1 Pulsed Electric Field (PEF) Treatment Chamber Optimisation

Draft manuscript: PEF treatment chamber optimisation

Pulsed Electric Field (PEF) Treatment Chamber Optimisation – 1

A Multiphysics Modelling Approach for Improving Treatment 2

Uniformity 3

Kai Knoerzer, Pascal Baumann, Roman Buckow 4

CSIRO Food and Nutritional Sciences, Innovative Foods Centre, Private Bag 16, Werribee, 5

VIC, Australia 6

7

Abstract 8

An important component of the Pulsed Electric Field (PEF) technology is the 9

treatment chamber in which the food is exposed to high electric field pulses. A 10

detailed knowledge of the electric field strength and the induced temperature 11

distribution in the chamber is essential to achieve efficient and gentle pasteurisation. 12

Experimental determination of such distributions is extremely difficult. However, 13

numerical simulation of the fluid dynamics coupled with the electric and thermal fields 14

inside the treatment chamber can provide this information at high spatial resolution. 15

A previously developed and validated full 3D Multiphysics model, describing the flow 16

pattern, the electric field, and the temperature distributions in a pilot-scale PEF 17

treatment chamber with co-linear electrode configuration, was simplified to a 2D axis-18

symmetrical model. This approximation allowed for a significant decrease in 19

computational demand and, therefore, to an increase in the rate of model solving. An 20

iterative algorithm was developed, which allows automatic modification of the electric 21

insulator geometry (i.e. the treatment zone), and solves and evaluates the models 22

with respect to electric field uniformity and treatment volume. As the pressure drop in 23

continuously operated flow through systems is highly relevant, this parameter was 24

also taken into consideration for the treatment chamber redesign. Thus, the 25

developed algorithm was capable of identifying insulator geometries that were 26

superior in electric field distribution to the current experimental system, while keeping 27


the pressure drop caused by decreasing insulator diameters low. A 3D Multiphysics 28

model of the improved PEF treatment chamber, incorporating the equations for 29

mass, momentum, energy and charge conservation was developed and validated by 30

means of fibre optic temperature measurements in the redesigned system. 31

32

1. Introduction 33

34

Pulsed electric field (PEF) processing is an innovative mild treatment technology, 35

which can be used for non-thermal pasteurisation of pumpable foods at low or 36

moderate temperatures. The mechanism of microbial inactivation is based on the 37

discharge of high voltage electric pulses (up to 70 kV·cm-1) of a few microseconds 38

into the liquid inside the treatment zone, which is located between a grounded and a 39

high-voltage electrode (Heinz et al., 2001; Angersbach et al., 2000). During the 40

treatment, the membrane potential of microbial, plant or animal cells is exceeded, 41

which leads to the formation of pores, causing a release of intracellular liquid and cell 42

death. Unlike in thermal pasteurisation, where heat conduction is a time limiting 43

factor, the delivery of the lethal treatment in PEF processing is instantaneous. 44

The efficiency of the PEF treatment depends on a number of process variables, 45

particularly the electric field strength, the specific energy input, the treatment 46

temperature and time, but also on the material properties, such as the electrical 47

conductivity, of the treated product. 48

The electric field strength E is commonly seen as the main process variable and can 49

be estimated by Equation1: 50

51

h

VE = (1) 52

Where V is the applied voltage and h is the distance between high voltage and 53

grounded electrode (typically in parallel plate configurations). 54


55

The dissipated energy into the liquid, Qspec, leads to an increase in temperature due 56

to ohmic heating and can be estimated by the electric field strength applied to the 57

product and its flow rate: 58

∫∞

− ⋅⋅⋅=0

21))(()( dttETfmQspec σ& (2) 59

Where σ(T) is the temperature (T) dependent media conductivity, f is the pulse 60

repetition rate (frequency) and m& is the mass flow rate. 61

62

The electric field strength required for liquid food pasteurisation is in the range of 20 63

to 50 kV cm-1 (Toepfl et al., 2006).To estimate the increase in temperature, Equation 64

3 can be applied: 65

)()( TCT

QT

p

spec

⋅=∆

ρ (3) 66

Where Cp(T) is the temperature dependent specific heat capacity and ρ(T) the 67

density of the treated product. 68

69

As many PEF process variables are almost impossible to determine experimentally 70

(at least without disturbing or influencing the entire process with measurement 71

equipment within the constrained space of the treatment zone), Multiphysics 72

modelling can be utilised to simulate and predict the electric field distribution, the flow 73

characteristics and the temperature distribution in PEF processing. 74

Several studies have shown that PEF leads to a considerable inactivation of 75

microbial cells in different products (Heinz et al., 2003; Toepfl et al., 2007; Puertolas 76

et al., 2009). A reliable and effective PEF treatment for microbial inactivation is highly 77

dependent on the electric field strength uniformity within the treatment zone of the 78

PEF chamber. Non-uniform electric fields lead to two major problems: Firstly, 79

occurrence of high electric field strength peaks causing potentially significant 80


increases in temperature and thus over-processing in areas where the high electric 81

field strength peaks are situated, and insufficient inactivation in regions where the 82

threshold for microbial inactivation is not reached. The second major problem of a 83

non-uniform electric field is the erosion of insulators and electrodes due to by arcing. 84

Peaks in the electric field strength increase the risk of arcing; hence, either the 85

applied peak voltages have to be decreased, which in turn causes lesser inactivation 86

of microorganisms in areas with lower electric field strength, or peaks must be 87

prevented by changing the chamber design and geometry (Fiala et al., 2001; Misaki 88

et al., 1982). 89

Recent studies on Multiphysics modelling of laboratory-scale PEF systems showed a 90

drastic increase of temperature near the chamber walls and, particularly, at sharp 91

electrode or insulator edges (Gerlach et al., 2008). These temperature hotspots were 92

explained by electric field maxima and insufficient mixing and recirculation of the 93

liquid inside the chamber due to laminar flow conditions. It was suggested to 94

introduce turbulent flow with static mixing devices (Lindgren et al., 2002) or grids 95

(Jaeger et al., 2009) to improve the effectiveness and treatment uniformity of PEF 96

pasteurisation processes. However, the application of such static mixing devices 97

limits PEF processing to non-particulate liquid foods of low viscosity and may 98

complicate cleaning and maintenance operations of the system. Furthermore, 99

industrial scale PEF processing usually provides liquid velocities that are sufficient to 100

create turbulence, which, in turn, may avoid or at least reduce the occurrence of 101

temperature hot spots (Buckow et al., 2010). 102

Another possibility to overcome the above mentioned issues is to modify the insulator 103

design by decreasing the bore diameter with a rectangular or elliptical (inward 104

concave) cross-section (see Figure 5). This allows both changes in the electric field 105

strength distribution and flow characteristics to ensure turbulent regimes in this 106

critical section of the treatment chamber, respectively. 107


The aim of the work presented here was to develop an improved chamber design 108

with respect to the shape, configuration and dimensions of insulators and electrodes; 109

thereby improving the uniformity of the PEF treatment and also preventing arcing, 110

thus, reducing erosion of the chamber material and dielectric breakdowns that may 111

occur during the treatment of dielectric materials (Gongora-Nieto et al., 2003). 112

The objective was to program an algorithm in MATLAB™ (The Mathworks Inc., 113

Natick, MA, USA) interfacing to a COMSOL Multiphysics™ (COMSOL AB, 114

Stockholm, Sweden) model, capable of progressively modifying the shape and 115

geometry of the treatment chamber as determined by the cross-section of the 116

insulator (e.g. decreasing diameter, electrode distance and tube diameter). By 117

extracting the models’ solutions and evaluating process performance (in terms of 118

electric field strength, associated uniformity, treatment volume and pressure drop 119

caused by the decreasing insulator bore diameter), it was possible to identify a 120

design superior in performance compared to the treatment chambers supplied by the 121

manufacturer. The performance elements were implemented as features in the 122

software routine in the form of a single dimensionless performance parameter (DPP). 123

Following the numerical studies, another objective was to manufacture the improved 124

chamber, develop a 3D Multiphysics model and validate it in the pilot-scale PEF 125

system. 126

127

2. Material and Methods 128

129

Pulsed electric field system 130

131

The Multiphysics PEF model was based on a Diversified Technologies Power Mod 132

25kW Pulsed Electric Field System (Diversified Technologies, Inc., Bedford, MA, 133

USA). The system consists of a PEF treatment enclosure and a modulator cabinet. 134


The PEF treatment chamber is connected to a liquid food handling system (two 150L 135

stainless steel supply and collection tanks, three tube heat exchangers (#PT 113-18-136

1500, Hipex Pty Ltd, Thomastown, Victoria, Australia), a pump (#SLA 80A-4, CMG 137

Pty Ltd, Rowville, Victoria, Australia) and the control systems for all other settings like 138

liquid flow rate, temperature and back pressure. The PEF system supplies mono-139

polar pulses of almost rectangular shape. The pulse widths (durations) can be set in 140

a range of 1-10 µs and the frequency can be modulated up to 3,000 Hz. The 141

maximum output voltage of the system is approximately 40 kV. 142

The temperature measurements for the validation of the model with the improved 143

chamber configuration were performed using a fibre optics system (# REFLEX 4 – 144

RFX321A, Neoptix Inc., Quebec, QC, Canada). The fibre optic temperature sensors 145

were inserted into the second grounded electrode in a similar fashion as in the work 146

of Buckow et al. (2010). 147

148

Pulsed electric field treatment chamber 149

Previously validated model 150

The geometry of the treatment chamber of the validated model developed by Buckow 151

et al. (2010) is illustrated in Figure 1. The chamber consists of two grounded 152

electrodes made of stainless steel, which are located at the top and the bottom of the 153

chamber, one high voltage electrode made of stainless steel which is situated in the 154

middle between the grounded electrodes, and two polytetrafluoroethylene (PTFE) 155

insulators, separating the high voltage and the grounded electrodes. 156

The CFD model was designed in 3D and is a good approximation of the rotation 157

symmetric pilot-scale treatment chamber. The two PTFE insulators have an outer 158

diameter of 98 mm, an internal diameter of 16 mm and a total height of 43 mm. 159

Serving as spacer between high voltage and grounded electrode (gap = 6.3 mm), the 160

internal diameter decreases to 5.3 mm centred along the height of the bore, creating 161

a zone with high electric field strength during processing. 162


The three electrodes have an outer diameter of 16 mm and an internal diameter of 163

5 mm. 164

165

FIGURE 1: Dimensions and geometries of the electrodes and insulator of the 166

former validated co-linear PEF treatment chamber (Buckow et al., 167

2010). 168

169

Justification to utilise 2D axis-symmetric models for optimisation studies 170

As the computational demand to solve one 3D model of the discussed system, 171

involving the solution of the conservation equations of mass, momentum, energy and 172

charge and the associated equations on the model boundaries, is high 173

(approximately 1.25 hours on a workstation with two dual core processors (each 2.33 174

GHz) and 20 GB RAM), it was not feasible to solve a large amount of models with 175

different chamber configuration (various shapes, diameters and gaps) in 3D. 176

However, since the geometry of the discussed treatment chamber is rotation 177

symmetric, a simplification of the 3D model to an axis-symmetric 2D model is 178

possible, leading to a significant decrease in computational demand. To validate this 179

approximation, 2D and 3D models were developed with identical dimensions (as per 180

Buckow et al., 2010; Figure 1), process conditions and material properties. The 181

potential at the high voltage electrode was set to 20 kV, the chamber inlet 182


temperature to 25°C, the liquid flow rate to 5 L·min-1, the pulse repetition rate to 500 183

Hz, the pulse width to 5 µs, and the liquid was assumed to have a constant electrical 184

conductivity of 5 mS·cm-1. The predicted electric field strengths, temperatures and 185

velocities of both models were compared. The comparison was performed in both 186

treatment zones; in each treatment zone 30 locations (covering an axis-symmetric 187

plane with a 3x10 matrix), at 3 different radial coordinates (symmetry axis, 1 mm 188

distance from symmetry axis and 2 mm distance from symmetry axis) and 10 189

different heights (2 mm steps, from 6 mm before the insulator region inlet to 6 mm 190

behind the insulator bore outlet) were selected (Figure 2). 191

(a) (b) 192

FIGURE 2: 3x10 matrix, covering an axis-symmetric plane in the treatment zone 193

of the 3D model (a) and the 2D model (b) for comparison of 194

predictions and justification to utilise 2D axis-symmetric models in the 195

optimisation study. 196

197

The results showed a very good agreement between the two models, with 198

coefficients of determination R² of greater than 0.99 for temperature and electric field 199

strength distribution and greater than 0.85 for the velocity distribution (Figure 3). The 200


reason for the lower R2 in the comparison of the velocities can be explained by the 201

fact that all velocity values are close (in the range of 3.9 to 4.4 m/s) and, thus, due to 202

the nature of the equation for R2 determination (see Equation 4), the value for R2 203

becomes small (i.e., as all values of iy are close to the mean y , the denominator 204

becomes small and, therefore, also the value for R2). 205

206

∑

∑−

−

−=

i

i

i

ii

yy

fy

R2

2

2

)(

)(

1 (4) 207

Where fi are the values from the 3D model, yi the values from the 2D model and y 208

the mean of the values from the 2D model. 209

210

For this reason, R² of greater than 0.85 suffices to justify a simplification from 3D to a 211

2D axis-symmetric model without the risk of obtaining inaccurate predictions, 212

particularly for the electric field strength distribution, which was selected as the main 213

optimisation variable (see Equations 24-29). 214

215


0.5 1 1.5 2 2.5 3

x 106

0.5

1

1.5

2

2.5

3x 10

6

E2D-model

(V/m)

E3

D-m

od

el (

V/m

) R2 = 0.99936

24 26 28 30 32 34

24

26

28

30

32

34

T2D-model

(°C)

T3

D-m

od

el (

°C)

R2 = 0.99977

3.8 4 4.2 4.4 4.6

3.8

4

4.2

4.4

4.6

U2D-model

(m/s)

U3D

-mo

de

l (m

/s)

R2 = 0.85146

(a)(b)

(c)

216

FIGURE 3: Parity plots for temperature (a), electric field strength (b) and velocity 217

(c) of 2D axis-symmetric and 3D models at an applied peak voltage of 218

20 kV, an inlet temperature of 25°C, a flow rate of 5 L·min-1, a pulse 219

repetition rate of 500 Hz, a pulse width of 5 µs and an electrical 220

conductivity of the processed liquid of 5 mS·cm-1. 221

222

Insulator configurations for optimisation studies 223

As discussed earlier, the insulator shape and the geometric properties (dimensions) 224

of the treatment chamber have a pronounced impact on the electric field distribution 225

inside the chamber. Apart from affecting the uniformity of the electric field, also the 226

magnitude of the electric field strength and, thus, the temperature increase is 227

affected greatly. Hence, the insulator shape and dimensions, the electrode gap and 228

the electrode diameter were chosen to be variables in the optimisation algorithm. 229

As possible candidates, four different insulator shapes were taken into consideration, 230

“no inset”, i.e., the insulator diameter was equal to the electrode diameter (see Figure 231


4a); “rectangular inset”, i.e., the insulator bore had a smaller diameter than the 232

electrodes (see Figure 4b); “elliptical inset”, i.e. the cross-section of the insulator bore 233

had an inward concave shape (see Figure 4c); and “rectangular rounded edge inset”, 234

i.e., the insulator had a smaller diameter than the electrodes, with the edges 235

chamfered by different radii (see Figure 4d). 236

Four models were developed with 30% inset, i.e., a minimum internal insulator 237

diameter of 70% that of the electrodes (except the “no inset” model), with an applied 238

voltage of 10 kV at the high voltage electrode (Figure 4). Comparison of the electric 239

field distributions clearly showed that the insulator shape has a significant influence 240

on the uniformity of the electric field and the associated strength of the electric field 241

peaks. The “no inset” model showed the highest electric field strength of 242

approximately 64 kV·cm-1 at the interface of insulator and electrode, which was about 243

four times the value of the maximum electric field strength of the “elliptical inset” 244

model prediction, showing a peak strength of 16 kV·cm-1 (Figure 4c). 245

(a) (b) (c) (d)

V·m-1

246

FIGURE 4: Comparison of the electric field distribution with four different insulator 247

shapes (30% inset). (For colour representation, the reader is referred to the online 248

version of this article) 249


250

Apart from the shape, other variables were also taken into consideration in the 251

optimisation studies. Four different geometry parameters were varied: the internal 252

diameter d of the electrodes ranging from 2 mm to 20 mm, the height h of the 253

electrode gap ranging from 1 mm to 30 mm, a total inset ins (i.e. the internal diameter 254

of the insulator) in a range of 0 to 90% of the electrode diameter d, and for the 255

“rectangular rounded edge inset” models also the chamfer radii rad ranging from 0 to 256

40% of the diameter reduction ins (Figure 5). 257

2d 2d 2d

(a) (b) (c) 258

FIGURE 5: Geometry variables for the different types of insets ((a) “rectangular 259

inset”, (b) “elliptical inset”, (c) “rectangular rounded edge inset”). 260

261

Governing Equations 262

Being a Multiphysics scenario, involving heat transfer, (turbulent) fluid flow and 263

electric fields, the fully coupled model of the PEF system requires the simultaneous 264

solution of the partial different equations describing the conservation of mass, 265

momentum, energy and electric charge. 266

267


Governing equations for electrostatics: 268

Based on the law of charge conservation, the governing equation for the electric 269

potential is: 270

271

( )( ) 0=−⋅∇⋅⋅∇ JVTσ (5) 272

Where J is the density of the electrical current. 273

274

Assuming static conditions, i.e., no generation of electromagnetic forces, the relation 275

of electric field and potential can be described by: 276

277

VE −∇= (6) 278

Where E is the electric field strength. 279

280

Governing equations for turbulent flow and heat transfer in the system: 281

The thermo- and fluid-dynamic behaviour of the pressure medium is described by 282

conservation equations of mass, momentum and energy (Chen, 2006). The 283

development of a flow field is governed by the continuity equation (mass balance): 284

285

( ) 0=⋅∇+∂

∂v

tρ

ρ (7) 286

Where v is the velocity vector. 287

288

Due to high velocities in the treatment chamber, the fluid flow was turbulent with 289

Re >> 2,300. Turbulence was solved by applying the k-ε model which included an 290

additional “turbulence viscosity” and “turbulent thermal conductivity” in the equations 291

for conservation of momentum and energy, respectively, to take the contributions of 292


turbulent eddies into account (Nicolaï et al., 2007; COMSOL Multiphysics, 2006). The 293

turbulent viscosity ηT is given by: 294

295

ερη µ

2kCT = (8) 296

where Cµ =0.09 (Launder and Spalding, 1974), k is the turbulent kinetic energy and ε 297

the dissipation rate of turbulence. 298

299

Here, the momentum equation (extended according to COMSOL Multiphysics 300

(2006)) gives the following expression: 301

302

( ) ( ) gvPvvt

vT ρηηρ +∇⋅+⋅∇+−∇=

∇⋅+

∂

∂)(

r

(9) 303

Where v denotes the average velocity, P is the pressure, η represents the dynamic 304

viscosity of the compressed fluid, and g represents the gravity constant. 305

306

In addition to the continuity equation, the k-ε closure includes two extra transport 307

equations solved for both k and ε using empirical model constants (COMSOL 308

Multiphysics, 2006). The k-ε closure equations were coupled with the energy 309

conservation equation for heat transfer through convection and conduction, assuming 310

non-isothermal flow. This equation was modified (from Kowalczyk et al. (2004) and 311

extended according to COMSOL Multiphysics (2006)) by including the turbulent 312

thermal conductivity kT (with kT = CP·ηT/PrT): 313

314

( )( )TkkQTvt

TC Teffp ∇+⋅∇+=

∇⋅+

∂

∂1ρ (10) 315


Where k1 is the thermal conductivity of the liquid domain, and PrT is the turbulent 316

Prandtl number. The source term Qeff arises from electric energy dissipation in the 317

liquid and can be expressed as: 318

319

2

EQeff ⋅⋅= σϕ (11) 320

Where φ is a factor for the time-averaged potential (to account for the pulsed 321

potential in a stationary solution), which can be estimated for ideal rectangular pulses 322

as the product of pulse repetition rate f and pulse width τ. 323

324

Boundary Conditions 325

For each physical phenomenon, a number of boundary conditions were defined to 326

account for the interactions at solid-liquid and solid-solid interfaces (between 327

subdomains). 328

329

Electrical interaction between subdomains 330

The boundaries of inlet, outlet and PTFE insulator were assumed to be electrically 331

insulated: 332

0=⋅ Jn (12) 333

The same boundary condition applies to the symmetry axis in the 2D axis-symmetric 334

model. 335

336

The boundaries of the high voltage electrode were set as electric potential with: 337

0VV = (13) 338

With V0 as the maximum output voltage during a pulse. 339

340

The other electrodes are grounded, i.e., the potential at the boundaries is zero 341

342


Fluiddynamic and thermal interaction between subdomains 343

Walls 344

Fluid-solid boundaries had to be defined for the k-ε closure on the liquid domain, 345

whereas thermal boundaries were defined for the energy balance for all domains. 346

For the 2D axis-symmetric models, symmetry boundary conditions were assumed on 347

the symmetry axis and can be simplified to the following expressions: 348

( ) 0=∇−⋅ Tkn and 0=⋅ vn (14) 349

350

A logarithmic wall function condition as described by Buckow et al. (2010) and 351

Knoerzer et al. (2007) is assumed at all fluid-solid boundaries, accounting for the thin 352

laminar boundary layer which is not resolved by the mesh. Similarly, a thermal wall 353

function was defined at the solid-liquid interfaces. Instead of assuming continuity of 354

the temperature across the thin (non-resolved) laminar layer, the thermal wall 355

function is used, accounting for a sudden temperature change between the solid 356

surface and the liquid due to the omitted laminar layer. For the outer wall, a heat flux 357

condition was applied. The default form of the heat flux boundary condition is given 358

as: 359

)( inf0 TThqqn heat −+=⋅− (15) 360

With n as the normal direction to the boundary, hheat as the heat transfer coefficient 361

and Tkq ∇−= (k is the thermal conductivity, which is replaced by k1+kT in the k-ε 362

closure): 363

( )( ) ( )TThqTkkn heatT −+=∇+−⋅−inf01 (16) 364

365

Continuity of heat flux is assumed at all solid-solid boundaries: 366

( ) ( )TknTkn ∇⋅=∇⋅ 21 (17) 367

Where k1 and k2 are the thermal conductivities of the two respective subdomains. 368


369

Fluid inlet and outlet 370

The boundary at the liquid inlet was defined as a velocity boundary in streaming 371

direction: 372

0vv = (18) 373

As the inlet velocity v0 changes for an adjusted volume flow at a temperature of 20°C 374

after exiting the heat exchanger at different set temperatures, this had to be into 375

consideration, following the expression: 376

A

C

TCV

v)20(

)()20( 0

0

°⋅°

=ρ

ρ&

(19) 377

With )20( CV °& as the volume flow rate at 20°C, ρ(T0) as the density of the liquid at 378

inlet temperature T0, ρ(20°C) as the density of the liquid at 20°C and A as the cross-379

section area of the inlet. 380

A pressure of 1.8 bar was defined at the treatment chamber outlet. 381

382

At the fluid inlet, a temperature boundary condition was applied: 383

0TT = (20) 384

A convective flux boundary was applied at the outlet. This condition states that the 385

heat transfer across this boundary is convection dominated and, therefore, radiation 386

is negligible: 387

( ) 0=∇−⋅− Tkn (21) 388

389

Material Properties 390

The thermophysical properties of the salt solution and apple juice (see “Experimental 391

setup for validation”) were assumed to be similar to pure water, except for the 392

electrical conductivity. Therefore, density, specific heat capacity, thermal conductivity 393


and viscosity were taken from the NIST/ASME database (Harvey et al., 1996) as 394

functions of temperature. The temperature dependent electrical conductivity of salt 395

solutions was taken from the previous study (Buckow et al., 2010): 396

( )

+

°

°−⋅⋅

⋅

°=

⋅ −−1

20024234.0

)20()(11 C

CT

cmmS

C

cmmS

T σσ (22) 397

With )(Tσ as the electrical conductivity at any given temperature T and )20( C°σ as 398

the electrical conductivity at a reference temperature of 20°C. 399

400

The electrical conductivity of apple juice (Westcliffe Apple Juice, ALDI, NSW, 401

Australia) was measured in the temperature range of 4-80°C, using an electrical 402

conductivity meter (WP-84 Conductivity-TDS-Temp. Meter, TPS Pty Ltd, 403

Springwood, QLD, Australia) and was accurately described (R2 > 0.99) by Equation 404

23: 405

( ) ( )

+

°

°−⋅⋅⋅= −

120

02593.0048.21

C

CTcmmSTσ (23) 406

407

Equations 22 or 23 were implemented into the models, describing the temperature 408

dependent electrical conductivity of the NaCl solution and apple juice, respectively. 409

The material properties for the insulators (PTFE, k = 0.24 W·m-1·K-1, ρ = 2200 kg·m-3, 410

Cp = 1050 J·kg-1·K-1) and the electrodes (stainless steel, k = 44.5 W·m-1·K-1, 411

ρ = 7850 kg·m-3, Cp = 475 J·kg-1·K-1) were taken from the material library of 412

COMSOL Multiphysics™. 413

Both liquids were assumed to be incompressible and Newtonian. 414

415

Computational Methods 416

The partial differential equations (PDE) describing the Multiphysics scenario, i.e., the 417

coupled equations for conservation of mass, momentum, energy and electric charge 418

were solved with the commercial software package COMSOL Multiphysics™. The 419


considered problems were discretised with the Finite Element Method (FEM), utilising 420

tetrahedral elements for the 3D model and triangular elements for the axis-symmetric 421

2D model, respectively. The mesh in critical regions inside the treatment chamber, 422

such as the insulator gap and the edges caused by the diameter difference of 423

insulator and electrodes, were refined until no further noticeable change in the 424

predicted process variables could be observed. 425

All computations were carried out on a workstation running the 64bit OS Windows 426

2003 server. Two dual-core processors (each 2.33 GHz) and 20 GB RAM allowed for 427

solving the fully coupled 3D models in approximately 75 minutes, the fully coupled 428

axis-symmetric 2D models in about 15 minutes and the axis-symmetric 2D models, 429

only solving for the electric field distributions, in less than 2 seconds. 430

431

Optimisation algorithm 432

The four basic insulator shape models (“no inset”, rectangular inset”, “rectangular 433

rounded edges inset”, and “elliptical inset”) were created within conductive media 434

mode, implemented in COMSOL Multiphysics™ (COMSOL Multiphysics, 2007), 435

applying the following settings: σ = 4 mS·cm-1(constant), V0 = 10 kV. The dimensions 436

of these default models were defined as being variable. An interface to the COMSOL 437

Multiphysics™ models was programmed in MATLAB 7.6™ (Mathworks, Natick, MA, 438

USA). Based on this interface, a software routine progressively modified the models’ 439

geometrical properties according to the parameters discussed in section “Insulator 440

configurations for optimisation studies“. Overall, 103,170 models were automatically 441

generated, solved and the solution stored for further analysis. The next step in the 442

algorithm included the conversion of the COMSOL Multiphysics™ data into 443

MATLAB™ matrices with a spatial resolution of 0.01 mm, followed by a performance 444

evaluation of the respective model predictions. 445

446

Performance evaluation and finding the optimum 447


For improving the treatment chambers often utilised in PEF processing, it was seen 448

important to take a number of dependent and independent parameters into 449

consideration. The treatment zone volume to allow high throughput, the uniformity of 450

the electric field distribution, including the prevention of areas with high electric field 451

strengths (peaks) and also the pressure drop caused by the diameter differences 452

between insulator and electrode bores. Five weighable and dimensionless 453

parameters were selected and an equation was derived to express the performance 454

of each modelled scenario with one dimensionless parameter, the DPP 455

(Dimensionless Performance Parameter): 456

54321 aaaaaEPVUVMVPDVTVVDPP ⋅⋅⋅⋅= (24) 457

With: 458

=

maxV

VTVV zone

, (25) 459

( )

−=

4

4

d

insdPDV , (26) 460

=

min

0

h

V

EMV av , (27) 461

=

±

total

percentageav

n

nUV , (28) 462

and 463

=

maxE

EEPV av (29) 464

Where Vzone is the volume of the treatment zone (insulator region) of the respective 465

scenario, Vmax the volume of the largest treatment zone (i.e., at d = 20 mm, h = 30 466

mm, and “no inset”), Eav is the average electric field strength of the insulator region, 467

V0 the applied potential, hmin the minimum electrode distance (gap) of all scenarios 468


investigated (hmin = 1mm), nav±percentage the number of elements with electric field 469

strengths within 10% of the average electric field strength, ntotal the total number of 470

elements in the treatment zone and Emax the maximum electric field strength in the 471

respective scenario. 472

473

Each of the weighable parameters is made dimensionless by relating the expression 474

in the numerator to their respective maximum values. Therefore, all parameters yield 475

values between 0 and 1, and, thus, also the DPP returns values between 0 and 1, 476

with 1 being the optimum achievable. 477

The first variable (TVV, treatment volume variable) expresses the volume inside the 478

treatment zone related to the volume of the largest treatment zone investigated in 479

this study, where the diameter of the insulator bore is equal to the electrode diameter 480

(20 mm), and the electrode gap is 30 mm. The second variable (PDV, pressure drop 481

variable) is a measure of the pressure drop caused by the diameter reduction of the 482

insulator bore which has been derived from a simplified Bernoulli equation (Equation 483

30), neglecting the level difference part. 484

2

2

21

2

1

22p

vp

v+

⋅=+

⋅ ρρ (30) 485

The third parameter (MV, magnitude variable) of the DPP expresses the electric field 486

strength magnitude of the analysed model, relating the average electrical field inside 487

the insulator region to the maximum electric field strength achievable in a parallel 488

plate configuration (minh

V) with the minimum electrode gap of 1 mm. The fourth 489

variable (UV, uniformity variable) indicates the electric field uniformity in the gap 490

region. The algorithm counts all elements inside the treatment zone that have an 491

electric field strength within a 10% range of the average electric field strength and 492

relates it to the total number of elements in this area. The last parameter in the DPP 493

equation looks at the electric field strength peaks (EPV, electric field strength peak), 494


indicating the magnitude of electric field strength peaks in the treatment zone by 495

relating the average value of the electric field strength to the maximum value in the 496

respective configuration. 497

498

The exponents, a1, a2, a3, a4, a5, can be adjusted and, thus, the different parameters 499

weighed according to their relevance. Increasing the exponents leads to a stronger 500

emphasis on the respective parameters. The weight of each parameter is hereby 501

strongly dependent on the particular application of PEF processing. 502

As for this study, special emphasis was put on the uniformity of the electric field 503

strength distribution and prevention of peaks; therefore, the exponents of MV, UV 504

and EPV were set to values greater than the ones for TVV and PDV. 505

As TVV and PDV were assumed to be almost equally important, their exponents 506

were set to similar values with a slightly greater emphasis on PDV as the pressure 507

drop needs to be kept low (a1 = 0.9 and a2 = 1). MV and EPV, i.e., the concentration 508

of the electric field in the treatment zone, ensuring a safe and efficient treatment, and 509

the prevention of pronounced electric field peaks, which may lead to over-processing 510

and erosion of electrodes and insulators, respectively, were seen equally important. 511

(a3 = a5 = 1.5). The main objective of this optimisation, however, was the uniformity of 512

the electric field strength inside the treatment zone. Hence, the highest exponent 513

(weight) was used for the uniformity variable UV (a4 = 2). 514

As all parameters return values between 0 and 1, also the DPP will yield values 515

below 1 and, thus, the maximum DPP from all simulated scenarios is seen to 516

determine the geometry with the best performance for this particular study. 517

Figure 6 illustrates the optimisation algorithm in a flow chart, highlighting the different 518

steps from model generation, over model solving, data extraction and performance 519

evaluation of the respective scenarios, to finding the best geometrical dimensions of 520

the co-linear treatment chamber configuration. 521


Con

vert

ing

CO

MS

OL

to

MA

TL

AB

Cre

atin

g

mod

els

Fin

din

g

optim

um

Automatically

generating models

for all geometric

properties

Solving all models and

storing predictions

Extracting solutions from

stored files

Allocating the

extracted data to

MATLAB matrices

with a resolution of

0.01 mm

Applying the DPP equation

to all MATLAB matrices

Creating generic

COMSOL models for the

4 insulator shapes

Selecting the

scenario yielding the

highest DPP as

optimum

MATLAB™ Algorithm

522

FIGURE 6: Flowchart of the optimisation algorithm (initial step: model generation 523

outside algorithm), including the generation of all scenarios, data 524

conversion from COMSOL Multiphysics™ to MATLAB™ and 525

determination of optimum. 526

527

Experimental setup for validating the Multiphysics model of the improved 528

treatment chamber 529

The optimised treatment chamber with the shape and dimensions as determined by 530

the optimisation algorithm (exact geometries shown in result section, Figure 11 and 531

12) was built to proof the validity of the model. The treatment chamber was 532

implemented into the pilot-scale PEF system (see “Materials and Methods – Pulsed 533

Electric Field System) at CSIRO Food and Nutritional Sciences (Werribee, Victoria, 534

Australia). 535


The process conditions were adjusted to an inlet volume flow rate of 8 L·min-1 for the 536

trials with the NaCl solution (conductivity of 2.6 mS·cm-1 (adjusted at 20°C)) and the 537

apple juice (measured conductivity of 1.8 mS·cm-1 (adjusted at 20°C)) to ensure 538

turbulent liquid flow (simulated Reynolds numbers ranging from 20,000 to 60,000). 539

The inlet temperature was set to 25 and 45°C, and the rectangular pulses were 540

regulated at the modulator cabinet to pulse widths of 2 and 4 µs, pulse repetition 541

rates of 500 and 700 Hz at an applied peak voltage of 40 kV. 542

Temperature measurements were performed in the second grounded electrode (at 543

the outlet of the second treatment zone) by insertion of an electrically inert fibre optic 544

probe. Inlet and air temperature in the treatment chamber cabinet were measured for 545

further use as boundary conditions in the Multiphysics models. The measured 546

temperature was recorded when the temperatures inside the treatment chamber 547

reached a stationary state after approximately 5-10 minutes. All experiments were 548

replicated in duplicate. Frequency, pulse width, pulse shape and voltage were 549

recorded with an oscilloscope (#GDS-1102, GW Instek, Taipei, Taiwan) attached to 550

the output ports of the PEF system. Time-averaged potentials were related to the 551

maximum potential to determine the factor φ (see Equation 11), while the maximum 552

potential was used as boundary condition of the high voltage electrode. 553

554

3. Results and Discussion 555

Results of the optimisation algorithm 556

The optimisation algorithm created more than 100,000 2D axis-symmetric models 557

and the distribution of the electric field was numerically predicted using the 558

implemented MATLAB™-COMSOL™ interface. For some selected models, the 559

predicted electric field distributions were compared to illustrate the impact of the 560

insulator geometries on the distribution of the electric field (Figure 7). 561


As already reported by other authors (e.g. Mastwijk et al. (2007)), the numerical 562

simulations from this study also showed that the electric field strength is highest in 563

close vicinity of sharp insulator edges. For example, such edges are created by the 564

diameter differences of insulator bore and electrodes, but also interfaces between 565

electrode and insulator for small “elliptical insets” and in the centre along the height 566

of an elliptical insulator shape for larger insets exceeding 50% of the electrodes’ 567

internal diameter (Figure 7). Towards the centre line (symmetry axis) of the treatment 568

zone the electric field strength peaks at the edges decrease, improving radial 569

uniformity with larger insulator insets. 570

571


(a)

(b)

(c)

572

FIGURE 7: Examples for the simulated distribution of the electric field strength in 573

the cross-section of the treatment zone for “elliptical” (a), “rectangular” 574

(b) and “rectangular rounded edge” (c) insulator shape insets (insets 0 575

to 60% of the electrodes’ internal diameter and radii of 50% of total 576

inset for the “rectangular rounded edge” configuration) with a constant 577

internal electrode diameter of 10 mm, an electrode gap of 15 mm, a 578

constant electric conductivity of 4 mS·cm-1 and an applied peak 579

potential of 10 kV). (For colour representation, the reader is referred to the online version 580

of this article) 581

582


For the determination of the treatment chamber quality features (treatment volume, 583

pressure drop due to the insulator inset, and magnitude and uniformity of the electric 584

field strength), the optimisation algorithm loops through all solved models, returning 585

geometric dimensions (shape, electrode diameter, insulator bore inset and insulator 586

height) and DPP values. For the chamber geometries without an insulator inset (i.e. 587

the “no inset” configuration), the varying geometry features were the internal 588

diameter of the electrodes and the electrode gap and, thus, the DPP values can be 589

illustrated in a 2D plot as a function of the tube radius and insulator height (electrode 590

gap) (Figure 8). 591

The greatest DPP value for the “no inset” scenario was found at a tube diameter of 2 592

mm and an electrode gap of 4 mm (DPP ≈ 2·10-4). As the emphasis of this study was 593

to improve the electric field strength uniformity and magnitude, the outcome of the 594

optimisation equation unveiled that only small treatment volumes allow a relative 595

uniform distribution of the electric field for a configuration without insulator inset. 596

5 10 15 20 25 30

2

4

6

8

Insulator height (mm)

Ele

ctr

ode a

nd insula

tor

bore

rad

ius (

mm

)

0

1

2

x 10-4

597

FIGURE 8: DPP value distribution for all “no inset” model geometries. (For colour 598

representation, the reader is referred to the online version of this article) 599

600

DP

P


The “rectangular” and “elliptical insulator inset” comprised as a further optimisation 601

variable the minimum diameter of the insulator bore. Therefore, the DPP values can 602

be illustrated in form of a 3D distribution, with electrode radius, electrode gap and 603

difference between the electrode diameter and the minimum diameter of the insulator 604

bore (i.e. “inset”) as axes (Figure 9). The highest DPP value for the “elliptical inset” 605

configuration was found at an electrode inner diameter of 20 mm, an electrode gap 606

(insulator height) of 11 mm and an insulator inset, i.e. diameter difference, of 25% of 607

the electrodes’ inner diameter (DPP ≈ 2.12·10-4). 608

As the “rectangular inset” configuration still exhibits pronounced electric field strength 609

peaks at the edges of the insulator bore, similar to the “no inset” configuration, the 610

total volume of the treatment area was found to be smaller for achieving more 611

uniform treatment. Therefore, the highest DPP value was determined for an electrode 612

diameter of 5 mm, an insulator height of 9 mm, but with an inset of only 5% of the 613

electrodes’ diameter (DPP ≈ 2.43·10-4). 614

(a) (b) 615

FIGURE 9: DPP value distribution of all model geometries for “elliptical” (a) and 616

“rectangular inset” (b). (For colour representation, the reader is referred to the online 617


619

For the “rectangular rounded edges” configuration, the chamfer radii at the insulator 620

edges had to be taken into consideration as a fourth parameter. Therefore, visual 621

DP

P


illustration of the DPP values was not possible in a single (3D) plot. For each radius 622

of the chamfered edges, a separate 3D DPP distribution was plotted. Figure 10 623

shows the DPP distributions for three chamfer radii, namely 10, 25 and 40% of the 624

diameter difference between the electrode and the insulator bore (i.e., insets). Some 625

slices in these plots appear incomplete, particularly for increasing insets and 626

increasing chamfer radii at low electrode gaps. This is caused by combinations of 627

insulator height (electrode gap), electrode radius, insets and chamfer radii, which are 628

physically not possible, i.e., when the insulator height is not sufficient for 629

incorporating chamfer radii of a certain percentage of the inset. 630

The results indicate best performance and, thus, highest DPP value 631

(DPP ≈ 3.53·10-4; clearly higher than the values of all other shapes investigated) for 632

an electrode internal diameter of 12 mm, an insulator height (electrode gap) of 20 633

mm, an inset of 15% of the electrode diameter (i.e., 0.9 mm), and a chamfer radius of 634

40% of the total inset (i.e., 0.36 mm). 635

0

1

2

x 10-4

(a) (b)

(c)

636

FIGURE 10: DPP value distribution for all model geometries for “rounded 637

rectangular edge inset” configuration for radii of 10% (a), 25% (b) and 638

DP

P


40% (c) of the difference of electrode and insulator bore diameter 639

(inset). (For colour representation, the reader is referred to the online version of this article) 640

641

The comparison of the maximum DPP values for all insulator configurations, at the 642

weighing exponent settings as discussed earlier, shows that the “no inset” 643

configuration gave the lowest global DPP value. Surprisingly, the “rectangular inset” 644

configuration yielded a higher maximum DPP value than the “elliptical inset”, but at a 645

lower treatment volume. Nonetheless, the “rectangular rounded edge inset” 646

configuration yielded the highest global DPP value, indicating superior performance 647

over all other configurations investigated. 648

The analysis of the optimisation parameters of the DPP equation for the “rectangular 649

rounded edge inset” scenario gave the following values for the improved chamber 650

geometry: 651

The treatment volume variable (TTV) had a value of 0.3405 which relates to 34.05% 652

of the maximum treatment volume of this study (i.e., diameter of 20 mm, electrode 653

gap of 30 mm and “no inset” configuration). Compared to the configuration of the 654

treatment chamber supplied by the manufacturer, the treatment volume was 655

increased by more than 600%, allowing for increased throughput or prolonged 656

exposure times, respectively. 657

The pressure drop variable (PDV) gave a value of 0.522. From this value alone, it is 658

not possible to draw conclusions on the actual pressure drop in the system; the fully 659

coupled 3D model (see section “3D model of improved treatment chamber”), 660

however, predicted a pressure drop of 0.02 bar in the entire treatment chamber, 661

whereas the total pressure drop in the original system was only 0.004 bar. Although 662

the original system performs better with respect to the pressure drop, a total pressure 663

drop of 0.02 bar, caused by the insulator inset, is negligible compared to the overall 664

pressure drop along the piping of the entire system, including the peripheral setup, 665

such as liquid handling system and heat exchangers. 666


The magnitude variable (MV) of the improved design resulted in a value of 0.0412, 667

which, in fact, was lower than for all other configurations. However, this was 668

expected as the MV is determined by dividing the average electric field strength for 669

the improved geometry through the maximum electric field strength that could be 670

achieved in this study. As the electric field can be estimated with Eq. 1, smaller gaps, 671

as determined for the other configurations, lead to higher electric field strengths and, 672

therefore, greater values for MV. The MV value of the original system was found to 673

be 0.101, i.e. the average electric field strength was about 2.5 times higher than for 674

the improved chamber design. 675

The uniformity variable (UV) of the optimised design yielded a value of 0.887, which 676

means that 88.7% of the treatment zone exhibits electric field strengths within the 677

±10% range of the average electric field strength of this chamber configuration. In 678

comparison, the original treatment chamber yields a UV value of only 0.3202, i.e. 679

less than one third of the treatment zone provides electric field strengths within the 680

predefined 10% range of the average electric field strength. 681

The last, and in this study most important (i.e., greatest weight) parameter of the 682

DPP equation, the electric field strength peak variable (EPV), showed a value of 683

0.4193 for the optimised design. This indicates that the average electric field strength 684

of the treatment zone has approximately 42% of the strength of the highest electric 685

field peak of the treatment chamber.This value is significantly better than the one of 686

the original setup, which had an EPV value of only 0.1099. Accordingly, the peak 687

electric field strength at the sharp edges of the original configuration is approximately 688

9 times higher than the average electric field strength of the chamber. Such electric 689

field peaks are likely to cause temperature hotspots, over-processing of the treated 690

liquid, arcing and associated erosion of the electrodes and insulators. 691

As discussed above, the improved design is superior in most parameters seen 692

relevant for PEF processing; i.e., treatment volume, uniformity and avoiding of peak 693

electric field strengths. Two of the discussed parameters of the original design yield 694


higher values: the pressure drop and the average electric field strength caused by 695

greater electrode distances in the improved design, which can be overcome by 696

applying higher voltages. 697

698

Design of the improved treatment chamber 699

Figures 11 and 12 illustrate the new design and dimensions of the improved 700

treatment chamber. The new PTFE insulators measure an outer diameter of 98 mm, 701

an internal diameter of 16 mm and a total height of 53 mm. The spacer between high 702

voltage and grounded electrode has a height of 20 mm and the internal diameter 703

decreases to 10.2 mm centred along the height of the bore with a rounded edge 704

radius of 0.36 mm (Figure 12). The three electrodes made of stainless steel for the 705

optimised chamber have an outer diameter of 16 mm and an inner diameter of 706

12 mm (Figure 11). 707

708

FIGURE 11: Dimensions and geometries of the electrodes and insulator of the 709

improved co-linear PEF treatment chamber. 710

711


712

FIGURE 12: Close-up of the design and dimensions of the improved insulator. 713

714

3D model of the improved treatment chamber 715

A fully coupled (i.e. simultaneously solving the conservation equations of mass, 716

momentum, energy and charge) 3D model of the improved chamber was developed 717

in COMSOL Multiphysics™, for simulating PEF processing of NaCl solutions and 718

apple juice (Figure 13). The results presented in this section for electric field, 719

turbulent flow and temperature distribution are all based on the following process 720

settings: Electrical conductivity at 20°C of 2.6 mS·cm-1 for the NaCl solution, applied 721

peak voltage of 40 kV, pulse width of 4 µs, pulse repetition rate of 700 Hz, flow rate 722

of 8 L·min-1 (adjusted at 20°C, prior to entering the heat exchanger), inlet temperature 723

of 25°C, and external air temperature of 20°C. 724

725


726

FIGURE 13: Three dimensional configuration of the improved PEF treatment 727

chamber with co-linear electrode configuration and magnified view on 728

the treatment zones. 729

730

Electric field distribution 731

Setting a peak potential of 40 kV at the high voltage electrode leads to an average 732

electric field strength of approximately 17 kV·cm-1 in the two treatment zones (Figure 733

14). Along the centre line of the tube, the electric field strength only fluctuates in a 734

small range between 13 and 17 kV·cm-1. In the vicinity of the insulator edge (0.01 mm 735

from the edge) the electric field strength peaks at 28.7 kV·cm-1 (Figure 15). This is 736

much closer to the average value of 17 kV·cm-1 (Figure 15) than in the original 737

chamber design, where the maximum electric field strength was found to be nine 738

times higher than the average value (Buckow et al., 2010). 739


740

FIGURE 14: Simulated distribution of the electric field strength in the treatment 741

chamber, including a close-up of both treatment zones. The settings 742

were: Electrical conductivity at 20°C of 2.6 mS·cm-1, applied peak 743

voltage of 40 kV, pulse width of 4 µs, frequency of 700 Hz, flow rate of 744

8 L·min-1, inlet temperature of 25°C, and external air temperature of 745

20°C. (For colour representation, the reader is referred to the online version of this article) 746

747

0.155 0.16 0.165 0.17

1.5

2

2.5

3x 10

6

Height (m)

Ele

ctr

ic fie

ld s

tength

(V

/m)

Symmetry line

0.1mm frominsulator wall

748

FIGURE 15: Axial distribution of the electric field strength along the tube centre and 749

at 0.1 mm distance from the insulator wall. 750

751


Flow characteristics 752

As sufficient mixing of the treated liquid in the treatment zone is important to prevent 753

(or minimise) the formation of temperature hotspots, turbulent flow and, therefore, the 754

Reynolds number and turbulent kinetic energy are of utmost relevance. The highest 755

turbulent kinetic energy was found at the outlets of the two treatment zones with up 756

to 0.36 m²/s² (Figure 16), as obstacles enforce a change of flow direction. The 757

Reynolds number (Equation 31) fluctuates in a range of 20,000 to 60,000 and, thus, 758

turbulence can be assured within the treatment zone (Figure 17). 759

η

νρ d⋅⋅=Re (31) 760

With ρ as density of the liquid, ν as velocity in flow direction, d as pipe diameter 761

and η as dynamic viscosity. 762

763

764

FIGURE 16: Simulated distribution of the turbulent kinetic energy in the treatment 765

chamber, including a close-up of both treatment zones (model settings 766

as discussed earlier). (For colour representation, the reader is referred to the online 767


769


770

FIGURE 17: Simulated Reynolds number distribution in the treatment chamber 771

(model settings as discussed earlier). (For colour representation, the reader is 772

referred to the online version of this article) 773

774

Temperature distribution 775

The simulation also showed a significant increase of the liquid temperature in both 776

treatment zones of the PEF chamber, which is caused by ohmic heating in the 777

regions of high electric field intensities. In chamber one, the liquid heats up by about 778

7.5°C and in the second chamber by approximately 10.5°C (Figure 18). The 779

difference in the heating extent in the two identical treatment zones can be explained 780

by the increase of the electrical conductivity and, therefore, greater conversion of 781

electrical into thermal energy. The results show that only marginal radial temperature 782

gradients occur in the improved design, with the highest difference being less than 783

2°C at the outlet of the second treatment zone (Figure 19). 784

Re


0 0.005 0.01 0.015 0.0225

30

35

40

45

Height of the gap (m)

Tem

pera

ture

(°C

)

Chamber 1

Chamber 2

785

FIGURE 18: Axial temperature profile of the liquid passing through the first and 786

second treatment zone of the improved co-linear treatment chamber 787

(model settings as discussed earlier). 788

0 1 2 3 4 5 6

x 10-3

0

0.5

1

1.5

2

distance from symmetry axis (m)

Tem

para

ture

gra

die

nt T

ma

x-T (

°C)

Outlet chamber 2

Outlet chamber 1

789

FIGURE 19: Radial difference of temperatures of the liquid from the maximum 790

value at the outlet of the first and second treatment zone of the 791

improved system (model settings as discussed earlier). 792

793

The electrodes exhibit a uniform rise of temperature due to the steel’s high thermal 794

conductivity. On the other hand, the insulators only experience a significant 795


temperature increase in the regions close to the liquid as their thermal conductivity is 796

low (Figure 20). 797

798

FIGURE 20: Simulated temperature distribution in the treatment chamber for liquid 799

and solid parts, including a close-up of both treatment zones (model 800

settings as discussed earlier). (For colour representation, the reader is referred to the 801

online version of this article) 802

803

Model Validation 804

Numerical simulations were performed according to the settings described in the 805

“Materials and Methods” section: An applied peak voltage of approximately 40 kV, 806

two different pulse lengths of 2 and 4 µs, pulse frequencies of 500 and 700 Hz, a flow 807

rate of 8 L·min-1, and two inlet temperatures of 25 and 45°C, respectively. The 808

dissipated energy into the liquid was in a range of 16 to 98 kJ·kg-1, and process 809

temperatures were in a range of 25°C to 71°C. 810

The measured temperatures at the outlet of the second treatment zone were 811

compared to the numerically simulated data for the NaCl solution and the apple juice, 812

respectively. As shown in Table 1 and Figure 21, the experimental data were well 813

predicted by the Multiphysics model, with the largest deviation found to be 814

approximately 1°C. The parity plot of Figure 21 visually illustrates the good 815


agreement between the simulation and measurement, yielding a coefficient of 816

determination R² close to one. 817

818

TABLE 1: Measured and predicted temperatures at the outlet of the second 819

treatment zone in the improved PEF treatment chamber for NaCl 820

solutions and apple juice at different settings. 821

σ (20 °C)

(mS/cm)

V

(kV)

τ

(µs)

f

(Hz)

V&

(L/min)

T0

(°C)

Tmeasured

(°C)

Tsimulated

(°C)

2.6 38.08 2 500 8 25 30.8 ± 0.14 31.06

2.6 37.92 2 500 8 45 52.9 ± 0.14 53.28

2.6 38.4 4 500 8 25 38.6 ± 0.14 38.85

2.6 38.08 4 500 8 45 63.0 ± 0.07 63.03

2.6 38.08 2 700 8 25 33.3 ± 0.28 33.52

2.6 37.92 2 700 8 45 55.8 ± 0.00 55.98

2.6 38.08 4 700 8 25 45.5 ± 0.35 44.56

2.6 38.08 4 700 8 45 71.7 ± 0.49 71.23

1.802 39.04 2 500 8 25 29.1 ± 0.00 29.22

1.802 39.04 2 500 8 45 49.9 ± 0.07 50.87

1.802 39.04 4 500 8 25 34.2 ± 0.07 34.28

1.802 39.04 4 500 8 45 57.6 ± 0.00 57.46

1.802 39.04 2 700 8 25 30.9 ± 0.14 30.78

1.802 39.04 2 700 8 45 53.2 ± 0.14 52.94

1.802 39.04 4 700 8 25 38.3 ± 0.07 38.44

1.802 39.04 4 700 8 45 63.3 ± 0.28 63.48

822


30 40 50 60 7025

30

35

40

45

50

55

60

65

70

75

Tmeasured

(°C)

Tsim

ula

ted (

°C)

R2 = 0.99906

bisecting line

Salt solution

Apple juice

823

FIGURE 21: Parity plot of predicted and experimentally determined temperature 824

values as shown in Table 1. 825

826

4. Conclusions and outlook 827

PEF processing is claimed to be highly effective for inactivation of vegetative 828

microorganisms in liquid foods with moderate temperature increases; therefore, it is 829

commonly referred to as a non-thermal pasteurisation treatment. It is mainly for this 830

reason, that PEF is considered a practicable preservation method, particularly for 831

liquid foods containing highly heat labile components. However, to ensure a 832

homogeneous and, thus, safe treatment, and to prevent partial over- or under-833

processing of the food, it is important to avoid temperature hotspots and peaks of the 834

electric field strength by improving the PEF treatment chambers’ designs and 835

configurations. 836

The purpose-developed optimisation algorithm presented in this work was able to 837

identify an improved configuration of a co-linear treatment chamber from more than 838


100,000 possible chamber geometries. According to the outcome of the algorithm, a 839

3D Multiphysics model was developed and a new treatment chamber was 840

manufactured. The model proved to accurately predict the stationary temperatures 841

distributions in the improved PEF treatment chamber, yielding a coefficient of 842

determination of greater than 0.99, when comparing the measurements and the 843

simulations of the processing of a salt solution and apple juice at varying process 844

conditions. Therefore, the conclusion can be drawn that the model also predicts other 845

important process variables, such as the electric field strength distribution and the 846

flow characteristics, at good accuracy. 847

The improved chamber design was capable of preventing extreme electric field 848

strength peaks, creating a more uniform distribution of the electric field, while 849

significantly increasing the treatment volume of the original system and keeping the 850

associated pressure drop caused by the diameter reduction in the treatment zone 851

low. 852

As the emphasis of the presented work was put on a good interaction of electric field 853

uniformity and magnitude, the improved design identified by the optimisation 854

algorithm is only one example, representing the optimum for one viewpoint of 855

emphasis. The weighing exponents of the Equation 24 have a significant impact on 856

the outcome of the algorithm. Hence, for each optimisation of this kind the first step 857

must be the definition of the weights (importance) of the variables in the DPP 858

equation, depending on objective process targets and food properties. The 859

optimisation algorithm, including the interface between MATLAB™ and COMSOL 860

Multiphysics™, was developed as a platform, therefore, allowing further studies for 861

improving the design of PEF treatment chambers, targeting varying emphasis on the 862

parameters in the DPP equation, or, alternatively, the definition of further parameters 863

that may be of relevance for industrial applications of PEF processes. 864

865

Acknowledgements 866


The authors gratefully acknowledge the Victorian State Government for the Science 867

and Technology Infrastructure grant enabling this work to be carried out. 868

Furthermore, we would like to thank Mr Phil Muller and Mr Piotr Swiergon for their 869

support in setup and maintenance of the PEF system, and the manufacture of the 870

improved treatment chamber. 871

872

Notation 873

A Cross-sectional area of treatment chamber inlet [mm2] 874

51−a Exponents (weights) of the DPP equation within the optimisation 875

algorithm 876

CP Specific heat capacity [J kg-1 K-1] 877

Cµ Model constant [m4 kg-4] 878

d Electrode diameter [mm] 879

E Electric field strength [V m-1] 880

avE Average electric field strength [V m-1] 881

maxE Maximum electric field strength [V m-1] 882

f Pulse repitition rate (frequency) [Hz] 883

fi Predicted values from 3D model 884

g Gravity constant [9.8 m s-2] 885

heath Heat transfer coefficient [W m-2·K-1] 886

h Electrode distance (gap) [mm] 887

hmin Minimum electrode distance (gap) of all scenarios investigated [1 mm] 888

ins Total insulator inset, i.e., diameter difference between electrode and 889

insulator bore [mm] 890

J Density of the electrical current [A m-2] 891

k Turbulent kinetic energy [m2 s-2] 892

k,k1,k2 Thermal conductivity [W m-1 K-1] 893


kT Turbulent thermal conductivity [W m-1 K-1] 894

m& Mass flow rate [kg s-1] 895

n Normal direction 896

percentageavn ± Number of mesh elements within a certain band of the average 897

electric field strength in the treatment zone of a PEF chamber 898

totaln Total number of mesh elements in the treatment zone (liquid domain) 899

P Pressure including a fluctuating term [Pa] 900

p Pressure [Pa] 901

PrT Turbulent Prandtl number 902

Qeff Heat source [W m-3] 903

Qspec Dissipated energy [kJ kg-1] 904

q, q0 Heat flux [W m-2] 905

rad, R Rounded edge (chamfer) radius [mm] 906

R2 Coefficient of determination 907

Re Reynolds number 908

T Temperature [K, °C] 909

T0 Inlet temperature [K, °C] 910

Tinf Reference bulk temperature [K, °C] 911

Tmeasured Temperature measured in validation experiments [°C] 912

Tsimulated Temperature predicted for model validation [°C] 913

t Time [s] 914

U Velocity for the 2D-3D comparison [m s-1] 915

v,v1,v2 Velocity [m s-1] 916

v0 Inlet velocity [m s-1] 917

→

v Velocity vector [m s-1] 918

V& Volume flow rate [m3 s-1] 919

V Voltage [V] 920


V0 Maximum potential of a pulse [V] 921

Vmax Maximum treatment zone volume [m3] 922

Vzone Volume of treatment zone of the different chamber configurations [m3] 923

yi Predicted values from 2D model 924

y mean of the predicted values from 2D model 925

926

Greek letters 927

ε Dissipation rate of turbulence energy [m2 s-3] 928

η Dynamic viscosity [Pa s] 929

ηT Turbulent viscosity [Pa s] 930

ρ Density [kg m-3] 931

σ Electrical conductivity [S m-1] 932

τ Pulse width [s] 933

φ Factor for time-averaged potential of PEF pulses 934

935

Abbreviations 936

2D Two dimensional 937

3D Three dimensional 938

CFD Computational Fluid Dynamics 939

DPP Dimensionless Performance Parameter 940

EPV Electric field strength peak variable 941

FEM Finite Element Method 942

HVE High Voltage Electrode 943

MV Magnitude Variable 944

NaCl Sodium Chloride 945

NIST National Institute of Standards and Technology 946

OS Operation System 947


PEF Pulsed Electric Field 948

PDE Partial Differential Equation 949

PDV Pressure Drop Variable 950

PTFE Polytetrafluoroethylene 951

RAM Random Access Memory 952

TVV Treatment Volume Variable 953

UV Uniformity Variable 954

955

Operators 956

∂ Partial differential 957

∆ Difference 958

∇ Nabla operator (vector differential operator) 959

960

References 961

962

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1 Pulsed Electric Field (PEF) Treatment Chamber Optimisation

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