DIPARTIMENTO DI INGEGNERIA CIVILE E INDUSTRIALE CORSO DI DOTTORATO IN INGEGNERIA INDUSTRIALE
Relazione sulle attività svolte nel corso del Dottorato Tema di Ricerca:
Analysis of fluiddynamic and heat transfer phenomena with supercritical fluids
Candidato: Andrea Pucciarelli
Relatori: W.Ambrosini, M.Sharabi, S.He Contro-relatore: N. Forgione
GENERAL OBJECTIVES OF THE RESEARCH
The objective of this research is obtaining a better understanding on the heat transfer phenomena occurring when dealing with fluids at supercritical pressure, with the aim of paving the way for the development of the Generation IV Supercritical Water Cooled Reactor (SCWR) nuclear power plant. At the beginning of the present work, no reliable technique for predicting heat transfer phenomena in these conditions was available, including both CFD and heat transfer correlations.
The phenomena occurring in heat transfer to supercritical fluids are in fact much more complex than the ones occurring in fluids in standard conditions. In particular, this is due to the strong variations of the thermodynamic properties occurring in the vicinity of the so called “pseudo-critical temperature”, which marks the single-phase transition from the liquid-like to the gas-like conditions. In addition, buoyancy phenomena imply both impairments and improvements of heat transfer conditions depending on the flow direction. In fact, in upward flows, the buoyancy forces may imply a relaminarization of the flow inducing a heat transfer deterioration phenomenon. Further along the heated length the same phenomena may induce new velocity distributions (M-shaped) which result in a recovery of the turbulence conditions and, as a consequence, in a new heat transfer improvement. In downward flow cases, instead, buoyancy forces always have a positive effect since they increase the shear stresses in the vicinity of the wall and, as a consequence, improve the heat transfer conditions.
Heat transfer deterioration and heat transfer recovery occurring in upward flows are the hardest conditions to deal with and a better prediction of these phenomena adopting CFD analysis is the topic of the present research. The RANS techniques adopted in the study do not require large computational effort and allow studying even complicate geometries; on the other hand, they are less accurate and reliable than LES and DNS. As a consequence, some particular phenomena may be neglected or modelled in a too simple way for dealing with supercritical fluids, making the results inaccurate. Different paths, as reported in the next sections, were considered in the present research project in order to find out which could be the lacking ingredient in the CFD models that are now providing us with better results.
WORK PERFORMED DURING THE FIRST YEAR
Participation to the GIF International Benchmark on supercritical flow in a 7-rod
Bundle and other heat transfer analyses
The work consisted in performing blind CFD simulations of three selected experimental cases in order to understand the capabilities of present codes in simulating supercritical heat transfer in rod bundles. The analyses considered different aspects of the problem, both related to the discretization of the domain and to a simple procedure which should help at understanding the reliability of the obtained results in the lack of experimental data to compare with. After the delivery of the experimental data, further analyses were performed in order to improve the obtained results, by considering different domain discretizations and boundary conditions.
Other experimental data concerning supercritical flow in a 4-rod bundle were also analysed during the first year. The operating conditions were very different from the ones considered for the GIF Benchmark and their comparison was very interesting in particular concerning the effect of the spacer grids. In fact, while in the Benchmark cases they turned out to have a negligible effect on fluid flow, in the 4-rod case, characterised by trans-pseudocritical conditions, they showed to be crucial in order to obtain realistic wall temperature trends.
The results obtained in the work were reported in a paper presented at the 7th International
Symposium on SCWR (ISSCWR-7) meeting in Helsinki and, subsequently, published on the Nuclear Engineering and Science Radiation Journal. In addition, a contribution from Pisa was present in a common paper (by Rohde, et al.) presented at the same conference.
Development of a simple methodology for accounting wall roughness effects when
dealing with Low-Reynolds turbulence models
As mentioned above, some physical phenomena are usually neglected by CFD codes; in particular, no consolidated methodology exists for accounting for wall roughness effects when using Low-Reynolds turbulence models. Low-Reynolds k-ε models can predict the occurrence of heat transfer deterioration, but they usually fail at predicting the recovery phase; the fact is also due to a too low predicted turbulent kinetic energy. It was then considered that accounting for roughness effects might help at introducing a lower bound for the turbulent kinetic energy after laminarisation, so that heat transfer recovery could be predicted. The proposed model includes an additional production term of turbulence and a corresponding production term of dissipation related to surface roughness. The methodology was tested and improved during the first year and the obtained model is now able to reproduce the Moody’s and Nikuradse diagrams using different fluids in very different flow conditions. The study was very important for providing us with a valid tool for including wall roughness effects when dealing with Low-Reynolds turbulence models. Its application to heat transfer to supercritical fluids, however, did not lead to decisive improvements in the results of the model, as roughness will certainly contribute but seemed a posteriori not to be the most overwhelming phenomenon affecting heat transfer in such conditions.
The performed work allowed us publishing two papers which, for misunderstanding with the journal editing team of Nuclear Engineering and Design are referred as just one: Ambrosini, et al. (2015)
WORK PERFORMED DURING THE SECOND YEAR
Implementation of AHFM in available turbulence model in STAR-CCM+
The algebraic heat flux model (AHFM) is an advanced technique for calculating the turbulent heat fluxes. For being adopted it requires using four-equation turbulence models since the distribution of the temperature variance must be known. AHFM was already considered during the candidate’s Master Thesis with the aim of calculating the buoyancy terms using an in-house code (THEMAT). The use of AHFM was reproposed even in STAR-CCM+, both for calculating buoyancy effects and for calculating the turbulent heat fluxes in the energy equation. Owing to limitations of the code, AHFM could not be used at is whole capabilities and was only used for obtaining a better estimation of the turbulent Prandtl number. In addition, the equation of the dissipation of the temperature variance could not be implemented because of stability problems, which were bypassed by adopting an algebraic relation relied upon in past literature works.
The obtained results are promising and cases that in the past were very hard or impossible to be predicted finally report reliable trends. Results improved in particular in near critical conditions while for cases at lower temperature the effect is less impressing. Nevertheless, this seemed to be the path to be followed in order to obtain better predictions. A new set of parameters for AHFM was proposed and a paper regarding this work was published on Nuclear Engineering and Design (Pucciarelli, et al., 2016). The use of AHFM even in the energy equation was then implemented in the in-house code THEMAT. Simulations were performed in the frame of a BSc Thesis to which it was given support in the present work, reporting some interesting information. Its findings were reported in a paper presented at ICONE24, (Papp et al., 2016).
The outcome of this work suggests that the use of AHFM even in the energy equation may be a solid help for identifying the lacking ingredient in the CFD receipt. Nevertheless, further analyses were required. In particular, different sets of parameters were considered for dealing with a very wide range of flow conditions. A methodology for classifying cases and choosing the most suitable set was then developed.
Proposal of a fluid-to-fluid scaling rationale
The research group in Pisa is very active on this topic and in past works both aspects related to stability analysis and heat transfer phenomena were addressed. Nevertheless, though in the frame of stability analysis the approach was successful, concerning the heat transfer problem only limited results were obtained in past attempts. In the present work, the lessons learned by those attempts were elaborated and a scaling methodology was finally proposed. The same dimensionless parameters adopted in previous works were used; nevertheless, some were reinterpreted from a different perspective. In particular, the geometry similarity (in terms of the L/D parameter) was abandoned in favour of corresponding values of the dimensionless bulk enthalpy. This choice was due to the acknowledgement that different fluids may require different development lengths in terms of the L/D ratio due to their different thermodynamic properties. Four reference cases were chosen and reproduced by RANS analyses with four selected fluids: H2O, CO2, NH3 and R23. A
methodology for obtaining a scaling factor for the heat fluxes was deduced and sensitivity analyses showing its suitability were performed.
A paper reporting the performed work (Pucciarelli and Ambrosini, 2016) was the outcome of this phase of the research.
WORK PERFORMED DURING THE THIRD YEAR
Improvements in predicting capabilities with RANS turbulence models
The new modelling approach developed in the frame of the past years was improved widening its applicability range. By acknowledging the need of imposing variable values for the AHFM coefficients, a new relation depending on the dimensionless enthalpy, which proved to be a relevant quantity in the frame of the work concerning fluid-to-fluid scaling, was proposed. As a result, better predictions were obtained in a wide enough range of experimental conditions, in particular if compared with the ones returned by the models that were already available at the beginning of this work; sensitivity analyses were also performed showing very promising capabilities in a wide range of addressed cases, reducing the number of cases for which model capabilities are still limited. A paper summarising the performed work was published on Annals of Nuclear Energy (Pucciarelli and Ambrosini, 2017). A presentation resuming and comparing the latest results with the ones obtained in the previous works was given at the HFSCP2016 held in Sheffield in August, 2016.
Further steps in fluid-to-fluid scaling
DNS and LES calculations were performed adopting the scaling technique proposed during the second year by the RANS techniques; in particular, DNS calculations were performed in the
frame of a six month period of stage at the University of Sheffield, which cooperates with the
University of Pisa in the frame of the ongoing 2nd IAEA CRP on SCWR. Extremely good results in support to the scaling methodology were obtained in DNS applications; the trends returned by the simulant and reference fluid were in fact almost identical, while LES analyses showed reasonable but less accurate correspondence, probably also because of the differences in the imposed operating and boundary conditions.
However, the results collected until now support the proposed scaling methodology. The identified relevant quantities can be clearly correlated to observed physical phenomena contributing at creating a solid theoretical basis and suggesting a possible application of the theory in setting up look-up tables for heat transfer. As a final remark, together with further analyses to be performed adopting LES and DNS calculation, the scheduling of possible future experimental campaign would be definitively useful. The latest results were summarised in a presentation in the frame of a IAEA technical meeting held in Sheffield in August 2016.
The present work aimed at improving the understanding and the obtained results for the considered topic; with respect to the state-of-the-art at the beginning of the PhD, relevant steps forward were moved. The effect of the wall roughness on supercritical heat transfer was investigated together with the evaluation of the capabilities of CFD codes in dealing with bundle analysis. In addition, with the introduction of AHFM in the energy equation, better results were obtained on the CFD side and a promising scaling methodology was developed. Further analyses presently under completion by DNS and LES represent the final step of the research.
PERIOD OF STUDY ABROAD
The candidate spent a six month period of study at the University of Sheffield (UK) from October 2015 till the end of March 2016
TABLE OF THE STUDY PROGRAMME
No. Performed Activities Period Hours
1 Calcolo Scientifico per l'Ingegneria Dec 2013 -Feb 2014 20
2 Aspetti teorici ed applicativi del Metodo degli Elementi Finiti Jan-Mar 2014 24
3 English for writing and presenting scientific papers Dec 2013-Feb 2014 20
4 Relap5/SCDAPSIM User Training Workshop Jun 18-20 2014 24
5 Studio di materiale inerente il Corso di Impianti Nucleari I Nov 2014-Feb-2015 60
6 Introduzione alle equazioni differenziali alle derivate parziali Feb 2015 – Apr 2015 16
OVERALL LIST OF PUBLICATIONS RELATING THE DOCTORATE COURSE
Pucciarelli, A., Borroni, I., Sharabi, M., Ambrosini, W. 2014. Results of 4-equation turbulence models in the prediction of heat transfer to supercritical fluids. Nuclear Engineering and Design, Volume 281, January 2015, Pages 5–14
Ambrosini, W., Pucciarelli, A., Borroni, I. 2015. A methodology for including wall roughness effects in k-ε Low-Reynolds turbulence models Part I and Part II. Part I: Basis of the Methodology. Nuclear Engineering and Design 286 (2015) 175–194.
Pucciarelli, A. and Ambrosini, W., 2015. CFD prediction of heat transfer in rod bundles with water at a supercritical pressure. The 7th International Symposium on Supercritical Water-Cooled Reactors ISSCWR-7 15-18 March 2015, Helsinki, Finland. Published also on Nuclear Engineering and Science Radiation (Pucciarelli and Ambrosini, 2016).
Rohde, M., Peeters, J.W.R, Pucciarelli, A., Kiss, A., Rao, Y.F., Onder, E.N., Muehlbauer, P., Batta, A., Hartig, M., Chatoorgoon, V., Thiele, R., Chang, D., Tavoulais, S., Novog, D., McClure, D., Gradecka, M., Takasem K., 2016. A blind, numerical Benchmark Study on Supercritical Water Heat Transfer Experiments in a 7-Rod Bundle. The 7th International Symposium on Supercritical Water-Cooled Reactors ISSCWR-7 15-18 March 2015, Helsinki, Finland.
Pucciarelli, A., Sharabi, M.. and Ambrosini, W., 2016. Improving the Prediction of Heat Transfer to Supercritical Fluids in Upward Flow Cases by CFD Models. Nuclear Engineering and Design, Volume 297, February 2016, Pages 257-266.
Pucciarelli, A. and Ambrosini, W., 2016. Fluid-to-fluid scaling of heat transfer phenomena with supercritical pressure fluids: Results from RANS analyses. Annals of Nuclear Energy, Volume 92, June 2016, Pages 21-35.
Papp, V., Pucciarelli, A., Sharabi, M., Ambrosini, W., 2016. Use of Algebraic heat flux models to improve heat transfer predictions for supercritical pressure fluids. Proceedings of the 24th International Conference on Nuclear Engineering, ICONE24, June 26-30, 2016, Charlotte, NC, USA.
Pucciarelli, A., Ambrosini, W., 2017. Improvements in the prediction of heat transfer to supercritical pressure fluids by the use of algebraic heat flux models. Annals of Nuclear Energy, Volume 99, January 2017, Pages 58-67.
