Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter July 14, 2022

Determination of heat flux leading to the onset of flow instability in MTR reactors

Salah El-Din El-Morshedy EMAIL logo
From the journal Kerntechnik


The prediction of heat flux leading to the Onset of Flow Instability (OFI) phenomena is an important consideration in the design of Material Testing Reactors (MTR) due to the possibility of flow excursion during postulated accident. From the thermal-hydraulic point of view, OFI is the critical phenomenon limiting MTR reactor power. In a previous work, an empirical correlation is developed to predict the subcooling at OFI in narrow vertical rectangular channels simulating a coolant channel of MTR. In the present work, an innovative model to determine the heat flux leading to OFI in MTR reactors is introduced based on the previous correlation. The developed model gives a very low deviation of only 1.65% from the experimental data of Whittle & Forgan that covers a wide range of MTR operating conditions. The heat flux leading to OFI is also predicted by both Whittle & Forgan and Fabrega correlations for comparison. The present model is then applied on the IAEA 10 MW MTR generic reactor to predict the Best-Estimate (BE) and Best-Estimate-Plus-Uncertainty (BEPU) Onset of Flow Instability Ratio (OFIR) and the power leading to OFI as well as the bubble detachment parameter under different coolant velocities and inlet temperatures. The model is also used to predict both the OFIR and bubble detachment parameter in the reactor under unprotected Loss-of-Flow transient for exponential flow decay with a time constant of 1.0 s (fast LOFA), 10, 15 and 25 s (slow LOFA) from a power level of 10 MW. For BEPU calculation, a combined statistical method with direct propagation of errors is adapted to treat the uncertainty factors for fuel fabrication and measured parameters in the BEPU calculation. The model results is analyzed and discussed.

Corresponding author: Salah El-Din El-Morshedy, Reactors Department, Egyptian Atomic Energy Authority, Cairo, Egypt; and Department of Mechanical Engineering, The American University in Cairo, Cairo, Egypt, E-mail:

  1. Author contributions: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author declares no conflicts of interest regarding this article.


Al-Yahia, O.S., Kim, T., and Jo, D. (2018). Flow Instability (FI) for subcooled flow boiling through a narrow rectangular channel under transversely uniform and non-uniform heat flux. Int. J. Heat Mass Tran. 125: 116–128, in Google Scholar

Bowering, R.W. (1962). Physical model based on bubble detachment and calculation of steam voidage in the subcooled region of a heated channel. Halden, Norway: HPR-10, Institute for Atomenergi, in Google Scholar

Chang, S.H., Kim, Y.I., and Beak, W.P. (1996). Derivation of mechanistic critical heat flux model for water based on flow instabilities. Int. Commun. Heat Mass Tran. 23: 1109–1119, in Google Scholar

Chatoorgooon, V., Dimmick, G.R., Carver, M.B., Selander, W.N., and Shoukri, M. (1992). Application of generation and condensation models to predict subcooled boiling void at low pressures. Nucl. Technol. 98: 366–378.10.13182/NT92-A34666Search in Google Scholar

El-Morshedy, S.E. (2012a). Predictive study of the onset of flow instability in narrow vertical rectangular channels under low pressure subcooled boiling. Nucl. Eng. Des. 244: 34–42, in Google Scholar

El-Morshedy, S.E. (2012b). Flow instability in material testing reactors. In: Mesquita, A.Z. (Ed.). Nuclear reactors. IntechOpen, London, pp. 25–46.Search in Google Scholar

Fabrega, S. (1971). Le calcule thermique des réacteurs de recherché refroidis a l’eau, CEA-R-4114.Search in Google Scholar

Ghione, A., Noel, B., Vinai, P., and Demazière, C. (2017). Criteria for onset of flow instability in heated vertical narrow rectangular channels at low pressure: an assessment study. Int. J. Heat Mass Tran. 105: 464–478, in Google Scholar

Giménez, M., Schlamp, M., and Vertullo, A. (2002). Uncertainties assessment for safety margins evaluation in MTR reactors core thermal-hydraulic design. In: International meeting on reduced enrichment for research and test reactors, Bariloche, Argentina, in Google Scholar

Gladbach, B. (1992). Safety analyses for the IAEA generic 10 MW reactor, IAEATECDOC-643, Vol. 2, Appendix A in Google Scholar

Griffith, P., Clark, J.A., and Rohsenow, W.M. (1958). Void volumes in subcooled boiling. In: ASME Paper 58-HT-19, U.S. National heat transfer conference, Chicago, in Google Scholar

Hari, S. and Hassan, Y.A. (2002). Improvement of the subcooled boiling model for low-pressure conditions in thermal-hydraulic codes. Nucl. Eng. Des. 216: 139–152, in Google Scholar

IAEA-TECDOC-233. (1980). IAEA research reactor core conversion from the use of high-enriched uranium to the use of low enriched uranium fuels guide book, in Google Scholar

IAEA-TECDOC-1332. (2003). Safety margins of operating reactors: analysis of uncertainties and implications for decision making, in Google Scholar

Khater, H.A., El-Morshedy, S.E., and Ibrahim, M.M.A. (2007a). Thermal-hydraulic modeling of the onset of flow instability in MTR reactors. Ann. Nucl. Energy 34: 194–200, in Google Scholar

Khater, H.A., El-Morshedy, S.E., and Ibrahim, M.M.A. (2007b). Prediction of the onset of flow instability in ETRR-2 research reactor under loss of flow accident. Kerntechnik 72: 53–58, in Google Scholar

Ledinegg, M. (1938). Instability of flow during natural and forced circulation. Die Wärme 61: 891–898.Search in Google Scholar

Lee, J., Chae, H., and Chang, S.H. (2013). Flow instability during subcooled boiling for a downward flow at low pressure in a vertical narrow rectangular channel. Int. J. Heat Mass Tran. 67: 1170–1180, in Google Scholar

Lee, S.C. and Bankoff, S.G. (1993). Prediction of the onset of flow instability in transient subcooled flow boiling. Nucl. Eng. Des. 139: 149–159, in Google Scholar

Mishima, K. and Nishihara, H. (1985). Boiling burnout and flow instabilities for water flowing in a round tube under atmospheric pressure. Int. J. Heat Mass Tran. 28: 1115–1129, in Google Scholar

Nair, S., Lele, S., Ishii, M., and Revankar, S.T. (19961996). Analysis of flow instabilities and their role on critical heat flux for two-phase downflow and low pressure systems. Int. J. Heat Mass Tran. 39: 39–48, in Google Scholar

Rogers, J.T., Salcudean, M., Abdullah, Z., McLead, D., and Poirier, D. (1987). The onset of significant void in up-flow boiling of water at low pressure and velocities. Int. J. Heat Mass Transfer 30: 2247–2260, in Google Scholar

Saha, P. and Zuber, N. (1974). Point of net vapor generation and vapor void fraction in subcooled boiling. In: Proceeding of the 5th international heat transfer conference, Vol. 4. Tokyo, Japan, pp. 175–179.10.1615/IHTC5.430Search in Google Scholar

Stelling, R., McAssey, E.V., Dougherty, T., and Yang, B.W. (1996). The onset of flow instability for downward flow in vertical channels. ASME J. Heat Transfer 118: 709–714, in Google Scholar

Whittle, R.H. and Forgan, R. (19671967). A Correlation for the minima in the pressure drop versus flow-rate curves for sub-cooled water flowing in narrow heated channels. Nucl. Eng. Des. 6: 89–99, in Google Scholar

Yuan, Z., Xiao, Y., Yanlin, W., Yanjun, L., and Yanping, H. (2012). Experimental study of two phase flow instability in parallel narrow rectangular channels. Ann. Nucl. Energy 50: 103–110, in Google Scholar

Zhang, X., Feng, W., Zhang, J., Guo, S., Ding, W., and Chen, H. (20202020). Experimental study on flow instability for downward flow in a narrow rectangular channel with flow pattern transition. Int. Commun. Heat Mass Tran. 114: 104586, in Google Scholar

Received: 2022-04-21
Published Online: 2022-07-14
Published in Print: 2022-10-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 9.12.2022 from
Scroll Up Arrow