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Progress on coolant routing and MHD M. S. Tillack UC San Diego ARIES Project Meeting 23-24 January 2012
Action Items From our previous meeting: Calculate various forces in key parts of the flow circuits and compare (inertia, viscosity, MHD body force, gravity). Develop collaboration with KIT. Document estimates of 3D currents in various elements. Check magnetic field strength near ring headers. Consider design alternatives, such as using full-width access channels or further exploitation of channel segmentation. New: Stagnation in curved first wall channels. Rib cooling.
4. Poloidal magnetic fields along the flow path • This issue arose in relation to the field strength at external manifolds. • We developed a MATLAB routine to evaluate an arbitrary set of rings. • For now, we are using ARIES-AT for our reference case. (Dahlgren et al.) 14 13 8 12 9 10 11 Internal manifold Field entry/exit External manifold
Poloidal Field Strength in ARIES-AT Our result (including plasma) (T) Dahlgren 2006 The plasma is modeled as a discrete ring
Radial and Axial Magnetic Fields for ARIES-AT Radial Field Strength (T) Axial Field Strength (T)
Fields along liquid metal flow path Not only are there large poloidal fields, but also significant gradients along and within the pipes.
6. Stagnation can occur in our FW channels • First order approximation to pressure gradient in an insulated duct. • In a curved duct, Ha varies from front to back. So u also varies. • The effect can be approximated by u~a (L. Buehler and L. Giancarli, “Magneto- hydrodynamic flow in the European SCLL blanket concept,” FZKA 6778, 2002). • For constant volume flow rate, the pressure gradient increases by 50%. • The full conduction/convection heat transfer equation with transverse varying velocity was solved by finite difference to determine the magnitude of this effect on heat transfer.
Convective heat transfer with laminar flow Energy balance equation (internal energy e=rCpT): Exact solution for constant velocity on a semi-infinite plane is equivalent to transient 1D conduction: slug Example slug result: T vs. z/v for several x, q”=0.2 MW/m2, v=4.2 m/s,L=8.3 m
Effect of stagnation on wall temperatures Exit temperature vs. depth Surface temperature vs. length Varying flow Varying flow Slug flow Slug flow • Peak velocity is 6.3 m/s for a 4.2 m/s average, q”=0.2 MW/m2 • Dp is 50% higher than slug flow case. • Peak surface temperature increases by only about 20˚C.
7. Evaluation of blanket internal rib cooling • Internal ribs can help stiffen the box, enabling thinner walls. • The slug flow model (transient 1D conduction) was used to estimate DT with a 5-mm volumetrically heated rib 10 W/cm3 11 cm/s 8.3 m long 5 mm thick • The maximum temperature increase in the rib is <40˚C above the bulk coolant temperature. • In the current reference design we do not employ internal ribs.
3. Semi-empirical formulation of 3D MHD effects Dp3d = k N (rv2/2) where N = Ha2/Re, and k is a semi-empirical constant (z=kN)` • For flows with geometrical changes in a uniform magnetic field 0.25 < k < 2. • For a change in transverse field strength k~0.1–0.2 (depending on the abruptness of the change in B). • For an inlet or outlet manifold, Smolentsev et al used k=1.5. • Depends on wall conductance, pipe shape (e.g. circular or rectangular) and other details. I.R. Kirillov, C.B. Reed, L.Barleon, K. Miyazaki, “Present understanding of MHD and heat transfer phenomena for liquid metal blankets, “Fusion Eng and Design 27 (1995) 553-569. S. Smolentsev, C. Wong, S. Malang, M. Dagher, M. Abdou, “MHD considerations for the DCLL inboard blanket and access ducts,” Fusion Eng and Design 85 (2010) 1007–1011.
1. Forces acting upon the coolant (F/A) FW blanket inertia gravity wall shear 3D MHD ru2 rgL suB2L/Ha kN (ru2)/2 160,000 8x105 190,000 3x106 100 8x105 475 7x105 u L g A
A note about “viscous drag” in MHD flows within insulated ducts Current distribution Velocity profile along z boundary layer if B=constant, The magnetic field alters the velocity profile, creating enhanced wall friction. The pressure gradient is the same as the body force in the core region. No net “body force”.
5. Design alternatives • The alternative manifolding concept presented last summer required many vessel penetrations, which are undesirable. • We continue to seek design solutions for the SCLL blanket that use manifolds inside the TF coils with minimum MHD uncertainties. • One powerful idea (credit to FN) is to keep the velocity in all manifolds low, and accelerate in a 2D MHD expansion. • Flow control can be applied using orifices or straight channel MHD control. 180˚ bend at the top
To keep 3d effects low, maintain constant Good Bad Ugly ARIES-AT B B
2. Plan for KIT collaboration • Visit to KIT on Dec. 5, 2011. • Meetings with Hesch, Buhler, Koehly (and others). • Agreement to work together on MHD issues, with an emphasis on manifolds. • Koehly assignment to begin in early 2012: • Configuration of flow loops • MHD issues and R&D needs • TOFE paper planned
Summary of SCLL power core findings • More detailed analysis of various MHD flow concerns has been performed as compared with the ARIES-AT study. • MHD pressure drop can be low (~0.2 MPa), provided 3D effects are avoided. • Designs are possible with only one source of 3D MHD: the manifolds. • The pressure drop and flow distribution caused by this 3D source are highly uncertain, requiring R&D (and a fully-detailed design). • Primary stresses were analyzed for various configurations (Wang) • For the case of 0.2 MPa pressure drop, a lot of design flexibility exists.(1 MPa may require some design changes). • We used ARIES-AT (same as ACT-1b) builds to develop design options. • Volume fractions can be determined from these designs, and then used to fine tune the builds. Volume fractions have changed only a few percent.
Next Steps for MHD and thermal hydraulics • Provide final guidance on MHD Dp. • Need to select the FW channel depth. • Need to choose k for inlet/outlet manifolds • Provide temperature boundary conditions for thermal stress analysis. • Need q” along scalloping (in toroidal direction). • Start analysis of DCLL blanket.