# Project B1: Transition between free, mixed and forced convection

PI: Robert Stieglitz (KIT)Partners: KIT-CN, KIT-CS, TUD

## 1. Scientific case for the project

### 1.1 Background

Forced convective heat transfer is the preferred mode for the operation of technical components facilitating the most compact and economic design.
Fig. 7: Sketch of the transitional flow test module to be integrated in the KASOLA loop of KIT. |
Mixed and buoyant convective heat transfer, however, also plays a crucial role since it can occur during start-up and shut-down, or due to hazards. The transition from forced to mixed convection and from there to buoyancy-dominated convection in fact is of central importance for the safe operation of surfaces with high heat load. Liquid metal flow of this type occurs in thermal storage systems, casting moulds, nuclear physics targets, solar receivers, etc. Most pronounced are these transitional effects for a heated section with large extension in the direction of gravity. A direct coupling of the velocity field with the temperature field only prevails with forced convection where the temperature acts as a passive scalar. Even at moderate flow rates a transition from forced to mixed convection occurs in case of high specific heat load (q“ > 1MW/m2), more precisely if the ratio of hydraulic Reynolds number to square root of Grashof number drops below unity. The transition between the different flow regimes so far has been investigated only rarely. Especially for liquid metals with high thermal conductivity the existing literature is sparse and unsatisfactory as pointed out in [1,2]. |

## 1.2 Most important goals of the planned work

Project B1 will be concerned with a vertical slender cavity subjected to a very large horizontal temperature gradient super-imposed to a main flow as sketched in Fig. 7. Different Nusselt number ranges will be investigated with relevance for various applications. To cover a wide range of applications a modular structure will be conceived, as depicted in the figure, and integrated in the KASOLA facility of KIT. The goal of the project as a whole is to provide essential steps relevant for all liquid metal application. Focus will be the study of the different flow regimes, and particularly the conditions under which these occur, depending on flow rate, heat load, and geometry. In contrast to project A1, project B1 investigates a flow without separation and shall account for the conjugate heat transfer inside the walls. Furthermore, the behaviour of a typical system into which such an element is integrated will be investigated. The goal here is to provide technological answers on how such an installation has to be operated, e.g. during start-up, and how the system has to be handled in case of accidents. The latter also requires reliable CFD prediction which hence will be developed here to complement the experiment, but also in its own right. The results of project A1 concerning turbulence modelling will be used in B1 and advanced for this new setting. The development of fast CFD tools which can be connected to system analysis tools playing the central role in the safety assessment and in the licensing of the plant is one central output of this project. The project closes the gap between projects A1 and A3 and requires intense cooperation with the YIG on measurement technologies.The particular goal of the experimental campaign is to provide high-precision experimental data for the heat transfer in turbulent liquid metal flow when simultaneously the Reynolds number and the Rayleigh number are high. Moreover, the program aims to identify the transition regions as a function of the leading parameters for different flow configurations. Nusselt number correlations in each of them will be determined to be used in system codes like RELAP, TRACE to assess the plant dynamics at all individual stages of its operation with the aim of a licensing.

The experimental approach is complemented by a numerical program. A constant turbulent Prandtl number approach cannot be applied for modelling, since the thermal and the velocity field behave very differently. DNS simulations rather show that the turbulent Prandtl number is a function of the mean flow rate and the position. Turbulence will hence be represented by nonlinear stress-strain correlations. These appear to be the best compromise with respect to accuracy and numerical stability and are suitable for RANS and URANS computations and higher modelling approaches like Reynolds stress models are notoriously numerically unstable. Assessment of turbulent heat flux models based on the experimental data is an important part of this work. Modelling results from project A1 will be employed and will be enhanced with appropriate extensions if required. Furthermore, other parts of the system will be simulated in order to provide more detailed information on these components and on the reaction of the system to the transition from one regime to another. In addition to the RANS simulation, DNS and LES will be conducted in order to validate and complement the experimental data with correlations which are difficult or expensive to obtain experimentally. Due to the high Reynolds and Rayleigh numbers these simulations will be extremely demanding and conducted at the edge of what will be possible at the time of execution. On the other hand, extremely valuable data is to be expected upon completion.

## 2. Existing competencies and infrastructure

At KIT-INR the experiments will be performed at KASOLA, the Karlsruhe Sodium laboratory. The group at KIT-CN has profound experience in sodium metal heat transfer experiments and stability investigations [3,4,5]. The experiments conducted have been devoted to a large variety of applications mainly in the energy transfer sector such as for fusion technology, nuclear safety but also to generic transfer questions as rapid cooling of steel bands or efficient heat removal systems for structure of matter research by means of liquid metals. KIT has long term experience in operating sodium systems at high safety standards and is one of the very few places in Germany where such an experiment can be run.The experiments will be complemented with numerical calculations performed by Institute of Fluid Machinery of KIT-CS. This group has a sound research record in numerical fluid mechanics [6]. They successfully investigated steady as well as unsteady flows of a large variety covering RANS, LES and also Hybrid-LES approaches. The focus has always been on developing fast and accurate numerical schemes for the prediction of complex flow fields.

J. Fröhlich of TUD has been studying natural convection since his PhD [7] and still has an activity on this topic [8]. The code PRIME [9] is an extremely efficient and versatile code appropriate for the given task. It is currently already being used for computations of forced convection of liquid metals and for turbulent heat transfer.

## 3. Resource planning and Budget Justification

The envisaged project requires due to the complexity of the experimental set-up and the operational aspects of handling liquid sodium an experienced scientist at KIT/INR, who will be in charge of the experimental design, the operation of the facility and a proper run of the measurement campaigns for a period of 45 month. This scientist will also be responsible for data acquisition, data reduction and will coordinate the physical analysis of experiments and simulations. The numerical computations on RANS basis are conducted at KIT-CS by a PhD student during the entire period. Additionally, a well-experienced scientist of TUD will contribute to the different packages WP2 to WP3 in the scope of 15 person months to perform highly-resolved LES or DNS computations for selected scenarios.
__Links:__ Close relations to A1, A3, B2 and the YIG are obvious.

## References

[1] G. Grötzbach, 2011, Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer, Nuclear Engineering & Design, Vol. 241(11), 4379-4390.[2] I. Otic, G. Grötzbach, M. Wörner, 2005, Analysis and modelling of the temperature variance equation in turbulent natural convection for low-Prandtl-number fluids, J. Fluid Mech. 525, 237 – 261.

[3] U. Müller, R. Stieglitz, 2009, The response of a two-scale kinematic dynamo to periodic flow forcing, Physics of Fluids, Vol. 21, DOI:10.1063/1.3097002.

[4] U. Burr, L. Barleon, P. Jochmann, A. Tsinober, 2003, Magnetohydrodynamic convection in a vertical slot with horizontal magnetic field, J. Fluid Mech., Vol. 475, 108-113.

[5] F. Roelofs, et al., 2008, European research on HLM thermal-hydraulics for ADS applications, J. Nuclear Materials , 376(3), p. 401-404.

[6] F. Magagnato, B. Pritz, M. Gabi, 2007, Calculation of the VKI turbine blade with LES and DES, Journal of Thermal Science, Vol. 16, No. 4, pp. 321-328.

[7] J. Fröhlich, R. Peyret, 1990, Calculations of non-Boussinesq convection by a pseudospectral method, Comp. Meth. Appl. Mech. Eng., Vol. 80, 425-433.

[8] O. Bouloumou, E. Serre, J. Fröhlich, 2009, A 3D Chebyshev-Fourier algorithm for convection equations in low Mach number approximation, Eur. J. Comput. Mech., Vol. 18, 607-625.

[9] T. Kempe, J. Fröhlich, 2012, An improved immersed boundary method with direct forcing for the simulation of particle laden flows, J. Comput. Phys, in press

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