# Project A1: Thermo-hydraulic flow in a sudden expansion

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

## 1. Scientific case for the project

### 1.1 Background

Flow separation at discontinuous changes of the cross sectional geometry in vertically arranged coolant ducts is of central importance in many devices, such as the in- and outflow of thermal storage containers, heat exchanger bundles, manifolds and collectors of power conversion systems, as well as highly heat loaded surfaces like in concentrating solar power plants. In technical applications of this type large temperature differences generally create sizable density stratification which can drastically limit the performance and the life time of the device.
The phenomenon has been investigated repeatedly for unity Prandtl number fluids such as water. Liquid metals, however, behave differently due to their considerably lower Prandtl number. The high specific thermal conductivity introduces a scale separation between thermal and viscous boundary layers. Moreover, most technical flows are turbulent and feature multi-scale flow structures for velocity and temperature fluctuations which makes the prediction of turbulent transport of momentum and heat particularly challenging. On top of that, buoyancy substantially affects the turbulence structure so that the accumulation of all these effects necessitates an anisotropic description of the turbulence in both the momentum and the temperature field [1] to model and predict the thermal load and the capacity for heat removal.
The most generic configuration featuring the above issues is the vertical backward facing step (BFS) illustrated in Fig. 2. This flow has been widely investigated in the iso-thermal case and several transitional phenomena have been discovered like vortex shedding, roller patterns and Kelvin-Helmholtz-instabilities [2,3]. Studies with imposed heat flux q'' [4] are substantially less frequent, and those of mixed convection [5] rare. Compared to the simple BFS problem, this feature substantially alters the dynamics of the overall heat exchange which, e.g., is the key parameter for the absorber of a concentrating solar power plant. |
Fig. 2: Sketch of the ther-mally affected backward facing step (TBFS) flow. |

### 1.2 Most important goals of the planned work

The major challenge of the turbulence modeling for the thermally affected BFS (TBFS) is to develop and validate anisotropic momentum and heat flux models which may be used in the future in commercial codes. Additionally, validity limits of existing model assumptions shall be assessed experimentally and regimes of transitional flow identified and analyzed. To this end the TBFS will be attacked with the following tripod strategy: A benchmark experiment will be conducted using liquid sodium. Since sodium has the largest thermal conductivity among the liquid metals it limits the geometric dimensions of the test section size (current estimates are a=60 mm, l=10a, h=0.25a) and simultaneously allows to apply conventional measurement equipment, such as magnetic permanent probes (MPP) [6], thermocouple rakes, and Ultrasound Doppler Velocimetry (UDV) to record the mean velocity and its fluctuations as well as the temperature distribution inside the duct. The experiment shall provide a complete set of reference data and will identify deficits of physical modelling assumptions. The experiment is accompanied by two types of numerical approaches.The Reynolds averaged Navier-Stokes (RANS) approach is most relevant for applications since it allows to compute technical flows at high Reynolds numbers efficiently by introducing a substantial amount of modelling. However, it has several deficits in treating anisotropic turbulent transport even in the momentum field. While some progress has been achieved in recent years by means of Algebraic Stress Models (ASM) significant deficits remain in the treatment of the turbulent heat fluxes. Modelling attempts are proposed in the literature based on transport equations for the temperature variance and its dissipation, but these transport equations contain triple correlations which are not accessible experimentally.

A remedy is to derive such relations from highly resolving unsteady simulations such as Direct Numerical Simulation (DNS) for the temperature field. This kind of simulation in fact is the only way to deduce these correlations and to assess the model assumptions of RANS in detail. Furthermore, scenarios of transition between laminar and turbulent flow, between free, mixed and forced convection, etc. can be investigated and stability limits defined. For higher Reynolds numbers, only Large Eddy Simulation (LES) is possible. This will be investigated as well, including models for the near-wall flow by means of sophisticated wall functions and hybrid LES/RANS methods [7].

## 2. Existing competencies and infrastructure

The proposed project is a concerted action of KIT with TUD. At the Institute for Neutron Physics and Reactor Technology (INR) of KIT the Karlsruhe Sodium laboratory (KASOLA) is currently erected. KIT has long term experience in the development of measurement techniques for liquid metals [8,9] and has conducted numerous experiments over many years [10,11] covering a large spectrum of applications, related to fusion technology, nuclear safety, generic heat transfer for rapid cooling of steel bands, efficient heat removal systems for material science, etc. The group also has long term experience in operating sodium systems at high safety standards. Own thermo-hydraulic measurements and calculations of the flow along a heated rod in an annular cavity [12] demonstrated the deficits of current RANS models and triggered the project proposed here.The group at the Institute of Fluid Machinery of KIT-CS has a long tradition in simulating and modeling laminar and turbulent flows, also with RANS [13,14], as well as two-phase and reacting flows [15]. The group developed an own parallel code which can solve high Reynolds number flows with a block structured Finite Volume scheme.

The Institute of Fluid Mechanics at TUD has long term experience in DNS and LES [16], as well as hybrid methods [7]. Recently, a new code was developed for efficient parallel simulation using immersed boundaries on Cartesian coordinates, for laminar and turbulent flows involving heat transfer, buoyancy, and MHD which is routinely used for liquid metal flows [17]. Buoyancy-driven flows have been investigated over many years [18,19]. The researchers of both numerical groups collaborate successfully since more than a decade in the framework of SFB 606.

## 3. Resource planning and Budget Justification

Due to the complexity of the experimental set-up and the challenges of operating with liquid sodium the project requires an experienced scientist at KIT who will be in charge of the experimental design, the facility operation, the realization of the measurement campaigns, and the analysis of experiments and simulations. The RANS computations and model developments will be conducted by a PhD student at KIT-CS. The DNS, LES, and Hybrid simulations, as well as the related modelling developments and the physical analysis will be performed by a PhD student at TUD.
__Links:__ Closely related to B1 and B2, and a strong involvement of YIG is required.

## References (general references before, own references behind the line break)

[1] Grötzbach, G., 2011, Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer, Nuclear Engineering & Design, Vol. 241(11), 4379-4390.[2] Le, H., Moin, P. & Kim, J., 1997, Direct numerical simulation of turbulent flow over a backward-facing step, J. Fluid Mech., Vol. 330 , 349 – 374.

[3] Barri, M. & Andersson, H.I., 2011, Turbulent flow over a backward-facing step. Part I: Effects of anti-cyclonic system rotation, J. Fluid Mech., Vol. (665), 2010, 382 – 417.

[4] Avancha, R.V.R., Pletcher, R.H., 2002, Large eddy simulation of the turbulent flow past a backward-facing step with heat transfer and property variations, Int. J. Heat Fluid Flow, Vol. 23, 601-614.

[5] Abu-Mulaweh, H.I., Chen, T.S., Armaly, B.F., 2002, Turbulent mixed convection flow over a backward-facing step––the effect of the step heights, Int. J. Heat Fluid Flow, Vol. 23, 758-765.

[6] Kapulla, R., 2000, Experimentelle Untersuchung von thermisch stratifizierten und unstratifizierten Mischungsschichten in Natrium und Wasser. Dissertation 13430, Eidgenössische Technische Hochschule Zürich, Schweiz.

[7] J. Fröhlich, D. von Terzi, 2008, Hybrid LES/RANS methods for the simulation of turbulent flows, Progr. Aerospace Sci., Vol. 44, 349-377.

[8] D. Buchenau, S. Eckert, G. Gerbeth, R. Stieglitz, M. Dierckx, 2011, Measurement technique developments for LBE flows, Journal of Nuclear Materials, Vol. 415, 396-403.

[9] Hillenbrand, M.P., Stieglitz, R., Neitzel, G.P., 2012, Detection of flowing liquid metal surface using the DLP measurement technique. Experiments in Fluids, Vol. 52, 179–192.

[10] Loges, A., Baumann, T, Marocco, L., Wetzel, T, Stieglitz, R., 2011, Experimental Investigation on Turbulent Heat Transfer in Liquid Metal Along a Heated Rod in a Vertical Annulus, Proc. 14th International Topical Meeting on Nuclear Reactor Thermalhydraulics NURETH-14, 25th-30th Sept. Toronto, Canada, Paper ID A12-2-439.

[11] R. Stieglitz, 2007, Liquid Metal Thermal Hydraulics (chapter 10), OECD/NEA, Handbook on Lead-bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-hydraulics and Technologies, ISBN 978-92-64-99002-9, OECD (2007).

[12] J. Zeininger, 2009, Turbulenter Wärmetransport in flüssigem Blei- Wismut an einem vertikalen Heizstab im Ringspalt, Dissertation Universität Karlsruhe, Fakultät Maschinenbau.

[13] F. Magagnato, 1995, Untersuchung von linearen und nichtlinearen Wirbelviskositätsmodellen. Dissertation TH-Darmstadt.

[14] F. Magagnato, 1999, Unsteady flow past a turbine blade using non-linear two-equation turbulence models, Third European Conference on Turbomachinery: Fluid Dynamics and Thermodynamics, Vol. A, 221-230.

[15] F. Magagnato, B. Pritz, H. Büchner, M. Gabi, 2005, Prediction of the Resonance Characteristics of Combustion Chambers on the Basis of Large-Eddy Simulation, J. Thermal Sci. 14, 156-161.

[16] J. Fröhlich, 2006, Large Eddy Simulation turbulenter Strömungen, Teubner.

[17] S. Heitkam, S. Schwarz, J. Fröhlich, 2011, Simulation of the influence of electromagnetic fields on the drainage in wet metal foam, PAMIR conference, Proc. 891-895.

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

[19] 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.