 1 at high pressure ranges (greater than 140 mm);
- Sample 3 provided a less consistent pattern. Once above the RMS pressure value of 45.23 mm wg the cycle length became more difficult to predict. However, above 100 mm wg the cycle length constantly increases
4. Model Development and Validation
4.1. Determining the Opening Area by the Linear Measurements
4.2. Model Validation
4.2.1. Physical Movement Validation
4.2.2. Fourier Spectral Analysis
4.2.3. Fourier Frequency Spectrum—Pressure and Device Opening/Closing
5. Conclusions
- an alternative to traditional water seals and can be beneficial since they cannot dry out and are not subject to siphonage problems;
- photogrammetric methods have been used to describe and model large engineering systems, but not for small flexible devices, such as the waterless trap;
- alternative analogue models have been found in the field of medicine where modelling vocal cords follow a similar pattern;
- digital coding of opening and closing provide an opportunity to describe the physical phenomenon and when linked to applied pressure data gives a holistic view of the device operation;
- the use of FFT is an appropriate means to validate the model.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Reference (Figure 1) | Description | Sample 1 | Sample 2 | Sample 3 |
---|---|---|---|---|
a | Total height | 55.25 mm | 54.4 mm | 53.45 mm |
b | Lip width | 35.1 mm | 39.44 | 36.18 mm |
c | Lip thickness | 0.16 mm | 0.20 mm | 0.35 mm |
d | Rim width | 3.04 mm | 2.74 mm | 6.39 mm |
e | Rim height | 4.00 mm | 3.80 mm | 3.90 mm |
f | External rim Ø | 33.16 mm | 38.86 mm | 38.72 mm |
g | Internal rim Ø | 27.08 mm | 33.38 mm | 25.94 mm |
Sample Number | Threshold Pressure |
---|---|
Sample 1 | 4.6 mm wg |
Sample 2 | 8.5 mm wg |
Sample 3 | 6.7 mm wg |
Radius | 62.5 Pixels | 31.89 mm |
---|---|---|
Max opening area of orifice (pixel2) | 12271.85 | 1028.1 mm2 |
Frame resolution | 30,720 pixels2 (256 × 120 pixels) | 2565.6 mm2 (73.98 × 34.68 mm) |
Opening Pressure | Sample 1 R² | Sample 2 R² | Sample 3 R² |
---|---|---|---|
Threshold | 0.9971 | 0.9859 | 0.9972 |
Low | 0.9829 | 0.9468 | 0.9871 |
Med | 0.9728 | 0.978 | 0.9643 |
High | 0.938 | 0.8878 | 0.8946 |
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Jean, N.; Gormley, M. A Photogrammetric Technique for Developing Boundary Equations for Flexible Sheath Waterless Trap Seals as Used in Building Drainage Systems. Buildings 2021, 11, 136. https://doi.org/10.3390/buildings11040136
Jean N, Gormley M. A Photogrammetric Technique for Developing Boundary Equations for Flexible Sheath Waterless Trap Seals as Used in Building Drainage Systems. Buildings. 2021; 11(4):136. https://doi.org/10.3390/buildings11040136
Chicago/Turabian StyleJean, Nicole, and Michael Gormley. 2021. "A Photogrammetric Technique for Developing Boundary Equations for Flexible Sheath Waterless Trap Seals as Used in Building Drainage Systems" Buildings 11, no. 4: 136. https://doi.org/10.3390/buildings11040136