Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor Cores
Abstract
:1. Introduction
- Strategy 1 (a-b-c): Decreasing the pebble diameter by , , and . This is a simple model-building approach of slightly decreasing the pebble diameter. Decreasing the pebble by was the most computationally expensive approach due to the very small gaps between the pebbles.
- Strategy 2 (a-b-c): Increasing the pebble diameter by , , and .
- Strategy 3 (a-b-c): Bridging—that is, chamfering contact pebbles with a given diameter (, , and in this study) and filling the volume with pebble material. This approach was considered the most similar to the true bed configuration when comparing its porosity to the true value, and thus it was selected as the baseline for comparison.
- Strategy 4 (a-b-c): Capping—that is, chamfering contact pebbles with a given diameter (, , and in this study).
2. Materials and Methods
2.1. Numerical Domain and Material Properties
2.2. Numerical Solvers
- Enabling the standard k- cubic constitutive relationship to improve anisotopic turbulence prediction of secondary flows and streamline curvature [19].
- Each pebble surface mesh face was used in the view factor calculation;
- Gray radiation with no wavelength dependence;
- Diffuse radiation with no angular emission dependence;
- The effective radiation temperature of the environment was specified as 250 °C;
- A pebble surface emissivity of 0.8; and
- Satisfaction of Kirchhoff’s Law, such that emissivity + reflectivity + transmissivity = 1. This forces the surface reflectivity to 0.2 because the transmissivity is 0.
2.3. Mesh Sensitivity
- Volume-averaged pebble fuel temperature, ;
- Maximum pebble fuel temperature, ;
- Volume-averaged fluid temperature, ;
- Volume-averaged fluid velocity magnitude, ;
- Maximum fluid velocity magnitude, ;
- Surface-averaged fluid temperature on plane Z2 (z = 0.1 m), ;
- Surface-averaged fluid velocity magnitude on plane Z2 (z = 0.1 m), ;
- The pressure drop across the entire bed, .
3. Results
3.1. Case 1: Full Power
3.2. Case 2: PLOFC
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
CFD | computational fluid dynamics. |
DNS | direct numerical simulation. |
FCC | face-centered cubic. |
HALEU | high-assay low-enriched uranium. |
LES | large-eddy simulation. |
PIV | particle image velocimetry. |
PLOFC | pressurized loss of forced cooling. |
QOI | quantity of interest. |
QOIs | quantities of interest. |
RANS | Reynolds-averaged Navier–Stokes. |
RMS | root mean square. |
TRISO | tristructural isotropic. |
URANS | Unsteady Reynolds-averaged Navier–Stokes. |
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Strategies | Pebble Volume [ m3] | Calculated Porosity | [m] | Porosity Error [%] |
---|---|---|---|---|
1a—Decrease | 4.5678 | 0.4780 | 0.0458 | 0.3284 |
1b—Decrease | 4.4979 | 0.4860 | 0.0473 | 2.0051 |
1c—Decrease | 4.4454 | 0.4920 | 0.0484 | 3.2647 |
2a—Increase 0.1% | N/A | N/A | N/A | N/A |
2b—Increase 0.5% | 4.6501 | 0.4686 | 0.0441 | −1.6459 |
2c—Increase 1.0% | 4.7184 | 0.4608 | 0.0427 | −3.2844 |
3a—Bridge 10% | 4.5820 | 0.4763 | 0.0455 | −0.0123 |
3b—Bridge 15% | 4.5839 | 0.4761 | 0.0454 | −0.0578 |
3c—Bridge 20% | 4.5892 | 0.4755 | 0.0453 | −0.1850 |
4a—Cap 10% | 4.5802 | 0.4766 | 0.0455 | 0.0309 |
4b—Cap 15% | 4.5790 | 0.4767 | 0.0455 | 0.0597 |
4c—Cap 20% | 4.5737 | 0.4773 | 0.0457 | 0.1869 |
True | 4.5815 | 0.4764 | 0.0455 |
Region | Boundary | Condition | Value |
---|---|---|---|
Pebble fuel region | symmetry | symmetry plane | N/A |
fuel to fuel-free | contact interface | conformal conduction | |
Pebble fuel-free region | symmetry | symmetry plane | N/A |
fuel-free to fuel | contact interface | conformal conduction | |
fuel-free to fluid | contact interface | conformal convection | |
fuel-free to reflector | temperature | 250 °C | |
Heat transport fluid | symmetry | symmetry plane | N/A |
inlet | inlet velocity 1 | −3 ms−1 | |
inlet temperature | 250 °C | ||
turbulence intensity | 0.01 | ||
turbulent viscosity ratio | 10 | ||
outlet | outlet pressure | Pa | |
fluid to reflector | temperature | 250 °C | |
fluid to fuel-free | contact interface | conformal convection |
Material Property | Pebble Fuel Region | Pebble Fuel-Free Region | Heat Transport Fluid |
---|---|---|---|
Density (kgm−3) | 1700 | 1700 | Ideal gas |
Specific heat (Jkg−1K−1) | 700 | 700 | 5200 |
Thermal conductivity (Wm−1K−1) | 25 | 25 | 0.155 |
Dynamic viscosity () | N/A | N/A | |
Molecular weight (kgkmol−1) | N/A | N/A | 4.00 |
Turbulent Prandtl number [12] | N/A | N/A | 0.7 |
Strategies | Porosity Error [%] | ΔP | ||||
---|---|---|---|---|---|---|
1a—Decrease 0.1% | 0.3284 | −0.3 | −0.4 | −0.1 | 0.0 | 0.0 |
1b—Decrease 0.5% | 2.0051 | −22.4 | −4.3 | 0.2 | 0.2 | 0.0 |
1c—Decrease 1% | 3.2647 | −33.0 | −7.3 | 0.3 | −0.1 | 0.0 |
2a—Increase 0.1% | N/A | N/A | N/A | N/A | N/A | N/A |
2b—Increase 0.5% | −1.6459 | 12.4 | 2.8 | 0.2 | 0.0 | 0.0 |
2c—Increase 1% | −3.2844 | 21.1 | 5.1 | 0.2 | 0.0 | 0.0 |
3a—Bridge 10% | −0.0123 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
3b—Bridge 15% | −0.0578 | 1.8 | −0.2 | 0.2 | 0.1 | 0.0 |
3c—Bridge 20% | −0.1850 | 3.1 | 0.5 | 0.6 | 0.3 | 0.0 |
4a—Cap 10% | 0.0309 | −13.1 | −1.9 | 0.0 | 0.0 | −0.1 |
4b—Cap 15% | 0.0597 | −22.8 | −3.6 | 0.2 | −0.4 | 0.0 |
4c—Cap 20% | 0.1869 | −27.3 | −4.4 | −0.4 | −0.3 | 0.0 |
GCI (%)—Bridge 10% | N/A | 3 | 0.1 | 3.4 | 0.6 | 0.1 |
Strategy | Case 2a | Case 2b | ||||
---|---|---|---|---|---|---|
1a—Decrease | 13.8 | 6.5 | 5.8 | 1.4 | 0.7 | 0.2 |
1b—Decrease | 20.2 | 9.7 | 8.9 | 1.6 | 0.7 | 0.4 |
1c—Decrease | 25 | 12.1 | 11.5 | 1.5 | 0.7 | 0.6 |
2a—Increase 0.1% | N/A | N/A | N/A | N/A | N/A | N/A |
2b—Increase 0.5% | −1.5 | −0.9 | −1.2 | 0 | 0 | −0.2 |
2c—Increase 1.0% | −4.3 | −2.5 | −3.1 | −0.6 | −0.2 | −0.4 |
3a—Bridge 10% | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
3b—Bridge 15% | −2.9 | −1.4 | −1.2 | −0.7 | −0.3 | −0.1 |
3c—Bridge 20% | −4.7 | −2.3 | −2 | −1.3 | −0.6 | −0.2 |
4a—Cap 10% | 15.6 | 7.8 | 8.1 | 0.5 | −0.5 | −1.3 |
4b—Cap 15% | 19.6 | 9.6 | 9.7 | 0.6 | −0.5 | −1.3 |
4c—Cap 20% | 22.8 | 11.1 | 11.1 | 0.8 | −0.4 | −1.2 |
Strategies | |||||
---|---|---|---|---|---|
1a—Decrease 0.1% | −1.2 | −0.4 | 0.0 | 0.0 | 0.0 |
1b—Decrease 0.5% | −8.6 | −2.3 | 0.1 | 0.0 | 0.0 |
1c—Decrease 1% | −19.1 | −5.1 | 0.2 | 0.1 | 0.0 |
2a—Increase 0.1% | N/A | N/A | N/A | N/A | N/A |
2b—Increase 0.5% | 9.8 | 2.3 | −0.1 | −0.1 | 0.0 |
2c—Increase 1% | 18.4 | 4.4 | −0.1 | −0.2 | 0.0 |
3a—Bridge 10% | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
3b—Bridge 15% | −0.4 | 0.2 | 0.0 | 0.0 | 0.0 |
3c—Bridge 20% | −0.9 | 0.5 | 0.0 | 0.1 | 0.0 |
4a—Cap 10% | −0.5 | 0.0 | 0.3 | 0.2 | 0.0 |
4b—Cap 15% | −2.3 | −0.5 | 0.3 | 0.1 | 0.0 |
4c—Cap 20% | −7.2 | −3.4 | 0.6 | −0.1 | 0.0 |
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Goth, N.; Nguyen, T.; Pointer, W.D. Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor Cores. Appl. Sci. 2024, 14, 7343. https://doi.org/10.3390/app14167343
Goth N, Nguyen T, Pointer WD. Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor Cores. Applied Sciences. 2024; 14(16):7343. https://doi.org/10.3390/app14167343
Chicago/Turabian StyleGoth, Nolan, Thien Nguyen, and William David Pointer. 2024. "Investigation of Point-Contact Strategies for CFD Simulations of Pebble-Bed Reactor Cores" Applied Sciences 14, no. 16: 7343. https://doi.org/10.3390/app14167343