A New Development of Cross-Correlation-Based Flow Estimation Validated and Optimized by CFD Simulation
<p>A general schematic of a hardware installation for CCF flow estimation [<a href="#B21-applsci-14-06687" class="html-bibr">21</a>].</p> "> Figure 2
<p>Sensor X and Sensor Y signals versus time [<a href="#B21-applsci-14-06687" class="html-bibr">21</a>].</p> "> Figure 3
<p>Computational domain used for CCF flow estimation, with fluid injection pipe, temperature sensor region, and flow direction shown.</p> "> Figure 4
<p>Computational domain, indicating the boundary conditions, including the injection fluid boundary conditions.</p> "> Figure 5
<p>One injection period for the injection pipe boundary condition in CFD simulations.</p> "> Figure 6
<p>One example of a meshing model for low-flow-rate simulation.</p> "> Figure 7
<p>Detailed meshing around the injection pipe.</p> "> Figure 8
<p>Temperature and velocity locations for the mesh sensitivity study.</p> "> Figure 9
<p>Area-weighted average temperature traces at (<b>a</b>) 0.1 m, (<b>b</b>) 0.3 m, and (<b>c</b>) 0.5 m from the inlet.</p> "> Figure 10
<p>Two local temperatures at the star-marked locations shown in <a href="#applsci-14-06687-f008" class="html-fig">Figure 8</a>.</p> "> Figure 11
<p>Area-weighted average velocity traces at (<b>a</b>) 0.1 m, (<b>b</b>) 0.3 m, and (<b>c</b>) 0.5 m from the inlet.</p> "> Figure 12
<p>Two local velocities at the star-marked locations shown in <a href="#applsci-14-06687-f008" class="html-fig">Figure 8</a>.</p> "> Figure 13
<p>One example of 3D velocity distribution of fully developed turbulent pipe flow.</p> "> Figure 14
<p>Absolute percentage errors between the meshing (area-weighted average velocity) at (<b>a</b>) 0.1 m, (<b>b</b>) 0.3 m, and (<b>c</b>) 0.5 m from the inlet.</p> "> Figure 15
<p>Absolute percentage errors of two local velocities.</p> "> Figure 16
<p><math display="inline"><semantics> <msup> <mi>u</mi> <mo>+</mo> </msup> </semantics></math> vs. <math display="inline"><semantics> <msup> <mi>y</mi> <mo>+</mo> </msup> </semantics></math> relationship based on G1, G2, and G3 meshing models.</p> "> Figure 17
<p>Temperature distribution when the target flow rate is at 178.3 GPM (highest flow rate).</p> "> Figure 18
<p>Temperature comparison under a low flow rate (∼40 GPM).</p> "> Figure 19
<p>Temperature comparison under a medium flow rate (∼133 GPM).</p> "> Figure 20
<p>Temperature comparison under a high flow rate (∼170 GPM).</p> "> Figure 21
<p>Velocity distribution under a low flow rate after water injection.</p> "> Figure 22
<p>Local flow-rate changes along the two sensor paths under a low flow rate.</p> "> Figure 23
<p>Velocity distribution under a high flow rate after water injection.</p> "> Figure 24
<p>Local flow-rate changes along the two sensor paths under a high flow rate.</p> "> Figure 25
<p>CCF flow estimation. The x-axis is the flow rate measured from the flow meter in the test facility.</p> "> Figure 26
<p>Candidate sensor locations.</p> "> Figure 27
<p>Top 10 temperature sensor pair locations for (<b>a</b>) low, (<b>b</b>) medium, and (<b>c</b>) high bulk flow rates with an 80 psi injection pressure.</p> "> Figure 28
<p>Top 10 temperature sensor pair locations for (<b>a</b>) low, (<b>b</b>) medium, and (<b>c</b>) high bulk flow rates with a 30 psi injection pressure.</p> "> Figure 29
<p>Two-dimensional heat map of the weighted performance of the sensor locations for (<b>a</b>) low, (<b>b</b>) medium, and (<b>c</b>) high bulk flow rates with an 80 psi injection pressure.</p> ">
Abstract
:1. Introduction
2. Cross-Correlation Function-Based Flow Estimation
3. Computational Methods
3.1. Computational Domain
3.2. Boundary and Initial Conditions
3.3. Meshing
3.4. Mesh Sensitivity Study
3.5. Computational Solver Setup and Fluid Properties
4. Results
4.1. Experimental Validation
4.2. Optimal Temperature Sensor Location Investigation
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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M1 | M2 | M3 | M4 | |
---|---|---|---|---|
Number of circular divisions | 40 | |||
Number of radial divisions (outer cylinder) | 14 | |||
Number of radial divisions (medium cylinder) | 10 | |||
Element size for the inner rectangle (m) | ||||
Number of divisions for the inner rectangle | 10 | |||
Inlet region length (m) | 0.07 | |||
Injection region length (m) | 0.06 | |||
Temperature collection region length (m) | 0.37 | |||
Number of divisions in the inlet region in the axial direction | 40 | 50 | 65 | 80 |
Number of divisions in the injection region in the axial direction | 28 | 40 | 52 | 60 |
Number of divisions in temperature collection region in the axial direction | 114 | 150 | 200 | 250 |
Low-Flow-Rate Group (G1) | Medium-Flow-Rate Group (G2) | High-Flow-Rate Group (G3) | |
---|---|---|---|
Flow rate (GPM) | 39.52∼93.53 | 101.95∼133.51 | 145.83∼178.30 |
First cell height (m) | 1.4 × | 6.0 × | 4.3 × |
Nodes | 406818 | 362198 | 374494 |
Elements | 459890 | 408016 | 421176 |
Flow Rate | TC1 | TC2 |
---|---|---|
Low (∼40 GPM, Figure 18) | 0.173 | 0.248 |
Medium (∼133 GPM, Figure 19) | 0.0853 | 0.202 |
High (∼170 GPM, Figure 20) | 0.128 | 0.268 |
Mean Flow Rate (GPM) | ||||
---|---|---|---|---|
39.52 | 123.84 | 178.30 | ||
Injection pressure (psi) | 80 | 0.07 | 0.12 | 0.22 |
30 | 0.07 | 0.20 | 0.20 |
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Gao, X.; Carasik, L.B.; Coble, J.B.; Hines, J.W. A New Development of Cross-Correlation-Based Flow Estimation Validated and Optimized by CFD Simulation. Appl. Sci. 2024, 14, 6687. https://doi.org/10.3390/app14156687
Gao X, Carasik LB, Coble JB, Hines JW. A New Development of Cross-Correlation-Based Flow Estimation Validated and Optimized by CFD Simulation. Applied Sciences. 2024; 14(15):6687. https://doi.org/10.3390/app14156687
Chicago/Turabian StyleGao, Xiong, Lane B. Carasik, Jamie B. Coble, and J. Wesley Hines. 2024. "A New Development of Cross-Correlation-Based Flow Estimation Validated and Optimized by CFD Simulation" Applied Sciences 14, no. 15: 6687. https://doi.org/10.3390/app14156687