Parametric study of efficient small-scale axial and radial turbines for solar powered Brayton cycle application

Energy Conversion and Management 128 (2016) 343–360

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Parametric study of efficient small-scale axial and radial turbines for solar powered Brayton cycle application Ahmed M. Daabo a,b,⇑, Ayad Al Jubori a, Saad Mahmoud a, Raya K. Al-Dadah a a b

The University of Birmingham, School of Engineering, Edgbaston, Birmingham B15-2TT, UK The University of Mosul, Mechanical Engineering Department, Ninawa, Iraq

a r t i c l e

i n f o

Article history: Received 30 June 2016 Received in revised form 30 August 2016 Accepted 18 September 2016

Keywords: Small scale turbines Axial and radial Brayton cycle Preliminary design and CFD Compressed air

a b s t r a c t The researchers’ main target in this work is to demonstrate the performance of small-scale (5–45 kW) axial and radial compressed air turbines which are able to operate at specific boundary conditions. These boundary conditions were chosen to be compatible with a small-scale solar powered Brayton cycle. The evaluation is dependent on the turbines’ efficiency, compactness and output power. Firstly, preliminary design work was completed in order to figure out the turbines’ shapes and find initial information about the impact of various factors on their efficiency values and output powers. Factors considered were: inlet pressure, inlet temperature, pressure ratio, rotational speed and the mass flow rate. Their performance during the off design conditions was also recorded. Subsequently, three-dimensional computational fluid dynamics modelling was completed for each turbine and at every single studied case in order to study in depth the effect of other factors and have accurate results. The results show that the radial turbine is superior when the main concern is working with low mass flow rate. On the other hand, the axial turbine is more desirable when the low rotational speed is of interest. The cycle results showed that an improvement in the cycle’s thermal efficiency ranging from 6% to 12% can be achieved with a turbine efficiency increase from 80% to 90% respectively for fixed cycle boundary conditions. Finally, two different data sets from the previous experimental work have been used to examine the accuracy of the current work and the outcomes were highly accurate. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Small-scale turbines are considered as a promising technology because of their low initial costs, low maintenance, durability and simple construction. The need for an efficient small-scale turbine, which can operate at low mass flowrates, relatively low pressure ratios and moderately high temperatures, was the driving force for investigating the Small-scale Axial Turbine (SSAT) and Small-scale Radial Turbine (SSRT). There are varying opinions about what characterises a small-scale turbine, however the significance of the power output is commonly agreed upon. Many of the references [1] give ranges from 5 to 500 kW. Several studies investigated separately different components of the cycle: such as the thermal cavity receiver of a small-scale solar Brayton cycle [2]; the effect of some boundary conditions on the overall cycle efficiency [3]; and the optimum performance of the cycle [4]. However, they neglected the turbines’ performance. The off-design ⇑ Corresponding author at: The University of Birmingham, School of Engineering, Edgbaston, Birmingham B15-2TT, UK. E-mail address: [email protected] (A.M. Daabo). http://dx.doi.org/10.1016/j.enconman.2016.09.060 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

performance of a small-scale humid air turbine cycle was studied by Wei et al. [5]. An evaluation of the microturbines and their application in the dual cycles was carried out in [6]. The lack of literature published that studied this range of turbine power outputs was the impetus for investigating the suitable boundary conditions for this range. In this study a comparison, with a range of around 5–45 kW was considered. From the perspective of the application, it is necessary to have a suitable turbine from the mentioned SSAT and SSRT which is able to work efficiently at some off-design conditions. It is stated that the axial flow type has been used specifically in aircraft gas turbine engines and they are also usually engaged in industrial and shipboard purposes [7]. Evaluation of the performance of micro gas-turbine for smallscale hybrid solar power plants using the thermodynamic analysis was achieved by Aichmayer et al. [8]. Klonowicz et al. [9] designed a small-scale single stage turbine uses R227ea as a working fluid. They revealed a good mutual agreement between the theoretical and measured values of the efficiency (55% and 53% respectively). However, they also concluded that it is unknown whether this model would be valid for different values of size parameter, expan-

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Nomenclature Symbols A b B c d f h H i k l m p PR r r Rc Re R s SC T U w W x Z

area blade width (m) axial chord (mm) absolute velocity (m/s) diameter (m) friction factor enthalpy (J/kg) blade height (mm) incident angle (deg) loss coefficient (–) length (m) mass flow rate (kg/s) pressure (Pa) pressure ratio radius (m) mean radius of curvature compressor pressure ratio Reynolds no. (–) degree of reaction entropy (J/kg K) swirl coefficient (–) temperature (K) rotor blade velocity (m/s) relative velocity (m/s) power (W) pressure loss coefficient blade number in radial turbine (–)

Greek symbols a absolute flow angle (deg.) b relative flow angle (deg.) h tangential/circumferential direction e clearance (m)

sion ratio or specific speed. Furthermore, a radial turbine was investigated by Fu et al. numerically [10] and then experimentally [11]. They developed an optimisation design approach to the aerodynamic performance, structural strength, and wheel weight of the radial turbine. The optimisation results showed high aerodynamic activity and satisfactory stress distribution. The influence of ambient temperature on the performance of micro gas turbine, for cogeneration system applications in the cold region, has been studied by Basrawi et al. [12]. The results showed that increasing the ambient temperature leads to a reduction in the electrical efficiency and an increase in the exhaust heat recovery. It was also found that by increasing the ambient temperature, the exhaust heat to mass flow rate and exhaust heat recovery to mass flow rate increased. Rahbar et al. [13] utilised the mean-line modelling and CFD techniques in order to develop a small-scale radial turbine, around 5 kWe. Then CFD techniques were used to evaluate the mean-line approach and improve the blade loading by some adjustment of the angles of the blades. Their results showed that achieving a high power output required a higher inlet temperature, mass flow rate and pressure ratio. The results also showed that the minimum number of rotor blades, which was suggested by meanline modelling, was overestimated. Different types of losses that are associated with turbines were included in the literature. For example, the impact of tip-gap losses on the stage efficiency was intensively studied in [14]. Furthermore, an assessment of different loss correlations for a small-scale impulse turbine working on ORC cycles was conducted in [15]. Enhancing the performance of a small-scale nozzle-less radial turbine with some detailed analysis

g c t q u

w x

f f⁄

efficiency (%) specific heat ratio velocity ratio (–) density (kg/m3) flow coefficient (–) loading coefficient (–) acentric factor (–) losses (–) nominal loss factor

Subscripts 1–6 station c compressor G gained hyd hydraulic m meridional direction r radial, rotor Rej rejected rel relative s isentropic, stator t total, stagnation, turbine th thermal ts total to static x axial Acronyms BCs boundary conditions CFD computational fluid dynamics PD preliminary design RMS root mean square S.S.A.T small-scale axial turbine S.S.R.T small-scale radial turbine SST small-scale turbines

for loss was achieved in [16]. However, only the VISUAL BASIC program was considered during their study. The flow losses of radial turbines with and without vanes were studied in [17]. An experimental study, using a laser Doppler velocimeter, for measuring the internal flow losses of small turbochargers was carried out in [18]. The study revealed that these losses occurred because of the fluid low energy suction surface of the blade, specifically on the shroud side. The secondary flow losses in the nozzle of a radial turbine were investigated, using both numerical and experimental studies, in [19]. A single stage small-scale radial inflow turbine with a rotor of 4.58 in. was studied by Jones [20]. A simple cycle gas turbine with 50 hp as a nominal power output with a capability to reach up to 100 hp minimal modification was used during his study. Their results showed that small inflow radial turbines were able to have good efficiencies: 86% total to static and 88% total to total, at high stage pressure ratio of 7. The researcher claimed that this level is higher than that of the multistage axial turbines can provide at the same boundary and design conditions. An optimisation procedure was established with the aim of determining the main dimension of the rotor (60,000 rpm and 60 kW electrical power) by Ebaid et al. [21]. In their research they developed a computer program to find the optimum dimensions of the rotor with the relevant number of blades. Optimizing the blade passage was also achieved by Mistry et al. [22] by designing a nozzle-less small capacity (20 kW) radial inflow gas turbine. They concluded that the maximum efficiency was achieved at the values of 0.54 and 0.41 absolute and relative

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Mach numbers respectively. The aerodynamic and thermodynamic factors were together investigated for designing a small-scale radial gas turbine of 600 kW; using a one dimensional code of FORTRAN language developed by multiple authors, mean line analysis [23] and 3D [24]. They claimed that the used code was an effective tool for predicting the turbine performance. Their results demonstrated good agreement when they compared them to the results of the CFD numerical solution. In this work, an innovative integrated approach is presented. It combines preliminary design and 3D simulation of efficient smallscale air turbines. Moreover, it compares two small-scale turbines of the well-known types, axial and radial turbines in order to characterise the performance of each type using different boundary conditions. By understanding the best outputs in both the on and the off-designs conditions, it can be known which type is more suitable for the application of small-scale solar Brayton cycle. The turbine preliminary design was established using the engineering equation solver (EES) software [25] to calculate the initial dimensions and performance of each type. Then it is integrated with ANSYSÒ15 CFX [26] to figure out the 3D turbine shape and evaluate their performance. In this procedure, their efficiencies were based on the thermodynamic operating conditions and inputted into the cycle in order to learn their effect on the cycle thermal efficiency. This study aims to identify an appropriate turbine to meet these requirements.

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tor or heat exchanger to exploit the exhaust energy, which would be otherwise lost to the environment. This recuperator preheats the cold air before entering the source of heat, which for the traditional Brayton cycle, is the combustion chamber. Thermal energy storage is used to store the excess heat from the solar system during the zenith time for example, and then send it back to cycle when there is not enough heat during dusk or in cloudy weather. The layout of the Brayton cycle system is shown in Fig. 1. The compressor power is given by [27]:

WC ¼

CpT 1 ðRC K  1Þ

gC

ð1Þ

where the compressor pressure ratio equals Rc = P2/P1 and in contrast the turbine pressure ratio is: Rt = P4/P5. The amount of heat supply by the solar receiver per unit mass of working fluid flow is:

Q Net ¼ ðT4  T3 Þ

ð2Þ

The heated working fluid exit from solar receiver passes through turbine to generate power, the power output from turbine is given by:

WT ¼ CpgT T 4 ð1  RT  KÞ

ð3Þ

where k = c  1/c. If the pressure loss coefficient is defined to be X, the above formula can be written as:

2. Thermodynamic analysis of Brayton cycle

WT ¼ CpgT T 4 ð1  ðXRc Þ  KÞ

The thermal Brayton cycle consists of the following components: a compressor; a component for heating the compressed air (usually a combustion chamber); a turbine to extract the air potential energy and transfer it to mechanical energy; a recupera-

The exhaust working fluid exits from the turbine to the atmosphere and through its way it will pass through recuperator. The heat gained by incoming compressed air and the heat rejected through the leaving air is given by the next two equations respectively:

Fig. 1. Schematic diagram of CSP-BC system.

ð4Þ

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_ 2  h3 Þ Q G ¼ mðh

ð5Þ

_ 5  h2 Þ Q cRej ¼ mðh

ð6Þ

The extent to which a regenerator approaches an ideal regenerator is called the effectiveness, e, and is defined as:

e¼

H3  H2 H  H2

ð7Þ

The net power output from the cycle is given by:

W net ¼ W t  W C

ð8Þ

This can also be written as:


 T 1 ðRC K  1Þ W net ¼ Cp gT T 4 ð1  ðXRc Þ  KÞ 

ð9Þ

gC

The thermal Brayton cycle efficiency is given by:

gth ¼

Wnet Q Net

ð10Þ

The above equation can be formulated in terms of temperatures and defined as following:

gth ¼

gt T 4 ð1  ðXRc Þ  KÞ  T 1



RK1 c



gc

  K1  T 4 ð1  ef1  gt ð1  ðXRc Þ  KÞgÞ  T 1 ð1  eÞ 1 þ Rcg c

ð11Þ As it is shown in Fig. 1, the cycle consists of different components; each of these components needs to be carefully designed in order to improve the overall cycle efficiency. The selection of the best design parameters of the turbine will lead to higher turbine isentropic efficiency, power output. This certainly will enhance the overall efficiency of the cycle and the system performance. Fig. 2A illustrates their T-s (temperature-entropy) diagram. 3. Axial and radial turbines characteristics There are some important similarities as well as differences between axial-flow turbines and radial-inflow turbines, so it is beneficial to mention some of them briefly [28–30]. Generally speaking, there are a few multistage radial-inflow turbines commercially available, but single stage applications are far more com-

mon. Moreover, in general radial-inflow turbines are particularly attractive for small units such as turbochargers and microturbines. By contrast, the axial-flow turbine has an advantage over the radial-inflow turbine in terms of efficiency. However, the higher the axial turbine efficiency the higher the blade profile accuracy level required, which could be impractical because of tolerance concerns. The radial turbine has far fewer blades per blade row, which can offer a major cost advantage, in particular in the smaller sized units. Flow capacity per unit frontal area of the axial-flow stage is significantly greater than for the radial-inflow stage. Knowing that, the rotor tip diameter is used to define the axial-flow stage’s frontal area, while the nozzle outer diameter is used for radial-inflow stage. However, from the mechanical point of view, when the Total- To-Total efficiency is based on inlet and discharge total thermodynamic conditions and is shown as a function of the ratio of the rotor speed to the optimum speed, the peak efficiency levels for the two stages are nearly identical with the axial-flow turbine showing a slight advantage. It can also be an advantage in terms of the work-per-stage capability. In contrast to the axial-flow turbine, the most effective approach to the performance analysis of radial-inflow turbine is the one-dimensional or mean-line method. It can be concluded that the two stage types offer comparable efficiency potential. So, production cost, mechanical integrity, manufacturing constraints and suitability to the specific application are more likely to determine which type will be the better option. 4. Governing equations and the preliminary design of the axial turbine In order to do the mean line design of the axial turbine the dimensionless parameters, flow coefficient, loading coefficient and degree of reaction, are need to be chosen and thereby the predicted initial efficiency and velocity triangles. Figs. 2B and 3 show the velocity triangles and their relative thermodynamic processes. The compressed air is enters the nozzle with a flow angle (a1) and absolute velocity (C1) and then leaves it at flow angle and absolute velocity (a2 and C2). The remaining angles and velocities are the inlet and outlet relative velocities and angles (w2, w3, b2 and b3 respectively). The relating equations are sorted below [31]: The loading coefficient and flow coefficient, which normally be the starting step in the turbines’ design, are determined by Eqs. (1) and (2)

Fig. 2. (A) T-S diagram of Brayton cycle and (B) H-S diagram of the turbine.

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347

Fig. 3. The mean line velocity triangle of; (A) axial turbine and (B) radial turbine [34].

rffiffiffiffiffiffiffiffiffiffi A5 2 þr 5hub

W¼

C h2 U2

ð12Þ

r 5t ¼

£¼

C m3 U2

ð13Þ

Z rotor ¼

The inlet flow angles can then be obtained using Eqs. (3) and (4). 2RÞ tan b2 ¼ ðW2/

) ð14Þ

tan b3 ¼ ðW2/þ2RÞ tan a3 ¼ ðW=2ð1RÞÞ /

ð15Þ

tan a2 ¼ ðW=2þð1RÞÞ /

rv olute

Next, both total to total, in case of more than one stage, and total to static, in case of single stage turbine, are determined as in the next two equations [16,17]:

gtt ¼ gts ¼

1 1þ

1þ

½fR w23 =2 h

þ

ðfS C 22 =2Þ=DW

þ

ðfS Cf22 =2Þ TT 32

1 fR w23 =2

 

ð16Þ

þ

C 23 =2

i

=DW

ð17Þ

Regarding the geometrical part of the calculations, the number of blade, Z, and the blade height, H, can be specified using the following formulas

Z¼

p 30

ð110  a1 Þtan a1

H ¼ rt  rh

ð18Þ ð19Þ

5. Governing equations and the preliminary design of the radial turbine The radial turbine, by contrast, also has the equations that cover it. So, loading and flow coefficients are firstly determined using Eqs. (20) and (21), [34]:

W¼

Dhactual U 24

ð20Þ

£¼

C m5 U4

ð21Þ

The relations that connect hub and tip diameter in radial turbine as well as the rotor number of vanes are:

p 30

ð110  a2 Þ tanða2 Þ

ð23Þ

After determining the fluid mass flow rate, its density and absolute velocity, the maximum radius and volute radius can be defined using the equations from [23–25,34,35].

A1 ¼

)

ð22Þ

p

_ working fluid m q1 C 1

ð24Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A1 ¼ ð0:75p þ 1Þ

dmax ¼ 2ðr 1 þ r v olute Þ

ð25Þ ð26Þ

The losses which are associated with volute geometry and then the total losses in enthalpy and the total to total efficiency are defined in the last three equations:

Dhloss;total ¼ Dhloss;v olute þ Dhfriction;nozzle þ Dhtip;clearance þ Dhsecondary þ Dhfrictio þ Dhexit ðgturbine;stage;ts Þnew ¼

Dhactual Dhactual þ Dhloss;total

ð27Þ ð28Þ

The designer can easily get the main specifications and thereby the mean line deign of the both turbines. These specifications, in brief, include Inlet boundary conditions such as pressures, temperature, pressure ratio, and output power as well as design parameters like, flow coefficient, loading coefficients, hub to tip radius ratio and number of blade. Finally, estimation the initial estimations of the overall efficiency initial, tip clearance. The flow chart of preliminary design program is showed in Fig. 4. The specifications of the studied boundary conditions BCs as well as the output geometry dimensions for both the small-scale axial turbine SSAT and the small-scale radial turbine SSRT are sorted in Tables 1 and 2 respectively. 6. 3D geometry and mesh generation The three dimensional blade generations ability which ANSYSÒ15 has enables the users to generate three dimensional TurboGrid models for the nozzle and the rotor of both the SSAT and SSRT (Figs. 5A, B and 6A, B respectively). When the Preliminary Design (PD) was performed, the blade geometry and dimensions

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Fig. 4. Algorithm procedure followed for the designed turbines.

for both stator and rotor, for each type, were exported to the detailed blade design module in ANSYSÒ15 called Blade-Gen to construct the blade geometry of turbine stage. CFX Turbo-Grid was used to mesh the fluid domain. As it is well known, the discretization of the domain has a direct effect on the quality of the solution in terms of accuracy and computational costs. The struc-

tured 3D mesh generation for blade-blade passage used in the simulations is shown in Fig. 7A and B for both SSAT and SSRT respectively. A grid size for the axial turbine model of 2,000,000 nodes was used; 1,000,000 for stator and 1,000,000 for rotor with a refined mesh near the blade wall. The radial turbine model, however, had around 1,000,000 nodes for stator and 2,000,000 for the

A.M. Daabo et al. / Energy Conversion and Management 128 (2016) 343–360 Table 1 Input parameter of the axial and radial turbines for the preliminary design. Parameter

Value

Output power (Target) Loading coefficient (W) Hub/tip radius ratio (rh/rt) Total PR Reaction (Rn) Rotational speed Total inlet temperature Working fluids

Axial

Radial

5.0–45 0.8–1.4 0.5 2–4 0.5 50–130 400–600 Air

5.0–45 0.6–1.2 0.3 2–4 0.9–1.4 50–130 400–600 Air

kW – – Bar – 1000 ⁄ RPM K –

Table 2 Turbines dimensions from the preliminary design. Parameter

Value

Hub diameter (Dh) Tip diameter (Dt) Rotor number of blade Stator number of blade Rotor Stagger angle Stator Stagger angle Tip clearance Tip width Blade height (H) Relative Inlet flow angle (b2) Relative outlet flow angle (b3) Absolute inlet flow angle (a1) Absolute outlet flow angle (a2)

Axial

Radial

20 40 6–16 9–17 43 35 0.45 – 13 29.32 51.66 0.0 66.18

20 – 11–19 22–30 39 41 0.45 1.95 – 11 77 0.0 70

mm mm – – Degree Degree mm mm mm Degree Degree Degree Degree

349

rotor. It is worth noting that in the zone near to the blade surface and walls, the grid was refined to maintain a good compromise between computational costs and solution accuracy. The grid’s sensitivity analysis was carried out based on turbine total to static efficiency as shown in Fig. 8 in order to reach the satisfied number of elements for the chosen mesh type. The k-x based on SST turbulence model was implemented to produce a highly accurate prediction by the inclusion of transport effects in terms of flow separation prediction into the formulation of the turbulent viscosity (eddy-viscosity). To account the wall effects in the simulation, an automatic wall treatment was applied, which allows smooth shift between wall functions formulation and low-Reynolds number through computational grids without a loss in accuracy [36]. y+ is the dimensionless distance from the wall which is used to check the distance from the wall to the first node. If there are any information about the inlet turbulence, the medium turbulence intensity (Intensity = 5%) is recommended option. The k  x transport equations are:

  @ @ @ @k þ G k  Y k þ SK ðqkÞ þ ðqkui Þ ¼ Ck @t @xi @xj @xj

ð29Þ

  @ @ @ @x þ Gx  Y x þ Sx ðqxÞ þ ðqxui Þ ¼ Ck @t @xi @xj @xj

ð30Þ

The k  w based SST model accounts for the transport of the turbulent shear stress and gives highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients.

Fig. 5. 3D view of the three dimensional configuration of; (A) Axial turbine and (B) radial turbine.

Fig. 6. 3D view of the rotor and a closer look on some of its blades of; (A) Axial turbine and (B) radial turbine.

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Fig. 7. 3D view for the grid passages of; (A) Axial turbine and (B) radial turbine.

Fig. 8. Mesh sensitivity based on turbine efficiency.

7. 3D numerical simulation The simulation of 3D turbulent viscous flow in the both types of SST geometry was performed using ANSYSÒ15-CFX solver. Steady-

state 3D viscous, single phase, compressible flow was used. Topology with a first order upwind advection scheme was chosen because it is numerically stable. These assumptions were suggested by [37]. A stage interface was applied for the interface between the stator and rotor. The GG1 (Generalized Grid Interface) feature of CFX was chosen for stage analysis and the steady state flow. The periodic boundary conditions were applied for blade passages for both the stator and the rotor. The shear stress turbulence model was chosen and combined with Navier-Stokes equations. For all runs the average value of y+ was kept at around unity as suggested in the CFX-Solver theory guide [26]. The applied BCs are: the total temperature, total pressure, flow direction, and the rotational speed as inlet conditions. A rotational, adiabatic wall was chosen for the blade and hub surface. The static pressure was chosen to be an output BC. The convergence criteria for the residuals of both velocity and the continuity equations were of the order of 105 while for the energy equation, 106. The solutions were achieved once the convergence criteria were satisfied. The block diagram of CFD simulation is shown in Fig. 9. Typical shapes of velocity distributions, for the both turbines are shown in Fig. 10A and B respectively. From these two figures it can be seen how the velocity was homoge-

Fig. 9. CFD procedure for the designed turbines.

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351

Fig. 10. Velocity distribution of; (A) Axial turbine and (B) radial turbine.

Fig. 11. Load distribution of; (A) Axial turbine and (B) radial turbine.

neously distributed along the blades’ height, which is essential in order to decrease secondary flow effects. Moreover, the load distributions shapes at three different pressure ratios (2, 3 and 4) for the axial and radial turbines respectively are also presented in Fig. 11A and B. They show the pressure profiles on the Suction Side (SS) and Pressure Side (PS) along the non-dimensional meridional coordinate. It can be seen that the differences between the PS and the SS is increased with changing the pressure ratio to higher values. In the hub region, the differences between PS and SS pressure are smaller for the SSRT than SSAT which indicates the light load on this region; however, the opposite is the case in the shroud area.

8. Validation Some validated experimental data is available in the literature [20,38–45]. As they have relatively sufficient data, the references [20,39] have been chosen and deeply investigated in order to validate the current work. The validation results showed good agreement between the current work and the two chosen studies. The first validation of the current work was with reference [39] and it was done using the CFD technique. However, in the second validation, with Ref. [20], only the one-dimensional approach was used because relatively little information was provided about the three- dimensional approach. Fig. 12A and B showed the comparison between the present work and the two mentioned research studies respectively. From these two figures it can be seen that even though very good agreement was achieved, there was some deviation in the results; however, it was within the acceptance limit. The maximum deviation was noticed in Fig. 12 A when it reaches to about 10%. This value seems to be relatively high because three-

dimensional analyses were conducted in this validation. On the other hand the deviation between the current results and those found in Ref. [20] did not exceed 2.3% as only 1D analyses were conducted, as shown in Fig. 12B.

9. Results and discussions 9.1. The effect of boundary conditions In this paper, the simulation of 3D turbulent viscous flow in both types of SST geometry has been performed by using ANSYSÒ15-CFX solver. As a result, the effect of each: pressure ratio, rotational speed and inlet temperature on each the total to static turbines’ efficiency and output power have been figured out. Some of these results are shown in Figs. 13–15. Generally speaking, the output powers at all the studied inlet air temperatures of (400–600 K) strongly depended on the pressure ratio, which increased from 2 to 4. Interestingly, both of the studied SST have almost the same trend with increasing both the pressure ratio and the rotational speed. Furthermore, an increase in the output power was not continuous with increasing SST rotational speeds. It can be seen that after a specific value, which seems to be the optimum speed, the output power begins to decrease. This optimum value of speed was different for each value of pressure ratio as well as turbine type. Moreover, comparing to its initial values, at 50,000 RPM, the output power became around 150% of the power output at the optimum rotational speed. Fig. 13 A shows the effect of the rotational speed on the turbine total to static efficiency and power output for both SSAT and SSRT at a PR of 2 and a turbine inlet temperature of 400 K. In comparison with SSRT it was noticed that the SSAT demonstrated higher efficiency for all the rotational speeds except 120 kRPM, for which

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Fig. 12. The efficiency of the current work against two experimental works.

SSRT shows higher efficiency. This indicates its ability to work more effectively at the off-design conditions. A maximum of about 13% difference was displayed at a very low rotational speed of 60 kRPM. As the rotational speed increased the difference between the two efficiency trend lines diminished, until they were closely matched at 110 KRPM. That was because increasing the rotational speed of SSRT allows a reduction in both the secondary and leakage losses. The efficiency peaked for SSAT at 90 KRPM at approximately 81%, this may be due to that the 90 KRPM was with the range of nominal conditions, while for SSRT the maximum was noticed at 120 KRPM with approximately 77%. Although the SSAT displayed higher efficiencies, the power output of the SSAT experienced lower values compared to SSRT through all the rotational speeds, except 110 and 120 KRPM. The reason for that was the ability of radial turbine of extracting higher power at the same value of mass flowrate. The maximum variance in the power output between both turbines was noticed at minimum rotational speed of 60 KRPM. Similarly, as the rotational speed increased the difference between the trend lines of the power output decreased, until they were closely matched at 107 KRPM. That was because of the sudden drop of the out power for SSRT. The peak power output values were around 6.7 kW and 8.7 kW at 87 KRPM and 80 KRPM for both the SSAT and SSRT respectively. Similarly, Fig. 13 B displays the effect of the rotational speed on the turbine total to static efficiency and power output for both SSAT and SSRT at PR of 2 and turbine inlet temperature of 500 K. In this figure, it can be noticed that the efficiency values were almost same and both of them hit the top at rotational speed of 90, KRPM with a values of 80%. These trends reflect the performance of each one of them during the on-design conditions. In the same way the trends of output power values for the SSAT and SSRT were represented with maximum values of 9.5 kW and 7.1 kW at the same rotational speed of 9 kRPM, indicating that the two turbines were working at their nominal conditions. Fig. 13C demonstrates the effect of the rotational speed on the turbine total to static efficiency and power output for both SSAT and SSRT at PR of 2 and turbine inlet temperature of 600 K. In this figure the value of optimum rotational speed, which produced the highest efficiency values, was clear. At rotational speeds lower than that value the preference was for the SSAT and the opposite was the case at higher rotational speeds. The reason for this is because a higher rotational speed of the SSRT allows reducing both the secondary and leakage losses and at the same time the total loss coefficient increases at higher rotational speeds. However, that was not the case for the amount of created power. It can be seen

that in spite of the big difference between the two trends at the mentioned optimum value of rotational speed with about 33%, that difference became very small, about 10.45 kW and 9.35 kW for the SSAT and SSRT respectively, at the highest investigated rotational speed. Fig. 14A displays the effect of the rotational speed on the turbine total to static efficiency and power output for both SSAT and SSRT at PR of 3 and turbine inlet temperature of 400 K. From this figure it can be seen that the tipping point was at 100 KRPM and the maximum divergence from the optimum efficiency was recorded to be about 20% for the SSRT with only about 10% for the SSAT. The values of extracted power for the SSAT, SSRT and the difference between their trends have also increased with increasing the rotational speeds to reach the maximum values of around 13.6 kW, 21.30 kW and 39% respectively. The mentioned values were at a rotational speed of 90 KRPM which was the nominal speed. Regarding their performance at the off design conditions, it can be that the SSAT behaves better at rotational speed values lower than the nominal one. In the same way, Fig. 14 B displays the effect of the rotational speed on the turbine total to static efficiency and power output for both SSAT and SSRT at PR of 3 and turbine inlet temperature of 500 K. As it can be seen, with respect to the efficiency of the SSAT through the different rotational speed values, from 97 kRPM the SSRT showed a greater efficiency and this continued to the maximum investigated rotational speed. Also, rotational speed values which are lower than the nominal ones, experienced lower efficiency of up to 11% with a preference rotational speed of the axial one. Again the reason for that is relating to the values of both secondary and leakage losses. A qualitative assessment of the output power for the two turbines, at the same Boundary Conditions (BCs), can be done comparing their trends. It can be seen that the higher rotational speed the higher difference in the extracted power values. The maximum achieved output power values were 12.85 kW and 23.7 kW for the SSAT and SSRT respectively. At this point it is importance to emphasize that same BCs were applied for the two investigated SST. The outcome of changing the rotational speed on the turbine total to static efficiency and power output for both SSAT and SSRT at PR of 3 and turbine inlet temperature of 600 K is figured out in f Fig. 14C. Again, similar behaviour has been noticed for the two SST in terms of both the total to static efficiency and the output power values. Having said that, the maximum efficiency values were 78.5% and 82% for the SSAT and SSRT respectively. Their performance at off design conditions was also different with an advan-

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Fig. 13. The T-S efficiency and power output for the two turbines at different rotational speed, PR = 2 and inlet temperature of; (A): 400 K, (B): 500 K and (C): 600 K.

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Fig. 14. The T-S efficiency and power output for the two turbines at different rotational speed, PR = 3 and Inlet Temperature of; (A): 400 K, (B): 500 K and (C): 600 K.

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Fig. 15. The T-S efficiency and power output for the two turbines at different rotational speed, PR = 4 and inlet temperature of; (A): 400 K, (B): 500 K and (C): 600 K.

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tage to the SSAT. The maximum extracted output power reached up to 20.5 kW and 27 kW for the SSAT and SSRT respectively when they worked at their highest values of rotational speed. Fig. 15A–C characterise the total to static efficiency and the output power values at PR of 4 and turbine inlet air temperature values ranged from 400 K to 600 K respectively. Specifically speaking, in Fig. 15A at inlet air temperature of 400 K, it can be seen that except the preference of the SSAT at all the investigated rotational speed values the trends of the efficiency was similar to the previous case. Also, the maximum values of the efficiency as well as the maximum divergence from the optimum efficiency values were 80% and 78% at 90 KRPM and 12% and 21% at 60 kRPM for the SSAT and SSRT respectively. The output power trends, however, were similar to its equivalent at PR 3 and maximum values of 17.4 kW and 22.1 kW for the SSAT and SSRT respectively. It can be seen from Fig. 15B that at an inlet air temperature of 500 K both turbines have followed almost similar behaviour to that

in the previous case for changing rotational speed values. However, the difference between the trends of their efficiency values was smaller than the previous case and the benefit of the SSAT did not continue to the maximum investigated rotational speed. The advantage switched to the SSRT at 110 KRPM because of the low values of both the secondary and leakage losses at higher rotational speed values. Regarding the amount of achieved output power, there is no remarkable difference from the previous case in terms of these amounts for the two investigated SST. The maximum values were 17.35 kW and 32.1 kW for the SSAT and SSRT respectively. Finally, in Fig. 15C it is clear that the SSAT is superior because of its ability to work at the off-design conditions and produce a higher efficiency at a relatively low rotational speed, lower than the nominal design speed. That said, the maximum extracted output power for the SSRT was, by far, higher compared to the SSAT. Those values hit the top at the maximum investigated rotational speed values with 20.1 kW and 34.1 kW for the SSAT and SSRT respectively.

Fig. 16. The T-S efficiency and power output for the SSRT at; (A): different number of rotor blades and (B): different values of trailing edge stator blade angle.

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9.2. The effect of the turbines’ parameters In this section the effect of four different parameters (two in each stator and two in each rotor) on the two turbines’ performance are highlighted. Those parameters have been chosen because they showed more influence on the two turbines’ performance. From Fig. 16A the effect of the number of rotor blades on both the SSR turbines’ output power and efficiency is presented. It can be seen that the output power is gradually decreasing with the increase in the number of rotor blades; it seems to be that the decrease of the mass flow rate amount is the main reason behind this decrease. The turbine’s efficiency on the other hand reaches the top at 82.9% when the blade number is 13, as this number was the design point. Fig. 16B demonstrates the effect of the trailing edge stator blade angle on the efficiency and the output power of the SSRT. From this figure it can be seen that the output power is decreasing from its maximum value, about 14.2 kW, with the increasing of the value of this angle; while the value of 67° demonstrated the highest efficiency. After this value the efficiency became lower because of increasing the loss generation as a result

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of the difference between the value of this angle and the leading edge rotor blade angle. In the same way, the relevant two factors were investigated in order to assess their effect on the performance of the SSAT. Fig. 17A shows how the output power was gradually decreasing from about 23 kW with the increasing of the rotor blade number. The main reason is because the throat area is inversely related with the blade number and as a result the amount of mass flow rate decreased. Finally, the effect of the of trailing edge stator blade angle on the efficiency and the output power of the SSAT was presented in Fig. 17B. It can be seen from this figure that the highest efficiency, 82.1%, was presented at the angle value of 60° as this value was the optimum design point and after this value both the efficiency and the output power decreased.

10. Off-design analysis In this section the characterization and the performance of the turbines during the off-design working conditions such as the turbine inlet pressure, temperature and rotational speed are inten-

Fig. 17. The T-S efficiency and power output for the SSAT at; (A): different number of rotor blades and (B): different values of trailing edge stator blade angle.

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Fig. 18. The effect of pressure ratio and turbine efficiency values at inlet temperature of; (A) 400 K, (B) 500 K and (C) 600 K on the cycle efficiency.

sively discussed; with the aim of determining the effect of each one of them on the overall turbine performance and as a result on the system. In fact, even some methods such as fuzzy logic system, artificial neural networks and, recently, the core control method [46] have been used in order to visualize the turbine’s performance in the off-design. It is still difficult to accurately predict know the effect of all these factors as this effect is inseparable from others in the turbines’ performance. Detailed information about the methods that can be used for calculating and visualizing components’ off design performances as well as the procedures followed in each method can be found in [47].

ically using a personal computer program [47]. Working with a pressure ratio higher than the designed ratio will not only result in some lost energy, but will also cause some structural defects on the blade body of the turbine, especially when the temperature of the working fluid is high. By contrast, the lower pressure ratio will obviously result in lower specific work which can be extracted by the turbine and also lead to a decrease in the temperature of the working fluid leaving the compressor. Both the higher and lower values of the designed pressure ratio are considered as factors that inversely affect the overall cycle efficiency. 10.2. Turbine inlet temperature

10.1. Turbine pressure ratio When the geometry of any component, turbine or compressor, is fixed, this component will have s specific performance map in both the on-design and off-design conditions [47]. Moreover, having specific performance modelling for the cycle during the offdesign condition is in fact an iterative process as the operating point for each component in the cycle needs to be separately determined and matches with the other components. The process of iteration is normally achieved by serial nested loops or a matrix solution, where both need to be correctly coded and solved numer-

The turbine inlet temperature variation has a strong influence on the turbine performance [48]. Generally speaking, if the inlet temperature is higher than the designed temperature, the amount of the input heat changes, the specific work will be higher and the exhaust temperatures will increase as the specific output power per unit mass flow will increase [49]. This effect of the outlet temperature is either reflected in the other stage (in case of a multistage turbine), in the compressor (if the cycle is single stage and close) or in the recuperator in preheated cycles. It is even relatively accepted in some applications (depending on the amount of tem-

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perature difference) to have higher temperatures for the incoming mass flow rate; however, their effect (thermal stresses and strains) on the blades’ material should not be neglected. When the exhaust working fluid is directed to the compressor, this will obviously decrease its efficiency and as a result, the system’s efficiency. In case where the recuperator is part of the system, inevitably there will be heat losses to the atmosphere after the some of the exhaust heat is transferred to the turbine inlet. On the other hand, when the mass flow rate reaches the turbine with a lower amount of heat, this leads to a decreasing in the amount of extracted power by the turbine and as a result, a deterioration in the cycle’s efficiency. More details on the effects of these factors on both the components and the system can be found in chapter seven of [47]. The relation between the actual and optimum turbine speed power [50] can be described in equation (30) which is claimed to be applicable for any turbine [51].

P POpt

¼2

 2 NPT NPT  NPT;Opt NPT;Opt

ð31Þ

10.3. Turbine rotational speed

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12. Conclusion In this paper, the performance of small-scale, 5–45 kW, axial and radial turbines with compressed air as a working fluid, have been investigated at different boundary conditions with the aim of choosing the most suitable one for our application, a smallscale solar Brayton cycle. Their performance at both the on and the off design conditions were also monitored. The results of the simulated work are validated using two experimental works found in literature. From this long study many important points can be briefly submitted below: 1. At low rotational speed the axial turbine has the ability to behave better than the radial at the off design conditions and this can achieve a relatively stable efficiency for the cycle. Having said that, the latter has the advantage when the high rotational speed was the case. 2. The radial is superior when the main concern is to provide more output power at a relatively low mass flow rate and low pressure ratio. The output power reaches double that of the axial at high pressure ratio. 3. Working with a relatively low mass flowrate is in fact suitable for the small-scale application where the collected heat is small and needs to raise the compressed air temperature to maximum possible level. 4. The radial turbine was more efficient at high rotational speeds where the opposite was the case at relatively low rotational speeds. 5. The optimum efficiency for the radial corresponds to a higher blade speed than for the axial. 6. An improvement in the cycle thermal efficiency ranges from about 6% to 12% can be achieved if the turbine efficiency increased from 80% to 90% at fixed other boundary conditions. 7. For the investigated scale, the highest efficiency was achieved with 10 and 13 rotor blades and at a trailing edge stator blade angle of 67o and at 60o for the SSAT and SSRT respectively.

As for other factors, working at off-design conditions because of the variation in the rotor rotational speed causes many problems for both the turbine (its components) and the cycle’s performance. Generally speaking, the variation in the rotational speed is initially dependant on some other factors such fluctuations in the amount of supplied mass flow rate, or even variation in the value of the pressure ratio. Specifically speaking, working at a rotational speed higher than the designed speed leads to a decrease in the duration of the turbine’s life as a result of fatigue. Other structural problems such as the vibration and the bearings’ misalignment, or an increase in their temperature, are considered very important concerns which need to be carefully analysed. By contrast, when the turbine is rotating at a lower rotational speed, the driven equipment will have some problems with its performance. The turbine’s rotational speed should be suitably matched with the driven equipment [4], otherwise a controller has to be put between these two components.

Acknowledgment

11. Results of Brayton cycle analysis

The author thanks the Higher Committee for Education Development in Iraq (HCED) for funding this project.

Using the Brayton cycle analysis in Eqs. (1)–(11) to predict the Brayton cycle efficiency for the various studied boundary conditions is shown in Fig. 18A–C. From these figures the cycle thermal efficiency at nominal boundary condition as well as other conditions is demonstrated. It can be seen that at the maximum turbine efficiency the highest cycle efficiency is achieved. At this point the importance of investigating each single parameter of turbines is essential in order to have as higher turbine efficiency as possible. Also, as it is well known the highest temperature, which can obtained by studying and improving the other important component in the cycle (the receiver) is necessary for gaining higher cycle efficiency. An enhancement in the cycle thermal efficiency ranging from about 6% to 12% can be achieved if the turbine efficiency increased from 80% to 90% at other fixed boundary conditions. This range is increased when each the pressure ratio and the inlet temperature of the compresses air increased. At this point it is worth emphasising the importance of having a relatively stable value of turbine efficiency, at off-design conditions. This has a direct influence on the overall cycle thermal efficiency. This improvement in cycle thermal efficiency is based on 3D CFD simulations which are able to predict and develop the turbine efficiency.

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