MODELING STATUS Presented by Sergey Smolentsev - PowerPoint PPT Presentation

MODELING STATUS Presented by Sergey Smolentsev ======================================== - Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model - “HIMAG”, HyPerComp – UCLA code for simulation LM MHD flows - Modeling LM MHD flows using 3-D thin-shear-layer approximation - Implementation of different MHD formulations ======================================= Electronic APEX Meeting 20 August 13, 15 2002 1

Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model • Calculations have been done for OB FW Flinabe flow, which take into account poloidal distribution of the heat flux and volumetric heating 100 120 80 T-Tinlet, K T-Tinlet, K 80 60 Average surface heat flux: 1.4 MW/m2 (parabolic) Average surface heat flux: 1.4 MW/m2 Average neutron heating: 7 MW/m2 40 (uniform) (parabolic) 40 Average neutron heating: 0 Surface Temperature Surface Temperature Bulk Temperature Bulk Temperature 20 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Distance from the inlet, m Distance from the inlet, m BEFORE AND AFTER 2

Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model • Calculations have been done to estimate the effect of turbulence reduction by a magnetic field in the blanket flows. 280 Calculations have been done to estimate turbulent heat transfer reduction by a magnetic field in a Flibe blanket flow using the “K-epsilon” model. 240 The flow parameters were chosen as follows: U=5 m/s (flow velocity); h=1 cm (channel width); 200 Duct Flibe Flow: Nu h vs. x / h B=10 T (magnetic field). Nu h h=1 cm (width); U=5 m/s; B=10 T Re=7000, Ha=0 The Nusselt number built through h (the channel 160 Re=7000, Ha=10 width), Nu h , was calculated for two cases: with a magnetic field and without a magnetic field. The difference in the fully developed Nusselt number 120 Dittus-Boelter formula between these two cases is about 10%. The case without a magnetic field agrees very well with the calculations based on the Dittus-Boelter formula. 80 0 10 20 30 40 50 x / h 3

Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon” model • Special calculations have been done to estimate turbulence suppression by a magnetic field in the spiral blanket flow (Igor Sviatoslavsky). ZONE I ZONE III Midplane channel: Side channels Channel dimension- 14 cm radial Channel dimension-14 cm in toroidal direction poloidal height- 6.7 cm at FW and 4.2 cm at shaft poloidal height same as above Length along FW 30cm length of channel 30 cm Magnetic field paralel to flow Magnetic field perpendicular to flow and varies Inboard 7.9 T, outboard 4.7 T Inboard from 8.3-7.9 T Average velocity 3 m/s outboard 4.7-4.2 T Average velocity 3 m/s ZONE II The magnetic field is perpendicular to the flow. The effect of Extremities channel: the magnetic field on the flow is pronounced. I calculated two Channel dimension-14 cm radial cases: with the Hartmann effect (there is a magnetic field poloidal height-6.7 cm at FW and 4.2 cm at shaft Length along FW 23 cm component perpendicular to the wall), and Magnetic field as above without the Hartmann effect (the magnetic field is completely Average velocity 3.1 m/s spanwise). The results are the following. The magnetic field is parallel to the main flow direction. This means 1. With the Hartmann effect: f=0.00487, Nu_fd=380. The that the effect of turbulence suppression by a magnetic field is weak higher value of f is explained by the Hartmann effect. comparatively to the case with the magnetic field perpendicular to the flow. The friction factor, f, and fully developed Nusselt number, 2. Without the Hartmann effect: f=0.00223, Nu_fd=365. Nu_fd, without the field are 0.00451 and 609 respectively. With the In both cases the turbulence suppression is very pronounced field, f=0.00446, and Nu_fd=605. This means that the effect of the and heat transfer reduction is by a factor of almost two. magnetic field on the flow and heat transfer is negligible. However, there is only neutron heating in Zone III, so that Nu number results are not applicable here. 4

Modeling of low-conductivity fluid flow and heat transfer using “K-epsilon • New data on heat transfer from the FliHy experiment are being incorporated into the “K-epsilon” model to take into account waviness effect on heat transfer through the turbulent Prandtl number distribution. Preliminary analysis shows the heat transfer enhancement by 1-2 times. SMOOTH INTERFACE (SUBCRITICAL) WAVY INTERFACE (SUPERCRITICAL) Heat transfer reduction due to the Heat transfer improvement due to - reducing the blockage effect blockage effect - breaking the surface - turbulence generation by the waves The results will be reported at the APEX Meeting in Princeton 5

“HIMAG”, HyPerComp – UCLA code for simulation LM MHD flows • S T A T U S S U M M A R Y 3-D unstructured grid code for simulation free surface MHD flows with Level Set Method for tracking the interface TASK STATUS I: Flow solver development Has been written and validated against canonical test problems ϕ -formulation, B-formulation have been II: MHD model development implemented and tested (Ha up to 10 3 ) for closed channel flows. Preliminary GUIs have been developed for pre- III: Graphical interface and postprocessing. IV: Solution acceleration technique Conjugate gradient method for PPE has been implemented. Parallelization will be started soon. V: Free surface models Level Set Method is being debugged. VI: Validation and accuracy Has been validated against closed channel flow cases. Benchmarks for free surface flows have been chosen. 6

“HIMAG”, HyPerComp – UCLA code for simulation LM MHD flows • Near-future plans 1. Jet flows under NSTX conditions 2. Chute-type flow in a 3-component B-field with the normal component varying in space 3. ARIES RS FW flows without penetrations 4. ARIES RS FW flows with penetrations 7

Modeling LM MHD flows using 3-D thin-shear-layer approximation • Model description and its applications 3-D thin-shear-layer equations for flows of conducting fluids in a magnetic field have been derived in orthogonal body-oriented coordinates. Unlike the classic boundary-layer-type equations, present ones permit information to be propagated upstream through the induced magnetic field. Another departure from the classic theory is that the normal momentum equation keeps the balance between the pressure gradient term, and those related to gravity, centrifugal forces, and Lorentz force. Thus, the normal pressure variations are allowed. The model describes basic 3-D effects due to the wall curvature and spatial variations of the applied magnetic field. The model can be applied to the following open-surface MHD flows: - flows with rotational symmetry; - chute-type flows in a gradient magnetic field (some restrictions); - flows around penetrations (some restrictions). At present, the model is being modified to include turbulence effects (NSTX case). 8

Modeling LM MHD flows using 3-D thin-shear-layer approximation • UCLA-HyPerComp benchmark case for 3-D open surface flow 1 0.9 0.8 0.7 0.6 y / h 0 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 x / h 0 Liquid flows down over a “bottle- Flow without a magnetic field. Velocity vector plot in the x - y plane. Changes neck” surface of revolution are due to the gravity force and geometrical variations. 1 1 = ν = Re U h / 23500 0.9 0.9 , 0 0 0.8 0.8 = = 2 Fr U /( gh ) 5 . 0 0.7 0.7 0 0 0.6 0.6 y / h 0 = σ νρ 0 . 5 = Ha B h [ /( )] 8500 y / h 0 0.5 0.5 0 0 0.4 0.4 = µ σ = Re U h 0 . 07 0.3 0.3 m 0 0 0 0.2 0.2 0.1 0.1 0 0 0 5 10 15 20 0 5 10 15 20 x / h 0 x / h 0 9 Flow with a magnetic field. Left: velocity vector plot. Right: induced magnetic field counter lines.

Modeling LM MHD flows using 3-D thin-shear-layer approximation • MHD flows around penetrations: problem formulation y � Boundary conditions at the Magnetic inlet/outlet, free surface and at the field solid wall are as usual Boundary conditions at Z= ±∞ � correspond to the undisturbed flow flow � Kinematic free surface condition x is used for tracking the free surface The approach can be used as an alternative to the HIMAG code or ∂ ∂ ∂ h h h + + = V | V | V | as a benchmark case. = = = 1 x h 3 x h 2 x h ∂ ∂ ∂ t x x 2 2 2 1 3 10