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1

Yamamoto, Atsumasa. Secondary flows and losses in two types of straight turbine cascades: Part 1-A Stator case. National Aerospace Laboratory, 1988.

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2

1939-, Okiishi T. H., and United States. National Aeronautics and Space Administration., eds. Effects of shrouded stator cavity flows on multistage axial compressor aerodynamic performance. National Aeronautics and Space Administration, 1996.

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3

United States. National Aeronautics and Space Administration., ed. Reynolds-averaged Navier-Stokes studies of low Reynolds number effects on the losses in a low pressure turbine. National Aeronautics and Space Administration, 1996.

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4

United States. National Aeronautics and Space Administration., ed. Reynolds-averaged Navier-Stokes studies of low Reynolds number effects on the losses in a low pressure turbine. National Aeronautics and Space Administration, 1996.

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5

United States. National Aeronautics and Space Administration., ed. Reynolds-averaged Navier-Stokes studies of low Reynolds number effects on the losses in a low pressure turbine. National Aeronautics and Space Administration, 1996.

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6

United States. National Aeronautics and Space Administration., ed. Reynolds-averaged Navier-Stokes studies of low Reynolds number effects on the losses in a low pressure turbine. National Aeronautics and Space Administration, 1996.

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7

Yamamoto, Atsumasa. Secondary flows and losses in two types of straight turbine cascades: Part 2-A Rotor case. National Aerospace Laboratory, 1988.

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8

United States. National Aeronautics and Space Administration., ed. Turbine rotor/stator plowfield analysis. Lockheed Missiles & Space Co., Inc., Huntsville Engineering Center, 1989.

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9

J, Kerschen Edward, and Lewis Research Center, eds. Influence of vane sweep on rotor-stator interaction noise. National Aeronautics and Space Administration, Lewis Research Center, 1990.

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10

J, Kerschen Edward, and Lewis Research Center, eds. Influence of vane sweep on rotor-stator interaction noise. National Aeronautics and Space Administration, Lewis Research Center, 1990.

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11

Center, Ames Research, ed. Three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction. National Aeronautics and Space Administration, Ames Research Center, 1988.

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12

V, Chima Rodrick, and United States. National Aeronautics and Space Administration., eds. An explicit Runge-Kutta method for unsteady rotor/stator interaction. National Aeronautics and Space Administration, 1988.

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13

V, Chima Rodrick, and United States. National Aeronautics and Space Administration., eds. An explicit Runge-Kutta method for unsteady rotor/stator interaction. National Aeronautics and Space Administration, 1988.

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14

V, Chima Rodrick, and United States. National Aeronautics and Space Administration., eds. An explicit Runge-Kutta method for unsteady rotor/stator interaction. National Aeronautics and Space Administration, 1988.

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15

Center, Ames Research, ed. Three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction. National Aeronautics and Space Administration, Ames Research Center, 1988.

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16

Jen-Ping, Chen, and United States. National Aeronautics and Space Administration., eds. Computation of rotor-stator interaction using Navier-Stokes equations: Final report. CFD Lab, NSF Engineering Research Center for Computational Field Simulation, Mississippi State University, 1995.

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17

Boretti, A. A. Three-dimensional Euler time accurate simulations of fan rotor-stator interactions. National Aeronautics and Space Administration, Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1990.

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18

Boretti, A. A. Three-dimensional Euler time accurate simulations of fan rotor-stator interactions. Lewis Research Centre, 1990.

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19

Jen-Ping, Chen, and United States. National Aeronautics and Space Administration., eds. Computation of rotor-stator interaction using Navier-Stokes equations: Final report. CFD Lab, NSF Engineering Research Center for Computational Field Simulation, Mississippi State University, 1995.

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20

Lewis Research Center. Institute for Computational Mechanics in Propulsion., ed. Three-dimensional Euler time accurate simulations of fan rotor-stator interactions. National Aeronautics and Space Administration, Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1990.

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21

Boretti, A. A. Three-dimensional Euler time accurate simulations of fan rotor-stator interactions. National Aeronautics and Space Administration, Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1990.

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22

Yamamoto, Atsumasa. Mechanisms of secondary flows and losses within a three dimensional turbine stator cascade. National Aerospace Laboratory, 1988.

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23

D, Lorenz Robert, and NASA Glenn Research Center, eds. Stator and rotor flux based deadbeat direct torque control of induction machines. National Aeronautics and Space Administration, Glenn Research Center, 2001.

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24

Kenny, Barbara H. Stator and rotor flux based deadbeat direct torque control of induction machines. National Aeronautics and Space Administration, Glenn Research Center, 2002.

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25

D, Lorenz Robert, and NASA Glenn Research Center, eds. Stator and rotor flux based deadbeat direct torque control of induction machines. National Aeronautics and Space Administration, Glenn Research Center, 2002.

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26

United States. National Aeronautics and Space Administration., ed. The use of cowl camber and taper to reduce rotor/stator interaction noise. National Aeronautics and Space Administration, 1995.

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27

Martinez, R. The use of cowl camber and taper to reduce rotor/stator interaction noise. National Aeronautics and Space Administration, 1995.

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28

Center, NASA Glenn Research, ed. Broadband noise of fans-with unsteady coupling theory to account for rotor and stator reflection/transmission effects. National Aeronautics and Space Administration, Glenn Research Center, 2001.

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29

Center, NASA Glenn Research, ed. Broadband noise of fans-with unsteady coupling theory to account for rotor and stator reflection/transmission effects. National Aeronautics and Space Administration, Glenn Research Center, 2001.

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30

Center, NASA Glenn Research, ed. Broadband noise of fans-with unsteady coupling theory to account for rotor and stator reflection/transmission effects. National Aeronautics and Space Administration, Glenn Research Center, 2001.

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31

D, Hathaway Michael, and United States. National Aeronautics and Space Administration., eds. Effects of stator indexing on performance in a low speed multistage axial compressor. National Aeronautics and Space Administration, 1997.

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32

Wilson, Jack. An experiment on losses in a three-port wave rotor. National Aeronautics and Space Administration, 1997.

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33

Saxer, André P. A numerical analysis of 3-D inviscid stator/rotor interactions using non-reflecting boundary conditions. Gas Turbine Laboratory, Massachusetts Institute of Technology, 1992.

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34

Center, NASA Glenn Research, ed. Linearized unsteady aerodynamic analysis of the acoustic response to wake/blade-row interaction. National Aeronautics and Space Administration, Glenn Research Center, 2001.

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35

C, Simonich John, and United States. National Aeronautics and Space Administration., eds. Low speed, 2-D rotor/stator active noise control at the source demonstration: Under contract NAS3-26618. National Aeronautics and Space Administration, 1997.

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36

L, Whitfield David, and United States. National Aeronautics and Space Administration, eds. Advanced 3-D viscous SSME turbine rotor stator CFD algorithms 6 September 85 - 5 September 86: Final report. National Aeronautics and Space Administration, 1986.

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37

L, Whitfield David, and United States. National Aeronautics and Space Administration, eds. Advanced 3-D viscous SSME turbine rotor stator CFD algorithms 6 September 85 - 5 September 86: Final report. National Aeronautics and Space Administration, 1986.

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38

L, Whitfield David, and United States. National Aeronautics and Space Administration., eds. Advanced 3-D viscous SSME turbine rotor stator CFD algorithms 6 September 85 - 5 September 86: Final report. National Aeronautics and Space Administration, 1986.

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39

L, Whitfield David, and United States. National Aeronautics and Space Administration., eds. Advanced 3-D viscous SSME turbine rotor stator CFD algorithms 6 September 85 - 5 September 86: Final report. National Aeronautics and Space Administration, 1986.

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40

J, Heidelberg Laurence, Envia Edmane, and NASA Glenn Research Center, eds. Coupling of low speed fan stator vane unsteady pressures to duct modes: Measured versus predicted. National Aeronautics and Space Administration, Glenn Research Center, 1999.

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41

J, Heidelberg Laurence, Envia Edmane, and NASA Glenn Research Center, eds. Coupling of low speed fan stator vane unsteady pressures to duct modes: Measured versus predicted. National Aeronautics and Space Administration, Glenn Research Center, 1999.

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42

Center, NASA Glenn Research, ed. TFaNS T̲one F̲a̲n N̲oise Design/Prediction S̲ystem. National Aeronautics and Space Administration, Glenn Research Center, 1999.

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43

F, Blair M., Joslyn H. David, and United States. National Aeronautics and Space Administration., eds. The effects of inlet turbulence and rotor stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. National Aeronautics and Space Administration, 1988.

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44

Dring, Robert P. The effects of inlet turbulence and rotor stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. National Aeronautics and Space Administration, 1986.

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45

Center, NASA Glenn Research, ed. Acoustic scattering by three-dimensional stators and rotors using the SOURCE3D code. National Aeronautics and Space Administration, Glenn Research Center, 1999.

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46

Yamamoto, Atsumasa. Mechanisms of endwall/leakage flows and the associated losses in a linear turbine rotor cascade with blade tip-clearance. National Aerospace Laboratory, 1988.

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47

Boguslawsky, Iliya, Nikolay Korovkin, and Masashi Hayakawa. Large A.C. Machines: Theory and Investigation Methods of Currents and Losses in Stator and Rotor Meshes Including Operation with Nonlinear Loads. Springer, 2018.

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48

Boguslawsky, Iliya, Nikolay Korovkin, and Masashi Hayakawa. Large A.C. Machines: Theory and Investigation Methods of Currents and Losses in Stator and Rotor Meshes Including Operation with Nonlinear Loads. Springer, 2016.

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49

Large A. C. Machines: Theory and Investigation Methods of Currents and Losses in Stator and Rotor Meshes Including Operation with Nonlinear Loads. Springer, 2016.

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50

Vaez-Zadeh, Sadegh. Machine Modeling. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198742968.003.0002.

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This chapter presents dynamic and steady-state modeling of permanent magnet synchronous (PMS) machines with the help of reference frames. The modeling starts with a machine model in terms of phase variables. An equivalent two-axis model in a stationary reference is then obtained by a reference frame transformation. A further transformation to a two-axis rotor reference frame, with its direct axis aligned with the axis of a permanent magnet rotor pole, is derived. Another transformation to a two-axis stator flux linkage reference frame is also presented. Finally, a motor model in polar coordina
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