Transient characteristics of a parabolic trough direct-steam-generation process

Accepted Manuscript Transient characteristics of a parabolic trough direct-steam-generation process

Lu Li, Jie Sun, Yinshi Li, Yaling He, Haojie Xu PII:

S0960-1481(18)31497-6

DOI:

10.1016/j.renene.2018.12.058

Reference:

RENE 10933

To appear in:

Renewable Energy

Received Date:

06 August 2018

Accepted Date:

13 December 2018

Please cite this article as: Lu Li, Jie Sun, Yinshi Li, Yaling He, Haojie Xu, Transient characteristics of a parabolic trough direct-steam-generation process, Renewable Energy (2018), doi: 10.1016/j. renene.2018.12.058

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ACCEPTED MANUSCRIPT

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Transient characteristics of a parabolic trough direct-steam-

2

generation process

3

Lu LI1, Jie SUN2*, Yinshi LI1, Yaling HE1, Haojie XU1

4 5

1Key

Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

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2School

8

Abstract

of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

9

Solar-powered direct steam generation (DSG) is attractive for power generation

10

and industrial utilization due to the combination of renewable-energy source and clean

11

energy carrier. An improved SIMPLE algorithm ensuring the dual roles of pressure

12

acting on velocity and density fields is developed to realize thermo-hydraulic

13

completely-coupled modeling of a typical DSG loop with transient phase-change and

14

multiple flow-patterns. The excitation-response characteristics of the loop were

15

investigated under various step-variations of direct normal irradiance (DNI), inlet mass

16

flowrate (min) and inlet temperature (tin). Increasing DNI (decreasing min) is found to

17

narrow the preheating-evaporation regions and expand the superheating region, and

18

vice versa. While under step-variations of tin, the evaporation region almost remains

19

unchanged (about 403 m). The water slides to a lower temperature faster than climbs to

20

a higher one under variations of DNI (up to 670s vs. 2960s) and min (up to 1184s vs.

21

4420s), simultaneously the outlet temperature (tout) staying a monotonical response-

22

trend. However, under tin variations, tout holds a higher-order trait. The response of both



Authors to whom correspondence should be addressed. Electronic mails: [email protected] (JS), [email protected] (YSL)

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ACCEPTED MANUSCRIPT 23

pressure and velocity are tightly coupled and always hold higher-order trait. The

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response time of the total mass in the loop is almost 2.5 to 5.5 times as fast as tout.

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Keywords: Solar energy; Concentrating solar power (CSP); Direct steam generation

26

(DSG); Transient characteristics; SIMPLE algorithm

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1. Introduction

29

Parabolic-trough-collector (PTC) solar-harvesting project occupies the largest

30

commercial share comparing to the other existing concentrating solar power (CSP)

31

technologies. As a widely-employed heat transfer fluid (HTF) in the PTC CSP plant,

32

synthetic oil holds unsatisfactory performance in environmental protection and

33

normally operates below 400 oC, which is the temperature limitation hinders further

34

improvement of Rankine efficiency [1, 2]. One of a promising alternative solution is

35

directly using water as HTF to produce desired steam, namely the direct steam

36

generation (DSG) technology [3]. The solar-powered PTC-DSG technology is

37

attractive and promising due to the optimal combination of renewable-energy source

38

and clean energy carrier. That it is able to be implemented without intermediate heat

39

exchanger will simplify the system to both reduce maintenance program and further

40

save investment cost [4, 5]. Unlike the solar-powered vapor generation at the surface

41

of porous structure using for water purification [6, 7], the PTC directly-produced steam

42

in the solar field can be used on a large scale for some industrial and civil scenarios

43

without additional processing [8], such as drying, dehydration, sterilization, cleaning,

44

food, textile [9, 10]. In the meanwhile, the technology can also be incorporated into

45

other energy-based system to improve economic performance and application

46

flexibility [11, 12]. Based on steady model, a fully-coupled multi-level analytical

47

methodology for CSP system was constructed in our previous works to address the

48

optical-hydraulic-thermal-elastic synergistic issue and good performance was acquired 3

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[13]. At the same time, the system thermodynamic performance and the receiver

50

thermal load and stress was also conducted [14, 15].

51

Nevertheless, the DSG technology has been facing challenges of stability and

52

controllability. On the one hand, the weather conditions are erratic and beyond control.

53

On the other hand, along the DSG loop there exist different flow regions, i.e. the

54

preheating, evaporation and superheating regions, where inside the density presents

55

large gradients in space and change-rate in timeline. The flow boiling process is

56

vulnerable to external variations of weather conditions. Therefore, the flow stability is

57

no guarantee. In order to improve the stability, thermal energy storage is currently the

58

best choice [16]. As for the controllability, it is necessary to primarily explore the

59

transient characteristics of the loop and further to develop reasonable control schemes

60

for the whole system [17, 18]. The dynamic maintenance and operation mode is critical

61

and needs improvement [19, 20]. In short, transient characteristic research of DSG

62

technology is pressing. Currently, the main difficulty of simulation still lies in transient

63

evaporation flow. There are various one-dimensional two-phase flow models for the

64

selection, including homogenous equilibrium model, drift flux model and two-fluid

65

model [21]. Depending on commercial software, the models have been used for the

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transient thermo-hydraulic research of DSG systems, such as ATHLET [22], RELAP5

67

[23] and Dymola/Modelica [24]. Considering the length of a complete DSG loop

68

normally over hundreds of meters long, the complicated two-phase flow model will be

69

highly time-consuming to implement dynamic investigations. So the homogenous 4

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equilibrium model is still acceptable for the transient research of DSG system. Besides,

71

a reasonable solution arrangement is required to avoid low resolution or solving failure

72

problems induced by the coexistence of multiple flow regions in a loop. Bonilla et al.

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[25, 26] developed finite volume method (FVM) with moving boundary method.

74

However, the high-frequency chattering issue which is the inherent defect of the method

75

requires smooth interpolation of thermodynamic properties to overcome. Feldhoff et al.

76

[27, 28] also by the means of distribution parameter model with moving boundary

77

method investigated the transient once-through loop problems. However, the transport

78

model is based on static momentum balance and constant property hypothesis, which

79

fails to capture the detailed information during the phase-change process. Guo et al.

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[29, 30] constructed a nonlinear distribution parameter model to study the dynamic

81

behaviors of DSG system. However, the reduced momentum equation based on an

82

empirical correlation of pressure and mass flowrate can be only used for some special

83

occasions. The classical Laplace transform is hardly to directly acquire the transfer

84

function [31, 32]. The SIMPLE algorithm based on FVM is classical to solve the

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incompressible Navier-Stokes equations by introducing pressure correction equation

86

[33, 34]. Whereas, phase-change occurs in the transient process, the density rendering

87

large gradient is highly sensitive to the pressure variation and just modifying the

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velocity field with pressure correction will fail to solve the problem.

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Considering the shortcomings of the existing model or method, the present work

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builds a completely-coupled thermo-hydraulic modeling of DSG loop with an improved 5

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SIMPLE algorithm by adding pressure-density correction term to keep the dual roles

92

of pressure acting on velocity field by momentum equation and density field by the

93

equation of state. The research on the excitation-response characteristics of DSG loop

94

under various step-variations of direct normal irradiance (DNI), inlet mass flowrate (min)

95

and inlet temperature (tin) has been carried out. The results demonstrate good

96

performance for a 600 m once-through DSG loop. The temporal-spatial distributions of

97

some key thermo-hydraulic parameters are acquired completely. Meantime, the

98

dynamic distributions of the three flow regions are obtained.

99 100

2. Modeling and methods

101

A number of PTCs consisting of the evacuated tubes and parabolic reflectors

102

constitute a parabolic trough loop (see Fig. 1). In the energy capturing process, the

103

parabolic trough reflector concentrate the solar rays on the evacuated tube to heat the

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HTF which flows through the loop and reaches the desired state. In order to reduce the

105

thermal loss by radiation and convection to the ambient, the receiver tube is covered

106

with selective coating material and the glass tube further contributes to maintaining

107

vacuum layer. For PTC-DSG loop, water is directly adopted as HTF and heated to the

108

desired superheated state. According to the state of water, the loop can be divided into

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preheating, evaporation and superheating regions. A complete mathematical

110

description of thermohydraulic problem consists of the general conservative equation

111

and the constitutive relationship. For a single typical DSG loop, there exist multiple 6

ACCEPTED MANUSCRIPT 112

flow regions at the same time, which requires different flow and heat transfer models.

113

In this work, the single-phase model is chosen for the preheating and superheating

114

regions and the two-phase homogenous equilibrium model for the evaporation region.

115 116

2.1 Mathematical model

117

For a PTC, the net energy gain is the total incident solar energy minus the total

118

energy loss including geometrical, optical and thermal losses. The net energy gain can

119

be calculated as [26]:

120

Qg  Aa  IAM opt  DNI  cos   Qth,loss

121

where Aa is the solar collector aperture area,  is the incident angle, DNI indicates the

122

direct normal irradiation. opt is the optical efficiency indicating the losses due to

123

reflectivity, transmittance, absorptivity, etc. With the one-axis tracking technique of

124

PTCs, the solar vector not perpendicular to the collector aperture leads to geometrical

125

loss which can be modified with incidence angle modifier (IAM). When 0    80 ,

126

IAM for LS-3 PTC is proposed as [26]:

127

IAM  1  2.23073e 4    1.1e 4   2  3.18596e 6   3  4.85509e 8   4

(1)

(2)

128

The thermal loss (due to convection and radiation to the ambient) strongly

129

correlated with the wall temperature of the receiver tube (tw) can be reduced with a

130

model as [26, 28]:

131

Qth,loss  (0.16155tw  6.4407e 9tw4 )l

7

(3)

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Regardless of the axial conduction, the transient heat transfer model of the receiver tube

133

is divided into two parts, as follows:

tw2 2πkr l (tw2  tw1 ) l  Qg   ln(r2 / r1 )

(4)

tw1 2πkr l (tw2  tw1 ) l  2πr1h0-1l (tw1  tf )  ln(r2 / r1 )

(5)

 r cr Ar

134

 r cr Ar

135 136

where tw1 is the inner wall temperature of receiver tube and tw2 is the outer. The energy

137

is transferred by convection to the HTF and the obtained energy in unit volume is

138

calculated as [28]:

qs 

139

hAh (tw1  tf ) V

(6)

140

where h is the heat transfer coefficient, Ah is the heat transfer area and V is the control

141

volume.

142

As for the HTF, the general one-dimensional transient descriptions of the transport

143

process including mass, momentum and energy governing equations are as follows [35]:

144 145 146 147

  u  0  z  u  uu p   f  z z  h  uh p    qs  z 

(7) (8) (9)

where f is the frictional force term, qs is the net source term calculated with Eq.6.

148

The other group of closure equations are mainly the flow and heat transfer relations.

149

The present work adopts Gnielinski equation and Blasius equation for the single-phase

150

heat transfer and pressure loss, and Gungor-Winterton correlation and Friedel

151

correlation for the evaporation process. See reference [36] for more details. In addition, 8

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the thermo-physical properties of working fluid (water/steam) are based on the

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International Association for the Properties of Water and Steam (IAPWS) formulation

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[37].

155

2.2 Numerical method

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The closely-coupled relation of the transport variables determines that the solution

157

must be implemented elaborately. Based on FVM, the spatial discretization is

158

conducted using staggered grid. In accordance with the mass-energy equations

159

integrated within the central control volumes and the momentum equation within the

160

staggered control volumes, the independent variables selected, including the specific

161

enthalpy (h), pressure (p) and wall temperature (tw), are calculated in the cell center,

162

and velocity (u) in the cell face (see Fig. 2). The other fluid properties are the function

163

of p and h. When the required variable is not defined at the cell center (or cell face), an

164

arithmetic mean value is used in place. All the governing equations are discretized with

165

semi-implicit format. The transient terms are dealt with backward Euler scheme and the

166

convection terms in QUICK (quadratic upstream interpolation for convective

167

kinematics) scheme.

168 169

Taking the momentum governing equation (Eq.8) for an example, the transient term is discretized as:  u (  u )  (  u )    

170 171

and the convection term as:

9

(10)

ACCEPTED MANUSCRIPT

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 uu 1 * * =   u i  1 ui  1    u i  1 ui  1  2 2  2 2 z i z 

173

where the superscript * represents the previous iteration value. The QUICK scheme is

174

given as [33]:

(11)

175

3 3 1 ui  1  ui  ui 1  ui 1 2 4 8 8

176

The source term, i.e. the frictional force in the momentum governing equation, requires

177

linearization to increase the robustness. The general relationship between the frictional

178

loss term and velocity can be formulated as f  f (u 2 ) , and a linear discretization

179

technique is implemented as:

fi* fi  * ui ui

180 181 182

184

(13)

The discrete equation of momentum is finally expressed as:

ai ui 

a

u  bi  (

nb nb

nb( i )

183

(12)

p )i z

(14)

According to the SIMPLE algorithm, the velocity correction arising from pressure variation is derived by means of Eq.14, as:

185

ui  dei ( pi  pi1 )

186

where dei is equal to 1 (ai z ) . Directly bringing Eq. 15 into the discrete equation of

187

mass to establish a pressure-correction equation is out of question in the incompressible

188

flow problems. However, when there exists transient phase-change process, the density

189

renders large gradient and is highly sensitive to the pressure variation. Therefore, the

190

pressure correction equation needs improvement. The dual roles of pressure acting on

191

velocity field by momentum equation and density field by the equation of state accounts 10

(15)

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for dual corrections of velocity and density to guarantee the mass conservation. The

193

density correction regarding pressure variation is derived by means of the equation of

194

state, as [33]:

i 

195

 p

pi

(16)

i ,h

196

Introducing the two correction and ignoring the second order correction term, the mass

197

flux (  u ) is corrected as: *   u     u    *u   u*

198 199

(17)

Combine with Eqs. 15~17 to discretize the continuity governing equation, as:

200

i*  i  i0 ((  u )*i 1  (  u )i 1 )  ((  u )*i  (  u )i )  0  z

201

Rearrange the equations and a sound equation system of pressure-correction is being

202

established. The type of pressure-correction equation is elliptic and the solver belongs

203

to the boundary value problems. Here, the fundamental boundary conditions are the

204

inlet velocity and the outlet pressure. The corresponding equivalent mathematical

205

descriptions are

(18)

p   0.  0 and pout z in

206

The discretization of energy equation is similar to the momentum equation and the

207

primary difference lies in the source term, which is connected with the wall temperature.

208

It is not difficult to perform semi-implicit scheme for Eqs. 4~5 to update the wall

209

temperature and further to update the energy source term with Eq. 6. Besides, the inlet

210

specific enthalpy is necessary for an inlet boundary. The spatial-space steps are 2s and

211

5m, respectively. The algorithm with semi-implicit feature implies that the calculation 11

ACCEPTED MANUSCRIPT 212

can be conducted without a fine time step. Considering the length of a DSG loop

213

adopting an excessively fine space-grid will hamper the computational efficiency.

214

Hoffmann et al. [22] had made a test calculation with a finer resolution in ATHLET

215

and shown no differences in the results.

216

The solving procedure is shown in Fig. 3. For a given time step, the outer iteration

217

is used for updating the specific enthalpy and wall temperature until convergence, and

218

the inner iteration for updating pressure and velocity. The solver layout of energy

219

update ahead of momentum and mass can achieve efficient iteration. Notably, an

220

appropriate relaxing factor (0.3) is necessary for the independent variables during the

221

iterative process. Once there is an updated correction of pressure or specific enthalpy,

222

the thermo-physical properties also get updated simultaneously.

223 224

2.3 Model validation

225

The present model is primarily validated by experimental data available from the

226

DISS project [28, 38]. The configuration of the facility is shown in Fig. 4 and the

227

detailed structural parameters are listed in Table 1. The DSG loop of the CSP system is

228

about 1000 m long including 16 modules. A series of dynamic tests on June 18, 2013

229

is performed when the average mass flowrate is 1.91 kg s-1 and DNI around 950 W m-

230

2.

231

locations within the evaporation region accompanied by DNI variation. At 13.0~13.25

232

h, 13.3~13.55 h and 13.6~14.14 h, PTCs 2~7, 1A~1B and OA~OB were defocused,

The results in Fig. 5 show the response of fluid temperature at various monitoring

12

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respectively. The red, green and blue colors are the outlet temperature of PTCs 12, 1

234

and OA, respectively. The maximum deviation of the temperature value is less than

235

6.5%. Another transient validation is within the superheating region when PTC 12 was

236

defocused and refocused at 13.43 h and 13.66 h, respectively. The facility was operated

237

under an average inlet mass flowrate of 1.32 kg s-1, DNI of 870 W m-2 and inlet

238

temperature of 270 oC on July 17, 2013. According to the results in Fig. 6, the maximum

239

deviation of the temperature is less than 1.5%. The downhill and uphill time responses

240

are 360 s and 430 s, respectively, which are well consistent with the experiment data.

241

It is seen that the above-mentioned satisfying agreements strongly demonstrate the

242

correctness and reliability of the present model and method.

243

3. Results and discussion

244

For a practical operating CSP plant, the meteorological conditions are the main

245

uncontrollable factors, among which DNI holds dominance over the output

246

performance of solar field. To guarantee the stability over a period of time, the effective

247

regulation is necessary. The most important tunable variables for a DSG loop in once-

248

through mode is min or tin. The following investigates the transient response of thermo-

249

hydraulic parameters under various step-variations of DNI, min and tin based on a 600

250

m once-through loop which is made up by 12 collectors (LS-3 type). Some related

251

parameters are shown in Table 2. The predesigned states include DNI being 850 Wm-2,

252

tin being 240 oC, min being 0.8 kg s-1 and outlet pressure (pout) being 60 bar.

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3.1 Transient characteristics with DNI change

255

The DSG loop is operated under predesigned condition before 100 s. Afterwards,

256

DNI produces step-changing with amplitudes of ±10%, ±20% and ±30%. The transient

257

distributions of flow region and steam mass quality are shown in Fig. 7. Within the

258

initial 100 s, the starting/ending position of evaporation region appears at 50 m/453 m.

259

In the cases of increasing DNI by 10%, 20% and 30%, the starting/ending positions are

260

brought forward to 47 m/412 m, 43 m/378 m, and 39 m/349 m, respectively. For the

261

decreasing DNI cases by 10% and 20%, the starting/ending positions are postponed to

262

54 m/504 m and 62 m /568 m, respectively. Notably, in the decreasing DNI case by

263

30%, the starting position is found at 69 m however the ending position is not seen

264

because there is wet steam at the loop outlet. Note that normally a certain degree of

265

superheating of the steam is necessarily guaranteed for the power generation and

266

industrial processing for safety reasons. Therefore, both accurate prediction and in-time

267

monitoring of the steam mass quality are crucial to the practical operation. It is

268

generally observed that increasing DNI narrows the preheating and evaporation regions

269

and simultaneously expands the superheating region, and vice versa. Before and after

270

the DNI change, the evaporation region occupies the largest portion, and the coverage

271

of superheating region holds the largest relative change-rate among the flow regions.

272

During the transient process, the starting and ending positions of evaporation region

273

shifting with time (see solid lines in Fig. 7) can be used to characterize the stability of

274

upstream flow regions. Taking the result of -10% DNI change case in Fig. 7 for an 14

ACCEPTED MANUSCRIPT 275

example, the starting position stabilizes at about 282 s (182 s after the DNI step-

276

changing) meaning the disturbance on the preheating region is significantly attenuated.

277

Similarly, the ending position stabilizes after about 924 s. It is found that no matter

278

increasing or decreasing DNI, it is the preheating region before the evaporation region

279

that settles the final distribution after the perturbation.

280

The results in Fig. 8 are the time-varying conditions of some major thermo-

281

hydraulic parameters, including the inlet pressure (pin), outlet temperature (tout), outlet

282

velocity (uout), outlet density (ρout), outlet mass flowrate (mout) and the total mass (M)

283

in the whole loop. The response time is defined as the time difference between the

284

moment when the disturbance is exerted and the moment when the relative deviation

285

of the change-rate of the observed parameter is found below 10-5. Corresponding to the

286

DNI change cases by 10%/-10%, 20%/-20% and 30%/-30%, the response times of tout

287

are 2402 s/1846 s, 2744 s/1466 s and 2960 s/670 s, respectively (default sequence of

288

the following data unless otherwise specified). It is found that all the response times of

289

DNI increasing cases are obviously longer than the corresponding decreasing cases.

290

Meanwhile, the working fluid slides to a lower temperature state much faster than

291

climbs to a higher temperature state. Unlike the response trend of tout, both pin and uout

292

show non-monotonic response characteristics. Take uout for an example, the transient

293

response curve can be divided into three stages. In the early stage of the response, uout

294

increases/decreases to a local maximum/minimum at about 160~190 s (specifically 19.4

295

ms-1/16.8 ms-1, 20.7 ms-1/15.3 ms-1 and 21.8 ms-1/13.7 ms-1). Afterwards, uout 15

ACCEPTED MANUSCRIPT 296

decreases/increases to another local minimum/maximum at about 530~550 s

297

(specifically, 18.5 ms-1/17.7 ms-1, 18.9 ms-1/17 ms-1 and 19.1 ms-1/16.1 ms-1). Finally,

298

uout gradually increases/decreases to the steady state.

299

In fact, it is the varying supply of solar energy in the first stage drives the change

300

of evaporation behavior, leading to the fluid volume in the DSG loop

301

expanding/shrinking quickly and becoming deviated from the initial balance capacity.

302

Therefore, the volumetric flowrate (proportional to velocity) increases/decreases

303

sharply. Subsequently, the redistribution of the mass and the momentum along the loop

304

weakens the superposition of the volumetric variation in the second stage, where the

305

evaporation effect is however still stronger than the last stage. The duration time of the

306

first two stages is about 410~460 s when the preheating-evaporation regions just

307

undergo major adjustments and the starting and ending positions change rapidly (see

308

Fig. 7). The response tendency of pin basically consistent with uout clearly suggests the

309

inherently tight coupling between these two parameters (see Fig. 8). It is seen that after

310

DNI increasing, mout becomes greater than 0.8 kg s-1 with M reduced and mounts up to

311

a maximum of 0.86 kg s-1/0.91 kg s-1/0.96 kg s-1 at about 175 s. When DNI decreases,

312

mout and M evolve towards the opposite tendencies. In addition, M in the loop adjusts

313

quickly and the response time varies between 828 s and 924 s, which just keeps pace

314

with the time when the starting and ending positions of evaporation region nearly reach

315

stable (see Fig. 7).

16

ACCEPTED MANUSCRIPT 316

To further illustrate the transient characteristics of the transport processes, the

317

temperature and velocity distributions after DNI step-changing of 20%/-20% are

318

respectively shown in Figs. 9~10. According to the temperature distribution, the

319

average temperature gradient along the loop monotonically changes from 0.7 oC m-1 to

320

0.9 oC m-1/0.6 oC m-1 in the preheating region and from 1.3 oC m-1 to 1.7 oC m-1/0.7 oC

321

m-1 in the superheating region. No matter how DNI changes, the temperature in the

322

superheating region shows the largest fluctuations comparing to the preheating and

323

evaporation regions. It can be inferred that stress fatigue of the receiver tube induced

324

by thermal fluctuation in superheating region is more serious and should be paid more

325

attention on. The evaporation region is more like a buffer connecting the other two. As

326

for the velocity distribution, the initial velocity gradients in the three regions are 7.0×10-

327

4

328

1/5.5×10-4 s-1,

329

stable conditions. In the first two stages of the velocity distribution, the velocity

330

gradients in the superheating region shows large fluctuations.

s-1, 2.5×10-2 s-1 and 5.1×10-2 s-1, respectively, and the values change to 8.6×10-4 s3.0×10-2 s-1/2.1×10-2 s-1 and 5.9×10-2 s-1/4.0×10-2 s-1, respectively, under

331 332 333

3.2 Transient characteristics with mass flowrate change Adjusting the inlet mass flowrate is a common resort to stabilize the desired outlet

334

parameters. Step-variations of min are deployed with variation amplitudes of ±10%, ±20%

335

and ±30%. The distributions of flow region and steam mass quality are shown in Fig.

336

11. When raising min, the preheating/evaporation region stabilizes at 210 s/554 s, 288 17

ACCEPTED MANUSCRIPT 337

s/842 s and 326 s/902 s. The steady starting and ending positions of evaporation region

338

are 57 m/500 m, 62 m/545 m and 67 m/591 m, respectively. When reducing min, the

339

stabilizing times are 206 s/678 s, 152 s/696 s and 134 s/694 s, and the starting and

340

ending positions are 47 m/409 m, 42 m/364 m and 37 m/319 m. The time-varying

341

distributions of flow regions reflect the heat-driven capacity. For example, after

342

increasing min, the starting position of evaporation region shifts toward the downstream，

343

which implies that more energy (more concentrated area) is required to achieve the

344

same temperature level of working fluid.

345

The response times of tout shown in Fig. 12 are 1810 s/2760 s, 1496 s/3560 s and

346

1184 s/4420 s, respectively. It is seen that the response process take more/less time to

347

reach a higher/lower temperature level when decreasing/increasing min. The transient

348

characteristics of pressure and velocity are obviously different from the varying DNI

349

conditions. The response tendency consists of two stages. When increasing/decreasing

350

min, uout (pin) quickly increases/decreases to a maximum/minimum at 521 s/590 s, 464

351

s/622 s and 446 s/639 s. (The time for pin is respectively 363 s/540 s, 325 s/590 s and

352

318 s/611 s). Then the parameters gradually downgrade/upgrade to a stable state. In the

353

first stage, the step-variation of min in preference to mout incurs the

354

increasing/decreasing of both M and the coverage of evaporation region, at the same

355

time the equivalent amount of evaporation produced. Therefore, the superposition of

356

the volumetric flowrate is weakened/strengthened and uout changes accordingly. The

357

temperature and velocity distributions after min step-changing with ±20% are 18

ACCEPTED MANUSCRIPT 358

respectively shown in Figs. 13~14. The average temperature gradient along the loop

359

changes from 0.7 oC m-1 to 0.6 oC m-1/0.8 oC m-1 in preheating region and from 1.3 oC

360

m-1 to 1.0 oC m-1/1.8 oC m-1 in superheating region. As for the velocity gradients in the

361

three region, changes are respectively from 7.0×10-4 s-1, 2.5×10-2 s-1 and 5.1×10-2 s-1 to

362

6.9×10-4 s-1/6.9×10-4 s-1, 2.6×10-2 s-1/2.5×10-2 s-1 and 5.1×10-2 s-1/4.8×10-2 s-1.

363 364

3.3 Transient characteristics with inlet temperature change The step-variations of tin are implemented with ranges ±10 oC, ±20 oC and ±30

365 366

oC.

367

According to the results, after the step-increasing of tin, evaporation region enlarges

368

rapidly over a short time and reaches a maximum length at about 410 s. At the same

369

time the preheating-superheating regions shrink to a minimum length. Afterwards, the

370

evaporation region retreats and the superheating region enlarges. The trends are

371

contrary to that under the step-decreasing conditions. When increasing/decreasing tin,

372

the evaporation regions stabilize at about 632 s/928 s, 580 s/1044 s and 500 s/1366 s,

373

respectively. Comparing with all the results, when the transport process stabilizes, the

374

length of evaporation region almost remains unchanged (about 403 m).

The distributions of flow regions and steam mass quality are shown in Fig. 15.

375

The variations of thermo-hydraulic parameters are shown in Fig. 16. Here the

376

response of tout is no longer a monotonic curve but holds higher-order characteristic.

377

Before the evaporation region becomes immobile, tout decreased/increased to a local

378

extremum. This is because of sudden disturbance of tin influencing the evaporation 19

ACCEPTED MANUSCRIPT 379

action and further changing the downstream mass /volumetric flowrate and the

380

evaporation length (see uout and mout in Fig. 16). Ultimately, the superheating degree of

381

steam is reduced. Afterwards, the disturbance spreads and tout gradually upgrades

382

/downgrades to stable state. The response time of tout is 2392 s/2500 s, 2482 s/2658 s

383

and 2500 s/2742 s, respectively. The parameters (including uout, ρout, mout and pin in Fig.

384

16) reach stable more rapidly at the same time a bigger fluctuation when increasing tin.

385

Increasing /decreasing tin, tout increases /decreases by 19.4 oC/-18.7 oC, 39.3 oC/-37.1 oC

386

and 59.7 oC/-54.9 oC, respectively. M in the loop still keeps the inverse trends against

387

tout. The significant adjustments of uout and mout in early stage influence the obtaining

388

heat per unit mass so that the temperature gradient along the loop changes accordingly.

389

The temperature and velocity distribution in Figs. 17~18 can give a glimpse of the

390

tendency. Besides, the temperature and velocity distributions present special trait,

391

namely, the average temperature/velocity growth gradients at stable state have no

392

change comparing with the initial state. The time-varying process just makes a spatial

393

translation for the evaporation region and the parameters in preheating-superheating

394

regions still keep the original gradient.

395 396

4. Conclusions

397

The present paper investigated the transient characteristics of solar-powered DSG

398

process. Based on a typical 600 m long once-through PTC DSG loop, a thermo-

399

hydraulic completely-coupled model is established to address the transient steam20

ACCEPTED MANUSCRIPT 400

generating problem. By further taking into account the effect of pressure on density,

401

the method improves the pressure correction equation by adding pressure-density

402

correction term to keep the dual roles of pressure acting on velocity and density fields.

403

The treatment overcomes the numerical difficulties, i.e. the coexistence of multiple

404

flow regions and transient evaporation action. The model validation and numerical

405

investigation have proved good coupling performance while acquiring detailed

406

information at the same time during transient phase-change process. The transient

407

characteristics of thermo-hydraulic parameters in the DSG loop have been investigated

408

under various step-variations of DNI, min and tin. The step-disturbance induces

409

redistribution of the preheating-evaporation-superheating regions and the evaporation

410

action exerts significant influence on the adjustments of mass and momentum. Some

411

important conclusions are summarized as:

412

1) Under step-variations of DNI and min, increasing DNI (decreasing min) narrows the

413

preheating and evaporation regions and simultaneously expands the superheating

414

region, and vice versa. While under step-variations of tin, the length of evaporation

415

region almost remains unchanged.

416

2) Comparing the time response of tout, the working fluid slides to a lower temperature

417

state much faster than climbs to a higher one under step-variations of DNI and min.

418

Contrary to the monotonical response-trend of tout, the response curve under step-

419

variations of tin holds higher-order trait. Primarily because of the change of evaporation

420

action, the responses of both pressure and velocity are tightly coupled and always hold 21

ACCEPTED MANUSCRIPT 421

higher-order trait. The outward flowrate rapidly responds to the step-disturbances to

422

adjust the containing mass in the whole loop. The total mass in the complete loop

423

increases with DNI decreasing, min increasing and tin decreasing, and vice versa.

424

3) The temperature and velocity gradients in the preheating/superheating region make

425

significant adjustments under step-variations of DNI and min, while under step-

426

variations of tin, the gradients show almost no change comparing to the initial state.

427

4) Regardless of the step-variation types, the working fluid temperature in the

428

superheating region holds the largest fluctuation comparing to the preheating and

429

evaporation regions. It can be concluded that thermal-load and thermal-stress fatigue of

430

the receiver tube in superheating region should be paid more attention on.

431 432

It should be pointed out that all the present pioneer work is preliminary and further transient studies on DSG systems are in progress.

433 434

Acknowledgements

435

This work was supported by the National Natural Science Foundation of China

436

(51776156, 51776196), Key Project of National Natural Science Foundation of China

437

(51436007), the National Basic Research Program of China (973 Program)

438

(2015CB251505) and the Fundamental Research Funds for the Central Universities

439

(xjj2018195). The authors are grateful to Dr. Tobias Hirsch at German Aerospace

440

Center (DLR) for his helpful technical supports.

441 22

ACCEPTED MANUSCRIPT Nomenclature Abbreviations CSP

concentrating solar power

DSG

direct steam generation

PTC

parabolic trough collector

HTF

heat transfer fluid

FVM

finite volume method

QUICK quadratic upstream interpolation for convective kinematics scheme Variables A

area (m2)

Aa

the aperture area of the solar collector (m2)

Ah

heat transfer area (m2)

a, b

coefficients in discretization equation

c

specific heat capacity (J kg-1 K-1)

DNI

direct normal irradiance (W m-2)

f

friction force term (pa m-1)

h

specific enthalpy (J kg-1); heat transfer coefficient (W m-2 K-1)

IAM

incidence angle modifier (-)

k

conduction coefficient (W m-1 K-1)

l

length (m)

m

mass flowrate (kg s-1) 23

ACCEPTED MANUSCRIPT M

total mass in a loop (kg)

p

pressure (pa)

Qg

the effectively absorbed thermal power (W)

Qth,loss

the net thermal loss power (W)

qs

heat source term (W m-3)

r

radius (m)

t

temperature (oC)

u

velocity (m s-1)

V

volume (m3)

x

steam mass quality (-)

z

coordinate along the collector loop

opt

the optical efficiency (-)



density (kg m-3)



time (s)



incident angle (o)

Subscripts 1

internal wall

2

outer wall

f

fluid

i

node number

in

inlet 24

ACCEPTED MANUSCRIPT nb

neighboring node number

out

outlet

r

receiver tube

w

tube wall

442 443

25

ACCEPTED MANUSCRIPT 444

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445

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446

Advanced CST teaching materials. enerMENA, 2011.

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thermal power plants with direct steam generation compared with HTF plants. J

449

Sol Energy Eng-Trans ASME 2010; 132:041001-1.

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[13]Li L, Sun J, Li Y. Prospective fully-coupled multi-level analytical methodology for

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[15]Li L, Sun J, Li Y. Thermal load and bending analysis of heat collection element of

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Engineering 2017; 127:1530–1542. 27

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temperature stability in a direct steam generation solar power plant. Solar Energy

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[19]Zarza E, Valenzuela L, León J, Weyers H-D, Eickhoff M, Eck M, et al. The DISS

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[20]Eck, M., Zarza E. Assessment of operation modes for direct solar steam generation

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computer code ATHLET. Kerntechnik 2014;79:175-186.

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[23]Serrano-Aguilera J.J., Valenzuela L., Parras L. Thermal hydraulic RELAP5 model

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for a solar direct steam generation system based on parabolic trough collectors

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operating in once-through mode. Energy 2017; 133:796-807

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[24]Hirsch T, Steinmann W, Eck M. Simulation of transient two-phase flow in

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parabolic trough collectors using Modelica. In: Proceedings of the 4th international

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modelica conference; Hamburg, Gernamy; 2005; p. 403–12.

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[26]Bonilla J., Yebra Muñoz L J, et al. Modeling and simulation of two-phase flow

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evaporators for parabolic-trough solar thermal power plants. Catálogo (2013).

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[27]Feldhoff J.F., Hirsch T, Pitz-Paal R, Valenzuela L. Transient models and

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characteristics of once-through line focus systems. Energy Proc 2015; 69: 626–37.

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[28]Feldhoff J.F., Analysis of once-through boiler concepts in parabolic troughs,

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chapter 3, Dissertation RWTH Aachen / DLR Stuttgart, Reihe Energietechnik,

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Shaker Verlag (2016).

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[29]Guo S, Liu D, Chu Y, Chen X, Shen B, Xu C, et al. Real-time dynamic analysis

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for complete loop of direct steam generation solar trough collector. Energy

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Convers Manag 2016; 126: 573–80. 29

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[30]Guo S, Liu D, Chen X, et al. Model and control scheme for recirculation mode

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direct steam generation parabolic trough solar power plants. Applied Energy

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2017;202: 700-714.

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[31]Ogunnaike B. A., Ray W. H., Process Dynamics Modeling and Control, New York: Oxford Univ. Press (1994). [32]Valenzuela L, Zarza E, Berenguel M, Camacho EF. Direct steam generation in solar boilers. IEEE Control Syst Mag 2004; 24(2):15-29. [33]Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics, chapter 13, Springer (2016).

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[34]Moukalled F, Darwish M, Moukalled F, Darwish M. A unified formulation of the

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segregated class of algorithms for fluid flow at all speeds class of algorithms for

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fluid flow. Numerical Heat Transfer, Part B: Fundamentals. 2000; 37:103-139.

537

[35]Eck M, Hirsch T. Dynamics and control of parabolic trough collector loops with

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direct steam generation. Sol Energy 2007; 81(2):268-79. [36]John R. Thome, Engineering Data Book III, chapter 10 & 13, Wolverine Tube Inc., Lausanne, Switzerland (2010).

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[37]Wagner W, Kretzschmar H J. IAPWS industrial formulation 1997 for the

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thermodynamic properties of water and steam[J]. International Steam Tables:

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Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97,

544

2008: 7-150.

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ACCEPTED MANUSCRIPT 545

[38]Hoffmann A. Numerical and experimental investigation of transient two-phase

546

flow phenomena in concentrated solar power plants with direct steam generation,

547

chapter 4, RWTH Aachen (2017).

548

31

ACCEPTED MANUSCRIPT 549

Figure captions

550

Figure 1. Configuration and structure of PTC loop.

551

Figure 2. Grid arrangement.

552

Figure 3. Flowchart of program.

553

Figure 4. Diagram of the DISS test facility in once-through mode configuration (details

554

of PTC shown in table 1).

555

Figure 5. Temperature response when Collectors 2~7 focus at 13.0~13.25 h, coll.

556

1A~1B at 13.3~13.55 h, coll. OA~OB at 13.6~14.14 h, average mass flow rate 1.91

557

kgs-1, DNI around 950 Wm-2, June 18, 2013 at DISS test facility [28].

558

Figure 6. Outlet temperature changes with collector 12 defocused and refocused,

559

average inlet mass flow 1.32 kgs-1, DNI 870 Wm-2, inlet temperature of the loop 270

560

oC,

561

Figure 7. Distributions of flow region and steam mass quality after step-variations of

562

DNI.

563

Figure 8. Transient characteristics of major thermo-hydraulic parameters (including

564

outlet temperature tout, outlet velocity uout, inlet pressure pin, outlet density ρout, outlet

565

mass flowrate mout and the total mass M) after step-variations of DNI.

566

Figure 9. Temperature distribution after step-variations of DNI with (a) 20% and (b) -

567

20%.

568

Figure 10. Velocity distribution after step-variations of DNI with (a) 20% and (b) -20%.

July 17, 2013 at DISS test facility [28].

32

ACCEPTED MANUSCRIPT 569

Figure 11. Distributions of flow region and steam mass quality after step-variations of

570

min.

571

Figure 12. Transient responses of major thermo-hydraulic parameters (including tout,

572

uout, pin, ρout, mout and M) after step-variations of min.

573

Figure 13. Temperature distribution after step-variations of min with (a) 20% and (b) -

574

20%.

575

Figure 14 Velocity distribution after step-variations of min with (a) 20% and (b) -20%.

576

Figure 15. Distributions of flow-region and steam mass quality after step-variations of

577

tin.

578

Figure 16. Transient responses of major thermo-hydraulic parameters (including tout,

579

uout, pin, ρout, mout and M) after step-variations of tin.

580

Figure 17. Temperature distribution after step-variations of tin with (a) 20 oC and (b) -

581

20 oC.

582

Figure 18. Velocity distribution after step-variations of tin with (a) 20 oC and (b) -20 oC.

583

33

ACCEPTED MANUSCRIPT 584

Table captions

585

Table 1. Main configuration features at the DISS test facility [38]

586

Table2. Operation and configuration parameters [26, 28, 38].

587

34

ACCEPTED MANUSCRIPT 1

Figures

2 3 4

Figure 1. Configuration and structure of PTC loop

ACCEPTED MANUSCRIPT 5

6 7 8

Figure 2. Grid configuration.

ACCEPTED MANUSCRIPT

9 10 11

Figure 3. Flowchart of program.

ACCEPTED MANUSCRIPT

12 13

Figure 4. Diagram of the DISS test facility in once-through mode configuration

14

(details of PTC shown in table 1).

15

ACCEPTED MANUSCRIPT 180 160

Experiment data

tout,OA tout,1 tout,12

Present results

tf /oC

140 120 100 80 60 40 13.0

16

13.2

13.4

13.6

13.8

14.0

14.2

 /h

17

Figure 5. Temperature response when Collectors 2~7 focus at 13.0~13.25 h, coll.

18

1A~1B at 13.3~13.55 h, coll. OA~OB at 13.6~14.14 h, average mass flow rate 1.91

19

kgs-1, DNI around 950 Wm-2, June 18, 2013 at DISS test facility [24].

20

ACCEPTED MANUSCRIPT 460

tout /oC

440

420

Experiment data Present result

400

380 13.4

13.5

21

13.6

 /h

13.7

13.8

22

Figure 6. Outlet temperature changes with collector 12 defocused and refocused,

23

average inlet mass flow 1.32 kgs-1, DNI 870 Wm-2, inlet temperature of the loop 270

24 25

oC,

July 17, 2013 at DISS test facility [24].

ACCEPTED MANUSCRIPT

26 27

Figure 7. Distributions of flow region and steam mass quality after step-variations of

28

DNI.

29

ACCEPTED MANUSCRIPT 30

31 32

Figure 8. Transient characteristics of major thermo-hydraulic parameters (including

33

outlet temperature tout, outlet velocity uout, inlet pressure pin, outlet density ρout, outlet

34

mass flowrate mout and the total mass M) after step-variations of DNI.

35

ACCEPTED MANUSCRIPT

36 37

(a)

(b)

38

Figure 9. Temperature distribution after step-variations of DNI with (a) 20% and (b) -

39

20%.

40 41

(a)

(b)

42

Figure 10. Velocity distribution after step-variations of DNI with (a) 20% and (b) -

43

20%.

44

ACCEPTED MANUSCRIPT

45 46

Figure 11. Distributions of flow region and steam mass quality after step-variations of

47

min.

48

ACCEPTED MANUSCRIPT

49 50

Figure 12. Transient responses of major thermo-hydraulic parameters (including tout,

51

uout, pin, ρout, mout and M) after step-variations of min.

52

ACCEPTED MANUSCRIPT

53 54

(a)

(b)

55

Figure 13. Temperature distribution after step-variations of min with (a) 20% and (b) -

56

20%.

57 58 59 60

(a)

(b)

Figure 14 Velocity distribution after step-variations of min with (a) 20% and (b) -20%.

ACCEPTED MANUSCRIPT

61 62

Figure 15. Distributions of flow-region and steam mass quality after step-variations of

63

tin.

64

ACCEPTED MANUSCRIPT

65 66

Figure 16. Transient responses of major thermo-hydraulic parameters (including tout,

67

uout, pin, ρout, mout and M) after step-variations of tin.

68

ACCEPTED MANUSCRIPT

69 70

(a)

(b)

71

Figure 17. Temperature distribution after step-variations of tin with (a) 20 oC and (b) -

72

20 oC.

73 74

(a)

(b)

75

Figure 18. Velocity distribution after step-variations of tin with (a) 20 oC and (b) -20

76

oC.

77

ACCEPTED MANUSCRIPT 78

Tables

79 80

Table 1. Main configuration features at the DISS test facility [38]

Name OA OB 1A 1B 1 2 3 4 5 6 7 8 9 10 11 12 81 82

Collectors Aperture Module length width (Norminal) (m) (m) 4.6 100(96) 4.6 100(96) 5.76 100(96) 5.76 100(96) 5.76 50(48) 5.76 50(48) 5.76 50(48) 5.76 50(48) 5.76 50(48) 5.76 50(48) 5.76 50(48) 5.76 50(48) 5.76 25(24) 5.76 25(24) 5.76 50(48) 4.6 100(96)

Connection pipes Norminal optical efficiency 0.763 0.754 0.651 0.701 0.694 0.714 0.641 0.664 0.709 0.702 0.727 0.681 0.556 0.659 0.666 0.737

Name

Length (m)

Number of 90o bends

OA-OB OB-1A 1A-1B 1B-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12

9.1 18.2 2.5 49 11.5 11.5 11.5 11.5 11.5 11.5 10.2 17.7 16.5 10.2 34.4

10 12 4 19 8 8 8 8 8 8 8 10 10 8 15

ACCEPTED MANUSCRIPT 83

Table2. Operation and configuration parameters [26, 28, 38]. Quality Rated DNI (W m-2) Rated mass flow rate (kg s-1) Inlet temperature (oC) Outlet pressure (bar) Ambient temperature (oC) Collector area (m2) Total collector number (-) Conduction coefficient of receiver tube (W m-1 K-1) Density of receiver tube (kg m-3) Capacity of receiver tube (J kg-1 K-1) Inner/outer diameter of receiver tube (m) Optical efficiency (-) Roughness of the tube (m)

84

Value 850 0.8 240 60 25 288 12 38 7850 540 0.055/0.07 0.7 4.6  10-5

ACCEPTED MANUSCRIPT    

Method for completely-coupled transient model of direct steam generation loop Insight the excitation-response characteristics of direct steam generation loop Fluid slides to a lower temperature state much faster than climbs to a higher one Superheating region holds the largest temperature fluctuation and stress fatigue