Skip to main content
SpringerLink
Log in

CFD validation of condensation heat transfer in scaled-down small modular reactor applications, Part 2: Steam and non-condensable gas

Experimental and Computational Multiphase Flow Aims and scope Submit manuscript

Abstract

This paper presents the computational fluid dynamics (CFD) validation and scaling assessment of the condensation heat transfer (CHT) models in the presence of non-condensable gas for the passive containment cooling system (PCCS) of the small modular reactor (SMR). The STAR-CCM+ software with 3D scaled-down SMR containment geometries was used in CFD simulations with steam and non-condensable gas (NCG). The limitations and approximations of the previous studies were resolved to avoid scaling distortion and uncertainties. Air was used as the NCG gas with steam. The multi-component gas model was used to define the steam-NCG mixture, and the condensation-seed parameter was used as the source term for the fluid film model. Three different turbulence models were used to check the heat flux performances and temperature distributions on the coolant side. The heat flux was estimated from the axial coolant bulk temperature, which was identical to the test data reduction method. An implicit-unsteady numerical solver was applied to the conjugate heat transfer models between the gas, liquid, and solid regions. Detailed simulations were performed, and simulation results were validated with the measured parameters experimentally. The condensation heat transfer performance was quantified using non-dimensional numbers and compared for different scaled geometries to identify the scaling distortions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

Abbreviations

ṁ :

mass flow rate (kg/s)

D :

diffusion coefficient (m2/s)

e :

energy per unit mass (J/kg)

f :

body force (kg·m/s2)

h :

heat transfer coefficient (W/(m2·K))

j :

species

k :

thermal conductivity (W/(m·K))

M :

mole fraction (%)

N :

number of condensation seeds

p :

pressure (N/m2)

q :

heat flux (W/m2)

R :

minimum radius of condensation seeds (m)

t :

time (s)

T :

temperature (°C or K)

T a :

coolant adiabatic wall temperature (°C or K)

T c :

steam-mixture central line temperature (°C or K)

T s :

vapor-liquid interfacial surface temperature (°C or K)

T sat :

steam saturation temperature (°C or K)

T wi :

condenser tube inner wall temperature (°C or K)

T wo :

condenser tube outer wall temperature (°C or K)

δ :

film thickness (m)

ρ :

density (kg/m3)

μ :

dynamic viscosity (Pa·s)

ν :

kinematic viscosity (m2/s)

Nu :

Nusslet number, hD / k

Re :

Reynolds number, ρνD / μ

CFD:

computational fluid dynamics

IAEA:

International Atomic Energy Agency

ID, OD:

inner diameter, outer diameter

LWR:

light water reactor

NCG:

non-condensable gas

PCCS:

passive containment cooling system

PRIS:

power reactor information system

SMR:

small modular reactor

1D, 2D, 3D:

one-, two-, three-dimensional

GW:

gigawatt

HTC:

heat transfer coefficient

MW:

megawatt

RSM:

Reynolds stress model

SCH:

pipe schedule

SST:

shear stress transport

TWh:

trillion watt hour

i, j, k :

tensor index for x, y, z

in:

inlet

out:

outlet

References

  • Ahammad, F., Mahmud, S., Islam, S. Z. 2019. Computational fluid dynamics study of yield power law drilling fluid flow through smooth-walled fractures. J Petrol Explor Prod Technol, 9: 2717–2727.

    Article  Google Scholar 

  • Ahmed, F., Ara, N., Deshpande, V., Mollah, A., Bhowmik, P. K. 2021a. CFD validation with optimized mesh using benchmarking data of pebble-bed high-temperature reactor. Prog Nucl Energy, 134: 103653.

    Article  Google Scholar 

  • Ahmed, F., Abir, M. A., Bhowmik, P. K., Deshpande, V., Mollah, A. S., Kumar, D., Alam, S. 2021b. Computational assessment of thermo-hydraulic performance of Al2O3-water nanofluid in hexagonal rod-bundles subchannel. Prog Nucl Energy, 135: 103700.

    Article  Google Scholar 

  • Alam, S. B., Kumar, D., Almutairi, B., Bhowmik, P. K., Goodwin, C., Parks, G. T. 2019. Small modular reactor core design for civil marine propulsion using micro-heterogeneous duplex fuel. Part I: Assembly-level analysis. Nucl Eng Des, 346: 157–175.

    Article  Google Scholar 

  • Bhowmik, P. K. 2016. Nanofluid operation and valve engineering of SUPER for small unit passive enclosed reactor. Master Thesis. Seoul National University, Republic of Korea.

    Google Scholar 

  • Bhowmik, P. K., Schlegel, J. P., Kalra, V., Mills, C., Usman, S. 2021a. Design of condensation heat transfer experiment to evaluate scaling distortion in small modular reactor safety analysis. J Nuclear Rad Sci, 7: 031406.

    Article  Google Scholar 

  • Bhowmik, P. K., Schlegel, J., Kalra, V., Alam, S., Hong, S., Usman, S. 2021b. CFD validation of condensation heat transfer in scaled-down small modular reactor applications, Part 1: Pure steam. Exp Comput Mulitph Flow, https://doi.org/10.1007/s42757-021-0115-5.

  • Bhowmik, P. K., Shamim, J. A., Chen, X., Suh, K. Y. 2021c. Rod bundle thermal-hydraulics experiment with water and water-Al2O3 nanofluid for small modular reactor. Ann Nucl Energy, 150: 107870.

    Article  Google Scholar 

  • Bhowmik, P. K., Suh, K. Y. 2021. Flow mapping using 3D full-scale CFD simulation and hydrodynamic experiments of an ultra-supercritical turbine’s combined valve for nuclear power plant. Int J Energy Env Eng, https://doi.org/10.1007/s40095-021-00394-0.

  • Bian, H., Sun, Z., Ding, M., Zhang, N. 2017. Local phenomena analysis of steam condensation in the presence of air. Prog Nucl Energy, 101: 188–198.

    Article  Google Scholar 

  • Buongiorno, J., Corradini, M., Parsons, J., Petti, D. 2019. Nuclear energy in a carbon-constrained world: Big challenges and big opportunities. IEEE Power Energy Mag, 17: 69–77.

    Article  Google Scholar 

  • Cheng, X., Bazin, P., Cornet, P., Hittner, D., Jackson, J., Jimenez, J. L., Naviglio, A., Oriolo, F., Petzold, H. 2001. Experimental data base for containment thermalhydraulic analysis. Nucl Eng Des, 204: 267–284.

    Article  Google Scholar 

  • Dehbi, A., Janasz, F., Bell, B. 2013. Prediction of steam condensation in the presence of noncondensable gases using a CFD-based approach. Nucl Eng Des, 258: 199–210.

    Article  Google Scholar 

  • Fu, W., Li, X., Wu, X., Corradini, M. L. 2016. Numerical investigation of convective condensation with the presence of non-condensable gases in a vertical tube. Nucl Eng Des, 297: 197–207.

    Article  Google Scholar 

  • Gharari, R., Kazeminejad, H., Kojouri, N. M., Hedayat, A. 2018. A review on hydrogen generation, explosion, and mitigation during severe accidents in light water nuclear reactors. Int J Hydrog Energy, 43: 1939–1965.

    Article  Google Scholar 

  • Hasan, F., Al Mahmud, K. A. H., Khan, M. I., Patil, S., Dennis, B. H., Adnan, A. 2021. Cavitation induced damage in soft biomaterials. Multiscale Sci Eng, 3: 67–87.

    Article  Google Scholar 

  • Huang, J., Zhang, J., Wang, L. 2015. Review of vapor condensation heat and mass transfer in the presence of non-condensable gas. Appl Eng, 89: 469–484.

    Google Scholar 

  • IAEA. 2018. Advances in small modular reactor technology developments. Austria: IAEA.

    Google Scholar 

  • Khan, M. I., Billah, M. M., Rahman, M. M., Hasan, M. N. 2017. Mixed convection heat transfer simulation in a rectangular channel with a variable speed rotational cylinder, In: Proceedings of the AIP Conference.

  • Kuhn, S. Z. 1995. Investigation of heat transfer from condensing steam-gas mixtures and turbulent films flowing downward inside a vertical tube. Ph.D. Thesis. University of California, USA.

    Google Scholar 

  • Li, J. D. 2013. CFD simulation of water vapour condensation in the presence of non-condensable gas in vertical cylindrical condensers. Int J Heat Mass Transf, 57: 708–721.

    Article  Google Scholar 

  • Mahaffy, J., Chung, B., Song, C., Dubois, F., Graffard, E., Ducros, F., Heitsch, M., Scheuerer, M., Henriksson, M., Komen, E., Moretti, F., Morii, T., Muehlbauer, P., Rohde, U., Smith, B. L., Watanabe, T., Zigh, G. 2007. Best practice guidelines for the use of CFD in nuclear reactor safety applications. Nuclear Energy Agency of the OECD (NEA).

  • Malet, J., Porcheron, E., Vendel, J. 2010. OECD international standard problem ISP-47 on containment thermal-hydraulics—Conclusions of the TOSQAN part. Nucl Eng Des, 240: 3209–3220.

    Article  Google Scholar 

  • Milinchuk, V., Klinshpont, E. R., Belozerov, V., Zagorodnyaya, A. 2017. Hydrozirconium reaction in heterogeneous compositions. Nucl Energy Technol, 3: 15–18.

    Article  Google Scholar 

  • Mishra, A. A., Girimaji, S. S. 2013. Intercomponent energy transfer in incompressible homogeneous turbulence: Multi-point physics and amenability to one-point closures. J Fluid Mech, 731: 639–681.

    Article  MathSciNet  Google Scholar 

  • Nian, V., Chou, S. 2014. The state of nuclear power two years after Fukushima—The ASEAN perspective. Appl Energy, 136: 838–848.

    Article  Google Scholar 

  • Power Reactor Information System (PRIS). 2019. The database on nuclear power reactors. International Atomic Energy Agency, Austria. Available at https://pris.iaea.org/pris/.

    Google Scholar 

  • Ravva, S. R., Iyer, K. N., Gupta, S., Gaikwad, A. J. 2014. Implementation and validation of the condensation model for containment hydrogen distribution studies. Nucl Eng Des, 270: 34–47.

    Article  Google Scholar 

  • Ritchie, H. 2018. What are the safest and cleanest sources of energy? Available at https://ourworldindata.org/safest-sources-of-energy.

  • Saha, S., Khan, J., Farouk, T. 2020. Numerical study of evaporation assisted hybrid cooling for thermal powerplant application. Appl Therm Eng, 166: 114677.

    Article  Google Scholar 

  • Shamim, J. A., Bhowmik, P. K., Chen Y. X., Suh, K. Y. 2016. A new correlation for convective heat transfer coefficient of water-alumina nanofluid in a square array subchannel under PWR condition. Nucl Eng Des, 308: 194–204.

    Article  Google Scholar 

  • Sharma, P. K., Gera, B., Singh, R. K., Vaze, K. K. 2012. Computational fluid dynamics modeling of steam condensation on nuclear containment wall surfaces based on semiempirical generalized correlations. Sci Technol Nucl Install, 2012: 1–7.

    Article  Google Scholar 

  • Sharma, S. L., Ishii, M., Hibiki, T., Schlegel, J. P., Liu, Y., Buchanan, J. R. 2019. Beyond bubbly two-phase flow investigation using a CFD three-field two-fluid model, Int J Multiph Flow, 113: 1–15.

    Article  MathSciNet  Google Scholar 

  • Su, J., Sun, Z., Zhang, D. 2014. Numerical analysis of steam condensation over a vertical surface in presence of air. Ann Nucl Energy, 72: 268–276.

    Article  Google Scholar 

  • Tagami, T. 1965. Interim Report on Safety Assessments and Facilities Establishment Project in Japan for Period Ending June 1965 (No. 1).

  • Uchida, H., Oyama, A., Togo, Y. 1964. Evaluation of post-incident cooling systems of light-water power reactors. In: Proceedings of the 3rd International Conference on the Peaceful Uses of Atomic Energy, USA.

  • Wheatley, S., Sovacool, B. K., Sornette, D. 2016. Reassessing the safety of nuclear power. Energy Res Soc Sci, 15: 96–100.

    Article  Google Scholar 

  • Yeoh, G. H. 2019. Thermal hydraulic considerations of nuclear reactor systems: Past, present and future challenges. Exp Comput Multiph Flow, 1: 3–27.

    Article  Google Scholar 

  • Zschaeck, G., Frank, T., Burns, A. 2014. CFD modelling and validation of wall condensation in the presence of non-condensable gases. Nucl Eng Des, 279: 137–146.

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the Small Modular Reactor Research and Education Consortium for the support to complete this study.

Author information

Authors and Affiliations

  1. Department of Nuclear Engineering and Radiation Science, Missouri University of Science and Technology, 1201 N. State St., Rolla, MO, 65409, USA

    Palash Kumar Bhowmik, Joshua Paul Schlegel, Varun Kalra, Syed Alam, Sungje Hong & Shoaib Usman

Authors
  1. Palash Kumar Bhowmik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joshua Paul Schlegel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Varun Kalra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Syed Alam
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sungje Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shoaib Usman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joshua Paul Schlegel.

Ethics declarations

The authors have no competing interests to declare that are relevant to the content of this article.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhowmik, P.K., Schlegel, J.P., Kalra, V. et al. CFD validation of condensation heat transfer in scaled-down small modular reactor applications, Part 2: Steam and non-condensable gas. Exp. Comput. Multiph. Flow 4, 424–434 (2022). https://doi.org/10.1007/s42757-021-0113-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42757-021-0113-7

Keywords

Search

Navigation