Journal of Industrial and Engineering Chemistry 20 (2014) 1411–1420

Mixing assessment by chemical probe

Charbel Habchi a, Thierry Lemenand b, Dominique Della Valle b,c, Mahmoud Khaled a,Ahmed Elmarakbi d, Hassan Peerhossaini e,*a Energy and Thermo-Fluids Group ETF, School of Engineering, Lebanese International University LIU, 146404 Mazraa, Beirut, Lebanonb LUNAM Universite, Thermofluid Complex Flows and Energy Research Group, Laboratoire de Thermocinetique de Nantes, CNRS UMR 6607, 44306 Nantes,

Francec ONIRIS, 44322 Nantes, Franced Department of Computing, Engineering and Technology, Faculty of Applied Sciences, University of Sunderland, Sunderland SR6 0DD, United Kingdome Univ Paris Diderot, Sorbonne Paris Cite, Institut des Energies de Demain (IED), CNRS FRE 3597, 75013 Paris, France

A R T I C L E I N F O

Article history:

Received 3 February 2013

Received in revised form 24 June 2013

Accepted 17 July 2013

Available online 9 August 2013

Keywords:

Micro-mixing

Turbulence energy dissipation rate

Chemical probe method

Mixing measurement

Iodide–iodate chemical system

A B S T R A C T

Quantification of micro-mixing is a fundamental issue in industrial chemical processes. Local mixing that

is not ‘‘fast enough’’ compared with the reaction kinetics reduces the selectivity of the reaction. Micro-

mixing can be characterized by chemical probe methods based on observation of a local chemical

reaction that results from the competition between turbulent mixing at micro-scales and the reaction

kinetics. However, real-world experimental conditions rarely comply with the grounding assumptions

of this method. Starting from physical considerations, the present study aims to establish some

guidelines for obtaining quantitative information from the chemical probe and for improving the

accuracy of the method by an adaptive protocol. For the first aspect, an analytical approach is proposed to

define the validity domain based on analysis of the turbulent time scales. For the second purpose, a novel

experimental procedure is suggested that entails targeting the concentrations of the chemical species

that can provide the optimal conditions for a relevant use of the chemical probe.

� 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights

reserved.

Contents lists available at ScienceDirect

Journal of Industrial and Engineering Chemistry

jou r n al h o mep ag e: w ww .e lsev ier . co m / loc ate / j iec

1. Introduction

Characterizing micro-mixing is an important issue in the‘‘Green Process’’ scheme, since it governs, in a broad class ofindustrial processes, byproduct effluents and consequently processefficiency. The selectivity of fast chemical reactions depends onreagent mixing at the molecular scale. In turbulent flows, thespecies aggregates are reduced in size by the turbulent cascade. Inthis process, the limiting mechanism occurs at smaller turbulencescales [1]. Thus, the sequence of micro-mixing is (i) engulfment inthe energetic vortices at Kolmogorov scale, (ii) stirring in theviscous-convective subrange, where the fluid particles are sub-jected to laminar stretching [2], and (iii) molecular diffusion atsub-Batchelor scales that rapidly dissipates the variance inconcentration. Understanding and quantifying this mechanism isessential in designing industrial processes involving fast reactionsthat can present characteristic reaction times smaller than thecharacteristic micro-mixing time.

The two final steps in the micro-mixing mechanism describedabove are ‘‘faster’’ [1–4] than engulfment at the Kolmogorov scale:

* Corresponding author. Tel.: +33 6 07 53 31 61.

E-mail address: hassan.peerhossaini@univ-paris-diderot.fr (H. Peerhossaini).

1226-086X/$ – see front matter � 2013 The Korean Society of Industrial and Engineer

http://dx.doi.org/10.1016/j.jiec.2013.07.026

as a consequence, micro-mixing depends on the turbulence energydissipation rate, which governs the time and length scale of thesmaller eddies. This fundamental property of the turbulent fieldcan be determined by classical velocimetry methods such as laserDoppler anemometry (LDA), particle image velocimetry (PIV), orhot-wire anemometry, all of which give access, in three-dimensional space, to the nine contributions of the turbulentenergy dissipation rate [5].

Alternative methods to characterize micro-mixing based onobservations of a chemical system have been developed over thelast few years [6–10], mostly for the cases where there is no opticalaccess to the flow to carry out reference methods like LDA or PIV,but also for their ability to give access to the result of a chemicalreaction, and thus to the straightforward result of the masstransfer. These methods were investigated especially by Bourne[11] (coupling of naphtol-1 and -2 with diazot sulfanilic acid), andFournier et al. [12] (Villermaux–Dushman reactions or the iodide/iodate method). These techniques, called ‘‘chemical probe meth-ods’’, are based on the competition between micro-mixing andwell-known chemical kinetics by the straightforward observationof reaction selectivity, i.e. the secondary product concentrations.Such experiments must be performed under controlled conditions,first by ensuring that the main reaction is not fully achieved: theselectivity must be ‘‘far’’ from 0 and 1 to make the reaction product

ing Chemistry. Published by Elsevier B.V. All rights reserved.

Nomenclature

ci concentration of species i (mol)

d needle diameter (m)

D reactor diameter (m)

Dt turbulent diffusivity (m2/s)

TKE, k turbulence kinetic energy (m2/s2)

t time (s)

tm micro-mixing time (s)

W local flow velocity (m/s)

Wi injection velocity (m/s)

W mean flow velocity (m/s)

Q flow rate (m3/s)

Xs segregation index

[] concentration (mol)

Greek symbols

e turbulence energy dissipation rate (m2/s3)

L integral length scale (m)

y kinematic viscosity (m2/s)

t time constant (s)

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–14201412

sensitive to the micro-mixing. Under optimal conditions theslowest reaction time is equal to the micro-mixing time. Fromknowledge of the chemical reaction (mechanism, kinetics andstoichiometry), the local turbulent energy dissipation rate canreadily be derived from the measured selectivity via phenomeno-logical micro-mixing models [3].

The appropriate choice of operating conditions (initial reagentconcentrations, injection flowrate, stoichiometry. . .) is not trivialand there is as yet no clear methodology for using chemical probes,especially for open-loop flows. The choice of initial concentrationsis generally made by ‘‘trial and error’’ and sometimes is notconvenient with respect to the reaction kinetics [13–15]. Accuratequantitative results can be obtained if certain conditions on theflow and the chemical system are fulfilled. The purpose of thepresent work is to establish guidelines for obtaining quantitativeinformation from the chemical probe when possible and forimproving the accuracy of the method by an adaptive protocol. Forthe first aim, an analytical approach based on analysis of thecompetition between the different turbulent time scales isproposed in order to assess the feasibility of chemical probemethod, i.e.to answer the question if the chemical probe is able ornot to give relevant information on the transfers in these peculiarconditions. For the second purpose, a novel experimental adaptiveprocedure is suggested, that entails targeting the optimalconcentrations of the chemical species providing more accurateand more ‘‘localized’’ observation of the mixing time, andsubsequently of the energy dissipation rate. These rules can begeneralized to any chemical-probe system and can be applied inany reactor geometry.

In the present work, the mixing scales analysis and theadaptive procedure are applied to an inline heat exchanger–reactor equipped with aligned vortex generators. The iodide/iodate reaction system [12,16,17] and the micro-mixing E-model [18] employed here, are widely used in batch andcontinuous-flow reactors [19–22]. The chemical probe methodand the micro-mixing model are succinctly reprised in Section 2.In Section 3, a scaling analysis of turbulence and of theinteractions among the different scales leads to the definitionof a validity domain for the chemical probe method. In Section 4,a novel experimental procedure is proposed to adapt the reagent

concentrations to the turbulence level and to check themeasurement volume at the injection point. Section 5 is devotedto some sample improvements that may result from the presentanalysis, specifically comparing a static mixer equipped withaligned vortex generators to previous experiments [23].Concluding remarks about the application opportunities of themethod are given in Section 6.

2. Chemical probe: chemical system and micro-mixing model

2.1. The iodide/iodate method

The iodide/iodate system [12,16,17] is based on competitiveparallel reactions: the quasi-instantaneous borate neutralization[Eq. (1)] and the Dushman reaction [24] [Eq. (2)], which is muchslower. The balanced reactions can be modeled as follows:

H2BO�3 þ Hþ$ H3BO3 (1)

5I� þ IO�3 þ 6Hþ$ 3I2 þ 3H2O (2)

The iodine I2 further reacts with iodide ions I�, yielding I�3 ionsfollowing the quasi-instantaneous equilibrium reaction:

I2 þ I�$ I�3 (3)

The kinetics of the three reactions was established byGuichardon et al. [17]. Only the characteristic time of the slowestreaction in Eq. (2) is described here, since it is used for furthercalculations:

tr2 ¼Min 3

5 I�½ �; 3 IO�3� �

; 12 Hþ� �� �

r2(4)

where the brackets denote the reagent concentration and r2 is therate of the second reaction:

r2 ¼ K2 I�½ �2 Hþ� �2

IO�3� �

(5)

where the constant K2 is a function of the ionic strength as given byPalmer et al. [25] and Guichardon et al. [17].

When the micro-mixing is limiting, a local overconcentration ofH+ can react after reaction (2) and produce iodine I2, which itselfreacts with iodide I� and yields I�3 ions [Eq. (3)]. The presence of I2

and I�3 is hence the manifestation of a mixing time smaller than thesecond reaction time and can be quantified by a segregation index.In continuous systems, it is defined by Fournier et al. [26] andFerrouillat et al. [27] as:

Xs ¼ 2I2½ � þ I�3

� �Hþ� �

0

1þQPQHþ

� �1 þ

H2BO�3� �

0

6 IO�3� �

0

!(6)

where Qp and QHþ are respectively the principal flow rate of theinitial mixture flow and the injection flow rate of sulfuric acid.XS = 0 for perfect micro-mixing and XS = 1 for total segregation onthe molecular scale.

In order to determine the I2 and I�3 concentrations in the Eq. (6),the output flow is driven to a spectrophotometer cell where thelight absorption, which is proportional to the concentration of I�3ions, is recorded. The iodine [I2] is derived from the mass balanceon iodine [26].

2.2. Micro-mixing model

The segregation index XS provides only qualitative informationon micro-mixing since it depends on the initial concentrations andon the ratio between the main and injection flows. The relatedquantitative parameter is the intrinsic micro-mixing time tm,

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–1420 1413

independent of the chemical system, which can be identified by amicro-mixing model.

Several micro-mixing models exist for determining micro-mixing time [26,28,29]. In the present work, the engulfment model(E-model) developed by Baldyga and Bourne [18] for fluids withhigh Schmidt number is used, since it gives more reliable resultsthan other models in the literature [30].

The mass balance, involving the growth of the uniform mixingzone of concentration ci, is given by the first-order temporaldifferential equation:

dci

dt¼ 1

tmci � cið Þ þ Ri (7)

where ci is the mean concentration value in the environmentbefore mixing is completed and Ri is the rate of formation ofsubstance i by a chemical reaction [18]. The system is composed ofnine nonlinear equations (for each species); Eq. (7) is integratedusing the Newton–Raphson iterative method. Actually, thesolution tm is the rate of the reactant formation yielding to theobserved experimental values. In practice, one integrates on timethe set of Eq. (7) for a range of tm values: for each value, a XS

‘‘computed value’’ can be derived from the final speciesconcentrations (till the whole consumption of H+). The ‘‘right’’tm value in this range is determined by providing a computed XS

equal to the experimental XS. This is done thanks to the ‘‘calibrationcurves’’ specific of the chemical system (Fig. 1) which globalizeXS ¼ F tmð Þ, where F is conceptually the temporal integration step.

Examples of calibration curves XS ¼ F tmð Þ for three differentinitial concentrations of sulfuric acid are shown in Fig. 1. It can beobserved that the curve is flat for both ‘‘small’’ and ‘‘large’’ tm

values, denoting a lack of sensitivity of XS to the micro-mixing time.This can be explained from phenomenological considerations.For small micro-mixing time, tm << tr2, micro-mixing is veryefficient and has no significant influence on XS, because locallythe reagents are ‘‘rapidly’’ homogenized. Eventually, if the large-scale transfers are limiting, the second reaction may develop on alarger volume and its selectivity is hence determined by theglobal mixing. At the other limit, for very large micro-mixingtime, tm >> tr2, reaction selectivity is completely governed bythe kinetics of the second reaction, and the hydrodynamic haveonly a weak effect on XS. Thus, the method will be less accuratewhen tr2 is very different of tm.

0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

X S

[H+]= 0.02 mo l L

-1

[H+]= 0.10 mo l L

-1

[H+]= 1.00 mo l L

-1

tm (s)

Fig. 1. Calibration curves from the E-model for different initial acid concentrations

and for the following concentrations of initial reagents: [KI]0 = 0.01165 mol L�1,

[KIO3]0 = 0.00233 mol L�1, [NaOH]0 = [H3BO3]0 = 0.001512 mol L�1, for f = 15, the

ratio between the main flow velocity and the injection velocity.

When tm is determined, the Baldyga and Bourne’s analysis [18]gives access to the TKE dissipation rate e:

e ¼ 297:22ytm

(8)

where y is the kinematic viscosity.

3. Analysis of the meso-mixing scales

Two meso-mixing mechanisms have been identified by Baldygaet al. [31]: first, the turbulent dispersion of the feed stream into themain flow, in both the radial and streamwise directions, andsecond the break-down of injected aggregates in the turbulentcascade, from the large integral scale to the Kolmogorov scales. Thecorresponding time scales are computed in this section.

3.1. Injection time scales

First, following concepts of Batchelor [2] and Corrsin [32],Baldyga et al. [30,33] defined, by scaling analysis, two characteris-tic times for the turbulent dispersion mechanism, in thestreamwise and radial directions relative to the injection, tD1

and tD2 respectively:

tD1 ¼Qi

WDt(9)

tD2 ¼d2

4Dt(10)

where d is the feed pipe internal diameter, Qi is the injection flowrate, W is the local flow velocity and Dt is the turbulent diffusivityof the main flow, which is classically modeled with the turbulentkinetic energy k and the dissipation rate e [24]:

Dt ¼ 0:1k2

e (11)

The injection flow rate Qi is expressed by the injection velocityWi:

Qi ¼pd2

4Wi (12)

Defining f by the ratio between the main flow velocity and theinjection velocity, f = W/Wi and the turbulent diffusivity coeffi-cient by its expression in Eq. (11), tD1 and tD2 can be expressed by:

tD1 ¼p

0:4

d2

fe

k2(13)

tD2 ¼d2

0:4

ek2

(14)

Second, when the scale of injected feed stream is larger than theturbulent eddies, the concentration fluctuations break down fromthe integral scale L (convective-inertial large scale) towardKolmogorov’s micro-scale by a mechanism called inertial-convec-

tive meso-mixing. For fully developed turbulence, the characteristictime (cascade time) is given by Batchelor [2] and Corrsin [32]:

tC ¼ 2L2

e

!1=3

(15)

If the injection momentum is moderate, the injected fluidparticles are instantaneously submitted to the main-flow velocityfield. In this case, with L0 the initial radius of the reactive jet that isconvected with local velocity W, it follows [31] by continuity that

0 5 10 15 20 25 30

0.0

0.5

1.0

1.5

2.0

d= 2 mm , D= 20 mm, W= 0.75 ms-1

1

2

3

1,

2,

3

Velocity ratio

(a)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

o= 15, D= 20 mm, W= 0.75 ms

-1

1

2

3

1,

2,

3

d (mm)

(b)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

W (ms-1 )

o= 15, d= 2 mm , D= 20 mm

1

2

3

1,

2,

3

(c)

Fig. 2. Validity domain of the chemical probe method in a straight pipe for

characterizing micro-mixing time depending on (a) velocity ratio, (b) feed pipe

diameter and (c) mean flow velocity.

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–14201414

Qi � pL20W , by assuming [35] that L = L0, leading to:

L ¼

ffiffiffiffiffiffiffid2

4f

s(16)

By combining Eq. (15) and Eq. (16), the inertial-convectivemeso-mixing characteristic time can be estimated by:

tC ¼ 1:26d2

fe

!1=3

(17)

In order to compare these three different time scales with themicro-mixing time, three dimensionless parameters are defined bythe ratio of the three characteristic times (tD1, tD2, tC) by the micro-mixing time tm, called respectively t1, t2 and t3, written as follows:

t1 ¼tD1

tm¼ 0:145p

d2

fy1=2

e3=2

k2(18)

t2 ¼tD2

tm¼ 0:145

d2

y1=2

e3=2

k2(19)

t3 ¼tC

tm¼ 0:073

d2=3

f1=3y1=2e1=6 (20)

These parameters provide a criterion for the domain in whichthe chemical probe method can reach the micro-mixing time, thatis when the three characteristic times are smaller than the micro-mixing time, i.e. the condition is: t1, t2 and t3 < 1. In this system,the independent parameters that may affect turbulent mixing nearthe injection are the feed needle (jet) diameter d and the velocityratio f for a given main flow rate. Eqs. (21)–(22) highlight thedependence on these parameters by expressing the turbulencekinetic energy and its dissipation rate with scaling analysis, withthe typical scales: W the average flow velocity and D the reactordiameter. In the same way, the local velocity W is also normalizedby the average velocity:

k ¼ CkW2

(21)

e ¼ CeW

3

D(22)

W ¼ CW W (23)

Assuming dynamical similarity for a narrow range of Reynoldsnumber, where the flow pattern does not change significantly, thecoefficients Ck, Ce and CW depend only on location and not on theReynolds number. By substituting Eqs. (21)–(22) into Eqs. (18)–(20), the characteristic time ratios read:

t1 ¼ 0:145pC3=2e

C2k D3=2y1=2

d2

fW

1=2(24)

t2 ¼ 0:145C3=2e

C2k D3=2y1=2

d2W1=2

(25)

t3 ¼ 0:073C1=6e

D1=6y1=2

d2=3

f1=3W

1=2(26)

An analytical study is carried out with Eqs. (24)–(26) toinvestigate the validity domain in an arbitrary case. The exampleused here is the flow in a straight pipe of hydraulic diameterD = 20 mm, with assumed local constants Ck = 0.455, Ce = 0.971 andCW = 0.125 (corresponding results are shown in Fig. 2). The valuesof these constants are adapted from Habchi et al. [22]. In Fig. 2, thecharacteristic time ratios are plotted successively as a function of

the three independent parameters f, d, and W, two of themassumed to be in the nominal state for each case. The region whereall the time ratios are less than 1 is hatched. In Fig. 2(a) a criticalvalue for the velocity ratio fo = 7 is obtained from the limitingcriterion t3 < 1, since it is the highest relative to t1 and t2. Fig. 2(b)shows that if the feed pipe diameter d is increased, meso-mixingovercomes micro-mixing as t2 becomes greater than 1. The criticalfeed pipe diameter is found to be around 2.20 mm in this case. Thehigher main flow rates as well lead to t2 > 1 in Fig. 2(c), since the

Fig. 3. Flowchart of the adaptive procedure for the chemical probe method for

micro-mixing characterization.

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–1420 1415

time ratios are increasing functions of W, a critical average flowvelocity W is around 1.20 m s�1 in this case. The scaling analysisproposed in this work shows that it is possible to evaluatetheoretically the optimal value of the velocity ratio f and of thefeed pipe diameter d for given conditions, and it then defines avalidity domain of the use of the chemical probe.

3.2. Measurement volume requirements

Micro-mixing is a local and small-scale mechanism, and thusshould be achieved at a short distance from the injection point,meaning that convective transfer by the main stream velocity issmall. Since the residence time scale in the reactor is tRes � L=W, itis self-evident that the condition tr2 << tRes must be verified inorder to get a local measurement.

Reciprocally, at velocity W, the second reaction length scale canbe evaluated by Lr2 � Wtr2. It is possible to ‘‘tune’’ tr2 so that Lr2 is atthe reactor scale, and in that case, the selectivity will be thesignature of the global mixing properties. This could be a deliberatechoice in experimental design in order to characterize the globalmixing efficiency.

3.3. Second reaction time-scale requirement

The sensitivity of the chemical probe is linked to partialachievement of the second reaction, requiring that this secondreaction time be close to tm. As discussed below, a recommenda-tion of the adaptive method is to reach conditions in which tr2 � tm.In this work, the species concentrations are fitted to the reactionkinetics, while other work in the literature uses constant speciesconcentrations.

4. An adaptive method

This section proposes a practical method for experiments byexploring the different degrees of freedom influencing theselectivity of the chemical probe system, as summarized in theflowchart of Fig. 3.

4.1. Measurable mixing time in a given injection flow

The first step consists to check the injection hydrodynamics:for a given feed needle (jet) diameter d, to ensure that theflow is not perturbed by the injection, the velocity ratio fmust be higher than the critical value, and this conditionmust be checked for all operating conditions. For a full rigdesign, the same logic allows evaluation of the maximal valueof the feed pipe diameter d for a given f. This case is relativelyrare and the reasoning here is confined to a given needle size.The limiting mixing times is computed from Eqs. (24) through(26).

4.2. Acid concentration based on second reaction time-scale

The second step consists to optimize species concentrations:the reagent concentrations are varied to target the greatestsensitivity of the segregation index XS to the flow dynamics, andfinally to the measurement of tm, when tm = tr2. Hence, the initialreagent concentrations must be adapted for each location,especially if the hydrodynamic and turbulence levels are nothomogeneous in the reactor. Since all the initial concentrationsare linked (except for the sulfuric acid, which is contained in aseparate reservoir), it is more tractable to modify the concentra-tion of the Hþ

� �ions, although the procedure might also be

applied by modifying the other reactive concentrations(that would be necessary in any event if the convenient Hþ

� �

would not be in stoichiometric defect). Then the measuredmicro-mixing time tm, obtained by the engulfment model, isplotted with the characteristic time for the second reaction tr2,computed from Eq. (4), versus the H+ concentrations. Theintersection between the curves tm and tr2 indicates the optimalH+ concentration, and the corresponding segregation index XS

can be retained as shown in Fig. 1.The experimental range of Hþ

� �can be estimated from the

turbulence energy dissipation rate in the flow from the pressuredrop. For example, if it is known that in a given flow the turbulenceenergy dissipation rate is of the order of 10 m2 s�3, then the micro-mixing time is about 5.5 ms. The criterion tm = tr2 gives the order ofmagnitude of tr2 and thus provides the concentration of H+, about0.5 mol L�1 in this example.

When the tm value resulting from the chemical probe methodyields a turbulence energy dissipation rate e far from the estimatedone e, then a new estimate of the concentration must be made toiterate the procedure for a more accurate value of e.

4.3. Measurement volume: local or global

The third step consists to examine the measurement volume inorder to check the local character of the chemical probe. If themeasurement length scale Lr2 � Wtr2 is smaller than the meso-scale length scale computed from Eq. (16), then the measurementcan be considered local and the micro-mixing process might bytargeted by the chemical probe. Conversely, if the measurementlength scale Lr2 is much larger than the meso-scale length scale,

Fig. 5. Schematic view of the flow structure downstream from the vortex generator

and locations of the measurement points.

Table 1Measurement locations.

B Bulk flow region y/R = 1.0 High velocity Low turbulence

Low gradients

S Shear layer region y/R = 0.2 Moderate velocity High turbulence

High gradients

W Wake of the tab y/R = 0.4 Low velocity Moderate turbulence

Low gradients

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–14201416

then the measurement cannot be considered local and thechemical probe characterizes in this case, not only the micro-mixing process but also the large-scale mixing.

5. Experiments

The meso-mixing scales analysis and the adaptive procedureare applied to an inline mixer of HEV type (ChemineersTM) that iswidely used in several practical applications and as a referencegeometry in many laboratory research works [39,41,44]. Thismixer presents very different local hydrodynamic conditions in thevolume, allowing testing a wide range of conditions following theinjection location.

5.1. Testing the procedure in a complex flow

The HEV geometry consists of a circular pipe equipped withseven aligned rows of longitudinal vortex generators placed at thewall, as shown in Fig. 4. The so-called vortex generators inducecoherent structures topologically similar to those found in concaveboundary layers and in wall turbulence [34–42]. Two mainfeatures are identified (Fig. 5) [45]:

� a streamwise counter-rotating vortex pair (primary CVP) with acommon up-flow in the symmetry plan of the vortex generator,and a pair of secondary CVP of very small size close to the wall,with an associated common inflow,� a periodic sequence of hairpin vortices convecting downstream

and riding on top of the CVP [39,41], corresponding to amaximum turbulence kinetic energy dissipation rate located at aradial position of around y/R = 0.4 [43].

The measurements are taken in the typical locations B, S and W,in the symmetry plane of the vortex generator, at the cross-section3 mm downstream from the first tab array, as shown in Figs. 4 and5. These three measurement locations have been chosen in order toget completely different flow conditions, given in Table 1, so as tocheck the validity of the adaptive procedure to provide reliable andaccurate measurements [22].

5.2. Experimental setup and methods

A schematic diagram of the experimental setup is shown inFig. 6. The chemical solution of the reaction system in Eqs. (1)and (2) is mixed by an immersed pump and its temperature iskept constant at 298 K by a helical heat exchanger whosetemperature is controlled by a thermostat (Crythermostat 71Huber). As shown in Fig. 6, the mixture is driven by a rotarypump into the hydraulic loop. The main flow rate is measured by

Fig. 4. Schematic views of (a) the static mixer (reference model) cross-section showing t

trapezoidal vortex generator.

a precision balance and data acquisition is realized byLabviewTM software.

The sulfuric acid injection system consists of a regulated stepmotor connected to a multi push-syringe system. The sulfuric acidis injected into the test section through an injection needle of0.6 mm inner diameter connected to the syringes by flexible tubes.The location of the needle in the reactor cross-section isdetermined by a displacement mechanism, as shown in Fig. 4,with an accuracy of 10 mm. The flow rate of the acid injection iscontrolled by a speed regulator on the angular velocity of thestepper motor via a PC. The test section is incorporated in thehydraulic loop elements by flexible tubes to avoid fluctuations dueto pump vibration. The reactor is preceded by a straight-pipepreconditioner of 1.50 m length to ensure fully developedturbulent pipe flow at the reactor inlet, and followed by apostconditioner of 0.30 m length. The final products of the reactionare analyzed in continuous flow through a channel placed 0.3 mdownstream from the reactor outlet and branched to a spectro-photometer (Jenway 6505TM) of resolution 0.1 nm and bandwidth

hree vortex generator rows and injection needle location and (b) dimensions of the

Fig. 6. Schematic diagram of the hydraulic loop and injection system.

Table 2Species concentrations.

Reagents H3BO3 NaOH KIO3 KI� H+

Concentrations

(�103 mol L�1)

1.512 1.512 2.33 11.65 200–1000

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–1420 1417

1.8 nm whose wavelength ranges between 190 nm and 1100 nm.The measurable absorbance range of the spectrophotometer liesbetween 0 and 3, with 0.1% accuracy. The measurements of the I�3ion absorbance are performed in the UV domain.

All runs are carefully performed with the constant concentra-tions given in Table 2 [23]. The measurements are made using theadaptive procedure described in Section 4 where the H+

concentration is swept between 0.2 and 1.0 mol L�1.The adaptive procedure is then applied in these conditions, for

Reynolds number 12,500 and for the three locations B, S, and Wrepresented in Fig. 5. Table 3 summarizes the constants Ck, CeandCW obtained from previous numerical simulations [41]. In fact, forany of the experimental studies these parameters can be assumedas an initial guess and do not need to be very accurate even to getaccurate results. However, to improve the convergence of themeasurements, these available data are used in this specific case.The effective velocity ratio f0 used for the measurements and thelocal velocity W for each location are also presented in Table 3. Inthe present study, the injection inner diameter is d = 0.6 mm andthe mean flow velocity is W ¼ 0:625 m s�1.

Table 3Local hydrodynamic parameters independent of Reynolds number and local values for

Measurement location Ck Ce CW

Bulk (B) 4.42 � 10�3 4.21 � 10�4 0.983

Shear (S) 0.24 0.70 0.169

Wake (W) 0.13 0.51 0.312

Source: Adapted from Habchi et al. [41]).

6. Results and discussion

The adaptive method is applied in order to assess the resultswhen the chemical probe is carried out: verification of the meso-mixing scales at the injection location, the appropriate acidconcentration, and finally the determination of the measurementvolume.

6.1. Injection hydrodynamics

The validity domain of the chemical probe is determined bysweeping the only ‘‘free’’ parameter, the velocity ratio f, as shownin Fig. 7. Following the approach described in Section 4, thehatched regions represent the validity domain in which micro-mixing is unaffected by the injection.

For measurements in the bulk region (location B) in Fig. 7(a), thevelocity ratio fo that defines the validity domain tends to zerounder the nominal conditions, meaning that the micro-mixing isalways the limiting process at this location and that any velocityratio f value can be used for measurements; here fmeasurement = 7.6.In Fig. 7(b), for measurements in the shear region (location S), thevelocity ratio f0 = 0.65 is given by the time scale t1, so that the localoperating value fmeasurement = 1.31 is consistent with the domainof validity. In Fig. 7(c), in the wake region (location W), it can beseen that the time scale t2 is always greater than 1. Therefore,whatever the velocity ratio in this region, the chemical probemethod cannot be applied because the condition t2 < 1 can never

Re= 12,500.

k (m2 s�2) e (m2 s�3) W (m s�1) f0

1.73 � 10�3 5.14 � 10�3 0.614 7.61

9.50 � 10�2 8.60 0.106 1.31

5.07 � 10�2 6.20 0.195 2.42

1 2 3 4 5 6 7 8 9 10

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1,

2,

3

Bulk region (y/R= 1.0)

1 2 3

measurement

(a)

1 2 3 4 5 6 7 8 9 10

0.00

0.25

0.50

0.75

1.00

1.25

1.50

measurement

Shear zone (y/R= 0.4)

1 2 3

1,

2,

3

(b)

1 2 3 4 5 6 7 8 9 10

0.00

0.25

0.50

0.75

1.00

1.25

1.50

measurement

Wake zone (y/R= 0.2)

1 2 3

1,

2,

3

(c)

Fig. 7. Time ratios in the (a) bulk region, (b) shear region and (c) wake region as

function of the velocity ratio f, for Re = 12,500.

0.0 0.2 0. 4 0.6 0. 8 1.0

0

2

4

6

8

10

12

14

[H+] (mol L

-1 )

tr2Micro-mixing time tm :

B: y/R= 1.0

S: y/R= 0. 4

W: y/R= 0.2

t m ,

t r2 (

ms

)

tm = tr2

Fig. 8. Determination of suitable H+ concentration for tm = tr2 in the bulk (B), shear

(S) and wake (W) locations, for Re = 12,500.

Table 4Nominal [H+] and results obtained from the chemical probe measurements in the

three locations B, S and W, for Re = 12,500.

Measurement location [H+] (mol L�1) XS tm = tr2 (ms) e (m2 s�3)

Bulk (B) 0.336 0.130 9.111 3.581

Shear (S) 0.434 0.106 5.741 9.019

Wake (W) 0.462 0.110 6.338 7.400

0.0 0.2 0. 4 0.6 0. 8 1.0

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.16

B: y/R= 1.0

S: y/R= 0. 4

W: y/R= 0.2

[H+] (mol L

-1 )

X S

Fig. 9. Determination of the segregation index for [H+] in the bulk (B), shear (S) and

wake (W) locations, for Re = 12,500.

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–14201418

be reached. The solution suggested to satisfy the time scalescondition would be to use a finer needle diameter in order todecrease the time scale t2 below 1.

6.2. Optimal [H+] for the micro-mixing measurement

By applying the adaptive method described in Section 4, themeasurements are performed in the three flow conditions bysweeping the H+ concentration between 0.2 and 1.0 mol L�1. Thesecond reaction time is computed by Eq. (4) as a function of [H+],and both are plotted in Fig. 8. The sulfuric acid concentration istaken where the second reaction time curve tr2 crosses the micro-mixing time curve tm. Hence, a convenient [H+] is determined for

the three locations B, S, and W, and the corresponding mixing timesand dissipation rates can be derived. From these values of [H+] it isthen possible to obtain the absolute value of the segregation indexXS, as shown in Fig. 9. These values are summarized in Table 4 forthe three locations.

6.3. Measurement volume

This section discusses the measurement volume by calculatingLr2 = W tr2 and comparing it to the meso-scale of Eq. (16).

In the bulk region (location B), the effective turbulence energydissipation rate obtained from numerical simulations [41] is rathersmall, about 0.70 m2 s�3, yielding a mixing time of about 0.020 s.Since the local flow velocity is high (0.614 m s�1), the length of themeasurement volume in the axial direction is Lr2 = Wtr2 = 18.9 mm,

6000 8000 10000 12000 14000 16000

0

2

4

6

8

10

12

14

16

18

20

(

m2 s

-3)

Re

Present results with adaptive procedure

Chemical probe with classical procedure (Mohand Kaci 2007)

LDV measurements (Habchi et al . 2010b)

Fig. 11. TKE dissipation rate e obtained by three different methods at the shear layer

region (location S) for different Reynolds numbers.

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–1420 1419

much larger than the 3.25 mm meso-scale computed at thislocation. Thus, the measurement is not local and the determinationof the turbulence energy dissipation rate in the bulk region,location B, is not possible with this injection needle (jet) diameter.Indeed the measurement by chemical probe obtained in B is notlocal, but influenced by the turbulence downstream from theinjection point.

In the shear layer (location S), the turbulence energy dissipationrate is higher 8:65 m2 s�3

� �and the corresponding mixing time is

about 5.88 ms; the measurement length is close toLr2 = W tt2 = 0.77 mm. Meanwhile the meso-scale is 6.89 mm, thechemical reaction takes place locally and the determination of themicro-mixing time and the local e is meaningful.

In the wake (location W), the chemical probe is not validbecause the turbulence in the main flow is dominated by theinjection flow. Nevertheless, the analysis of the measurementvolume can be carried out: e = 6.06 m2 s�3 provides a mixing timeof 7.0 ms. The measurement length is around 0.88 mm, lower thanthe meso-scale which is found to be 5.61 mm. It would benecessary to decrease the needle inner diameter to minimize theinjection turbulence for obtaining satisfactory results, in spite ofthe perfectly local aspect of the measurement.

6.4. Discussion on the adaptive procedure

In Fig. 10, it is possible to compare the turbulent energydissipation rates obtained by the adaptive method with thoseobtained from previous chemical probe measurements using theconcentration values suggested in the literature [15,23]; the latterwere carefully carried out by Mohand Kaci [23] but withoutassessment of the validity criteria proposed here (by Mohand Kaci[23]; Habchi et al. [15]). Independent arbitration values, quotedfrom CFD and LDV (laser Doppler velocimetry) measurements,allow an objective discussion of the values accuracy.

The locations B and W are disqualified for two different reasons:

- in the bulk zone (location B), we have shown that the limitation isdue to the non-local character of the measurement. Theturbulence is weak and the velocity is high, so that the convectiveeffects dominate the behavior of the chemical species. The newmeasurement is, as expected, not better than the former with theconventional concentrations, and cannot be improved with thepresent needle diameter.

- in the wake zone (location W), the adaptive method cannot bringbetter information, as mentioned in the local analysis of time

W S B

0

1

2

3

4

5

6

7

8

9

10

11

12

13

(

m2 s

-3)

Wake BulkShear

B: out of domain conditions

for quantitative measurement

S: significant

accuracy improvement

W: all methods

are questionable

Present results w ith adaptiv e procedure

Chemical probe w ith classical procedure (Mohand Kaci 2007)

LDV measurements (Habchi et al . 2010b)

Numerical simulations (Habchi et al . 2010b)

Fig. 10. Improvement in e determination by the adaptive method for Re = 12,500.

scales (Section 4), but it can be noted that all the velocimetrymethods lose their reliability in the case of zero average velocityfields. It could provide reliable measurements only if a finerneedle diameter d permits to obtain a characteristic time t2 < 1.

Finally, only the location S conditions is qualified to provide alocal measurement of e. Indeed, a significant accuracy improve-ment is obtained by following the adaptive procedure. Theconventional chemical probe method gives more than 50%deviation from LDV results, while the adaptive procedure givesvalues within 15% of CFD and LDV references.

Additional measurements are performed at the location S(shear layer) for different Reynolds numbers ranging from 7500 to15,000 to assess the accuracy gain. The results, plotted in Fig. 11,are also compared to those obtained by the classical method [23]and by LDV measurements [41]. The new results are much closer toLDV ones and the relative error is about 50% at Re = 7500 and 8% atRe = 15,000, while, for the classical method, the error is 163% atRe = 7500 and 35% at Re = 15,000.

7. Concluding remarks

The present analytical and experimental investigation of micro-mixing quantification using chemical probe methods provides abetter understanding of the different limitations that arise in thefinal determination of local turbulence energy dissipation rate. Thefirst part of this study details the chemical probe principle, focusingon the iodide/iodate method and its two parallel-competitivechemical reactions. The segregation index leads to a measure of themixing time by the engulfment micro-mixing model, and thecorresponding turbulence energy dissipation rate is determined by aphenomenological model developed by Baldyga and Bourne [18].

This study proposes a generic experimental procedure to ensurethe validity and enhance the accuracy of such methods. In the firststep, scaling analysis based on the hydrodynamics of the injectionsuggests checking if three independent key parameters (ratios oftime scales), determining which mechanism controls the turbulencemixing, are simply less than unity, criteria that define the validitydomain of the chemical probe. In the second step, optimal values forthe operating conditions are set by sweeping the injected acidconcentration in an appropriate range, estimated by the order ofmagnitude of the mass energy dissipation rate. The retainedconcentrations correspond to equality of the micro-mixingtime and the reaction time. The third step is aimed at checking ifthe measurement volume size ensures local measurement of

C. Habchi et al. / Journal of Industrial and Engineering Chemistry 20 (2014) 1411–14201420

micro-mixing. Accomplishing these three steps can guarantee thatthe measurement is local and accurate.

The three-step analysis is then applied to an inline mixerequipped with aligned vortex generators. Measurements arecarried out at three locations exhibiting very different flowconditions. On the one hand, it informs on the consistency ofthe chemical probe method in given conditions. On the other hand,it permits to significantly improve the chemical probe accuracyover the conventional method when the method is applicable.

The scaling analysis and the adaptive procedure proposed in thepresent work can be extended to large-scale industrial heatexchangers–reactors when other velocimetry methods are nottractable, to localize the high and poor mixing regions, and helpdesigning reactors able to enhance the selectivity and reduce theeffluents.

Acknowledgments

The authors gratefully thank Dr. H. Mohand Kaci for his help inmeasurements using the chemical probe method. The authorsthank also the technical staff of the LTN for the construction of thehydraulic loop and injection system. This work was partiallysupported by ADEME. The authors would like to acknowledge thecontinuous support of Dr. G. Guyonvarch, head of the industrialand agricultural process department of ADEME, and also of Dr. C.Garnier, monitor of this grant. C.Habchi was supported by ADEMEand CNRS.

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