Development and validation of a 1D model for turbocharger compressors under deep-surge operation

Accepted Manuscript Development and validation of a 1D model for turbocharger compressors under deep-surge operation

Vincenzo De Bellis, Rodolfo Bontempo PII:

S0360-5442(17)31714-0

DOI:

10.1016/j.energy.2017.10.045

Reference:

EGY 11689

To appear in:

Energy

Received Date:

09 August 2017

Revised Date:

04 October 2017

Accepted Date:

10 October 2017

Please cite this article as: Vincenzo De Bellis, Rodolfo Bontempo, Development and validation of a 1D model for turbocharger compressors under deep-surge operation, Energy (2017), doi: 10.1016/j. energy.2017.10.045

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ACCEPTED MANUSCRIPT

Highlights



Unsteady flow measurement under deep-surge condition



Steady 1D compressor model for extended map evaluation



Validation of unsteady 1D compressor model in deep-surge regime



Comparison of instantaneous inlet mass flow rate and inlet/outlet compressor pressure

ACCEPTED MANUSCRIPT 1

Development and validation of a 1D model for turbocharger compressors under deep-surge operation

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Vincenzo De Bellis a, Rodolfo Bontempo b Industrial Engineering Department, Mechanic and Energetic Section, University of Naples “Federico II”, via Caludio 21, 80125, Naples, Italy

Abstract The paper presents the validation of a 1D compressor model (1DCM) applied to the simulation of deep-surge operation. The compressor is described following an enhanced map-based approach, where proper "virtual pipes" are placed upstream and downstream the compressor to deal with the mass and energy storage and wave propagation effects. The proposed methodology, which takes into account main flow and thermal loss mechanisms, is based on the employment of "extended" compressor maps obtained through a steady version of the 1DCM. The tuning and validation of the 1DCM have been carried out comparing its results with the experimental data. Preliminarily, the steady version of the 1DCM is tuned against to the measured map for various rotational speeds. Subsequently, it is used to derive the extended map, including both direct and reverse flow branches. Finally, the unsteady version of the 1DCM is validated against experimental data denoting a satisfactory agreement, especially in terms of pulse frequency, amplitude and global shape. Summarizing, the proposed model, combining the reduced computational effort typical of 1D simulation with the adoption of advanced features such as "virtual pipe" and extended compressor map, shows the capability to capture the phenomenology of the compressor surging. Keywords Compressor surge; 1D compressor model; extended compressor map; surge experimental characterization.

1 Introduction

38

In recent years, the need of complying with more and more stringent limitations for

39

pollutant [1] and CO2 [2] emissions obliges the vehicle manufacturer to investigate

40

advanced technical solutions. At the same time, costumers are becoming more

41

sensitive to fuel economy issue, without renouncing to the vehicle performance.

42

Various strategies are currently under development to cope with the above needs. A

43

very effective technique is the electric hybridization of the powertrain, which allows a b

[email protected] Corresponding author. Tel.: +39-081-7683264; [email protected]

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the internal combustion engine (ICE) to work more frequently close to the maximum

45

efficiency area of its operating plane [3]. Other solutions, such as cooled EGR [4, 5],

46

water injection [6], advanced valve actuation strategies [7,8], and variable

47

compression ratio [9,10], directly affect engine efficiency, determining a reduction of

48

the brake specific fuel consumption. Recently, engine downsizing coupled to

49

turbocharging proved to be a very effective path to enhance fuel economy. In fact, it

50

allows to reduced intake throttling at part load, improving hence the fuel consumption,

51

while preserving the maximum power thanks to the intake boosting [11,12,13]. Some

52

restrictions however arise at high load, mainly due to the onset of knocking

53

combustion [14,15]. In addition, especially at low engine speeds, rated torque is

54

usually limited by unstable compressor operation, commonly known as surge [16,17].

55

The latter phenomenon bounds the maximum boost level and, consequently, limits the

56

engine performance (low-end torque).

57

Surge appears as an unstable compressor operation, where periodic fluctuations of

58

both mass flow rate and pressure occur. According to the frequency and amplitude of

59

the above oscillations, it is commonly classified as soft- and deep-surge [18]. While

60

soft-surge is usually characterized by a higher pulse frequency and a reduced

61

amplitude of mass and pressure oscillations, deep surge has opposite features,

62

including also flow reversals [19]. Even few deep-surge cycles may damage the

63

compressor, hence they have to be mandatorily avoided [20,21].

64

During the engine design phase, steady-state maps are usually utilized to carry out the

65

engine/compressor matching, and, in particular, to select an appropriate compressor,

66

so to avoid or minimize the risk of surge onset during ICE steady state operation.

67

However, the compressor experiences unsteady conditions when coupled to an ICE,

68

because of the opening and closure of the intake valves. This is even more true in case

69

of small engines, constituted by a reduced number of cylinders and a small intake

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circuit volume. The engine-induced unsteadiness substantially affects compressor

71

behavior [22] and, in particular, its capability to locally operate close to the surge [23,

72

24]. During ICE steady state operation, only soft-surge usually occurs, while deep-

73

surge may arise in case of transient maneuvers, such as a sudden load drop. This issue

74

is usually faced by the installation of a recirculation or blow-off valve [25,26].

75

For turbocharged engines, 1D models are commonly used for turbo-matching

76

calculations, performance evaluation and analysis of transient maneuvers. To this aim,

77

the classical quasi-steady approach, based on compressor and turbine characteristic

78

maps, is usually followed [27]. To better consider the effects of pulsating flow, the

79

turbomachine geometry can be synthetized in terms of 1D equivalent ducts [28,29].

80

However, since typical steady maps do not include information about the unstable and

81

reverse flow domains, their employment within a 1D code highly limits the possibility

82

to describe surge phenomena. A proper map treatment is mandatory to cope with this

83

issue.

84

Among the proposals which can be found in the literature, the Greitzer model (GM)

85

[30,31,32] is widely employed to describe the surge both for axial and centrifugal

86

compressors [33,34,35]. The GM follows a quasi-steady 0D approach, neglecting

87

pressure wave propagation in the ducts upstream and downstream the compressor. In

88

particular, it describes the dynamic behavior of a compression system consisting of a

89

compressor, a duct, a plenum volume and a throttle valve. The model is based on a

90

non-linear lumped parameter theory and provides mass flow rate and pressure

91

temporal fluctuations both in the plenum and in the ducts. A proper time delay is

92

applied to inquire the compressor map, with the aim of mimicking the time shift

93

between the onset and the fully establishment of the instability. However, this

94

approach still employs steady-state compressor maps and, in addition, requires the

95

knowledge of a complete map, including the negative mass flow rate region. The latter

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is usually unavailable because of difficulties in their experimental measurement [36].

97

For this reason, an arbitrary extrapolation of the compressor map is generally carried

98

out. However, because of its “lumped parameters” nature, the GM cannot be directly

99

coupled to a 1D simulation of the whole engine. A possible solution [23,37] is the

100

employment of a first order variation model to simulate the damping effect exerted by

101

the fluid inertia within the device. This approach is still based on the steady-state

102

extended map, including mandatorily negative branches.

103

The main aim of this work is to validate a refined 1D numerical methodology (see

104

section 2) to describe compressor behavior under deep-surge operation. The validated

105

methodology will be hence employed in the next development of this research activity

106

to simulate transient maneuver of an ICE, including compressor surge, with the aim

107

to numerically investigate technical solution to limit or avoid the above phenomenon.

108

It could be also useful to select, design and estimate the effectiveness of an anti-surge

109

device.

110

Experimental and numerical activities are carried out with reference to a small

111

turbocharger which generally equips engines characterized by a power and

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displacement range of 37–96 kW and 400–1200 cm3, respectively. The tested

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rotational speed of the turbo-shaft spans from 120000 to 200000 rpm. The turbine

114

mass flow rate goes from 130 to 188 kg/h, while its expansion ratio in choked

115

conditions is equal to 2.5. The compressor, which has a maximum pressure ratio of

116

about 2.7, can deliver a corrected mass flow rate in the range 68 – 354 kg/h. Finally,

117

to give an idea of the compressor size, its most important geometrical features are

118

detailed in Table 1.

119

The aforementioned experimental tests are performed in a dedicated test rig [26, 39],

120

operating at the University of Naples (see section 3). In a first stage, the steady

121

characteristic map of the considered compressor is obtained at various rotational

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speeds. It is limited within the stable operating domain, namely between chocking and

123

surging operations. In a second stage, surging behavior is investigated, for a rotational

124

speed of 120’000 rpm.

125

The experimental data are employed to tune and validate a 1D compressor model

126

(1DCM) developed by the authors in the recent years [40,41]. First, a steady version

127

of the 1DCM is tuned with reference to the measured steady map (see section 4). This

128

advanced methodology is based on the solution of the 1D steady-state flow equations

129

within the stationary and rotating channels constituting the device, starting from a

130

reduced set of geometrical data. A direct modelling of main phenomena and losses is

131

performed, also referring to correlations from the literature. The compressor model

132

provides as an output a complete map, extended to the unstable and reverse flow

133

domains. To validate the unsteady version of the 1DCM, the experimental apparatus

134

is modeled within the well-assessed 1D software GT-Power™ (see section 5). The

135

compressor is described following an “enhanced” map-based approach, in which two

136

“properly sized” “virtual pipes” are included upstream and downstream the

137

compressor-junction, to account for the mass and energy accumulation and wave

138

propagation effects within the turbomachine. Also, the methodology is able to handle

139

the extended compressor maps derived by the steady 1DCM. The extended map and

140

the “virtual pipe” included in the 1D model represent the key features of the proposed

141

approach to improve the surge description. Finally, in section 6, model validation is

142

carried out based on the instantaneous signals of pressure and mass flow rate measured

143

along the test rig under deep-surge operation. The advantages with respect to more

144

conventional methodologies are finally discussed.

145 146 147

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2 1D compressor model

150

The compressor model includes a geometrical module that provides the data required

151

to solve the 1D flow equations inside the different ducts composing the device. In

152

particular, the geometrical schematization is composed of four pipes: inlet duct,

153

impeller, diffuser and volute. Figure 1 draws the main stations along the fluid path.

154

In the following, the 1D compressor model is recalled, including a brief description

155

of the geometrical schematization, the 1D flow equations holding in stationary and

156

rotating ducts, and the boundary conditions and flow losses. A more detailed

157

illustration of the model is reported in [40,41].

158 159 160

2.1 Geometrical schematization

161

The compressor is schematized as follows (Figure 1):

162

•

A short inlet pipe (from section 0 to 1) of constant diameter and length;

163

the inlet pipe end section is characterized by a sudden area contraction,

164

due to the impeller eye obstruction.

165

•

The impeller (from section 1 to 2), composed of Z rotating pipes, Z being

166

the number of blades. A sub-module rebuilds the 3D impeller geometry

167

based on a reduced set of data (inlet and outlet blade angles, diameters,

168

number of blades, etc.), which can be easily measured on the real

169

component. The procedure provides as an output the cross-section area,

170

the hydraulic diameter, the local blade/rotation angles and the radius

171

evolution along the curvilinear abscissa of the blade-to-blade duct.

172 173

•

The vaneless diffuser (from section 2 to 3); it is considered as a diverging pipe of constant width along the radial direction.

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•

The volute (from section 3 to 4); it is schematized as a constant diameter

175

duct, collecting the flow coming from the diffuser and ending with a cone.

176

The volute equivalent diameter is derived by the diffuser outlet area. An

177

equivalent length is considered as half the volute centerline length.

178 179

2.2 1D flow model

180

2.2.1 Fixed ducts

181

The flow motion in the stationary ducts is described by the following steady 1D

182

equations:

183

F  C    SC x

184

185

     C   c   E   C

(1)  c    F C   c2  p    cH  C  

   c    f c  SC     c 2    2  d c    q   cH c  4  d 

           

(2)

(3)

186

The terms , c, p, HC=cpT0= cpT+c2/2 in the system (1) – (3) represent the density,

187

the absolute velocity, the static pressure, the total enthalpy per unit mass, respectively.

188

The source term, SC, accounts for the friction coefficient, f, the rate of heat exchange,

189

q, and the duct area variation,  = 1/ d/dx. The latter is provided by the previously

190

described geometrical module at various locations along the duct meanline.

191

2.2.2 Rotating ducts

192

The system (1) – (3) is solved for the inlet pipe and the volute, while, within the

193

impeller, the following balance equations apply [42]:

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195

F  W    SW s

(4)  w    F  W     w2  p    wH  W  

(5)

     w      2 f w  2 fs c       w2    i   c 2 w   u 2W     d w d c i s         wH   4   qh  qs    wu 2    W W   d d s   h  

(6)

     W   w   E   W

196

SW

197

In the above equations, w is the relative velocity, u=r is the tangential velocity (blade

198

speed) and HW=cpT0w=cpT+w2/2 is the total enthalpy in the relative motion. The

199

source term SW includes additional contributions arising from pipe rotation. They are

200

related to the centrifugal forces acting on the fluid particle and are computed as a

201

function of the radius variation along a streamline: W = 1/r dr/ds. The friction forces

202

are subdivided in two contributions, the first one related to flow interaction with the

203

impeller surface and the second one to the friction with the case inner surface. The

204

heat exchange is subdivided in two terms, the first one depending on impeller/flow

205

interaction and the second one arising from the heat exchange on the case.

206

2.2.3 Diffuser flow

207

Along a flow streamline in the vaneless diffuser, a variation of both radial, cr, and

208

tangential velocity components, cu, occurs. The flow is assumed to be axisymmetric.

209

The equations system solved for the vaneless diffuser is hence:

210

F  D    S D r

211

   c    D r  c  u   ED  

(7)   cr   2  c  p F  D   r    cr cu   c H   r D

(8)

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212

 cr     c f    cr2   cu2 D   c 2 r   b c   SD    f  2 cu  c c    c c    c r u r u D   b c    2 q f 2 2 cu    cr cu  D   cu c   cr H D   b b c 

213

being HD=cpT0=cpT+cr2/2. With this definition of HD, the energy balance equation

214

shows an additional term deriving from tangential component of friction force. In this

215

case, along the radial direction: D = 1/r.

216

2.2.4 Equation solution procedure

217

Each pipe is discretized using a 1D grid. The starting and ending sections of each pipe

218

are always included in the computational domain. The simulation cycle starts

219

imposing the thermodynamic state and the mass flow rate at the compressor inlet

220

(outlet) in direct (reverse) flow operation. An “upwind approach” is followed, namely

221

the thermodynamic and flow state in each section is computed based on the one in the

222

previous section moving in the flow direction. An iterative procedure is applied,

223

solving simultaneously mass, energy and momentum equations. The state in the

224

ending node of each pipe is defined based on the previous one. The first node of the

225

subsequent pipe is computed imposing the mass and total enthalpy conservation, and

226

a drop in the total pressure, passing from the last section of a pipe (where the

227

thermodynamic and flow state is known) to the first section of the subsequent pipe

228

(where the state is unknown, and is computed by the solution of “boundary condition”

229

problem). An iterative procedure is applied to solve the pipe-to-pipe junction problem,

230

as well.

231

The computation ends when thermodynamic and flow state is defined in each section

232

of the computational domain. Subsequently, the mass flow rate is changed at the

233

compressor end, and a new computation cycle begins. The procedure finishes when

(9)

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sonic flow occurs in a section within the compressor (typically at the impeller inlet).

235

In this way, a complete compressor map is estimated, including stable, unstable and

236

reverse flow domains.

237

2.2.5 Boundary conditions

238

The boundary conditions in the nodes of adjacent ducts are specified by applying a

239

classical quasi-steady pipe-to-pipe junction problem. Mass and energy conservation

240

at the junction are imposed, while the momentum equation is substituted by a total

241

pressure loss relationship. Formally, the total pressure loss is computed as a function

242

of a Mach number expressing the total head loss, as: 

243

p0ex

   1 2   1  p0in 1  M loss  2  

(10)

244

Loss related Mach number is opportunely specified depending on the junction and

245

loss mechanism. The model takes into account the main losses occurring in the

246

compressor [43,44], the slip effect [45,46] and the heat exchange [47]. Incidence

247

losses at impeller inlet [48,49], and volute losses [50] are considered, as reported in

248

detail in [40,41]. The head reduction related to each loss mechanism is computed by

249

simple correlations. Due to intrinsic limitations of the adopted approach in describing

250

complex 3D phenomena, each loss correlation is multiplied by a tuning constant. The

251

proper value of each of these parameters is identified with the help of experimental

252

tests and of an optimization procedure described in section 3 and 4, respectively.

253 254

3 Experimental setup

255

To validate the 1DCM, a dedicated experimental campaign has been carried out

256

through an in-house developed turbocharger test rig which can be employed to

257

investigate both steady and unsteady operating regimes. As schematically shown in

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Figure 2, a compression-ignition engine is used to feed the turbine circuit. This allows

259

to control mass flow and temperature by changing engine speed and load, respectively.

260

In order to fully span the operating range of the turbocharger, the flexibility of the

261

bench is improved by an after-burner installed along the engine exhaust pipe.

262

Moreover, to further improve the flexibility of the rig, the engine is supercharged

263

through a 2-stage screw compressor. More in detail, the compressed air is stored in a

264

2 m3 reservoir equipped with a valve which, by means of a PID controller, can be

265

operated to set the ICE boost.

266

The turbocharger compressor is inserted in a separate circuit and it is operated through

267

a remotely controlled backpressure valve. The suction branch of the compressor

268

circuit is composed of a piping of variable diameter, whose total length is of about

269

3700 mm with an average diameter of 54 mm. The delivery branch has a length of

270

1150 mm and constant diameter of 43 mm. Actually, no plenum is placed ahead and

271

behind the compressor.

272

The turbocharger lubricating circuit is composed of a 0.02 m3 thermostated reservoir,

273

a 50 cm3 volumetric pump and a by-pass system for oil flow rate control.

274

In order to investigate the turbocharger behaviour both in steady and unsteady

275

operating regimes, the test article is equipped with several measurement systems. In

276

particular, the temperature signals at the inlet and outlet of the compressor and turbine

277

are collected through standard K-type thermocouples. For steady-state operation, low

278

frequency response flow anemometers (Rosemount 3095 MFA) are installed in the

279

compressor and turbine circuits, whereas fast response hot-film Bosch HFM-5 MFA

280

are employed to properly acquire the compressor mass flow rate during surge. On the

281

turbine side, only low frequency response water cooled pressure sensors (EWCT-

282

312M) are installed, while the compressor branch is equipped with both low (Druck

ACCEPTED MANUSCRIPT 283

PTX 1000, Druck PTX 1400) and high (Kulite XTEL-190M) frequency response

284

transducers.

285 286

4 Steady-state results and model validation

287

The steady version of the 1DCM, summarized in section 2, is completely defined once

288

the geometrical data and loss correlations tuning constants are specified. In [41], a

289

refined tuning methodology has been proposed with reference to different

290

compressors. The latter is based on an optimization code, aiming to minimize the error

291

between computed and measured maps of pressure ratio and efficiency. The same

292

approach is here applied to the considered compressor. The agreement with the

293

experimental map is very good both in terms of pressure ratio and efficiency maps, as

294

shown in Figure 3. Some inaccuracies arise for the operating conditions close to

295

choke, where some model correlations may fail. However, the above problem will not

296

affect the calculations under surging operation, presented in the following section,

297

being mainly related to map prediction at lower flow rates.

298

Solving steady-state flow equations in the unstable and reverse flow regions, the

299

extended characteristic maps, reported in Figure 4, are obtained. In case of reverse

300

flow, the conventional adiabatic efficiency definition is meaningless. For this reason,

301

to describe the fluid/impeller work exchange in the whole operating conditions, a

302

corrected total head map can be utilized, as reported in Figure 4b. It presents a

303

discontinuity at zero mass flow rate, due to a sudden modification of velocity triangles

304

at impeller inlet and outlet. In real operations close to zero mass flow rate, occurring

305

under deep surge regime, the discontinuity of pressure ratio and head, predicted under

306

steady conditions, are expected to not appear, since unsteady effects prevail leading

307

to smoother transitions.

ACCEPTED MANUSCRIPT 308

The model also provides as an output the map of the compressor heat exchange, here

309

not reported for sake of brevity. While head map of Figure 4b can be used in a 1D

310

simulation to compute the power absorbed by the compressor, the heat map plays the

311

role to correct the compressor outlet temperature, which depends on both work and

312

heat exchange.

313

The extended maps are computed without modifying the tuning of the loss

314

correlations, which, as stated above, is identified based on the sole stable region of the

315

compressor map. Despite the absence of an explicit model validation, the trend of the

316

rising branches in the unstable region of the map (Figure 4a) qualitatively resembles

317

the experimental evidences reported in [36]. Similar considerations apply for the

318

reverse flow region of the computed map. Consistently with published literature data

319

[32,37], the negative branches of the pressure ratio map look like throttle valve

320

characteristics.

321

In the analyzed literature, complex experimental techniques [37] or arbitrary

322

extrapolation practices are employed to have information about the negative side of

323

the map [51, 52]. Still more complex is the estimation of the head in reverse flow.

324

Many authors hypothesize an isothermal process [37] or a very low constant efficiency

325

[53]. Others extrapolate compressor torque/speed parameter to negative mass flow

326

rate region [52]. The present investigation highlights that the impeller actually

327

furnishes work to the fluid also in case of reverse flow (Figure 4b). Nevertheless,

328

despite the abovementioned fluid energization, the pressure ratio is still positive,

329

namely the fluid expands passing through the compressor, because of the pressure

330

losses. Increasing losses at increasing flow rate explains the shape of the negative

331

branches of pressure ratio map (Figure 4a). Because of the above fluid energization,

332

a positive power is expected to be absorbed by the compressor under surging regime.

ACCEPTED MANUSCRIPT 333

This may impact the instantaneous torque balance on the turbocharger shaft, as shown

334

in the following.

335 336

5 1D model description

337

5.1 1D schematization of the experimental test rig

338

Once validated the 1DCM under steady flow, a 1D model of the experimental test rig

339

is developed in the GT-Power environment with the aim to investigate the compressor

340

behavior under surging condition. To this end, the line on the compressor side is

341

schematized in detail, reproducing section variations and bends from the inlet section

342

up to the backpressure control valve. The “virtual” sensors are located in the same

343

stations as in the real circuit: pressure sensors are placed just upstream and

344

downstream the compressor, while the mass flow sensor is positioned about 2500 mm

345

upstream the compressor.

346

The turbine line instead is described in a rougher way, where a pipe of constant

347

diameter is placed both upstream and downstream the turbomachine. The same length

348

and volume as the real turbine line is reproduced in the related 1D schematization.

349

The choice of realizing a detailed schematization for the compressor line and a

350

rougher one for the turbine circuit depends on the need to properly describe the wave

351

dynamic effects in the former case, not expected in the latter case.

352

Experimental ambient pressure and temperature at both inlet and outlet sections of

353

compressor and turbine lines are imposed as boundary conditions in the simulations.

354

Turbocharger speed is not assigned, but it is derived by the torque balance on the

355

turbocharger shaft. The only degree of freedom for the simulation is represented by

356

the backpressure valve opening. The latter is modeled by a circular orifice, whose

357

diameter is identified in preliminary simulations under steady-state operation. In those

358

simulations, it is adjusted to reproduce the “stable” points of the compressor map (the

ACCEPTED MANUSCRIPT 359

ones on the right side of the surge line in Figure 4). In this way, for each turbocharger

360

speed, the orifice diameter realizing operation at surge-borderline is detected. This

361

information is employed in subsequent calculations, where deep-surge operation will

362

be investigated. A slight reduction of the orifice dimension has proved to be enough

363

to establish unstable conditions for the compressor, including flow reversal.

364 365

5.2 Compressor and surge modelling

366

As already pointed out, in 1D codes, the turbomachines are usually described

367

following a quasi-steady map based approach [54]. A very common methodology

368

consists in accessing the compressor map based on the current rotational speed and

369

pressure ratio to derive the mass flow rate. Such approach correctly works in the stable

370

zone of the map, where the branches are characterized by a negative slope. If the

371

compressor operates close to the surge line, where the map is almost flat, small

372

variations in the pressure ratio may induce relevant oscillations in the mass flow rate.

373

To avoid the onset of noised and unphysical solutions, proper damping mechanisms

374

are usually implemented. Most common ones are based on a first order variation

375

model, applying a certain time delay in the pressure ratio used to access the

376

compressor map [37]. This issue becomes even more important when the pressure

377

ratio locally overtakes the maximum of the steady map, causing the impossibility to

378

inquire the map. To overcome this problem, the map is hence arbitrarily extended in

379

the unstable region through “virtual” negative slope branches. This solution, even if

380

based on a heuristic approach, has shown the capability to satisfactorily describe the

381

compressor behavior, even under close-to-surge operation, without flow reversal.

382

An alternative option consists in accessing the compressor map based on the rotational

383

speed and on the mass flow rate to derive the pressure ratio. This solution, on one side,

384

does not need to employ the “virtual” negative slope branches in the unstable zone of

ACCEPTED MANUSCRIPT 385

the compressor map, but, on the other hand, still requires the introduction of a proper

386

damping effect to avoid flow reversal as soon as the instantaneous operating point

387

moves on the left side of the characteristic curve maximum.

388

Whichever is the mode to inquire the compressor map, the above methodologies

389

present some limitations in describing deep surge onset and development. To this aim,

390

in fact, an extended compressor map is mandatory, also including the branches with

391

negative mass flow rate. This issue has been addressed in previous works, where,

392

however, the reverse flow region of the compressor map was estimated by purely

393

mathematical extrapolation techniques [51, 52, 55, 56].

394

In this work, extended compressor maps, computed by the steady version of the

395

1DCM, are employed. The proposed approach still follows a map based method, so

396

to guarantee a reduced computational effort, but presents some advanced features, as

397

described below. Since the standard “compressor object” in the GT-Power framework

398

does not allow to handle extended maps, the compressor is modeled by a “User Flow

399

Domain” object, where “user-programmed” routines can be implemented. The “user

400

procedure” inquires pressure ratio, enthalpy head and heat maps at each simulation

401

step, based on the current pressure ratio, to derive mass flow rate and the enthalpy

402

increase occurring across the compressor. The choice of not inquiring the map based

403

on the mass flow rate is due to the logics imposed by the GT-Power environment for

404

“user-programmed” objects. This obliges to ignore the compressor map in the

405

unstable region, and to replace the rising branches with “virtual” negative slope

406

branches. Otherwise, for some couples of rotational speed and pressure ratio, two

407

values of mass flow rate could be identified, introducing an ambiguity in the map

408

access. In addition, such methodology forces a special treatment of flow reversal. This

409

critical issue is faced in a very simple way, as schematically represented in Figure 5.

410

In case of direct flow, a “negative slope” branch in the unstable zone is introduced to

ACCEPTED MANUSCRIPT 411

handle pressure ratio higher than the ones included in the map (from A to B in Figure

412

5). By a proper tuning of the branch slope, compressor resistance to soft-surge

413

(without flow reversal) can be heuristically mimicked. When the current pressure ratio

414

overtakes the level at null flow of the “virtual branch”, a negative mass flow rate is

415

suddenly imposed in the compressor-junction, derived from the negative branch of

416

the characteristic curve (from B to C in Figure 5). Similarly, when the pressure ratio

417

becomes lower than the minimum level of the characteristic curve in reverse flow

418

region, a positive mass flow rate is imposed, derived from the positive branch of the

419

characteristic curve (from D to E in Figure 5). During surging operation, it is expected

420

that the compressor stably works along the stable branches of the map (from E to B –

421

for direct flow – and from C to D – for reverse flow), while the mass flow rate

422

suddenly changes during flow reversal (from B to C and from D to E).

423

A certain fluctuation damping is reproduced in the model by the introduction of

424

“virtual pipes” upstream and downstream the compressor-object. They take into

425

account the mass and energy storage and the wave propagation inside the

426

turbomachine, mimicking a physical fluctuation damping. Heat and pressure losses

427

are cancelled in the “virtual pipes”, since the related losses are already considered in

428

the compressor map. The pipe dimensions (length, diameter and volume), usually not

429

available and difficult to estimate, are evaluated by the geometrical module of the

430

1DCM (recalled in section 2.1). In particular, the upstream pipe corresponds to the

431

compressor inlet duct, while the downstream pipe accounts for the equivalent length

432

and volume of impeller, diffuser and volute. Of course, this approach allows for a

433

more physical description of dynamic effects, if compared with the previously

434

described traditional methodology, based on the mathematical damping of the

435

fluctuations.

ACCEPTED MANUSCRIPT 436

As final remark, it is worth to underline that the proposed approach for surge

437

modelling does not require any tuning, excepting the slope of the “virtual branch” in

438

the unstable zone of the compressor map. On one side, the negative branches of the

439

map are univocally defined by a physical model and the intensity of the damping

440

effects is determined by the “virtual pipe” dimensions. On the other side, as stated

441

before, the slope of the “virtual branch” mainly controls the compressor behavior

442

under close-to-surge operation, without flow reversal. This is not the main topic of

443

this work. However, in order to assign a reasonable slope of the virtual branches,

444

based on the authors’ experience from previous studies on compressor soft-surge,

445

linear branches having a slope of -2% are applied. A parametric analysis, not reported

446

here for sake of brevity, confirms that the predicted compressor behavior under deep-

447

surge operation is not significantly affected by this tuning parameter.

448 449

6 Model validation under deep-surge regime

450

To define reference unsteady trends for model validation under deep surge regime,

451

measured signals of pressure at compressor inlet and outlet, and mass flow rate along

452

the intake circuit are processed by a phase averaged technique [57]. This processing

453

is needed to give a proper description of the not deterministic pressure and mass flow

454

oscillations typical of surging phenomenon, which cannot be expected to be captured

455

by a 1D approach.

456

As stated in section 5.1, preliminary simulations are carried out to verify the

457

consistency of the 1D schematization of the experimental setup and of the compressor

458

modelling. In these calculations, the stable steady points of the map in Figure 3 are

459

reproduced in terms of pressure ratio and mass flow rate, by adjusting the diameter of

460

the orifice representing the backpressure valve. Starting from the stable and “closer-

461

to-surge” operating point with a corrected rotational speed of 120’000 rpm, depicted

ACCEPTED MANUSCRIPT 462

in Figure 4a by a star, the orifice diameter has been slightly reduced to promote deep-

463

surge.

464

It is worth to underline that, excepting the heuristic procedure employed to identify

465

the orifice diameter, no tuning showed to be needed to improve the model accuracy.

466

In fact, neither adjustments of the compressor and turbine maps (by global

467

multipliers), nor tuning of the dimensions of the “virtual” pipes proved to be necessary

468

to better agree with the experimental data under deep surge operation.

469

The numerical results, in terms of instantaneous pressure at compressor inlet and

470

outlet, are compared with the related experimental findings in Figure 6. The latter

471

depicts about two consecutive surge cycles. The phasing of numerical and

472

experimental traces is arbitrarily chosen so to realize the best possible agreement on

473

the inlet pressure trace. The phasing of outlet pressure and mass flow rate trends are

474

hence univocally determined by the above choice.

475

Figure 6 shows that the model is able to correctly reproduce the fundamental

476

frequency of the pressure fluctuations, together with a certain pulse delay between

477

inlet and outlet pressure traces. This latter result is a consequence of the introduction

478

of the “virtual pipes” accounting for wave propagation inside the device. The global

479

shape of the pressure fluctuations can be considered satisfactorily captured by the

480

model, both in terms of pulse amplitude and phasing.

481

The numerical/experimental mass flow rate comparison is depicted in Figure 7: once

482

again, the model shows the capability to detect the global shape and frequency of the

483

related experimental signal. In this case, the fluctuation amplitude is overestimated,

484

especially in terms of positive peak. Also, the rate during the descending phase is

485

overestimated. The reason of this inaccuracy can be ascribed to the flow reversal

486

treatment, as described below.

ACCEPTED MANUSCRIPT 487

The discussed results are summarized in Figure 8, which reports the instantaneous

488

compressor operating point, in terms of inlet mass flow rate and outlet pressure. The

489

time-averaged points are plotted under the form of symbols. It can be noted that the

490

predicted average point is very close to the experimental one, especially in terms of

491

pressure. The mass flow rate is underestimated of about 7.8 kg/h, representing the 3.7

492

% of the overall mass flow rate fluctuation. Concerning the instantaneous results, the

493

global shape and dimension of numerical and experimental hysteresis loops are quite

494

comparable. Main inaccuracies regard the estimation of mass flow and pressure

495

variations during flow reversal, both from positive to negative, and vice-versa. In both

496

cases, a too fast transition is predicted, where pressure changes too slowly if compared

497

to the mass flow rate, especially when the flow pass from positive to negative. This

498

can be mainly explained by flow reversal treatment, as described in section 5.2. It

499

seems clear that the damping effect exerted by the “virtual pipes” is not enough to

500

properly fit the experimental data. A possible path to improve this point in the next

501

development of this activity could be a different way to access the compressor map,

502

based on the mass flow rate. This would allow for more dampened flow reversal, not

503

being required any sudden jump in the mass flow rate to be imposed in the

504

compressor-junction.

505

Summarizing, the numerical results of Figure 6-Figure 8 depend on model consistency

506

both of the compressor and the circuit. On one hand, the compressor map, both in

507

direct and reverse flow region, mainly determines amplitude and shape of the surging

508

loops. On the other hand, the circuit length and volume more directly drive the

509

oscillation frequency of pressure and mass flow. Despite the above discussed

510

inaccuracy in the description of flow reversal, the model outcomes can be judged

511

globally satisfactory, also considering the simplicity and the reduced computational

512

effort required by the proposed approach.

ACCEPTED MANUSCRIPT 513

In the light of the above observations, the model is assumed validated. It will be hence

514

employed to analyse in detail the time evolution of further thermodynamic and

515

mechanical quantities, not easily measurable under deep-surge regime.

516

As an example, the instantaneous temperatures at compressor inlet and outlet are

517

plotted in Figure 9, together with the mass flow rate in the compressor-junction. It can

518

be observed that, when the mass flow rate is positive, as in the period roughly between

519

time 0.02 and 0.04 s, the outlet temperature attains a slightly increasing trend, related

520

to the regular compression across the turbomachine. When a flow reversal occurs, as

521

in the period between 0.04 and 0.06 s, the inlet temperature suddenly increases, at a

522

level even higher than the outlet one. This is due to an additional fluid/impeller

523

interaction (both work and heat exchange) during reverse flow. On the other hand, the

524

outlet temperature reduces because of the discharge pipe emptying.

525

When the flow goes back to being direct, as in the period 0.06 and 0.07 s, the outlet

526

temperature presents a local peak, due to the compression of the residual hot gasses

527

that fill the inlet pipe. However, after a certain time, all hot gasses pass again through

528

the compressor, the inlet temperature falls to the ambient level and a new surge cycle

529

begins. It is worth to underline that the above phenomenology, even if not supported

530

by experimental evidences, appears reasonable from a physical point of view.

531

An additional numerical result is the instantaneous trace of the power absorbed by the

532

compressor, represented in Figure 10. It can be noted that the compressor always

533

requires a positive power, even when the mass flow rate is negative. Compressor

534

power fluctuations cause oscillations of the turbocharger rotational speed, while the

535

average level does not significantly change passing from stable to surging operation.

536

This observation is in substantial agreement with the experimental evidence, which

537

highlights only a slight variation of the TC speed (about 120’000 rpm) passing from

538

the last “close-to-surge” stable point of the steady map to the deep surging. This

ACCEPTED MANUSCRIPT 539

indirectly proves how the model correctly estimates the power absorbed by the

540

compressor also when it instantaneously works in the unstable region of the map and

541

under reverse flow. Further verifications, not reported here for sake of brevity, show

542

that a null power absorption during flow reversal induces unphysical turbocharger

543

speed increase.

544

To assess the advanced features of the proposed numerical methodology, additional

545

simulations are carried out employing more conventional approaches. A first one

546

follows the classical map-based method, not considering at all compressor volume

547

and/or equivalent length (labelled as “MB” in the following). A second methodology

548

assumes the compressor presence concentrated in 0D volumes (labelled as “0DCM”

549

in the following), placed upstream and downstream the compressor-junction, whose

550

volume is the same as “virtual pipes” of the 1DCM. In other words, passing from the

551

MB model to the 0DCM, the presence of the compressor volume is taken into account,

552

while passing from the 0DCM to the 1DCM, not only the compressor volume, but

553

also its equivalent length is considered.

554

The above approaches provide comparable results to the 1DCM-ones, in terms of

555

instantaneous trends, averaged levels and fluctuation amplitude. For sake of brevity

556

detailed comparisons are not reported here. Main differences among numerical

557

approaches concern predicted surge frequency and pulse amplitude of mass flow rate.

558

In Figure 11 and Figure 12, the above parameters, derived from 1DCM, 0DCM and

559

MB methodologies, are compared to the experimental data. It can be observed that the

560

1DCM denotes a higher accuracy, if compared to the other numerical approaches. In

561

fact, both 0DCM and MB estimate a higher surge-frequency and amplitude of mass

562

flow rate oscillation. Such a behaviour can be explained by an underestimation of the

563

distance covered by the pressure waves during surge, related to the absence of the

ACCEPTED MANUSCRIPT 564

“virtual pipes” of the 1DCM. A slightly improved accuracy is proved by the 0DCM,

565

since proper compressor equivalent-volumes are considered.

566

Summarizing, the proposed 1DCM, resorting to advanced features such as an

567

extended compressor map and “virtual pipes”, demonstrated to correctly capture

568

compressor behaviour during surging operation. In addition, the advantages with

569

respect to more simple approaches, not considering the compressor volume and

570

equivalent length, are showed.

571 572 573

7 Conclusions

574

In this work, the behaviour of a small in-series turbocharger compressor is analysed

575

experimentally and numerically, with particular reference to surging operation. In a

576

first stage, the pressure ratio and adiabatic efficiency steady maps are measured for

577

various speeds at a dedicated test rig. Then, the compressor surging is promoted by

578

closing a backpressure valve. An operating point with an average rotational of

579

120’000 rpm is investigated.

580

The experimental test facility is then modelled within the GT-Power environment. A

581

refined map-based approach is followed for the compressor behaviour description,

582

where proper “virtual pipes” are introduced upstream and downstream the

583

compressor-junction to take into account the mass and energy storage and wave

584

propagation effects. Extended maps are employed in the calculations, derived by a 1D

585

steady compressor model, properly tuned based on the measured steady map.

586

The proposed numerical approach is validated under deep-surge operation, in terms

587

of instantaneous inlet and outlet pressure, and inlet mass flow rate. The

588

numerical/experimental comparisons show globally a satisfactory agreement, both in

589

terms of pulse shape and frequency. Some inaccuracies mainly regard the description

ACCEPTED MANUSCRIPT 590

of mass flow during flow reversal. Predicted traces of temperature at compressor inlet

591

and outlet, and of absorbed power, even if not verified by experimental surge-cycle

592

resolved instantaneous data, are coherent with the physical expectations concerning

593

the energy exchange between fluid and compressor during flow reversal. Finally, the

594

advantages of the proposed model in surge frequency and mass flow rate fluctuation

595

computation are proved with respect to more conventional map based approaches. In

596

the next development of this research activity, the model will be validated for different

597

turbocharger rotational speeds.

598

Summarizing, the numerical results show the potential to properly describe a complex

599

phenomenon like the compressor surge on the basis of a simple 1D approach,

600

combining the reduced computational effort typical of 1D simulation with the

601

adoption of advanced features such as “virtual pipes” and extended compressor map.

602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627

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10.1016/j.egypro.2014.01.117. 40. Bozza, F. and De Bellis, V., "Steady and Unsteady Modeling of Turbocharger Compressors for Automotive Engines," SAE Technical Paper 2010-01-1536, 2010, doi:10.4271/2010-01-1536. 41. De Bellis, V., Bozza, F., Bevilacqua, M., Bonamassa, G. et al., "Validation of a 1D Compressor Model for Performance Prediction," SAE Int. J. Engines 6(3):1786-1800, 2013, doi:10.4271/2013-24-0120. 42. Leonard O., Adam O., “A Quasi-One Dimensional CFD Model for Multistage Turbomachines”, Journal of Thermal Science, 17(1): 7-20, 2008. 43. Traupel, W., Die Theorie der Strömung durch Radialmaschinen, Braun, Karlsruhe, 1962; 44. Dubitsky, O., Japikse, D., Vaneless Diffuser Advanced Model, ASME Journal of Turbomachinery, 130, 011020, 2008; 45. Qiu, X., Japikse, D., Zhao, J., Anderson, M., R., Analysis and Validation of a Unified Slip Factor Model for Impellers at Design and Off-Design Conditions, ASME J. Turbomach., 133, 041018-1, 2011, doi: 10.1115/1.4003022. 46. Wiesner F., J., A review of slip factors for centrifugal compressors, ASME J. of Eng. Power, ASME Transaction, 89, 558-72, 1967. 47. Gnielinski, V., New equations for heat and mass transfer in turbulent pipe and channel, Int. Chemical engineering, 1976. 48. Pelton R., J., One-Dimensional Radial Flow Turbomachinery Performance Modeling, Master Thesis, Science Department of Mechanical Engineering, Brigham Young University, 2007. 49. Japikse, D., Turbomachinery Performance Modeling, SAE Paper 2009-01-0307, Cliff Garrett Turbomachinery and Applications Engineering Award, 2008. 50. Eynon, P., A., Whitfield, A., Pressure recovery in a turbocharger compressor volute, Proc IMechE Vol 214 Part A, 599-609, 2000. 51. Gravdahl, J.T., Egeland, O., Vatland, S.O., “Active surge control of centrifugal compressors using drive torque”, Proceedings of the 40th IEEE Conference on Decision and Control, pp. 1286 – 1291, 2001. 52. Rakopoulos, C.D., Michos, C.N., Giakoumis, E.G., “A computational study of compressor surge during transient operation of turbocharged diesel engines”, Int. J. Alternative Propulsion 1(2):250-273, 2007. 53. Leufven, O., Eriksson, L., “Surge and Choke Capable Compressor Model”, Proceedings of the 18th IFAC World Congress, 10653-10658, 2011, http://dx.doi.org/10.3182/20110828-6-IT-1002.00694 54. GT-Power V2016, User's Manual, Gamma Technology Inc., 2016. 55. Leufven, O., Eriksson, L., “A surge and choke capable compressor flow model— Validation and extrapolation capability”, Control Engineering Practice, 21: 1871-1883, 2013. 56. Chesse, P., Hetet, J.,F., Tauzia, X., Roy, P. Inozu, B., “Performance Simulation of Sequentially Turbocharged Marine Diesel Engines With Applications to Compressor Surge”, J. Eng. Gas Turbines Power 122(4): 562-569, 2000. 57. Bontempo, R., Cardone, M., Manna, M., Vorraro, G., “A statistical approach to the analysis of the surge phenomenon”, Energy, 124: 502–509, 2017, doi: 10.1016/j.energy.2017.02.026 Glossary Notations C

Vector of conservative variables in absolute motion

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c cp cr cu cw D d E F f H M p q r S s T u x W w Z

Absolute velocity Specific heat at a constant pressure Absolute velocity component along the radial direction in the diffuser Absolute velocity component along the tangential direction in the diffuser Absolute velocity component along the meanline in the impeller Vector of conservative variables in axisymmetric flow Equivalent diameter Total internal energy per unit mass Flux terms vector Friction coefficient Total enthalpy per unit mass Mach number Pressure Specific rate of heat exchange Radius Vector of the source terms Impeller curvilinear abscissa Temperature Tangential blade velocity Stationary ducts abscissa Vector of conservative variables in relative motion Relative velocity Number of wheel blades

Notations  Duct area variation term  Specific heats ratio  Radius variation term along a streamline  Density  Cross section area  Angular speed Subscripts 0 Total conditions C Referred to stationary ducts D Referred to diffuser ex Referred to the outlet h Hub i Impeller in Referred to the inlet loss Referred to the flow losses s Spatial derivative for rotating ducts, Shroud x Spatial derivative for stationary ducts W Referred to rotating ducts w Referred to the relative motion, Wheel Acronyms 0,1,3D Zero, One, Three - dimensional 0DCM 0D compressor model 1DCM 1D compressor model MB Map Based

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GM Greitzer model ICE Internal combustion engine EGR Exhaust gas recirculation

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Inlet pipe

Wheel-outlet

Diffuser-outlet

Outlet pipe

41.1

41.0

76.0

30.0

Table 1. Diameters in mm of the most important geometrical features of the compressor

Figure 1. Main compressor stations

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3.0

0.9 Exp Model

220k

2.6

Adiabatic Efficiency, -

Total_to_Total Pressure Ratio, -

Figure 2. Experimental setup

200k 2.2

180k 160k

1.8

140k 120k

1.4

(a)

1.0 0

50

100

150

200

250

300

350

400

0.8 0.7 0.6 0.5 0.4 Exp Model

0.3

(b)

0.2

450

0

50

100

150

200

250

300

350

400

450

Corrected Mass Flow Rate, kg/h

Corrected Mass Flow Rate, kg/h

Figure 3. Comparison between experimental and numerical pressure ratio (a) and

3.0

200 Reverse Flow

Unstable Region

Stable Region

Corrected Total Head, kJ/kg

Total_to_Total Pressure Ratio, -

efficiency (b) maps

2.6 2.2 1.8 1.4 Base Extended

1.0 -200

-100

(a) 0

100

200

300

Corrected Mass Flow Rate, kg/h

400

Base Extended

160 120 80 40

(b)

0 500

-200

-100

0

100

200

300

400

500

Corrected Mass Flow Rate, kg/h

Figure 4. Computed extended pressure ratio (a) and corrected total head (b) maps

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Pressure Ratio

Reverse Flow

Unstable Region

B

C

Stable Region

A

E

D

Mass Flow Rate Figure 5. Schematic representation of surge treatment

1.6

Pressure, bar

1.5 1.4 1.3

Outlet

1.2

Exp Model

Inlet

1.1 1.0 0.9 0

0.02

0.04

0.06

0.08

0.1

0.12

Time, s Figure 6. Experimental/numerical comparison of compressor inlet and outlet pressure traces

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Mass Flow Rate, kg/h

300

Exp Model

200 100 0 -100 -200 0

0.02

0.04

0.06

0.08

0.1

0.12

Time, s

Compressor Outlet Pressure, bar

Figure 7. Experimental/numerical comparison of compressor inlet mass flow rate

1.8 Exp Model

1.7 1.6 1.5 1.4 1.3 1.2 1.1 -150

-100

-50

0

50

100

150

200

250

Inlet Mass Flow Rate, kg/h Figure 8. Experimental/numerical comparison of compressor operating point on the steady map

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400 370 340

300

310

200

280

100

250

0

220

-100 0.00

0.02

0.04

0.06

0.08

0.10

Compressor Mass Flow Rate, kg/h

Temperature, K

430

0.12

Time, s Figure 9. Computed compressor inlet and outlet temperature

1.2 0.8 0.4

200

0.0

100

-0.4

0

-0.8

-100 0

0.02

0.04

0.06

0.08

Time, s Figure 10. Computed power absorbed by the compressor

0.1

0.12

Compressor Mass Flow Rate, kg/h

Compressor Power, kW

1.6

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Surge Frequency, Hz

17.5

17.0

16.5

16.0

15.5

Exp

1DCM

0DCM

MB

Figure 11. Assessment among 1DCM, 0DCM and MB approaches in terms of surge

Mass Flow Rate Fluctuation Amplitude, kg/h

frequency against the experimental datum

350

300

250

200

150

Exp

1DCM

0DCM

MB

Figure 12. Assessment among 1DCM, 0DCM and MB approaches in terms of mass flow rate oscillation amplitude against the experimental datum