Energy harvesting

1. Manuscript Details
Manuscript number TSEP_2019_103
Title Performance Investigation of Micro Scale Compressed Air Axial Turbine for
Domestic Solar Powered Cycle Applications
Short title Performance Investigation of Micro Scale Compressed Air Axial Turbine for
Domestic Solar Powered Cycle Applications
Article type Full Length Article
Abstract
This research investigation aims to characterize the aerodynamic and structural performance of a micro scale axial
turbine operated with the Brayton cycle, at various boundary conditions, by using the numerical integration finite
element method and 3D computational fluid dynamics; the stresses on the rotor blade, in particular, were investigated.
Firstly, the turbine was designed with a power output of 0.5-1 kW an efficiency of 81.3%. Then, together the turbine’s
shaft and its blades were structurally investigated under a variety of loading conditions, with the purpose of visualising
the effect of different geometrical and operational factors on the stress values, distributions and displacements over
the rotor’s blades. After evaluating the structural stresses, rotor blade design changes to decrease these stresses will
be proposed, to achieve the best turbine performance, through multidisciplinary optimization; these will be reported in
the next research publication from this study. The results showed that the maximum von Mises and maximum principle
stresses are highly influenced by the rotor stagger and trailing edge wedge angles, the turbine’s rotational speed and
the working fluid inlet temperature. Additionally, the maximum allowable deformation was highly influenced by the
rotational speed. Moreover, the fatigue life was also determined and both the rotor stagger and trailing edge wedge
angles significantly affected its value. Such a result can open the doors for more researches and investigations to
make this (domestic) system applicable on the ground.
Keywords Axial turbine, CFD Analysis, FE Analysis, Domestic Applications.
Corresponding Author A Daabo
Corresponding Author's
Institution
University of Birmingham
Order of Authors A Daabo, Tomas Lattimore
Suggested reviewers Mohanad Alfellag, Ali Maka, Silvio Barbarelli, O.P. Sharma
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2. Thermal Science and Engineering Progress
Dear Editor:
Please find attached for your kind review our manuscript entitled “Performance Investigation of
Micro Scale Compressed Air Axial Turbine for Domestic Solar Powered Cycle”.
In this paper, an assessment for both; the aerodynamic and structural performance of a Micro Scale
Axial Turbine MSAT by integrating Computational Fluid Dynamic CFD and Finite-Element Method
FEM was carried out. Starting from the preliminary design, a 0.5-1 kW output power was firstly
devised to have a very high efficiency of 81%. Then both; the turbine’s shaft and its blades were
structurally analysed under various loading conditions in order to visualise the effect of various
rotational speed values and blade shapes on the stress distribution and displacement over the blades.
The modal analysis was also included in the followed section in order to visualize the natural
frequency and the mode shapes of the turbine. Such a turbine can improve the overall solar cycles
efficiencies to be employed in domestic applications.
Four potential intendent reviewers who have excellent expertise in the review of this paper are:
S. Barbarelli silvio.barbarelli@unical.it
Mohanad Abdulazeez Abdulraheem Alfellag mohanadheete@uoanbar.edu.iq
Ali O.M. Maka aom2@hw.ac.uk
O.P. Sharma opsharma.iitd@gmail.com
I would very much appreciate if you would consider the manuscript for publication in the Thermal
Science and Engineering Progress.
Most sincerely,
A Daabo

3. 1- Aerodymnamci and structural analyses were integrated to evaluate MSAT.
2- Various BDs, by using the numerical integration FEM and 3D CFD were examined.
3- Inserting the final design of MSAT in a domestic SPBC to find out its suitability.

4. 1
Performance Investigation of Micro Scale Compressed Air
Axial Turbine for Domestic Solar Powered Cycle
Applications
A. Daaboa,b*
, T. Lattimore a,c
a
The University of Birmingham, School of Mechanical Engineering,
Edgbaston, Birmingham, B15-2TT, UK
b
The University of Mosul, School of Mechanical Engineering, Mosul, Iraq
c
Department of Engineering, German University of Technology, Oman
*
Email: axd434@bham.ac.uk, ahmeddaboo@yahoo.com
Abstract
This research investigation aims to characterize the aerodynamic and structural performance of a
micro scale axial turbine operated with the Brayton cycle, at various boundary conditions, by using
the numerical integration finite element method and 3D computational fluid dynamics; the stresses on
the rotor blade, in particular, were investigated. Firstly, the turbine was designed with a power output
of 0.5-1 kW an efficiency of 81.3%. Then, together the turbine’s shaft and its blades were structurally
investigated under a variety of loading conditions, with the purpose of visualising the effect of
different geometrical and operational factors on the stress values, distributions and displacements over
the rotor’s blades. After evaluating the structural stresses, rotor blade design changes to decrease these
stresses will be proposed, to achieve the best turbine performance, through multidisciplinary
optimization; these will be reported in the next research publication from this study. The results
showed that the maximum von Mises and maximum principle stresses are highly influenced by the
rotor stagger and trailing edge wedge angles, the turbine’s rotational speed and the working fluid inlet
temperature. Additionally, the maximum allowable deformation was highly influenced by the
rotational speed. Moreover, the fatigue life was also determined and both the rotor stagger and trailing
edge wedge angles significantly affected its value. Such a result can open the doors for more
researches and investigations to make this (domestic) system applicable on the ground.
Keywords: Axial turbine, CFD Analysis, FE Analysis, Domestic Applications.
1. Introduction
The ever increasing worldwide requirement for electrical power, which comes at the same time as
ever stricter restrictions on gaseous emissions resulting from combustion, have increased the necessity
for clean energy systems. Micro Scale Turbines (MSTs) in the application of the Solar Powered
Brayton Cycle (SPBC) are capable of producing a wide range of output power values, which make
them suitable to be used for small to large scale systems. Solar energy offers sustainable energy
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5. 2
solutions, as solar energy is widely available, solar panels are relatively cheap and they are
environmentally friendly. Yet, the solar radiation which spreads on the Earth’s surface is still not
efficiently utilized with this technology. The main advantage of Concentrated Solar Power (CSP) over
Photo Voltaic (PV) panels is that it does not have the significant environmental dangers accompanied
with the materials employed in solar PV, such as Chromium, Cadmium, Germanium, and Gallium. By
contrast, the technology used in CSP, such as the parabolic dish and central receiver, are completely
environmentally friendly, when air is operated as the working fluid, such as in the Brayton cycle
application. Despite the fact that CSP technology was first investigated around 50 years ago, it is only
more recently that this technology has gained the interest of both researchers and investors around the
world [see Figure (1)].
Figure (1): The advantages of CSP [1, 2].
There are varying opinions from previously published research articles about what characterises a
small scale turbine, however, the significance of the power output is something which has been
commonly agreed upon. Many of the published research articles [3-5] state the range of 1 – 500 kW
for micro turbines. However, Refs. [6-8] claimed that the SST is a turbine in the range of 5- 500 kW.
More recently, some research studies have been published which consider various analyses for
different types of turbines. For example, modal analysis for gas turbines was reported by Prasad et al
[9, 10]. A parametric study for a gas turbine power plant was a study achieved by Alfellag et al [11].
In their work the effect of different parameters such as the pressure ratio, the reheating temperature,
the recuperator and turbine efficiency values on the the specific fuel consumptionand the thermal
efficiency f the power plant was included.
Meguid et al [12] used the finite element technique (2D and 3D models) for the fir-tree region in a
turbine disc to look at the effect of some important geometrical factors like the teeth number, flank
angle and length upon the stress vaues in the disc.
A few research studies [13-15] investigated some components in detail, such as the cavity receiver
and they optimised the cycle performance; however, they ignored the turbines’ performance. Others
research studies [16-18], considered the cycle analysis, for small scale or even micro turbines.
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6. 3
Several researchers [19-23] have enhanced, aerodynamically, the performance of SSTs; but, they did
not conduct a structural analysis of the SST. For instance, the turbine aerodynamic performance has
been discussed as a function of various operational conditions, for instance the mass flow rate,
pressure ratio and rotational speed, using both Soderberg’s correlation [23] and a 3D Computational
Fluid Dynamic (CFD) assessment. Furthermore, Shadreck et al. [24] used a preliminary design for a
Small Scale Axial Turbine (SSAT), which was designed to be operated in an Organic Rankine Cycle
(ORC) application, with some emphasis on its cost. For the same application, different correlations for
SSAT losses were investigated by Zhdanov et al [25]. In addition, an attempt was made by
Richardson et al. [26] to present a large-scale technology to calculate the thermomechanical
simulations performance which can solve proplems with up to degrees of freedom. The considred
components was a turbomachinery model with around 3.3 * 109
degrees-of-freedom.
The performance of a scroll expander was observed numerically and experimentally by Zhang et al.
[27]. In addition, the vane geometry of a variable geometry turbine for a Garrett turbocharger was
experimentally optimized by Hatami et al. [28] with the aim of improving the overall efficiency of the
turbocharger. Furthermore, an effort was made to aerodynamically optimize the rotor part of an
impulse turbine for an oscillating water column was performed by Gomes et al. [29].
Some research studies have conducted structural analysis of the turbine blade [30- 33] but those were
about other turbines’ categories. Nevertheless, in recent times, some research studies, counting
structural analysis, were established by not many researchers. For example, a coupled Computational
Fluid Dynamic and Finite Element Method (CFD-FEM) study for a quite high-level of pressure ratio
radial inflow turbine was conducted by Shanechi et al. [34]. The authors, launching the mean-line
designed with a three dimensional for radial inflow turbine and they put emphasis on on the blades
geometry, to improve both the turbine’s efficiency and output power. Correspondingly, the structural
study was involved in their research articles, in which they studied the blades’ deformation and
stresses. Yet, there was no fatigue analysis included in their analysis, despite the fact that fatigue is
considered as one of the most critical problems easpcially for rotary parts. Furthermore, the ranges of
boundary conditions as well as the output power were different from the ranges which this study aims
to analyse.
To improve the aerodynamic performance and reduce the thermal stress of a micro-gas radial turbine,
a multi-disciplinary optimisation was conducted by Barsi et al. [35]. With modifiing the rotor blade
half thickness and parameterizing its camber, about 5% improvement in the turbine’s efficiency. In
addition, after the blade design modifications, it could now withstand the maximum stress that is was
expected to be subjected to throughout its lifetime. Again, as with other studies, a large scale was used
in the computational analysis and no fatigue analysis was conducted.
Improving the impeller hub strength as a result of optimizing the blade shape was a study established
by Feng et al. [36]. A micro-turbine of the 100 kW scale was studied by the researchers’, and their
results indicated that the flow inlet incident angle of the impeller’s affects each; the structural and the
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7. 4
aerodynamic performance. Thus, they concluded that the -32˚
of this angle leads to better
aerodynamic performance as well as better stress distributions within the structure of the turbine. The
inverse design method jointly with both CFD and FEM was employed to optimize the micro-radial
turbine. In their studies, the two key parameters which were utilized were the blade profile and the
blade thickness. Their results demonstrated that the method they used has a high reliability, since it
effectively increased the blade strength through modifying the design of the blade, without
significantly decreasing the turbine efficiency. Finally, Fu et al. [37] developed a turbine in order to
improve the output power, the aerodynamic performance, as well as the weight and strength, of the
turbine design, for s similar radial turbine scale. The results showed that around 50% increament in
the output power was achived which and simultaneuosly better stress distribution for the turbine
structure was realised. Last but not least, more recently, a research study [38], which investigated the
effect of a micro-scale turbine’s wall heat transfer rate on its performance was published. The authors
suggested that the turbine wall heat transfer rate parameter has an important influence on the
aerodynamic performance, which leads to a considerable but necessary re-design process in order to
optimize the turbine design.
To the best knowledge of the authors’ of this research article, no research has been published on the
proposed (SSAT) scale of axial turbines, that conducts analysis on the aerodynamic design, the
structural strength and the fatigue performance of the turbines; a summary of the current known
research published to date is shown in Table (1). Therefore, this research study has attempted to
improve the global performance of SSATs by conducting all the cited analyses and thus come across
the optimized SSAT geometry. The mdel’s preliminary design was conducted using 1-D analysis in
order to determine the preliminary design as well as performance of each model. Then, it was
combined with ANSYS CFX [37] in order to determine the 3D shape of the designed turbine and to
assess its aerodynamic performance. This design was then optimized using the ANSYS18 Design
Exploration package for the purpose of 3D optimization of the design, based on genetic algorithms.
Once that done, the structural analyses were conducted with the aim of producing the top structural
requirements for further design optimizations.
Table 1: Summary of the currently published research articles about SSTs.
Aerodynamic Analysis only Structural Analysis without
considering Fatigue
Structural and Fatigue
Analyses
[4, 9, 11, 16-22, 24-29] [7, 10, 12, 13] [-]
2. Methodology
In the current study, the preliminary design for the SSAT was developed using the Engineering
Equation Solver (EES) software [38]. Then, the 3D model was extracted using the ANSYS CFX18
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8. 5
tool with the aim of accurately determining the aerodynamic behaviour of the flow within the model.
Following this, some analyses were conducted in order to obtain more precise and better outcomes for
the design of the SSAT.
Once these steps were completed, the design was developed using the SSAT model and it was
analysed further using the static structural analysis, in order to create a robust design, with an
effective performance, for the required application. By utilising the integrated CFX-FE Workbench
feature, which can be found in ANSYS18, the optimum design of the SSAT was found, it was
extracted from the optimum design point, and then it was analysed in the structural analysis FEA
software, in order to conduct both the fatigue and the stress analysis. Figure 2 summarises the
procedure used in the present work.
Figure (2): Overview process of the analysis procedures followed for the SSAT.
3. Governing Equations
In the mean line design, dimensionless factors such as the degree of reaction, loading coefficient and
the flow coefficient, need to be wisely selected in order to reduce the time and effort required during
the 3D analysis, as well as in the aerodynamic optimization. This can be achieved by predicting the
velocity triangles, which leads to an estimate of the initial turbine efficiency. As shown in Figure 3,
the compressed air enters the nozzle with an absolute velocity (C1) and flow angle (α1), and then, in
the same way, it exits at an absolute velocity and flow angle (C2 and α2). Thus, the values of these
parameters can be determined using the outlet relative angles and velocities (w2 & w3, β2 & β3,
respectively).
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9. 6
The most relevant equations for the turbine design have been selected from the relevant published
research studies and they are shown below [41-44]. The first step in designing any turbine is to
determine the loading coefficient and the flow coefficient, which can be found with Equations 1 & 2,
respectively:
Figure (3): Velocity triangles for the SSAT.
𝚿 =
𝐂𝛉𝟐
𝐔𝟐
(1)
∅ =
𝑪𝒎𝟑
𝑼𝟐
(2)
The losses in the nozzle and the rotor, in terms of the Enthalpy, are presented in Equations 3 & 4,
respectively.
𝐘𝐒𝐭𝐚𝐭𝐨𝐫 =
𝐡𝟐−𝐡𝟐𝐒
𝐡𝐨𝟏−𝐡𝟐
(3)
𝐘𝐑𝐨𝐭𝐨𝐫 =
𝐡𝟑−𝐡𝟑𝐒
𝐡𝐨𝟐,𝐫𝐞𝐥−𝐡𝟑
(4)
Similarly, the total loss coefficient for the stator and the rotor are respectively presented in the next
two correlations:
𝐘𝐒𝐭𝐚𝐭𝐨𝐫 = (
𝟏𝟎𝟓
𝐑𝐞
)
𝟏
𝟒
⁄
[(𝟏 + 𝛇∗) (𝟎.𝟗𝟗𝟑 + 𝟎.𝟎𝟕𝟓
𝐥
𝐇
) − 𝟏] (5)
𝐘𝐑𝐨𝐭𝐨𝐫 = (
𝟏𝟎𝟓
𝐑𝐞
)
𝟏
𝟒
⁄
[(𝟏 + 𝛇∗) (𝟎. 𝟗𝟕𝟓 + 𝟎. 𝟎𝟕𝟓
𝐥
𝐇
) − 𝟏] (6)
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10. 7
For the constant value of the axial component of the flow velocity, the height of the turbine blade can
be specified from the continuity equation, by using the mass flow rate of the turbine stage, as shown
below:
𝐦
̇ = 𝛒𝐀𝐱𝐜𝐱 (7)
where Ax is the annulus area, which can be determined by using the following equation:
𝐀𝐱 = 𝐦/𝛒𝐜𝐱= 𝐦/𝛒∅𝐔 ≅ 𝟐𝛑𝐫𝐦𝐛 (8)
where 𝑏 and 𝑟𝑚 are the blade height and the mean radius, respectively, and they can be calculated by
using the blade linear speed 𝑈 and the rotational speed Ω, as shown below:
𝐛 =
𝐦Ω
̇
𝟐𝛑𝛒∅𝐔𝟐 (9)
𝐫𝐦 = 𝐔 Ω
⁄ (10)
Using Zweifel’s correlation, the turbine blade pitch, 𝑠, can be determined using the blade solidity
(𝑠 𝐶
⁄ ) for the lowest pressure loss.
𝐙 = 𝟐(
𝐬
𝐂
)𝐜𝐨𝐬𝟐
𝛃𝟑(𝐭𝐚𝐧𝛃𝟑 + 𝐭𝐚𝐧𝛃𝟒) (11)
Next, both efficiency (total-to-total), in the case of more than one stage, and efficiency (total-to-
static), in the case of single stage turbine, are determined by using the following two equations:
𝛈𝐭𝐭 = [𝟏 +
𝛇𝐑𝐰𝟑
𝟐
+𝛇𝐍𝐜𝟐
𝟐
𝐓𝟑 𝐓𝟐
⁄
𝟐(𝐡𝟏−𝐡𝟑)
]
−𝟏
(12)
𝛈𝐭𝐬 = [𝟏 +
𝛇𝐑𝐰𝟑
𝟐
+𝛇𝐍𝐜𝟐
𝟐
+𝐜𝟏
𝟐
𝟐(𝐡𝟏−𝐡𝟑)
]
−𝟏
(13)
4. Numerical Analysis and CFD Model
ANSYS CFX is a high-performance computational fluid dynamics tool which supplies accurate and
robust solutions for a wide range of CFD and multi-physics applications. It is recommended because
of its excellent robustness, accuracy and computational speed, which are especially designed to deal
with rotating machinery such as fans, compressors, pumps and turbines. The turbine geometry has
been generated by defining some critical factors such as hub diameter, shroud diameter and blade
width and number. The mentioned critical design factors were suggested based on the preliminary
design initiated as a code using the EES, while the full turbine model, as shown in Figure 4, was made
using the BladeGen feature, which can be found inside the CFX.
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11. 8
Figure (4): Stator of the SSAT created using the Blade Generation feature.
Next, the model was imported to the Turbogrid with the aim of creating 3D meshes for the blade
body, the hub, the shroud, the inlet and the outlet. In order to confirm that the best element size had
been chosen, a grid sensitivity study, with respect to the turbine efficiency, as shown in Figure 5, was
carried out.
Figure (5): Mesh sensitivity with respect to the SSAT efficiency.
At this point, it is important to mention that all of the mentioned steps are part of what is known as the
CFX solver, which offers a particular setup methodology for turbo-machines, in order to make the
setup procedure more efficient.
Before solving the model, some settings for the thermodynamic and physical properties, such as
specifying the state (transient or steady), the rotor rotational speed, as well as the working fluid type,
and setting the model boundary conditions, like the pressure and the temperature, need to be
input/completed.
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12. 9
Figure 6 shows the interface between the stator and the rotor domains. In regards to the solver type,
the SST k − ω turbulence model was chosen; it is a two equation eddy viscosity turbulence model,
which is recommended for flow with adverse pressure gradients [43].
Figure (6): The three dimensional shape for the blades and their domains.
The model mentioned in Figure 6 is the new model, developed by Menter [44], which hybrids both
the standard k − ω and the k − ε models (i.e. it utilizes the advantages of each of them and it is
considered the most accurate and appropriate model choice for adverse pressure gradients). That led
to the two equations, which can be found in the eddy viscosity SST k − ω model.
The K equation in the mentioned model is addressed, as shown in the following equation:
𝛛
𝛛𝐭
(𝛒𝐤) +
𝛛
𝛛𝐱𝐣
(𝛒𝐤𝐮𝐢) =
𝛛
𝛛𝐱𝐣
((µ +
µ𝐭
𝛔𝐤𝟑
)
𝛛𝐤
𝛛𝐱𝐣
) + 𝐏𝐤 − 𝛃 ∗ 𝐊𝛚 (14)
while the 𝟂 equation is:
𝛛
𝛛𝐭
(𝛒𝛚) +
𝛛
𝛛𝐱𝐢
(𝛒𝛚𝐮𝐣) =
𝛛
𝛛𝐱𝐣
((µ +
µ𝐭
𝛔𝛚𝟑
)
𝛛𝛚
𝛛𝐱𝐣
) + (𝟏 − 𝐅𝟏)𝟐𝛒
𝟏
𝛔𝛚𝟐𝛚
𝛛𝐊
𝛛𝐱𝐢
𝛛𝛚
𝛛𝐱𝐣
+ 𝛂𝟑
𝛚
𝐊
𝐏𝐤 − 𝛃𝟑 ∗ 𝐊𝛚𝟐
(15)
The velocity distribution, temperature and pressures contours of the SSAT are presented in Figure 7:
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13. 10
Figure (7): Velocity, temperature and pressure contours for the analysed SSAT.
5. Validation of the Numerical Study
In order to validate the current research study, the presented results have been successfully compared
with a similar model, found in Ref. [45], which was manufactured and experimentally tested in the
laboratory of the researchers. At this point, it is important to highlight that the cited experimental
study involved modelling and analysis in 3D. Figure 8 presents the results of the comparison between
the current study and the model found in Ref. [45] in terms of the SSAT’s efficiency. In general, it
can be seen that there is a maximum deviation of only 9% between the values obtained in the studies,
thus, the results of the 3D model of this research study had an excellent agreement with the
experimental work of the cited study (the model used in the validation of this study).
Figure (8): Comparison between the SSAT efficiency values for the current research study and that
found in Ref. [41].
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14. 11
6. Structural Analysis
6.1 Mathematical Model
The stress fields result from the combined consequence of the dynamic stress, the thermal gradient
and the vibratory stress. The thermal stress can be computed as:
𝛔 = 𝐃. 𝛆 (16)
where 𝜎 , D and 𝜀 are: stress, the elasticity matrix and the strain. The considered material for the
current study was the structural steel which is assumed to be isotropic (see Table 2) and for the stress
it’s subjected to, it is within the elastic deformation range, thus, the relations of the stress–strain has
been written in Cartesian coordinates such as the forms of equations 17-19.
Table 2: Structural Steel > Isotropic Elasticity.
Young's Modulus, MPa Poisson's Ratio Bulk Modulus, MPa Shear Modulus, MPa
2e+5 0.3 1.6667e+5 76,923
𝛆𝐱 =
𝟏
𝐄
[𝛔𝐱 − 𝐕𝐩(𝛔𝐲 + 𝛔𝐳)] + 𝛂∆𝐓(𝐱, 𝐲, 𝐳) (17)
𝛆𝐲 =
𝟏
𝐄
[𝛔𝐲 − 𝐕𝐩(𝛔𝐱 + 𝛔𝐳)] + 𝛂∆𝐓(𝐱, 𝐲,𝐳) (18)
𝛆𝐳 =
𝟏
𝐄
[𝛔𝐳 − 𝐕𝐩(𝛔𝐱 + 𝛔𝐲)] + 𝛂∆𝐓(𝐱, 𝐲, 𝐳) (19)
𝐸: is the modulus of elasticity 𝑉
𝑝 is the Poisson’s ratio and 𝛼 is the coefficient of thermal expansion.
The temperature gradient at a points (𝑥, 𝑦, 𝑧) is reresented by ∆T(𝑥, 𝑦, 𝑧). The temperature fields were
directly interpolated by using the CFD results.
The dynamic stresses result from both the centrifugal force (which significantly be influenced by the
rotor rotational speed) and the fluid pressure on the blades surfaces. The vibratory stresses, on the
other hand, which are caused by the disturbance that takes place during the fluid flow and from the
phenomena of resonance [46], are out of the scope of the current analysis. The centrifugal force can
be determined using the following equations:
𝐅𝐜𝐟 = 𝐦𝐫𝛚𝟐
(20)
where 𝐹𝑐𝑓, r, m and 𝜔 are the centrifugal force, radius of rotation, the blade mass, and the rotational
speed of the rotor, in that order. In spite of this, computing the precise centrifugal force value can be
attained when considering only a small element of the blade section and then integrating it to take
account of the whole blade body, as presented below:
𝐝𝐟𝐜𝐟 = 𝐝𝐦. 𝛚𝟐(𝐑𝐫 + 𝐳) (21)
where;
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15. 12
𝐝𝐦 = 𝛒. 𝐀(𝐳)𝐝𝐳
and (22)
𝐝𝐟𝐜𝐟 = 𝛒𝛚𝟐
. 𝐀(𝐳). (𝐑𝐫 + 𝐳)𝐝𝐳 (23)
𝐅𝐜𝐟(𝐱) = ∫ 𝛒. 𝛚𝟐
. 𝐀(𝐳). (𝐑𝐫 + 𝐙)𝐝𝐳
𝐥𝐛
𝐱
(24)
where, 𝜌 is the blade material density, A is the blade area, z is the blade thickness and 𝑅𝑟 is the radius
at the blade root. By considering the blade as a cantilever with variable cross section area [47], the
following relation can be made:
(
𝐀(𝐳)
𝐀𝐫
)
𝐥𝐛
= (
𝐀𝐭
𝐀𝐫
)
𝐳
(25)
𝐀(𝐳) = 𝐀𝐫. (
𝐀𝐭
𝐀𝐫
)
𝐳/𝐥𝐛
(26)
As a final point, the centrifugal force at any position of the blade can be computed via the next
equation:
𝐅𝐜𝐟(𝐱) = 𝛒𝛚𝟐 [
𝐀𝐫.(
𝐀𝐭
𝐀𝐫
)
𝐳
𝐥𝐛.𝐑𝐫.𝐥𝐛
𝐥𝐧(
𝐀𝐭
𝐀𝐫
)
+
𝐀𝐫.(
𝐀𝐭
𝐀𝐫
)
𝐳
𝐥𝐛.𝐳.𝐥𝐛
𝐥𝐧(
𝐀𝐭
𝐀𝐫
)
−
𝐀𝐫.(
𝐀𝐭
𝐀𝐫
)
𝐳
𝐥𝐛.𝐥𝐛𝟐
[𝐥𝐧(
𝐀𝐭
𝐀𝐫
)]
𝟐 ]
𝐱
𝐥𝐛
(27)
where 𝑙𝑏 is the blade length, 𝐴𝑡, the cross sectional area at the tip and 𝐴𝑟 is cross sectional area at
the root.
6.2 Analysis Settings
Once the aerodynamic analysis was successfully completed, the complete SSAT rotor was modelled
by using the Mechanical Workbench, ANSYS18, in order to extract the solid model from its air
domains. Then, both the model of the CFD and the static-structural model were coupled with the aim
of evaluating the turbine’s stress and deformation values. This was achieved when the aerodynamic
pressure values, which were computed using the CFD model, were passed on the structural model
through system coupling. Also, the temperature values, which the initial rotor design was based on,
was input into the solid model, in order to conduct the turbine thermal analysis using the ANSYS
Steady State Thermal section. A satisfactory element concentration, using 3D solid elements for the
hub and the rotor blades, was implemented in the model. So that precisely complete the structural
analysis, the locations of interest for the stresses and strains, were necessitated to have a reasonably
fine mesh, as contrasted to the parts of the model which were not of interest.
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16. 13
One more essential issue is whether the model required the generation of a full mesh for the entire
rigid body or only a surface contact mesh. This was controlled via the rigid body behaviour.
Perceptibly in this paper, the option of dimensionally reduced was chosen, in order to reduce the
required computational time. A further important factor in the mesh evaluation is the transition ratio,
which is defined by using the controller that determines the rate at which adjacent elements grow; the
values of the transition ratio can be set between 0 and 1. In this paper, the value was set as 0.272 since
it is recommended by Ref. [48]. More information about the elements which were employed in the
model can be found in the Appendix.
7. Results and Discussions
At the beginning of the simulation, when the turbine was simulated at the conditions it was optimized
for, to achieve around 84.4% efficiency and 7 kW output power, it was observed from the simulation
results that the stress was concentrated at the hub where the minimum life point was also located, as
shown in Figure 9. The maximum deformation, on the other hand, was observed to be located at the
tip of the shroud part of the blades, as shown in Figure 10. Similarly, Figures 11 and 12 show some of
other parameters of the current design. In fact, these Figures clearly indicate that the current design
needs to be further investigated, in order to know whether or not it will withstand conditions it was
not specifically optimized for, as it is expected for these types of turbo-machinery to work across a
wide range of operating conditions. Consequently, the influence of the working pressure ratio values,
at various compressed air temperatures of the SSAT, on the deformation, the stress, the fatigue life
and the factor of safety, are respectively presented in the following four Figures.
Figure (9): Stress Distribution across the rotor part for the SSAT model.
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17. 14
Figure (10): Deformation distribution across the rotor part for the SSAT model.
Figure (11): Factor of Safety across the rotor part for the SSAT model.
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18. 15
Figure (12): Biaxiality Indication across the rotor part for the SSAT model.
From Figure 13 and Figure 14, it is clear how both the working pressure ratio and the working fluid
temperature values play a vital role in terms of the von Mises and shear stress values, as a result of the
centrifugal force effect, which is highly influenced by the rotor rotational speed value. With this in
mind, it is obvious that the compressed air temperature had less of an effect than the working fluid
pressure ratio on the mentioned stress values. The maximum values calculated for the von Mises and
shear stress were, at a PR of 2, only approximately 23 and 18 MPa, respectively, as compared to
approximately 81.5 and 56.8 MPa, respectively, at a PR of 5; both sets of values were calculated at an
inlet air temperature of 450 K. Yet, at 500 and 550 K, the stresses increased significantly to 90.35 and
66.3 MPa, and 108.7 and 73.8 MPa, respectively for the two temperatures, and respectively for the
two stress values.
The maximum deformation (which occurred at the tip of the blades, as discussed previously), can be
seen in Figure 15. At PR equals to 2, the maximum deformations reached to approximately 21.1, 32.3
and 38.7 µm with air temperatures of 450, 500 and 550 K, respectively, whereas at PR equals to 5,
those values increased significantly to approximately 38.2, 42.7 and 49.5 µm. The displacement
values are relatively small and that, in fact, because of the investigated scale turbine which is
relatively small. As regards the displacement alteration with respect to the working fluid temperature,
it can be noticed that the fluid temperature had slight effect on the rotor’s displacement. Possibly, this
results from the material’s properties, which enable it to resist the examined fluid temperatures’ range.
The third examined factor in this work is the fatigue. In Figure 16, it can be seen that both the PR and
the compressed air temperature, have a direct influence on the number of cycles during which the
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19. 16
rotor is able to operate without experiencing fatigue failure. For example, the numbers of cycles
within the endurance limit at PR = 2 were calculated in the simulation as approximately 1.00E+06,
6.74E+05 and 3.97E+05, when the compressed air temperature was set at 450, 500 and 550 K
respectively. These values at PR = 5 reduced to 3.11E+05, 1.84E+05 and 1.57E+05 cycles at 450, 500
and 550 K in that order. At this instant, it is essential to mention that the calculated numbers are the
minimum ones of cycles (i.e. the expected component life based upon fatigue behaviour). Overall, the
calculated fatigue life values are not very satisfactory and the main reason for that is the material
chosen for the rotor, structural steel, which was only selected in this research in order to analyse the
blade design and to make comparisons between different operating conditions. If this rotor was
manufactured for a real-life turbine, a material with superior fatigue properties would, of course, be
selected, in order to significantly improve the fatigue life of the component.
Finally, the overall safety factor of the studied SSAT, as shown Figure 17, was calculated in
connection with both; the compressed air temperature and its PR. The lowest safety factor values were
calculated to occur when both the temperature and the PR were at their highest values. This might be
justified by empathizing the effect of the structural and thermal stresses, which together, have a linked
consequence on the rotor structure. The maximum factor of safety values at PR = 2 were calculated to
be 3.85, 2.07 and 1.57, at the working fluid temperatures of 450, 500 and 550 K, respectively. When
the rotor was simulated at its maximum investigated pressure ratio, PR = 5, the values decreased to
1.330, 0.780 and 0.338, respectively, for the three temperatures.
Figure (13): The equivalent stress at various pressure ratio and temperature values
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20. 17
Figure (14): The maximum shear stress at various pressure ratio and temperature values
Figure (15): The maximum deflection at various pressure ratio and temperature values
Figure (16): The minimum number of cycles at various pressure ratio and temperature values.
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21. 18
Figure (17): The minimum safety factor at various pressure ratio and temperature values.
8. Optimizing the Current Design:
As the previous analysis showed, while the current design achieved a relatively high aerodynamic
performance, its structural characteristics were not satisfactory. So, an evaluation for the SSAT’s
blades was conducted with the aim of decreasing the associated stresses, without adversely affecting
the aerodynamic performance of the SSAT. Moreover, from the topology viewpoint, analysing only
the most important carefully selected blade parameters will ensure that the excellent aerodynamic
performance, achieved with the current design, will be maintained. Thus, the inlet and outlet blade
angles were fixed, in order to decrease the relative associated flow angles; only the trailing edge
wedge angle and the stagger angle were chosen to be modified in this study, in order to enhance the
structural performance for the rotor of the SSAT. Figure 18 highlights the most important angles for
the studied SSAT blades.
Similar parametric studies were conducted in order to investigate the effect of each of the parameters
mentioned above on the aerodynamic and structural performance of the SSAT. Figure 19 indicates
that the stagger angle of 31 leads to the lowest stress and deformation values on the rotor part of the
SSAT, which results in a higher safety factor. Figure 20 shows how the stresses increased as the
stagger angle was increased. Compared to the previous Figure, these values are higher, however, they
are still lower those shown in Figure 21, which represents the values when the trailing edge wedge
angle was set as 7˚.
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22. 19
Figure (18): The main angles used in defining the blade geometry of the SSAT.
Figure (19): The effect of the stagger angle values on the four studied factors at a trailing edge wedge
angle of 1˚
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23. 20
Figure (20): The effect of the stagger angle values on the four studied factors at a trailing edge wedge
angle of 3˚
Figure (21): The effect of the stagger angle values on the four studied factors at a trailing edge wedge
angle of 7˚
From the aerodynamics viewpoint, decreasing the trailing edge wedge angle contributes in decreasing
the mentioned factors without a significant negative influence on the aerodynamic performance; i.e.
the efficiency and the power extracted by the SSAT; the trailing edge wedge angle of 1˚ and the
Stagger angle of 23˚ produced the highest turbine efficiency and power output, as shown in Figure 22.
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24. 21
Figure (22): The efficiency and power output at various stagger angles and trailing edge wedge angle
values.
Finally, Figure 23 shows the enhancement achieved in terms of the stress distribution and even the
maximum efficiency and power output values of the SSAT rotor. It can be further seen from this
Figure that the two factors, the trailing edge wedge angle and Stagger angle, have a direct influence
on the maximum equivalent stress distribution and values.
Figure (23): Stress Distribution enhancement across the rotor part for the SSAT model.
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25. 22
9. Conclusions
The effect of numerous operational conditions, such as the compressed air inlet temperature, its
pressure ratio and the rotor rotational speed, on the SSAT performance for SPBC applications, has
been studied in the present work using 3D analysis. The most important conclusions of this study are
as follows:
1- The pressure ratio has a significant effect on the deflection and stress values, where a maximum
increase of 77% and 91% deformation and stress, respectfully, were calculated at 550 K and at the
maximum studied pressure ratio. However, the deflection and stress values only increased by around
33 and 29%, respectively, at an air temperature of 450 K.
2- In regards to the location of the stress concentrations, they were mainly focused in the area which
joins the rotor’s hub with the blades; therefore, this part should be increased in its cross-section to
reduce the stress concentration value in this area.
3- The point of maximum deflection was calculated to occur at the blade tip of the rotor, across
approximately 16.5% of it, laterally, close to the location of the shroud, thus, a reasonable gap
between the shroud and blade tip should be maintained in the turbine design.
5- In regards to the fatigue analysis, the maximum studied working fluid temperature contributed to
the decline of the rotor fatigue life by around 38%, at the maximum pressure ratio. The point of the
turbine blade which experienced the most fatigue was located in the connection between the blades
and the rotor’s hub.
6- This study indicates that structural analysis is a powerful tool for the study of the fatigue life,
deflections and stresses of a SSAT. Therefore, a parametric study was carried out which focused on
two most significant parameters, the trailing edge wedge and stagger angles, in order to decrease the
stresses associated, while maintaining the aerodynamic performance of the SSAT.
7- The results of this analysis contributed to an improvement in the turbine rotor design, which
resulted in a better distribution of the stresses acting upon the rotor as well as decreasing their
maximum values to approximately 81% of their initial vales. Moreover, the deformation above the
blade was also decreased to about 75% as compared to its initial value.
Nomenclature:
A: Blade area (m2
)
b Blade width (m)
B Axial chord (mm)
c Absolute velocity (m/sec)
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26. 23
Cp: Specific heat (J/kg.K)
E: Modulus of elasticity (Pa)
εx: Strain in X-direction
εy: Strain in Y-direction
εz: Strain in Z-direction
d Diameter (m)
f Friction factor
h Enthalpy (J/kg)
H Blade height (mm)
i Incident angle (deg)
k Loss coefficient (-)
F: Force (N)
l: Blade length (M)
m: Blade mass (Kg)
m Mass flow rate (kg/sec)
p Pressure (Pa)
PR Pressure ratio
σx: Stress in X- direction (Pa)
𝜎𝑦: Stress in Y- direction (Pa)
𝜎𝑧: Stress in Z- direction (Pa)
α: Thermal expansion coefficient
Vp: Poisson’s ratio
∆T: Temperature gradient
g: Gravity (Kg)
ρ: Blade material density (Kg/m3
)
r: radios of rotation (m)
r Radius (m)
Rc Compressor pressure ratio
Re Reynolds No. (-)
R Degree of Reaction
s Entropy (J/kg.K)
SC Swirl coefficient (-)
T: Temperature (K)
t: Time (Sec)
U Rotor blade velocity (m/s)
w Relative velocity (m/sec)
W Power (W)
x Pressure loss coefficient
ω: Rotor rotational speed (rad/sec)
x: Coordinate
Z Blade number in radial turbine (-)
z: blade thickness (m)
Subscripts
b: Blade
cf: Centrifugal force
FEA: Finite Element Analysis
r: Root
SPBC: Solar Powered Brayton Cycle
SST: Small Scale Turbines, Shear Stress Transport
SSAT: Small Scale Axil Turbine
t: Tip
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Appendix:
Figure I shows the element density distributed across the turbine model. After the mesh was made, the
related side of the blade and hub surfaces were selected as the structure’s support and then the
pressure side of the rotor blade was selected in the model to apply the centrifugal forces, through the
input of the rotaionsl velocity, which was originally bring in from the rotor angular velocity in the
aerodynamic analysis. At this moment, it is essential to emphasise that the compressed air’s
temperature was brought to the structural analysis as well. The rotor mesh independence is presented
in Figure II.
Figure (I): Structural mesh, with a close-up view of the refined mesh of the SSAT model.
Figure (II): Mesh Independence
The imported load and temperatures are demonstrated in Figure III and Figure IV respectively. It can
be seen in Figure III that the pressure side of the blade is where the incoming air flow is located, as an
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aerodynamic load, in order for the model to calculate the correct amount of torque acting upon the
blades. Figure IV demonstrates the temperature distribution on the blades of the SSAT. The maximum
temperature value is located at the tip of the inlet rotor blades, as the incoming air flow rate is at its
highest temperature value; it then gradually decreased when the compressed air became distributed
across the area of the other blades, especially at the leading edge side of the blades. Table I details
some of the properties for one of the chosen structural meshes. Furthermore, Table II highlights the
operating conditions for which the turbine blade design was optimized for.
Figure (III): Imported loads on FEA model for the SSAT model.
Figure (IV): Imported temperature on FEA for the SSAT model.
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Table I: Mesh information
Physics Preference Mechanical
Sizing
Relevance Centre Medium
Initial Size Seed Active Assembly
Smoothing Medium
Transition Fast
Span Angle Centre Coarse
Minimum Edge Length 5.4573e-002 mm
Inflation
Inflation Option Smooth Transition
Transition Ratio 0.272
Maximum Layers 5
Growth Rate 1.2
Inflation Algorithm Pre
Patch Independent Options
Topology Checking Yes
Advanced
Shape Checking Standard Mechanical
Element Mid-side Nodes Program Controlled
Extra Retries For Assembly Yes
Rigid Body Behaviour Dimensionally Reduced
Statistics
Nodes 39,371
Elements 19,351
Table II: Operating conditions of integrated aerodynamic and structural analyses of the SSAT.
Parameter Range/value
Loading coefficient (-) 0.8-1.4
Flow coefficient (-) 0.1-0.5
Shroud Exit/Shroud Inlet (-) 0.8
Hub Exit/Hub Inlet (-) 0.22
Rotational speed (rpm) 50,000-90,000
Inlet total temperature (K) 450 - 550
Inlet total pressure (bar) 2 -5
Mass flow Rate (kg/sec) 0.03 – 0.05
Working fluids (-) air
Cp (J/kg K) 1,005
Inlet blade velocity (m/s) 253.1
Exit blade velocity (at shroud) (m/s) 202
Inlet relative velocity(m/s) 65.8
Exit relative velocity(m/s) 206.3
Inlet absolute velocity(m/s) 250.5
Exit absolute velocity(m/s) 14.7
Rotor inlet density(kg/m3
) 1.153
Rotor inlet Mach (abs) (-) 0.7
Rotor inlet Enthalpy (J/kg) 109,463
Rotor outlet Enthalpy (J/kg) 95,288.8
Rotor Enthalpy at the leading edge (J/kg) 107,811
Rotor Enthalpy at the trailing edge(J/kg) 87,117
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ACKNOWLEDGMENT
The authors would like to thank the Higher Committee for Education Development in Iraq HCED for
funding this project and the University of Birmingham and the University of Mosul for the facilities
provided for the current research study.
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33. To Thermal Science and Engineering Progress;
The authors whose names are listed below certify that they have NO affiliations with or
involvement in any organization or entity with any financial interest (such as honoraria;
educational grants; participation in speakers’ bureaus; membership, employment,
consultancies, stock ownership, or other equity interest; and expert testimony or patent-
licensing arrangements), or non-financial interest (such as personal or professional
relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in
this manuscript
A. Daabo
T. Lattimore