Energy Harvesting Using Solar ORC System and Archimedes Screw Turbine Combination with Different Refrigerant Working Fluids

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Energy Conversion and Management

journal homepage:www.elsevier.com/locate/enconman

Energy harvesting using solar ORC system and Archimedes Screw Turbine (AST) combination with different refrigerant working fluids

K. Shahverdi

^a,d,⁎

, Reyhaneh Loni

^b,e

, B. Ghobadian

^b

, M.J. Monem

^a

, S. Gohari

^d

, S. Marofi

^c

, G. Najafi

^b

aWater Structures Engineering Department, Tarbiat Modares University, Tehran, Iran

bDepartment of Biosystems Engineering, Tarbiat Modares University, Tehran, Iran

cWater Research Institute, Bu-Ali Sina University, Hamedan, Iran

dWater Science Engineering Department, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran

eDepartment of Biosystems Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

A R T I C L E I N F O Keywords:

Archimedes Screw Turbine Numerical optimization Power generation

Parabolic trough concentrator

A B S T R A C T

In this research, an energy harvesting system was developed for power generation using a combination of an Archimedes Screw Turbine (AST) and a solar Organic Rankine Cycle (ORC) system. An AST was numerically used and optimized for producing mechanical power as an energy harvesting technique. Different structural parameters including the screw inclination angle, number of flights and the screw length were considered. A parabolic trough concentrator was numerically modeled as a heat source of the ORC system. Two different types of absorber were considered using a smooth and corrugated tube. Different ORC working fluids were in- vestigated in the solar ORC system including R134a, R245ca, R245fa, R152a, R113, R11, and R114b. The results of numerical modeling were validated with experimental results and good agreement was found. The results revealed that R113 at the saturated condition at turbine inlet gave the highest ORC net power, ORC efficiency, and total efficiency compared to the other investigated working fluids. The solar PTC system with the corrugated tube showed the higher ORC net power, and overall efficiency compared to the smooth tube as the PTC receiver.

The highest efficiency resulted in the screw length of 1.5 m was 58.24% with inclination angle of 25° and flight number of 1. Finally, the optimized characteristics of power generation system including a solar ORC system and a screw turbine (hybrid system) were presented to harvest energy. Application of the presented hybrid system is an acceptable way for increasing and optimizing the ORC power generation.

1. Introduction

Nowadays, increasing CO and CO2emissions due to the fossil fuel consumption have caused many problems such as global warming, ozone depletion, and acid rain. Application of renewable energies can relieve these problems significantly. There are different kinds of the renewable energy such as solar, hydropower, wind, geothermal [1].

The solar and hydropower energies are available and easily accessible kinds of renewable energies for supplying human energy demand[2].

Solar collectors can be introduced as an exchanger for converting solar energy to thermal energy[3]. There are two kinds of solar collectors including non-concentrating in which the collector aperture area is equal to its absorbed area, and concentrating solar collectors in which the collector aperture area is bigger than the absorbed one. Parabolic Trough Concentrator (PTC) is an efficiently concentrating solar

collectors for absorbing solar energy[4].

Bellos et al.[5]numerically investigated the effect of internal fins in the PTC. Air, helium, and carbon dioxide were used as the solar working fluids. Among the investigated working fluids, helium showed the best exegetically performance. Some researches [6] numerically were considered a PTC with different working fluids with details. The optimum mass flow rate for each working fluid was calculated. It was found the pressurized water and carbon dioxide were suitable working fluids for medium temperature and high-temperature applications, re- spectively. Optimization of a solar-driven hybrid using parabolic con- centrator was conducted by[7]. Different nanofluids were tested as solar working fluids. They recommended the solar ORC system with application of CuO nanofluid as an efficient system for power genera- tion. Reddy and Kumar[8]predicted the convection and radiation heat losses from a trapezoidal cavity receiver as a solar absorber of a linear

https://doi.org/10.1016/j.enconman.2019.01.057 Received 2 October 2018; Accepted 11 January 2019

⁎Corresponding author.

E-mail address:Shahverdi2006@gmail.com(K. Shahverdi).

0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

T

Nomenclature AST Modeling

A_o the cross-sectional area of the downstream canal AQ the average cross-sectional area within the AST As Wetted area

A_w Wetted area

B Bucket number

dAf1 wetted surfaces area of the flights at downstream surface dAf2 wetted surfaces area of the flights at upstream surface dr radial element

d angular element dV Partial volume Di Inner diameter Do Outer diameter f Fill factor F Shear forces

Gw Gap width

g Gravitational constant H Net water head

h_{f ht,} Overall head loss due to hydraulic friction in the transport direction

L Total screw length N Number of flights p Hydrostatic pressure

p1 pressure at downstream surfaces of the flights p2 pressure at upstream surfaces of the flights Pout Total output power

Pl b, Bearing power loss

Pl OE, Overall outlet expansion power loss

P_{f ht,} Power loss due to hydraulic friction in the transport di- rection

Pr s, Generated power loss due to central shaft friction P_{f f,} power loss due to flights friction

Pmech Mechanical power Phyd Hydraulic power

Q_b Volume flow rate of a bucket Qs total flow passing through the screw Qgl Volume flow rate of gap leakage Q_nd non-dimensional flow

Q_o Overflow leakage

Qt Total volume flow rate passing through the system r radial position

S the pitch of the screw T total generated torque T_b Bucket torque V_b Bucket volume

vt the transport velocity of the buckets along the screw length

v_{r s,} relative shaft velocity

w aligned axis with screw centerline

z Water level

z₁ vertical positions of any point on the downstream z₂ vertical positions of any point on the upstream

zmin Minimum value of vertical point occurs at the downstream z_max Maximum value of vertical point occurs at the down-

stream zwl Water level

mech screw mechanical efficiency

o the Borda-Carnot coefficient µ the flow coefficient

Fluid density angular position rotation speed

angular position

the Darcy-Weisbach friction factor for either the trough or central shaft

r s, Darcy-Weisbach friction factor central shaft shear stresses Solar and ORC Modeling

A area, m²

c, m, and n Constant

cp constant pressure specific heat, J/kgK d Inner diameter (m)

D Outer diameter (m)

h Convection heat transfer coefficient, W/m²K h^* enthalpy, kJ/kg

h^Â internal heat transfer coefficient, W/m²K I_sun solar irradiance (W/m²)

kab,K thermal conductivity, W/mK m system mass flow rate, kg/s Nu Nusselt number, −

Pa Absolute pressure at annular (mmHg) Pr Prandtl number

Pr_w Prandtl number at wall temperature

q Incident heat transfer flow per length at a boundary (W/

Q_net m)net heat transfer rate, W

Q rate of available solar heat at receiver, W Q_loss loss rate of heat loss from the receiver, W R thermal resistance, K/W

Ra Rayleigh number Re Reynolds number, − T Temperature, K

Ta Temperature at a boundary (°C) Tdew Dew point (°C)

T Ambient temperature (°C)

¯T_ab Temperature difference between a and b boundaries (°C)

W _{power, W}

Greek symbols

Specific heat ratio

a Emittance at a boundary η efficiency, −

ρ Density, kg/m³

Molecular diameter of annular gas (cm)

σ Stefan-Boltzmann constant [=5.67∙10⁻⁸W/m²K⁴] Subscripts

0 initial inlet to receiver

ap aperture

ab absorber

c condenser

cond due to conduction conv due to convection cr critical

evp evaporator

f fluid

II second law of thermodynamic inlet at the inlet

n receiver section number

net net

optical optical overall overall

P pump

Fresnel concentrator. Cagnoli et al. [9] studied the thermal perfor- mance of a linear Fresnel concentrator using an encapsulated as evac- uated tubes. The solar receiver consisted of an evacuated tube collector, which was located at the focal point of a compound parabolic con- centrator. They concluded that this design of the receiver had a good performance for solar absorption. Bellos et al.[10]experimentally and numerically considered a linear Fresnel concentrator using a flat plate receiver. They predicted the useful absorbed heat for the investigated collector as well as different seasons. Bellos et al. [11]numerically considered a parabolic trough concentrator using different gas working fluids for high-temperature application. They optimized the mass flow rate for each working fluid. A PTC was considered using different na- nofluids in [12]. Hoseinzadeh et al.[13]optimized structural para- meters of a PTC using Monte Carlo method. Thermal performance of the solar system was increased by application of nanofluid. Simulation of a PTC using different nanofluids were studied in[14]. Thermal efficiency improved by the nanofluid application. Aroonrat et al. [15] in- vestigated the internal heat transfer in the grooved tubes based on some experimental tests. They used water as the working fluid. Variation of the tube pitch was considered on the internal heat transfer coefficient.

The thermal enhancement factor of the helical grooved tubes was higher than the straight grooved tube.

Organic Rankine Cycle (ORC) is an effective way for power gen- eration from thermal energy. Different sources can be used as the ORC heat sources such as solar collectors, geothermal energy, waste heat, etc. There are some researchers investigated solar ORC systems[16].

Delgado-Torres and García-Rodríguez[17]studied a solar ORC system.

They considered the effect of both different solar stationary collectors and different ORC working fluids. They determined the operational parameters for minimizing the collector aperture area. Jing et al.[18]

optimized a solar CPC system as a ORC heat source for producing power. They reported the characteristics of the optimized system.

Marion et al.[19]numerically and experimentally investigated an ORC system with a flat plate collector as a ORC heat source. The results reveal that the net mechanical power has a direct relationship with flow rate. Tchanche et al.[20]presented a study related to the organic fluid selection for the solar ORC systems. They concluded that R134a was the most favorable fluid for application in the small-scale solar ORC system.

Bellos and Tzivanidis [21] investigated an ORC system while solar energy and waste heat were used as the ORC heat source. Effect of different organic fluids were studied as the ORC working fluid.

Hydropower energy is a favorite kind of renewable energy resources which can be found throughout the world. Hydropower energies have been used widely as large-scale hydropower plants in large dams.

Although almost all of the large-scale hydropower opportunities have already been exhausted, there is a strong potential for small-scale hy- dropower (micro hydropower) resources to exploit. Some of these re- sources are small rivers, irrigation systems, drinking water networks, wastewater networks, cooling systems, etc. In the hydropower plants, the hydraulic power of water is converted to the mechanical power using a turbine for electricity generation. Recently, inverse use of the conventional Archimedes screw pump is considered as an accessible technology to be used as a turbine for electricity generation from flowing water, named Archimedes Screw Turbine (AST). Traditionally, the Archimedes screw was used to pump water from a lower level to a higher one or to convey water in a horizontal or inclined plane[22].

There are different types of the turbine for electricity generation including Kaplan, Pelton, etc. Comparing the relative costs of an AST and the more common Kaplan turbine for a small-scale hydropower site showed that for an energy output of about 15% more, the AST cost is about 10% less and its annual capital cost 22% cheaper[23]. Besides, the AST is an environmental and fish friendly structure which needs low civil works for installation in even existing structures[24]. Previous researches showed screw efficiency decreases when rotation speed in- creases at higher speed because the friction forces become unexpectedly large. Also, the smaller screw has greater efficiency losses than greater screw due to leakage losses[25].

Numerical researches on the real performance of ASTs are limited.

Rorres[26]derived relationships using analytical and numerical ana- lysis for the water levels, flow rates and flow leakages based on actual Archimedes screw geometry as a pump with modern computing tech- niques. Müller and Senior [27] presented a simple two-dimensional theory of the Archimedes screw. They developed a model based on the geometry parameters of the Archimedes screw. They assumed the hy- drostatic pressure creates torque and causes the screw rotation. Ques- tionnaire investigation on about 400 installed ASTs in Europe showed that outer diameter is equal to pitch and the inner diameter is half the outer diameter in most of the screws. Also, the mean and max electrical efficiencies of ASTs were calculated as 69% and 80%, respectively[28].

The effect of the upstream canal water level on the screw diameter was considerable, and for screw inclination angle of 34.8°, the AST electrical efficiency has reported 84%[29]which is high efficiency. C Zafirah and Nurul Suraya[30]investigated the helix turns and many flights to optimize the AST performance using CFD (Computational Fluid Dynamic) method. The results showed that the highest perfor- mance of 81% could be obtained for a screw with flights number of 3 and the helix turns of 3. Also, the screw with flights number of 2 has higher performance than flights number of 3 for any helix turns. Ster- giopoulou, Stergiopoulos and Kalkani[31]studied screw performance with horizontal, vertical, and inclined axes using CFD and explained the methodology, but they did not present any results about screw perfor- mance. Lashofer, Hawle and Pelikan[32]tested both screws with ro- tating trough meaning the trough is fixed to the flights and screw with the fixed trough. They found that the screw with fixed trough has higher efficiency than that of for rotating trough. They investigated screw efficiency for a wide range of geometry parameters and reported the efficiency up to 90%. Also, the Ritz-Atro company in Germany re- ported the screw efficiency up to 90% (www.ritz-atro.de). However, increasing the AST efficiency is being studied.

A complete performance model of ASTs was described in Lubitz, Lyons and Simmons[33]and Kozyn and Lubitz[34]. In the first work, the ideal model of an AST was numerically developed. Also, the screw performance was investigated experimentally. The developed numeric model was validated using experimental data. The validated model was used for screw efficiency prediction. The predicted mechanical power and efficiency showed good agreements with associated experimental results. Moreover, the maximum efficiency was approximately 80%.

Kozyn and Lubitz[34]developed a complete power losses model to real screw efficiency prediction. The complete model was implemented in MATLAB. In that research, the ideal power and efficiency were pre- dicted using Lubitz, Lyons and Simmons[33]ideal model, and then real mechanical power and efficiency experimentally estimated. All power Ref reflector

rad due to radiation s surface of the inner tube

T turbine

Th thermal

total total amb, air environment

Abbreviations

AST Archimedes Screw Turbine ORC Organic Rankine cycle PTC Parabolic Trough Concentrator

losses were calculated using ideal and real mechanical power and ef- ficiency difference. Finally, each power loss was determined using the developed power losses model. This model was validated using an in- stalled AST in Waterfored, Ontario, Canada.

Mehrpooya et al.[35]considered a hybrid solar driven power plant and energy storage system. They applied a PTC as the solar collector.

They estimated amount of total exergy destruction as 216.7 MW for the investigated system. Bahar[36]suggested a new solar hybrid gas tur- bine. Solar heat gained was used for preheating the compressed air.

Basir Khan et al.[37]investigated a new multiple optimal combinations of hybrid renewable energy systems based on combination of solar, wind, micro-hydro and diesel systems. They optimized system for a case study in a resort island in the South China Sea.

As seen from aforementioned literature review, there is not any reported paper related to a power generation system combining a solar ORC system and an AST system. In the current study, the performance of a hybrid power generation system including a solar ORC and AST systems was optimized as a novel research subject. A numerical method was developed for the solar ORC system modeling which was coupled with the AST system for power generation for the first one in the world.

A parabolic trough concentrator with a conventional receiver was nu- merically modeled as the heat source of the ORC system. Two different types of absorber using smooth and corrugated tube were considered.

Different ORC working fluids were investigated in the solar ORC system including R134a, R245ca, R245fa, R152a, R113, R11, and R114b. In the next stage, an optimum AST was numerically designed. Different structural parameters were considered including screw inclination angle, flights number and the screw length for this purpose.

2. Modeling and description

The current research was done in different steps. In the first step, a PTC was optically and thermally investigated. Then, the PTC was used as the heat source of an ORC system. The solar ORC system was ther- modynamically investigated using different Chlorofluorocarbon (CFCs) as the ORC working fluids. In the next step, an AST was designed and coupled with the solar ORC system. Finally, different structural para- meters of the AST were optimized. It should be mentioned that the power is generated using two different turbines: the ORC turbine is the first one, and the AST is the second one. The variation of turbine inlet

Fig. 1.A schematic of the investigated system including a combination of a solar ORC system and AST system.

Table 1

A summary of the investigated methodology in the current study.

temperature in the ORC cycle was investigated. The temperature of the solar working fluid at the inlet of the AST turbine was studied at a constant temperature.Fig. 1 displays a schematic of the investigated system including a combination of a solar ORC system and AST system for power generation. Also, a summary of the investigated methodology in the current study is given inTable 1.

It should be mentioned that the pressure difference before and after the AST is due to the solar PTC structure in the solar cycle. It means that the receiver must be located at a higher level than the pump which is H.

Therefore, the oil exiting from the heat exchanger has potential energy of H. The screw outlet is located on the ground. Therefore, the head difference between the inlet and outlet of the screw is equal to H which provides a potential energy for rotating the screw. The main advantage of the suggested hybrid system is additional power generation from the waste hydraulic power using the AST system. Another advantage of the combined system is ejection more heat from the solar working fluid by moving the solar working fluid in the AST system which causes higher solar performance. The high initial cost is a disadvantage of this hybrid system.

2.1. Screw power system 2.1.1. AST components

An AST exploits the kinetic and potential energies of a liquid in places with very low head or nearly zero head. The kinetic and the potential energies of a fluid are transformed into the mechanical work for rotating the screw and generating a torque. A coupled generator to the screw converts the mechanical energy into the electrical one. The potential sites for AST installing like rivers, irrigation systems such as canals and conduits, stormwater systems and water distribution sys- tems, drinking water networks, wastewater networks, cooling systems, and even a desalination plant, etc. with nearly zero to 6.5 m head and flow rate of less than 6.5 m³/s are the most common places.

An AST system consists of different parts including screw, trough, upstream canal and downstream canal. Water inflows from upstream canal to the screw inlet and causes the screw to rotate, and a torque is generated. As the water reaches to the screw end, it inters to the downstream canal witch has a constant water level.

In the AST system, water is supplied by an upper resource to the inlet of the inclined AST. Water moving down from upstream of the screw to the downstream is entrapped between two adjacent screw flights. Water level difference between the upstream and downstream elevation of either side of the flights creates pressure force acting on the

flights and producing a torque that causes mechanical rotation of the screw. Finally, flow is entered into the lower reservoir. The hydraulic and mechanical parameters can be used to compute the mechanical power and efficiency. A bucket is a volume of water trapped between two successive flights. There is a gap between the flights and the fixed trough, named Gap width (Gw), which allows the screw to rotate freely within the trough, and it causes a gap leakages to be occurred.

The geometrical parameters of an AST are shown inFig. 2. They are outer diameter (Do), inner diameter (Di), the pitch of the screw (S), total length (L), number of flights (N), and screw inclination angle ( ). These parameters should be optimized for any values of the net water head (H) and the total volume flow rate flowing through the screw (Q_t).

2.1.2. AST model developing

As shown inFig. 3, consider an AST with an inclination angle of β (related to the horizontal axis and in a cylindrical coordinate system) in whichwis aligned with screw centerline,ris the radial position of the considered element from the centerline andθis the angular position of the component from the centerline in the w axis. Steady-state flow

Fig. 2.Geometrical parameters of an AST.

Fig. 3.Coordinate system of a rotating screw.

condition (constant rotation speed ω, and volume flow rateQ_t) was assumed for hydraulic modeling. An individual bucket was considered to calculate its torque (Tb) and volume (Vb) and calculate them using numerical integration. All buckets were assumed to have the same be- havior; therefore, total torque and volume flow rate can be calculated based of the single bucket torque and volume.

According to the geometry of the screw, geometric parameters are defined as below[34]:

=

w r( ) r (1)

=

w w

( ) 2 S

(2)

=

z r S

cos( ) cos( )

2 sin( )

1 (3)

=

z r S S

cos( ) cos( ) N

2 sin( )

2 (4)

in whichz1andz2are the vertical positions of any point (r_{, ) on the} downstream and upstream surfaces of the flights, respectively. Also, the minimum (z_min) and maximum (zmax) value of the vertical point occur at the downstream and upstream surfaces of the flights, respectively (Fig. 4).

For a bucket, ranges between 0 and2 _{, and}rranges betweenD_i/2 and Do/2; therefore, by substituting = _, r=Do/2 in Eq. (3), and

=2 ,r=Di/2in Eq.(4),zminandzmax can be calculated using fol- lowing Equations:

=

z D S

2 cos( )

2sin( )

min o (5)

=

z D S

2 cos( )

2sin( )

max o (6)

Introducing fill factor f as relative depth in the screw section, the actual water level can be defined as following:

= +

zwl zmin f z(max zmin) (7)

If f=0thenz=zmin, and the bucket is empty. Whenf=1, the water level reaches the top point of the central shaft of the screw andz=z_max. The volume of water in a bucket (Vb) can be calculated by numerical integration of Eq.(8):

=

> >

>

< >

( )

dV

z z z z

rdrd z z z

rdrd z z z z

0 ,

, ,

wl wl

z z

z z S

N wl

S

N wl wl

2 1

2 1

2 1

wl 1

2 1

(8) Volume flow rate of a bucket (Qb) is defined asVbmultiplying in rotation speed as Eq.(9), and total flow passing through the screw (Q_s) is defined as Eq.(10):

= Q V

b 2b

(9)

=

Qs Q Nb. (10)

The gap leakage is not contributed to the screw torque generation.

Nagel (1968) suggested an empirical model as Eq.(11)to estimate gap leakage (Qgl) whenf=1. This model has been used widely in previous researches. Note thatf=1corresponds to the optimum point, and it is used for designing in this research; hence, Nagel model will be used.

=

Qgl 2.5G Dw o1.5 (11)

When fill factor becomes greater than 1, an overflow leakage (Q_o) will occur. According to Aigner (2008) assumption (reported in Nuernbergk and Rorres[25]), this leakage is similar to the V-notch overflow weir and can be calculated as following.

= +

Q 4µ g z z

15 2 1

tan( ) tan( ) ( )

o wl max 2.5

(12) in whichµis the flow coefficient and is equal to 0.537 according to Nuernbergk and Rorres [25]. Finally, the overall flow (Qt) passing through the system is calculated as following:

= + +

Qt Qs Qgl Qo (13)

The hydrostatic pressure (p) created at a pointzdue to the weight of water within the bucket and corresponding torque (Tb) are calculated using Eqs.(14) and (15), respectively. The total generated torque (T_{) is} given by Eq.(16):

= >

p z<z

g z z z z

0

( )

wl

wl wl (14)

= =

=

=

T = p p S

rdrd

( )

b 2

r Di r Do

/2 /2

0 2

1 2 (15)

= T T NL

b S (16)

in whichp₁andp₂are the pressure at downstream and upstream surfaces of the flights, respectively. Total output power (Pout) produced due to the flow passing through the system is calculated by Eq.(17):

=

P_out . . ( / )T Q Q_{s t} (17)

This Equation shows that only flow passing the screw (Q_s) con- tributes to mechanical power generation.

When water enters the AST, some power losses are occurred redu- cing generated mechanical power. These losses are bearing power loss, hydraulic friction power loss, outlet expansion power loss and outlet submersion power loss. The bearing friction power loss occurs due to the screw rotation. The higher rotation speed leads to higher bearing power loss. Typically, bearing power loss (Pl b,) is a function of rotation speed given by bearing manufacture. In this research, the screw mate- rial was considered as smooth steel with power loss equation as

= +

P_{l b,} 0.0003 0.0082.

When water flows between two different cross-section areas, a power loss occurs. Flowing water from AST trough with lower cross- section area to the receiving outlet canal with greater cross-section area faces cross-section expansion power loss. The overall outlet expansion power loss (Pl OE, ) can be calculated using Borda-Carnot relation defined as Eq.(18):

=

P gQ v

. g

l OE o2t

,

2

(18) in which ois the Borda-Carnot coefficient defined as following:

= A

1 A

o

Q o 2

(19)

Fig. 4.Position of the minimum (zmin) and maximum (zmax) value of vertical point.

whereA_ois the cross-sectional area of the downstream canal andA_Qis the average cross-sectional area within the AST calculated using Eq.

(20):

= A VN

Q bS (20)

in whichvtis the transport velocity of the buckets along the screw length defined as Eq.(21):

=

v S

t 2 (21)

Hydraulic friction power loss occurs due to the fluid motion and its viscosity within the screw and trough. In an AST system, a portion of the trough, central shaft and flights are directly in contact with the water passing through it. These contacts produce some frictions in two directions, including transport direction and rotational direction.

In the transport direction, the screw flight produces no torque. The trough and central shaft shear stresses ( ) due to the fluid viscosity can separately be calculated using Eq.(22):

= v 8

t2

(22) where is the Darcy-Weisbach friction factor for either the trough or central shaft. It can be estimated using Manning's friction factor coef- ficient (n). Note that the relationship between the two mentioned friction factor coefficients can be driven using Darcy-Weisbach and Manning equilibrium easily. The associated shear forces (F_{) on the} wetted area (Aw) can be calculated by Eq.(23):

=

F BA_w (23)

Note that the total shear force is the sum of the shear force on the trough and central shaft. Finally, overall head loss (hf ht, ) and power loss (Pf ht, ) due to the hydraulic friction in the transport direction are given by Eqs.(24) and (25), respectively:

=

h BV g

f ht FLb

, (24)

=

Pf ht, gQhf ht, (25)

Hydraulic friction power loss in the rotational direction has two components including friction between water and central shaft, and friction between water and flights. The relative shaft velocity (v_{r s,}), generated shear stress and power loss (Pr s,) can be calculated using Eqs.

(26)–(28), respectively:

=

v D

r s 2i

, (26)

= v

r s 8r s

, 2,

(27)

=

P v

8 BA

r s r s r s

s

, , 2,

(28) in which r s,is Darcy-Weisbach friction factor andAsis the shaft wetted area.

Determining shear stress between water and flights are somewhat complicated. Relative moving of water has two components; the radial component which is orthogonal to the shaft axis and the component parallel to the shaft which causes no friction loss. The relative velocity between water and flights, related shear stress and power loss depend on the radial position of the considered element; therefore, to calculate the power loss due to the flights friction (Pf f,), Eq.(29) must be in- tegrated from^D₂ⁱto^D₂^o, and radial position from 0 to2 .

= +

P B r dA B r dA

8 8

f f Di

f

f Di

f

f ,

2 0

2 1 3 3

1

2 0

2 2 3 3

2

Do Do

2 2

(29) in which subscriptions 1 and 2 are power losses due to the upstream

surface and downstream surface of the flights, respectively. The values of the wetted surfaces area of the flights (dAf1anddAf2) are calculated using Eqs.(30) and (31), respectively:

= >

dA + z z

rdrd z z

0 ,

f ,

wl

r S

r wl

1

1 4

2 1

2 2 2

(30)

= >

dA + z z

rdrd z z

0 ,

f ,

wl

r S

r wl

2

2 4

2 2

2 2 2

(31) To calculate submersion power loss (P_{l S,} ), Kozyn and Lubitz [34]

empirical equations was derived from experimental results and was used in this research for our allowed submersion ranges (Eq.(32)).

= +

Pl S, (0.01765Qnd 0.1397Qnd 0.1989).Pout (32) in whichQndis the non-dimensional flow calculated using Eq.(33)

=

Q S

Q D D

2 ( )

nd t o2 i2

(33) Subtracting the power losses from output power gives the me- chanical power defined by Eq.(34).

= + + + +

Pmech Pout (Pl b, Pf f, Pr s, Pl OE, Pf ht, Pl S,) (34) Note that generator power loss is not included in the above equation as well as in this research.

The hydraulic power (P_hyd) of fluid flows between two sections with difference head ofH, and discharge ofQtis calculated using Eq.(35):

=

Phyd gQ Ht (35)

Finally, the screw mechanical efficiency (mech) is calculated using Eq.(36):

=P

mech Pmech

hyd (36)

2.1.3. Calculation process

Based on the described Equations above, a mathematical model of AST was implemented in MATLAB environment to design appropriate AST for any condition. The hydraulic parameters like water depths and volume flow rate are calculated using ICSS (Irrigation Conveyance System Simulation) model. The AST mathematical model is started to run based on the inputs parameters as well as the ICSS output para- meters, and the following steps are done: 1. calculating geometric parameters using Eqs. (1)–(7); 2. calculating bucket volume, bucket flow, flow through the screw, gap leakage, overflow leakage, and total flow by Eqs.(8)–(13); 3. calculating pressure, torque and mechanical power afterward; 4. using Eqs.(18)–(33), all power losses are calcu- lated separately; 5. subtracting power losses from mechanical power, the mechanical power can be calculated and by dividing it into the hydraulic power, mechanical efficiency is calculated.

For this purpose, the bucket volume flow rate and torque were calculated for a single bucket for determining the optimum value of the radial element as well as the angular element. Assuming that all buckets are similar, total torque and total volume flow rate were calculated. To find the optimum values of the radial element (dr) and angular element (d ) for numerical integration, the angular element was first assumed to be ₃₆₀² and several radial elements were then investigated. The model convergence results showed that the volume and torque of a single bucket remain constant for dr 0.0075; therefore,dr=0.0075 was selected to the calculations. About tendr values greater than the op- timum value were investigated.

2.2. Solar system modeling 2.2.1. Optical modeling

A PTC solar reflector was optically modeled in this section. SolTrace as a practical software was used for optical modeling of the investigated solar system. The application of this software was recommended by some references for the optical analysis of the concentrator solar sys- tems[3,16,38]. The SolTrace software simulates based on the Monte Carlo ray tracing method. The SolTrace modeling assumptions were presented inTable 2. Dimensions of the steel mirror reflector are pre- sented inTable 3. The results of optical modeling were used for de- termination of the optimum position of the cavity receiver in the PTC collector based on the concentrator optical performance. The distribu- tion of the solar heat flux in the investigated cavity receiver was de- termined by SolTrace.

2.2.2. Thermal modeling

A PTC consists of a concentrator, a receiver tube, a glass cover, and a one-direction tracking system. The incoming solar radiation is con- centrated at the focal line of the PTC, where the receiver tube is located.

The concentrated solar heat flux is absorbed by the working fluid flowing in the receiver tube. A glass tube was used around the receiver tube for reducing convection heat losses. Different heat losses accrues in the PTC system are the natural and radiation heat losses in the annular region, conduction heat losses from the glass cover, and external con- vection and radiation heat losses. Thermal modeling using the energy balance equations was developed for the thermal investigation of the solar PTC system.

The energy balance equations of the PTC can be presented as fol- lowing:

=

Q_net Q Q_{loss total,} (37)

in Eq.(37),Qnetis defined as the net power absorbed by the solar system [39]:

=

Q optical refl solarQ (38)

In Eq.(38),Q (W) is defined as the received solar heat flux to the cavity receiver. In this equation, optical is calculated using Eq. (40).

Parameter of the reflis defined as the PTC reflectivity efficiency which was assumed equal to 0.75 in this analysis, based on the optical char- acteristic of the investigated PTC system[4].

=

Qsolar I Asun ap PTC, (39)

In Eq.(39),Q_solar(W) is defined as the total received solar heat flux by the PTC reflector. In Eq.(39),Isunis defined as the beam solar ra- diation which is equal to 810.56 (W/m²) in this modeling based on a real environmental condition (seeTable 4). Also, in Eq.(39),A_{ap PTC, is} defined as the aperture PTC dimensions which is equal to 1.4 m²in this modeling[39].

= Q

optical Q ab

PTCreceives (40)

In this equation, opticalis the optical efficiency defined, as the ab- sorbed heat flux (output of the SolTrace software) to the received solar radiation on the concentrator surface (output of the SolTrace software) [39].

The total heat losses of the solar PTC system were modeled using the thermal resistance approach as seen in Fig. 5. The total heat losses (Qloss total, ) of the solar PTC system can be calculated using the following equations[39]:

=

Q T T

loss total sR air

total

, (41)

The total thermal resistance of the PTC receiver can be calculated as following[39]:

= + +

Rtotal Rtotal,1 R3 Rtotal,2 (42)

A schematic of the thermal resistance of the solar receiver is de- picted inFig. 5. TheRtotal,1is defined for the thermal resistance of the PTC receiver between the absorber tube and the cover glass in an an- nual region as following[39]:

= ×

R R +R

R R

total,1 1 2

1 2 (43)

The thermal resistance from the PTC receiver to the environment can be defined as following[39]:

= ×

R R +R

R R

total,2 4 5

4 5 (44)

Amounts of different heat losses from the receiver were explained as following:

•

Natural Annular Convection

The heat transfer coefficient of the natural annular convection can be defined as following[40]:

=

+

(

₊

)

× ⁺ +

( ) ( ) ( )

h 1

ln 2.331 10 1

(45)

D d

D

T P

d D 1

2

9 5

2( 1) 20 237

a 23 2

•

Radiation in Annual Region

The heat transfer due to the radiation in the annual region between the receiver tube and the glass cover can be defined as following[41]:

= + ⁺ q D T( _D T_d)

D d Â

2

4 4

1 (1 )

d

D

D (46)

•

Conduction from Glass Cover

The conduction heat transfer from the glass cover can be defined as following[41]:

=

q k T

2 ln_D

D Â

3 45 45

5

4 (47)

•

Natural External Convection

The Nusselt number of the natural external convection of the PTC receiver can be calculated as bellow[42]:

= +

(

+

^{( )} )

Nu Ra

0.6 0.378

1

natural

Pr 4,

1/6 0.599 9/16 8/27

2

(48)

•

Cross-flow External Forced Convection

The Nusselt number of the cross-flow external forced convection of Table 2

SolTrace modeling assumed constants.

The parabolic dish rim angle 90°

The optical error¹ 0–35 mrad

The tracking error² 1°

The sun-shape pillbox

The half-angle width 4.65 mrad

Number of ray intersections 10,000

The reflectance of the cavity walls (black cobalt coating) 15%

1 Optical error = (4(slope error²) + (specularity error²))^1/2.

2 The error between a movement of mirror surface and receiver.

the PTC receiver can be defined as following[43]:

=

Nu cRe Pr Pr

forced m n Pr

4, w

1/4

(49) Consequently, the total Nusselt number of the external heat losses form the PTC receiver due to the natural and forced convection can be calculated as following[39]:

= +

Nu4,total (Nunatural3.5 Nuforced3.5 1/3.5) (50)

•

External Radiation

The external radiation heat losses from the PTC receiver can be calculated as bellow[44]:

=

q^Â₅ D T( _D⁴ T_ci⁴) (51)

where

=

Tci T ⁴ ci (52)

=0.711+0.56T + T T = °

100 0.73

100 ; [ C]

ci dew dew

dew 2

(53)

2.2.3. Calculation method

In the advanced thermal modeling, the surface temperature (Ts n, ) and the net heat transfer rate (Qnet n, ) at different tube positions are determined by solving Eqs. (55) and (54) simultaneously using the Newton–Raphson Method[39]. It should be mentioned that the PTC receiver was divided to smaller elements along the PTC receiver tube.

The net heat gained from the PTC system at each element of the re- ceiver tube can be defined as bellow[39]:

=

Q Q A

R (T T )

net n n n

total s n amb

, ,

(54) On the other hand, the internal convection heat transfer from the solar working fluid at each element of the receiver tube can be defined as following[39]:

=

+

=

( )

( )

Q

T T

net n

s n i

n Q

m c inlet

kA m c

,

, 1

1 ,0

1 1

2 net i

p

n p

, 0

0 (55)

In Eq.(55), the heat transfer coefficient for the examined case is calculated according to Eq.(21):

= k Nu K

d

inner fluid

tube (56)

where, Nusselt number of the inner convection heat transfer can be calculated as following:

= +

Nu

( )

Re Pr

Pr

. .

1 12.8. . ( 1)

inner

f f 8

8 0.68 r

r (57)

In this equation the friction factor (f_r) can be separately calculated for the corrugated and smooth tube based on Eqs.(62) and (63), re- spectively.

= +

f Re D

0.316. 0.41. D

r ri min

ri

0.25 , 0.9

(58)

=

f_r (0.79lnRe 1.64) ²

It should be mentioned that all of the numerical thermal modeling was written in Maple software. Finally, the thermal efficiency of the PTC system can be calculated as following:

=Q /( Q )

th net refl sun (60)

The thermal Behran oil was taken as the solar working fluid. The thermal conductivity of the thermal Behran oil were obtained with the following correlations[45]:

= ×

k T W

0.1882 8.304 10 ( ) mK

f 5 f

(61) The heat capacity of the thermal oil as the solar working fluid can be calculated as bellow[45]:

= + ×

c T kJ

0.8132 3.706 10 ( ) kgK

p f, 3 f

(62) Thermal oil density as the solar working fluid can be calculate as a function of the oil temperature as following[45]:

= T kg

1071.76 0.72( ) m

f f 3 (63)

Finally, the Prandtl number of the thermal oil as the solar working fluid is calculated as bellow[45]:

= ×

Pr 6.73899 10 ( )21Tf 7.7127 (64)

Table 3

Dimensions of steel mirror reflector.

Description Dimension

Parabola length (Lc) 2 m

Parabola aperture (w) 70 cm

Focal distance (f) 17.5 cm

Aperture area (Aap) 1.4 m²

Rim angle ( ) 90°

Thickness (mean value) 0.8 mm

Table 4

Environmental condition for 28 September 2016, Tehran, Iran.

Time Ibeam(W/m²) Tamb(C°) Vwind(m/s)

13:45 810.56 31.00 2.10

Fig. 5.A schematic of the investigated thermal resistance approach for thermal heat losses modeling.

2.3. ORC modeling

2.3.1. Thermodynamic analysis

Fig. 5displays the entropy-temperature diagram of the ORC system for R113[46]. In the ORC system, four steps are necessary for produ- cing power. In the first step, 1–2 onFig. 5, the ORC working fluid is pressurized in the pump under isentropic condition. Then, the ORC working fluid absorbed heat for converting to the saturated or super- heated fluid under constant pressure in the evaporator (see 2–3 on Fig. 6). In the next step, 3–4 onFig. 6, the saturated or superheated fluid generates power in the turbine at the isentropic condition. Finally, the exiting fluid from the turbine is cooled in the condenser under constant pressure (see 3–4 onFig. 6). In the current research, the ORC system was thermodynamically analyzed at constant evaporator pres- sure of 3 MPa and the condenser temperature of 311 K.

REFPROP.8 software was used for calculation of the thermodynamic properties of the ORC working fluids [46]. For simplicity, some as- sumptions were accounted as following:

•

The internal irreversibility are neglected;

•

The pressure drops in the heat exchangers and the pipelines are ignored;

•

The heat losses from the pipes are neglected;

•

And, the ORC system was investigated in a steady-state condition.

The thermodynamic performance of each part of the ORC system can be calculated as below. In this analysis, it was assumed that all of the absorbed heat by the cavity receiver would be transferred to the ORC working fluid in the evaporator. Consequently, the mass flow rate of the ORC working fluid can be estimated using Eq.(65) [47]:

=

m Q

h h

( )

ORC evp

3 2 (65)

In whichQ_evp(W) is equal to the cavity heat gain,h₂ (kJ/kg) is the working fluid enthalpy at the inlet of the evaporator, andh_{2(kJ/kg) is} the working fluid enthalpy at the outlet of the evaporator.

The generated power in the turbine can be estimated using the following equation[47]:

=

WT mORC(h3 h4) (66)

In whichh₃ (kJ/kg) is the working fluid enthalpy at the inlet of the turbine, andh₄(kJ/kg) is the working fluid enthalpy at the outlet of the turbine.

Also, the ejected heat in the condenser can be evaluated using Eq.

(67) [47]:

=

Qc mORC(h4 h1) (67)

In whichh and h_{4 1} (kJ/kg) are the working fluid enthalpy at the inlet and the outlet of the condenser, respectively.

Finally, the consumed power in the pump is calculated as following [47]:

=

WP mORC(h2 h1) (68)

In whichh and h_{1 2} (kJ/kg) are the working fluid enthalpy at the inlet and the outlet of the pump, respectively. The net power of the ORC system is calculated as:

= =

W_net W_T W_P m_ORC[(h₃ h₄) (h₂ h₁)] (69) The ORC efficiency can be defined as bellow:

=W /Q

ORC net evp (70)

On the other side, overall solar ORC efficiency can be evaluated as following:

=W / (I .A )

overall net beam ap dish, (71)

Finally, second thermodynamic law efficiency is calculated as fol- lowing:

= T

/ 1 T

II overall L

H (72)

2.3.2. ORC working fluid

The selection of the appropriate working fluid in an ORC system is very critical for generating the highest power. In the current research, seven types of refrigeration working fluid were selected as the ORC working fluid. The thermodynamic properties of the working fluids were investigated using REFPROP software. The thermo-physical properties of the considered working fluids are presented inTable 5.

2.4. Validation

To validate the developed Archimedes screw model, Lubitz et al.

[33] experimental data were used. The screw specification used in Lubitz et al.[33]model is given inTable 6. The results of the Lubitz et al. [33]experimental model and the developed model in this re- search are illustrated inFig. 7. As shown, the model results have good agreement with the experimental data, and could accurately predict the screw power specifically around optimum point, i.e., for rotation speeds of 7–14 rad/s.

Fig. 6.The entropy-temperature diagram of the ORC system for R113.

3. Result and discussion 3.1. Solar ORC performance 3.1.1. Different ORC working fluids

In this section, the effect of different ORC working fluids including R134a, R245ca, R245fa, R152a, R113, R11 and R114b were considered in the solar ORC system.Fig. 8displays the variation of ORC mass flow rate under variation of the turbine inlet temperature (TIT) for the corrugated tube as the receiver. As seen inFig. 8, the ORC mass flow rate of the different working fluids decrease by increasing turbine inlet temperature. Also, it can be concluded from Fig. 8, R134a has the highest mass flow rate and R152 shows the lowest mass flow rate among all investigated working fluids under the same condition of the solar PTC system as the heat source.

Variation of generated turbine power under variation of the turbine inlet temperature (TIT) for different working fluids are shown inFig. 9.

The corrugated tube was used as the PTC receiver and different ORC working fluids including R134a, R245ca, R245fa, R152a, R113, R11, and R114b were evaluated in the solar ORC system. It can be seen in Fig. 9, the generated turbine power for all of the working fluid de- creases by increasing turbine inlet temperature. As seen inFig. 9, R113 have the highest generated power compared to other investigated working fluids. Also, there is a peak point of the turbine inlet tem- perature for R134 and R152a as the working fluid. This is due to the change phase of the working fluid in the condenser. The maximum power generated was calculated for working fluid at a saturated con- dition temperature in the turbine.

Also,Fig. 10depicts the variation of ORC net power under change of the turbine inlet temperature (TIT) for different working fluids. It can be concluded that the net power has a similar trend compared to the Table 5

Thermo-physical properties of the considered working fluids.

Working fluid Molecular mass (kg/kmol) Tbp(K) Tcr(C) Pcr(MPa)

R134a 102.03 −26.1 101 4.059

R245ca 134.050 25.15 174.42 3.9250

R245fa 134.045 15.14 154.01 3.651

R152a 66.05 −24.0 113.3 4.520

R113 187.38 47.6 214.1 3.439

R11 137.37 296.86 471.11 4.408

R141b 116.95 32.0 204.2 4.249

Table 6

Lubitz et al. (2014) experimental screw specification used for validation.

Parameter Variable Unit Value

Outer diameter Do cm 14.6

Inner diameter Di cm 8.03

Screw length L cm 0.584

Pitch S cm 0.146

Flights Number N – 3

Rotation speed rad/s 10

Volume flow rate Q l/s 1.13

head H cm 25

Inclination angle ° 24.9

Gap width G_w cm 0.0762

Fig. 7.Model validation using Lubitz et al. (2014) experimental data.

Fig. 8.Variation of ORC mass flow rate under variation of the turbine inlet temperature (TIT) for different working fluids.

Fig. 9.Variation of turbine generated power under variation of the turbine inlet temperature (TIT) for different working fluids.

Fig. 10.Variation of ORC net power under variation of the turbine inlet tem- perature (TIT) for different working fluids.

power generated in the turbine (Fig. 9). Also, R113 have the highest net power generated among all investigated working fluids.

Figs. 11 and 12depict the variation of ORC efficiency and total efficiency under change of the turbine inlet temperature (TIT) for dif- ferent working fluids. Effect of different working fluid including R134a, R245ca, R245fa, R152a, R113, R11, and R114b were considered on the ORC performance. As seen, the ORC efficiency and total efficiency of R113 show the highest value of efficiency compared to other working fluids. Also, it could be concluded that the trend of efficiency data is similar to the net power generation and turbine power generation.

Based onFigs. 11 and 12, R113 at the saturated temperature inlet of the turbine could be recommended as the efficiently ORC working fluid for the investigated solar ORC system.

3.1.2. Comparison of smooth and corrugated tubes

In this section, the effect of two shapes of receiver tubes including smooth and corrugated tube were considered as the heat source of the solar ORC system.Fig. 13displays the variation of ORC mass flow rate under variation of the turbine inlet temperature (TIT) for smooth and corrugated receiver tube. The R113 was the most efficiently ORC working fluid based on the previous section used in this part analysis.

As seen inFig. 13, the ORC mass flow rate of the solar ORC system had higher amount for the corrugated tube compared to the smooth tube.

This issue was due to the higher receiver heat gain using corrugated tube compared to the smooth tube.

Fig. 14depicts the variation of the ORC net power under change of the turbine inlet temperature (TIT) for smooth and corrugated receiver tubes. As seen inFig. 14, the net power of the solar ORC system shows the higher amount for the corrugated tube compared to the smooth one.

A variation of total efficiency under variation of the turbine inlet

temperature (TIT) for smooth and corrugated receiver tubes are pre- sented inFig. 15. The corrugated tube shows the higher total efficiency of the solar ORC system compared to the smooth tube. Also, it could be seen that the efficiency data had a similar trend compared to the ORC net power (Fig. 14). Consequently, the corrugated tube could be re- commended as an efficiency receiver tube for solar ORC system.

3.2. Screw power generation 3.2.1. Screw length optimization

In this section, the AST performance under variation of different structural parameters including the screw length, flights number, and inclination angle was considered and optimized. Fig. 16 shows the screw efficiency variation under the screw length and inclination angle variations with flight number of 1. As shown, with an increase of the inclination angle, the screw efficiency increases for all lengths until it reaches the peak point and then it decreases quickly. Since volume flow rate is constant, the screw rotation speed must rise with the increase of inclination angle, and consequently, mechanical power increases as well as efficiency. After peak point, both hydrostatic pressure and generated torque decrease and friction power losses increase which cause efficiency decreases quickly.

In case of peak point on the curves, peak point for screw length of 1.5 m is 58.24%. As the screw length increases, bucket numbers and consequently torque, mechanical power and efficiency all increase as well as friction power losses. In screw length of 1.5 m, the produced mechanical power is highest for the inclination angle of 20°. With the growth of the inclination angle and corresponding rotation speed, the friction power losses are increasing quickly and dominating in the system; therefore, the efficiency is decreasing suddenly.

In case of peak point on the curves, the peak point for screw length of 1 m is 50.45%. As the screw length increases, bucket numbers and consequently torque, mechanical power and efficiency all increase as well as friction power losses. In screw length of 1.5 m, the produced mechanical power is highest, and friction power losses are not yet dominant in the system. Increasing the screw length to 2 m and greater than 2 m, mechanical power is still constant, but the values of the friction power losses are very high (friction power loss in the rotational direction is a function of rotation speed with the order of 3), and therefore peak point falls down. As seen inFig. 16, the highest effi- ciency was obtained 58.24% for the screw length of 1.5 m, inclination angle of 20° and flight number of 1.

3.2.2. Screw flights number optimization

For the optimum screw length, efficiency variation under the screw inclination angle and flights number variations are shown inFig. 17.

Inclination angle ranges between 1° and 45°, and flight numbers change Fig. 11.Variation of ORC efficiency under variation of the turbine inlet tem-

perature (TIT) for different working fluids.

Fig. 12.Variation of total efficiency under variation of the turbine inlet tem- perature (TIT) for different working fluids.

Fig. 13.Variation of ORC mass flow rate under variation of the turbine inlet temperature (TIT) for smooth and corrugated receiver tube.