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High speed and high efficiency synchronized electric motors are favored in the automotive industry and turbo machinery industry worldwide because of the demands placed on efficiency. Herein an electric motor thermal control system using cooling air which enters from the drive end of the motor and exits from the non-drive end of the motor as the rotor experiences dissipates heat is addressed using CFD. Analyses using CFD can help to find the appropriate mass flow rate and windage losses while satisfying temperature requirements on the motor. Here, the air flow through a small annular gap is fed at 620 L/min (0.011 kg/sec) as the rotor spins at 100,000 rpm (10,472 rad/sec) and the rotor dissipates 200 W. The CFD results are compared with experimental results. Based upon the CFD findings, a novel heat transfer correlation suitable for large axial Reynolds number, large Taylor number, small annular gap Taylor-Couette flows subject to axial cross-flow is proposed herein.

Due to demands placed on efficiency, high speed and high efficiency synchronized electric motors are favored in the automotive industry and turbo machinery industry worldwide. In general, direct coupling the electric motor to the drive shaft will yield simplicity of the mechanical design and deliver high system efficiency. However, the demand of high rotational speeds and high efficiencies can sometimes present difficulties when the RPM reaches 30,000 RPM to 100,000 RPM. The drag created in the air gap between the rotor and stator can result in significant “windage” losses that impact efficiency and increase motor cooling requirements. In some applications involving high power density electric motors forced air cooling is used to cool the rotor. The high rotational speed combined with the cooling air that travels in the axial direction creates very complex fluid dynamic flow profiles with coupled heat transfer and mass transfer. The relationship between the amount of the cooling air flow, windage generation and maximum temperature which the rotor can sustain is one of the most important factors in high speed electric motor design. Computational Fluid Dynamics (CFD) analysis must be performed to ensure proper cooling with low windage losses in order to achieve high efficiencies. Windage is a force created on an object by friction when there is relative movement between air and the object. There are two causes of windage: the first type is when the object is moving and being slowed by resistance from the air and the second type is where a wind is blowing producing a force on the object. The term windage can refer to: the effect of the force, for example the deflection of a missile or an aircraft by a cross wind or the area and shape of the object that make it susceptible to friction, for example those parts of a boat that are exposed to the wind. As shown in

As outlined above, in high-speed electronic motors air cooling is often employed in order to maintain the device within acceptable temperature operational limits. To date several investigations have been carried out on this topic. The pioneering work of Gardiner and Sabersky [^{5} < Re < 10^{7} are considered and it is found that the inflow enhances the turbulence. In the research of Poncet and Schiestel [^{5} < Re < 1.44 ´ 10^{6} . From the study of Poncet et al. [

together with a correlation for the Nusselt number along the rotor which shows a much larger dependence on the axial Reynolds number than expected from previous published works, while it depends classically on the Taylor number to the power 0.145 and on the Prandtl number to the power 0.3 i.e. Nu-Ta^{0.145}Pr^{0.3}. The work of Kuosa et al. [^{0.4}Re^{0.262} 1,000 < Re < 100,000 and 100 < Nu < 1.000. The work of Seghir-Ouali et al. [_{r} < 100,000 100 < Nu < 1000. The current study extends the previous studies into the realm of very large Taylor numbers, large axial Reynolds numbers, and small annular gap distances. The small annular gap is fed at 0.011 kg/sec while the rotor spins at 100,000 rpm while dissipating 200 W. The major objective of this present CFD analysis was to ascertain the drag force acting on the rotor of the motor. Comparisons of experimental power and numerical predictions are used to correlate the CFD model. One particular unique contribution of the present work is the extension of the current database of literature for Nusselt number and heat transfer coefficient into the Taylor/Reynolds number parameter space Ta > 10^{8}/Re > 10^{4} range of turbulent flow with coherent vortex structures and heat transfer.

The governing equations solved in STAR-CCM+ [

where

where

where

The k-w SST turbulence model of Wilcox [

where k denotes the turbulent kinetic energy and e denotes the rate of dissipation of turbulent kinetic energy.

The turbulent viscosity is modeled as

with the turbulence mixing length scale given by

The CD-Adapco STAR-CCM+ CFD code uses the following transport equations for the k-w SST high Reynolds number flow turbulence model

where

and the evolution equation for w reads

where the last term in Equation (12) is due to cross-diffusion. The model k-w SST constants are given by

A wall function based CFD turbulent simulation typically requires that y+ of the first cell outside of the wall lies in the log-layer, which starts at approximately y+ = 20 and depending on the Reynolds number extends to about y+ = 200. In the log-layer, there is equilibrium between production and dissipation of the turbulent kinetic energy, thus decreasing turbulent instability in near-wall simulations. The wall-treatments available in STAR CCM+ include, high-y+, low-y+ and all-y+. The all y+ wall treatment makes no assumption about how well the viscous sub layer is resolved. By using a blended wall log law of the wall to approximate the shear stress, the result is similar to the low y+ wall treatment if the mesh is fine enough. If the mesh is coarse enough, y+ > 30 the wall law is equivalent to a logarithmic profile. The all-y+ wall treatment is a hybrid method which attempts to emulate the high-y+ wall treatment for coarse meshes and the low-y+ wall treatment for fine meshes.

At the wall, a Neumann boundary condition is employed for the turbulent kinetic energy, k, i.e. ¶k/¶n = 0 at the wall. The specific dissipation rate w is prescribed in the wall cells according to the wall treatment being employed. When defining values for flow boundaries, region and initial conditions, the STAR CCM+ code allows users to 1) enter the values of k, w directly or 2) allows the CFD code to derive them from the turbulence intensity and length scale using

where u'/U is the turbulence intensity, V_{t} is the turbulent velocity scale and b^{*} is a turbulent model constant.

The experimental test set-up is shown schematically in

Speed (rpm) | Experimental air exit temp. (˚C) | Experimental windage power (Watts) | CFD air exit temp. (˚C) | CFD windage power (Watts) | Percentage error (%) |
---|---|---|---|---|---|

20,000 | 32.5 | 124 | 34.5 | 147 | 19 |

40,000 | 37.1 | 181 | 40.0 | 215 | 19 |

60,000 | 46.7 | 292 | 51.0 | 342 | 17 |

80,000 | 62.6 | 477 | 68.7 | 551 | 16 |

100,000 | 81.4 | 690 | 87.8 | 767 | 11 |

a. Inlet air flow rate = 620 L/min at T = 21.5˚C.

at similar rotational speeds and air flowrates albeit for a larger gap size then addressed herein.

as compared to the same parameters from the CFD model. The last column of ^{3}. ^{2} = 0.9995 for the CFD data and R^{2} = 0.9997 for the empirical data.

In this section the results of the CFD study are given. First the fluid mechanics of the small annulus flows considered herein are compared with existing literature. Then, heat transfer analysis using the CFD results is given. Finally, a Nusselt number based on the findings of the present research is proposed.

The flow structures shown in

as noted in _{1} = 24.78 mm, the outer cylinder radius, R_{2} = 27.89 mm, the annular gap thickness, e = R_{2} − R_{1} = 3.11 mm, the cylinder length, L = 98.54 mm, the radius ratio, h = R_{1}/R_{2} = 0.888, the cylindrical gap ratio, f = e/R_{1} = 0.126, and the axial ratio, G = L/(R_{2} − R_{1}) = 31.685. The cooling fluid was air at 22˚C, with a mass density of r = 1.16 kg/m^{3}, specific heat ratio, C_{p} = 1011 J/kg×K, thermal conductivity, k = 0.0260 W/m∙K, kinematic viscosity, n = 1.51 ´ 10^{−5} m^{2}/sec, mean rotor temperature, T_{r} = 112.5˚C, mean stator temperature, T_{s} = 130˚C. The results comparing the various correlations for Nusselt number listed in _{p}/mk = 0.681, Tangential Reynolds Number, Re_{t} = V_{t}D_{h}/n = 1.015 ´ 10^{5}, where D_{h} = D_{2} − D_{1} = hydraulic diameter of the annulus. The axial Reynolds Number, Re_{a} = V_{a}D_{h}/n = 7.589 ´ 10^{3} while the Taylor

Heat transfer correlation author | Radius ratio | Cylindrical gap ratio | Axial ratio | Axial Reynolds number | Taylor number | Nu/h (W/m^{2}・K) |
---|---|---|---|---|---|---|

Tachibana & Kukui | 0.937 | 0.1700 | 11.3 | 4.2E3 | 3.4E3 | 76/317 |

Hanagida & Kawasaki | 0.990 | 0.0094 | 283.0 | 1.0E4 | 2.0E5 | 62/256 |

Nijaguan & Mathiprakasam | 0.750 | 0.1650 | 195.0 | 2.0E3 | 3.6E5 | 370/256 |

Boufia et al. | 0.956 | 0.0450 | 98.4 | 3.1E4 | 4.0E5 | 193/805 |

Korsterin et al. | 0.780 | 0.0271 | 77.5 | 3.0E5 | 8.0E5 | 149/623 |

Grosgeorge | 0.980 | 0.0200 | 200.0 | 2.7E4 | 4.9 | 144/600 |

Childs & Turner | 0.869 | 0.1500 | 13.3 | 1.4E6 | 1.2E11 | 463/1800 |

Present study | 0.888 | 0.0017 | 31.7 | 7.6E3 | 3.3E8 | 318/1329 |

Number,^{3} 1/sec to 7.4 ´ 10^{5} 1/sec together with the velocity vector field of

In order to compare the current data to other researchers including Sebastin and Egbers [

The data of ^{7}. It should be noted that the correlation presented herein as Equation (18) holds for Taylor-Couette-Poiseuille

flows, whereas the works of Dubrulle and Hersant [

88˚C − 25˚C = 63˚C which is consistent with the test data and CFD data of ^{2}∙K. It should be noted the local heat transfer coefficient in

The results of the present study for heat transfer coefficient and Nusselt number were compared to several previous studies where the rotor of the machine being studied was heated including the works of Childs and Turner [^{8}, Re > 10^{3}. The majority of correlations with which our current data was compared against lie within the “turbulent and vortices” region of Taylor-Couette- Poiseuille flow, as shown in

current database of literature into the large Ta > 10^{8}/Re > 10^{4} range of turbulent flow with coherent vortices. The parameters used to compare our current work are summarized in ^{8} and the smallest cylindrical gap ratio f = 0.0017. The correlation with the best agreement to our results which is in the same realm of Taylor numbers is that of Childs and Turner [^{11} with a cylindrical gap ratio f = 0.15, i.e. two orders of magnitude larger than the current study. Nevertheless, the heat transfer coefficient of the current study h = 1800 W/m^{2}・K vs. the value of h = 1329 W/m^{2}・K of Childs and Turner [

with a stated correlation coefficient of R^{2} = 0.9713. The correlation of Equation (19) extends the findings of Poncet et al. [^{8}. Thus, the correlation offered herein as Equation (19) addresses large Taylor-large axial Reynolds number-small gap, Taylor-Couette-Poiseuille flows with heat transfer.

This paper has presented the results of using the commercial Computational Fluid Dynamics (CFD) package STAR CCM+ to simulate air cooling and windage losses in a high-speed electric motor. The primary objective

of this CFD analysis was to ascertain the drag force acting on the rotor of the motor. This work is significant in that it provides designers of high-speed air cooled motors a means that can be used to quickly assess the impact of windage losses on motor thermal performance. The CFD results are found to match the empirical data to within 20%, thus affording a conservative, correlated CFD model. The local heat transfer coefficient contours for the flow field ranging from 1456 < h < 6641 W/m^{2}×K, while the local Nusselt number falls in the range of 346 < Nu < 1580. A novel Nusselt number correlation based on the CFD results of this study is proposed in the form Nu = 1.5975Ta^{0.3282}.

The authors would like to acknowledge Dr. Angela Shih, Mechanical Engineering Department Chair for support of this research.