Chapter 16
Development of a CFD Model
for the Estimation of Windage Losses
Inside the Narrow Air Gap
of an Enclosed High-Speed Flywheel
Mahmoud Eltaweel, Christos Kalyvas, Yong Chen,
and Mohammad Reza Herfatmanesh
Abstract Concerns over global warming and the need to reduce carbon emissions
have prompted the development of novel energy recovery systems. During urban
driving, a significant amount of energy is lost due to continuous braking, which can be
recovered and stored. The flywheel energy storage system can efficiently recover and
store the vehicle’s kinetic energy during deceleration. In this study, a Computational
Fluid Dynamics (CFD) model was developed to assess the impact of air gap size, and
rotor cavity pressure environment on the aerodynamic performance of an enclosed
non-ventilated flywheel energy recovery system. Consequently, the flywheel rotor
skin friction coefficients for various air gap sizes have been numerically determined
to predict the windage losses over a wide operating range. The presented study aims
to identify a correlation that accurately fits the rotor skin friction coefficients for a
range of air gap sizes and operating conditions. Model validation was carried out
to assess the validity of the CFD results, which showed good agreement between
numerical and experimental data. The results demonstrated that the increase in the
air gap size can lead to up to a 19% reduction in the windage loss depending on
the operating speed of the flywheel, while the windage loss can be reduced by 33%
when the operating pressure is reduced to 500 mbar. Windage losses can be reduced
by 45% when the airgap size is greatest, and the operating pressure is lowest.
Keywords Energy recovery system · Mechanical storage · Taylor-Couette flow ·
Skin friction coefficient
M. Eltaweel (B) · C. Kalyvas · Y. Chen · M. R. Herfatmanesh
School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield,
Hertfordshire AL10 9AB, England
e-mail: m-eltaweel@outlook.com
© The Author(s) 2023
J. D. Nixon et al. (eds.), Energy and Sustainable Futures: Proceedings of the 3rd ICESF,
2022, Springer Proceedings in Energy, https://doi.org/10.1007/978-3-031-30960-1_16
157
158 M. Eltaweel et al.
16.1 Introduction
Flywheel energy storage systems (FESS) are mechanical energy storage devices that
use the moment of inertia of a rotating disc to store mechanical energy. By speeding
or decelerating the flywheel rotor with an electric motor, generator, or Continuous
Variable Transmission (CVT), energy can be provided to or withdrawn from the
flywheel. FESS is designed for short-term energy storage, which is ideal for fault
protection, peak shaving, frequency management, and vehicles. The optimal design
for the flywheel rotor in FESS can improve energy storage performance while also
lowering the cost of the system, making it a more commercially feasible energy
storage solution [1].
The performance of a FESS can be influenced by rotor design parameters such
as material, operating speed, overall size, topology, and shape. These affect the
FESS’s energy capacity by determining the moment of inertia and allowing for a
uniform stress distribution. The total stored energy is influenced by the operating
speed. The yield strength and density of the rotor material determine the maximum
permitted stress and mass of the flywheel rotor, which in turn affect the maximum
allowable stress of the flywheel rotor. To create an optimum flywheel for a given
application, the rotor design and operating speed of the flywheel must be tuned
[2]. The total standby losses, which contribute to self-discharge and might affect
the FESS’s overall efficiency, are influenced by the operating speed and rotor shape.
Mechanical losses due to bearing friction and windage are the main causes of standby
power losses. To assess standby losses, as well as run-time losses that occur while
charging or discharging the FESS, literature studies have employed simulations based
on analytical models [3] and empirical models based on experiments [4].
Gurumurthy et al. [5] used an experimental flywheel system at atmospheric pres-
sure to measure the mechanical and electrical losses in the FESS. They increased the
rotational speed of the FESS to 15,000 rpm and then allowed it to decelerate in various
load and no-load scenarios. Mechanical losses, particularly drag losses, dominated
power losses in their studies, accounting for 72% of total power losses at very high
speeds. Skinner [4] investigated the mechanical and no-load electrical losses caused
by the rotor’s self-discharge during standby using a cylindrical composite rotor FESS
accelerated to speeds of up to 5000 rpm. Mechanical losses were significantly affected
by the running speed and vacuum pressure inside the FESS enclosure. Amiryar and
Pullen [3] used analytical and empirical methods to calculate the windage and bearing
friction losses in a cylindrical steel flywheel running at various low pressures and
speeds ranging from 10,000 to 20,000 rpm. While windage losses increased nonlin-
early with running speed, they could be significantly reduced by adjusting the vacuum
pressure and the space between the rotor and the enclosure. In contrast, air pressure
had little effect on bearing losses, which can be attributed to speed-dependent and
load-dependent loss components. Furthermore, as operating speed increased, speed-
dependent losses increased significantly more than load-dependent losses. As a result,
16 Development of a CFD Model for the Estimation of Windage Losses … 159
the operating speeds selected during FESS design may have a significant impact on
these losses. The previous study discovered that FESS design parameters such as
vacuum pressure, air gap, and operation speed had a significant impact on overall
system standby power losses.
To create ideal FESS rotors with improved energy storage properties, it is crit-
ical to understand the relationship between critical rotor design parameters such as
rotor length, airgap size, speed, and pressure level [2]. The goal of this paper is to
first determine the effects of simultaneously changing multiple design parameters,
such as operating speed and airgap size, on the rotor shape optimization problem,
and to see if such an approach can offer a significant improvement in the FESS’s
energy storage characteristics. This will allow for the investigation of a much larger
portion of the rotor design space, resulting in improved optimal rotor designs. A few
studies have shown an interest in calculating windage losses inside FESS with small
air gaps. Almost all empirical equations for estimating windage losses are derived
from experimental apparatus with properties that differ significantly from those of
FESS [6, 7]. As a result, the primary goal is to create some realistic tools that will
enable designers to account for windage losses in their designs. Then, in this study,
a numerical approach based on CFD calculations is used to quantify windage losses
inside narrow air gaps of high-speed FESS. A parametric study was carried out to
characterise the influence of rotation speed, air gap geometry, and pressure levels. A
correlation based on CFD data is provided for the estimation of the rotor skin friction
coefficient for a wide range of operations.
16.2 Numerical Models
The current article suggests a numerical model of a smooth, narrow, and closed air
gap. CFD methods are used to describe the air gap flow structure and predict the
rotor skin friction coefficient. In order to estimate the skin friction coefficient, the air
velocity distribution must be determined.
16.2.1 Mesh Generation and Boundary Conditions
The CFD programme used for this work is ANSYS Fluent 19.2 due to the improve-
ment in the numerical analysis and its popularity in fluid and thermal analysis of
complex designs. The parameter used in this study to define the airgap is a dimen-
sionless parameter called the radius ratio which is η = Ri /Ro where Ri is the
rotor radius and Ro is the internal housing radius. Another parameter is aspect ratio
= L/g where L is the rotor length and g is the airgap width (g = Ro − Ri ). The
radius of the rotor was chosen to be 0.075 m. The values of the studied parameters are
160 M. Eltaweel et al.
Table 16.1 Studied
parameters values
Airgap g (m) 0.0015 0.0048 0.0083
Radius ratio η 0.98 0.94 0.90
Rotor length L (m) 0.1 0.15 0.2
Rotor cavity pressure (mbar) 1000 750 500
Symmetry
Plane
Periodic
Region
Fig. 16.1 The simplified geometry of FESS with periodic region and symmetry plane
shown in Table 16.1. The allowable maximum rotational velocity for a solid cylinder
rotor with a factor of safety of two was calculated to be 41,000 rpm when the rotor’s
material is steel 4340 [8].
The rotor and the housing walls are subjected to isothermal boundary conditions
with an initial temperature of 24 °C. The FESS used in this investigation is shown
in Fig. 16.1. To reduce the computational costs, the simulation was conducted on a
10◦-slice from the FESS with a symmetry plane from the middle of it too.
16.2.2 Mesh Independence Analysis
Mesh independence analysis is essential before performing numerical analysis to
select the appropriate mesh. A structured quadrilateral mesh is used in all of the airgap
models in this study. The goal of this process is to find the best mesh that provides
a solution independent of the mesh. To test the system, three different meshes were
chosen. The airgap was 0.1–0.2 mm in size, and the rotor and housing were 1–
2 mm in size. The average temperature of the air, rotor, and housing at a rotational
speed of 40,000 rpm and atmospheric conditions were used for the independence
16 Development of a CFD Model for the Estimation of Windage Losses … 161
test. Figure 16.2 depicts the average temperature of the flywheel components for the
three different meshes at different radius ratios. Mesh 2 was the most suitable mesh
for this work for all radius ratios because the temperature of the airgap, rotor, and
housing changed insignificantly between meshes 2 and 3. Further mesh refinement
increases the computational time and costs of CFD modelling, making mesh 2 the
best option. The inflation layers and the mesh used in the simulations are shown in
Fig. 16.3.
CFD simulation was used to investigate the machine’s steady-state operation, as
such steady-state models were used. Time-averaged steady-state solutions for the
rotor’s relative motion are modelled using a moving reference frame (MRF). This
method is appropriate for steady-state analysis and can resolve most flow character-
istics such as mass flow rates and pressure rises and drops across the rotating compo-
nents [9]. A turbulence model was required because the airgap had a Reynolds number
in the turbulent region for all rotational velocities. Reynolds averaged Navier–Stokes
(RANS) equations were solved using SST k-omega model. Based on a review of the
existing literature for turbulence modelling of Taylor-Couette flow within concentric
cylinders, the SST k-omega turbulence model is shown to be effective in estimating
the fluid flow and heat transfer characteristics in concentric cylinders [10, 11]. The
air was assumed to be an ideal gas and the viscosity was used under three equations
sutherland and the effect of gravity was ignored. Thermal conductivity and specific
heat were constant. The boundary conditions used in the solution are that the system
Fig. 16.2 Temperature values for the tested meshes for a η = 0.98, b η = 0.94, c η = 0.90
Case
Rotor
Airgap
Inflation Layers
Fig. 16.3 The mesh used for the system
162 M. Eltaweel et al.
is closed with no inlet or outlet. The surfaces of the rotor and the housing are smooth
with no-slip condition. Ambient temperatures of 24 °C and heat transfer coefficients
of 30 W/m2 K were used for the overall thermal boundary condition of the housing.
The initial temperature for all the system components were selected to be 24 °C,
room temperature. Wall treatment models were used to define the flow profiles in
wall boundary layers because of the turbulence models’ inability to accurately model
the boundary layer regions affected by viscous effects. Near-wall flow velocities and
distances are presented in the CFD section. The wall cell y+ ≤ 1 was used to create a
boundary layer mesh with a high resolution in order to resolve the viscous sublayer.
Numerical discretization of the governing equations was carried out using a finite
volume method to solve a linear algebraic equation system for each cell. The second-
order upwind discretization scheme was used to simultaneously solve these problems
based on mass, momentum, energy and turbulence parameter conservation. In order
to ensure that the CFD solution is converged for each run, iterations were properly
converged with respect to each other. The convergence criteria for all the residuals
were set to be 10−5 expect for energy which was set at 10−7.
16.2.3 Validation
The skin friction coefficient variation as a function of Taylor number was compared to
a number of experimental data points presented by Donnelly [12], Castle and Mobbs
[13], and Siong [14], where the radius ratio was close enough to be compared with
the experimental data. Figure 16.4 depicts the skin friction coefficient and Taylor
number distributions. There are three distinct zones, the first of which is when the
Taylor number is less than 1714 and the flow is laminar with no vortices, the second
is a laminar flow with Taylor-Couette vortices, which can be referred to as non-linear
theory due to the nonlinear aspect of the skin friction coefficient distribution, and the
third zone is a turbulent flow in which the confined air is fully mixed. The numerically
obtained critical Taylor numbers are in good agreement with the values proposed in
the literature. Furthermore, when Taylor vortices form in the air gap, the skin friction
coefficients estimated by CFD methods match well with Castle and Mobbs [13] and
Siong [14], and the CFD calculations accurately reproduce the distribution of skin
friction coefficients in the first zone. The predictions of the CFD model match the
experimental data very well.
16.3 Results and Discussion
The effect of radius ratios on the skin friction coefficient for the rotor and disc sides of
the flywheel at different rotational speeds is investigated. The outer cylinder (housing)
is fixed. The inner cylinder (rotor) rotates at an angular velocity of 40,000 rpm, which
is limited by the safety factor. The spike-shaped flow is caused by the creation of a
16 Development of a CFD Model for the Estimation of Windage Losses … 163
Fig. 16.4 The variation
between the skin friction
coefficient of the rotor with
respect to Taylor number
Taylor-Couette flow in the airgap. The air velocity closest to the housing is close to
zero, while the velocity closest to the rotor is the greatest. A Taylor number critical
value of 350 rpm can be obtained, indicating that the flow is not stable and Taylor
vortices occur inside the airgap at all rotational speeds investigated. The intensity of
the vortices increases as the rotational speed increases. Figure 16.5 represents the air
velocity distribution plot for the Taylor vortices at the investigated rotational speeds.
Within the air gap, Taylor vortices are symmetrical in the axial direction, where
viscous forces are overcome by increasing rotational speed and inertial forces. The
size of the Taylor vortex is affected by the speed of the rotor, where the vortices are
reduced in terms of number at higher speeds. where the increase in rotational speed
increases the distance between Taylor vortices.
Three rotor cavity pressure levels were investigated: 1000 mbar, 750 mbar, and
500 mbar. The rotor cavity pressure environment has little influence on the skin
friction coefficient for both the rotor and disc surfaces; the only influencing parameter
is the radius ratio with Taylor number, as shown in Fig. 16.6. While the effect is minor,
lowering the pressure will result in a lower skin friction coefficient for both the rotor
and the disc surfaces; however, the pressure will also lower the Taylor number under
the same rotational velocity. Windage losses, on the other hand, are heavily influenced
by rotor cavity pressure; lowering the pressure reduces windage losses, as illustrated
in Fig. 16.7. For all radius ratios studied, the lowest pressure has the least windage
losses, while the highest pressure has the most windage losses. Windage losses are
significantly affected by pressure. The difference in total windage losses between
500 mbar for η = 0.98 and 750 mbar for η = 0.90 is less than 1%, making the choice
of a larger airgap size with higher pressure a better solution in terms of complexity,
because the lower the pressure, the more complex the vacuum system. Windage
losses can be reduced by 16% and 33% for pressure environments of 750 mbar
and 500 mbar, respectively, when compared to atmospheric pressure. Reducing the
radius ratio from 0.99 to 0.94 and 0.90, on the other hand, can reduce total windage
losses by 12% and 19%, respectively, under the three pressure environments studied.
164 M. Eltaweel et al.
When comparing η = 0.90 and 500 mbar to η = 0.98 and 1000 mbar, it is possible
to achieve a 45% reduction in total windage losses, which could nearly double the
standby time of a flywheel energy storage system.
(a)
(b)
(c)
(d)
(e)
Fig. 16.5 Air velocity distribution inside 0.90 radius ratio airgap for rotational speeds of (a)
1000 rpm, (b) 10,000 rpm, (c) 20,000 rpm, (d) 30,000 rpm, and (e) 40,000 rpm
Fig. 16.6 Taylor number for different radius ratios and pressure levels with skin friction coefficient
for (a) rotor surface, and (b) disc surface
16 Development of a CFD Model for the Estimation of Windage Losses … 165
Fig. 16.7 Variation of the
total windage losses as a
function of the rotational
speed for three different
pressure levels and radius
ratios
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000
To
ta
l W
in
da
ge
L
os
se
s (
W
)
Rotational Speed (rpm)
η=0.98|P=1000mbar
η=0.98|P=750mbar
η=0.98|P=500mbar
η=0.94|P=1000mbar
η=0.94|P=750mbar
η=0.94|P=500mbar
η=0.90|P=1000mbar
η=0.90|P=750mbar
η=0.90|P=500mbar
16.3.1 Dimensionless Analysis
Based on the parametric study described above, a dimensionless analysis is performed
to provide a piecewise expression of the rotor skin friction coefficient as a function
of the studied parameters. The skin friction coefficient for the rotor and disc surfaces
was expressed using two dimensionless parameters, the Reynolds number, and the
radius ratio. This paper aims to establish new dimensionless parameter to better
describe the skin friction coefficient for both the rotor and the disc surfaces for a
pressure environment higher than 500 mbar. The proposed formulation is as follows:
C f r = 0.3553 × (1 − η)0.3 × Re−0.4108 r (16.1)
C f d = 0.4429 × (1 − η)0.1 × Re−0.4120 d (16.2)
where C f r is the rotor skin friction coefficient, C f d is the disc skin friction coeffi-
cient, Rer is the Reynolds number between two concentric cylinders, and Red is the
Reynolds number between a rotating disc and stationary wall.
16.4 Conclusion
Continuous braking causes a significant amount of energy to be lost while driving in
cities, but this energy can be recovered and stored. The vehicle’s kinetic energy during
deceleration can be effectively recovered and stored by the flywheel energy storage
system. The aerodynamic performance of an enclosed non-ventilated flywheel energy
166 M. Eltaweel et al.
storage system was examined in this study using a computational fluid dynamics
(CFD) model to determine the effect of air gap size, and rotor cavity pressure envi-
ronment. In order to predict the windage losses over a broad operating range, the
flywheel rotor skin friction coefficients for different scenarios have been numerically
determined. Model validation was done to determine the validity of the CFD results,
showing a good agreement between the numerical and experimental data. Based on
the flywheel’s operating speed, the results showed that increasing the air gap size can
reduce windage loss by up to 19%, while lowering the operating pressure to 500 mbar
can reduce windage loss by 33%. When the operating pressure is the lowest and the
airgap size is the largest, windage losses can be reduced by 45%. A piecewise corre-
lation was proposed for the estimation of the skin friction coefficient for the rotor
and the disc surfaces for a variety of air gap sizes and operating circumstances.
Acknowledgements This work is supported by the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie grant agreement No 801604.
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