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HIMAG HyPerComp Incompressible MHD solver for Arbitrary Geometry
Appendix II: Benchmark Cases
HIMAG 2019 HyPerComp, Inc.
2629 Townsgate Rd, Suite
105
Westlake Village, CA 91361
http://www.hypercomp.net
(T) 805-371-7500
Release 1.0
July 2019
http://www.hypercomp.net/
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HIMAG 2019
CONTENTS
1
Pre-Defined
Cases in HIMAG
1.1 Rectangular Duct, Insulating Walls
1.1.1 No MHD (Pure Hydrodynamics)
1.1.2 MHD with Uniform B Field
1.1.3 MHD with Exponential B Field
1.2 Rectangular Duct, Conducting Walls
1.2.1 No MHD (Pure Hydrodynamics)
1.2.2 MHD with Uniform B Field
1.2.3 MHD with Exponential B Field
1.3 Half Rectangular Duct, Insulating Walls
1.3.1 No MHD (Pure Hydrodynamics)
1.3.2 MHD
1.4 Half Rectangular Duct, Conducting Walls
1.4.1 No MHD (Pure Hydrodynamics)
1.4.2 With MHD
1.5 Circular Duct, Conducting Walls
1.5.1 Pure Hydrodynamics without Non-Orthogonal
Correction
1.5.2 Pure Hydrodynamics with Orthogonal Correction
1.5.3 MHD without Non-Orthogonal Correction
1.5.4 MHD with Non-Orthogonal Correction
1.5.5 MHD with Constant B Field
2
Benchmark Cases
2.1 Alex
2.2 Broken dam
2.3 Cavity
2.4 Cir3d_Re100
2.5 Cirful_Ha100 (Fully Developed)
2.6 Cirful_Re1k (Fully Developed)
2.7 Cond3d_Ha100
2.8 Demo1_Hunt3d
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HIMAG 2019
2.9 Demo2_sher3d
2.10 Dissp_Full (Fully Developed)
2.11 Duct2d_Re10
2.12 Duct3d_Re15k
2.13 Ductful (Fully Developed)
2.14 Entrance
2.15 Ha500_2d
2.16 Huntful_Ha100_io2 (Fully Developed)
2.17 Huntful_Ha300 (Fully Developed)
2.18 Ppe_MHD
2.19 Sherful_Ha300 (Fully Developed)
2.20 Sherful_Ha500_io2 (Fully Developed)
2.21 Therm
2.22 Wall
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HIMAG 2019
1 | M A I N I N D E X
1 CASES WITH PRE-DEFINED GRIDS IN
HIMAG GRID
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HIMAG 2019
2 | M A I N I N D E X
Case 1.1 : Rectangular Duct, Insulating Walls
Location : Home> work> himag> predef> case1
Grid Generation :
The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:
L = 25 (For Pure Hydrodynamic Case, L = 85) a = 1 b = 1 Ha = 500 Re = 10 CPU = 1 nxcel = 32 nycel = 42 nzcel = 40
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 1.1 Rectangular Duct Grid
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HIMAG 2019
3 | M A I N I N D E X
Case 1.1.1 : No MHD (Pure Hydrodynamics)
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 1.00E-01, rho1 = 1.0, sleng = 1.0, ubar = 1.0, dpdx = -0.0, iuvw = 1, ichan = 0, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nvel = 0, iortho = 1, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,
Output: 50000th Iteration
ppe-CG step = 50000 0 -1.66045E+01 Tstep = 50000 1.00000E-03 -1.97761E-03 3.99802E+00 2.07680E+00 1.65479E-01
Mass Flow Rate : 3.99802E+00
Time : 120 min
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HIMAG 2019
4 | M A I N I N D E X
++ pres_res
Fig. 1.2a Pressure Residual
𝜕𝑝
𝜕𝑥= −0.711 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 14)
Fig. 1.2b Dpdx plot
𝜕𝑝
𝜕𝑥= −0.6912
0.711 – 0.6912 = 2.79% 0.711
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
5 | M A I N I N D E X
Case 1.1.2 : MHD with Constant B Field
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 5000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, dpdx = -0.0, nbf = -1, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0, Output: 5000th Iteration mhd-CG step = 5000 2 -1.01381E+01 -2.21411E+00 ppe-CG step = 5000 100 -5.44430E+00 Tstep = 5000 8.00000E-05 -9.11307E-03 3.99089E+00 4.93355E+00 -2.57849E-01
Mass Flow Rate : 3.99089E+00
Time : 379 min
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HIMAG 2019
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## pres_res
++ mhd_res
Fig. 1.3a Pressure and MHD Residual
𝜕𝑝
𝜕𝑥= −52.08 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 14)
Fig. 1.3b dpdx plot
𝜕𝑝
𝜕𝑥= −52.50
52.50 – 52.08 = 0.81% 52.08
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
7 | M A I N I N D E X
Case 1.1.3 : MHD with exponent B Field
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, iuvw = 1, dpdx = -0.0, ibf = 2, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,
Output: 10000th Iteration
mhd-CG step = 10000 99 -1.00513E+01 -1.96048E+00 ppe-CG step = 10000 100 -7.14327E+00 Tstep = 10000 8.00000E-05 -9.07993E-03 3.99092E+00 9.97569E+00 -5.21621E-01
Mass Flow Rate : 3.99092E+00
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HIMAG 2019
8 | M A I N I N D E X
Time : 441 min
## pres_res
++ mhd_res
Fig. 1.4a Pressure and MHD Residual
𝜕𝑝
𝜕𝑥= −52.08 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 14)
Fig. 1.4b dpdx plot
𝜕𝑝
𝜕𝑥= −52.23
52.23 – 52.08 = 0.3% 52.08
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
9 | M A I N I N D E X
Case 1.2 : Rectangular Duct with Conducting Walls
Location : Home> work> himag> predef> case2
Grid Generation :
The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:
L = 25 (For pure Hydrodynamic Case, L = 85) a = 1 b = 1 Ha = 500 Re = 10 Cw = 0.1 CPU = 1 nxcel = 32 nycel = 50 nzcel = 48
Mass Flow Rate (rho*ubar*area) = 3.14
Fig 1.5 Rectangular duct grid
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HIMAG 2019
10 | M A I N I N D E X
Case 1.2.1 : No MHD (Pure Hydrodynamics)
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iuvw = 1, ibf = 2, ichan = 2, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nvel = 0, iortho = 1, ngrad = 5, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,
Output: 50000th Iteration
ppe-CG step = 50000 0 -1.61488E+01 Tstep = 50000 1.00000E-03 -1.62970E-03 3.99837E+00 2.06296E+00 2.25365E-01
Mass Flow Rate : 3.99837E+00
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HIMAG 2019
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Time : 180 min
++ Pres_res
Fig 1.6a Pressure Residual
𝜕𝑝
𝜕𝑥= −0.711 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈)
Fig. 1.6b dpdx plot
𝜕𝑝
𝜕𝑥= −0.68
0.711 – 0.68 = 4.36%
0.711
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
12 | M A I N I N D E X
Case 1.2.2 : MHD with Uniform B Field
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 5000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, nbf = -1, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 1, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,
Output: 5000th Iteration
mhd-CG step = 5000 35 -1.02013E+01 -1.94567E+00 ppe-CG step = 5000 100 -8.96444E+00 Tstep = 5000 8.00000E-05 -2.24607E-01 3.77539E+00 9.38867E+00 1.45105E-02
Mass Flow Rate : 3.77539E+00
Time : 369 min
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HIMAG 2019
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Residual Plot:
## pres_res
++ mhd_res
Fig 1.7a Pressure and MHD Residual
𝜕𝑝
𝜕𝑥= −1458.88 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 14)
Fig. 1.7b dpdx plot
𝜕𝑝
𝜕𝑥= −1439.033
1458.88 – 1439.033 = 1.36% 1458.88
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
14 | M A I N I N D E X
Case 1.2.3 : MHD with Exponent B Field
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iuvw = 1, ibf = 2, ichan = 1, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, nvel = 0, iortho = 1, ngrad = 5, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,
Output: 50000th Iteration
mhd-CG step = 50000 4 -1.62384E+01 -5.06762E+00 ppe-CG step = 50000 100 -1.35522E+01 Tstep = 50000 8.00000E-05 -2.24605E-01 3.77539E+00 9.90765E+00 -1.09580E+00
Mass Flow Rate : 3.77539E+00
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HIMAG 2019
15 | M A I N I N D E X
Time : 1810 min for 50000 iter.
Residual Plot:
## pres_res
++ mhd_res
Fig 1.8a Pressure and MHD Residual
𝜕𝑝
𝜕𝑥= −1458.88 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 14)
Fig. 1.8b dpdx plot
𝜕𝑝
𝜕𝑥= −1425.35
-1458.88 + 1425.35 = 2.29% -1458.88
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
16 | M A I N I N D E X
Case 1.3 : Half Rectangular Duct with Insulating Walls
Location : Home> work> himag> predef> case3
Grid Generation :
The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:
L = 25 a = 1 b = 1 Ha = 500 Re = 10 CPU = 1 nxcel = 32 nycel = 21 nzcel = 40
Mass Flow Rate (rho*ubar*area) = 3.14
Fig 1.9 Half Rectangular Duct Grid
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HIMAG 2019
17 | M A I N I N D E X
Case 1.3.1 : No MHD (Pure Hydrodynamics)
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, dpdx = -0.0, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 0, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,
Output: 10000th Iteration
ppe-CG step = 10000 100 -7.28344E+00 Tstep = 10000 8.00000E-05 8.63320E-05 2.00009E+00 1.83297E+00 1.39289E-05
Mass Flow Rate : 2.00009E+00
Time : 10000 iterations in 150 min
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HIMAG 2019
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Residual Plot:
## pres_res
Fig 1.10a Pressure Residual
𝜕𝑝
𝜕𝑥= −0.711 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈)
Fig. 1.10b dpdx plot
𝜕𝑝
𝜕𝑥= −0.7027
0.711 – 0.7027 = 1.17% 0.711
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
19 | M A I N I N D E X
Case 1.3.2 : With MHD
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 1.00E-10, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.00E+00, dpdx = -0.0, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,
Output: 10000th Iteration mhd-CG step = 10000 10 -1.00398E+01 -2.04951E+00 ppe-CG step = 10000 100 -7.69985E+00 Tstep = 10000 8.00000E-05 -4.53992E-03 1.99546E+00 9.97569E+00 -5.21560E-01
Mass Flow Rate : 1.99546E+00
Time : 10000 iterations in 500 min
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HIMAG 2019
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Residual Plot :
## pres_res
++ mhd_res
Fig 1.11a Pressure and MHD Residual
𝜕𝑝
𝜕𝑥= −52.08 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 )
Fig. 1.11b dpdx plot
𝜕𝑝
𝜕𝑥= −52.52
52.52 – 52.08 = 0.85% 52.08
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
21 | M A I N I N D E X
Case 1.4 : Half Rectangular Duct with Conducting Walls
Location : Home> work> himag> predef> case4
Grid Generation :
The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:
L = 25 (For Pure Hydrodynamic case, L = 85) a = 1 b = 1 Ha = 500 Re = 10 Cw = 0.1 CPU = 1 nxcel = 32 nycel = 25 nzcel = 48
Mass Flow Rate (rho*ubar*Area) = 3.14
Fig 1.12 Half Rectangular Duct Grid
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HIMAG 2019
22 | M A I N I N D E X
Case 1.4.1 : No MHD (Pure Hydrodynamics)
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iuvw = 1, ibf = 2, ichan = 2, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nvel = 0, iortho = 1, ngrad = 5, nskp = 10, ipmax = 100, immax = 100, lambdu = 1.0, epsmin = -16.0,
Output: 50000th Iteration ppe-CG step = 50000 100 -7.34940E+00 Tstep = 50000 8.00000E-05 4.12956E-05 2.00004E+00 2.05773E+00 1.42469E-05
Mass Flow Rate : 2.00009E+00
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HIMAG 2019
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Time : 50000 iterations in 285 min.
## pres_res
Fig 1.13a Pressure Residual
Dpdx plot : 𝜕𝑝
𝜕𝑥= −0.711 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈)
Fig. 1.13b dpdx plot
𝜕𝑝
𝜕𝑥= −0.7039
0.711 – 0.7039 = 1.01% 0.711
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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HIMAG 2019
24 | M A I N I N D E X
Case 1.4.2 : With MHD
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 8.00E-05, visc1 = 1.00E-01, rho1 = 1.0, sgmf1 = 2.50E+04, sgmw1 = 2.50E+04, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iortho = 1, nvel = 0, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 2, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,
Output: 10000th Iteration
mhd-CG step = 10000 0 -1.00606E+01 -2.02677E+00 ppe-CG step = 10000 100 -7.67125E+00 Tstep = 10000 8.00000E-05 -1.12304E-01 1.88770E+00 9.90583E+00 -1.10797E+00
Mass Flow Rate : 1.88770E+00
Time : 10000 iterations in 510 min.
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HIMAG 2019
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Residual plot :
## mhd_res
++ pres_res
Fig 1.14a Pressure and MHD Residual
𝜕𝑝
𝜕𝑥= −1458.88 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈)
Fig. 1.14b dpdx plot
𝜕𝑝
𝜕𝑥= −1426.88
-1458.88 + 1426.88 = 2.19% -1458.88
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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Case 1.5 : Circular Duct with Conducting Walls (No MHD)
Location : Home> work> himag> predef> case5
Grid Generation :
The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:
L = 85 t = 0.1 Ha = 0 Re = 400 CPU = 1 nxcel = 32 nycel = 19 nzcel = 50
Mass Flow Rate (rho*ubar*area) = 3.14
Fig 1.15 Circular duct grid where length of the duct is 85m
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Case 1.5.1 : Pure Hydrodynamics without Correction
Input File : nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.50E-03, rho1 = 1.0, sleng = 1.0, ubar = 1.0, dpdx = -0.0, iortho = 1, nvel = 1, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, iuvw = 1 ichan = 11, nskp = 10, ipmax = 40, immax = 40, lambdu = 1.0, epsmin = -16.0,
Output: 50000th Iteration
ppe-CG step = 50000 40 -1.23276E+01 Tstep = 50000 1.00000E-03 2.17465E-04 3.13355E+00 1.93643E+00 1.84521E-01
Mass Flow Rate : 3.13355E+00
Time : 155 min. on a single cpu for 50000 iter.
𝜕𝑝
𝜕𝑥= −
𝑄
(𝜋𝜌𝑎4
8𝜇 )= −0.02
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Fig. 1.16a dpdx plot
𝜕𝑝
𝜕𝑥= −0.0205
0.0205 – 0.02 = 2.5% 0.02
Convergence:
++ Mass Flow Rate
Fig 1.16b Mass Flow Rate
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## pressure_res
Fig 1.16c Pressure Residual
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Case 1.5.2 : Pure Hydrodynamics with Non-Orthogonal Correction
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 50000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.50E-03, rho1 = 1.0, sleng = 1.0, ubar = 1.0, dpdx = -0.0, iuvw = 1, ichan = 11, iortho = 2, nvel = 1, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, nskp = 10, ipmax = 40, immax = 40, lambda = 1.0, epsmin = -16.0,
Output: 50000th Iteration
ppe-CG step = 50000 40 -1.35374E+01 Tstep = 50000 1.00000E-03 2.17486E-04 3.13355E+00 1.93643E+00 1.84521E-01
Mass Flow Rate : 3.13355E+00
Time : 510 min on single cpu for 50000 iter.
𝜕𝑝
𝜕𝑥= −
𝑄
(𝜋𝜌𝑎4
8𝜇 )= −0.02
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Fig. 1.17a dpdx plot
𝜕𝑝
𝜕𝑥= −0.0204
0.0204 – 0.02 = 2.0%
0.02
Convergence History
++ Mass Flow Rate
Fig 1.17b Mass Flow Rate vs Number of Iterations
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xx Press_res
Fig 1.17c Pressure Residual
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Case 1.5.3 : Circular Duct with Conducting Walls (for MHD)
Location : Home > work > himag_08_27_2015 > predef > case5
Grid Generation :
The grid for this case was made using the HIMAG Grid Generation code “xyz” using the following parameters:
L = 25 t = 0.1 Ha = 100 Re = 500 nxcel = 32 nycel = 19 nzcel = 50
Mass Flow Rate (rho*ubar*Area) = 3.14
Fig 1.18 Circular duct grid where length is 25m
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Case 1.5.3 : MHD without Non-Orthogonal Correction
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.00E-03, rho1 = 1.0, sgmf1 = 2.00E+01, sgmw1 = 1.00E+01, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iortho = 1, nvel = 1, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 11, nskp = 10, ipmax = 20, immax = 20, epsmin = -10.0,
Output: 10000th Iteration
mhd-CG step = 10000 10 -1.00890E+01 -3.69640E+00 ppe-CG step = 10000 20 -6.46667E+00 Tstep = 10000 1.00000E-03 -3.27690E-03 3.12304E+00 1.71703E+00 -2.55336E-03
Mass Flow Rate : 3.12304E+00
Time : 150 min. on a single cpu for 10000 iter.
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𝜕𝑝
𝜕𝑥= −1.1876 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 58)
Fig. 1.19a dpdx plot
𝜕𝑝
𝜕𝑥= −1.172
1.1876 – 1.172 = 1.31%
1.1876
Convergence:
++ Mass Flow Rate
Fig 1.19b Mass Flow Rate vs Number of Iterations
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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** mhd_res ## ppe_res
Fig 1.19c Pressure and MHD Residual
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Case 1.5.4 : MHD with Non-Orthogonal Correction
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.00E-03, rho1 = 1.0, sgmf1 = 2.00E+01, sgmw1 = 1.00E+01, sgmw2 = 1.00E-02, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iortho = 2, nvel = 1, nmomt = 1, nppe = 1, nmhd = 1, nheat = 0, ilevels = 0, ngrad = 5, ichan = 11, nskp = 10, ipmax = 20, immax = 20, epsmin = -10.0,
Output: 10000th Iteration
mhd-CG step = 10000 0 -1.00089E+01 -3.66591E+00 ppe-CG step = 10000 0 -1.01164E+01 Tstep = 10000 1.00000E-03 -3.42491E-03 3.12289E+00 1.70492E+00 – 2.73358E-03
Mass Flow Rate : 3.12289E+00
Time : 190 min on single cpu for 10000 iter.
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𝜕𝑝
𝜕𝑥= −1.1876 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝐀𝐩𝐩𝐞𝐧𝐝𝐢𝐱 𝐈𝐈𝐈 𝑝𝑔. 58)
Fig. 1.20a dpdx plot
𝜕𝑝
𝜕𝑥= −1.2004
1.2004 - 1.1876 = 1.08%
1.1876
Convergence:
** Mass Flow Rate Fig 1.20b Mass Flow Rate vs Number of Iterations
file:///C:/Users/Rupanshi/Desktop/HIMAG/HIMAG/Documentation/Manual/2015/HIMAG_AppendixIII.pdf
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** mhd_res
## ppe_res
Fig 1.20c Pressure and MHD Residual
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Case 1.5.5 : MHD with Constant B Field
Input file :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 100, nmax = 10000, iskip = 1000, nwrite = 1000, dtime = 1.00E-03, visc1 = 2.00E-03, rho1 = 1.0, sgmf1 = 2.00E+01, sgmw1 = 1.00E+01, sgmw2 = 1.00E-02, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 1.00E-01, dpdx = -0.0, iuvw = 1, ibf = 2, nbf = -1, ichan = 11, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, nvel = 1, iortho = 2, ngrad = 5, nskp = 10, ipmax = 40, immax = 40, lambdu = 1.0, epsmin = -16.0,
Output: 10000th Iteration
mhd-CG step = 10000 0 -1.60745E+01 -6.68121E+00 ppe-CG step = 10000 40 -1.55832E+01 Tstep = 10000 1.00000E-03 -3.34826E-03 3.12297E+00 1.46962E+00 3.65132E-03
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Mass Flow Rate : 3.12297E+00
Time : 10000 Iteration in 155 min.
𝜕𝑝
𝜕𝑥= −1.1876 (𝑢𝑠𝑖𝑛𝑔 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 ℎ𝑖ℎ𝑎. 𝑝𝑑𝑓 𝑝𝑔. 58)
Fig. 1.21a dpdx plot
𝜕𝑝
𝜕𝑥= −1.2011
1.2011 - 1.1876 = 1.14%
1.1876
Convergence:
** mhd_res ## ppe_res
Fig 1.21b Pressure and MHD Residual
file:///C:/Users/Rupanshi/Desktop/HIMAG/Documentation/hiha.pdf
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2 BENCHMARK CASES
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Case 2.1 : ALEX
Half circular duct with conducting walls, polar grid
Case 5 Location : Home > mhd > bench > alex
Grid Generation :
L = 25 Ha = 10 Re = 10 CPU = 04 Total number of cells : 16313
Mass Flow Rate (rho*ubar*area) = 1.57
Fig 2.1a Rectangular duct grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 10000, iskip = 5000, nwrite = 5000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 10.0, sgmw1 = 10.0, sgmw2 = 1.0e-4, alpha = 1.0, omega = 1.00, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.1, dpdx = -2.00451775, iortho = 2, nvel = 1, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, icha = 12, nskp = 10, lpois = 1, ipmax = 20, immax = 20, igmax = 2,
Output :
mhd-CG step = 10000 20 -1.17200E+01 -4.83119E+00 ppe-CG step = 10000 20 -7.32769E+00 Tstep = 10000 1.00000E-03 -3.93677E-03 1.56654E+00 1.53059E+00 3.73055E-02
Mass Flow Rate : 1.56654E+00
Time : 60 min on 4 CPUs
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Fig 2.1b U_contour1
Fig 2.1c U_contour2
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Fig 2.1d U-in-out
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Case 2.2 : BROKEN DAM
Level Set Case
Case 5 Location : Home > mhd > bench > brokendam
Grid Generation :
L = 5 Ha = 0 Re = 0 CPU = 2 Total number of cells : 3000
Mass Flow Rate (rho*ubar*area) = 0
Fig 2.2a Rectangular duct grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 1500, iskip = 100, nwrite = 2000, dtime = 2.0e-3, dratio = 1000., vratio = 1000., visc1 = 1.e-3, rho1 = 1.0, omega = 1.00, sleng = 2.2, ubar = 0.0, dpdx = 0.0, lambda = 1.0, ssig = 1.0e-2, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 11, ichan = 0, nskp = 1, ipmax = 20, irmax = 10, irinit = 10, epsmin = -16.0, igravt = 1, gx = 0, gy = -1, gz = 0,
Output :
ppe-CG step = 1500 20 -7.04451E+00 level set residual= -9.84345E-01 reinitialization res at it = 11 -2.56133E+00 Tstep = 1500 2.00000E-03 0.00000E+00 0.00000E+00 2.85237E+00 -1.70767E+00
Mass Flow Rate : 0.00000E+00
Time : 41 sec on 2 CPUs
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Fig.2.2b rho – x (1500)
Fig.2.2c rho – x (800)
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Case 2.3 : CAVITY
Heat Transfer for Cavity Problem
Case 5 Location : Home > mhd > bench > cavity
Grid Generation :
L = 1 Ra = 1.0E+06 Ha = 0 Re = 1.4085 CPU = 2 Total number of cells : 200
Mass Flow Rate (rho*ubar*area) = 0.00
Fig 2.3a Rectangular duct grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 5000, iskip = 5000, nwrite = 5000, dtime = 2.0e-4, sleng = 1.0, visc1 = 0.71, rho1 = 1.00, alpha = 1.0, omega = 1.00, dpdx = -0.0, hk1 = 1.0, cp1 = 1.0, hkw1 = 1.00, cpw1 = 1.00, tref = 0.00, deltT = 1.00, gras = 1.4084507e6, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 0, nheat = 6, ncase = 22, ilevels = 0, ichan = 0, nskp = 10, ipmax = 20, ihmax = 100, ibuoy = 1, igravt = 0, idissp = 0, gx = 0.0, gy = -9.81, gz = 0.0,
Output :
ppe-CG step = 5000 1 -1.63597E+01 Heat step = 5000 -2.57268E+01 9.74582E-01 2.75067E-02 6.83897E-13 1.06108E+01 Tstep = 5000 2.00000E-04 0.00000E+00 0.00000E+00 1.26413E+02 2.43162E+02
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Mass Flow Rate : 0.00000E+00
Time : 10 sec for 2 CPUs
Fig. 2.3b T-xy
Fig.2.3c Streamlines
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Fig. 2.3d Iso_therm
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Case 2.4 : CIR3D_RE100
Half Circular Duct, 3-D Polar Grid
Case 5 Location : Home > mhd > bench > cir3d_re100
Grid Generation :
L = 10 Ha = 0.00 Re = 100.00 Cw = 0.00 CPU = 2 Total number of cells = 8800
Re = rho*ubar*r0/visc1 Therefore, r0 = 1
Mass Flow Rate (rho*ubar*area) = 15.7
Fig 2.4a Half Circular Duct 3-D Polar Grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 7000, iskip = 5000, nwrite = 7000, dtime = 1.0e-1, visc1 = 1.0e-1, rho1 = 10., alpha = 1.0, omega = 1.92, sleng = 1.0, ubar = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -0.8, iortho = 2, nvel = 1, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, iuvw = 1, ntrit = 0, iwall = 0, ngrad = 5, ichan = 12, nskp = 10, igmax = 2, ipmax = 20, epsmin = -16.0,
Output :
ppe-CG step = 7000 20 -1.20818E+01 Tstep = 7000 1.00000E-01 -6.79206E-03 1.56360E+01 1.84022E+00 2.95802E-02
Mass Flow Rate : 1.56360E+01
Time : 16 min. on 2 CPUs
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Fig 2.4b x_u_p
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Case 2.5 : CIRFUL_HA100
Half Circular Duct, Fully-Developed, Polar Grid
Case 5 Location : Home > mhd > bench > cirful_ha100
Grid Generation :
Ha = 100 Re = 10 Cw = 0.00 CPU = 2 Total number of cells = 1080
Re = rho*ubar*r0/visc1 Therefore, r0 = 1
Mass Flow Rate (rho*ubar*area) = 1.57
Fig 2.5a Half Circular Duct Grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 1000., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.92, sleng = 1.0, ubar = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -12.363593, iortho = 2, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, iuvw = 1, ntrit = 0, iwall = 0, ngrad = 2, ichan = 12, nskp = 10, igmax = 2, immax = 200, epsmin = -16.0,
Output :
mhd-CG step = 2000 200 -1.58628E+01 -5.86315E+00 Tstep = 2000 1.00000E-04 1.15510E-15 1.57178E+00 1.21579E+00 8.13749E-03
Mass Flow Rate : 1.57178E+00
Time : 1 min. on 2 CPUs
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Fig 2.5b U_yz
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Case 2.6 : CIRFUL_RE1K
Half Circular Duct, Fully-Developed, Polar Grid
Case 5 Location : Home > mhd > bench > cirful_Re1k
Grid Generation :
Ha = 0.00 Re = 1000 Cw = 0.00 CPU = 2 Total number of cells = 960
Re = rho*ubar*r0/visc1 Therefore, r0 = 1
Mass Flow Rate (rho*ubar*area) = 157.04
Fig 2.6a Half Circular Duct Grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 10000, iskip = 10000, nwrite = 10000, dtime = 1.00e-1, visc1 = 1.0e-1, rho1 = 100., alpha = 1.0, omega = 1.92, sleng = 1.0, ubar = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -0.8, iortho = 2, nvel = 1, nmomt = 1, nppe = 0, nmhd = 0, nheat = 0, ilevels = 0, ichan = 12, nskp = 10, igmax = 2, ipmax = 20, epsmin = -16.0,
Output :
Tstep = 10000 1.00000E-01 1.75005E-08 1.57303E+02 1.97379E+00 2.89501E-02
Mass Flow Rate : 1.57303E+02
Time : 31 sec. on 2 CPUs
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Fig 2.6b U_yz
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Case 2.7 : COND3D_HA100
Hunt’s 3D Conducting Walls
Case 5 Location : Home > mhd > bench > condo3d_ha100
Grid Generation :
L = 20 a = 1 b = 1 Ha = 100 Re = 10 CPU = 2 Total number of cells = 11520
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.7a Rectangular Duct Grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 1000., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.1, dpdx = -82.2700358, lambda = 1.0, iuvw = 1, ibf = 2, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 2, ichan = 1, nskp = 10, ipmax = 50, immax = 50, epsmin = -16.0,
Output :
mhd-CG step = 2000 50 -1.10602E+01 -3.30402E+00 ppe-CG step = 2000 50 -8.22705E+00 Tstep = 2000 1.00000E-03 -1.77026E-01 3.82297E+00 3.94303E+00 -3.82977E-01
Mass Flow Rate : 3.82297E+00
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Time : 5.3 min on 2 CPUs
Fig 2.7b V_Comp
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Case 2.8 : DEMO1_HUNT3D
Hunt’s Half, 3-D Conducting Walls
Case 5 Location : Home > mhd > bench > demo1_hunt3d
Grid Generation :
L = 25 Ha = 100 Re = 10 CPU = 2 Total number of cells : 9216
Mass Flow Rate : (rho*ubar*area) = 2.00
Fig2.8a Half Rectangular Duct Grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1000, iskip = 1000, nwrite = 1000, dtime = 1.0e-3, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 1000., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, sleng = 1.0, ubar = 1.0, bval = 1.0, bx0 = 4.0, twal = 0.1, dpdx = -82.2700358, iortho = 1, nvel = 0, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 2, ichan = 2, nskp = 10, ipmax = 100, immax = 100, epsmin = -10.0,
Output :
mhd-CG step = 1000 43 -1.00262E+01 -2.96729E+00 ppe-CG step = 1000 100 -9.25421E+00 Tstep = 1000 1.00000E-03 -8.91579E-02 1.91084E+00 4.07225E+00 -5.36657E-05
Mass Flow Rate : 1.91084E+00
Time : 3.1 min on 2 CPUs
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Fig 2.8b V_Comp
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Case 2.9 : DEMO2_SHER3D
Shercliff’s 3-D Flow
Case 5 Location : Home > mhd > bench > demo2_sher3d
Grid Generation :
L = 25 Ha = 500 Re = 10 CPU = 4 Total number of cells : 13440
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.9a Rectangular duct grid
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Input File :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 20000, iskip = 10000, nwrite = 5000, dtime = 2.5e-5, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 25000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.0, dpdx = -52.0854546, iortho = 1, nvel = 1, nmomt = 1, nppe = 5, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, ipmax = 50, immax = 50, epsmin = -16.0,
Output :
mhd-CG step = 20000 50 -9.44869E+00 -1.63220E+00 ppe-CG step = 20000 50 -7.02311E+00 Tstep = 20000 2.50000E-05 -3.68205E-03 3.99632E+00 9.75060E+00 -5.40673E-01
Mass Flow Rate : 3.99632E+00
Time : 90 min. on 4 CPUs
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HIMAG 2019
71 | M A I N I N D E X
Fig.2.9b V_Comp.
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72 | M A I N I N D E X
Case 2.10 : DISSP_FULL
Fully- Developed Heat Transfer with Dissipation
Case 5 Location : Home > mhd > bench > dissp_full
Grid Generation :
L = 1 Ha = 0 Re = 1 CPU = 2 Total number of cells : 450
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.10a Rectangular Duct Grid
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73 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 400, iskip = 400, nwrite = 4000, dtime = 1.0e-1, visc1 = 1.0, rho1 = 1.0, omega = 1.00, dpdx = -7.11353706, hk1 = 1.00, cp1 = 1.00, hkw1 = 1.00, cpw1 = 1.00, tref = 1.00, deltT = 0.00, gras = 9.81, iortho = 1, nvel = 0, nmomt = 1, nppe = 0, nmhd = 0, nheat = 6, ncase = 23, ilevels = 0, ichan = 0, nskp = 1, ihmax = 1000, nbcg = 1, ibuoy = 0, igravt = 0, idissp = 1, gx = 0.0, gy =-1.0, gz = 0.0,
Output :
Heat-BCG step = 400 539 -1.60108E+01 2.09351E+00 1.00107E+00 2.84225E+01 7.62144E+00 Tstep = 400 1.00000E-01 4.77919E-16 4.01701E+00 2.09078E+00 2.80072E-03
Mass Flow Rate : 4.01701E+00
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74 | M A I N I N D E X
Time : 27 sec on 2 CPUs
Fig 2.10b UT_y
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HIMAG 2019
75 | M A I N I N D E X
Case 2.11 : DUCT2D_RE10
2-D (XY) Duct Flow, Irregular Grid
Case 5 Location : Home > mhd > bench > duct2d_re10
Grid Generation :
L = 20 Ha = 0 Re = 10 CPU = 2 Total number of cells = 400
Mass Flow Rate (rho*ubar*area) = 2.00
Fig 2.11a 2D XY Duct Grid
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76 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 500, iskip = 500, nwrite = 5000, dtime = 2.0e-2, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, omega = 1.00, alpha = 1.0, iortho = 2, nvel = 20, invel = 20, nmomt = 1, nppe = 5, nmhd = 0, nheat = 0, ichan = 0, nskp = 1, ipmax = 40, epsmin = -16.0,
Output :
ppe-CG step = 500 0 -1.60811E+01 Tstep = 500 2.00000E-02 -7.34826E-03 1.99674E+00 1.50294E+00 4.81897E-02
Mass Flow Rate : 1.99674E+00
Time : 6 sec. on 2 CPUs
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HIMAG 2019
77 | M A I N I N D E X
Fig 2.11b dpdx
Fig 2.11c Velocity Profile
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HIMAG 2019
78 | M A I N I N D E X
Case 2.12 : DUCT3D_RE15
3-D Duct Flow, Hex Grid
Case 5 Location : Home > mhd > bench > duct3d_re15
Grid Generation :
L = 35 Ha = 0 Re = 15250 CPU = 4 Total number of cells = 20000
Mass Flow Rate (rho*ubar*area) = 2.2005
Fig 2.12a Rectangular Duct Grid
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79 | M A I N I N D E X
Input File :
nodes = 4, iread = 0, grid_scale = 4.39e-2, istart = 0, nmax = 10000, iskip = 5000, nwrite = 5000, dtime = 5.0e-3, visc1 = 8.2175e-4, rho1 = 865.0, alpha = 1.00, omega = 1.00, sleng = 1.0, ubar = 0.33, dpdx = -1.000945, lambda = 0.0, lambda = 0.0, iortho = 1, nvel = 1, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, ichan = 0, nskp = 10, lpois = 1, ipmax = 50, igmax = 2, epsmin = -16.0,
Output :
ppe-CG step = 10000 50 -1.41983E+01 Tstep = 10000 5.00000E-03 -1.37814E-07 2.20037E+00 3.81456E-01 1.58111E-05
Mass Flow Rate : 2.20037E+00
Time : 65 min on 4 CPUs
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HIMAG 2019
80 | M A I N I N D E X
Fig 2.12b U profile
Fig 2.12c U-yz
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81 | M A I N I N D E X
Case 2.13 : DUCTFUL
Fully-Developed Duct Flow
Case 5 Location : Home > mhd > bench > ductful
Grid Generation :
L = 1 Ha = 0 Re = 10 CPU = 2 Total number of cells : 800
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.13a Rectangular Duct Grid
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HIMAG 2019
82 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 1.0e-2, visc1 = 1.0e-1, rho1 = 1.0, ubar = 1.0, dpdx = -0.711354, iuvw = 1, iortho = 1, nvel = 1, nmomt = 1, nppe = 0, nmhd = 0, nheat = 0, ilevels = 0, ichan = 0, epsmin = -16.0,
Output :
Tstep = 2000 1.00000E-02 -7.96012E-15 4.01195E+00 2.09102E+00 3.09946E-03
Mass Flow Rate : 4.01195E+00
Time : 2 sec approx. on 2 CPUs
Fig 2.13b U Profile
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83 | M A I N I N D E X
Fig 2.13c V_Comp
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HIMAG 2019
84 | M A I N I N D E X
Case 2.14 : ENTRANCE
Heat Transfer for Entrance Problem
Case 5 Location : Home > mhd > bench > entrance
Grid Generation :
L = 20 Ha = 0 Re = 1000 CPU = 2 Total number of Cells : 1750
Mass Flow Rate (rho*ubar*area) =
Fig 2.14a Rectangular Duct Grid
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85 | M A I N I N D E X
Input File(s) : ent_hex.input/ent_prm.input/enter_prm_nppe1.input/ent_prm1.input
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 500,/../2500/.. iskip = 500,/../2500/.. nwrite = 5000, dtime = 2.0e-2,/../../1.0e-2 cfl = 2.70, visc1 = 1.0e-4, rho1 = 1.0, alpha = 0.75,/../1.00 omega = 1.00, ubar = 1.0, dpdx = -0.0, lambda = 1.0, hk1 = 1.0e+2, cp1 = 1.0e+4, hkw1 = 1.00, cpw1 = 1.00, tref = 0.00, deltT = 1.00, gras = 1.0e+3, iortho = 2, nvel = 20, nmomt = 1, nppe = 3,/../1/3 (nppe = 5 does not work for this case) nmhd = 0, nheat = 6,/../1 ncase = 21, ilevels = 0, ichan = 0, nskp = 10,/../1/.. ipmax = 50, ihmax = 2000,/../../- epsmin = -16.0, ibuoy = 0, igravt = 0, idissp = 0, gx = 0.0, gy =-9.81, gz = 0.0,
Time : 35 sec on 2 CPUs
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HIMAG 2019
86 | M A I N I N D E X
Fig 2.14b T- Contour
Fig 2.14c T-Profile
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HIMAG 2019
87 | M A I N I N D E X
Case 2.15 : HA500_2D
2-D Hartmann Flow, Hex Grid
Case 5 Location : Home > mhd > bench > ha500_2d
Grid Generation :
L = 25 Ha = 500 Re = 10000 CPU = 2 Total number of cells : 1425
Mass Flow Rate (rho*ubar*area) = 2.00
Fig 2.15a Rectangular Duct Grid
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HIMAG 2019
88 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 2000, iskip = 2000, nwrite = 2000, dtime = 5.0e-4, cfl = 2.70, visc1 = 1.0e-4, rho1 = 1.0, sgmf1 = 25., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, ubar = 1.0, bval = 1.0, bx0 = 6.0, twal = 0.0, dpdx = -0.0, iortho = 1, nvel = 20, nmomt = 1, nppe = 5, nmhd = 3, nheat = 0, ichan = 0, nskp = 10, lpois = 3, ipmax = 50, epsmin = -10.0,
Output :
ppe-CG step = 2000 5 -1.00622E+01 Tstep = 2000 5.00000E-04 -2.22499E-02 1.98419E+00 1.48317E+00 4.17737E-04
Mass Flow Rate : 1.98419E+00
Time : 22 sec on 2 CPUs
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HIMAG 2019
89 | M A I N I N D E X
Fig 2.15b U-Profile
Fig 2.15c U-Y
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HIMAG 2019
90 | M A I N I N D E X
Fig 2.15d P,u - x
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HIMAG 2019
91 | M A I N I N D E X
Case 2.16 : HUNTFUL_HA100_IO2
Hunt’s Fully-Developed with Conducting Walls, Triangle Grid
Case 5 Location : Home > mhd > bench > huntful_ha100_io2
Grid Generation :
L = 1 a = 1 b = 1 Ha = 100 Re = 10 CPU = 2 Total number of cells : 3168
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.16a Rectangular Duct Triangle Grid
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92 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1000, iskip = 1000, nwrite = 1000, dtime = 5.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1000., sgmw1 = 500., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.50, ubar = 1.0, bval = 1.0, twal = 0.1, dpdx = -52.7434288, c_rest = 0.0, lambda = 1.0, iortho = 2, nvel = 0, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 2, ichan = 1, nskp = 10, immax = 200, igmax = 3, epsmin = -16.0,
Output :
mhd-CG step = 1000 200 -8.43045E+00 -2.07532E+00 Tstep = 1000 5.00000E-04 2.02790E-15 4.05495E+00 1.96898E+00 9.00497E-03
Mass Flow Rate : 4.05495E+00
Time : 6.2 min on 2 CPUs
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Fig 2.16b Velocity Profile
Fig 2.16c V_Comp
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94 | M A I N I N D E X
Case 2.17 : HUNTFUL_HA300
Hunt’s Fully-Developed Conducting Walls, Hex Grid
Case 5 Location : Home > mhd > bench > huntful_ha300
Grid Generation :
L = 1 Cw = 0.05 Ha = 300 Re = 10 CPU = 2 Total number of cells : 1058
Mass Flow Rate (rho*ubar*area) = 4.00
‘
Fig 2.17a Rectangular Duct Hex Grid
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95 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1000, iskip = 1000, nwrite = 1000, dtime = 2.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 9000., sgmw1 = 4500., sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.92, ubar = 1.0, bval = 1.0, twal = 0.1, dpdx = -374.896134, c_rest = 0.0, lambda = 1.0, iuvw = 1, ibf = 2 iortho = 1, nvel = 0, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 1, nskp = 10, immax = 50, epsmin = -16.0,
Output :
mhd-CG step = 1000 28 -1.60258E+01 -5.18635E+00 Tstep = 1000 2.00000E-04 -3.42418E-15 4.10837E+00 3.63715E+00 1.06906E-02
Mass Flow Rate : 4.10837E+00
Time : 12 sec on 2 CPUs
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Fig. 2.17b Velocity Profile
Fig. 2.17c V_Comp
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HIMAG 2019
97 | M A I N I N D E X
Case 2.18 : PPE_MHD
Poisson’s Equation Only, for PPE and MHD
Case 5 Location : Home > mhd > bench > ppe_mhd
Grid Generation :
L = 1 Ha = 0, 1.58, 3.16 Re = 0 CPU = 2 Total number of cells : Between 600-4800
Input File : mhd50/mhd51/mhd52/mhd53/mhd54.input
nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1, iskip = 1, nwrite = 100, dtime = 1.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1.0, sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0/../0.7/1.0/1.0 omega = 1.00, sleng = -/-/-/1.0/.. ubar = 0.0, bx0 = -10., twal = 0.0, dpdx = -0.0, iortho = 2/../../1/2 nvel = 0, nmomt = 0, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0,
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98 | M A I N I N D E X
ncase = 0/1/2/3/4 ngrad = 2 ichan = 0/../../../10 nskp = 1, ipmax = 5000, immax = 5000, epsmin = -16.0/../-10.0/-16.0/.. Input File : ppe50/ppe51/ppe52/ppe53/ppe54/ppe56.input nodes = 1, iread = 0, grid_scale = 1.0, nmax = 1, iskip = 1, nwrite = 100, nout = -/-/-/0/-/- dtime = 1.0e-4, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 1.0, sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0/../0.7/1.0/../.. omega = 1.00, sleng = -/-/-/1.0/../- ubar = 0.0, bx0 = -10., dpdx = -0.0, ibcpat = -/-/-/-/-/1, iortho = 2, nvel = 0, nmomt = 0, nppe = 5, nmhd = 0, nheat = 0, ilevels = 0, ncase = 0/1/2/3/4/6, ichan = 0/../../../10/0, nskp = 1, ipmax = 5000, immax = 5000, epsmin = -16.0/../-10.0/-16.0/-8.0/-16.0,
Boundary Conditions:
ncase = 0
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99 | M A I N I N D E X
x=0,1: (42222) dphi/dn=0 y=-1,1: (51221) phi=0 z=-1: (51221) phi=0 z=1: (51221) phi=1
ncase = 1
x=0,1: (42222) dphi/dn=0 y=-1,1: (52222) dphi/dn=0 z=-1: (51221) phi=-1 z=1: (51221) phi=1
ncase = 2
x=0,1: (42222) dphi/dn=0 y=-1,1: (52222) dphi/dn=0 z=-1,1: (52222) dphi/dn=0
ncase = 3
x=0,1: (42222) dphi/dn=0 y=0: (41221) phi=sin(pi*z) y=1: (41221) phi=exp(pi)*sin(pi*z)+0.5*z*z z=0: (41221) phi=0 z=1: (41221) phi=0.5*y*y
ncase = 4
x=0,1: (42222) dphi/dn=0 r=1: (51221) phi=z
ncase = 6
x=0,: (21221) phi=1 x=4: (41221) phi=0 y=-1,1: (52222) dphi/dn=0 z=-1,1: (52222) dphi/dn=0
Mass Flow Rate :
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HIMAG 2019
100 | M A I N I N D E X
Fig. 2.18a
Fig. 2.18b
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101 | M A I N I N D E X
Fig. 2.18c
Fig. 2.18d
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102 | M A I N I N D E X
Fig.2.18e
Fig.2.18f
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103 | M A I N I N D E X
Fig. 2.18g
Fig. 2.18h
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104 | M A I N I N D E X
Fig. 2.18k
Fig. 2.18m
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105 | M A I N I N D E X
Fig. 2.18n
Fig. 2.18p
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HIMAG 2019
106 | M A I N I N D E X
Case 2.19 : SHERFUL_HA300
Shercliff’s Fully-Developed Flow
Case 5 Location : Home > mhd > bench > sherful_ha300
Grid Generation :
L = 1 a = 1 b = 1 Ha = 300 Re = 10 CPU = 2 Total number of cells : 648
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.19a Rectangular Duct Grid
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HIMAG 2019
107 | M A I N I N D E X
Input File :
nodes = 2, iread = 0, grid_scale = 1.0, istart = 0, nmax = 7000, iskip = 7000, nwrite = 7000, dtime = 2.0e-4, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 9000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, ubar = 1.0, bval = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -31.6583368, iortho = 1, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, immax = 40, epsmin = -16.0,
Output :
mhd-CG step = 7000 40 -1.01823E+01 -2.23337E+00 Tstep = 7000 2.00000E-04 -1.22081E-15 4.04134E+00 1.06584E+00 7.40785E-03
Mass Flow Rate : 4.04134E+00
Time : 1 min approx. on 2 CPUs
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HIMAG 2019
108 | M A I N I N D E X
Fig. 2.19b U Profile
Fig. 2.19c U-yz
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109 | M A I N I N D E X
Fig. 2.19d V_Comp
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HIMAG 2019
110 | M A I N I N D E X
Case 2.20 : SHERFUL_HA500_IO2
Shercliff’s Fully-Developed Flow, Irregular Grid
Case 5 Location : Home > mhd > bench > sherful_ha500_io2
Grid Generation :
L = 1 Ha = 500 Re = 10 CPU = 2 Total number of cells : 840
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.20a Rectangular Duct Irregular Grid
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HIMAG 2019
111 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, grid_scale = 1.0, istart = 0, nmax = 20000, iskip = 10000, nwrite = 10000, dtime = 7.5e-5, cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 25000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, alpha = 1.0, omega = 1.00, ubar = 1.0, bval = 1.0, bx0 = 0.0, twal = 0.0, dpdx = -52.0854546, c_rest = 0.0, iortho = 2, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, ilevels = 0, ngrad = 5, ichan = 0, nskp = 10, immax = 20, igmax = 3, epsmin = -16.0,
Output :
mhd-CG step = 20000 20 -8.73220E+00 -1.16976E+00 Tstep = 20000 7.50000E-05 -3.14916E-15 4.03484E+00 1.12313E+00 3.42424E-03
Mass Flow Rate : 4.03484E+00
Time : 6 min approx. on 2 CPUs
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112 | M A I N I N D E X
Fig. 2.20b Velocity Profile
Fig. 2.20c U-yz
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113 | M A I N I N D E X
Fig. 2.20d V_Comp
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114 | M A I N I N D E X
Case 2.21 : THERM
Heat Transfer
Case 5 Location : Home > mhd > bench > therm
Grid Generation :
L = 1 Ha = 0 Re = 0 CPU = 1 or 2 Total number of cells : 300-600
Mass Flow Rate (rho*ubar*area) = 0.00
Fig 2.21a Rectangular Duct Grid
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HIMAG 2019
115 | M A I N I N D E X
Fig 2.21b Rectangular duct grid
Input File : heat10_prm / heat11_prm / heatk2_prm.input
nodes = 2 /1 /1 iread = 0, grid_scale = 1.0, nmax = 1, iskip = 1, nwrite = 5000, dtime = 1.0e-2 /.. /5.0e-2 cfl = 2.70, visc1 = 1.0e-1, rho1 = 1.0, alpha = 1.0 /.. /0.4 omega = 1.92, ubar = 0.0, dpdx =-0.0, hk1 = 1.00, cp1 = 1.00, hkw1 = 1.00 /.. /4.00 cpw1 = 1.00, tref = 1.00, deltT = 1.00 /2.00 / 1.00 iortho = 2, nvel = 0, nmomt = 0, nppe = 0, nmhd = 0,
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HIMAG 2019
116 | M A I N I N D E X
nheat = 2, ncase = 10 /11 /12 ilaw = 0, ilevels = 0, ichan = 0 /.. /4 nskp = 10, ipmax = 2000, ibuoy = 0, igravt = 0, idissp = 0, gx = 0.0, gy =-9.81, gz = 0.0,
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HIMAG 2019
117 | M A I N I N D E X
Case 2.22 : WALL
Wall Function at Hartmann Layer, Shercliff’s Flow
Case 5 Location : Home > mhd > bench > wall
Grid Generation :
L = 1 a = 1 b = 1 Ha = 500 Re = 10 CPU = 2 Total number of cells : 630
Mass Flow Rate (rho*ubar*area) = 4.00
Fig 2.22a Rectangular Duct Grid
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HIMAG 2019
118 | M A I N I N D E X
Input File :
nodes = 1, iread = 0, nmax = 3000, iskip = 3000, nwrite = 10000, dtime = 5.0e-5, visc1 = 1.0e-1, rho1 = 1.0, sgmf1 = 25000., sgmw1 = 1.0e-10, sgmw2 = 1.0e-2, omega = 1.0, dpdx = -52.0854546, iortho = 1, nvel = 1, nmomt = 1, nppe = 0, nmhd = 5, nheat = 0, iuvw = 1, ngrad = 2, ichan = 0, nskp = 10, immax = 50,
Output :
mhd-CG step = 3000 50 -1.07411E+01 -2.55980E+00 Tstep = 3000 5.00000E-05 7.24459E-15 4.28830E+00 1.11648E+00 2.87488E-02
Mass Flow Rate : 4.28830E+00
Time : 26 sec on 2 CPUs
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HIMAG 2019
119 | M A I N I N D E X
Fig. 2.22b U profile
Fig. 2.22c Velocity
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120 | M A I N I N D E X
Fig. 2.22d Jy Jz
Fig. 2.22e Current
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HIMAG 2019
121 | M A I N I N D E X
Fig. 2.22f U_Contour