Y. C. Chong
*
,
D. A. Staton
#
,
M. A. Mueller
J. Chick
†
†
,
,
*, #
Motor Design Ltd., Ellesmere, SY12 0EG, U.K.
†
The Institute for Energy Systems, School of Engineering, University of Edinburgh, Edinburgh, EH9 3JL, U.K.
Abstract
This study investigates the pressure loss of flow through straight circular ducts rotating about an axis parallel to the duct axis. The experimental measurements found that the flow passing through the rotating ducts is affected by an additional pressure loss when compared with stationary condition. For stationary condition, the experimental results agreed with the values of pressure loss estimated using theoretical/empirical correlations.
For the rotational pressure loss, it is mainly caused by rotor ducts entrance loss and additional friction loss due to the effect of rotation. These losses have been isolated in the present study. The coefficient of entrance loss has been correlated with a dimensionless parameter, rotation ratio. Correlations for entrance loss coefficient of rotor ducts of different proximity to the rotor periphery were proposed. The correlations are useful for predicting flow distribution and thermal-fluid modelling of rotating machines.
Keywords
Pressure Drop; Flow Network Analysis; Rotating Machines; Thermal Analysis

1. INTRODUCTION
The power output of an electrical machine is strongly affected by its thermal performance because machine operating temperature limits the electric loading. An electrical machine thermal performance is predominantly affected by two factors. One is amount of heat sources within the machine generated from losses. The other one is how well the generated heat can be transported out from the machine. From the cooling point of view, the most effective cooling method is to duct the coolant to the sources of losses. Therefore, accurate prediction of flow distribution in the cooling paths and their pressure losses are essential for accurate thermal modelling. The coupled thermal-fluid modelling between equivalent thermal network and flow network has been adopted by
(Sun and Cheng, 2013) for a dual mechanical port machine, (Scowby et al., 2004) for an axial flux permanent magnet (AFPM) machine and (Li et al., 2013) for a turbogenerator.
For rotating machines, the convective heat transfer in straight circular ducts which rotate about a parallel axis has been studied by a number of researchers. (Mori and Nakayama, 1967) and (Woods and Morris, 1974) investigated the rotating effects to laminar flow heat transfer in rotating duct using theoretical analysis and numerical methods respectively. (Nakayama, 1968) also performed a theoretical analysis of heat transfer in rotating pipe for fully developed turbulent flow. (Le Feuvre, 1968) performed a dimensional analysis to investigate the heat transfer enhancement for developing turbulent flow due to rotation for air passing through axial cooling ducts in a rotor. His experimental data shows quantitative agreement with the experimental results obtained by (Humphreys et al., 1967). Using the method suggested by (Morris and Woods, 1978) to obtain a heat transfer correlation in rotating duct, (Morris, 1981) correlated the experimental data reported by (Le Feuvre,
1968; Humphreys et al., 1967) and this gives an equation having similar characteristics to that proposed by
(Morris and Woods, 1978). A number of heat transfer correlations have been proposed by the above researchers.
In order to make use of those correlations, the flow distribution between the ventilation paths of a rotating machine needs to be known. (Johnson and Morris, 1992) performed an experimental investigation into the influence of rotation on the flow resistance of adiabatic developing air flow in a circular tube and found the increase in friction factor due to the Coriolis effect can be correlated with a rotational Reynolds number.
(Bennett and Poole, 1967) determined the pressure loss factor of a fluid flowing axially into holes on a rotating shaft. However, the loss factor that has been obtained is a compound factor for a particular geometry, so it is less generic to be applied for other machines. (Webb, 1964) experimentally investigated the pressure drop of air passing through axial rotor ducts of a mock-up throughflow ventilated machine. The author attempted to separate the additional pressure loss due to the abrupt change of air flow direction entering into rotor ducts due to rotation, namely “shock loss”, from other losses which result from changes in cross-section (e.g. contraction and expansion losses) and friction. However, the additional friction loss due to rotation as described by (Johnson and
Morris, 1992) was neglected by the author. Furthermore, the relationship between the leakage flow passing outside the rotor and the pressure drop across the rotor by blocking the rotor ducts was used to determine the flow rate passing through the rotor ducts with rotor duct unblocked. By ignoring interaction between rotor duct outflow and rotor-stator gap outflow, the author likely underestimated the flow rate passing through the rotor ducts while overestimated the flow rate passing through rotor-stator gap.
Therefore, the objective of this paper is to characterise the entrance loss of rotor duct by taking the above factors into account. A dimensional analysis is performed to identify the important parameters that affect the entrance loss. The experimental test rig was built for the present study. The experimental results are compared with the theoretical results for the stationary condition beforehand. Then, it is used to investigate the rotational pressure losses.
2. METHOD OF CALCULATION
For real fluids, a flow in a piping system undergoes energy losses due to friction and flow separation effects as defined by (Douglas et al., 1995). Due to the flow separation effect, the flow separates from the pipe walls when it passes through a disturbance resulting in the formation of turbulence eddies and consequent pressure loss.
Owing to the nature of turbulence, the coefficient of a flow separation loss is normally determined experimentally. The coefficients of various flow separation losses are documented in (Idelchik, 2007). A flow separation loss is usually quantified by the product of empirical loss coefficient ( K ) and flow kinetic energy as:
∆𝑝 = 𝐾 ×
1
2 𝜌𝑈 2
(1) where ρ is the fluid density and U is the average fluid velocity in the flow path. Therefore, the pumping pressure in a piping system is mainly used to compensate the pressure losses and maintain the motion of the pipe flow.
2.1
Pressure Losses in Rotor Ducts

Due to rotation, the total pressure drop in a throughflow ventilated electrical machine can be divided into stationary pressure loss ( ∆𝑝 𝑠
) and rotational pressure loss (
∆𝑝 𝑟
) by assuming the stationary loss preserves in the same amount in the rotating condition. Therefore, the pressure loss of rotor duct can be expressed:
∆𝑝 = ∆𝑝 𝑟
+ ∆𝑝 𝑠
(2)
Firstly, based on the experimental method, the relationship between the stationary pressure loss and inlet flow rate was obtained. For stationary condition, the experimental results agreed with the pressure loss values estimated using theoretical/empirical correlations as shown in Section 5.1. The stationary loss along a rotor duct is the sum of sudden contraction loss, friction loss that accounting for developing flow and expansion loss as:
∆𝑝 𝑠
= [𝐾 𝑐𝑜𝑛
+ 𝐾 𝑓
0
+ 𝐾 𝑒𝑥𝑝
] ×
1
2 𝜌𝑈 2
(3) where
𝐾 𝑐𝑜𝑛 and
𝐾 𝑒𝑥𝑝
is the sudden contraction loss coefficient,
is the expansion loss coefficient.
𝐾 𝑓
0
is the frictional loss coefficient for stationary condition
Then, the rotational loss can be separated from the stationary loss using Eq. (2) as the rotational loss is
the excess pressure drop for a given flow rate. For rotor ducts, the rotational losses are assumed to be in the form of additional frictional loss along the ducts and entrance loss at the duct entry. Therefore, the entrance loss coefficient of rotor duct can be obtained by non-dimensionlizing the entrance loss with the kinetic energy of flow through the rotor ducts as:
∆𝑝 𝑟
= [(𝐾 𝑓 𝑟
− 𝐾 𝑓
0
) + 𝐾 𝑒𝑛
] ×
1
2 𝜌𝑈 2
(4)
𝐾 𝑒𝑛
=
2∆𝑝 𝜌𝑈 2 𝑟 − (𝐾 𝑓 𝑟
− 𝐾 𝑓
0
)
(5) where
𝐾 𝑓 𝑟
is the frictional loss coefficients for rotating condition and
𝐾 𝑒𝑛 coefficient.
is the rotor duct entrance loss
2.2
Frictional Loss in Rotor Ducts
For circular cross-sectional tubes rotating about a parallel axis, the experimental study performed by
(Johnson and Morris, 1992) demonstrated that rotation induces secondary flow in the entrance region of the tubes due to the Coriolis effects and increases the flow resistance in the tubes. The increases in the friction factor of adiabatic flow can be estimated using the empirical correlations for the ratio of rotating case to stationary case as:
For axial Reynolds number ( Re ) between 900 and 9880,
𝐶 =
𝐾 𝑓𝑟
𝐾 𝑓0
For axial Reynolds number ( Re ) above 9880,
= 0.503𝐽 0.16
𝑅𝑒 −0.03
𝐶 =
𝐾 𝑓𝑟
𝐾 𝑓0
= 0.842𝐽 where
𝐽
is the rotational Reynolds number for rotating duct.
0.023
𝑅𝑒 0.002
(6)
(7)
2.3
Dimensional Analysis
Due to the complexity of flow in a rotating duct, a dimensional analysis is performed to establish the functional relationship between geometric dimensions of flow path, operating condition (e.g. rotor speed) and flow condition on the rotor duct entrance loss coefficient. The dimensional analysis is used to identify the parameters that affect the entrance loss. Initially, the general functional equation of coefficient of rotational loss can be written as:
𝐾 𝑟
= 𝑓 (
𝐿 𝑑
, 𝑒 𝑑
,
𝐻 𝑎
,
𝐻 𝑑
, 𝑤 𝑑
,
𝑉
𝑇
𝑈
, 𝐽, 𝑅𝑒, 𝑃𝑟) (8)

where e is the surface roughness height, d is the duct diameter and a is the rotor outer radius. To satisfy the
principle of dimensional homogeneity, all the terms in Eq. (8) are defined in dimensionless form. For fluid
mechanics, the length-to-diameter ratio (
𝐿/𝑑
) is a measure of equivalent length of a flow path in terms of its hydraulic diameter. It is normally used to account for the developing flow. The surface roughness of the flow path is taken into account by the relative roughness (
⁄
). Both
𝐿/𝑑
and 𝑒/𝑑
are assumed to be only important
for friction loss. Therefore, they can be discarded from Eq. (8). The geometric effect of rotor ducts is specified
by ratios of
𝐻/𝑎
,
𝐻/𝑑
and 𝑤/𝑑
.
𝐻
is the pitch-circular radius of the rotor ducts, thus
𝐻/𝑎
is a measure to indicate the proximity of the duct to the rotor periphery. Eccentricity parameter (
𝐻/𝑑
) is a ratio of the pitchcircular radius of duct to the duct diameter. Duct spacing ratio ( 𝑤/𝑑
) is a ratio of the spacing between two adjacent rotor ducts to the duct diameter.
Other dimensionless groups of fluid mechanics used by the published literature such as rotation ratio (
𝑉
𝑇
/𝑈
), rotational Reynolds number for rotating duct (
𝐽
), axial Reynolds number ( Re ) and Prandtl number ( Pr ) are also
included in Eq. (8). In order to reduce the number of terms in Eq. (8), it is necessary to discard those
dimensionless groups which are irrelevant and unimportant for the present study. As the review of cooling methods for electrical machines reveals that the cooling medium used for the passages in rotor is mostly air,
hence the Prandtl number is removed from Eq. (8) because air is only the focus. Both rotational Reynolds
number for rotating duct and axial Reynolds number can be combined as follows:
𝐽
𝑅𝑒
= 𝜌𝜔 𝑚 𝜇 𝑑
2
⁄ 𝜌𝑈𝑑 𝜇
=
2𝑉
𝑇
𝑈
(9) where 𝜔 𝑚
is the angular velocity, μ is the dynamic viscosity,
𝑉
𝑇
here is the rotor duct tangential velocity and U
is the axial flow velocity. Equation (9) shows that the ratio of the rotational Reynolds number for rotating duct to
the axial Reynolds number results in a dimensionless parameter, which is similar to the rotation ratio (Note: the constant in front of a dimensionless parameter is normally ignored based upon the basis of dimensional analysis).
In the review of existing literature, the rotation ratio was already suggested in (Le Feuvre, 1968; Bennett and
Poole, 1967; Webb, 1964) to account the effects of rotation on the heat transfer and pressure drop for rotating ducts. Thus, the functional equation of the entrance loss coefficient of rotor duct is simplified to:
𝐾 𝑟
= 𝑓 (
𝐻 𝑎
,
𝐻 𝑑
, 𝑤 𝑑
,
𝑉
𝑇
𝑈
)
(10)
The number of dimensionless parameter is reduced from nine to four in the dimensional analysis. This considerably simplifies the process of investigation of the rotor duct entrance loss.
3. EXPERIMENTAL TEST RIG
Fig. 1. Experimental setup
Fig. 1 shows the experimental setup used to investigate the effects of rotation on the pressure drop of air
flow passing through the rotor-stator system. The test section is a geometric mock-up of throughflow ventilated machine. The aim of experiment is to measure the pressure drop due to air entering the rotor ducts over a range of flow rate with and without rotor rotating.

The experimental test rig consists of a fan inlet tube that connecting between an inlet orifice meter and a centrifugal fan that connected to a variable frequency supply, a transparent fan outlet tube that connected to the fan through an expansion adaptor and a test section that accommodates a stator and a rotor driven by an inverter drive induction motor. The rotor can rotate up to 3000 rpm which was calibrated using a RS TM-2011
Tachometer. During operation, air is drawn into the test rig, passes though the test section and exits from the outlet of the test section to the atmosphere. The volumetric air flow rate through the test rig is measured using a
BS 848-1 inlet orifice meter, (BSI, 1997). The inlet orifice meter measurement was calibrated with traverse measurements using Pitot-static tube after the NEL (Spearman) flow conditioner.
In the fan outlet tube, a total of 12 pressure tapping holes were drilled at cross section planes of distance of
1 D , 2 D and 3 D from the flow conditioner. D is the fan outlet tube inner diameter. On each cross section plane, four pressure tapping holes are arranged at 90° intervals. The static pressure at each cross section plane was measured from four pressure tappings that were connected together in a “triple-T” arrangement. As the static pressure measurement is required to make under developed flow condition, it was conducted at 3 D , which is
Plane 3 as shown in Fig. 4. The pressure measurements were conducted using an Omega PX277-05D5V
differential pressure transducer of having an uncertainty of 1 %.
In the test section, the stator and rotor are made of steel laminations to simulate the surface condition of electrical machine. They are formed by welding 100 steel laminations of thickness of 1.5 mm together. Therefore,
the axial length of stator laminations and rotor laminations are approximately equal to 150 mm as shown in Fig.
2. The surface roughness of steel laminations was examined using a standardized method, namely RepliSet
(Struers, 2010). Under microscopic examination, the average roughness height is 17.6 ± 4 μm. The stator laminations have an inner diameter of 158 mm and outer diameter of approximately 190 mm to suit the inner diameter of fan outlet tube. The stator laminations are positioned by the stator sleeves (of the same inner and outer diameters of stator laminations) to ensure the stator laminations are placed right over the rotor laminations.
The rotor laminations have the outer diameter of 150 mm. This forms a rotor-stator annular gap of 4 mm. The rotor laminations are mounted on a shaft and are held in place by two bearing mounting plates. The distances between the bearing mounting plate and rotor laminations are approximately 77 mm for the front and rear ends.
The rotor has a series of ducts, which is parallel to the axis of the rotor. The details of the rotor ducts in the test rig are as follows:

6 ducts of diameter 14 mm on pitch-circular diameter of 75 mm,

6 ducts of diameter 12 mm on pitch-circular diameter of 75 mm,

12 ducts of diameter 12 mm on pitch-circular diameter of 112.5 mm,

12 ducts of diameter 10 mm on pitch-circular diameter of 112.5 mm.
Fig. 2. Internal view of test section
The purpose of the arrangement of rotor ducts in Fig. 3 is to investigate the influence of duct size, duct
pitch-circular diameter (PCD) and duct spacing to the additional pressure losses suffered by the air flow passing through the rotating ducts. By blocking some of the rotor ducts, various configurations of rotor ducts can be
tested. The configurations of rotor ducts that were tested are tabulated in Table 1.
When the flow exits from the rotor ducts, it deflects radially outwards and interferes with the outflow from the rotor-stator gap due to the centrifugal effect. This affects the pressure drop of rotor-stator gap. Therefore, a

flow guard was attached onto the rotor end above the rotor ducts as shown in Fig. 2 to stop the interaction
between the rotor ducts and rotor-stator gap outflows as demonstrated by (Chong, 2015).
Fig. 3. Positions and sizes of holes in rotor lamination (unit: mm)
Table 1. Configurations of rotor ducts that were tested
Test
6 D12 PCD113
12 D12 PCD113
12 D10 PCD113 d (mm) n H (mm) a (mm) L (mm) H/a ratio H/d ratio L/d ratio w/d ratio
12 6 56.25 75 150 0.75 4.69 12.5 4.91
12
10
12
12
56.25
56.25
75
75
150
150
0.75
0.75
4.69
5.63
12.5
15.0
2.45
2.95
6 D12 PCD75 12 6 37.5
6 D14 PCD75 14 6 37.5
4. ANALYTICAL MODELLING TOOL
75
75
150
150
0.50
0.50
3.13
2.68
12.5
10.7
3.27
2.80
Rotor ducts Airgap Flow guard
Fig. 4. Equivalent flow network of the studied ventilation system built using Portunus Flow Library

The flow network analysis is an analysis of fluid flow through a pipe network involving the process of defining the mathematical model of the fluid transport and distribution in a flow system. It is commonly used for water supply network, heat, ventilation and air conditioning (HVAC) design, hydropower, etc. Basically, a flow network is composed of various flow components (e.g. friction, expansion, contraction, bend and etc.). Based on the empirical loss coefficients for the flow components as described in Section 2, the flow network analysis is capable of determining the flow rates and pressure drops in the individual flow components. Therefore, the flow network analysis method is employed for the present study for modelling air flow in rotating machines. The knowledge of flow distribution in rotating machines could benefit the accurate prediction of convective heat transfer coefficients and thus the cooling power that can be achieved.
Portunus is chosen as a computational tool for flow network analysis because the library and model management of the software provides options to create user-defined models. Therefore, the characteristic of each flow components were described in a new library, namely “Flow Library”. They were coded in VHDL-AMS language. The Flow Library was also expanded to code the flow components that are suitable to model rotating
ducts. Fig. 4 shows the equivalent flow network of the test rig.
5. RESULTS
5.1 Stationary Loss
Q
airgap
Q
ducts
Q
inlet
Fig. 5. Flow resistance curves of ventilation with rotor ducts and airgap for stationary case
For flow analysis, the pressure drop of a system is commonly plotted against the volumetric flow rate to
indicate the flow resistance of the system. Fig. 5 shows the flow resistance curves of different rotor ducts
configurations as described in Table 1. The pressure at Plane 3 reflects the pressure drop from Plane 3 to the
atmosphere. The flow resistance curve of ventilation with airgap only is also plotted (i.e. black line). The rotor ducts considerably reduces the flow resistance of the ventilation system. The experimental results demonstrate that the number of rotor ducts and duct size play important roles in reducing pressure drop by means of flow cross-sectional area. For examples, the pressure drop for 6 D12 PCD113 and 6 D12 PCD75 are similar due to the same flow cross-sectional area, but the pressure drop is not affected by ducts’ pitch circular diameter. Also,
12 D10 PCD113 and 6 D14 PCD75 give the similar pressure drop due to the similar flow cross-sectional area.
In order to analyse the pressure loss in rotor ducts, it is necessary to determine the flow rate through the rotor ducts. However, the measured flow rate using inlet orifice meter (
𝑄 𝑖𝑛𝑙𝑒𝑡 and rotor ducts flow (
𝑄 𝑑𝑢𝑐𝑡𝑠
) is the sum of airgap flow (
𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
). Therefore, the rotor ducts flow need to be separated from the airgap flow. By
) blocking the rotor ducts, the relationships between pressure loss and rotor-stator gap flow rate were obtained over a range of speed. After unblocking the rotor ducts, the rotor ducts flow rate can be separated from the airgap flow rate because in theory a flow is induced by a differential pressure. The airgap flow rate as a function of the measured pressure at Plane 3 can be derived from the experimental results by making the
∆𝑝
3
𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
is a dependence of
∆𝑝
3
in the following equations. For stationary case,
as a variable and
𝑅𝑃𝑀 = 0, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
= 7.6 × 10 −3 + 8.8 × 10 −5 (∆𝑝
3
) − 5.2 × 10 −8 (∆𝑝
3
) 2
(11)
The Eq. (11) is only applicable for
∆𝑝
3 experimental data. For rotating cases,
from 78 Pa to 524 Pa in order to obtain a good fitting for the

𝑅𝑃𝑀 = 600, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
𝑅𝑃𝑀 = 1200, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
𝑅𝑃𝑀 = 1800, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
𝑅𝑃𝑀 = 2100, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
𝑅𝑃𝑀 = 2400, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
𝑅𝑃𝑀 = 2700, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
𝑅𝑃𝑀 = 3000, 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
= 2.43 × 10 −4 (∆𝑝
3
= 2.10 × 10
= 1.66 × 10
−4
−4
(∆𝑝
(∆𝑝
3
= 1.72 × 10
= 1.34 × 10
= 1.28 × 10
= 1.20 × 10
−4 (∆𝑝
3
−4 (∆𝑝
3
−4 (∆𝑝
3
−4 (∆𝑝
3
3
) − 8.64 × 10 −7 (∆𝑝
3
) − 5.37 × 10 −7 (∆𝑝
3
) 2
) − 2.43 × 10 −7 (∆𝑝
3
) − 3.17 × 10 −7 (∆𝑝
3
) − 1.15 × 10 −7 (∆𝑝
3
) − 1.02 × 10 −7 (∆𝑝
3
) − 8.64 × 10 −8 (∆𝑝
3
) 2
) 2
)
)
)
)
2
2
2
2
(12)
(13)
(14)
(15)
(16)
(17)
(18)
Equations (12)-(18) are limited by the fact that
∆𝑃
3
needs to be within a specific range of pressure as provided by (Chong, 2015). Therefore, extrapolation for
𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
using the above equations is not recommended. These equations were used to split the flow rate between the rotor ducts and airgap as follows:
𝑄 𝑑𝑢𝑐𝑡𝑠
= 𝑄 𝑖𝑛𝑙𝑒𝑡
− 𝑄 𝑎𝑖𝑟𝑔𝑎𝑝
(19)
With the flow guard, the interaction between the airgap outflow and rotor ducts outflow is negligible as demonstrated by (Chong, 2015). Therefore, for a given pressure, the flow rate through the airgap with the rotor ducts unblocked is the same as that of the rotor ducts blocked. The flow distribution between the rotor ducts and air gap for 12 D12 PCD113
is shown in Fig. 6(b) for stationary case and Fig. 8 for rotating case.
(a) Pressure drop (b) Flow distribution
Fig. 6. Comparison between experimental and calculated results for 12 D12 PCD113 for stationary case
Fig. 6 shows the comparison between the experimental results and the values calculated using the analytical
flow network analysis for 12 D12 PCD113 for stationary case. The flow network analysis assumes the flow rate passing through the rotor ducts is evenly distributed into each duct. The comparison demonstrates that the flow network analysis is not only capable of predicting the stationary pressure requirements for flow entering the rotor ducts and airgap, but also capable of predicting the flow distribution between the rotor ducts and airgap.
5.2 Rotational Loss
Based on the experimental measurements, the effect of rotation to the pressure loss of different rotor ducts
configurations is clearly shown in Fig. 7. Rotation increases the system pressure drop above the stationary
condition. The air flow through the rotor ducts is affected by additional pressure loss. However, the influence of rotation is less marked at higher flow rate. Due to the consistency of the experimental results, the relationships
between the inlet flow rate and the stationary pressure loss from the Plane 3 to the outlet as shown in Fig. 5 are
used to separate the stationary loss from the rotational loss.
By using Eq. (12)-(18), Fig. 8 shows the flow distribution between the airgap and rotor ducts for
12 D12
PCD113 from stationary to 3000 rpm. The flow rate passing through the airgap and rotor ducts become less due to the effect of rotation. Furthermore, the percentage of reduction in flow rate for the airgap is not proportional to that of the rotor ducts. Thus, the flow distribution between the airgap and rotor ducts for the rotating condition is not the same as the stationary condition. Therefore, it is necessary to take the effect of rotation into account when performing thermal-fluid modelling of a rotating machine.

(a) 12 D12 PCD113 (b) 12 D10 PCD113
(c) 6 D12 PCD113 (d) 6 D12 PCD75
(d) 6 D14 PCD75
Fig. 7. The relationship between pressure drop and flow rate for speed up to 3000 rpm
Fig. 8. Flow distribution between airgap and rotor ducts for 12 D12 PCD113 over a range of speed

Fig. 9. The variation of entrance loss coefficient of rotor ducts with rotation ratio (
𝑉
𝑇
⁄ 𝑈
)
As the rotational pressure loss and the air flow rate through the rotating ducts can be determined
experimentally, the coefficient of entrance loss of a rotating duct was calculated by applying the Eq. (5). The
testing of 6 D12 PCD113 was repeated to ensure the experimental measurements were consistent. As shown in
Fig. 9, the entrance loss increases considerably for the increase in rotation ratio, but it can be neglected when the
rotation ratio is less than 0.5 approximately. The correlation of entrance loss coefficient proposed by (Webb,
1964) is also plotted in Fig. 9. The experimental results demonstrate that the entrance loss of the rotor ducts is
not influenced by the range of duct size ( d ), duct length-to-diameter ratio ( L/d ), eccentricity parameter ( H/d ) and duct spacing ratio ( w/d
) as shown in Table 1. However, the entrance loss is clearly affected by the proximity of
the rotor ducts to the rotor periphery ( H/a ). Hence, for H/a ratio of 0.75, the entrance loss coefficient can be correlated with the rotation ratio as:
𝑉
𝑉
𝑇
𝑇
𝐾
𝐾 𝑒𝑛 𝑒𝑛
= 0.234(𝑉
𝑇
= 0
⁄ ) 2 − 0.043(𝑉
𝑇
𝑈
(20)
For H/a ratio of 0.5, the entrance loss coefficient can be correlated with the rotation ratio as:
𝑉
𝑇
𝑉
𝑇
𝐾 𝑒𝑛
𝐾 𝑒𝑛
= 0.474(𝑉
𝑇
= 0
⁄ ) 2 − 0.156(𝑉
𝑇
𝑈
(21)
The correlations are valid for the axial Reynolds number in the rotor ducts ranges from 3200 to 17000, the rotational Reynolds number up to 4000, the rotation ratio,
𝑉
𝑇
⁄ 𝑈
up to 3.7 for H/a = 0.75, and the rotation ratio,
𝑉
𝑇
⁄ 𝑈
up to 2 for H/a = 0.5. The extrapolation of the shock loss correlations must be implemented with care.
These entrance loss correlations were incorporated into the analytical modelling tool in Section 4.
6. DISCUSSION
With rotation, the comparison between the experimental results and the values predicted using analytical flow network analysis for 12 D12 PCD113
is shown in Fig. 10(a). The predicted pressure loss agrees reasonably
well with the measurements. The equivalent flow network is illustrated in Fig. 4. The experimentally validated
flow network was used to investigate the breakdown of the pressure loss from Plane 3 to the outlet of the test rig.
The stacked columns in Fig. 10(b) display the percentage of the main flow components contribute to the total pressure loss in Fig. 10(a). The analysis shows that the rotor duct entrance loss increases with the increase in
rotor speed, but it is less marked for higher flow rate. The entrance, friction, contraction and expansion losses of rotor ducts are the major loss components contributing over 96% of the total loss for the test case. This agrees
with Eq. (1) as the pressure drop in a passage is directly proportional to the square of the local flow velocity.
Without the flow guard, the interaction between the airgap outflow and rotor ducts outflow is also investigated experimentally. The comparison between the flow resistance curves for 12 D12 PCD113 with and
without the flow guard is illustrated in Fig. 11. The pressure losses are plotted against the inlet flow rate for rotor
speed at 0, 1800, 2400 and 3000 rpm. The experimental results demonstrate an additional pressure loss as the pressure loss is higher for the case without the flow guard due to the interaction between the airgap outflow and rotor ducts outflow as described earlier. The deflection of the outflow from rotor ducts due to the centrifugal effect interrupts the outflow from the airgap. This leads to non-recoverable pressure loss arisen from flow separation and subsequent turbulent mixing, namely “combining flow loss”. The interruption is assumed to affect the pressure loss of airgap only.

(a) (b)
Fig. 10. (a) Comparison between experimental and calculated results and (b) the breakdown of pressure loss components for 12 D12 PCD113 at 3000 rpm
Fig. 11. Flow resistance curves of 12 D12 PCD113 with and without flow guard for rotor speed up to 3000 rpm
Fig. 12. Flow distribution between airgap and rotor ducts without flow guard for 12 D12 PCD113 over a range of speed
Similar to the airgap flow rate determination, the flow rate of the rotor ducts as a function of the measured
pressure can be derived from the experimental results as shown in Fig. 8. As the interruption does not affect the
pressure loss of rotor ducts, therefore, for a given pressure, the flow rate through the rotor ducts without the flow guard is the same as that of with the flow guard as demonstrated by (Chong, 2015). This gives the direct
correlations to split the flow rate between the rotor ducts and airgap. Fig. 12 shows the flow distribution between

the rotor ducts and rotor-stator gap for 12 D12 PCD113
without the flow guard. When compared with Fig. 8,
12
D12 PCD113 without the flow guard shows reduction in airgap flow rate while the rotor ducts flow rate remain the same. The combining flow loss can be characterized as the flow distribution and rotational pressure loss are known, but this is not the scope of this paper.
7. CONCLUSIONS
The characteristic of flow passing through straight circular ducts rotating about a parallel axis was investigated experimentally in this paper. Rotation significantly increases the pressure loss of flow through the rotor ducts above the stationary condition. Based upon dimensional analysis, correlations of entrance loss coefficient of the rotor ducts are obtained. Such correlations provide a significant contribution to the field of thermal-fluid modelling of rotating machines. In this paper, the experimental measurements also disclose the interaction between the rotor ducts outflow and airgap outflow can result in an additional pressure loss to the flow through the airgap.
ACKNOWLEDGEMENTS
The authors are very grateful for the funding, advice and support provided by NGenTec Ltd., Motor Design
Ltd., Edinburgh University and Energy Technology Partnership (ETP) to the research. The authors wish to thank
Fountain Design Ltd. for their help on building the test rig for the research.
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