Scaling Analysis

By Mary Weaver,2014-09-30 04:41
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Scaling Analysis

    Comparative scaling analysis for ITER and DEMO in the Thermofluid / MHD area

    (mostly for poloidal flows !)

    Sergey Smolentsev


    A. Definition of the dimensionless parameters and their role

    Uam1. Reynolds number, Re;

    In purely hydrodynamic duct flows is responsible for the flow development length. It is also used as a Re

    criterion of laminar to turbulent transition. In MHD flows, using only to estimate the flow development Re

    length or to judge about the flow regime is not sufficient.

    2. Hartmann number, Ha;Bb0?,

    2HaIt is the most important MHD parameter. is a ratio of the electromagnetic force to the viscous force.

    3gTaGr;3. Grashoff number, 2

    The most important parameter that characterizes buoyancy effects in the flow. It is strongly affected by the

    3aTdimension since enters the formula for Gr as . Both and the temperature difference that drives the aaa

    natural convection should be properly defined in accordance with the flow physics.

    Gr4. r; 2a(HaReb~

    This is another dimensionless parameter that characterizes contribution of the buoyancy effects. It is constructed in a special way to take into account the forced flow effect, the MHD effect and the influence of the duct aspect ratio. It appears that this parameter is the best characteristics for the mixed MHD convection. When doing scaling analysis, this parameter should be considered first. See, S. Smolentsev, N. B. Morley, M. Abdou, R. Munipalli, R. Moreau, Current Approaches to Modeling MHD Flows in the Dual Coolant Lead Lithium Blanket,

    Magnetohydrodynamics, 42, 225-236 (2006).

    2Ha5. Interaction number, N; Re

    It is the ratio of electromagnetic to inertia forces. It is especially important when considering flow development effects but not important for fully developed flows.

    Ha6. Re

    It is often used in Magnetohydrodynamics to judge about the flow regime (laminar or turbulent). Usually if this parameter is higher than its critical value (about 1/200), ordinary 3-D turbulence is suppressed but 2-D MHD may exist. When analyzing turbulence, either 2-D or 3-D, this parameter should be considered together with another parameter that stands for the wall electrical conductivity, since in electrically conducting ducts, stronger turbulence suppression will occur due to Joule dissipation.

    Ha7. Gr

    HaHaIt is similar to but unlike this parameter, which is used in the analysis of forced MHD flows, applies to ReGr

    buoyancy driven MHD flows.

    Gr8. Re

In ordinary flows, it is a measure of the influence of free convection in comparison with that of forced

    convection on a flow. In MHD flows, parameter seems to be more relevant. r

9. Something related to the electrical conductivity

    twwcIn duct flows with electrically conducting walls, a relevant parameter is the wall conductance ratio, . ;wb

    However, in the flows with FCI, using just would not be correct, since the electric circuit is closed through cw

    bFCIc;both the Fe wall and the FCI. A parameter suggested by Neil Morley is . FCItFCI

10. Aspect ratio, a/b

    The aspect ratio does not play a significant role, providing it is close to 1.

11. Dimensionless flow length, L/aand L/b

    It is an important parameter when justifying if the flow is developing or fully developed


    b is half of the duct dimension parallel to the magnetic field (toroidal dimension), m

     is half of the duct dimension perpendicular to the magnetic field (radial dimension), m a

L is the channel length, m

     is the applied magnetic field, T B0

     is the fluid bulk velocity, m/s U0

    qa* is the temperature difference, which drives natural convection, K T;k

     2 is the neutron wall loading, W/m q*

     is the fluid thermal conductivity, W/m-K k

     2g is acceleration due to gravity, m/s

is the fluid thermal expansion coefficient, 1/K

     is the fluid electrical conductivity, S/m

     2 is the fluid kinematic viscosity, m/s

     3 is the fluid density, kg/m

    B. Physical properties of PbLi

k = 20 W/m-K

    -4 = 1.8210 1/K

    6 = 0.710 S/m

-72 = 1.0810 m/s

     3 = 9300 kg/m

    C. Dimensional blanket parameters

Parameter ITER DEMO Outboard/Inboard

    2a 0.066 m 0.22 m

    2b 0.12 m 0.22 m

    L 1.66 m 2 m

    22q0.78 MW/m 3.08/1.75 MW/m*

    U 0.1 m/s 0.06/0.04 m/s* 0

    B4 T 4/10 T 0

    * 0.06 was taken from the old DEMO data set for the outboard blanket. The new one may be different.

     Velocity in the inboard blanket can also be different (lower). We use 0.04 m/s at the inboard.

    D. Dimensionless parameters

Parameter ITER DEMO Outboard/Inboard

    Re 30500 61000/40600

    Ha 6350 11640/29100

    91212Gr 7.2210 3.5210/210

    r11.1 70.3/41

    N 1320 2217/20860

    Ha/Re0.208 0.190/0.716 577Gr/Re 2.3610 5.7610/4.9210

    -7-9-8Ha/Gr 8.8010 3.3110/1.4510

    -5-3c* 8.5710 3.1410 FCI

    a/b 0.55 1.0

    L/a 50 18

    L/b 28 18

     *cwas calculated assuming t=5 mm and =5 S/m (ITER), =100 S/m (DEMO) FCI FCIFCIFCI

    E. Conclusions related to extrapolation of ITER test results to DEMO (outboard)

    1. If to consider only magnetohydrodynamic parameters, such as , , , the difference between ReHaNHa/Re

    DEMO and ITER is not so big. This is because the magnetic field in both scenarios is the same, 4 T, but the cross-sectional dimensions do not differ much. However purely magnetohydrodynamic regimes will occur only in ITER HH. In ITER DT and DEMO, the flow structure will be sufficiently changed by the volumetric heating. This means that extrapolation of results of the MHD tests obtained in ITER HH to DEMO conditions is possible but limited to the particular sub-flows, where volumetric heating does not play a major role. Similarity between ITER HH and DEMO is expected with regard to the inlet manifold, flow distribution in the module, electromagnetic coupling, effectiveness FCI as electric insulator, turbulence, MHD pressure drops and the flow development length. However, flows in the long poloidal ducts in ITER HH will be sufficiently different from those in other two scenarios (DEMO and ITER DT), where the volumetric heating is of primary importance.

    2. Heat transfer issues will be checked in ITER DT and then the ITER test results will be extrapolated to DEMO conditions. The heat transfer tests will mostly address such an issue as effectiveness of FCI as a thermal insulator and the temperature field in the FCI as affected by the flow conditions in the long poloidal ducts. The most important phenomenon here is associated with natural convection and turbulence and their effect on the formation of high-velocity near-wall jets. The relevant dimensionless parameters are Gr,

    Gr/ReHa/Gr, and . The electrical conductivity of the FCI will also play a major role. The key question is r

    to what degree heat transfer/flow conditions in ITER DT are similar to those in DEMO. Unfortunately, the

    GrGr/ReHa/Granswer is more negative. If to look for example at , and , one can see a difference from 2 to

    3 orders of magnitude. In these conditions, I foresee not only large quantitative but also significant qualitative differences (like different flow regimes) between ITER DT and DEMO. This is for sure that under DEMO conditions, the flow will be strongly agitated by the buoyancy effects, but to a smaller degree

     values in ITER DT are related to two factors. First, volumetric heating in in ITER. Sufficiently smaller Gr

    ITER is roughly 4 times lower than that in DEMO. Second, the radial dimension in ITER is smaller. This a

    4adimension enters the formula for the Grashoff number as . Thus, the most effective way to increase the

    Grashoff number in ITER tests (to be closer to DEMO conditions) is to increase radial depth of the poloidal channel. However, still the difference with DEMO will be pronounced because of lack of neutrons in ITER DT.

    F. Observations related to implementation of reduced size modules

    1. It is obvious that the full scale TBM (half port size) has some advantages over the reduced size modules, since, generally speaking, it provides better similarity with the DEMO blanket. However, using reduced (quarter port) modules may be beneficial from the point of view of decoupling different flow phenomena, allowing for more accurate characterization of the key processes. This would also allow studying these key processes in a more aggressive manner.

    2. It is also obvious that different flow components in the blanket have different sensitivity to changes of the basic dimensions. For example, reduction of the module height from 1.66 m to 0.8 m may have a strong effect on the poloidal flows, while the flow in the inlet manifold will not be affected. When designing reduced size modules one can consider many options leading to smaller module dimensions, for example using less than 6 channels (current ITER design), or reducing the poloidal length. In either approaches, there is a risk that some key MHD/Heat Transfer phenomena can be seriously modified, so that the test results may loose their value. Below, I tried to summarize what we could expect when reducing either (A) the cross-sectional dimensions of the original half port module (via reduction of the number of the poloidal channels or via reduction of the duct cross-sectional dimensions) or (B) the poloidal length while keeping the same cross-sectional dimensions and the number of channels.

    2.1. Reduction of the poloidal length. The main risk is associated with the poloidal flows, namely one can expect that the reduced flow length would not be enough to have a fully developed flow here. In DEMO

    =18, while it is 50 in ITER (current half port design). Reducing from 50 to 25 will result in the L/aL/a

    flow length even closer to the corresponding DEMO value. However, judging about the flow development length will also require a comparison of other parameters (, , etc.), which are not the ReHa

    same in ITER and DEMO. Unfortunately, accurate correlations for the flow development length in duct MHD flows are not available. A generally observed tendency is that in a stronger magnetic field the flow development length is shorter. One can expect that under a 4 T magnetic field in both ITER and DEMO the transitional length associated with either flow inlet or outlet is no longer than 5 characteristic duct dimensions. This means that at least over the half of the poloidal duct length of 25 duct dimensions, the flow will demonstrate fully developed features or will be close enough to being fully developed. From this point of view, considering a reduced length sub-module seems to be very reasonable.

    2.2. Reduction of the number of channels or/and their cross-sectional dimensions. Reduction of the cross-sectional dimensions themselves does not look too bad providing the basic dimensionless parameters are not changed much, say, the maximum change is by a factor of 2 or less. This would assure that the flow regime is essentially the same (compared to the current half port design), although some quantitative variations in the flow are quite possible. Reduction of the number of channels may be associated with higher risks of loosing information. First of all it is related to the flow distribution in the whole module and especially in the inlet manifold, flow balancing and electromagnetic flow coupling. On the other hand, such key phenomena as natural convection and turbulence and effectiveness of the FCI as thermal insulator can hardly be affected.

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