## THERMAL SCIENCE

International Scientific Journal

### DISCUSSION ON IMPROVED METHOD OF TURBULENCE MODEL FOR SUPERCRITICAL WATER FLOW AND HEAT TRANSFER

**ABSTRACT**

The turbulence model fails in supercritical fluid-flow and heat transfer simulation, owing to the drastic change of thermal properties. The inappropriate buoyancy effect model and the improper turbulent Prandtl number model are several of these factors lead to the original low-Reynolds number turbulence model unable to predict the wall temperature for vertically heated tubes under the deteriorate heat transfer conditions. This paper proposed a simplified improved method to modify the turbulence model, using the generalized gradient diffusion hypothesis approximation model for the production term of the turbulent kinetic energy due to the buoyancy effect, using a turbulence Prandtl number model for the turbulent thermal diffusivity instead of the constant number. A better agreement was accomplished by the improved turbulence model compared with the experimental data. The main reason for the over-predicted wall temperature by the original turbulence model is the misuse of the buoyancy effect model. In the improved model, the production term of the turbulent kinetic energy is much higher than the results calculated by the original turbulence model, especially in the boundary-layer. A more accurate model for the production term of the turbulent kinetic energy is the main direction of further modification for the low Reynolds number turbulence model.

**KEYWORDS**

PAPER SUBMITTED: 2019-08-13

PAPER REVISED: 2019-11-07

PAPER ACCEPTED: 2019-11-25

PUBLISHED ONLINE: 2020-01-19

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 5**, PAGES [2729 - 2741]

- Jackson, J.D., and Hall, W.B., Forced convective heat transfer to fluids at supercritical pressure, Turbulent Forced Convection in Channels and Bundles, Hemisphere, 2(1979), pp. 563-611
- Pioro, I.L., et al., Heat transfer to supercritical fluids flowing in channels—empirical correlations (survey), Nuclear Engineering and Design, 230(2004), 1, pp. 69-91
- Jackson, J.D., and Hall, W.B., Influences of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions, turbulent forced convection in channels and bundles, Hemisphere, 2(1979), pp. 613-640
- McEligot, D.M., and Jackson, J.D., ‘‘Deterioration'' criteria for convective heat transfer in gas flow through non-circular ducts, Nuclear Engineering and Design, 232(2004), 3, pp.327-333
- Jiang, P.X., et al., Convective heat transfer of supercritical pressure carbon dioxide in a vertical micro tube from transition to turbulent flow regime, International Journal of Heat and Mass Transfer, 56(2013), 1，pp.741-749,
- Xu, R.N., et al., Buoyancy effects on turbulent heat transfer of supercritical co2 in a vertical mini-tube based on continuous wall temperature measurements, International Journal of Heat and Mass Transfer, 110(2017), pp.576-586
- Mokry Sarah, et al., Supercritical-water heat transfer in a vertical bare tube, Nuclear Engineering and Design, 240(2010), 3, pp.568-576
- Song, J.H., et al., Heat transfer characteristics of supercritical fluid flow in a vertical pipe, Journal of Supercritical Fluids, 42(2008), 2, pp.164-171
- Li, Z.H., et al., Experimental investigation of convective heat transfer of co2 at supercritical pressures in a vertical circular tube, Experimental Thermal and Fluid Science, 47(2008), 8, pp.998-1011
- Gu H. Y., et al., Experimental studies on heat transfer to supercritical water in circular tubes at high heat fluxes, Experimental Thermal and Fluid Science, 65(2015), pp.22-32
- He S.S., et al., A computational study of convective heat transfer to co2 at supercritical pressures in a vertical mini tube, International Journal of Thermal Sciences, 2005, pp.521-530
- He S.S., et al., A computational study of convective heat transfer to carbon dioxide at a pressure just above the critical value, Applied Thermal Engineering, 2008, pp.1662-1675
- Kim W.S., et al., Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection, International Journal of Heat and Mass Transfer, 2008, pp.1298-1312
- Wen Q.L., and Gu H.Y., Numerical simulation of heat transfer deterioration phenomenon in supercritical water through vertical tube, Annals of Nuclear Energy, 37(2010), pp.1272-1280
- Zhang Y., et al., Numerical simulation of heat transfer of supercritical fluids in circular tubes using different turbulence models, Journal of Nuclear Science and Technology, 48(2011), pp.366-373
- Rosa M. D., et al., Lessons learned from the application of CFD models in the prediction of heat transfer to fluids at supercritical pressure, The 5th Int. Sym. SCWR (ISSCWR-5), British Columbia, Canada, March 13-16, 2011
- Liu L., et al., Heat transfer deterioration to supercritical water in circular tube and annular channel, Nuclear Engineering and Design, 255(2013), pp. 97-104
- Chu X., et al., A computationally light data-driven approach for heat transfer and hydraulic characteristics modeling of supercritical fluids: from DNS to DNN, International Journal of Heat and Mass Transfer, 123(2018), pp.629-636
- Pandey S., et al., Buoyancy induced turbulence modulation in pipe flow at supercritical pressure under cooling conditions, Physics of Fluids, 30(2018), pp.065105-1-22
- Nemati H., et al., Mean statistics of a heated turbulent pipe flow at supercritical pressure, International Journal of Heat and Mass Transfer, 83(2015), pp.741-752
- Kim W. S., et al., Assessment by comparison with DNS data of turbulence models used in simulations of mixed convection, International Journal of Heat and Mass Transfer, 51(2008), 5, pp.1293-1312
- Zhang G., et al., Experimental and numerical investigation of turbulent convective heat transfer deterioration of supercritical water in vertical tube, Nuclear Engineering and Design, 248(2012), 1, pp.226-237
- Pucciarelli A., and Ambrosini W., Improvements in the prediction of heat transfer to supercritical pressure fluids by the use of algebraic heat flux models, Annals of Nuclear Energy, 99(2017), pp.58-67
- Xiong J., and Cheng X., Turbulence modelling for supercritical pressure heat transfer in upward tube flow, Nuclear Engineering and Design, 270(2014), pp.249-258
- Bazargan M. ， and Mohseni M., Effect of turbulent prandtl number on convective heat transfer to turbulent flow of a supercritical fluid in a vertical round tube, Journal of Heat Transfer, 133(2011), pp.295-302
- Mohseni M., and Bazargan M., A new correlation for the turbulent prandtl number in upward rounded tubes in supercritical fluid flows, Journal of Heat Transfer, 138(2016), 8, pp. 1701-1710
- Tang G.l., et al., A variable turbulent Prandtl number model for simulating supercritical pressure CO2 heat transfer, International Journal of Heat and Mass Transfer, 102(2016), pp.1082-1092
- Bae Y.Y., A new formulation of variable turbulent Prandtl number for heat transfer to supercritical fluids, International Journal of Heat and Mass Transfer, 92(2016), pp.792-806.
- Bae Y.Y., et al., Numerical simulation of supercritical pressure fluids with property dependent turbulent Prandtl number and variable damping function, International Journal of Heat and Mass Transfer, 101(2016), pp.488-501
- Jaromin M., and Anglart H., A numerical study of heat transfer to supercritical water flowing upward in vertical tubes under normal and deteriorated conditions, Nuclear Engineering and Design, 264(2013), pp.61-70
- ANSYS Inc., ANSYS fluent theory guide release 13.0.
- Kays W. M., Turbulent Prandtl number. Where are we?, ASME Transactions Journal of Heat Transfer, 116(1994), 2, pp.284-295
- Abe K., et al., A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flow, International Journal of Heat and Mass Transfer, 37(1994), pp.139-151
- Ince N.Z., and Launder B.E., Three-dimensional and heat-loss effects on turbulent flow in a nominally two-dimensional cavity, International Journal of Heat and Mass Transfer, 16(1995), pp.171-177