Direct Numerical Simulation of Turbulent Heat Transfer with a Supercritical Fluid

Principal Investigator:
Eckart Laurien

Institute of Nuclear Energy and Energy Systems (IKE), University of Stuttgart (Germany)

Local Project ID:

HPC Platform used:
Hazel Hen of HLRS

Date published:

In the quest for efficiency enhancement in energy conversion, supercritical carbon dioxide (sCO2) is an attractive alternative working fluid. However, the heat transfer to sCO2 is much different in the supercritical region than the subcritical region due to the strong variation of thermophysical properties which bring the effects of flow acceleration and buoyancy. The peculiarity in heat transfer and flow characteristics cannot be predicted accurately by using conventional correlations or Reynolds-Averaged Naiver-Stokes (RANS) simulations based on the turbulence models. Therefore, direct numerical simulation (DNS) is used in this ongoing project at Institute of Nuclear Energy and Energy Systems (IKE) at the University of Stuttgart. In DNS, the Naiver-Stokes equations are numerically solved without any turbulence models. For this accurate and reliable approach, one needs to resolve very fine spatial and temporal scales, which ultimately results in the requirement of high-performance computing platforms, such as Hazel Hen at HLRS.

Methodology and results:

In this project, researchers at IKE aim to use DNS to investigate the role of turbulence in sCO2 heat transfer. For the investigations, a computational fluid dynamics (CFD) code based on finite volume method was used with a low-Mach number assumption. A small pipe was selected due to simpler geometry and its resemblance to the channel used in heat exchangers. The geometrical domain was discretized using hexahedral cells with a resolution ranging from 80 Million to 200 Million cells. The results from cooling of sCO2 in downward flow in a pipe are shown below. The streamwise mean velocity profile flattens out in the middle of the pipe, which results in decreased turbulence and deteriorated heat transfer. This profile does, however, become M-shaped nearer to an outlet or the location that both turbulence and heat transfer ultimately recover.

Figure 2 shows iso-surfaces of low- and high-speed streaks along with the iso-surface of the coherent turbulent structure for downward flow. The vortex (shown in red) starts reducing in the downstream direction and coherent structures start shifting away from the wall. The low-speed streaks (iso-surface in blue color) are suppressed and the strength of the coherent structures is also reduced. The high-speed streaks (shown by green color) stretched out in the streamwise direction close to the wall. Near to the outlet, turbulence structure reappears where M-shaped velocity profile was observed earlier.

Figure 3 shows the instantaneous fluctuations of velocity in the circumferential direction at three different locations in the near-wall region. The formation and breakdown of streaks can be observed in the inlet section at all three positions but after that streaks start stretching in the streamwise direction indicating ‘rod-like’ turbulence. The low-speed streaks disappear from the flow in the deteriorated heat transfer regime. The high-speed streaks become intense in their magnitude and start breaking down into small scales which ultimately results in the heat transfer recovery.

The DNS investigations from this project provided new information regarding the impaired heat transfer in sCO2. In addition to the knowledge gained, a comprehensive DNS database is developed for sCO2 which includes different flow and heat transfer conditions in a pipe. This database has been used to train the machine using the deep neural network (DNN) and it showed excellent predicting capabilities as shown in Figure 4, which was much better than the conventional correlation and RANS simulations.

Future Outlook:

As a next step, the new boundary condition for intermittent heat flux in both the spatial and temporal domains is being developed. This boundary condition will help simulations resemble the heat flux in solar, nuclear and other realistic applications. Additionally, the next phase of the project aims to deploy a high-order CFD code with fully compressible equations using the highly accurate equation of state. This new phase will provide a high-fidelity simulation while the code’s high scalability will allow the use of thousands of cores at HLRS.

References and further reading:

1. S. Pandey, X. Chu, E. Laurien, “Direct numerical simulation database for supercritical carbon dioxide”, Institute of Nuclear Technology and Energy Systems (IKE), University of Stuttgart, Stuttgart, Germany (2018).

2. S. Pandey, X. Chu, E. Laurien, “Investigation of in-tube cooling of carbon dioxide at supercritical pressure by means of direct numerical simulation”, International Journal of Heat and Mass Transfer, Volume 114, Pages 944-957, ISSN 0017-9310 (2017).

3. X. Chu, E. Laurien, D.M. McEligot: “Flow stratification in the horizontal pipe with heated supercritical CO2”, The Journal of Supercritical Fluids 116, Pages 172-189 (2016).

4. X. Chu, W. Chang, S. Pandey, J. Luo, B. Weigand, E. Laurien, “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, Volume 123, Pages 629-636, ISSN 0017-9310 (2018).

5. X. Chu, E. Laurien, D. M. McEligot, “Direct numerical simulation of strongly heated air flow in a vertical pipe”, International Journal of Heat and Mass Transfer, Vol. 101, Pages 1163–1176 (2016).

Scientific Contact:

Sandeep Pandey (M.Tech.)
Institute of Nuclear Technology and Energy Systems (IKE)
University of Stuttgart
Pfaffenwaldring 31, D-70569 Stuttgart (Germany)
e-mail: sandeep.pandey[at]

July 2018


Tags: Universität Stuttgart HLRS CSE