Performance investigation and design optimization of micro scale compressed air axial turbine for domestic solar powered Brayton cycle

Sustainable Energy Technologies and Assessments 37 (2020) 100583

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Performance investigation and design optimization of micro scale compressed air axial turbine for domestic solar powered Brayton cycle

T

Ahmed M. Daaboa, , Khalid E. Hammob, Omar A. Mohammedb, Ali A. Hassanc, Thomas Lattimored ⁎

a

The University of Mosul, College of Petroleum and Mining Engineering, Mining Eng. Dept. Almajmoa, Mosul 41200, Iraq The University of Mosul, College of Engineering, Mechanical Eng. Dept. Almajmoa, Mosul 41200, Iraq c The University of Birmingham, School of Engineering, Edgbaston, Birmingham B15-2TT, UK d Department of Engineering, German University of Technology, Oman b

ARTICLE INFO

ABSTRACT

Keywords: Axial turbine CFD analysis FE analysis Domestic applications

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 and 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 attain the best turbine performance, using 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, the inlet pressure and the working fluid inlet temperature. Additionally, the maximum allowable deformation was highly influenced by the rotational speed, around 16.5%. Moreover, the fatigue life was also determined and both the rotor stagger and trailing edge wedge angles significantly affected its value. The simulated increases in fluid temperature lead to a decrease in the rotor fatigue life of 38%, at an inlet pressure of 5 bar. Such a result can open the door for more research studies and investigations to develop this (domestic) system for ground based (i.e. sea level) uses.

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 sources or solutions, as solar energy is widely available, solar panels are relatively cheap and they are environmentally friendly. Yet, the radiation of the solar which spreads on the Earth’s surface is quiet 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 solar PV materials for example (Chromium, Cadmium, Germanium, and Gallium). On the other hand, the CSP technology, such as the parabolic dish and central receiver, are completely environmentally friendly, when air (as the working fluid) is operated, like the case of Brayton cycle application. Despite the fact this 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. Other environmentally friendly technologies are the small scale wind turbines [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 [3,4] state the range of 1–500 kW for micro turbines. However, Refs. [5,6] claimed that the SST is a turbine in the range of 5–500 kW. More recently, some

Corresponding author. E-mail address: [email protected] (A.M. Daabo).

https://doi.org/10.1016/j.seta.2019.100583 Received 21 July 2019; Received in revised form 14 October 2019; Accepted 12 November 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A b B c h i F lb m m p w x Z z

α ρ ω

Blade area (m2) Blade height (m) Axial chord (mm) Absolute velocity (m/sec) Enthalpy (J/kg) Incident angle (deg) Force (N) Blade length (m) Blade mass (Kg) Mass flow rate (kg/sec) Pressure (Pa) Relative velocity (m/sec) Coordinate (–) Blade number in radial turbine (–) blade thickness (m)

η φ ψ Subscripts B cf n r t

Blade Centrifugal force Nozzle Root Tip

Abbreviation CFD FEA MSAT MSTs SPBC SST TEWA

Greek symbols ε_x ε_y ε_z σ_x σ_y σ_z

Thermal expansion coefficient Blade material density (Kg/m3) Rotor rotational speed (rad/sec) Loss Coefficient (–) Efficiency (%) Flow coefficient (–) Loading coefficient (–)

Strain in X-direction (–) Strain in Y-direction (–) Strain in Z-direction (–) Stress in X-direction (Pa) Stress in Y-direction (Pa) Stress in Z-direction (Pa)

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. [7,8]. A parametric study for a gas turbine power plant was a study achieved by Alfellag et al [9]. In their work the effect of different parameters such as the inlet pressure, the reheating temperature, the recuperator and turbine efficiency values on the specific fuel consumption and the thermal efficiency of the power plant were studied. A few research studies [10,11] investigated some components in detail, such as the cavity receiver and they optimised the cycle performance, other [12,13] tried to decrease the production cost and enhancing the solar collector, however, they ignored the turbines’ performance. Others research studies [14,15], considered the cycle analysis, for small scale or even micro turbines. Quite a lot of researchers [16–18] have enhanced, aerodynamically, the behaving 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 pressure ratio, rotational speed and mass flow rate values using both Soderberg’s correlation [19] and a 3D Computational Fluid Dynamic (CFD) assessment. Furthermore, Shadreck et al. [20] 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 [21]. In addition, an attempt was made by Richardson et al. [22] to present a large-scale technology to calculate the thermo mechanical simulations performance which can solve problems with up to 6 degrees of freedom. The considered component was a turbomachinery model with around 3.3 × 109 degrees-of-freedom. The performance of a scroll expander was investigated numerically and experimentally by Shahverdi et al. [23]. In addition, the vane geometry of a variable geometry turbine for a Garrett turbocharger was experimentally optimized by Hatami et al. [24] in order to increase the overall efficiency of the turbocharger. Furthermore, an effort was made to have the best rotor shape for an impulse turbine aerodynamically. That was utilized for an oscillating water column and performed by

Computational Fluid Dynamics Finite Element Analysis Micro Scale Axil Turbine Micro Scale Turbines Solar Powered Brayton Cycle Small Scale Turbines, Shear Stress Transport Trailing Edge Wedge Angle (Deg.)

Gomes et al. [25]. Some research studies have conducted structural analysis of the turbine blade [26,27] 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. [28]. The authors, launching the mean-line designed with a three dimensional for radial turbine and they put emphasis on the blades geometry, to improve both the turbine’s efficiency and its 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 especially for rotary parts. Additionally, the ranges of the output power, based on the difference in the boundary conditions were unalike the target of this study. To decrease the thermal stress and improve the aerodynamic operation of a micro-gas radial turbine, a multi-disciplinary optimisation was conducted by Barsi et al. [29]. With modifying the rotor blade to half of its thickness and parameterizing its camber, about 5% enhancement in the turbine’s efficiency was achieved. In addition, after the blade design modifications, it could withstand the maximum stress that 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 shape of the blade was a study established by Feng et al. [30]. A microturbine 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 aerodynamic performance. Thus, they concluded that the −32° of this angle leads to better stress distributions within the structure of the turbine. The inverse design method jointing the FEM and CFD analyses was utilized to optimize the micro-radial turbine where both; the blade thickness and profile were the employed parameters. The results confirmed that the high reliability of the operated method, since it effectively increased the blade 2

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strength by amending the design of the blade, without significantly decreasing the turbine efficiency. Finally, Fu et al. [31] developed a turbine through 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% increments in the output power was achieved which and simultaneously better stress distribution for the turbine structure was realised. Last but not least, more recently, a research study [32], 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 put out on the suggested (MSAT) Micro Scale of Axial Turbines, that conducts analysis on the aerodynamic design, the structural strength and the fatigue performance of the turbines. Therefore, this research study has attempted to improve the overall performance of MSAT by conducting all the cited analyses and thus come across the optimized MSAT geometry. The model’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 [33] in order to determine the 3D shape of the designed turbine and to assess its aerodynamic performance. Then, this model was aerodynamically optimized by means of the ANSYS18 Design Exploration package, using genetic algorithms. Once that done, the structural analyses were conducted with the aim of producing the top structural requirements for further design optimizations.

within the model. Following this, some analyses (like the mesh sensitivity and solution accuracy) were conducted to obtain more precise and better results for the MSAT design. Once these steps were completed, the design was developed using the MSAT model and it was analysed further using the static structural analysis, 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 MSAT shape 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. Fig. 1 summarises the procedure used in the present work.

Methodology

Governing equations

In the present study, the preliminary design for the MSAT was developed using the Engineering Equation Solver (EES) software [34]. Then, the 3D model was extracted using the ANSYS CFX18 tool with the aim of accurately determining the aerodynamic behaviour of the flow

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

Fig. 2. Velocity triangles for the MSAT.

Fig. 1. Overview process of the analysis procedures followed for the MSAT. 3

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achieved by predicting the velocity triangles, which leads to an estimate of the initial turbine efficiency. As shown in Fig. 2, the compressed air enters the nozzle with a flow angle (α1) and absolute velocity (C1), and then, in the same way, it exits at flow angle (α2) and absolute velocity (C2). Thus, the values of these parameters can be determined using the outlet relative angles (β2 & β3) and outlet relative velocities (w2 & w3). The most relevant equations for the turbine design have been selected from the relevant published research studies and they are shown below [35–38]. The first step in designing any turbine is to determine the loading and the flow coefficients, which are found with Equations (1) & (2), respectively:

=

C2 U2

(1)

=

Cm3 U2

(2)

Fig. 3. Stator of the MSAT created using the Blade Generation feature.

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 Fig. 3, was made using the BladeGen feature, which can be found inside the CFX. 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. With the aim of confirming that the best size of element had been selected, a separate study for the grid sensitivity corresponding to the efficiency of the turbine, as presented in Fig. 4, was carried out and the element number of 1,534,327 was chosen. Here, it should be highlighted 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 i.e. completed. Fig. 5 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 [40]. The model mentioned in Fig. 6 is the new model, developed by Menter [41,42], 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:

The losses in the nozzle and the rotor, in terms of the Enthalpy, are presented in Equations (3) & (4), respectively.

YStator =

h2 h2S h o1 h2

(3)

YRotor =

h3 h3S h o2,rel h3

(4)

Similarly, the total loss coefficient for the stator and the rotor are respectively presented in the next two correlations [19,39]:

105 Re

1/4

YStator =

105 Re

1/4

YRotor =

(1 +

) 0.993 + 0.075

l H

1

(1 +

) 0.975 + 0.075

l H

1

(5) (6)

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: (7)

m = Ax c x

where Ax is the annulus area, which can be determined by using the following equation:

Ax = m/ c x = m/

U

2 rmb

(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 , as shown below:

b=

m 2

(9)

U2

(10)

rm = U/

Using Zweifel’s correlation, the turbine blade pitch, s, can be determined using the blade solidity (s /C ) for the lowest pressure loss.

s Z = 2( )cos2 3 (tan C

3

+ tan 4)

(11)

t

Subsequently, the turbine efficiency is resolved by means of equation (12). ts

= 1+

2 R w3

+

2(h1

2 N c2

+ c12

xj

( kui) =

xj

(µ +

µt k ) + Pk k3 xj

K

(13)

while the ω equation is:

1

h3)

( k) +

(12)

t

(

)+

xi

(

uj) =

xj

(µ +

µt ) + (1 3 xj

F1)2

1 2

K + 3 P xi x j K k

3

K 2

(14)

Numerical analysis and CFD model

The velocity distribution, temperature and pressures contours of the MSAT are presented in Fig. 6,

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 4

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Fig. 4. Mesh sensitivity with respect to the MSAT efficiency.

Validation of the numerical study

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).

In order to validate the present research study, the presented results have been successfully compared with a similar model, found in Ref. [43], 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. Fig. 7 presents the results of the comparison between the present study and the model found in Ref. [43] in terms of the MSAT’s efficiency. It can be seen that there is a maximum deviation of only 9%

Structural analysis Mathematical model The stress fields result from the combined consequence of the

Fig. 5. The three dimensional shape for the blades and their domains. 5

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Fig. 6. Velocity, temperature and pressure contours for the analysed MSAT. Table 1 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

dynamic stress, the vibratory stress and the thermal gradient. To compute the thermal stress, the following equation is employed: (15)

= D.

where , and D are: stress, the strain and the matrix of elasticity. The considered material for the present study was the isotropic structural steel (Table 1) 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.

Fig. 7. Comparison between the MSAT efficiency values for the present research study and that found in Ref. [43].

x

6

=

1 [ E

x

Vp (

y

+

z)]

+

T(x, y, z)

(16)

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Fig. 8. Stress Distribution across the rotor part for the MSAT model.

Fig. 9. Deformation distribution across the rotor part for the MSAT model.

y

=

1 [ E

y

Vp (

x

+

z)]

+

T(x, y, z)

(17)

z

=

1 [ E

z

Vp (

x

+

y )]

+

T(x, y, z)

(18)

The dynamic stresses result from both the centrifugal force 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 compressed air flow as well as the resonance phenomena [44], are beyond the framework of the present analysis. The centrifugal force is calculated from the next equations:

E: is Young modulus, is the coefficient of thermal expansion and Vp is Poisson’s ratio. The temperature gradient, which is precisely bought from the CFD aerodynamic results, at points (x , y , z ) is represented by T(x , y, z ) .

Fcf = mr 7

2

(19)

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Fig. 10. Factor of Safety across the rotor part for the MSAT model.

Fig. 11. Biaxiality Indication across the rotor part for the MSAT model.

where Fcf , r, m and 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 tiny element of the blade and at that point integrating it to take account of the whole blade body, as presented below:

df cf = dm.

2 (R

r

+ z)

(21)

dm = . A(z)dz And

df cf = Fcf (x) =

(20)

2.

A(z). (Rr + z)dz lb

x

.

2.

A(z). (Rr + Z)dz

(22) (23)

The material of blades density is; , the area of blade is A, the thickness of the blade is z and the blade root radius is Rr . The blade shape can be treated to be a variable cross sectional area cantilever

where 8

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Table 2 Equivalent stress, maximum shear stress, maximum deflection, minimum safety factor and the minimum number of cycles at various inlet pressure and temperature values. Inlet Temperature Equals 450 (K)

VonMises Stress (Mpa)

Shear Stress (Mpa)

Deformation (mm)

Safety Factor (–)

Fatigue Life (Cycle)

2 3 4 5

22.4 51.5 70.5 81.53

18.5 22.9 30.5 56.84

2.13E−05 2.88E−05 3.18E−05 3.82E−05

3.846 2.99E+00 1.88726 1.3333

1.00E+06 7.83E+05 6.13E+05 3.11E+05

Bar Bar Bar Bar

A

Fcf(x) =

24.8 59.2 85.8 90.35

19.8 25.3 33.6 66.31

3.19E−05 3.75E−05 3.95E−05 4.21E−05

2.0704 1.6616 1.13202 0.3383

6.74E+05 4.34E+05 2.14E+05 1.84E+05

Inlet Temperature Equals 550 (K) 2 Bar 3 Bar 4 Bar 5 Bar

27 65.9 91.4 108.69

22.5 28.8 39 73.76

3.81E−05 4.01E−05 4.21E−05 4.95E−05

1.5704 1.10E+00 0.8851 0.33754

3.97E+05 2.57E+05 1.97E+05 1.57E+05

=

At Ar

A (z) = Ar .

At Ar

Ar

( ) At Ar

+

r

ln

( ) At Ar

A

lb

z

Ar . ( At ) lb . lb2 r

ln

( ) At Ar

2 x

where lbisthebladelength, At , the tip cross sectional area and Ar is the root cross sectional area. Analysis settings Once the aerodynamic analysis was successfully completed, the complete rotor of the MSAT was prepared 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 model of the “staticstructural” 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. Satisfactory 3D solid elements intensity for the rotor’s hub and blades was implemented in the model. 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. 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 organised using what is known as “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 controlled using the “elements grow”; the values of the transition ratio can be flanked by 0 and 1. In this paper, the value was set as 0.272 since it is recommended by Ref. [44]. More information about the elements which were employed in the model can be found in the Appendix.

[45,46]; the following relation can be made: lb

r

ln

z

A

Ar . ( At ) lb . z. lb

(26)

Inlet Temperature Equals 500 (K) 2 Bar 3 Bar 4 Bar 5 Bar

A (z)

2

z

Ar . ( At ) lb . Rr . lb

z

(24) z/lb

(25)

As a final point, to calculate the centrifugal force at any position of the blade, equation (26) is employed.

Fig. 12. The main angles used in defining the blade geometry of the MSAT. 9

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Fig. 13. The effect of the stagger angle values on the four studied factors at a trailing edge wedge angle of 1°.

Fig. 14. The effect of the stagger angle values on the four studied factors at a trailing edge wedge angle of 3°.

Results and discussions

deformation, on the other hand, was observed to be located at the tip of the shroud part of the blades, as shown in Fig. 9. Similarly, Figs. 10 and 11 show specific parameters of the present design. In fact, these Figures clearly indicate that the present 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 turbomachinery to work across a wide range of operating conditions.

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 Fig. 8. The maximum 10

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Fig. 15. The effect of the stagger angle values on the four studied factors at a trailing edge wedge angle of 7°.

Fig. 16. The efficiency and power output at various stagger angles and trailing edge wedge angle values.

Consequently, the influence of the working inlet pressure values, at various compressed air temperatures of the MSAT, on the deformation, the stress, the fatigue life and the factor of safety, are respectively presented in Table 2. From Table 2, it is clear how both the working inlet pressure 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 inlet pressure on the mentioned stress values. The maximum values calculated for the von Mises and shear stress were, at inlet pressure of 2 Bar, only approximately 23 and 18 MPa, respectively, as compared to approximately 81.5 and 56.8 MPa, respectively, at an inlet pressure of 5 Bar; both sets of values 11

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Fig. 17. Stress distribution enhancement across the rotor part for the MSAT model.

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 highest deformation, located at the blades’ tip, as discussed before, can be seen in Table 2. At an inlet pressure equals to 2 Bar, 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 inlet pressure equals to 5 Bar, 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 regard to the compressed air temperature, it is 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 Table 2, it is clear that both the inlet pressure and the temperature values of the compressed air have a straight influence on the fatigue number of cycles. For example, that value at the endurance limit at inlet pressure equals 2 Bar were calculated in the simulation as approximately 1.00E +06, 6.74E+05 and 3.97E+05, once the working fluid temperature was set at 450, 500 and 550 K respectively. These values at inlet pressure equals 5 Bar reduced to 3.11E+05, 1.84E+05 and 1.57E+05 cycles at 450, 500 and 550 K in that order. Here, it is essential to point out 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 satisfactory as the structural steel is chosen to be the material for the rotor, 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 MSAT, as shown Table 2, was calculated in connection with both; the compressed air temperature and its inlet pressure. The lowest safety factor values were calculated to occur when both the temperature and the inlet pressure 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 inlet pressure equals 2 Bar were calculated to be 3.85, 2.07 and 1.57, at the compressed air temperatures of 450, 500 and 550 K, in that order. When the rotor was simulated at its maximum investigated inlet pressure, 5 Bar, the values decreased to 1.330, 0.780 and 0.338, respectively, for the three temperatures. Optimizing the present design As the previous analysis showed, while the present design achieved a relatively high aerodynamic performance, its structural characteristics were not satisfactory. So, an evaluation for the MSAT’s blades was conducted with the aim of decreasing the associated stresses, without adversely affecting the aerodynamic performance of the MSAT. Moreover, from the topology viewpoint, analysing only the most important carefully selected blade parameters will ensure that the excellent aerodynamic performance, achieved with the present 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 MSAT. Fig. 12 highlights the most important angles for the studied MSAT 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 MSAT.

12

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distribution of the MSAT rotor. It can be further seen that the trailing edge wedge angle and Stagger angle, have a direct influence on the maximum equivalent stress distribution and values.

Fig. 13 shows the effect of the stagger angle value for the rotor part of the MSAT on each; the equivalent stress, the shear stress, the deformation and the safety factor values at trailing edge wedge angle equals 1°. It is clear from the figure that the stagger angle had almost no effect on the deflection the occurred in the rotor blades while its effect is clear on the values of the three other mentioned factors. Quantitatively, the equivalent stress was around 32 Mpa at stagger angle equals 20° and it reached approximately 34 Mpa at stagger angle value of 45°. The shear stress showed similar behaviour when replacing the two values, mentioned earlier, by 17.7 Mpa and 18.6 Mpa respectively. Moreover, the stagger angle of 31° led to the lowest values of both; the equivalent stress and shear stress, i.e. only 24 Mpa and 12.9 Mpa, as well as highest value of the safety factor, i.e. 3.6. In the same way Figs. 14 and 15 show the effect of the rotor stagger angle on each; the equivalent stress, the shear stress, the deformation and the safety factor values at trailing edge wedge angles of 3° and 5° respectively. It is clear from the figures that the stagger angle had a significant influence on all the mentioned factors. Quantitatively, the equivalent stress values were 25 and 37 Mpa at stagger angle equals 20° and reached about 34 and 61 Mpa at the stagger angle of 45°. That was for trailing edge wedge angles of 3° and 5° respectively. Similarly, the shear stress values were 14 and 21 Mpa at stagger angle equals 20° and became around 16.7 and 31 Mpa at a stagger angle of 45°. That was for trailing edge wedge angles of 3° and 5° respectively. Similarly, the safety factor values were 3.4 and 2.2 at stagger angle equals 20° and they decreased to about 2.5 and 1.5 at a stagger angle of 45° and trailing edge wedge angles of 3° and 5° respectively. At this point, it is important to mention that the deflection was influenced by only changing the trailing edge wedge angle to 3° and at various stagger angles. So, for trailing edge wedge angle equals 3°, the deflection was about 1.1 mm at stagger angle equals 20° and became only 0.4 mm at the stagger angle of 45°. Furthermore, the stagger angle that gives the best values, for the four studied factors, was observed to decrease when the trailing edge wedge angle was increased. 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 MSAT. Fig. 16 presents the effect of rotor stagger angle values on the MSAT performance at trailing edge wedge anglse of 1°, 3° and 7°. These values were chosen because they showed good structural performance, specifically good stress and deflection values, for the studied MSAT. From this figure it is clear that the trailing edge wedge angle of 1˚ and the Stagger angle of 23˚ produced the highest turbine efficiency and power output with about 83.5% and 773 W respectively. Finally, Fig. 17 displays the progress achieved in terms of the stress

Conclusions The effect of numerous operational conditions, such as the compressed air inlet temperature, its inlet pressure and the rotor rotational speed, on the MSAT performance for solar powered Brayton cycle applications, has been studied in the present work using 3D analysis. The most important conclusions of this study are as follows: - 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. - The maximum studied working fluid temperature contributed to the decline of the rotor fatigue life by around 38%, at the maximum inlet pressure, 5 Bar. The point of the turbine blade which experienced the most fatigue was located in the connection between the blades and the rotor’s hub. - This study indicates that structural analysis is an effective tool for the study of the fatigue life, deflections and stresses of a MSAT. 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 MSAT. - 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. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment The authors would like to the University of Birmingham and the University of Mosul for the facilities provided for the present research study.

Appendix Fig. A1 shows the element density distributed across the turbine model. After the mesh was made, the related blade side and hub surfaces were nominated 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 rotational velocity, which was originally bring in from the rotor angular velocity in the aerodynamic analysis. Here, it is essential to highlight that the temperature of the working fluid was brought to the structural analysis as well. The rotor mesh independence is presented in Fig. A2. The launched temperature and load are given respectively in Figs. A3 and A4. It is clear from Figs. A3 that the aerodynamic load, from the incoming air, is located on of the blade pressure side of the blade in order for the model to calculate the torque value acting upon the blades. Fig. A4 shows the temperature allocation on the MSAT’s blades. The highest temperature is to be found at the inlet rotor blades tip (incoming working fluid flow is at its peak temperature); it then bit by bit declined when the working fluid became circulated across the area of the other blades. Table A1 details some of the structural meshes properties chosen during the solution. Furthermore, Table A2 highlights the operating conditions for which the turbine blade design was optimized for.

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Fig. A1. Structural mesh, with a close-up view of the refined mesh of the MSAT model.

Fig. A2. Mesh Independence.

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Fig. A3. Imported loads on FEA model for the MSAT model.

Fig. A4. Imported temperature on FEA for the MSAT model.

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Table A1 Mesh information. Physics Preference

Mechanical

Sizing Relevance Centre Initial Size Seed Smoothing Transition Span Angle Centre Minimum Edge Length

Medium Active Assembly Medium Fast Coarse 5.4573E−002 mm

Inflation Inflation Option Transition Ratio Maximum Layers Growth Rate Inflation Algorithm

Smooth Transition 0.272 5 1.2 Pre

Patch Independent Options Topology Checking

Yes

Advanced Shape Checking Element Mid-side Nodes Extra Retries For Assembly Rigid Body Behaviour

Standard Mechanical Program Controlled Yes Dimensionally Reduced

Statistics Nodes Elements

39,371 19,351

Table A2 Operating conditions and chosen dimensions of the MSAT. Parameter

Value

Blade number for the Stator Blade number for the Rotor Cp (J/kg K) Flow coefficient (–) Inlet total pressure (Bar) Inlet total temperature (K) Loading coefficient (–) Mass flow Rate (kg/sec) Rotor inlet Mach (abs) (–) ShroudExit/ShroudInlet (–) Working fluids (–)

8 9 1.005 0.35 2–5 450–550 0.95 0.013 0.69 0.77 air

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