ＯＴＥＣ
Vol. 24 (2019)，1 〜 7

Characteristics of pulsatile flow with the reverse flow in the grooved channel

Characteristics of pulsatile flow with the reverse flow inthe grooved channel
Junxiu PAN*1, Yongning BIAN*1, Hirofumi ARIMA*2 and Yasuyuki IKEGAMI*2*1

State Key Laboratory of Structural Analysis for Industrial Equipment
Dalian University of Technology, 116024, China*2

Institute of Ocean Energy, Saga University, 840-8502, Japan

Abstract
The characteristics of pulsatile flow with the reverse flow in the grooved channel are investigatedexperimentally. Three flow parameters are considered: the net flow Reynolds number, the oscillatory fraction of theflow rate and the oscillatory frequency. The flow structures are visualized using the aluminum dust method. It isobserved that the flow tends to be more unstable in the deceleration phase for the pulsatile flow. Meanwhile, theexperimental oscillatory fraction of the flow rate is easier to reach the theoretical value at lower oscillatory frequency.
Furthermore, it is found that the oscillatory fraction of the local pressure decreases with the increase of the periodof oscillation, and the oscillatory fraction of the downstream local pressure is larger than that of the upstream localpressure.
Keywords: pulsatile flow, grooved channel, flow visualization, oscillatory fraction
1. Introduction
Ocean thermal energy conversion (OTEC) is a system which takes advantages of the temperature difference
between the warm water at the surface of the ocean and cold water of the depths. However, the typical thermal
efficiency of the Rankine cycle is only 3–5% which is primarily limited by the finite temperature difference (Khanet al., 2017). The authors and other researchers made researches about how to improve the thermal efficiency of theOTEC system (Bian et al., 2019). It was found that both double flute tube-type and plate-type heat exchangers are
best fitted for the OTEC (Uehara et al., 1984).
In recent years, the characteristics of heat transfer in grooved channels have attracted many researchers’attention. Nishimura et al. (2004) studied mass-transfer enhancement and fluid dynamic behavior in a wavy-walledtube for pulsatile flow. They concluded that the unstable flow leads to remarkable fluid mixing and contributes tothe mass-transfer enhancement. Bian et al. (2009) studied the relationship between the transitional characteristic
and the enhancement mechanism in an axisymmetric wavy-walled tube under steady flow. They pointed that themost effective mass transfer enhancement occurred just before the transition flow regime. Zhang et al. (2018)
experimentally analyzed the oscillatory flow in the grooved channel. They proposed that there is some difference
between the experimental oscillatory fraction and the theoretical oscillatory fraction, and the experimental
oscillatory fraction is close to the theoretical value with a lower Reynolds number. Huang et al. (2017) carried out
the experimental study in the relationship between the characteristics of the pressure drop and the laminar pulsatile
flow. They found that the overall pressure drop decreases with increase of the oscillatory frequency. Sun et al. (2010)
studied the self-sustained flow in grooved channels. They found that the internal pressure of the channels strongly
affects the amplitude of the self-sustained wave and increasing the pressure of the channels makes the amplitude
higher.
Received date 2019.7.1
Email of the corresponding author: ybian@dlut.edu.cn1

2

Junxiu PAN, Yongning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMI

The present study deals with the characteristics of the pulsatile flow in the grooved channel. The effects ofoscillatory frequency and Reynolds number on the experimental oscillatory fraction and the oscillatory fraction of
the overall pressure drop and the local pressure are examined.
2. Experimental system
The diagram of the experimental system is shown in Fig. 1 and all the experimental apparatus are consistent withthe previous ones. The city water is used as the working fluid and the net flow is provided by a centrifugal pump.
The volumetric flow rate of the pulsatile is given as:
𝑄𝑄� = 𝑄𝑄� + 𝑄𝑄� sin(2𝜋𝜋𝜋𝜋𝜋𝜋𝜋(1)where Qs is the net flow rate which is determined with a flow-meter, f is the frequency of the pulsatile flow, t is theflow time, Q0 is the amplitude of the pulsatile flow and it is expressed as:
𝑄𝑄� = 2𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋𝜋�� /4)(2)

where , Dp =50mm is the diameter of the piston.
The test section is depicted in Fig. 2. The grooved channels consist 55 grooved modules and the length of every
grooved module is 𝐿𝐿 𝐿𝐿𝐿𝐿𝐿, 𝑙𝑙 𝑙 𝑙𝑙𝑙𝑙, 𝑊𝑊 𝑊𝑊𝑊𝑊𝑊𝑊, ℎ = 2.5mm. The local pressures 𝑃𝑃� (n=1,2,3…8) aremeasured at different locations which are shown in Fig. 3.
⑧

⑦⑤
④
⑥
③

① Circulating pump
② Centrifugal pump
③ Control valve④ Piston pump
⑤ Test zone②①

⑥ Differential transducer⑦ Flow-meter⑧ Overflow tankFig. 1 Diagram of the experimental systemh2hW

flow directionlLFig. 2 Dimensions of the grooved channels

P1P290

P3210

P4210

P590P6210

1100

Fig. 3 Locations of the local pressure measurement

P7120

P890

3Characteristics of pulsatile flow with the reverse flow in the grooved channel

To get a better understanding of the pulsatile flow, some parameters are defined as follows:
The net flow Reynolds number (Re)𝑅𝑅𝑅𝑅 𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅(3)
where 𝜌𝜌 and 𝜇𝜇 are the density and the viscosity of water respectively. The characteristic velocity of the flow u is
calculated by:𝑢𝑢𝑢 𝑢𝑢𝑢 𝑢 𝑢𝑢�
(4)
where 𝑢𝑢� is calculated as follow(5)𝑢𝑢� = 𝑄𝑄� /(2𝑊𝑊𝑊𝑊The oscillatory fraction (P) of the flow rate
𝑃𝑃 𝑃𝑃𝑃� /𝑄𝑄�
(6)The oscillatory fraction of the overall pressure drop (P’)(7)
𝑃𝑃� = (∆𝑃𝑃��� − ∆𝑃𝑃�)/∆𝑃𝑃��
where ∆𝑃𝑃��� is the instantaneous max value of the overall pressure drop, ∆𝑃𝑃 is the time-averaged pressure drop.
The oscillatory fraction of the local pressure (𝑃𝑃�� )�� )/𝑃𝑃��(8)
𝑃𝑃�� = (𝑃𝑃� − 𝑃𝑃�where 𝑃𝑃� (i=3,5,7) is the instantaneous value of the local pressure, 𝑃𝑃� is the time-averaged value of the localpressure.
The instantaneous velocity 𝑢𝑢� is depicted as:(9)𝑢𝑢� =𝑢𝑢� + 𝑃𝑃 𝑃𝑃𝑃� ∗ sin(2𝜋𝜋𝜋𝜋𝜋𝜋𝜋The aluminum dust method is used to visualize the flow patterns. The aluminum dust method, i.e. perfusion with asuspension of aluminum particles which are about 40 m in diameter, enables us to observe the pathlines
approximately corresponding to streamlines in the whole flow field. Besides, the flow patterns are recorded by adigital video camera. All the experiments are conducted at the room temperature.
3. Results and discussion
3.1 Filter processing
In order to reduce the interference of noise in the experiment, the experimental data, i.e. the signal of thevolume flow rate and the pressure drop, need to be filtered. As can be seen in Fig. 4, all the experimental data areprocessed 1Hz low pass fit filter. Though there is a slight deviation between the experimental data and the filtereddata at the beginning and end of the experiment, the filtered data in the middle section are consistent with theexperimental data. Therefore the following discussions are based on the filtered data in the middle section.
140

P=0.8, Re=250, f=0.0432Hz

120p120

p (Pa)p (Pa)

80
60

80
60
40

40202000.0

1Hz low pass fft filter of p

100

100

0.3

0.6

0.9

1.2

00.0

1.5

0.3

0.6t/TQ

P=0.8, Re=250, f=0.0432Hz

100

80

80

60
40
20
0
0.0

0.9

1.2

1.5

1.2

1.5

1Hz low pass fft filter of Q

120

100

Q (ml/s)

Q (ml/s)

120t/T

60
40
20

0.3

0.6

0.9t/T

1.2

1.5

0
0.0

0.3

0.6

0.9t/T

Fig. 4 Comparison of the experimental data with the filtered data.

4Junxiu PAN, Yongning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMI

3.2 Experimental flow patterns
4 kinds of flow patterns during one oscillation cycle for P=1.6 Re=250 and f=0.0721 deserves attention. As isshown in Fig. 5, when t/T=0, two stable symmetric vortexes form in the grooved area and the pathlines of the main
flow are parallel to each other. It belongs to “stable” state and marked as “+”. It is easy to notice that when t/T=0.25,
i.e. the instantaneous flow reaches a peak value, the particle pathlines are highly disturbed and the main flow
becomes unstable. It indicates the turbulent motion and marked as “-”. It is apparent that when t/T=0.625 andt/T=0.875, the grooved area is filled with two large vortexes, and locations of all particles are almost motionless.
Phenomenon like these implies the flow almost stops (i.e. the flow rate is close to 0) and marked as “s”. Besides
when t/T=0.75, the fluid mixing area of the grooved region and the mainstream region appears at the upstream of
the groove. It suggests there exists a reverse flow and marked as “r”. Moreover, it is interesting to observe that theparticle pathlines at t/T=0.375 are more unstable than that at t/T=0.125 although their flow rates are the same. Thesame phenomenon can be seen when t/T=0 and t/T=0.5, therefore the flow tends to be more unstable in thedeceleration phase. Which has been validated in Nishimura et al. (2004). Furthermore, based on Eq. (9) the flowrate is 0 only when t/T=0.607 and t/T=0.893, and the flow should be a reverse flow when t/T=0.625 and t/T=0.875.
However, the actual behavior shows obviously different results with the theoretical value. Besides the errors fromexperimental photographing, it is deduced that the experimental oscillatory fraction (P) of the flow rate is lower
than the theoretical value (P0) based on Eq. (9).
3.3 Difference between P and P0.
To investigate whether the experimental oscillatory fraction of the flow rate (P) reaches the theoretical value(P0), the experimental oscillatory fractions of the flow rate at different working conditions have been calculated andplotted in Fig. 6 and Fig. 7. Figure 6 shows the relationship between P and the periods of oscillation (T) at different
P0 and Re=375. It is not difficult to notice that P increases with T. Which means P is easier to reach P0 at lower f.
Furthermore, P is easier to reach P0 when P0 is set lower.
Figure 7 illustrates the relationship between P and the pulsation strokes (s) at different Re and P0=1.6. It isnoted that P increases with s, which also means P is easier to reach P0 at lower f based on Eq. (2). Besides, P
decreases with the increase of Reynolds number. Which means P is easier to reach P0 at lower Reynolds number.
3.4 The effect of the T on P’ and 𝑷𝑷�𝒊𝒊 .
Figure 8 describes the effect of T on P’ under different theoretical oscillatory fractions of the flow rate (P0). P’
increases with the increase of T, and it rises with the increase of P0. It is almost identical to P. It suggests the flow
tends to be more unstable at lower f.
Figure 9 describes the effect of T on 𝑃𝑃�� under different P0. It is seen that 𝑃𝑃�� decreases with the increase of T.
Moreover, it is interesting to note that the oscillatory fraction of the downstream local pressure is larger than that ofthe upstream local pressure. It indicates that downstream flow is more unstable than upstream flow. In addition, 𝑃𝑃��rises as P0 increases.

Characteristics of pulsatile flow with the reverse flow in the grooved channel

Fig. 5 Experimental flow patterns for P=1.6 Re=250 and f=0.0721.

5

6Junxiu PAN, Yongning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMI

1.6

Re=3751.4

P0=0.81.2

PP0=1.0P0=1.21.0

P0=1.40.8

P0=1.6

0.6
0.4
0.2

02468101214161820T

Fig. 6 Relationship between P and T at different P0 and Re=375.

1.6
1.4

P

1.2
1.0

Re=250
Re=375
Re=500P0=1.6

0.8
0.6
0.4
0.2
20

4060

80

100120s (mm)Fig. 7 Relationship between P and s at different Re and P0=1.6.

0.9

Re=375P0=0.8

0.8
0.7

P'

P0=1.0

0.6
0.5
0.4
0.3
0.2

0481216T

Fig. 8 Effect of T on P’ under different P0.

20Characteristics of pulsatile flow with the reverse flow in the grooved channel

0.50

Re=3750.45

P'P0=0.8
P3'P0=1.0
P3'P7'P7'P5'0.40

P5'0.350.30
0.25
246810121416TFig. 9 Effect of T on 𝑃𝑃�� under different P0.

4. Conclusions
In this paper, the characteristics of the pulsatile flow in the grooved channel are explored experimentally. The
main conclusions are obtained as follows:(1) For the pulsatile flow, the flow tends to be more unstable in the deceleration phase.
(2) P is easier to reach P0 at lower f, lower P0 or lower Reynolds number.
(3) P’ increases with the increase of T, and it rises with the increase of P0.
(4) 𝑃𝑃�� decreases with the increase of T, and the oscillatory fraction of the downstream local pressure is larger thanthat of the upstream local pressure.
The above results can be used as a useful reference for the design and operation of high efficiency heat exchangers.
Acknowledgment
This study is sponsored by the cooperative Research Program of IOES(No. 18A07).
References:
Khan, N., Kalair, A., Abas, N., & Haider, A., Review of ocean tidal, wave and thermal energy
technologies, Renewable and Sustainable Energy Reviews, Vol.72, (2017), pp. 590-604.
Bian, Y., Pan, J., Liu, Y., Zhang, F., Yang, Y., & Arima, H., Performance analysis of a combined power andrefrigeration cycle, Energy Conversion and Management, Vol.185, (2019), pp. 259-270.
Uehara, H., Kusuda, H., Monde, M., Nakaoka, T., & Sumitomo, H., Shell-and-plate-type heat exchangers for
OTEC plants, Journal of solar energy engineering, Vol.106, No.3 (1984), pp. 286-290.
Nishimura, T., Bian, Y. N., & Kunitsugu, K., Mass‐transfer enhancement in a wavy‐walled tube by imposed
fluid oscillation, AIChE journal, Vol.50, No.4 (2004), pp. 762-770.
Bian, Y., & Jia, B., Mass transfer characteristics in an axisymmetric wavy-walled tube for pulsatile flow withbackward flow, Heat and mass transfer, Vol.45, No. 6 (2009), pp. 693-702.
Zhang, F., Bian, Y., Arima, H., & Ikegami, Y., Difference between Experimental and Theoretical Pulsatile Flow in
Grooved Channel, OTEC, Vol.23, (2018), pp. 1-6.
Huang, H., ARIMA, H., BIAN, Y., & IKEGAMI, Y., Pressure Drop Characteristics of Laminar Pulsatile Flow inGrooved Channel with Different Groove Lengths, OTEC, Vol.22, (2017), pp. 1-6.
Sun, F., Bian, Y., Arima, H., Ikegami, Y., & Xu, X., Strength characteristics of the self-sustained wave in grooved
channels with different groove length, Heat and mass transfer, Vol.46, No.11, (2010), pp. 1229-1237.

7