experimental study of mixing layer in a closed compound channel

TECHNICAL PAPER

Experimental study of mixing layer in a closedcompound channel

Jhon Goulart • Luciano Noleto • Sergio V. Moller

Received: 10 July 2012 / Accepted: 5 December 2012 / Published online: 21 August 2013

� The Brazilian Society of Mechanical Sciences and Engineering 2013

Abstract This paper presents an experimental study per-

formed in a given compound channel under steady-state

incompressible air flow. Hot wire probes and Pitot tube were

employed to measure mean velocity and velocity fluctua-

tions characteristics in a turbulent flow between parallel

plates. Test sections were formed by two parallel plates

attached on a side wall of a wind channel, forming a slot with

width d and depth p. Results showed that this sort of channel

produces unstable velocity profiles and periodical traces of

velocity as well, quite similar to a mixing layer. Using local

scales of velocity and length both, velocity profiles and

Strouhal number could be described, regardless of the

channel’s dimension or its depth. Despite a certain scattering

of the dimensionless frequency, the Strouhal numbers

remained almost constant for any p/d-ratio. In this paper ten

test sections were studied covering p/d-ratio from 5.00 up to

12.50. The Reynolds number was defined using a velocity

reference, Uref; the hydraulic-diameter of the test section, Dh

and the kinematic viscosity, m.

Keywords Mixing layer � Turbulent flow �Compound channels � Coherent structures � Hot wires

List of symbols

Be Bandwidth (Hz)

d Width of test section (m)

Dh Hydraulic-diameter (m)

L Length of the test section (m)

p Depth of test section (m)

Re Reynolds number, Re ¼ Uref Dh

m

Str Strouhal number, axial and transversal

components Stu and Stw�u Time-average velocity (m/s)

u0v0 Shear stress (m2/s2)

U1, U2 Lower and higher velocities inside mixing layer

(m/s)

Uc Convection velocity (m/s)

Uref Reference velocity (m/s)

DU Velocity difference (m/s)

v02 r.m.s transversal turbulent velocity (m2/s2)

X Streamwise coordinate

W Width channel outlet (m)

y Vertical coordinate

y1, y2 Border of mixing layer (m)

yc Coordinate of the center of mixing layer (m)

Greek symbols

d Mixing layer thickness (m)

g Similarity parameter, g ¼ y�yc12dðxÞ

m Molecular viscosity (m2/s)

mt Eddy-viscosity (m2/s)

q Density (kg/m3)

r Spreading rate, XdðxÞ

[/]u Autospectral density function axial velocity

fluctuation component,m=s=Hz

�1

dðxÞDU

Technical Editor: Francisco Cunha.

J. Goulart (&) � L. Noleto

University of Brasılia, Brasılia, Brazil

e-mail: [email protected]

L. Noleto


S. V. Moller

Federal University of Rio Grande do Sul, Porto Alegre, Brazil


123

J Braz. Soc. Mech. Sci. Eng. (2014) 36:411–420

DOI 10.1007/s40430-013-0081-3

[/]v Autospectral density function transversal velocity

fluctuation component,m=s=Hz

�1

dðxÞDU

sxy Shear stress (N/m2), qu0v0

1 Introduction

Compound channels are found in nuclear and process

industry, in channels like rod bundles, heat exchangers and

coolers of modern electronic devices. This subject has been

studied since early 1960s, even though the concept of

compound channel has been recently introduced. Com-

pound channels are characterized by the presence of a

narrow region of the channel connected to one or more

wider regions. Fined tubes or assembly of rod bundles of

nuclear reactors are good examples. All of them present

adjacent subchannels connected by a narrow gap, Fig. 1.

The structure of turbulent flow in compound channels is

affected by the presence of narrow gaps. The gaps are

responsible for a new mass distribution inside channel,

producing inflectional profiles of mean velocity and,

therefore, unusual shear stresses distribution [5, 12, 15].

One of the most impressive characteristics of flow in these

sorts of channels are the gap instabilities. The flow in the

gap region may present periodical traces of velocity fluc-

tuations called flow pulsations. An extensive review on this

subject was done by Meyer [12]. According to author these

structures, from the turbulent flow, are the true reason for

rising mixing rates in the gap region. The works of Knight

and Shiono [8], Moller [13], Meyer and Rehme [10, 11],

and Guellouz and Tavoularis [7], showed flow pulsations

phenomenon occurrence in closed as in open channels.

Flow pulsations in rod bundles were first reported by

Rowe et al. [17]. In his experimental findings, periodical

path in axial velocity component was reported. The fre-

quency associated with this phenomenon increased when

the distance between the rods was reduced. Although this

fact has been very well reported, numerical calculations

presented by Chang and Tavoularis [4] have demonstrated

that for very tight gaps the coherent motion essentially

disappeared due to viscous effect. The authors studied a

compound channel containing only one rod into a

rectangular channel. The main parameter evaluated was

d/D-ratio. In this work d, was the gap width and D the rod

diameter.

In the work of Moller [13] hot wire anemometry was

employed to determine the origin and characteristics of this

phenomenon. The results demonstrated that the flow pul-

sations were associated with the strong vorticity field near

the gaps. According to author, the dimensionless frequency

St was a function of the geometry of the channel and

inversely proportional to gap size. The Strouhal number

was defined with mean frequency f, the rod diameter D, and

the friction velocity in the narrow gap between the rods u*.

Using as test section a trapezoidal channel containing a

single tube (Fig. 1c), Wu and Trupp [21] carried out exper-

imental work to know main characteristics of the flow near

the gap. The results showed pronounced peaks in spectra

confirming the strong dependence of the frequency on geo-

metrical parameters and the flow velocity. However, the

Strouhal number did not agree with the correlations proposed

by Moller [13] leading the authors to suggest a new corre-

lation for the determination of the dimensionless frequency.

Meyer and Rehme [11] using hot wire anemometry

studied the flow characteristics in a channel with two or

several parallel plates attached to a wall (Fig. 2). The

compound channel was formed by the connection between

main channels and lateral slot. The main dimensionless

geometrical parameter was d and g, the depth and the width

of the slot, respectively. The investigations were performed

for several values of d/g. The dimensionless parameter

ranged from 1.66 up to 10.00.

The authors observed peaks of Reynolds stresses near

the gap and a strong periodicity of flow velocities signs, as

well. The findings suggested that large-scale structures

dominate the gap region. The presence of coherent struc-

tures in the gap was found for all test sections with

d/g C 2; however, the authors did not comment anything

about the location streamwise where visualizations were

performed. A correlation for the Strouhal number was

purposed. The dimensionless frequency was based on the

main frequency in the spectra f the mean axial velocity

measured in the edge of the plates Ued and the square root

of the product of d and g. According to the authors, the

Fig. 1 Some examples of

compound channels

412 J Braz. Soc. Mech. Sci. Eng. (2014) 36:411–420

123

scales produced different Strouhal number for each type of

channel studied. The Strouhal numbers were found to be

0.066, 0.080 and 0.050 for test sections in Fig. 2a–c,

respectively. In addition, the authors noticed that important

discrepancies were observed for d/g values [7.

Recently, laminar flow in a compound channels was also

investigated. Piot and Tavoularis [15] performed flow visu-

alizations in an eccentric annular channel under laminar

flow. The authors observed the onset of instabilities as

eccentricity was increased and Reynolds number was kept

constant. Furthermore, it was noticed that two mixing layers,

with a turning point, were present on either side of the gap.

According to authors the flow instabilities in the gap may be

attributed by shear layers instabilities. Soon after, Chang and

Tavoularis [5] through numerical calculations, confirmed the

presence of shear layers in the same compound channel. The

also pointed the inflectional field of mean axial velocity.

This paper is aimed at investigating the mean and

fluctuant quantities of turbulent flow in simulated com-

pound channel. It is also our expectation the establishment

of a relationship between these quantities and the well-

known and established mixing layer theory, which may

give us a useful tool to handle with problems in more

complex geometries. In order to reach such objective mean

velocity and mean turbulent quantities, profiles were

measured and analyzed. The investigation on the presence

of large-scale structures in this kind of channel was also

done for ten test section with p/d ranging from 5.00 up to

12.50. From mean axial velocity profile length and velocity

scales are proposed to define Strouhal number. Despite

some scattering the Strouhal number was found in 0.17.

2 Test sections and experimental technique

The test section, Fig. 3, consists on a 3,320-mm-long

channel with 146 mm height and a variable width, W. The

channel’s width could be changed using a moving plexi-

glass wall along the channel’s long. Three different values

of W were adopted, namely 60, 120 and 150 mm.

Working fluid was air at room temperature, driven by a

centrifugal blower controlled by a frequency inverter. After

passing through a diffuser and a set of honeycombs and

screens the flow reaches the test sections with a turbulence

intensity\1 %. After the screens, a Pitot tube is placed on a

fixed position responsible for measuring of the reference

velocity Uref, during the experiments. The Pitot tube is always

positioned in the middle of channel. The reference velocity

was taken within 13.50–14.50 m/s, for all experiments.

Inside the channel two metal plates with thickness

e = 1.2 mm and length L were mounted onto a side wall to

form a canyon-like slot with depth ‘‘p’’ and width ‘‘d’’.

Fig. 2 Compound channel

studied by Meyer and Rehme

[11]

Fig. 3 Schematic view of the

test section. a Lateral view; b,

c cross-sectional, geometrical

parameters and symmetry line

location; d coordinates system

J Braz. Soc. Mech. Sci. Eng. (2014) 36:411–420 413

123

Table 1 shows the dimensions of the test sections and the

Reynolds numbers of each experiment. Reynolds numbers

were defined using as scales the velocity reference, Uref,

and the hydraulic-diameter, Dh.

Measurements of velocity and velocity fluctuations were

performed by a hot wire DANTEC StreamLine system.

Using a double wire probe with a slant wire (45�) and

another one perpendicular to the main flow, simultaneous

axial and transversal components (u, v) of the velocity

vector could be measured. Transversal velocity component

is parallel to y-axis, Fig. 3d.

Collis and Willans [6] method with modifications by

Olinto and Moller [14] was applied to evaluate the ane-

mometer signals. Velocity field was previously measured

by a Pitot tube. Measurements were performed 20 mm

before channel’s outlet.

Data acquisition was performed using a 16 bit National

Instruments NI USB-9162 A/D converter board, with a

sampling frequency of 3 kHz and a low pass filter set at

1 kHz. Temporal series were 43.69 s long.

Uncertainties about velocity fluctuations and the product

between them were evaluated. With regard to the shear

stress, u0v0=DU2, uncertainties were calculated from 2.8 up

to 10.5 %. Mixing layers thickness, obtained by means Pitot

tube, produced uncertainties from 2 up to 7 %. Uncertain-

ties about reference velocity are estimated to be 3 %.

3 Results and discussion

3.1 Velocity profiles

Figure 4 presents the velocity distribution along the sym-

metry line of test section DP-02 (Table 1).

In Fig. 4 one can see the velocity profile divided into

three different zones. In zones 1 and 3 the velocity

distribution is strongly influenced by the lateral walls. On

the other hand, the velocity distribution in zone 2 has

characteristics of a mixing layer beginning in the region

between the plates and extending towards the main chan-

nel. At this region the velocity profile has a turning point

near the interface between sub/main channel. All velocity

profiles measured in this paper presented this characteristic.

Similar formations has been reported by Shiono and Knight

[18] and Soldini et al. [19] when the authors performed

measurements in an open channel with flooding plains.

Although Meyer and Rehme [11] had not noticed this

fact, their results also showed similar characteristics to

those ones found in this paper.

Figure 5a, b presents the mean axial velocity distribu-

tion along the symmetry line for test sections DP-01 to 06

(Table 1). In general, the same features depicted in Fig. 4

can be observed. Through the velocity profiles the mixing

layers formation are clearly defined, mainly for test section

from 01 to 03 (Fig. 5a).

Mixing layers are characterized by velocity and length

scales. The main velocity scales are the highest and lowest

values of velocity, U2 and U1, respectively. Through these

values the velocity difference DU and the convective

velocity Uc can be calculated. Another scale is the mixing

layer thickness, d(x). This length scale is calculated through

the velocity difference and the maximum velocity gradient

value.

By observing the velocity profiles the highest value of

mixing layer velocity, U2, takes place in the main channel,

at position y2. Typically, the maximum value of mean axial

velocity gradient (turning point) occurs near the gap/main

channel interface and at this point, named yc, the convec-

tion velocity Uc, takes place as well. Figure 6 shows the

mean axial velocity and its derivative form for test section

DP-09, both were made dimensionless.

0 0.025 0.064 0.12 0

2

4

6

8

10

12

14

y

u

Shear Layer

Δ U

(y)

zone 1 zone 3 zone 2

p = 0.04

(m)

Fig. 4 Axial velocity profile on the symmetry line, section DP-02

Table 1 Test section configurations and Reynolds number (dimen-

sions in mm)

Test section W p d L p/d W/p Re

DP-01 150 50 10 1,250 5 3 1.49 9 104

DP-02 120 40 8 1,000 5 3 1.10 9 104

DP-03 60 20 4 500 5 3 7.40 9 103

DP-04 150 50 10 500 5 3 1.30 9 104

DP-05 120 40 8 500 5 3 1.35 9 104

DP-06 60 20 4 250 5 3 7.30 9 103

DP-07 150 50 4 1,250 12.5 3 1.65 9 104

DP-08 120 40 4 1,000 10 3 1.36 9 104

DP-09 150 50 4 500 12.5 3 1.30 9 104

DP-10 120 40 4 500 10 3 1.26 9 104


123

To evaluate the lowest velocity, U1, it is necessary to

determine the position where the wall influence ends and

the shear layer begins. This position, called y1, is placed at

somewhere inside the subchannel (gap) and it is recognized

by the presence of a turning point inside the gap, Fig. 6.

The turning point inside the gap marks where wall influ-

ence ends and the beginning of mixing layer. So, this is the

point where U1 occurs.

3.2 Velocity distribution in mixing layers

Regardless of the pressure gradient and admitting two-

dimensional flow, we can figure out this problem as a

steady-state plane turbulent mixing layer. The momentum

equation is written as:

uou

oxþ v

ou

oyþ ou0v0

oy¼ m

o2u

oy2ð1Þ

where u and v, are the mean axial and transversal velocity

components, respectively, and, m is the kinematic viscosity.

The resulting closure problem is classically resolved by

modeling the shear stress, u0v0 caused by velocity fluctua-

tions using an eddy-viscosity, mt:

uou

oxþ v

ou

oy¼ ðmþ mtÞ

o2u

oy2: ð2Þ

Thus, seeking self-similar solution, Lesieur [9]

uðyÞ ¼ Uc þ DUf ðgÞ ð3Þ

where DU difference between the lower and the upper

velocities in the mixing layer, U1 and U2, respectively; Uc

convective velocity, defined by

Uc ¼U2 þ U1

2ð4Þ

g = similarity parameter, defined according to van

Prooijen and Uijttewaal [16]

g ¼ y� yc

12dðxÞ

ð5Þ

where yc = coordinate of the center of the mixing layer,

where convective velocity takes place; d(x) = mixing layer

thickness

dðxÞ ¼U2 � U1

ouoy

��max:

: ð6Þ

According to Lesieur [9] the self-similar solution for Eq.

(4) leads to an error function for the mixing layer velocity

profile. However, a hyperbolic tangent function (tanh) is

used instead, thus

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

y/p

u

50x 10 x1230 # 140x 08 x 980 # 220x 04 x 480 # 3

max.

p d X

(y)

U

(a)

0 0.5 1 1.5 2 2.5 30

0.2

0.4

0.6

0.8

1

y/p

u

50 x 10 x 500 # 440 x 08 x 500 # 520 x 04 x 250 # 6

max.

p d X

U(y)

(b)

Fig. 5 Axial velocity distribution along the symmetry line: a DP-01,

2 and 3. b DP-04, 5 and 6

0.65 1.5-0.2

0.2

0.4

0.6

0.8

1

y/p1.0

-0.2

0

1

U 1

U 2

u U max

Mixing Layer

(y)

y

y

y = y =1 2

1

2

y c

Fig. 6 Gradients and mean velocity profiles form test section DP-09


123

uðgÞ ¼ Uc þDU

2tanhðgÞ ð7Þ

or

Uad ¼ 2u� Uc

DU¼ tanhðgÞ: ð8Þ

Figure 7 shows mean axial velocity distribution in the

mixing layer for all test sections. Experimental data were

plotted as a function of the similarity parameter g, and

fitted by Eq. (8).

In fact, the hyperbolic tangent function presented a good

agreement with experimental data for all test sections

investigated. However, sometimes, U1 evaluation may be a

difficult task, implying in a poor agreement between

experimental data and the hyperbolic function, for example

DP-09.

3.3 Reynolds stresses distribution

The shear stresses profiles, u0v0, were obtained for every

test section and are presented in Fig. 8. The values are

made dimensionless by using the velocity difference, DU,

and plotted as a similarity coordinates function.

In a qualitatively analysis, the results are similar to those

ones found in Townsend [20] and Yang et al. [22] con-

cerning the classical problems involving mixing layers.

The shear stresses distribution showed the same

behavior for all cases, reaching the maximum value at the

center of mixing layer, g = 0, where the maximum value

was ou=oy. After this position a quick decrease towards the

main channel can be observed. Despite a certain scattering

of the data, all shear stresses distribution showed null

values outside the mixing layer, as expected. Related to the

maximum values of u0v0=DU2, experimental data ranged

from 0.007 up to, roughly, 0.030.

Using Boussinesq’s hypothesis it is possible to describe

a correlation for shear stress:

sxy ¼ �qu0v0 ¼ qmt

ou

oyþ ov

ox

� �

: ð9Þ

Scaling mean quantities

x ¼ X

y ¼ d

u ¼ DU;

ð10Þ

where X is the streamwise position where measurements

were carried out, d mixing layer thickness, and DU the

velocity difference.

Through mass conservation equation the transversal

mean velocity v can be computed is as v ¼ DU dX:

For d � X, we can conclude that ouoy� ov

ox, yielding

�qu0v0 ¼ qmt

ou

oy

� �

: ð11Þ

Rearranging Eq. (11) and taking maximum values it is

possible to determine eddy-viscosity.

Figure 9, presents eddy-viscosity as function of length

and velocity scale, d(x) and DU, respectively, both from

mean flow. One can see the linear behavior between

experimental eddy-viscosity and the product between

velocity difference and mixing layer thickness. A linear

regression of the experimental data shows the slope curve

as 0.0162. The linear regression coefficient is R2 = 0.93.

This linear approach implies that the Reynolds stress

scaled by the velocity difference square, �u0v0

DU2 �C is a

constant, as predicted in Townsend [20].

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

η

U PL - 01PL - 02PL - 03PL - 04PL - 05PL - 06PL - 07PL - 08PL - 09PL -10U(η)=c*tanh(η)

ad

Fig. 7 Mean axial velocity distribution in the mixing layer and its

approximation by hyperbolic tangent function

-3 -2 -1 0 1 2 3-0.01

0

0.01

0.02

0.03

0.04

0.05

η

-u'v' Δ U²

DP- 01DP- 02

DP- 03

DP- 04

DP- 05DP- 06

DP- 07

DP- 08

DP- 09DP- 10

Fig. 8 Shear stress profiles


123

3.4 Coherent structures in the flow

Another noteworthy feature in developing mixing layers

concerns the streamwise vortex formation. According to

Bonnet and Delville [2], coherent structures, in these kind

of flows, has been well known for at least the last two

decades. The identification and characterization have been

done for several purposes. First, from the energetic view

point, according to Browand and Ho [3] more than 50 % of

the turbulent kinetic energy is attributable to the large

eddies. Secondly, because of the dynamical properties,

coherent structures play an essential role in mixing pro-

cesses, drag, noise emission, heat transfer, and others dif-

fusive processes.

Figures 10 and 11 show the autospectral density func-

tions for the axial and transversal velocity components. The

spectra are shown in dimensionless form. All of them were

taken at g = 0.

The Strouhal number is defined by Eq. (12), such as shown

by Browand and Ho [3] and Bonnet et al. [1]. Spectra of the

axial and transversal velocity components are [/]u and [/]v,

are done dimensionless by using velocity difference and the

mixing layer thickness, DU and d(x), respectively.

Str ¼f dðxÞUc

/½ � ¼ u02

dðxÞDU Hz

ð12Þ

where ‘‘f’’ is the fundamental frequency in the autospectral

density function.

For all autospectral density functions, the bandwidth is

the same, Be = 2.92 Hz, and the error in the Strouhal

number evaluation ranges from 3 to 7 %.

0 0.1 0.2 0.3 0.4 0

2

4

6

8

ΔU δ (x)

u'v' ∂u ∂y max.

max.

R² = 0.93

x 10 -3

Fig. 9 Eddy-viscosity evaluation

10-3

10-2

10-1

100

101

10-5

10-4

10-3

10-2

10-1

100

Str

η =0.04

[φ] u

[φ] v

[φ]

(a)

10-3

10-2

10-1

100

101

10-5

10-4

10-3

10-2

10-1

100

Str

[φ] u

v [φ]

η = 0.03 [φ]

(b)

10-3

10-2

10-1

100

101

10-5

10-4

10-3

10-2

10-1

100

Str

η = -0.03

[φ] u

v[φ]

[φ] (c)

Fig. 10 Autospectral density functions for the axial and transversal

velocity fluctuation components. a Test section DP-03. b Test section

DP-07. c Test section DP-08


123

Figure 10a–c shows the autospectral density functions

for the axial and transversal velocity fluctuation compo-

nents measured at the mixing layer center, for the test

sections DP-03, 07 and 08.

Autospectral densities show only one important peak

throughout the symmetry line, at the same Strouhal num-

ber, St = 0.17. However, Strouhal number of the axial

component presents a slightly displacement towards lower

frequencies, which yields a lower Strouhal number, around

0.15.

The difference in the behavior of the Strouhal numbers

to axial and transversal components of velocities fluctua-

tions is also mentioned in Bonnet et al. [1]. Using hot wire

probes, the authors performed measurements in a mixing

layer caused by a splitter plate. The spectral analysis

showed Strouhal number on streamwise direction, until

50 % lower than those measured on the transversal

direction; both being Strouhal number components defined

by the same scales.

Due to different scales employed the Strouhal numbers

in this paper did not agree with those ones found by Meyer

and Rehme [10, 11]. However, as already pointed by the

authors, the periodic characteristics of the velocity series

seems to vanish when velocity series are taken in the main

channel.

Here, no discrepancies were found for p/d [ 7. The

Strouhal number remains constant even for the deepest

section p/d = 12.50—DP-07.

Figure 11a–d shows autospectral analysis for test sec-

tions DP-01, 06, 09 and 10.

For these test sections p/d-ratio ranged from 5 to 12.50.

In these section peaks in the spectra were not found. This

fact suggests either large-scale structures are not present in

the flow or present measurement technique was unable to

10-3

10-2

10-1

100

10110

-5

10-4

10-3

10-2

10-1

100

Str

[φ] u

[φ] v

[φ] η = -0.06

(a)

10-3

10-2

10-1

100

10110

-5

10-4

10-3

10-2

10-1

100

Str

[φ] u

[φ]

[φ] v

η = -0.18

(b)

10-3

10-2

10-1

100

10110

-5

10-4

10-3

10-2

10-1

100

Str

[φ] u

v [φ]

[φ] η = 0

(c)

10-3

10-2

10-1

100

10110

-5

10-4

10-3

10-2

10-1

100

Str

η = 0

[φ] u

v[φ]

[φ]

(d)

Fig. 11 Autospectral density functions for the axial and transversal velocity fluctuation components. a Test section DP-01. b Test section DP-

06. c Test section DP-09. d Test section DP-10


123

identify periodical traces of velocity in these sections.

Absence of periodical traces of velocity was also found in

the test section DP-02, 04 and 05.

The interesting point is that the quasi-periodical

behavior of velocity fluctuations was found only in test

sections with smallest gap. Moreover, although section

tests from DP-01 up to DP-03, keep the same p/d, W/p and

L/d-ratios, only DP-03, presented indicative of coherent

structures (Fig. 10a). This fact suggests that the large-scale

vortex appearance may not be ruled only by one geomet-

rical parameter—e.g. p/d—and the gap width seems to play

an important role in this case.

This fact leads us to observe a new dimensional

parameter and its relationship with the periodicity of

velocity fluctuations. Periodic traces of velocity were found

only when d(x)/d [ 2. An experimental relationship

between p/d-ratio and large vortices appearance were not

found in this paper, despite Meyer’s results [11] (Fig. 12).

Figure 12 shows the Strouhal number for axial and

transversal velocity fluctuation and its relationship between

non-dimensional parameter d(x)/d.

The transversal Strouhal numbers distribution showed a

constant behavior and were well defined in Strv = 0.17. On

the other hand, for axial component the Strouhal number

Stru seems to increase with d(x)/d-ratio increasing. How-

ever, due the few results a general conclusion about the

axial Strouhal number growth cannot be formalized.

4 Conclusions

In this paper, an experimental study of mean and fluctu-

ating quantities distribution of turbulent flow in a kind of

compound channels is presented. The compound channel is

formed by to parallel plates attached on a side wall of wind

channel. This work is also an attempt to establish a rela-

tionship between the main results from this paper and the

well-known established mixing layer theory. The velocity

and length scales for a Strouhal number definition were

obtained too.

The results of the velocity measurements showed mean

velocity distribution quite similar to a mixing layer.

Despite some scattering of the data mean and fluctuant

quantities of turbulent flow seem to be functions of the

streamwise position.

Strouhal number defined with length and velocity scales

(dðxÞ;Uc), from own mean flow lead to satisfactory results,

suggesting these scales are representative of this kind of

flow. Moreover, through these scales the eddy-viscosity at

the main/sub-channel interface could be evaluated, show-

ing that �u0v0

DU2 is a constant. These results also imply that

mixing layer thickness may be a linear function of

streamwise position. However, this question will be dele-

gated to future research.

Remarkable peaks in the spectra were found in some test

sections, implying periodical behavior of velocity fluctua-

tions. Dimensionless frequencies were found in 0.15 and

0.17 for axial and transversal velocity component. These

values are lower than 0.2, found by [3] and Bonnet et al. [1]

in their study of free shear layers. Despite this fact the

Strouhal number remained constant even for deepest sec-

tion p/d-ratio 12.50.

It is important to note that the presence of large-scale

structures in the flow seems no longer depend only on p/d-

ratio. A new dimensionless parameter was tested, d(x)/d.

The main results showed that peaks were observed in the

spectra for d(x)/d [ 2.

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Fig. 12 Relationship between Strouhal numbers and flow develop-

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experimental study of mixing layer in a closed compound channel

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