PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Experimental Investigation of the oscillating flow dynamics at the exit ofregenerator meshes with different configurations
Islam Ramadan1; Helene Bailliet; Jean-Christophe ValiereInstitut Pprime, Centre National de la Recherche Scientifique, Université de Poitiers, Ecole Nationale
Supérieure de Mécanique et d’Aérotechnique, Département Fluides-Thermique-Combustion, Ecole
Nationale Supérieure d’Ingénieurs de Poitiers, 6 Rue Marcel Doré Bâtiment B17-BP 633, 86022 Poitiers
Cedex, France
ABSTRACTRegenerators (often consisting in stack mesh-wires) and heat exchangers are the core of thermoacoustic
devices and, as such, key elements for the efficiency of these systems. In this study, the oscillating flow
velocity field at the exit of different regenerators has been measured using Particle Image Velocimetry (PIV)system. Three different mesh wire sizes have been selected with respect to the size of the viscous penetration
depth. The influence of the randomness of stacking the mesh wires on the oscillating flow dynamics has also
been investigated. Measurements are performed for different acoustic levels. In the conference, the structureof oscillating flow will be discussed, especially in terms of vorticity fields for the different regenerators at
different phases over the acoustic cycle. The evolution from low to high acoustic amplitudes will bepresented.
Keywords: Thermoacoustics, End-effects, Oscillating flow, PIV

1. INTRODUCTION
The design of heat exchangers is a crucial issue for the development of efficient thermoacoustic
devices. The improvement of such design requires a better understanding of flow patter ns andassociated heat exchange processes at the exit of the regenerator/stack. The present study aims atparticipating in progressing in this understanding. The synthesis of the literature on the study ofoscillating flow at the exit of a thermoacoustic core is complicated by the fact that there is noagreement on the choice of the relevant dimensionless parameters. Blanc-Benon et al. [1] investigatedvortex shedding from a stack of parallel plates with PIV. They studied the flow for two plate
thicknesses and identified the generation of two symmetrical vortices for each plate that had different
forms depending on the plate thickness. For plate thicknesses larger than the viscous penetration
depth concentrated vortices were observed near the edge of the plate whereas for thinner plates
elongated layers were observed without any well-defined eddies; for the range of velocity amplitudes
investigated there was not any vortex street observed whatever the thickness of the plates. Mao et al.
[2] compared the flow generated at the exit of a stack of plates for different plate thicknesses andfound two distinct modes of generation of a vortex street: elongated shear layer on one side (observed
for thin plates) and bluff-body type of shedding on the other side (observed for thick plates). They
found that for high amplitudes (Reynolds numbers), vortices are shed in an alter nate fashion and theStrouhal number based on the shedding velocity and acoustic amplitude is around 0.2 for all the
Reynolds numbers studied. Aben et al. [3] used Strouhal and Reynolds numbers based on the plate
thickness, acoustic amplitude just outside the stack, and acoustic frequency. They considered thevorticity fields for different amplitudes and different frequencies at the phase of maximum outward
displacement (and zero velocity) and divided them in four categories: ‘‘two vortices’’, ‘‘four
vortices’’, ‘‘transition area’’ and a ‘‘vortex street’’. One of their conclusion is that for high porosity
thermoacoustic core the plate thickness is the relevant characteristic length whereas at low porosity
1

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islam.ramadan@univ-poitiers.fr

the spacing between plates is the relevant characteristic length. Shi et al. [4] used hot wire
anemometry and PIV to study the flow at the exit of a stack of parallel plates for several plate
thicknesses, plate spacing and Reynolds numbers (76 different flow cases). They found that only one
St=f(Re) relationship was needed to correctly fit all the cases for Reynolds numbers based on plate
thickness from 200 to 5000. Here the Strouhal number was defined using the vortex shedding
frequency and the reference velocity was the local acoustic velocity amplitude. Then, in their studyof vortex shedding at the exit of a stack of plates, Shi et al. [5] proposed to use three similarity
parameters: the Reynolds number based on the plate thickness, the Keulegan–Carpenter number (KC,ratio of particle displacement amplitude to plate thickness) and lastly the Womersley number (Wo,ratio of the spacing between adjacent plates and viscous penetration depth) or equivalently the ratioof the spacing to the thickness of plates. They studied 108 different cases (different stack andamplitudes) and identified eight distinct vortex wake pattern types, among which four types havebeen observed and reported in previous works while the remaining four were new findings. Berson
and Blanc-Benon [6] studied the flow within the gap between two stacks as a model for a stack-heatexchanger couple. They defined a Reynolds number based on the viscous boundary layer th ickness
and velocity amplitude inside the stack as used for the study of transition to turbulence in oscillati ng
flow (Merkli and Thomann [7]). The Strouhal number they formed is based on the convection velocity
of flow vortices and the shedding frequency. Their results showed that the Strouhal number based on
the plate spacing takes values around 0.44 for all the configurations under study, whatever the
Reynolds number. Also they found that at high amplitude the flow is not rep eated from one acoustic
period to another which involve oscillation of the cooling load viewed by the heat exchanger.
This brief bibliographic presentation shows that, even if a stack of plates is rarely used in practice,
this geometry has been the most studied for what concerns end effects investigation. Flow at the exitof mesh grid regenerator, which is the most common geometry in practical devices, has never beenstudied to our knowledge. In the following section, the experimental setup and measurement
procedure will be explained. In section 3, the results will be discussed and then the conclusions will
be drawn in section 4.

2. Experimental Apparatus
2.1 Experimental setup
A schematic for the experimental setup is shown in Figure 1a. Two 8-inch loudspeakers (PHL –
B2410) are mounted at both ends of the resonator which is filled with air at atmospheric conditions.
The resonator is made of a square duct with inner side length of 44 mm and total length of 2645 mm.
The loudspeakers are connected to a power amplifier which is driven by a function generator. They
are synchronized to achieve a velocity antinode at the middle of the resonator at a resonance frequency(݂) of 31 Hz. The regenerator is placed near the middle of the resonator. It consists of mesh wires
stacked either randomly or forming straight channels inside a canister. The four different regenerators
used in the study are shown in Figure 1b. A description of the mesh wires used in each regenerator ispresented in Table 1.
In usual thermoacoustic designing tools, regenerators are described in terms of their hydraulicradius, volumetric porosity, thermal conductivity and length along the guide axis. In the present study,
the mesh wire dimensions are selected to cover a plausible range for these parameters. In particular
the ratio ࢘࢕ Ȁࢾ࢜ is chosen to be credible for stack-based devices (Reg#1 and 2) or for regeneratorbased devices (Reg#3 and 4). Here ࢘࢕ is the hydraulic radius, which represents the ratio between thegas volume to the gas-solid contact area, and ࢾ࢜ ൌ ටߥൗߨ݂ is the viscous penetration depth where ߥis the kinematic viscosity of the air. For standing-wave thermoacoustic systems, this ratio should belarger than unity and the term “stack” is used, whereas for travelling-wave system the ratio should beless than unity and the term “regenerator” is used [8].
The velocity field at one end of the regenerator is measured using PIV. The PIV system consistsof a ND-YAG laser source for illuminating the seeding particles existing in the flow. An atomizer
seed generator (TOPAS – ATM 210) is used to atomize oil producing droplets with mean particle
diameter of 0.5 μm. Images are recorded with two 2048 × 2048 pixels 2 LAVISION cameras(maximum sampling frequency of 15 Hz). Two cameras are employed to increase the size of themeasurement area without reducing the spatial resolution (i.e. 185 × 185 μm 2 ) of the imaging system.
The PIV system is triggered by a reference external TTL signal, which is phase-locked to the acoustic

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cycle.

(a)(b)

Figure 1- (a) Schematic of the experimental setup. (b) Image for the regenerators used in the study anddefining parameters for the mesh wires.
Table 1: Description of the mesh wires used in each regenerator.
Name
Reg#1
Reg#2
Reg#3
Opening (D), mm
2.24
2.24
1.12
Wire diameter (d), mm
0.355
0.355
0.22
Volumetric porosity (%)
0.879
0.879
0.85
Hydraulic radius (࢘࢕ ሻ, mm
0.646
0.646
0.33
1.6
1.6
0.8
࢘࢕ Ȁࢾ࢜
Stacking configuration
Straight channels
RandomRandom

Reg#4
0.56
0.16
0.801
0.162
0.47
Random

2.2 Experimental conditions
As mentioned previously, Aben et al. [3] used Reynolds number (ܴ݁) and Strouhal number (ܵ‫)ݐ‬௎ ௗ௙ௗܴ݁ ൌ ೖ ,ܵ‫ ݐ‬ൌ
ఔ௎ೖwhere ܷ௞ is the velocity amplitude at a reference point (k) (see Figure 1a) to describe the flow at theexit of a stack plates and observed three different flow patterns (i.e. two/four vortices, transition area
and Vortex Street). Accordingly, the oscillating flow velocity amplitude (ܷ௞ ) is adjusted so that thecurrent experiments lay at different zones observed by [3] and hence our results can be comparedwith their observations. On the other hand, Shi et al. [5] found that Keulegan–Carpenter number (‫)ܥܭ‬,which is defined as flows:ܺ௔௠௣‫ ܥܭ‬ൌ
݀௎where ܺ௔௠௣ is the axial displacement amplitude (ܺ௔௠௣ ൌ ೖ ), has a significant effects on the flowଶగ௙pattern. The experimental conditions of all the experiments, presented in Table 2, show that even if
KC and St are associated with the same physics (effect of unsteadiness), in our experiments thecondition for the Strouhal number is always St<<1 whereas KC goes from ≈1 to >>1.

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Exp#
1
2
3
4
5
6
7
8
9
10
11
12

ࡾࢋ
1.3×101
1.0×1022.3×102
1.3×101
9.3×101
2.2×102
3.1×100
2.9×101
7.1×101
2.2×100
1.0×101
2.0×101

Table 2 - The experimental conditions of different experiments
Observed patternࡿ࢚ࡷ࡯ࢁ࢑ (m/s) Reg# Pattern ref [5]2.0×10 -2 8.0×100
0.56
1
2/4 vortices
shear layer
2.8×10 -3 5.8×101
4.0
1
Vortex street
Chaotic
1.1×10 -3 1.4×102
9.6
1
Vortex street
Chaotic
2.0×10 -2 8.0×100
0.55
2
2/4 vortices
shear layer
2.8×10 -3 5.7×101
3.95
2
Vortex street
Chaotic
1.2×10 -3 1.3×102
9.1
2
Vortex street
Chaotic
3.2×10 -2 4.9×100
0.21
3
2/4 vortices
no/weak vorticity
3.5×10 -3 4.6×101
1.95
3Vortex street
shear layer
1.4×10 -3 1.1×102
4.87
3Vortex street
Chaotic
2.4×10 -2 6.7×100
0.21
4
2/4 vortices
no/weak vorticity
5.1×10 -3 3.1×101
0.97
4Transitional
shear layer
2.7×10 -3 6.0×101
1.87
4Vortex street
shear layer

2.3 Measurement procedure and post processing
Before each experiment, the seeding holes placed at the extremities of resonator (see Figure 1a)are opened and the seeded air flow is introduced through one of these holes to create a homogenous
seeding particles distribution over the measurement area. After closing the holes, the loudspeakers
are turned on. The PIV measurements are started 2 minutes later, to ma ke sure that the effect of theseeding flow on the measurements is eliminated.
As shown in Figure 2, the measurements are performed at 12 different phases over the acoustic
cycle. The total number of double-images taken at each phase is 100 (this number of images were
found, in previous studies [9] [10], to be sufficient for achieving the convergence of the data).

Figure 2- The acoustic velocity at different phases over the acoustic cycle at the reference point (k).
In order to produce the velocity vector maps, the acquired images are processed by DAVIS
software. A low pass filter is applied to remove the light reflections from the solid walls. Then, across-correlation algorithm is applied to estimate the mean particles displacement within eachinterrogation area; finally the displacement is divided by time between two laser pulses to obtain thevelocity. The time between pulses is adjusted to allow for a particle displacement equals to about ¼
the interrogation window. The ensemble-averaged vector maps and vorticity fields are calculated foreach phase by averaging the 100 vector maps. In the following section, the results of the 12
experiments are discussed.

3. Results and discussions
In order to investigate the vortex patterns originated at the exit of the regenerator, the vorticity ateach point in the field is calculated as follows:݀‫ݑ݀ ݒ‬߱௭ ൌെ݀‫ݕ݀ ݔ‬2069

where ‫ ݑ‬and ‫ ݒ‬are the axial and transverse velocity components, respectively. In Figure 3 thevorticity field is plotted for all experiments at 4 phases of the acoustic cycle: ‫׎‬ଵ ǡ ‫׎‬ସ ǡ ‫׎ ݀݊ܽ  ଻׎‬ଵ଴(we consider the vorticity at only 4 phases to facilitate the presentation of the results). The axial
distance is normalized by the axial displacement amplitude ( ܺ௔௠௣ ), whereas the transverse distanceis normalized by the half width of the resonator (W).
Exp#

1

2

3

4

5

6

7

8

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‫׎‬૚ Max displ out‫׎‬૝ Max velo in‫׎‬ૠ Max displ in‫׎‬૚૙ Max velo out

9

10

11

12

Figure 3 - The vorticity fields for all experiments at different phases over the acoustic cycle in s -1.
3.1 Effects of the acoustic amplitude
As the building of more powerful thermoacoustic systems becomes a necessity, the acoustic
amplitudes of these systems should be increased. However, the design of thermoacoustic systems
depends mainly on the linear theory which cannot predict the non-linear phenomena especially athigh acoustic amplitudes. Hence, it is important to discuss the effect of the acoustic amplitude on theoscillating flow patterns at the exit of the regenerator. For this purpose, the first three experiments
are considered because the same regenerator is used but at different acoustic velocity amplitudes. As
shown in Figure 3 (Exp# 1, 2 and 3), at the end of the suction stage (‫׎‬ૠ ), there is no vortex patternnear the exit of the regenerator because the main flow moves inwards the regenerator channels . At
the beginning of the ejection stage (i.e. the flow moves outward the regenerator channels), elongatedshear layers start to form and evolve till the maximum vorticity value is achieved at (‫׎‬૚૙ ). At very
low amplitude (Exp#1), the vorticity field at ‫׎‬૚૙ shows the emergence of alternatively opposite shear
layers. These shear layers have elongated as the flow moved away from the regenerator and reach tothe maximum axial normalized distance (‫ݔ‬Ȁܺ௔௠௣ ) of 2 at ‫׎‬૚ . Such vorticity layers extending out of
the thermoacoustic core during ejection stage (and that prolongate the oscillating boundary layers
developed inside the core) were reported by other authors for low amplitudes flow out a stack plates[6], [2]. It is also quite similar to the Elongated Symmetric vortex structures described by [5]. During
the suction phase ( ‫׎‬૝ ), the generated vortices are convected with the main flow towards theregenerator. At medium amplitude (Exp#2), the succession of elongated counter-rotating vortices isalso observed. However, these elongated vortices break up at axial distance ( ‫ݔ‬Ȁܺ௔௠௣ ) of 0.5 to form
many rolled up vortices that extend to an axial distance (‫ݔ‬Ȁܺ௔௠௣ ) of 1. These rolled up vortices movewith the main flow while breaking up into very small structures that extend to an axial distance(‫ݔ‬Ȁܺ௔௠௣ ) of 2.5 as shown at ‫׎‬૚. At very high amplitude (Exp#3), the flow pattern breaks down into
small structures at the end of the ejection (phase ‫׎‬૚૙ ), that merge to form larger structures during thesuction phases (‫׎‬૚ ). Therefore, conversely to several previous studies [2], [6], [3] we do not observe
any alternate shedding of vortices neither breaking up of the shear layers into an organized vortex
street. This can be interpreted as being due to the fact that these previous studies dealt with a stackof plates whereas we are concerned with mesh grid regenerator. However, the pattern observed in thepresent study for high amplitude cases (Exp#2 and 3) can be classified in the “chaotic flow state andvortex merging” pattern observed by Shi et al. [5] at the exit of a stack of plates. This regime wascharacterized by [5] as corresponding to large KC (>>1) and Reynolds numbers (10 2 to 10 3). The

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values of both Re and KC of Exp#2 and 3 fall within the range defined by [5]. As mentioned
previously, the Strouhal number for all experiments is less than unity. Hence, we can consider Re andKC are the characterizing parameters for the flow patterns at the exit of the regenerator.
3.2

Effects of the stacking configuration
In order to study the effects of stacking configurations, the flow pattern at the exit of two
regenerators (Reg#1 and 2) is investigated at the same flow conditions (i.e. Re, St and KC). The
results of Exp#1, 2 and 3 are compared with the results of Exp#4, 5 and 6, respectively. At very low
amplitude at ‫׎‬૚, it is observed that the flow pattern in the case of random stacking (i.e. Exp#4) isless organized than in the case with straight channels (i.e. Exp#1); in particular the repeatability inthe vertical direction observed for the straight channel is not as marked in the random stacking case.
At medium amplitude at ‫׎‬૚૙, the beak up of the flow in numerous small structures occurs for ashorter distance from the regenerator end in the case of random stacking (i.e. Exp#5) than in the caseof straight channels (i.e. Exp#2). At very high amplitude, the stacking configuration seems to ha ve
no much influence on the flow pattern (comparing Exp#3 and 6).
3.3

Effects of the mesh-wire size
To investigate the effects of the mesh-wire size on the flow pattern, the flow pattern at the exitof 3 different regenerators (Reg#2, 3 and 4) is investigated at different experimental conditions. The
flow conditions are adjusted so that KC number has the same order of magnitude at different mesh wire sizes. For instance, the KC number of Exp# 4, 7 and 10 has the same order of magnitude whereas
the mesh-wire size in these three experiments is different. For this purpose, the results of Exp#4, 5
and 6 are compared with either Exp#7, 8 and 9 or Exp#10 and 11/12, respectively. It is worthwhile tomention that the intensity of the vorticity field has been reduced in the cases of Reg#3 and 4. Hence,the scale of the vorticity in Exp#7 to 12 has been reduced by half (+/-250 instead of +/-500) to makethe flow patterns visible.
As shown in Figure 3, at very low velocity amplitudes (Exp#4, 7 and 10), the decrease of themesh-wire size results into a decrease in the intensity of the vorticity field. According to theobservations of [3] in the case of parallel-plates stack, the flow pattern in these three experiments(Exp#4, 7 and 10) should be similar. In the current study, we observed that the flow pattern is different
from the observations of [3] in the case of large mesh-wire size (Exp#4). With smaller mesh-wires
size (Exp#7 and 10), the vorticity is negligible over the whole cycle. At medium flow velocity
amplitudes (Exp#5, 8 and 11), it is observed that (see ‫׎‬૚) the elongated vortices break up into smaller
vortices with large mesh-wire size (Exp#5) whereas the breakup of the elongated vortices was notobserved with smaller mesh-wire size (Exp#8 and 11). At high flow velocity amplitudes (Exp#6, 9
and 12), it is observed that (see ‫׎‬૚) the elongated vortices beak up with the cases of large and medium
mesh-wire sizes (Exp#6 and 9) whereas there is no breakup observed with the case of small meshwire size. As was concluded from section 3.1, it appears then that the flow classification and similarity
parameters chosen by Aben et al. [3] for their study of end effects for a stack of plates do notcorrespond to the observation made in our study.

4. CONCLUSION
In the current study, the oscillating flow patterns at the exit of different regenerators have been
investigated. Three main flow patterns were observed namely; no/weak vorticity pattern, shear layer
pattern and chaotic pattern. The effects of different parameters on the flow patterns have been
investigated. First, the effects of the flow velocity amplitude have been investigated. We found thatboth Re and KC are well suited similarity parameters for the flow pattern at the exit of the regenerator.
Second, the effects of the stacking configuration of the mesh-wires in the regenerator have been
investigated. The random stacking of the mesh-wires altered the flow patterns at low and medium
velocity amplitudes whereas the flow pattern does not changed at higher velocity amplitudes. Finally,
the effects of the mesh-wire size on the flow pattern have been investigated. Reducing the mesh-wiresize results in decreasing the intensity of the vorticity, which confirm the validity of the Reynolds
number as similarity parameter.

ACKNOWLEDGEMENTS
This research is financially supported by Agence Nationale de la Recherche (Projet-ANR-17-CE06-0007-

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01). The authors also appreciate the technical assistance provided by Pascal Biais, Laurent Philippon andPhilippe Szeger.

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