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Thermal stress analysis of eccentric tube receiver using concentrated solar radiation
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Solar Energy 84 (2010) 1809–1815 www.elsevier.com/locate/solener
Thermal stress analysis of eccentric tube receiver using concentrated solar radiation Fuqiang Wang, Yong Shuai, Yuan Yuan, Guo Yang, Heping Tan * School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China Received 28 March 2010; received in revised form 24 June 2010; accepted 8 July 2010 Available online 21 August 2010 Communicated by: Associate Editor Brian Norton
Abstract In the parabolic trough concentrator with tube receiver system, the heat transfer fluid flowing through the tube receiver can induce high thermal stress and deflection. In this study, the eccentric tube receiver is introduced with the aim to reduce the thermal stresses of tube receiver. The ray–thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. During the sequential coupled numerical analyses, the concentrated heat flux distribution on the bottom half periphery of tube receiver is obtained by Monte-Carlo ray tracing method, and the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The temperature distributions and thermal stress fields are obtained by the CFD and FEA analyses, respectively. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated. It is recommended to adopt the eccentric tube receiver with optimum eccentricity and 90° oriented angle as tube receiver for the parabolic trough concentrator system to reduce the thermal stresses. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Eccentric tube receiver; Thermal stress; Fitting function method; Concentrated solar radiation; Ray tracing
1. Introduction The parabolic trough concentrator with tube receiver system is extensively employed for solar power generation. The incoming solar radiation is converged on the bottom periphery of tube receiver by a parabolic trough concentrator, and then the concentrated solar radiation is converted to heat by the heat transfer fluid flowing through the tube receiver. The tube receiver is enclosed by a glass envelope to reduce the heat losses to surroundings (Almanza et al., 1997). The tube receivers are designed to operate under extremely nonuniform heat flux, cyclic weather and cloud transient cycle conditions, which in turn will produce high *
Corresponding author. Tel.: +86 451 8641 2308; fax: +86 451 8641 3208. E-mail address: [email protected] (H. Tan). 0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.07.005
temperature gradients and large deflection of tube receiver. The high temperature gradients will generate the large thermal stresses which may cause the failure of tube receiver, and the deflection of tube receiver will induce the rupture of glass envelop which will result in the increase of heat loss (Reddy et al., 2008). Therefore, it is necessary to seek some new approaches to reduce the thermal stresses and deflection of the tube receiver. Hitherto, mainly three methods have been proposed to reduce the thermal stresses or deflection of receiver: Optimizing the size of tube receivers or operation parameters, such as, employing small diameter tubes (Lata et al., 2008), or controlling the fluid flow rate (Verlotski and Flores, 1997). Receivers with homogenous solar radiation heat flux distribution on the surface. Generally, these kinds of
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F. Wang et al. / Solar Energy 84 (2010) 1809–1815
receivers are designed using ray tracing methods to obtain the isosurface of solar radiation (David et al., 2008; Shuai et al., 2008a,b). At present, the literature survey indicates that the research on receivers with homogenous solar radiation heat flux distribution remains at the theory stage, and a large amount of manufacturing problems wait to solve further. Compound wall copper–steel receiver. The compound wall receiver is composed of two parts: the internal tube stratified is made of copper to obtain an excellent heat transfer performance to reduce the temperature gradients, and the external tube stratified is made of steel to strengthen the intensity of the tube receiver. The compound wall copper–steel tube receivers have been applied to the Solar Power Plant of the National University of Mexico (Flores and Almanza, 2004). Though the compound wall copper–steel receiver can reduce the deflection of tube receiver, it will introduce the contact resistance if the two stratifications cannot contact well and the efficiency of solar radiation absorption will be affected. In this study, a new type of tube receiver for the parabolic trough concentrator system is introduced with the aim to reduce the thermal stresses. The ray–thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of tube receiver. 2. Construction of the new type receiver 2.1. The aim of the new type receiver is to Reducing the thermal stresses effectively; Without adding the mass of tube receiver; Easy to manufacture.
2.2. Construction of eccentric tube receiver To meet the above requirements of the new type receiver, the eccentric tube receiver for parabolic trough concentrator system is introduced. Fig. 1 shows the diagram of the eccentric tube receiver. The eccentric tube receiver is proposed on the basis of concentric tube receiver. As seen from this figure, the center of internal cylinder surface of concentric tube receiver is moved upward (or other directions), which is not located at the same coordinate position with the center of external cylinder surface. Therefore, the wall thickness of the bottom half section of tube receiver will increase without adding any mass to the entire tube receiver. With the same boundary conditions for numerical analyses, the increase of wall thickness will not only strengthen the intensity to enhance the resistance of thermal stress, but also can increase the thermal capacity, which in turn will be benefit to alleviate the extremely nonuniform temperature distribution situation. As seen from Fig. 1, the origin of coordinate system is placed at the center of the external cylinder surface. In this study, the vector eccentric radius~ r (the origin of coordinate system points to the center of the internal cylinder surface); the vector eccentricity~ e (the projection of vector ~ r on the yaxis); and the oriented angle / (the angle between the vector ~ r and the x-axis) are introduced to describe the shape of eccentric tube receiver (Manglik and Fang, 1995). The ray– thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated in this study. 3. Methodology
y Top half periphery
r ϕ
x rout
Bottom half periphery Fig. 1. Schematic diagram of physical domain and coordinate system for the eccentric tube receiver.
At the first step, the concentrated solar radiation heat flux distribution qc on the bottom half periphery of tube receiver, which is used as the input data for the CFD analyses, will be calculated by the solar concentration system program with the Monte-Carlo ray tracing method developed in Harbin Institute of Technology (Shuai et al., 2008a,b). The Monte-Carlo ray tracing method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. Due to the Monte-Carlo method is a stochastic technique and does not have the truncation error as the other numerical methods of discrete differential–integral equation, the solutions of the MonteCarlo method are generally used to be the reference datum of the other numerical methods (Tan et al., 2006). The thermal model proposed for the solar parabolic concentrator with tube receiver system is illustrated in Fig. 2. The geometrical parameters of the parabolic trough concentrator and tube receiver for this study are illustrated in Table 1. As seen from this table, the transmissivity of the glass
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
Sun
Fluid Outlet
Fluid Inlet
y
External Cylinder Surface
Fluid Inlet
Fluid Outlet
z x
Internal Cylinder Surface
Fig. 2. Schematics diagram of the tube receiver with solar parabolic trough system.
envelop is highly close to 1 and the thickness of glass envelop is very thin, therefore, the values and distribution of heat flux are impacted very slightly when passing through the glass envelop. Hence, the impact of the glass envelop in this investigation is neglected. During the heat flux distribution calculation process, the external cylinder surface of tube receiver will be discretized to 300 nodes along the circumference and 300 nodes along the tube length direction. Therefore, the solar concentration system program will obtain 300 300 heat flux values on the discrete nodes. No optical errors or tracking errors were considered for the solar concentration system program, and the calculation conditions are: the non-parallelism angle of sunlight is 160 and the solar radiation flow is 1000 W/ m2 (Hasuike et al., 2006), the sunshape is taken to be a distribution with a circumsolar-ratio of 0.05 and a limb darkening parameter of 0.8 (Shuai et al., 2008a,b). At the second step, the concentrated heat flux distribution calculated by the Monte-Carlo ray tracing method will
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be employed as input data for the CFD analyses by means of using the boundary condition function in Ansys software. In Steven’s study (Steven and Macosko, 1999), the receiver is divided into 16 sections, and the average solar radiation heat flux of each section is calculated. The average heat flux is used as boundary condition for each corresponding section in the thermal analysis model. This method is fairly straightforward and simple, but the deviations generated during the heat flux transformation process are enormous. In this study, the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The solar radiation heat flux distribution calculated by the Monte-Carlo ray tracing method along the bottom half periphery of tube receiver will be divided into several sections, and the heat flux distribution of each section will be fitted by a polynomial regression function with highly fitted precision. The calculated heat flux distribution on the bottom half periphery of tube receiver is shown in Fig. 3. Six polynomial regression functions are employed as the fitted functions and illustrated as follows: 8 q ¼ 12 x 2 ½35; 17:82 > > > > > q ¼ 13740:23 þ 770556:99 x x 2 ½17:82; 16:54 > > > < q ¼ 43418:96 þ 2:57 x x 2 ½16:54; 0 > q ¼ 43418:96 2:57 x x 2 ½0; 16:54 > > > > > q ¼ 13740:23 770556:99 x x 2 ½16:54; 17:82 > > : q ¼ 12 x 2 ½17:82; 35 ð1Þ The six fitted function curves are also drawn in Fig. 3. As seen from this figure, the fitted function curves can match the calculated heat flux distribution well with high precision. At the third step, the CFD analyses will obtain the temperature distributions. Thermal oil (Syltherm 800) and stainless steel are used as the heat transfer fluid and the
Fitted Curves Calculated
Parabolic trough concentrator and tube receiver
Value
Focal length of parabolic trough concentrator Length of parabolic trough concentrator Opening radius of parabolic trough concentrator Height of parabolic trough concentrator Outer diameter of tube receiver (rout) Inner diameter of tube receiver (rin) Glass cover diameter Length of tube receiver Reflectivity of parabolic trough collector Absorptivity of tube receiver Transmissivity of glass over
2000 mm 2000 mm 500 mm 1500 mm 70 mm 60 mm 100 mm 2000 mm 0.95 0.9 0.965
Heat Flux W/m
Table 1 Geometrical parameters of the parabolic trough concentrator and tube receiver.
2
40000
30000
20000
10000
0 -30
-20
-10
0
10
20
30
X mm Fig. 3. Calculated heat flux distribution on the bottom half periphery of tube receiver and the fitted function curves.
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
Table 2 Thermal-physical properties of heat transfer fluid and tube receiver. Property
Fluid Thermal oil
Tube receiver Stainless steel
Density (kg m3) Specific heat (J kg1 K1) Viscosity (106 Pa s) Thermal conductivity (W m1 K1) Poisson ratio Young’s modulus (GPa) Thermal expansion coefficient (106 K1)
881.68 1711 3.86 0.1237 – – –
7900 500 – 25 0.25 220 17.2
material of tube receiver, respectively (Kumar and Reddy, 2009). The thermal-physical properties of the thermal oil and stainless steel are presented in Table 2. As the key point of this paper is to put forward a new type of tube receiver, the comparisons between the new type receiver and concentric tube receiver are carried out under the same boundary condition with the hypothesis that there are no air bubbles in the flow. The boundary conditions applied on both the eccentric and concentric tube receivers are illustrated as follows: The flow has a uniform velocity u = 0.15 m/s at the atmosphere temperature at the tube receiver inlet; The top half periphery of tube receiver is subjected to a uniform heat flux distribution which is the sun average radiation in the air (the value is 1000 W/m2); The bottom half periphery of tube receiver is subjected to the concentrated heat flux distribution calculated by the Monte-Carlo ray tracing method which is fitted by six polynomial regression functions; Zero pressure gradient condition is employed across the fluid outlet boundary. At the forth step, the finite element analysis (FEA) will obtain the Von-Mises thermal stress fields, which is a synthesis stress of radial stress, axial stress and circumferential stress. The governing thermal stress equations for hollow cylinders (Fauple and Fisher, 1981) are expressed as follows: Z ro Ea 2 rz ¼ T ðrÞ r dr T ðrÞ ð2Þ ð1 mÞ r2 r20 r2i ri Ea rr ¼ ð1 mÞ r2 2 Z ro Z r r r2i 2 T ðrÞ r dr T ðrÞ r dr r0 r2i ri ri rh ¼
ð3Þ
Ea ð1 mÞ r2 2 Z ro Z r r þ r2i 2 2 T ðrÞ r dr þ T ðrÞ r dr T ðrÞ r r0 r2i ri ri ð4Þ
rvon
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ r2z þ r2r þ r2h ðrz rr þ rr rh þ rh rz Þ
ð5Þ
where rr, rz, rh and rvon are the radial stress, axial stress, circumferential stress and Von-Mises stress, respectively. The resulted temperature fields defined at the nodes of CFD analysis meshes are interpolated as input data to the nodes of the thermal stress analysis meshes. This simulation approach is fairly straightforward and has been adopted by many investigators (Steven and Macosko, 1999; Qin et al., 2004; Jae and Allan, 2006; Friedrich et al., 2008; Knaus et al., 2005; Wetzel et al., 2007). The validation of this simulation approach have been described in Friedrich et al. (2008), Knaus et al. (2005), Wetzel et al. (2007), and the comparisons between the simulation results and the experimentations reveals a high level of compliance. Compared to meshes of the CFD analysis, a much finer solid part meshes are used for the FEA analysis to produce a reasonably accurate degrees of freedom solution.
4. Results and discussion 4.1. Comparison between the concentric and eccentric tube receiver The eccentric tube receiver with the center of internal cylinder surface 3 mm moved upward along the y-axis (the magnitude of vector eccentricity~ r is 3 mm, and the oriented angle / is 90°) is chosen for the comparison research. The temperature distributions and thermal stress fields of eccentric tube receiver are compared with those of concentric tube receiver under the same boundary conditions and material physical properties. Fig. 4 shows the temperature distributions along the internal circumference at the outlet section for both the concentric and eccentric tube receivers. As seen from this figure, the concentric tube receiver has a higher value of peak temperature which is about 11 °C higher than that of eccentric tube receiver. Along the bottom half internal
420
Temperature K
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Concentric Eccentric
400 380 θ
360 340 320 0
60
120
180
θ
240
300
360
o
Fig. 4. Temperature profiles along the internal circumference at the outlet section for both the concentric and eccentric tube receivers.
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
4.2. Effect of the eccentricity variation on the thermal stresses The way how the variation of eccentricity affecting the thermal stresses of eccentric tube receiver is investigated with the objective to give instructions to the designer of eccentric tube receiver. Fig. 6 presents the relationship between the eccentricity variation and the peak Von-Mises thermal stress values of tube receiver, while keeps the center of internal cylinder surface locating at the y-axis. As seen from this figure, not all the eccentric tube receivers can reduce the
320
240
ε
200 160 120 80 -3
-2
-1
0
1
2
3
Eccentricity ε Fig. 6. Relationship between eccentricity variation and peak thermal stress values.
thermal stresses of tube receiver. The peak thermal stress values of tube receivers are increased significantly when the direction of vector eccentricity switches from positive to negative (the center of internal cylinder surface is moved downward). The thermal stress reduction of tube receiver only occurs at the positive direction of vector eccentricity ~ r when adopting eccentric tube receiver as the tube receiver for parabolic trough concentrator system, and the larger magnitude of vector eccentricity is, the greater reduction of thermal stresses is. However, the manufacturing cost will increase with the magnitude of vector eccentricity increasing. The eccentric tube receiver should employ an optimum magnitude of eccentricity to minimize the thermal stresses and prevent the failure of tube receiver while not incurring excessive manufacturing cost.
320
160
Concentric Eccentric θ
120
Concentric Eccentric
280
Thermal Stress (MPa)
Effective Stress MPa
Concentric Eccentric
280
Thermal Stress (MPa)
circumference (the h is between 180° and 360°) where the peak temperatures of both the concentric and eccentric tube receivers are found, the temperature gradients of concentric tube receiver are higher than those of eccentric tube receiver which can lead to the higher thermal stresses Ifran and Chapman (2009, 2010), the cause of this phenomenon should be attributed to the thermal capacity increase on the bottom section of tube receiver due to the wall thickness increase on this section. The Von-Mises thermal stress fields along the internal circumference at the outlet section for both the concentric and eccentric tube receivers are presented in Fig. 5. The peak thermal stress values of the two profiles are both found at h = 270° where the peak temperature values are also located at. Attributed to the lower temperature gradients and intensity strengthen on the bottom half section of tube receiver, the peak thermal stress value of the eccentric tube receiver which is only 80.7 MPa is much lower compared to that of the concentric tube receiver which is 137.01 MPa. Therefore, adopting eccentric tube receiver as the tube receiver for the parabolic trough concentrator system can reduce the Von-Mises thermal stresses effectively up to 41.1%, which means the eccentric tube receiver can meet the requirements of the new type receiver.
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80
40
240 ϕ
200 160 120 80
0 0
60
120
180
θ
240
300
360
o
Fig. 5. Thermal stress profiles along the internal circumference at the outlet section for both the concentric and eccentric tube receivers.
-90
-60
-30
0
30
60
90
Oriented Angle ϕ Fig. 7. Relationship between oriented angle variation and peak thermal stress values.
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F. Wang et al. / Solar Energy 84 (2010) 1809–1815
4.3. Effect of the oriented angle variation on the thermal stresses The effect of the oriented angle variation on the VonMises thermal stresses of eccentric tube receiver is also performed with a constant eccentric radius value (r = 3 mm). The eccentric tube receiver has symmetric property with the variation of oriented angle, therefore, instead of dealing with the whole oriented angle range, analyses of half range of the oriented angle can yield complete results. As seen from Fig. 7, the variation of oriented angle has a big impact on the thermal stresses of eccentric tube receiver. The peak thermal stress value of eccentric tube receiver is less than that of the concentric tube receiver only when the oriented angle varies between 0° and 90°. The eccentric tube receiver with 90° oriented angle has the lowest peak thermal stress value. Therefore, it is recommended to employ eccentric tube with 90° oriented angle and optimum eccentricity as the tube receiver for parabolic trough concentrator system to reduce the thermal stresses.
5. Conclusion Aiming at reducing the thermal stresses of tube receiver, the eccentric tube receiver is introduced in this investigation. The ray–thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. The fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model, and the fitted function curves can match the calculated heat flux distribution well with high precision. The sequential coupled numerical analysis results indicate that adopting eccentric tube as the tube receiver for parabolic trough concentrator system can reduce the Von-Mises thermal stress effectively up to 41.1%. The way how the variation of eccentricity and oriented angle affect the thermal stresses of eccentric tube receiver are also investigated with the objective to give instructions to the designer of eccentric tube receiver. When adopting eccentric tube receiver, the thermal stress reduction of tube receiver only occurs at the positive direction of vector eccentricity, and the larger magnitude of vector eccentricity is, the greater reduction of thermal stresses is. The oriented angle has a big impact on the thermal stresses of eccentric tube receiver. The thermal stress reduction of tube receiver only occurs when the oriented angle is between 0° and 90°. Therefore, employing eccentric tube receiver with optimum eccentricity and oriented angle for parabolic trough concentrator system can reduce the thermal stress and enhance the reliability of tube receiver effectively.
Acknowledgements This work was supported by the National Key Basic Research Special Foundation of China (No. 2009CB220006), the key program of the National Natural Science Foundation of China (Grant No. 50930007) and the National Natural Science Foundation of China (Grant No. 50806017). A very special acknowledgement is made to the editors and referees whose constructive criticism has improved this paper. References Almanza, R., Lenz, A., Jime´nez, G., 1997. Receiver behavior in direct steam generation with parabolic troughs. Solar Energy 61, 275–278. David, R.R., Marcelino, S.G., Claudio, A.E., 2008. Three-dimensional analysis of a concentrated solar flux. ASME Journal of Solar Energy Engineering 130, 014503/1–014503/4. Fauple, J.H., Fisher, F.E., 1981. Engineering Design – A Synthesis of Stress Analysis and Material Engineering. Wiley, New York. Flores, V., Almanza, R., 2004. Behavior of the compound wall copper– steel receiver with stratified two-phase flow regimen in transient states when solar irradiance is arriving on one side of receiver. Solar Energy 76, 195–198. Friedrich, B., Wolfram, K., Yang, C., 2008. Virtual temperature cycle testing of automotive heat exchangers by coupled fluid structure simulation. SAE Technical Paper, No. 08-01-1210. Hasuike, H., Yoshizawa, H., Suzuki, H., 2006. Study on design of molten salt solar receivers for beam-down solar concentrator. Solar Energy 80, 1255–1262. Ifran, M.A., Chapman, W.C., 2009. Thermal stresses in radiant tubes due to axial, circumferential and radial temperature distributions. Applied Thermal Engineering 29, 1913–1920. Ifran, M.A., Chapman, W.C., 2010. Thermal stresses in radiant tubes: a comparison between recuperative and regenerative systems. Applied Thermal Engineering 30, 196–200. Jae, S.K., Allan, W., 2006. Transient conjugate CFD simulation of the radiator thermal cycle. SAE Technical Paper, No. 06-01-1577. Knaus, H., Weise, S., Ku¨hnel, W., Kru¨ger, U., 2005. Overall approach to the validation of charge air coolers. SAE Technical Paper, No. 05-012064. Kumar, N.S., Reddy, K.S., 2009. Thermal analysis of solar parabolic collector with porous disc receiver. Applied Energy 86, 1804–1812. ´ ., Lara, M.A., 2008. High flux central Lata, J.M., Rodrı´guez, M.A receivers of molten salts for the new generation of commercial standalone solar power plants. ASME Journal of Solar Energy Engineering 130, 0211002/1–0211002/5. Manglik, R.M., Fang, P.P., 1995. Effect of eccentricity and thermal boundary conditions on laminar fully developed flow in annular ducts. International Journal of Heat Fluid Flow 16, 298–306. Qin, Y.F., Kuba, S., Naknishi, N., 2004. Coupled analysis of thermal flow and thermal stress of an engine exhaust manifold. SAE Technical Paper, No. 04-01-1345. Reddy, K.S., Kumar, K.R., Satyanaryana, G.V., 2008. Numerical investigation of energy-efficient receiver for solar parabolic trough concentrator. Heat Transfer Engineering 29 (11), 961–970. Shuai, Y., Xia, X.L., Tan, H.P., 2008a. Radiation performance of dish solar concentrator/cavity receiver systems. Solar Energy 82, 13–21. Shuai, Y., Xia, X.L., Tan, H.P., 2008b. Numerical study of radiation characteristics in a dish solar collector system. ASME Journal of Solar Energy Engineering 130, 021001/1–021001/8. Steven, G., Macosko, R.P., 1999. Transient thermal analysis of a refractive secondary solar concentrator. SAE Technical Paper, No. 99-01-2680.
F. Wang et al. / Solar Energy 84 (2010) 1809–1815 Tan, H.P., Xia, X.L., Liu, L.L., Ruan, L.M., 2006. Numerical Calculation of Infrared Radiation Properties and Transfer. Harbin Institute of Technology Press, Harbin. Verlotski, V., Flores, V., 1997. A solar thermal MgO-powder receiver with working temperatures of more than 1600 °C: model investigation by
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using a laser as an irradiation source. Solar Energy Materials and Solar Cells 45 (3), 227–239. Wetzel, T., Brotz, F., Lo¨ffler, B., Boermsa, A., Fernandez, N., Heckenberger, T., 2007. Coupled aerothermodynamic and structural analysis of transient charge air cooler operation modes. VTMS8, Paper 07VTMS-38.
Solar Energy 84 (2010) 1809–1815 www.elsevier.com/locate/solener
Thermal stress analysis of eccentric tube receiver using concentrated solar radiation Fuqiang Wang, Yong Shuai, Yuan Yuan, Guo Yang, Heping Tan * School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin 150001, PR China Received 28 March 2010; received in revised form 24 June 2010; accepted 8 July 2010 Available online 21 August 2010 Communicated by: Associate Editor Brian Norton
Abstract In the parabolic trough concentrator with tube receiver system, the heat transfer fluid flowing through the tube receiver can induce high thermal stress and deflection. In this study, the eccentric tube receiver is introduced with the aim to reduce the thermal stresses of tube receiver. The ray–thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. During the sequential coupled numerical analyses, the concentrated heat flux distribution on the bottom half periphery of tube receiver is obtained by Monte-Carlo ray tracing method, and the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The temperature distributions and thermal stress fields are obtained by the CFD and FEA analyses, respectively. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated. It is recommended to adopt the eccentric tube receiver with optimum eccentricity and 90° oriented angle as tube receiver for the parabolic trough concentrator system to reduce the thermal stresses. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Eccentric tube receiver; Thermal stress; Fitting function method; Concentrated solar radiation; Ray tracing
1. Introduction The parabolic trough concentrator with tube receiver system is extensively employed for solar power generation. The incoming solar radiation is converged on the bottom periphery of tube receiver by a parabolic trough concentrator, and then the concentrated solar radiation is converted to heat by the heat transfer fluid flowing through the tube receiver. The tube receiver is enclosed by a glass envelope to reduce the heat losses to surroundings (Almanza et al., 1997). The tube receivers are designed to operate under extremely nonuniform heat flux, cyclic weather and cloud transient cycle conditions, which in turn will produce high *
Corresponding author. Tel.: +86 451 8641 2308; fax: +86 451 8641 3208. E-mail address: [email protected] (H. Tan). 0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.07.005
temperature gradients and large deflection of tube receiver. The high temperature gradients will generate the large thermal stresses which may cause the failure of tube receiver, and the deflection of tube receiver will induce the rupture of glass envelop which will result in the increase of heat loss (Reddy et al., 2008). Therefore, it is necessary to seek some new approaches to reduce the thermal stresses and deflection of the tube receiver. Hitherto, mainly three methods have been proposed to reduce the thermal stresses or deflection of receiver: Optimizing the size of tube receivers or operation parameters, such as, employing small diameter tubes (Lata et al., 2008), or controlling the fluid flow rate (Verlotski and Flores, 1997). Receivers with homogenous solar radiation heat flux distribution on the surface. Generally, these kinds of
1810
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
receivers are designed using ray tracing methods to obtain the isosurface of solar radiation (David et al., 2008; Shuai et al., 2008a,b). At present, the literature survey indicates that the research on receivers with homogenous solar radiation heat flux distribution remains at the theory stage, and a large amount of manufacturing problems wait to solve further. Compound wall copper–steel receiver. The compound wall receiver is composed of two parts: the internal tube stratified is made of copper to obtain an excellent heat transfer performance to reduce the temperature gradients, and the external tube stratified is made of steel to strengthen the intensity of the tube receiver. The compound wall copper–steel tube receivers have been applied to the Solar Power Plant of the National University of Mexico (Flores and Almanza, 2004). Though the compound wall copper–steel receiver can reduce the deflection of tube receiver, it will introduce the contact resistance if the two stratifications cannot contact well and the efficiency of solar radiation absorption will be affected. In this study, a new type of tube receiver for the parabolic trough concentrator system is introduced with the aim to reduce the thermal stresses. The ray–thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of tube receiver. 2. Construction of the new type receiver 2.1. The aim of the new type receiver is to Reducing the thermal stresses effectively; Without adding the mass of tube receiver; Easy to manufacture.
2.2. Construction of eccentric tube receiver To meet the above requirements of the new type receiver, the eccentric tube receiver for parabolic trough concentrator system is introduced. Fig. 1 shows the diagram of the eccentric tube receiver. The eccentric tube receiver is proposed on the basis of concentric tube receiver. As seen from this figure, the center of internal cylinder surface of concentric tube receiver is moved upward (or other directions), which is not located at the same coordinate position with the center of external cylinder surface. Therefore, the wall thickness of the bottom half section of tube receiver will increase without adding any mass to the entire tube receiver. With the same boundary conditions for numerical analyses, the increase of wall thickness will not only strengthen the intensity to enhance the resistance of thermal stress, but also can increase the thermal capacity, which in turn will be benefit to alleviate the extremely nonuniform temperature distribution situation. As seen from Fig. 1, the origin of coordinate system is placed at the center of the external cylinder surface. In this study, the vector eccentric radius~ r (the origin of coordinate system points to the center of the internal cylinder surface); the vector eccentricity~ e (the projection of vector ~ r on the yaxis); and the oriented angle / (the angle between the vector ~ r and the x-axis) are introduced to describe the shape of eccentric tube receiver (Manglik and Fang, 1995). The ray– thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. The effects of eccentricity and oriented angle variation on the thermal stresses of eccentric tube receiver are also investigated in this study. 3. Methodology
y Top half periphery
r ϕ
x rout
Bottom half periphery Fig. 1. Schematic diagram of physical domain and coordinate system for the eccentric tube receiver.
At the first step, the concentrated solar radiation heat flux distribution qc on the bottom half periphery of tube receiver, which is used as the input data for the CFD analyses, will be calculated by the solar concentration system program with the Monte-Carlo ray tracing method developed in Harbin Institute of Technology (Shuai et al., 2008a,b). The Monte-Carlo ray tracing method is a powerful tool for performing radiative equilibrium calculations, even in complex geometries. Due to the Monte-Carlo method is a stochastic technique and does not have the truncation error as the other numerical methods of discrete differential–integral equation, the solutions of the MonteCarlo method are generally used to be the reference datum of the other numerical methods (Tan et al., 2006). The thermal model proposed for the solar parabolic concentrator with tube receiver system is illustrated in Fig. 2. The geometrical parameters of the parabolic trough concentrator and tube receiver for this study are illustrated in Table 1. As seen from this table, the transmissivity of the glass
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
Sun
Fluid Outlet
Fluid Inlet
y
External Cylinder Surface
Fluid Inlet
Fluid Outlet
z x
Internal Cylinder Surface
Fig. 2. Schematics diagram of the tube receiver with solar parabolic trough system.
envelop is highly close to 1 and the thickness of glass envelop is very thin, therefore, the values and distribution of heat flux are impacted very slightly when passing through the glass envelop. Hence, the impact of the glass envelop in this investigation is neglected. During the heat flux distribution calculation process, the external cylinder surface of tube receiver will be discretized to 300 nodes along the circumference and 300 nodes along the tube length direction. Therefore, the solar concentration system program will obtain 300 300 heat flux values on the discrete nodes. No optical errors or tracking errors were considered for the solar concentration system program, and the calculation conditions are: the non-parallelism angle of sunlight is 160 and the solar radiation flow is 1000 W/ m2 (Hasuike et al., 2006), the sunshape is taken to be a distribution with a circumsolar-ratio of 0.05 and a limb darkening parameter of 0.8 (Shuai et al., 2008a,b). At the second step, the concentrated heat flux distribution calculated by the Monte-Carlo ray tracing method will
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be employed as input data for the CFD analyses by means of using the boundary condition function in Ansys software. In Steven’s study (Steven and Macosko, 1999), the receiver is divided into 16 sections, and the average solar radiation heat flux of each section is calculated. The average heat flux is used as boundary condition for each corresponding section in the thermal analysis model. This method is fairly straightforward and simple, but the deviations generated during the heat flux transformation process are enormous. In this study, the fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model. The solar radiation heat flux distribution calculated by the Monte-Carlo ray tracing method along the bottom half periphery of tube receiver will be divided into several sections, and the heat flux distribution of each section will be fitted by a polynomial regression function with highly fitted precision. The calculated heat flux distribution on the bottom half periphery of tube receiver is shown in Fig. 3. Six polynomial regression functions are employed as the fitted functions and illustrated as follows: 8 q ¼ 12 x 2 ½35; 17:82 > > > > > q ¼ 13740:23 þ 770556:99 x x 2 ½17:82; 16:54 > > > < q ¼ 43418:96 þ 2:57 x x 2 ½16:54; 0 > q ¼ 43418:96 2:57 x x 2 ½0; 16:54 > > > > > q ¼ 13740:23 770556:99 x x 2 ½16:54; 17:82 > > : q ¼ 12 x 2 ½17:82; 35 ð1Þ The six fitted function curves are also drawn in Fig. 3. As seen from this figure, the fitted function curves can match the calculated heat flux distribution well with high precision. At the third step, the CFD analyses will obtain the temperature distributions. Thermal oil (Syltherm 800) and stainless steel are used as the heat transfer fluid and the
Fitted Curves Calculated
Parabolic trough concentrator and tube receiver
Value
Focal length of parabolic trough concentrator Length of parabolic trough concentrator Opening radius of parabolic trough concentrator Height of parabolic trough concentrator Outer diameter of tube receiver (rout) Inner diameter of tube receiver (rin) Glass cover diameter Length of tube receiver Reflectivity of parabolic trough collector Absorptivity of tube receiver Transmissivity of glass over
2000 mm 2000 mm 500 mm 1500 mm 70 mm 60 mm 100 mm 2000 mm 0.95 0.9 0.965
Heat Flux W/m
Table 1 Geometrical parameters of the parabolic trough concentrator and tube receiver.
2
40000
30000
20000
10000
0 -30
-20
-10
0
10
20
30
X mm Fig. 3. Calculated heat flux distribution on the bottom half periphery of tube receiver and the fitted function curves.
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
Table 2 Thermal-physical properties of heat transfer fluid and tube receiver. Property
Fluid Thermal oil
Tube receiver Stainless steel
Density (kg m3) Specific heat (J kg1 K1) Viscosity (106 Pa s) Thermal conductivity (W m1 K1) Poisson ratio Young’s modulus (GPa) Thermal expansion coefficient (106 K1)
881.68 1711 3.86 0.1237 – – –
7900 500 – 25 0.25 220 17.2
material of tube receiver, respectively (Kumar and Reddy, 2009). The thermal-physical properties of the thermal oil and stainless steel are presented in Table 2. As the key point of this paper is to put forward a new type of tube receiver, the comparisons between the new type receiver and concentric tube receiver are carried out under the same boundary condition with the hypothesis that there are no air bubbles in the flow. The boundary conditions applied on both the eccentric and concentric tube receivers are illustrated as follows: The flow has a uniform velocity u = 0.15 m/s at the atmosphere temperature at the tube receiver inlet; The top half periphery of tube receiver is subjected to a uniform heat flux distribution which is the sun average radiation in the air (the value is 1000 W/m2); The bottom half periphery of tube receiver is subjected to the concentrated heat flux distribution calculated by the Monte-Carlo ray tracing method which is fitted by six polynomial regression functions; Zero pressure gradient condition is employed across the fluid outlet boundary. At the forth step, the finite element analysis (FEA) will obtain the Von-Mises thermal stress fields, which is a synthesis stress of radial stress, axial stress and circumferential stress. The governing thermal stress equations for hollow cylinders (Fauple and Fisher, 1981) are expressed as follows: Z ro Ea 2 rz ¼ T ðrÞ r dr T ðrÞ ð2Þ ð1 mÞ r2 r20 r2i ri Ea rr ¼ ð1 mÞ r2 2 Z ro Z r r r2i 2 T ðrÞ r dr T ðrÞ r dr r0 r2i ri ri rh ¼
ð3Þ
Ea ð1 mÞ r2 2 Z ro Z r r þ r2i 2 2 T ðrÞ r dr þ T ðrÞ r dr T ðrÞ r r0 r2i ri ri ð4Þ
rvon
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ r2z þ r2r þ r2h ðrz rr þ rr rh þ rh rz Þ
ð5Þ
where rr, rz, rh and rvon are the radial stress, axial stress, circumferential stress and Von-Mises stress, respectively. The resulted temperature fields defined at the nodes of CFD analysis meshes are interpolated as input data to the nodes of the thermal stress analysis meshes. This simulation approach is fairly straightforward and has been adopted by many investigators (Steven and Macosko, 1999; Qin et al., 2004; Jae and Allan, 2006; Friedrich et al., 2008; Knaus et al., 2005; Wetzel et al., 2007). The validation of this simulation approach have been described in Friedrich et al. (2008), Knaus et al. (2005), Wetzel et al. (2007), and the comparisons between the simulation results and the experimentations reveals a high level of compliance. Compared to meshes of the CFD analysis, a much finer solid part meshes are used for the FEA analysis to produce a reasonably accurate degrees of freedom solution.
4. Results and discussion 4.1. Comparison between the concentric and eccentric tube receiver The eccentric tube receiver with the center of internal cylinder surface 3 mm moved upward along the y-axis (the magnitude of vector eccentricity~ r is 3 mm, and the oriented angle / is 90°) is chosen for the comparison research. The temperature distributions and thermal stress fields of eccentric tube receiver are compared with those of concentric tube receiver under the same boundary conditions and material physical properties. Fig. 4 shows the temperature distributions along the internal circumference at the outlet section for both the concentric and eccentric tube receivers. As seen from this figure, the concentric tube receiver has a higher value of peak temperature which is about 11 °C higher than that of eccentric tube receiver. Along the bottom half internal
420
Temperature K
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Concentric Eccentric
400 380 θ
360 340 320 0
60
120
180
θ
240
300
360
o
Fig. 4. Temperature profiles along the internal circumference at the outlet section for both the concentric and eccentric tube receivers.
F. Wang et al. / Solar Energy 84 (2010) 1809–1815
4.2. Effect of the eccentricity variation on the thermal stresses The way how the variation of eccentricity affecting the thermal stresses of eccentric tube receiver is investigated with the objective to give instructions to the designer of eccentric tube receiver. Fig. 6 presents the relationship between the eccentricity variation and the peak Von-Mises thermal stress values of tube receiver, while keeps the center of internal cylinder surface locating at the y-axis. As seen from this figure, not all the eccentric tube receivers can reduce the
320
240
ε
200 160 120 80 -3
-2
-1
0
1
2
3
Eccentricity ε Fig. 6. Relationship between eccentricity variation and peak thermal stress values.
thermal stresses of tube receiver. The peak thermal stress values of tube receivers are increased significantly when the direction of vector eccentricity switches from positive to negative (the center of internal cylinder surface is moved downward). The thermal stress reduction of tube receiver only occurs at the positive direction of vector eccentricity ~ r when adopting eccentric tube receiver as the tube receiver for parabolic trough concentrator system, and the larger magnitude of vector eccentricity is, the greater reduction of thermal stresses is. However, the manufacturing cost will increase with the magnitude of vector eccentricity increasing. The eccentric tube receiver should employ an optimum magnitude of eccentricity to minimize the thermal stresses and prevent the failure of tube receiver while not incurring excessive manufacturing cost.
320
160
Concentric Eccentric θ
120
Concentric Eccentric
280
Thermal Stress (MPa)
Effective Stress MPa
Concentric Eccentric
280
Thermal Stress (MPa)
circumference (the h is between 180° and 360°) where the peak temperatures of both the concentric and eccentric tube receivers are found, the temperature gradients of concentric tube receiver are higher than those of eccentric tube receiver which can lead to the higher thermal stresses Ifran and Chapman (2009, 2010), the cause of this phenomenon should be attributed to the thermal capacity increase on the bottom section of tube receiver due to the wall thickness increase on this section. The Von-Mises thermal stress fields along the internal circumference at the outlet section for both the concentric and eccentric tube receivers are presented in Fig. 5. The peak thermal stress values of the two profiles are both found at h = 270° where the peak temperature values are also located at. Attributed to the lower temperature gradients and intensity strengthen on the bottom half section of tube receiver, the peak thermal stress value of the eccentric tube receiver which is only 80.7 MPa is much lower compared to that of the concentric tube receiver which is 137.01 MPa. Therefore, adopting eccentric tube receiver as the tube receiver for the parabolic trough concentrator system can reduce the Von-Mises thermal stresses effectively up to 41.1%, which means the eccentric tube receiver can meet the requirements of the new type receiver.
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80
40
240 ϕ
200 160 120 80
0 0
60
120
180
θ
240
300
360
o
Fig. 5. Thermal stress profiles along the internal circumference at the outlet section for both the concentric and eccentric tube receivers.
-90
-60
-30
0
30
60
90
Oriented Angle ϕ Fig. 7. Relationship between oriented angle variation and peak thermal stress values.
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F. Wang et al. / Solar Energy 84 (2010) 1809–1815
4.3. Effect of the oriented angle variation on the thermal stresses The effect of the oriented angle variation on the VonMises thermal stresses of eccentric tube receiver is also performed with a constant eccentric radius value (r = 3 mm). The eccentric tube receiver has symmetric property with the variation of oriented angle, therefore, instead of dealing with the whole oriented angle range, analyses of half range of the oriented angle can yield complete results. As seen from Fig. 7, the variation of oriented angle has a big impact on the thermal stresses of eccentric tube receiver. The peak thermal stress value of eccentric tube receiver is less than that of the concentric tube receiver only when the oriented angle varies between 0° and 90°. The eccentric tube receiver with 90° oriented angle has the lowest peak thermal stress value. Therefore, it is recommended to employ eccentric tube with 90° oriented angle and optimum eccentricity as the tube receiver for parabolic trough concentrator system to reduce the thermal stresses.
5. Conclusion Aiming at reducing the thermal stresses of tube receiver, the eccentric tube receiver is introduced in this investigation. The ray–thermal–structural sequential coupled numerical analyses are adopted to obtain the concentrated heat flux distributions, temperature distributions and thermal stress fields of both the eccentric and concentric tube receivers. The fitting function method is introduced for the calculated heat flux distribution transformation from the Monte-Carlo ray tracing model to the CFD analysis model, and the fitted function curves can match the calculated heat flux distribution well with high precision. The sequential coupled numerical analysis results indicate that adopting eccentric tube as the tube receiver for parabolic trough concentrator system can reduce the Von-Mises thermal stress effectively up to 41.1%. The way how the variation of eccentricity and oriented angle affect the thermal stresses of eccentric tube receiver are also investigated with the objective to give instructions to the designer of eccentric tube receiver. When adopting eccentric tube receiver, the thermal stress reduction of tube receiver only occurs at the positive direction of vector eccentricity, and the larger magnitude of vector eccentricity is, the greater reduction of thermal stresses is. The oriented angle has a big impact on the thermal stresses of eccentric tube receiver. The thermal stress reduction of tube receiver only occurs when the oriented angle is between 0° and 90°. Therefore, employing eccentric tube receiver with optimum eccentricity and oriented angle for parabolic trough concentrator system can reduce the thermal stress and enhance the reliability of tube receiver effectively.
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