THERMODYNAMIC OPTIMISATION AND EXPERIMENTAL COLLECTOR OF A DISH- - - PowerPoint PPT Presentation

1

THERMODYNAMIC OPTIMISATION AND EXPERIMENTAL COLLECTOR OF A DISH- MOUNTED SMALL-SCALE SOLAR THERMAL BRAYTON CYCLE

Department of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa February, 2015

WG LE ROUX

Study-leaders:

• Prof. T. Bello-Ochende
• Prof. J.P. Meyer

Submitted in partial fulfilment of the requirements for the degree PhD (Mechanical Engineering)

2

Presentation Outline

• 1. Introduction
• 2. Background
• 3. Literature Study
• 4. Modelling and Optimisation
• 5. Analytical Results
• 6. Experimental Study
• 7. Conclusion
• 8. Recommendations

3

• 1. Introduction

Long-term average of direct normal solar irradiance

• n a world map showing the potential of solar power generation in

southern Africa (GeoModel Solar, 2014) Parabolic dish concentrator for a Stirling engine

(Image extracted from Pitz-Paal, 2007)

A typical micro-turbine (the GT1241) as available from Honeywell, Garrett proposed for the small-scale solar thermal Brayton cycle

(Image extracted from Garrett, 2014)

4

• 1. Introduction

Problem

• Solar-to-electricity technologies are required which are
• more competitive
• more efficient
• cost-effective

Purpose of the study

Small-scale dish-mounted open solar thermal Brayton cycle

• ptimise solar receiver and recuperator - method of total entropy generation minimisation
• test optimised receiver

Objectives

• Second law of thermodynamics
• Entropy generation minimisation
• Ray-tracing software
• Geometry optimisation
• Experimental receiver test

Scope of Research – Thermodynamic Optimisation

• Open and direct solar thermal Brayton cycle
• Second Law of Thermodynamics
• Entropy Generation Minimisation
• Maximise net power output
• Optimise geometry of recuperator and receiver
• Heat Transfer & Fluid Flow Irreversibilities
• Experimental setup
• 2. Background

Solar resource – South Africa Why Solar?

Solar resource - World

• According to DLR

Solar resource – South Africa Why Solar?

The Department of Minerals and Energy places South Africa’s annual direct normal irradiation (DNI) between 2 500kWh/m2 and 2 900 kWh/m2 with an average of almost 300 days of sunshine per year.

200 400 600 800 1000 1200 1400 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Irradiance (W/m^2)

Time (h)

Irradiance of beam Mean irradiance of global radiation, tracked Mean irradiance of global radiation horizontal

Solar resource – South Africa, Pretoria Meteonorm

CSP - Concentrating methods

Dish Trough Tower

12

Background Brayton cycle

• mobility, cost benefits
• micro-turbines
• hybrid system
• storage systems
• water heating
• efficient and highly competitive.

Maximum net power output

• combined effort of
• heat transfer,
• fluid mechanics and
• thermodynamics

Compressor Recuperator Load Air in 1 Air out 3 6 4 7 8 9 10

c t net

W W W      Receiver 11 5 * Q  2 Turbine

Small-scale solar power

• Photovoltaic cells
• Solar water heaters
• CSP (Concentrated solar power)

– Trough

• Rankine Cycle

– Dish-mounted

• Stirling Engine
• Brayton cycle

Solar tracking - Elevation

• SunEarthtools

Solar tracking - Azimuth

• 150
• 100
• 50

50 100 150 6 7 8 9 10 11 12 13 14 15 16 17 18 Azimuth angle Time (h) Morning measurements Noon measurements Afternoon measurements SunEarthTools

Measured angle of tracking system versus real azimuth angle

• f the sun

Mousazadeh et al. (2004), Poulek and Libra (2000)

Two-axis solar tracking required for dish

Solar tracking Active Passive Micro- processor and electro-

• ptical

sensor based Auxiliary bifacial solar cell based Date and time based or a combination

• f sensor and

date/time based Fluid Bi- metallic strips

16

• 3. Literature Study

Compressor Recuperator Load Air in 1 Air out 3 6 4 7 8 9 10

c t net

W W W      Receiver 11 5

* Q  2 Turbine

The open and direct solar thermal Brayton cycle

17

• 3. Literature Study

Test set-up of a solar thermal Brayton cycle

(Image extracted from Heller et al., 2006)

Small-scale open and direct solar thermal Brayton cycle with recuperator

• Advantages

– High recommendation – Air as working fluid – Hot air exhaust

• Water heating
• Space heating
• Absorpsion refrigeration

– Recuperator

• high efficiency and
• low compressor pressure ratios
• Disadvantages

– recuperator and receiver pressure losses – turbo-machine efficiencies – recuperator effectiveness – Heat losses

irreversibilities

Compressor Recuperator Load Air in 1 Air out 3 6 4 7 8 9 10

c t net

W W W     

Receiver 11 5 * Q  2 Turbine

Solar thermal Brayton - Recuperator

Solar thermal Brayton - Recuperator

Image extracted from: Stine, B.S., Harrigan, R.W., 1985, Solar energy fundamentals and design. New York: John Wiley & Sons, Inc.

21

• 3. Literature Study

Receiver type Reference number or model Tout (K) Tin (K) P (kPa) (kg/s) Working fluid ΔP (Pa) Pressurised volumetric PLVCR-5 (Ávila-Marín, 2011) 71% 1 323

• 420
• Air
• PLVCR-500

(Ávila-Marín, 2011) 57% 1 233 300 415

• Air
• DIAPR

(Karni et al., 1997), (Ávila-Marín, 2011) 79% 1 477 308 1 800 0.0222 Air 25 000 REFOS (Buck et al. 2002), (Ávila-Marín, 2011) 67% 1 073

• 1 500
• Air

1 800 Dickey, 2011 88% 871 542 273 0.409 Air 2 900

rec



m 

Efficiencies of different solar receivers – Pressurised volumetric

22

• 3. Literature Study

Efficiencies of different solar receivers - Tubular

Receiver type Reference number or model Tout (K) Tin (K) P (kPa) (kg/s) Working fluid ΔP (Pa) Tubular Cameron et al., 1972 51%* 1 089 865 370 0.73 He-Xe 7 000 Kribus et al., 1999

• 1 023

300 1 600 - 1 900 0.01 Air 40 000 Heller et al., 2006

• 823

573 650

• Air

10 000 Neber and Lee, 2012 82% 1 500**

• 760

0.0093 Air 40 Amsbeck et al., 2010 43% 1 076 876 384 0.526 Air 7 330 Amsbeck et al., 2010 39.7% 1 055 871 375 0.516 Air 7 400 Solugas (Quero et al., 2013)

• 873

598 850 5.6 Air *calculated by author **proposed rec



m 

23

• 3. Literature Study

Particle receiver

(Image extracted from Miller and Koenigsdorff, 1991)

Open volumetric receiver – HiTRec

(Image extracted from Ávila-Marín, 2011)

24

• 3. Literature Study

Closed volumetric receiver, REFOS

(Image extracted from Buck et al., 2002)

Longitudinal tubular receiver

(Image extracted from Amsbeck et al., 2008)

25

• 3. Literature Study

Coiled tubular receiver

(Image extracted from Kribus et al., 1999)

Ceramic counterflow plate-type recuperator

(Image extracted from Pietsch and Brandes, 1989)

26

• 3. Literature Study

2 4 6 8 10 12 1.4 1.6 1.8 2 2.2 2.4 (kW)

Q1 Q2 Q3 Q4 Q5 Q6 Q7 T1 T2 T3 T4

Q1 = 6.8 kW, T1 = 1 308 K, Q2 = 8.3 kW, T2 = 1 179 K, Q3 = 9.7 kW, T3 = 1 054 K, Q4 = 11.2 kW, T4 = 904 K Q5 = 12.7 kW, Q6 = 14.1 kW, Q7 = 15.9 kW

Performance map (in different weather conditions)

• small-scale open solar thermal

Brayton cycle

• fixed optimised geometries

27

• 4. Modelling and Optimisation

c t net

W W W     

* Q 



j j loss

Q

,

 m  m  Control volume for the open solar thermal Brayton cycle

28

• 4. Modelling and Optimisation

Example of an analysis done for the solar dish and receiver

Solar receiver - SolTrace

29

• 4. Modelling and Optimisation

Rectangular open-cavity solar receiver Heat loss from the

• pen-cavity receiver

Solar receiver

30

• 4. Modelling

Solar receiver air heating

• Rectangular open cavity tubular receiver
• Stainless steel
• Pressure drop (Colebrook equation)

Variables

• Tube diameter,
• Inlet temperature,
• Mass flow rate

31

• 4. Modelling

Solar receiver – conduction heat loss [1]

Assumptions:

• Wind speed: 2.5 m/s
• T0 = 300 K
• P0 = 86.6 kPa
• 100 mm insulation thickness
• Conductivity of 0.061 W/mK at

550 °C average temperature [2]

• Elevation angle of 45 °

   

 

n ins ins n

• ut

n s cond n s n n cond loss

A k t A h T T R T T A Q / / 1

, , , ,

    

 



77 . 1 ) / / 1 (  

ins ins

• ut

k t h

[1] Le Roux, W.G., Bello-Ochende, T. and Meyer, J.P., 2014, The efficiency of an open cavity solar receiver for a small-scale solar thermal Brayton cycle, Energy Conversion and Management 2014;84:457–70. [2] Harris, J.A., Lenz, T.G., 1983, Thermal performance of solar concentrator/cavity receiver systems, Solar Energy 34 (2), pp. 135-142.

32

• 4. Modelling

Solar receiver – radiation heat loss

 

4 4 , , , 

  T T A Q

n s ap rad n loss

 

 



 

 

N j j s j n s n j n n n

T T F A Q

1 4 , 4 ,

    

33

• 4. Modelling

Solar receiver – convection heat loss [2]

[1] Le Roux, W.G., Bello-Ochende, T. and Meyer, J.P., 2014, The efficiency of an open cavity solar receiver for a small-scale solar thermal Brayton cycle, Energy Conversion and Management 2014;84:457–70. [2] Harris, J.A., Lenz, T.G., 1983, Thermal performance of solar concentrator/cavity receiver systems, Solar Energy 34 (2), pp. 135-142.

 



  T T A wh Q

n s n inner n conv loss , , ,



 

4 / 1 2 . 3 2

Pr ) (cos 52 . 2

L inner cav

Gr a h Nu    

For aopt = 0.25 m [1]: hinner = 2.75 W/m2K w = 2

Koenig and Marvin heat loss model [2]

34

• 4. Modelling and Optimisation

Recuperator geometry Recuperator design in SolidWorks

35

• 4. Modelling

Recuperator

Lreg a b t H

• Counterflow plate-type recuperator
• Pressure drop : Colebrook equation
• Fully developed laminar flow
• t = 1 mm
• Geometry variables: a, b, L, n

36

• 4. Modelling

Recuperator

Efficiency modelling: Updated version of the ε-NTU – method [3]

• Includes heat loss to the environment
• Since recuperator operates at high temperature

 

            

 

1 , 1 1 , 1

1 1 h X h h X h

Cr Cr Cr                  

 

1 , 1 1 , 1

h X h h X c

Cr Cr Cr   



 

              

 h E h E c h h X

Cr e Cr e Cr B 1 1 1  

   

1 1

1

      

  h X h c h X

Cr NTU  

   

1 1             

h h h h c h

Cr Cr Cr NTU B  

 

1  

h h Cr

NTU E

[3] Nellis, G.F. and Pfotenhauer, J.M., 2005, Effectiveness-NTU relationship for a counterflow heat exchanger subjected to an external heat transfer, Journal of Heat Transfer 127, pp. 1071 – 1073. c p c h p h h

c m c m Cr

, ,

  

h p h h

c m UA NTU

,

   

in c in h h loss h

T T UA Q

, , ,

   

 

in c in h c loss c

T T UA Q

, , ,

   

37

• 4. Modelling

Micro-turbine

Standard off-the-shelf micro-turbines from Honeywell

• Geometry not optimised
• Compressor map
• Isentropic efficiency
• Corrected mass flow rate
• Pressure ratio
• Rotational speed

38

• 4. Modelling

Micro-turbine

Standard off-the-shelf micro- turbine from Honeywell

• Parameter: turbine
• perating point
• Turbine map
• Corrected mass flow

rate

• Pressure ratio
• Maximum efficiency
• Efficiency as function of

pressure ratio found using blade speed ratio (BSR)

2 / 1 1

1 2 2 60 2                    

 k k t in t

r h D N BSR                  

2 max ,

6 . 6 . 1 BSR

t t

 

39

• 4. Modelling

Receiver heat flux

• Receiver heat flux determined with SolTrace
• Solar tracking error of 1°
• Optical error of 10 mrad
• Dish reflectivity of 85%
• Direct normal irradiance of 1 000 W/m2

40

• 4. Modelling

Net absorbed heat rate

Determined for each tube section

                           



  , 1 1 , , ,

2 1 1

p n in n i p i net n s n net

c m hA T c m Q T Q    

   

           

            

                      

 

T T R A c T m A T F A c T m F A c T m A Q Q R T T A T T A h T T F A T T F A Q Q Q Q Q Q Q

n s cond n n s n n n n N j j s j j n n n s n n n solar n net cond n s n n s n n j n s n n n N j j s j n s n j n n n solar n net n cond loss n conv loss n rad loss n solar n net , 2 , 2 4 1 1 , 1 1 , 1 , , , , 4 4 , 1 4 , 4 , , , , , , , , , , ,

/                       

• Equations are solved

simultaneously with Gaussian elimination

• Radiation heat loss term

is linearised

41

• 4. Modelling

Net absorbed heat rate

Determined for each tube section

• Equations are solved

simultaneously with Gaussian elimination

• Radiation heat loss term

is linearised

200 400 600 800 1000 1200 1400 5 10 15 20 25 Tube position - bottom to top

42

• 4. Modelling

Net power output

 

                    

   11 1 11 1 int ,

ln * * 1 T T c T m T T c m Q T T S T W

p p gen net

        

 

   

 

   

 

       

 

   

 

   

 

89 8 9 8 9 8 7 8 7 67 6 7 6 7 5 6 5 6 45 4 5 4 5 / 3 9 4 10 3 9 4 10 23 2 3 2 3 2 1 2 1 int ,

/ ln / ln / / ln / ln / ln / ln / / ln / ln * * / ln / ln / / ln / ln / ln / / ln / ln

Duct p l turbine p Duct p l receiver p loss Duct p l r recuperato l c R p Duct p l compressor p gen

P P R m T T c m T Q P P R m T T c m P P R m T T c m T Q P P R m T T c m T Q T Q P P R m T T c m T Q T Q P P P P T T T T c m P P R m T T c m T Q P P R m T T c m S

p

                                                                             

      

  519

/ 460 7 . 14 /

7 7

   T P m m

tCF t

 

• Steady-state

temperatures and pressures found with iteration, written in terms of isentropic efficiencies, recuperator efficiency, geometry variables Objective function:

43

• 4. Modelling

Net power output

Assumptions:

• Connecting tubes
• Insulation
• 0.18 W/mK conductivity
• 10 mm thick
• T8 = T9, T2 = T3
• P8 = P9, P2 = P3
• V1 = V11
• Z1 = Z11
• Pressure drop – Colebrook equation (rough stainless steel friction factor)
• T1 = 300 K
• P1 = P10 = P11 = 86 kPa
• Steady-state temperatures and pressures found with iteration, using

isentropic efficiencies, recuperator efficiency

Compressor Recuperator Load Air in 1 Air out 3 6 4 7 8 9 10

c t net

W W W      Receiver 11 5 * Q  2 Turbine

44

• 4. Modelling

Net power output

MATLAB: For 3 different receiver tube diameters For 5 different micro-turbines For the different operating points of the turbine For 625 different recuperator geometries Find temperatures and pressures in the cycle with iteration Determine net power output

Compressor Recuperator Load Air in 1 Air out 3 6 4 7 8 9 10

c t net

W W W      Receiver 11 5 * Q  2 Turbine

Optimisation: Run through all different combinations of receiver diameters, recuperator geometries, micro- turbines and micro-turbine

• perating points

45

• 4. Modelling

Constraints

• Maximum receiver surface temperature
• 1200 K
• Recuperator total plate mass
• 300 kg
• 400 kg
• 500 kg

46

• 4. Modelling - Flownex

Flownex modelling of the small-scale solar thermal Brayton cycle.

47

• 5. Analytical Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.01 0.02 0.03 0.04 0.05 0.06 Optical error = 5 mrad Optical error = 20 mrad Optical error = 35 mrad Optical error = 50 mrad

Optical efficiency of a solar dish and receiver with a tracking error of 1°

• SolTrace

A’ =Area ratio (Aaperture/Aconcentrator)

48

• 5. Analytical Results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.002 0.004 0.006 0.008 0.01 Optical error = 5 mrad Optical error = 10 mrad Optical error = 15 mrad Optical error = 20 mrad Optical error = 35 mrad

Overall receiver efficiency for a solar tracking error of 1° with receiver surface emissivity of 0.7

• Heat loss

A’ =Area ratio (Aaperture/Aconcentrator)

49

• 5. Analytical Results

10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Heat flux (kW/m^2) Position - bottom to top Top Side1 Opposite Side1 Side2 Opposite Side 2

Heat flux rate at different positions on the different receiver inner walls for a tracking error of 1°

• SolTrace

50

• 5. Analytical Results

200 400 600 800 1000 1200 1400 5 10 15 20 25 Tube position - bottom to top

Temperatures and net heat transfer rates for a 0.0833 m receiver tube diameter with a tracking error of 1° and optical error of 10 mrad.

51

• 5. Analytical Results

0.5 1 1.5 2 2.5 1.2 1.4 1.6 1.8 2 2.2 Wnet (kW) rt D = 0.0833 D = 0.0625 D = 0.05

Maximum net power output of the solar thermal Brayton cycle with a micro-turbine selected from Garrett

rt = Turbine pressure ratio D = Receiver tube diameter (m)

52

• 5. Analytical Results

200 400 600 800 1000 1200 1 2 3 4 5 6 7 8 9 10 T (K) Position in the cycle Flownex Matlab

Predicted temperatures at different positions in the solar thermal Brayton cycle

• Matlab model
• Flownex model

Compressor Recuperator Load Air in 1 Air out 3 6 4 7 8 9 10

c t net

W W W      Receiver 11 5 * Q  2 Turbine

Micro-turbine GT2560R at 87 000 rpm

53

• 6. Experimental Study

54

• 6. Experimental Study

Solar dish and tracking system

Assembly of 4.8 m diameter parabolic solar dish in the laboratory (upside down): Test set-up showing solar dish on two-axis solar tracking system:

• SolidWorks
• As constructed

for experiment

55

• 6. Experimental Study

Solar dish and tracking system

56

• 6. Experimental Study
• 20
• 15
• 10
• 5

5 10 1 2 3 4 5 6 7 8 9 10 11 12 Error (mm) Segment number Pre-assembly On tracker

Measured error of the end-height of the 12 dish arms during pre-assembly and

• n the tracker:

2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 11 12 Slope error (mrad) Segment number

Absolute slope error per dish arm as installed on the solar tracking system:

57

• 6. Experimental Study

Measurement of the solar resource

Solar measuring station to measure the DNI of the sun (SOLYS 2):

• Roof of Engineering Building 1

58

• 6. Experimental Study

Solar receiver

Manufacturing of solar receiver

59

• 6. Experimental Study

Solar receiver

Manufacturing of solar receiver

Inlet Outlet

Side view of solar receiver

Position of three weldpad themocouples

60

• 6. Experimental Study

Solar receiver

On the insulation before installation Top view of the solar receiver with aperture shown at the bottom.

61

• 6. Experimental Study

1 2 4 5 3

Layout of the experimental set-up. 1– Solar receiver with insulation; 2 – Leaf blower at receiver inlet; 3 – Receiver support structure; 4 – Parabolic dish; 5 – Thermocouple wires to data logger. Test A – With blower Test B – Without blower

62

• 6. Experimental Study

A bottom view of the solar receiver and its support structure

63

• 6. Experimental study - results

10 20 30 40 50 60 200 400 600 800 1000 1200 1400 Temperature (°C) Time (s) Top Bottom Air out Air in

Test A - Receiver surface temperature and air temperature measurements at the inlet (bottom) and outlet (top)

64

• 6. Experimental study

Day 1 1 2 2 2 3 3 3 3 Blower setting 6 1 5 4 3 2 4 4 3 Start time 12:37 14:36 11:18 12:27 14:26 10:13 11:24 12:25 14:28 Steady-state time 13:00 14:56 11:34 12:52 14:40 10:41 12:01 12:45 14:41 Receiver inlet (°C) 39.2 38.8 35.5 38.4 35.9 35.5

• 38.0

36.2 Receiver middle (°C) 45.5 44.9 41.7 45.7 44.4 44.6

• 46.6

45.0 Receiver outlet (°C) 50.4 50.6 46 54.1 50.0 50.1

• 52.2

48.0 Air ambient (°C) 19.8 20.4 17 16.4 18.6 15.9 18.4 19.1 19.9 Air outlet (°C) 52 51 42 49 49 46 50 52 45.0 Collector efficiency (%) 29.5 23.2 19.9 24.9 22.4 21.0 25.3 26.3 21.2 Optical efficiency (%) 53.6 42.2 36.2 45.3 40.7 38.2 46.0 47.8 38.5

Test A - Steady-state receiver surface temperature and air temperature measurements at the inlet, outlet and in the middle of the receiver

65

• 6. Experimental study

Test A - Expected ray performance of the experimental collector during the second test of Day 2, according to SolTrace.

For a dish with

• 5 mrad slope error,
• 25 mrad specularity error,
• 1° tracking error,
• 55% dish reflectivity,
• DNI of 700 W/m2 and
• 85% receiver tube

absorptivity. According to SolTrace, such a collector would have an efficiency of 21%. This efficiency compares well with the efficiency of 23.2%

• btained experimentally during

the second test on Day 1 when the DNI was 700 W/m2.

66

• 6. Experimental study

Test B - Receiver surface temperature increase as a function of time

• No blower

273 323 373 423 473 523 573 623 673 5000 10000 15000 20000 Temperature (K) Time (s) Top Middle Bottom Insulation Air

67

• 6. Experimental study

273 323 373 423 473 523 573 623 5000 10000 15000 20000 Temperature (K) Time (s) Measured Calculated

Test B - Receiver average surface temperature as a function of time

• as measured experimentally
• as calculated with
• h = 6.5 W/ m2K before steady state
• and h = 1 W/m2K after steady state

68

• 6. Experimental study

Test B - Conduction heat loss from the receiver

• as measured experimentally
• as calculated with
• h = 6.5 W/ m2K before steady state
• and h = 1 W/m2K after steady state

50 100 150 200 250 300 5000 10000 15000 20000 Heat loss (W) Time (s) Measured Calculated

69

• 6. Experimental study

Test B - Receiver insulation change Heat loss from the receiver at an average temperature of 590 K with different insulation arrangements

10 20 30 40 50 60 70 80 90 100 1 2 Percentage of total heat loss (%) Test Number Conduction Convection Radiation

1 2

70

• 6. Experimental study

100 200 300 400 500 600 700 2000 4000 6000 8000 10000 12000 Temperature (K) Time (s) Top Middle Bottom

Receiver insulation change Receiver surface temperature rise after insulation change

71

• 7. Conclusion
• The method of total entropy generation minimisation was found to be a holistic
• ptimisation approach whereby the components of the small-scale solar

thermal Brayton cycle could be optimised.

• A method to determine the surface temperatures and net heat transfer rates

along the length of the open-cavity receiver tube was presented.

• The factors contributing to the temperature and net heat transfer rate profiles
• n the receiver tube were divided into two components:
• geometry-dependent and
• temperature-dependent.
• It was found that many errors existed due to the solar collector – modelled with

SolTrace

• An optimum receiver-to-concentrator-area ratio of A’ ≈ 0.0035
• for 1° solar tracking error,
• 10 mrad optical error and
• 45° rim angle was found for the open-cavity tubular solar receiver.

72

• 7. Conclusion
• The open-cavity tubular solar receiver surface temperature and net heat

transfer rate for heating air depended on

• the receiver size,
• mass flow rate through the receiver,
• receiver tube diameter,
• receiver inlet temperature and
• dish errors.
• Receiver efficiencies of between 43% and 70% were found for the open-

cavity tubular receiver

• with a = 0.25 m,
• 0.06 kg/s ≤ mass flow rate ≤ 0.08 kg/s,
• 0.05 m ≤ d ≤ 0.0833 m and
• 900 K ≤ Tin,0 ≤ 1 070 K,
• operating on a 4.8 m diameter dish with 10 mrad optical error and

maximum solar tracking error of 1°.

73

• 7. Conclusion
• The higher the mass flow rate through the receiver, the lower the surface

temperatures and the more efficient the receiver.

• A high receiver efficiency was not necessarily beneficial for the small-

scale solar thermal Brayton cycle as a whole but the second law efficiency was more important.

• The small-scale open solar thermal Brayton cycle could generate a

positive net power output with solar-to-mechanical efficiencies in the range of 10-20% with much room for improvement.

• Optimum receiver and recuperator geometries were found.
• Good comparison between the Matlab results and Flownex results were

found (within 8%), except for the recuperator outlet temperature, which differed because of the use of different ε-NTU methods to calculate the recuperator efficiency.

74

• 7. Conclusion
• A 4.8 m parabolic aluminium dish with rim angle of 45° and two-axis

tracking system was designed and built.

• A tubular stainless steel solar cavity receiver was built and tested.
• The efficiency of the collector was determined with a flow test.
• A high-temperature test was performed to validate heat loss models.
• The higher the inlet temperature, the less efficient the receiver

became and the higher the maximum receiver surface temperature.

• The convection heat transfer coefficient was determined
• The heat loss rate due to convection and conduction was

significantly reduced with the proper insulation arrangement.

• The use of SolTrace was validated to a certain extent.
• It is concluded that the small-scale dish-mounted open solar

thermal Brayton cycle with tubular receiver and recuperator does have merit and it is recommended that it be investigated further experimentally.

75

• 8. Recommendations
• To make the small-scale open solar thermal Brayton cycle a success:
• large receiver tube diameter,
• very precise solar tracking system,
• high-specularity, high-reflectivity dish,
• 1° tracking error and 10 mrad optical error with reflectivity

above 90% should be sufficient

• Future work
• A smaller, more accurate and efficient dish and tracking system
• Testing of the optimised open-cavity tubular receiver at a temperature of 1 150 K for fatigue

loadings and thermal expansion

• The optimised receiver should be coupled to an optimised recuperator and micro-turbine to

determine the net power output of the system experimentally

• A cost-effective high-temperature and low-emissivity stainless steel receiver coating should be

developed.

• Optimisation of the cycle at receiver surface temperatures below 700 °C so that black

chromium can be used as low-emissivity coating.

• A moulded receiver cover to insulate the receiver
• so that air cannot flow around the receiver tubes but only on the inner side of the receiver cavity
• good thermal contact between the insulation and the receiver should be achieved regardless of

thermal expansion

• thermal expansion of the receiver should be considered

76

Acknowledgements

Assistance while building the fairly large experimental set-up:

• Chris Govinder,
• Donald Keetse,
• Evan Huisamen,
• Rupert Stander,
• Koos Mthombeni,
• Clyde Engineering,
• Marcelino Benjamin,
• Matsemela Zacharia (Zakes)
• Mogashoa, Milton Griffiths,
• Otto Scheffler,
• Ruan Fondse,
• Wian van den Bergh,
• Johannes Joubert,
• Andries Tiggelman,
• Bera Chirwa,
• Ryan Capitani,
• Suzanne Roberts,
• Jacob Masingi,
• Milga Manufacturing,
• Werner Scholtz,
• Phenyo Zobane,
• Erick Putter,
• Edwyn Mothabine,
• Alan Naidoo,
• Tebogo Mashego,
• Johan Clarke,
• Modupe Matolo,
• Israel Mabuda,
• Thato Mahlatji,
• James Gerber
• Zimase Dlamini.
• Prof Bello-Ochende
• Prof Meyer
• I thank my wife and my family for their

support. This work is based on the research supported by the National Research Foundation (NRF), University of Pretoria, CRSES, the Solar Hub between the University of Pretoria and Stellenbosch University, TESP, NAC, EEDSH Hub, Energy-IRT and the CSIR. The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed and conclusions arrived at are those of the author and are not necessarily to be attributed to the NRF.

77

I thank God for good health and an injury-free research period.

78

Journal Publications

• 1. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2011. Operating conditions of an open and

direct solar thermal Brayton cycle with optimised cavity receiver and recuperator. Energy, Vol. 36, pp. 6027-6036.

• 2. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2012. Thermodynamic optimisation of the

integrated design of a small-scale solar thermal Brayton cycle. International Journal of Energy Research, Vol. 36, pp. 1088-1104.

• 3. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2012. Optimum performance of the small-

scale open and direct solar thermal Brayton cycle at various environmental conditions and

• constraints. Energy, Vol. 46, pp. 42-50.
• 4. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2013. A review on the thermodynamic
• ptimisation and modelling of the solar thermal Brayton cycle. Renewable and Sustainable

Energy Reviews, Vol. 28, pp. 677-690.

• 5. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2014. The efficiency of an open-cavity solar

receiver for a small-scale solar thermal Brayton cycle. Energy Conversion and Management,

• Vol. 84, pp. 457-470.

79

Conference papers

• 1. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2011. Optimum performance of the small-scale open and direct solar thermal Brayton cycle at

various environmental conditions and constraints. In: Proceedings of the International Green Energy Conference (IGEC-VI), 5-9 June, Eskisehir, Turkey.

• 2. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2011. Optimum operating conditions of the small-scale open and direct solar thermal Brayton

cycle at various steady-state conditions. In: Proceedings of the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2011), 11-13 July, Mauritius.

• 3. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2011. Maximum net power output of the recuperative open and direct solar thermal Brayton
• cycle. In: Proceedings of the 5th International Conference on Energy Sustainability (ASME, ES 2011), 7-10 August, Washington, USA.
• 4. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2012. Optimum small-scale open and direct solar thermal Brayton cycle for Pretoria, South
• Africa. In: Proceedings of the 1st Southern African Solar Energy Conference (SASEC 2012), 21-23 May, Stellenbosch, South Africa.
• 5. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2012. Optimum small-scale open and direct solar thermal Brayton cycle for Pretoria, South
• Africa. In: Proceedings of the 6th International Conference on Energy Sustainability (ASME, ES 2012-91135), 23-26 July, San Diego, California,

USA.

• 6. Le Roux, W.G., Mwesigye, A., Bello-Ochende, T., Meyer, J.P., 2014. Tracker and collector for an experimental setup of a small-scale solar

thermal Brayton cycle. In: Proceedings of the 2nd Southern African Solar Energy Conference (SASEC 2014), 27-29 January, Port Elizabeth, South Africa.

• 7. Le Roux, W.G., Bello-Ochende, T., Meyer, J.P., 2014. Optimisation of an open rectangular cavity receiver and recuperator used in a small-scale

solar thermal Brayton cycle with thermal losses. In: Proceedings of the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT2014), 14-16 July 2014, Orlando, Florida, USA.

• 8. Le Roux, W.G., Meyer, J.P., Bello-Ochende, T., 2015. Experimental testing of a tubular cavity receiver for a small-scale solar thermal Brayton

cycle (SASEC 2015), 11-13 May, Skukuza, Kruger National Park, South Africa.

80

Thank you Questions? willemleroux@gmail.com