Numerical and experimental MHD studies of Lead-Lithium liquid metal flows in multichannel test-section at high magnetic fields

Fusion Engineering and Design 132 (2018) 73–85

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Numerical and experimental MHD studies of Lead-Lithium liquid metal flows in multichannel test-section at high magnetic fields

T

⁎

P.K. Swaina,b, , A. Shishkoc, P. Mukherjeea, V. Tiwaria, S. Ghoruia,b, R. Bhattacharyayd, A. Pateld, P. Satyamurthyd, S. Ivanovc, E. Platacisc, A. Ziksc a

ADS Target Development Section, Bhabha Atomic Research Center, Mumbai, 400 085, Maharashtra, India Homi Bhabha National Institute, Anushaktinagar, Mumbai, 400 094, Maharashtra, India c Institute of Physics, University of Latvia, Salaspils, 2169, Latvia d Institute for Plasma Research, Gandhinagar, 382428, Gujarat, India b

A R T I C LE I N FO

A B S T R A C T

Keywords: Liquid metal Lead-Lithium Electrically coupled wall MHD pressure drop Hartmann number Test blanket module

Numerical simulation and experiments have been performed at high magnetic fields (1–3T) to study the MHD assisted molten Lead-Lithium (PbLi) flow in a model test-section which has typical features of multiple parallel channel flows as foreseen in various blanket module of ITER. The characteristics Hartmann number of the presented case study is up to 1557 which is relevant to typical fusion blanket conditions. Symbols B0, a, σ, μ in the definition of Hartmann number are strength of the applied magnetic field, characteristic length scale which is half the channel width parallel to the magnetic field, electrical conductivity and dynamic viscosity of PbLi respectively. Flow distribution in two electrically coupled parallel channels that are fed from a common inlet manifold has been analyzed by measuring the side wall potential difference data of individual channels and by numerical simulation. Both the results of numerical prediction and measured flowrate indicate unequal distribution in parallel channels and the variation is a function of the total flowrate and applied magnetic field strength. Also 3-D currents generated due to the complex geometrical flow path play a key role in distribution of the flow among the parallel channels. A similarity coefficient (K) is proposed for quantitative estimation of the similarity between numerical and corresponding experiment data of wall potential distribution. The measured pressure drop in the test-section is analyzed for different flow conditions to verify the applicability of laminar flow model.

1. Introduction Analysis of self-cooled Pb-Li liquid metal flow in multiple parallel poloidal flow channels under high transverse magnetic fields is of practical interest for design of various proposed Test Blanket Modules (TBMs) by international parties for International Thermonuclear Experimental Reactor (ITER) program. In particular, electrically coupled parallel channel flows are commonly encountered in the Indian concept of Lead-Lithium Cooled Ceramic Breeder (LLCB) TBM where Pb-Li serves dual purpose of cooling and tritium breeding as a hybrid concept of both solid and liquid breeder [1]. The parallel flow configuration which is fed from a common header has an advantage of reduction in overall Magnetohydrodynamic (MHD) pressure drop [2]. However, thermal hydraulic performance of the TBM is significantly affected by the flowrate, velocity distribution, duct aspect ratio, laminar/two dimensional MHD turbulence, etc in the individual channels. The stability of the flow in general is function of characteristics ⁎

Hartmann number (Ha = B0 a σ μ ) and interaction parameter (N = σ a B02/ρU0) and associated geometric parameters like orientation of inlet axis with respect to the applied magnetic field, relative wall conductance ratio and channel layout [3]. Here, B0, σ, μ, ρ are the strength of the applied magnetic field, electrical conductivity, dynamic viscosity and density of Pb-Li. Variable ‘a’ and ‘U0’ is characteristics length and velocity scale. The flow path of liquid metal Pb-Li in LLCB TBM is complex due to multiple L/U bends and coupled electric channels. Theoretical prediction of flowrate distribution, velocity profile, wall potential distribution etc is challenging not only due to liquid metal complex flow path but also complicated MHD issues at relevant fusion conditions. The level of complexity is even more in the case of conducting channels, as the difference in induced potential caused by uneven flowrate and varying direction of the flow that drive 3-D currents in liquid metal as well as in the structural walls and consequently modify the flow behavior [4]. To address these complex issues, number of experiments and

Corresponding author at: ADS Target Development Section, Bhabha Atomic Research Center, Mumbai, 400 085 Maharashtra, India. E-mail address: [email protected] (P.K. Swain).

https://doi.org/10.1016/j.fusengdes.2018.04.125 Received 2 August 2017; Received in revised form 16 March 2018; Accepted 28 April 2018 0920-3796/ © 2018 Elsevier B.V. All rights reserved.

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computational studies have been performed in scaled down test-sections to generate engineering data base, to validate numerical model and possible extrapolation of the numerical code performances at fusion relevant conditions. MHD experiments with NaK at high Hartmann number (up to Ha = 4000) have been studied by K Starke, L. Buhler, S. Horanyi in a scaled mock of HCLL TBM to study the effect of poloidal manifolds on flow partitioning in breeder units. Each breeder unit is consisting of electrically coupled multiple parallel radial channels formed by internal walls [5]. Numerical simulations have also been carried out for fully developed flow in the same geometry by C. Mistrangelo, L. Buhler using modified CFX code [6]. For US DCLL TBM, numerical simulation of Pb-Li MHD flow in poloidally running parallel channels with toroidally oriented manifold has been carried out by N. B. Morley, etc using advanced HIMAG computer code based on consistent and conservative scheme for determination of current density [7]. Recently, experiments and numerical simulations of NaK MHD flow have been carried out in a test-section consisting of parallel flow channels with multiple sub ducts subject to uniform transverse magnetic field and variable applied field along inlet/outlet manifold [8]. In this paper, the results of experiments and numerical analysis carried out in a scale down test-section corresponding to the proposed Indian LLCB TBM, are presented. In addition to reduction in the size of the channels, only two channels of parallel flow (as against 5 channels proposed in the Indian TBM [1]) and a parallel counter flow channel and thus a total of 3 electrically coupled poloidal channels are provided due to the constraint of the magnet dimension. Experiments are carried out in this test-section at Institute of Physics University of Latvia (IPUL) MHD loop to study the flow distribution in parallel channels under uniform transverse applied magnetic field up to 3T and for various flowrates. Although the test-section model is not exactly the scaled down replica of LLCB TBM, the PbLi flow path in the experiment simulate some of the features of LLCB TBM flow configuration. As the strength of the applied magnetic field that determine the Hartmann layer thickness and imposes constraint in numerical modelling, the present experimental data and numerical simulation up to B0 = 3T may be considered to be relevant to assess the actual blanket scenario. Further, in the present experiment, 3D flow field is similar to that of actual LLCB TBM. 3-D numerical simulation has been performed for the exact physical model based on the laminar approximation and is presented in this paper. The comparison of such calculations with the experimental data makes it possible to decide, to a certain extent, on the applicability of the laminar approach. The side wall electric potential difference at different location of all the channels, pressure drop in the test-section is compared with measured values. The validity of numerical results of wall potential distribution based on laminar model is verified by a proposed similarity coefficient. Numerical prediction of flowrate distribution in parallel channels for different applied magnetic field strength is compared with the estimated values from the measured side wall potential difference data. Non dimensional numerical profile for side wall potential distribution is used to estimate the flowrate in each channel instead of using fully developed model. A qualitative discussion on flow profile asymmetry in parallel channels as obtained by the numerical solution is presented. The dominance of electromagnetic flow regime with variation of Ha/Re ratio is identified from total pressure drop in test-section.

Fig. 1. (a): Photograph of the Pb-Li liquid metal experiment loop with testsection. (b): Schematic of flow path in the test-section.

through a variable speed MHD pump and the flowrate in the loop is measured by a DC electromagnetic flowmeter placed outside the superconducting magnet. It is to be noted that no wetting issue is observed for structural material SS with PbLi eutectic in the long experience of corrosion studies at IPUL. This is primarily due to the higher operating temperature of the loop (300–350C). Further, as a standard practice, Pb-Li is circulated in the loop for several hours prior to start of the experiment to ensure proper wetting of the structural material. The flowmeter is equipped with detachable permanent magnets and provides linear relationship between flowrate Q (m3/s) and potential difference U (mV) measured across its channel width. The photograph of the experimental loop and schematics of flow path in the test-section is shown in Fig. 1(a) and (b) respectively. Experiments are carried out at different magnetic fields (maximum up to 3T) and the flowrate has been varied at each magnetic field so that characteristics MHD flow parameters of Hartmann number (Ha) and interaction parameter (N) is achieved in the range of 519–1557 and 3–431 respectively. Physical value of the characteristic length scale is 0.025 m which is half the channel width along the direction of applied magnetic field and characteristic velocity U0 is considered as the average velocity in channel-3.

2. Experiments Experiments have been carried out at IPUL in the mock up testsection consisting of electrically coupled multiple parallel flow paths and with liquid metal Pb-Li as working fluid. Pb-Li flows at 350 °C in the test-section experience transverse magnetic field up to 3T produced by cylindrical superconducting magnet of 300 mm diameter and 1000 mm length. The test-section is placed at the central bore location of the superconducting magnet where the magnetic field is uniform both in axial and radial direction. Liquid metal circulation is achieved

2.1. Test-section and diagnostics Test-section, made of SS316 material, consists of vertically oriented 74

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Fig. 2. (a): Test-section with detailed dimension of various edges in mm unit. (b): Test-section with various diagnostic locations (B, M, T) at different Channel.

field in the entire test-section except at the inlet/outlet pipe. All the outer walls of the test-section are made of 4 mm and internal partition walls are of 3 mm thick SS316 plates. Wall electric potential distribution is measured with potential pins welded at various locations of the test-section. Side wall potential difference along the applied magnetic field direction is measured by array of 5 pairs of potential pins at 3 different heights (B, M &T) of the parallel channels. Photograph of the test-section with various diagnostic locations and channel nomenclature is shown in Fig. 2(b). Five pairs of potential pins are uniformly placed with 8 mm gap over 50 mm width of the side wall. Measured signals were in the range 0.6–36 mV depending on the flowrate and magnetic field strength. Prior to the experiment, spatial variation of the magnetic field is measured with a Hall probe. The variation of magnetic field strength in the test-section including the inlet/outlet pipe is less than 0.1%. Pressure drop in the test-section with extended inlet outlet pipe line is measured with pressure transmitter located at A1 and A2 (see Fig. 1). Liquid metal pressure is obtained by measuring the cover gas pressure of expansion tanks provided at these locations. Change in gas pressure with variation of liquid metal level in the expansion tank is assumed isothermal. Along the flow path the pressure is also recorded at various locations from the pressure sensors attached with B1, B2, B3, B4 and B5 expansion tanks. These expansion tanks are located outside the superconducting magnet and attached to the test-section through connecting pipes.

two electrically coupled parallel rectangular channels with a common inlet header attached with inlet pipe and a similar return channel of counter flow path connected to the outlet pipe through bottom collector duct (see Fig. 2(a)). Working fluid PbLi is supplied to the two parallel flow channels from the common inlet header at the bottom, recombine again at the top header and then return through similar parallel duct of larger width which is then connected to the outlet pipe through bottom outlet header. The parallel flow channels are separated by 9 mm thick dummy breeder zones encased with 3 mm thick SS plates. No heat source is provided within the dummy breeder boxes. Liquid metal enter or exit from the bottom inlet/outlet header of the test-section through pipes oriented parallel to the axial magnetic field of superconducting magnet. Design of the test-section flow path is envisaged to simulate the flow configurations of scaled down Indian LLCB TBM. Liquid metal PbLi is supplied to the test-section through inlet pipe (1/2″ schedule 40) parallel to the axial magnetic field of superconducting magnet. After taking a 900 turn at the exit of inlet pipe the flow spreads into the bottom inlet collector duct (25 mm × 50 mm) of the vertically oriented test-section and enters into two parallel rectangular channels each having a flow cross section of 20 mm × 50 mm. Then the flow combines at the top collector duct (20 mm × 50 mm) and returns through a rectangular duct of flow cross section 25 mm × 50 mm which is parallel to the other two vertical channels. Similar to the inlet pipe, the flow comes out from the test-section through outlet pipe connected to the bottom outlet collector duct of same cross section as in the return channel. Bottom inlet and outlet collector ducts are separated by a 3 mm thick partition plate. Flow path of Pb-Li is transverse to the applied magnetic 75

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computation domain is confined to 0 ≤ X ≤ 0.138 m, 0 ≤ Y ≤ 0.221 m and 0 m ≤ Z ≤ 0.098 m (see Fig. 2). Uniform magnetic field is applied along → z direction. Two vertical channels with co-current flow (channel1 & channel-2) start at Y = 0.057 m from bottom inlet collector duct (0.033 ≤ Y ≤ 0.057 m) and subsequently combines at top collector duct extends from 0.057 ≤ Y ≤ 0.077 m. The return channel (channel3) extends from 0.033 ≤ Y ≤ 0.219 along with the bottom collector duct starts from 0.004 ≤ Y ≤ 0.029 m. For computation, the length of the inlet and outlet pipe is taken as 40 mm (0.058 ≤ Z ≤ 0.098 m).

3. Flow modeling 3.1. Governing equations The following system of equations governing the steady state MHD flow of incompressible, electrical conducting fluid under the influence of external magnetic field has been solved in FLUENT [9] code. The effects of induced magnetic field is neglected due to small magnetic Reynolds number (Rem < 1) [10] and the electromagnetic body force, as source term in the momentum equation is coupled with other equations based on electric potential formulation. In view of electrical conducting channels and moderate characteristic parameters (Ha > 1038, N > 20) the flow is expected to be laminar as Ha/Re value is above the critical number of transition (Ha/Re > 0.02) from turbulent to laminar regime [11].

→ → ( U · ∇) U =

→ −∇p ρ

→ + ν∇2 U +

→ ⎯→ ⎯ J × B0 ρ

4.1. Grid details and physical properties The geometry is meshed with multi-block hexahedral structure grid with total number of volume elements ∼2.05 million. Hartmann layers and side layers (Shercliff boundary) are resolved with 3 elements (δH ≈ 1.6 × 10−5m) and 12 elements (δs ≈ 0.63 × 10−3m) respectively for maximum Hartmann number of 1557. The optimum grid structure is obtained by performing the grid independent analysis for 3 different grid structures as shown in Appendix A. To optimize the computation, the flow cross section is meshed with variable spaced grid points and structural walls are meshed with uniform spacing for 5 numbers of elements along the thickness. The properties of the PbLi are taken as 9402 kg/m3, 7.7616 × 105 S/m, 1.8 × 10−3 Pa.s, for density (ρ), electrical conductivity (σ) and dynamic viscosity (μ) respectively and electrical conductivity (σw) of the structural wall (SS) are taken as 1.01 × 106 S/m in present numerical simulation [13].

[Modified Navier − Stokes equation]

(1)

→→ ∇ · U = 0 [Conservation of mass]

(2)

→ → → ⎯→ ⎯ J = σ(− ∇ ϕ + U × B0 ) Generalised Ohm′s law

(3)

→→ ∇ · J = 0 [Conservation of charge]

(4) → Here, ρ, U , ν, σ are density, velocity, kinematic viscosity, electrical → ⎯→ ⎯ conductivity of the fluid whereas p, J , B0 , ϕ are pressure, electric current density, magnetic field induction, and electric potential respectively. Eqs. (3) and (4) are combined in potential method formulation to solve electric potential ϕfrom the following equation,

→ → ⎯→ ⎯ ∇2 ϕ = ∇ ·(U × B0 )

5. Numerical results and comparison with experiment Although experiments are carried with different flowrates at each magnetic field (1–3T), numerical analyses have been presented for higher magnetic fields (2 & 3T) and for two flowrates for each case. Flow parameters of different numerical case studies and respective non dimensional parameters are shown in Table 1. The characteristics non dimensional value for Reynolds number (Re) and interaction parameter (N) as presented in Table 1 corresponds to the channel-3 (Return path) of the test-section. For individual channel, these values will be different since the mean velocity in respective channel varies from case to case. The flowrate in the test-section used for numerical simulation is based on readings of flowmeter integrated in the loop.

(5)

Here, B0 is the strength of applied magnetic field. In the solid domain the following equation is solved for the electric potential

∇2 ϕw = 0

(6)

Here ϕw is the potential distribution in the walls. At the fluid-wall interface, in addition to no-slip condition for the velocity, continuity of the normal component (to the walls) of current density (Jn = Jnw) and continuity of electric potential at the interface (ϕi,f = ϕi,s = ϕi) have been applied. Here Jn refers to the normal component of current density on the fluid side and Jnw corresponds to the wall side, ϕi is electric potential at the interface and index ‘i’, ‘f’, ‘s’ stands for interface, fluid and solid respectively.

5.1. Wall electric potential distribution and estimation of flowrate The measured side wall electric potential difference (Δϕj, j = 1–5) at location ‘M’ and location ‘T’ of all Channels is shown in Figs. 3 and 4 respectively for different flowrates and applied magnetic field strength. Results of numerical estimations as shown by continuous lines in Figs. 3 and 4 are compared with corresponding measured values. For convenient presentation of the potential difference profile of all the channels, the Z-coordinate is linearly shifted to new coordinate ζ as defined by ζ = Z + 0.07 × (3 − i), where i = 1, 2, 3 for channel-1, 2 and channel-3 respectively. In all these cases the measured profile of Δf at each location (B, M and T) is somewhat lower than the corresponding numerical estimations (see Figs. 3 and 4). The cause of this deviation with experiment data is primarily due to the following reasons. One is the validity of numerical model and computation code capability, and

3.2. Boundary conditions For velocity field, no-slip condition has been used at the solid surface. At the inlet uniform velocity and at the outlet, a homogenous Dirichlet pressure condition (P = 0) is applied. For the electric potential, insulation is assumed beyond the outer walls and a homogeneous Neumann condition ∂ϕ/∂n = 0 is applied. 4. Numerical simulation

Table 1 Characteristics parameters of presented numerical case studies.

Numerical simulations in the test-section have been carried out in the CFD facility of VJTI, Mumbai, India using FLUENT code to obtain the flow field solutions and compared with experimental values. Benchmarking and model validation of the code has already been reported for a straight duct (with Hunt’s analytical model), for a testsection consisting of multiple 900 bends (with experiments at high Hartmann number up to Ha = 2060) [12] and also MHD flow in parallel channels at 1T field [8]. Dimensional limits of the test-section 76

B0 (T)

Volume flowrate (cm3/s)

Mass flowrate (kg/s)

Ha

N

Re

Ha/Re

2.0 2.0 3.0 3.0

242.2 492.5 240.2 490.7

2.278 4.631 2.259 4.614

1038 1038 1557 1557

42.6 20.95 96.7 47.4

25310 51454 25096 51263

0.041 0.02 0.062 0.03

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numerical calculation based on the flowmeter measured value is higher than the actual flowrate in the loop. In order to have a better estimate for the real flowrate(Qreal) in the loop as well as in experiment test-section, numerical results of the sidewall potential difference data of channel-3 is compared with the corresponding measured value. We assume that the measured valu eof potential difference for each pair of side wall pins at three different locations Δϕ3,ℓ,j exp t is proportional to the corresponding numerically calculated one Δϕ3,ℓ,j num with some proportionality factor A. The value of this coefficient A and real flowrate(Qreal) can be defined from the minimum of the root mean square deviation (σQ) as defined in Eq. (7). Here, index ‘ℓ’ corresponds to the location B, M and T for ℓ = 1, 2 & 3 respectively. 2

σQ =

⎡ 3 ⎤ 5 ⎛ ℓ, num − Δϕ3,ℓ,j exp t ⎞⎟ ⎥ ⎢∑ℓ = 1 ∑ j = 1 ⎜AΔϕ3, j ⎝ ⎠ ⎣ ⎦ 15

(7)

For the present case studies as defined in Table 1, the coefficient A is determined from the particular case of B0 = 3 T and Qnum value of 240.2 cm3/s for which MHD interaction parameter N is highest. The case with highest N is considered in view of better compliance of the numerical results based on laminar model. It is assumed that, in a small range of Q close to Q = 240.2 cm3/s, all the sidewall potential difference data is proportional to the corresponding flowrate and the proportionality coefficient is same in the given range. Using Eq. (7) and from the condition of minimum of the function σQ with respect to A (dσQ dA = 0 ), follows that

Fig. 3. Comparison of measured side wall electric potential difference data with the corresponding numerical counterpart (represented by continuous lines) in each channel at location ‘M’ for different flow rates and applied magnetic field strength.

3

A=

5

∑ℓ = 1 ∑ j = 1 Δϕ3,ℓ,j num Δϕ3,ℓ,j exp t 2

= 0.9451

∑ℓ = 1 ∑ j = 1 ⎜⎛Δϕ3,ℓ,j num⎟⎞ ⎝ ⎠ 3

5

(8)

The coefficient A defined in this way characterizes the difference between the actual flowrate in the experimental model and the flowrate measured by the flowmeter. Hence the real flowrate in the experiment can be evaluated using Eq. (9)

Qreal = 0.9451·Qflowmeter

(9)

It should be noted that although better estimation for flowrate has been performed using Eq. (9), the flowmeter measured data is presented throughout the document and has been used in the numerical simulation.

Fig. 4. Comparison of measured side wall electric potential difference data with the corresponding numerical counterpart (represented by continuous lines) in each channel at location ‘T’ for different flow rates and applied magnetic field strength.

5.2. Distribution of flowrate in parallel channel At the location ‘M’ (Y = 0.127 m) which is ∼2.8 times the characteristic length (a = 0.025 m) from the bottom and top manifold, the flow under single channel flow configuration is expected to be fully developed due to stronger electromagnetic forces at high Hartmann number. However, 3D currents are generated not only due to potential difference in top and bottom wall of the test-section, but also due to flow turning at nearby 900 bends in the upstream and downstream. These additional current loops are closed though the liquid metal and breeder walls of parallel channels and modify the flow distribution continuously and hence the flow does not attain fully develop configuration. To ascertain this, the normalized wall electric potential distribution for various flowrates and higher applied magnetic field strength (2T and 3T) are compared with the corresponding theoretical estimations based on fully developed theory [15] as shown in Fig. 5(a) and (b). As can be seen, although the side wall potential distribution is symmetric, it is significantly deviated from the asymptotic profile even at higher magnetic field strength of 3T. So the conventional approach of estimating the flowrate in individual channels from side wall potential

other is the correctness of input data used for numerical simulation. Since the numerical model and simulation methods are already benchmarked with various experiments, the input parameter especially the flowrate, used in numerical simulation, is anticipated for prime cause of deviation. The flowrate of numerical simulation is based on the flowmeter data which was already calibrated in a liquid metal PbLi loop [14]. The change in field strength of the flowmeter due to stray magnetic field of the superconducting magnet is also ruled out as it is placed at far away (2.5–3 m) distance from the superconducting magnet and the same has been verified by measuring the field strength prior to the flowmeter installation. However, a systematic misreading of this instrument may be possible, specifically due to small relative change in position of the flow channel within the pole gap of the flowmeter permanent magnets. This may lead to possible change the calibration factor of the flowmeter. The consistent prediction of higher potential difference at all the locations indicates the assumed flowrate of the 77

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individual channel. The induced voltage measured by pair of potential sensors across the side walls of a given flow cross section is proportional to the local average velocity. Unlike the open-circuit configuration where proportionality constant is one, correction factors must be included in determining the voltage signal as function of flow velocity to account return currents in the finite thickness of side walls. In the present case of electrically coupled walls, numerical values of local non dimensional side wall electric potential difference (Δϕj*num) is used as the proportionality constant to estimate the local average velocity. The average velocity in the cross section may be calculated by averaging the velocities estimated by each pair of side wall potential pins in that cross section. Using this assumption, the measured flowrate in each channel is estimated from the side wall potential difference data Δϕm j (j = 1–5) measured by jth pair of potential pins across the channel width. The average velocity (U ij , j = 1–5) at jth location of cross section ‘M’ of ith channel is estimated from the following relation.

U ij = Δϕm j (B0 wi Δϕj *num )

(10)

is the non dimensional potential difference at j location Where, Δϕj obtained from the numerical simulation, ‘B0’ is the applied magnetic field intensity, ‘wi’ is the channel width transverse to the applied field direction. The average velocity (Ui) in respective channel cross section is estimated as follows, *num

th

5

Ui =

1 5

∑

U ij

j=1

(11)

Here i = 1, 2, 3 for channel-1, channel-2 and channel-3 respectively. Using Eqs. (10) & (11), the average velocity and corresponding flowrate in each channel is estimated. For illustration, the local average velocity (j = 1–5) estimated from numerical non dimensional potential difference for channel-1 is shown in Table 2 for various case studies. The estimated flowrate (QE) is then compared with corresponding numerical counterpart in Table 3. It should be noted that numerical flowrate (Qnum) in the channel-3 as presented in Table 3 is based on Flowmeter measured value. As can be seen in Table 3, the estimated flowrate (QE) based on the measured side wall potential of channel-3 is always lower than the flowmeter measurement. The integral of estimated flowrate in channel-1 and channel-2 is close to the estimation in channel-3 with maximum deviation of less than 2.7% which may be attributed partly to the error in side wall potential measurement at low voltages. Thus, the consistent estimation of a lower flowrate from the side wall potential data necessitates calculation of actual flowrate as obtained in Eq. (9). However, as far as flowrate distribution is concerned, the fraction of flow in individual channel as predicted by numerical model and evaluated from the side wall potential measurement is more or less same. The fraction of flowrate in channel-2 for various case studies as shown in Table 3 is matching within 1% deviation. Using Eq. (9) the actual flowrate in the test-section for various case studies is estimated and compared with the estimated flowrate from side wall electric potential profile as shown in Table 4. The actual flowrate obtained from Eq. (15) matches well with the estimated values from side wall potential data with maximum deviation of less than 1% at higher magnetic field (B0 ≥ 2.0 T). Thus we believe that the average velocity in individual channel and hence flowrate as estimated from Eq. (10) is realistic and is close to the actual flowrate in respective channels.

Fig. 5. (a): Normalized side wall electric potential difference (Δϕ*) distribution and comparison with corresponding theoretical profile (dotted line) in all the channels at location ‘M’ for different flow rates and B0 = 2 T. (b): Normalized side wall electric potential difference (Δϕ*) distribution and comparison with corresponding theoretical profile (dotted line) in all the channels at location ‘M’ for different flow rates and B0 = 3T.

data, assuming the flow to be fully developed, [16,17] may not be applicable for the present experimental test-section. However, we can use non dimensional numerical profile of side wall potential distribution as a reference profile to estimate the flowrate provided the variation is insignificant of flowrates and applied magnetic field strength in that range. The assumption holds true at locations free from bend effects and at large interaction parameter. As can be seen in Fig. 5(a) and (b), the non dimensional electric potential (Δϕi/wU0iB0) profiles are nearly identical with maximum deviation of less than 1% for various flowrates at each applied magnetic field. Here U0i, (i = 1–3) is the average velocity in the ith Channel estimated from the numerical simulation and ‘w’ is the respective channel width (20 mm for channel-1 and channel-2) along the transverse direction of applied magnetic field. The dimensionless reference potential difference profile which is obtained from numerical simulation accounts all the geometrical coupling factors and is nearly independent of the specific flowrate as presented in Table 1. This reference profile along with measured side wall potential distribution data is used to estimate the flowrate in respective

5.3. Discussion on flowratre distribution in parallel channel Assessment of factors affecting the flowrate distribution in parallel channels is required to foresee the blanket performance at ITER condition. Apart from the effects of flow inertia and applied magnetic field strength, the present simulation indicates axial currents also play a key 78

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Table 2 Local average velocity at Location ‘M’ of channel-1 estimated from measured side wall potential for various case studies. jth location.

j = 1 (Z = 0.013 m)

B0 = 2T, flowrate = 242.2 cm /s, mean velocity in channel-1 (U1) = 9.92 cm/s 3.061 Δϕm j [mV]

j = 2 (Z = 0.021m)

j = 3 (Z = 0.029m)

j = 4 (Z = 0.037 m)

j = 5 (Z = 0.045 m)

3

3.94

4.17

4.18

3.57

Δϕj *num

0.8515

1.0003

1.0551

1.0025

0.8537

Uj [cm/s]

8.98

9.85

9.88

10.42

10.45

B0 = 2T, flowrate = 492.5 cm3/s, U1 = 20.52 cm/s Δϕm j [mV]

6.67

8.11

8.58

8.39

7.27

Δϕj *num

0.8515

0.9987

1.0515

0.9998

0.8526

Uj [cm/s]

19.58

20.3

20.4

20.98

21.32

B0 = 3T, flowrate = 240.2 cm3/s, U1 = 10.93 cm/s Δϕm j [mV]

5.05

6.26

6.62

6.5

5.49

Δϕj *num

0.8097

0.961

1.0143

0.9624

0.8126

Uj [cm/s]

10.39

10.86

10.88

11.26

11.26

B0 = 3T, flowrate = 490.7 cm3/s, U1 = 21.63 cm/s Δϕm j [mV]

10.74

13.01

13.68

13.26

11.28

Δϕj*num Uj [cm/s]

0.8521 21.01

1.0033 21.61

1.059 21.52

1.0048 21.99

0.8543 22.01

the channel-1 is more (3.5 mm) as compared to the channel-2 (3 mm), the coefficient of resistance (RH) is lesser (RH2 = 0.0964) for channel-2 as compared to the channel-1 (RH1 = 0.102) for B0 = 3T and hence expected to draw more flow in channel-2. The unequal flow distribution in the parallel channels can be explained by analyzing the axial currents (Jy) generated in the inlet collector header where the flow turns from parallel (In the inlet pipe) to perpendicular direction (in the test-section) of the applied magnetic field. 3D currents are generated by the top wall and bottom partition plate which is common to inlet/outlet collector ducts. Also, the difference in induced wall potential in different channel due to difference in flowrate and turning of flow at bends leads to the generation of 3D currents. The contour of electric potential in different walls of the testsection is shown in Fig. 6. Since there is a gradient of potential in the upper as well as lower side wall of the extended inlet/outlet header region with opposite polarities, 3D currents are generated in this region that closes the path in the bottom inlet header. The axial current (Jy) induced in this region in the presence of transverse magnetic field ( B 0→ z ) give rise to electromagnetic forces which redistribute the flow in channels depending upon its strength and direction. The profile of Jy current along the centre of the channel-1 including the bottom inlet header region is shown in Fig. 7. As can be seen, the magnitude Jy current increase with increasing the field strength which gives electromagnetic force in → x direction and hence draws more flow towards the channel-1. For a given applied magnetic field, as the flowrate increases the current Jy increases and consequently balances the inertial force.

Table 3 Estimated flowrate distribution based on the measured side wall potential data and comparison with numerical prediction for different case studies. B0 (T).

2.0 2.0 3.0 3.0

*Numerical flowrate (cm3/s) based on Flowmeter(Qnum)

Estimated flowrate (cm3/s) using measured potential data (QE)

cha-3

cha-2

cha-1

% flow in cha2

cha-3

cha-2

cha-1

% flow in cha2

242.2 492.5 240.2 490.7

128.2 265 124.7 260.1

114.2 227.5 115.5 230.6

52.9 53.8 51.9 53

223.1 462.4 227.3 467.2

117.8 248.3 116.5 246

99.2 205.2 106.1 216.3

52.8 53.7 51.3 52.6

Table 4 Actual flowrate for various case studies and its comparison with estimated flowrate based on measured side wall potential profile. B0 (T)

Flowrate by Flowmeter Q (cm3/s)

Actual Flowrate Qreal(cm3/s)

Estimated Flowrate QE(cm3/s)

Deviation (%)

2.0 2.0 3.0 3.0

242.2 492.5 240.2 490.7

228.9 465.5 227.0 463.8

223.1 462.4 227.3 467.2

2.5 0.7 0.1 0.7

role in distributing the flow in parallel channels. These axial currents are generated by the complex flow path and various geometrical constraints like top and bottom plate, partition plate at the bottom inlet/ outlet collector duct of the test-section. For a given magnetic field strength, percentage of flow in channel-2 is rising with increase in total flowrate. Even though fluid enters into parallel channels from the common inlet header after a 90 ° turn from the inlet pipe, effects of inertia lead to uneven flow distribution. However, with increasing N, flow distribution tends to saturate depending upon the coefficient of resistance (RHi ) of the individual channel as defined in the following relation.

RHi = ∇Pi/ σ Ui B0 2

5.4. Similarity relation between experiment and numerical simulation The presented results demonstrate that the real flowrate in the physical experiment, in all cases, was a little (by ∼5%) lower than that from the results of numerical modelling. This was caused by an inaccuracy in the data of the loop flowmeter. Apart from the flowrate deviation, the electric potential field ϕnum(x, y, z) as realized in numerical simulation may defer from the experiment observations due to complex nature of liquid metal flow path in the test-section. If the correctness of the numerical model is determined first of all by the adequacy of the utilized mathematical description of the complex enough MHD flow and by the accuracy of the numerical calculations, the latter pattern depends on the experimental possibilities of the precise

(12)

Here, ∇Pi is the pressure gradient in the i channel, assuming the flow to be fully developed. Since the effective thickness of the side walls of th

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,exp t K inum = ,j

, Δϕinum ,j

exp t

, exp t Δϕ3,num j

(13)

Here, index i = 1, 2 corresponds to for channel-1 and channel-2 and index j = 1–5 stands for five pair of pins at each location (B, M and T) and Δϕ3,j is the potential difference data of jth pair pins of channel-3 (return channel). The abbreviation ‘num’ and ‘expt’ corresponds to the numerical and experimental data. The closeness of numerical factors exp t (K inum , j )and experiment factors (K i, j ) will determine the degree of similarity between the numerical and experiment model. In the ideal exp t case, K inum , j ^K i, j . The proposed version of the similarity coefficient eliminates to some extent, the systematic error attributed to inaccuracy in the flowrate measurement and, also the coefficient may be used to quantitatively estimate the correspondence between the calculated and the experimental data. ,exp t Comparison of the similarity coefficients (K inum ) at each location ,j (B, M and T) for a specific case of B = 3T and Q = 240.2 cm3/s is shown in Table 5. As can be seen with the proposed version of similarity coefficient for electric potential distribution ϕ(x, y, z), K inum of in,j dividual channel-1 & channel-2 has excellent agreement with the t ) and more or less close to the numerical measured values (K iexp ,j num ). The root mean square deviation of the similarity average ( K i coefficients at each location σiB, M , T and overall deviation σi for individual channel-1 and channel-2 have been estimated using Eqs. (14) and (15) as shown in Table 6 for all the cases studies. The overall deviation σ1 and σ2 for channel-1 and channel-2 with the average numerical similarity coefficient is within 5% in most of the places except at bottom location of channel-1. Hence it may be concluded that results of numerical calculation based on laminar approximation is satisfactory in the bulk of the flow domain. However, higher deviation of in channel-1 indicates possible measurement error at low voltages and limitation of the laminar model to account presence of larger residual turbulence near the bends at higher flowrates and lower magnetic fields.

Fig. 6. Contours of electric potential and iso-surfaces in various walls of the test-section. Level-1, 2. 3, 4, 5, 6 and 7 corresponds to potential value (mV) of −6, −5, 4, 2, 0, 3 and 4 mV respectively.

σiℓ =

σi =

⎡∑5 (K ℓ, num − K ℓ, exp t )2 ⎤ i, j ⎢ j = 1 i, j ⎥ ⎦ ⎣ 5

(14)

⎡∑3 ∑5 (K ℓ, num − K ℓ, exp t )2 ⎤ i, j ⎥ ⎢ ℓ = 1 j = 1 i, j ⎣ ⎦ 15

5.5. Pressure The total pressure drop in the test-section including the inlet/outlet pipeline is measured with the pressure transmitter located at A1 and A2 for various flowrates and applied magnetic fields. The results of wall potential distribution as discussed in the previous sections, the numerical results based on laminar model is matching reasonably well with the experiment and the same trend is also expected to follow in the measured pressure drop. In this present experiment, there is no provision to detect local turbulence. So the measured integral pressure drop in the test-section is used as an alternative mean for verifying the applicability of laminar flow model. A parametric study of the total pressure drop variation is studied for various flowrates and applied magnetic field strength. At higher magnetic fields, the pressure drop is expected to follow the linear trend with flowrate as in the case of a typical MHD flow due to stronger electromagnetic effects in electric conducting channel. However, at high flowrates and lower magnetic field strength, the effects of turbulence (Q2D) may prevail in the flow characteristics due to multiple L/U bends the test-section. So analysis of the observed pressure drop variation is carried out in various flow condition to verify the applicability of laminar model for the present case.

Fig. 7. Axial current (Jy) profile along the centre of the channel-1 including the bottom inlet header region.

measurement of a large number of weak electrical signals. In view of this, it has been suggested that specific proportion between any arbitrary selected differences of potentials calculated in the numerical experiment should not differ significantly from similar relations between the same potential differences measured in the physical experiment. In the present analysis, the simplest form of specific relation proposed in Eq. (13) which is interpreted as similarity coefficients (Ki,j) and applied independently to numerical as well as experiment picture of wall potential distribution. With this procedure, all similarity coefficients do not vary with respect to certain percentage change in the flowrate. 80

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Table 5 Similarity coefficients of numerical and experimental data for case of B = 3T and Q = 240.2 cm3/s. B = 3T, Flowrate (Q) = 240.2 cm3/s, Locations: B//M//T jth pair Δϕ at locations B//M//T.

J = 1, Z = 0.013m B//M//T 5.78//5.81//5.81

J = 2, Z = 0.021m B//M//T 6.73//6.87//6.88

J = 3, Z = 0.029m B//M//T 7.08//7.25//7.27

J = 4, Z = 0.037m B//M//T 6.74//6.87//6.88

J = 5, Z = 0.045m B//M//T 5.8//5.81//5.81

Δϕ2num [mV] j

6.51//6.51//6.51

7.73//7.79//7.79

8.16//8.25//8.25

7.73//7.79//7.79

6.52//6.51//6.51

Δϕ3num j [mV]

12.26//12.26//12.25

14.24//14.19//14.09

14.95//14.89//14.75

14.24//14.19//14.09

12.26//12.26//12.25

t Δϕ1exp [mV] j

5.00//5.05//5.09

6.10//6.26//6.27

6.46//6.62//6.6

6.37//6.5//6.33

5.46//5.49//5.22 5.97//6.05//6.05

Δϕ1num j [mV]

t [mV] Δϕ2exp j

6.18//6.07//6.04

7.19//7.31//7.39

7.54//7.55//7.78

7.18//7.43//7.43

t Δϕ3exp [mV] j

11.47//11.58//11.43

13.5//13.52//13.30

14.05//13.97//13.82

13.47//13.42//13.22

11.53//11.60//11.5

K1,num j

0.471//0.474//0.474

0.473//0.484//0.488

0.474//0.487//0.493

0.473//0.484//0.488

0.473//0.474//0.474

K1,exp j

t

0.436//0.436//0.445

0.452//0.463//0.471

0.46//0.474//0.478

0.473//0.484//0.479

0.473//0.473//0.454

K2,num j

0.531//0.531//0.531

0.543//0.549//0.553

0.546//0.554//0.559

0.543//0.549//0.553

0.532//0.531//0.531

t K2,exp j

0.539//0.524//0.528

0.533//0.541//0.556

0.537//0.540//0.563

0.533//0.554//0.562

0.518//0.522//0.526

To determine the existence of different flow regime the normalized measured pressure drop (ΔP* = ΔP/(0.5 * ρ * U02 * Ha)) is plotted with corresponding Ha/Re values as shown in Fig. 8(a). Here, U0 is the average velocity in channel-3. It is observed that at higher magnetic fields, the normalized pressure drop is increasing linearly with Ha/Re and hence the dimensional pressure drop is proportional to the σ a U0B02 as expected in typical MHD flow. But at lower magnetic field (B = 1T), the pressure drop falls from a peak value at Ha/Re = 0.013. By comparing all the pressure drop data at lower Ha/Re values (see Fig. 8(b)) it is seen that there is jump at Ha/Re = 0.013 and thus indicates a likely transition of flow regime. So the analysis of measured values of total pressure drop again confirms the validity of laminar approximation in the present numerical model. However, it should be noted that the observed transition at Ha/Re = 0.013 may be considered for applicable to the present test-section only. Further study is required to establish if there exists a threshold value of Ha/Re ratio for such transition in arbitrary conducting channel. In the laminar flow regime, the MHD normalized pressure drop (ΔP/σ aU0B02) decreases as ∼N−0.72 as shown in Fig. 9. Similar observations of the normalized pressure drop with N were also made in insulating rectangular duct [17]. This indicates 3-D pressure drop due to axial currents at various bends and electrical coupling of different structural walls decreases with increasing N. The total pressure drop in the test-section including inlet/outlet pipe estimated from the numerical simulation is compared with measured pressure drop by A1 & A2 pressure transmitter as shown in

Table 7. The inlet/outlet pipeline extension upto A1 & A2 pressure transmitter locations consists of 3 different sections. Test-section inlet is connected with smaller pipe of inner dia. 15.8 mm (length 98.5 mm) followed by pipeline of inner dia.16.5 mm (length 464.5 mm) which is then integrated with the main loop pipe of 27.3 mm inner dia (length790 mm up to location A1) through a 90 ° bend (see Fig. 10.). Outlet pipe extension up to location A2 is similar to the inlet section, but the larger pipe (inner dia. 27.3 mm) of length 980 mm is attached without any bending. Since the axial magnetic field is very low and parallel to the flow direction in the inlet/outlet pipeline section except at the bending, the flow is assumed turbulent for estimation of pressure drop beyond the computation domain (ΔPpipe). As can be seen in Table 7, reasonably good agreement is observed for the numerical and measured values for case of B0 = 2T. However, more deviation is observed as the applied magnetic field strength is increased to B0 = 3T. The higher deviation is anticipated from the fact that non account of additional MHD pressure loss in the bending region of the inlet section where flow path is transverse to the axial magnetic field. The additional pressure loss due to very weak field strength and higher velocity at this bending location is expected to be higher for case of 3T as compare to the case of 2T and hence more deviation. 6. Discussion on velocity distribution In Fig. 11 the numerical velocity profile across the side walls of all the channels is shown at the centre of different flow cross sections for

Table 6 Root mean square deviation of similarity coefficients. Deviation (%)

σB Case B = 3T Q = 240.2 cm3/s channel-1 0.012873 channel-2. 0.018955 Case B = 3T Q = 490.7 cm3/s channel-1 0.011875 channel-2 0.010402 Case B = 2T Q = 242.2 cm3/s channel-1 0.035179 channel-2 0.038707 Case B = 2T Q = 492.5 cm3/s channel-1 0.03804 channel-2 0.0077

K num

σM

σT

σ

0.013826 0.019652

0.008047 0.00912

0.011855 0.01662

0.465467 0.5527

2.55 3.0

0.01068 0.00911

0.011313 0.005292

0.0113 0.00855

0.47754 0.5424

2.4 1.6

0.033599 0.033006

0.036666 0.018094

0.03517 0.009977

0.476036 0.546403

7.38 1.83

0.0224 0.0058

0.0185 0.0134

0.0276 0.0095

0.4715 0.5536

5.85 1.72

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the case of B0 = 3T and flowrate of 240.2 cm3/s. The liquid metal enters into the test-section as a high velocity submerged jet from the inlet pipe. Then it spreads into the common inlet header after striking the back wall opposite to the inlet pipe. Subsequently the flow is redistributed in the two parallel channels. In the parallel channels, the characteristics M-profile of axial velocity profile is highly asymmetric at the entrance due to bend effects. Then the flow gradually approaches to fully developed (asymptotic) profile as it advances along the vertical direction. Asymmetric profiles are developed at location ‘M ’of channel1 and channel-3 is primarily due to different wall thickness and electrical coupling with channel-2. The higher the wall thickness lower is the adjacent side layer peak velocity. Interestingly, although both the side wall thickness of channel-2 is same (3 mm) relative increase of the side layer peak velocity adjacent to return channel is observed. This inequality of side layer peak velocity can be explained by analyzing the current path linked with the corresponding side walls. Due to unequal flowrates and transverse width of channel-3 (25 mm) and channel-2 (20 mm), unequal voltage is developed at either side of the common partition wall. This lead to flow of leakage current from higher potential side wall (right) of channel-3 to lower potential side wall (left) of channel-2 through the dummy breeder walls. In addition to this leakage current, transverse current from the top and bottom wall also enters into the common partition wall. As a result of multiple current path, the effective wall thickness of the side adjacent to return path is less compare to the other side wall of channel-2. The effective lower thickness leads to lower relative wall conductance ratio and hence increases the peak velocity. The difference in side layer peak velocity of channel-3 is attributed to unequal thickness of the side walls. The changing velocity profile along the flow path even at the high magnetic field of 3T indicates the length of the channel height is not sufficient to achieve fully developed flow. The longer development length as compared to the case of isolated channel is mainly due to 3-D currents originated from top and bottom walls and also from the bend effects that continuously modify the velocity profile. Across the Hartmann walls of all the channels, the velocity profile is symmetric and the same symmetry is observed with the measured side wall potential difference profile. 7. Summary and conclusions

Fig. 8. (a): Variation of normalized measured pressure drop (Δp*) in Test-section including inlet/outlet pipe (up to A1 &A2) with respective Ha/Re values. (b) Variation at lower Ha/Re region.

Experiments and numerical analyses for Pb-Li MHD flow in a test–section having coupled parallel and antiparallel flow configuration, L and U-type bends, have been carried out at high characteristics parameters relevant to fusion blanket conditions. Although the testsection model is not exactly the scaled down replica of LLCB TBM, the Pb-Li flow paths in the model simulate some of the features of LLCB TBM flow configuration. Wall electrical potentials were measured at various locations of the test-section and the respective values are compared with the results of numerical simulation. The total flowrate and its distribution in parallel channels are estimated from the measured side wall potential and non dimensional numerical profile of respective channel. It is observed that numerical prediction of potential difference data is consistently higher than the measured values. This deviation of numerical results is attributed to the change in calibration factor of the flowmeter. The deviation with the real flowrate is found to be ∼5% of the flowmeter measured value. The fraction of flowrate in individual channel as predicted by the numerical computation is confirmed with the estimated values based on measured side wall potential data. The matching is reasonably well taking into account the correction factor in the flowmeter measured value. A similarity coefficient (K) is proposed for quantitative estimation of the similarity between numerical and corresponding experiment data of wall potential distribution. It is observed that the degree of similarity is close to 97% at higher magnetic fields (B0 ≥ 2T) and hence proves the validity of numerical model in these flow regimes. It is also observed that a higher fraction of flow is drawn by the channel adjacent to the return channel of opposite

Fig. 9. Variation of normalized pressure drop with Interaction parameter (N).

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Table 7 Comparison of total pressure drop obtained by numerical solution and corresponding values of experiments for various case studies. ΔpNum. (bar)

Case

ΔpTS (bar)

Δppipe (bar).

ΔpTotal(bar)

0.446 1.187 0.84 1.99

0.139 0.561 0.137 0.557

0.585 1.748 0.98 2.55

a

3

B0 = 2T, Q = 242.2 cm /s B0 = 2T, Q = 492.5 cm3/s B0 = 3T, Q = 240.2 cm3/s B0 = 3T, Q = 490.7 cm3/s a b

b

ΔpExpt. (bar)

Deviation with experiment%

0.584 1.763 1.126 2.876

0.2 0.9 13 11.3

ΔpTS is the pressure drop in the test-section including inlet and outlet pipe of axial length 40 mm. Δppipe is the pressure drop in the extended pipe line up to pressure transmitter A1 and A2.

Fig. 10. Photograph of inlet/outlet pipe and their extension towards pressure transmitters A1 and A2.

flow path. The unequal flow distribution is attributed to the interaction of circulating 3-D currents with the applied magnetic fields in the bottom manifold region and geometrical factors of inlet flow conditions. 3-D currents which are generated from the top and bottom walls of the test-section is responsible for the continuous change of velocity profile throughout the vertical height of the channel. The magnitude of 3-D currents is higher at lower N and saturates at higher values. Measured pressure drop in the test-section indicates a linear proportionality to the scaling parameter of σ aU0B02 at higher Ha/Re values as anticipated in typical MHD flow regime. The analysis indicates that FLUENT code based on laminar model can be used to simulate liquid metal MHD flow in electrically conducting multiple parallel channels under high characteristic flow parameters. Moreover, the results of such numerical studies can be used for further comparison with the results of a future flow model which accounts the effects of flow turbulence. Appendix A. Grid independent study To ensure proper resolution of Hartmann and Side layers, numerical computation of a single case study (B0 = 3T and mass flowrate of 2.26 kg/s) has been performed in three different grid structure named as Grid-1, Grid-2 and Grid-3. The test case with B0 = 3T and mass flowrate of 2.26 kg/s is considered for grid performance analysis. Table A1 summarize the number of elements in the Hartmann layer (N_δH), Side layer (N_δS), across the channel width along X-direction (N_X) and Z-direction (N_Z) of the flow cross section and total volume element of computation domain. The number of elements in Hartmann layer is kept same for Grid-2 and Grid-3 but the later having higher elements

Fig. 11. Velocity profile across the side walls of all the channels at the centre of different flow cross sections for flow rate of 240.2 cm3/s and applied magnetic field of 3T.

Table A1 Mesh structure of different Grid in a typical flow cross section. Grid Type

N_X

N_Z

N_δS

N_δH

Total vol. cell

Grid-1 Grid-2 Grid-3

40 50 50

50 50 60

8 12 12

6 3 3

1529600 2051800 2382700

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Fig. A1. Axial velocity profile (Uy) across the side walls of all channel in different grid structure at location ‘M’ and centre of the cross section. Table A2 Side layer peak velocity of different channel and their deviation with corresponding results of Grid-2. Channel

channel-1 (left leg) channel-1 (right leg). channel-2 (left leg) channel-2 (right leg) channel-3 (left leg) Channel-3 (right leg)

Side layer peak velocity (m/s)

Deviation with respect to Grid-2

Grid-1

Grid-2

Grid-3

Grid-1

Grid-3

0.425

0.475

0.481

10.6%

1.3%

0.484

0.447

0.447

8.1%

0%

0.604

0.571

0.567

5.7%

0.7%

0.438

0.501

0.507

12.5%

1.2%

−0.673

−0.717

−0.719

6.1%

0.3%

−0.77

−0.778

−0.78

1.0%

0.3%

Table A3 Comparison of side wall voltage of each channel in different grid structure at the location ‘M’. B = 3T, Flowrate (Q) = 240.2 cm3/s, Locations: M jth pair Δϕ at locations.

Δϕ1num j [mV]

J = 1, Z = 0.013m Gr-1//Gr-2//Gr-3 5.62//5.8//5.83

J = 2, Z = 0.021m Gr-1//Gr-2//Gr-3 6.67//6.87//6.9

J = 3, Z = 0.029m Gr-1//Gr-2//Gr-3 7.04//7.25//7.28

J = 4, Z = 0.037m Gr-1//Gr-2//Gr-3 6.68//6.87//6.91

J = 5, Z = 0.045m Gr-1//Gr-2//Gr-3 5.64//5.81//5.84

Δϕ2num [mV] j

6.62//6.51//6.51

7.94//7.78//7.8

8.39//8.25//8.25

7.94//7.79//7.8

6.62//6.51//6.52

Δϕ3num j [mV]

12.19//12.26//12.28

14.16//14.19//14.23

14.83//14.89//14.91

14.16//14.19//14.23

12.19//12.26//12.28

across the Hartmann walls. In these three type of grids, the axial velocity profile across the side walls of all channels is compared at cross section ‘M’ (Y = 0.127 m) as shown in Fig. A1. Considering the results of Grid-2 as reference, larger deviation is observed while comparing side layer jet peak velocity of Grid-1. The maximum deviation in channel-2 peak velocity is 12.5% at the right leg side and minimum deviation of 1% at channel-3 right leg. On the other hand, smaller deviation is observed with the results of Grid-3. The maximum deviation in side layer peak velocity is 1.3% at left leg side of channel-1. Table A2 summarizes the peak velocity in side layer jet of different channel and their deviation with respect to results of Grid-2 at location ‘M’. However, no significant changes are observed in the wall electric potential distribution of these three types of grid structure. Numerical results of side wall voltage of each channel at location ‘M’ is compared with different grid structure as shown in Table A3. The maximum deviation in side wall voltage is 3.1% at j = 1 (Z = 0.013 m, Y = 0.127 m) of channel-1 whereas, deviation with Grid-3 is less than 1% at all places of cross section ‘M’. Thus we assume that mesh in Grid-1 is relatively coarser as compare to the Grid-2 and Grid-3. However, in view less deviation and faster computation time due to lesser volume elements (2.05 million), we have presented the results of all other case studies in Grid–2 mesh structure.

TBM to increaseneutronic and thermo-hydraulics performances, Fusion Eng. Des. 85 (2010) 1054–1058. [3] Sergey Smolentsev, Rene Moreau, Mohamed Abdou, Characterization of keymagnetohydrodynamic phenomena in PbLi flows forthe US DCLL blanket, Fusion Eng. Des. 83 (2008) 771–783. [4] C. Mistrangelo, L. Bühler, Liquid metal magnetohydrodynamic flows in manifolds of dualcoolant lead lithium blankets, Fusion Eng. Des. 89 (2014) 1319–1323.

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