21ＯＴＥＣ
Vol. 25（2020），21 ～ 28

Characteristics of flow patterns under pulsatile flow with same
oscillatory fraction in the grooved channel
Yunjie YANG1, Yongning BIAN1*, Hirofumi ARIMA2 and Yasuyuki IKEGAMI2
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 flow structure under pulsatile flow with same oscillatory fraction in the grooved channel
are investigated experimentally. The flow patterns under pulsatile flow in the grooved channel are divided into
4kinds in this study. The effects of frequency, groove length and t/T on the flow patterns are analyzed. The results
showed that the instability of the flow enhances with t/T during the deceleration phase. As the frequency increases,
the onset of the unstable flow state is postponed, but the strongly unstable state (3) starts to appear and advancegradually. Moreover, the onset of the unstable state gradually advances as the increase of groove length.
Keywords: pulsatile flow; grooved channel; flow visualization; oscillatory fraction
1. Introduction
Development and utilization of marine energy is the key research direction with the problem of low energy andincreasingly serious environmental pollution. As an environmentally friendly and sustainable new energy, ocean
thermal energy conversion (OTEC) has attracted more and more attention. OTEC uses the temperature difference
between the warm seawater at the surface and cold seawater at the depths. However, the thermal efficiency of thepresent OTEC is very low because of the finite temperature difference. Improving the heat transfer efficiency ofexchanger is one way to improve the thermal efficiency of OTEC.
Bian et al. [1] conducted a series of the flow characteristics for pulsatile flow in grooved channels
experimentally, the results showed that the local pressure and the overall pressure drop change significantly withthe groove length. Zhang et al. [2] discover that the pressure drop decreases with the frequency of the pulsatile flowin the laminar flow and transitional flow for the same oscillatory fraction, while it has an inflection point and thenincreases in the turbulent flow. Huang et al. [3] studied pressure drop characteristics of laminar pulsatile flow ingrooved channel with different groove lengths experimentally. Their results suggested that the relation between
amplitude and frequency of pulsatile is the same to different grooved channel. Pan et al. [4] observed that theexperimental oscillatory fraction of the flow rate is easier to reach the theoretical value at lower oscillatory frequency.
Zhang et al. [5] found that the oscillatory fraction decreases with frequency of pulsatile flow by the flow
visualization results.
In this study, the characteristics of the pulsatile flow in the grooved channel are analyzed. The effects of t/T,frequency and groove length (l) on the flow patterns are examined.
* Received date: 2020.11.10

Email of the corresponding author: ybian@dlut.edu.cn

22Yunijie YANG, Youngning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMI

2. Experimental system
Fig. 1 shows the dimensions of a typical module and each test zone consists of 55 modules. The periodic length,
width and height of the groove are 20mm, 200mm and 2.5mm respectively. There are 4mm, 6mm, 8mm, 10mm and12mm modules of different lengths.
The volumetric flow rate of the pulsatile is given as:(1)
𝑄𝑄� � 𝑄𝑄� � 𝑄𝑄� sin�2����
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:(2)
𝑄𝑄� � 2�������� /4�

where Dp =50mm is the diameter of the piston.
To get a better understanding of the pulsatile flow, some parameters are defined as follows:
The net flow Reynolds number (Re)�� � 𝜌𝜌𝑢𝑢�/𝜇𝜇(3)where 𝜌𝜌 and 𝜇𝜇 are the density and the viscosity of water respectively. The characteristic velocity[6] of the flow u
is calculated by:(4)
𝑢𝑢 � 3/2 ∗ 𝑢𝑢�
where 𝑢𝑢� is calculated as follow(5)𝑢𝑢� � 𝑄𝑄� /�2���
The oscillatory fraction (P) of the flow rate� � 𝑄𝑄� /𝑄𝑄�(6)
The instantaneous velocity 𝑢𝑢� is depicted as:(7)𝑢𝑢� � 𝑢𝑢� � � ∗ 𝑢𝑢� ∗ sin�2����
The entire experimental setup is shown in Fig. 2. Fig. 3 shows a schematic of the experimental system. The
city water is used as the working fluid and feed water is stored at the circulating tank. The flow is supplied to thetest zone by a centrifugal pump and the flow rate is adjusted by the control valve. The piston pump driven by aservo motor through the Scotch-yoke mechanism to cover a range of pulsating flow parameters is used to obtain theimposed oscillatory flow. After passing through the test zone, the overall pressure drop of the test zone and the flowrate are measured by the differential transducer and flow-meter respectively. The relative uncertainty of thedifferential transducer and flow-meter are �1mL/s and �0.065kPa respectively.
In this experiment, the aluminum dust method is used to visualize the flow patterns. Some of aluminum
particles which are about 40μm in diameter are added to observe the streamlines in the whole flow field. Since theinstantaneous velocity fields repeat periodically in the fully developed area, the flow patterns of the 50th groove
were taken as an example.
h2hW

flow direction
lLFig. 1 Dimensions of the grooved channels

Characteristics of flow patterns under pulsatile flow with same oscillatory fractionin the grooved channel

23Fig. 2 Entire experiment setup⑧⑦⑤④⑥③②①① Circulating tank
② Centrifugal pump
③ Control valve④ Piston pump
⑤ Test zone

⑥ Differential transducer⑦ Flow-meter⑧ Overflow tankFig. 3 Diagram of the experimental system

3. Results and discussion
As is shown in Fig. 4 and Fig. 5, 4 kinds of flow patterns deserve attention for l = 10mm, P=1 and Re=570.The
locations of all particles are almost motionless in Fig. 5(g), the intension of flow mixing is worst in this time, itbelongs to “motionless” and marked as “0”. Two stable symmetric vortexes form in the grooved area and thepathlines of the main flow are parallel to each other in Fig. 4(a), it belongs to “stable” state and marked as “1”. The
pathlines of the main flow are unstable, but vortexes form in the grooved area and the main flow can be distinguished
in Fig. 4(c), it is marked as “2”. The flow in the grooved area and main flow can’t be distinguished in Fig. 4(e), theintension of flow mixing is best at this time, it is marked as “3”.
3.1 The effect of t/T on the flow patterns
Fig. 4 shows the flow patterns at Re=570, P=1, f=0.6160 and l=10mm, it can be seen that the unstable flow
state occurs during the period of t/T=0.25-0.75, and the flow mixing at t/T=0.5-0.75 is better than that at t/T=0.250.375, but the flow is stable during the period of t/T=0.875-0. It is because that the velocity of main flow is very
high during the period of t/T=0.875-0 so that the flow of the main flow is stable. But the velocity of main flow is24

Yunijie YANG, Youngning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMI

slower and slower and the velocity of vortexes in the grooved area is hysteretic, so the recirculation vortex has a
gradual effect on the main flow during the period of t/T=0.25-0.75, this is why the flow mixing intensity at t/T=0.5
is better than that at t/T=0 even though they have same instantaneous Reynolds numbers. Therefore, the flow mixing
intensity belongs to the deceleration phase is better than that during the acceleration phase, and the instability of theflow enhances with t/T during the deceleration phase.

(a) t/T=0,1(b) t/T=0.125

1(c) t/T=0.25

2(d) t/T=0.3752(e) t/T=0.5

3(f) t/T=0.625

3(g) t/T=0.75

3(h) t/T=0.875

1Fig. 4 Experimental flow patterns for Re=570, P=1, l=10mm and f=0.6160

25

Characteristics of flow patterns under pulsatile flow with same oscillatory fractionin the grooved channel

3.2 The effect of frequency on the flow patterns
Fig. 5 shows the pulsatile flow patterns at Re=570, P=1, f=0.1173 and l=10mm, it can be seen that unstableflow state occurs during the period of t/T=0.125-0.625, the unstable flow is earlier than that at f=0.6160, a part offluid in the mainstream flows into the grooves due to the flow in instability. The flow is almost at static when theperiod of t/T=0.75, and the instantaneous Reynolds number is 0 at this time. An interesting phenomenon can bediscovered, it is no flow patterns that is similar to Fig. 4(e) at f=0.1173, so the heat mass transfer at f=0.6160 isbetter than that at f=0.1173.

(a) t/T=01(b) t/T=0.1252(c) t/T=0.25

2(d) t/T=0.3752(e) t/T=0.52(f) t/T=0.6252(g) t/T=0.75

0(h) t/T=0.875

Fig. 5 Experimental flow patterns for Re=570, P=1, l=10mm and f=0.1173

1

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Yunijie YANG, Youngning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMI

Based on a lot of results for flow visualization, the flow patterns are concluded for different frequencies asshown in Table 1. It can be seen that the instantaneous Reynolds number Rei=0 disappears is around f=0.1297. As
the frequency increases, the onset of the unstable flow state is postponed, but the onset of the pulsatile flow patternsof “3” state appears and advances gradually. The flow mixing intensity of the mainstream and the recirculationvortex increases as pulsatile frequency.
3.3 The effect of groove length (l) on the flow patterns
In order to explore if the groove length (l) affects the characteristics of the flow patterns, a serious of flow
visualization results under different l have been obtained in Table 2. For the forward flow, as the increase of l, theonset of the unstable state gradually advances, the duration of the unstable state augments and the instability of theflow enhances. Furthermore, it is easy found that the onset of the unstable flow state is still postponed with thefrequency even if the pulsatile flow in the different groove length.
Table 1 Stable and unstable state of flow patterns during a pulsating cycle for different frequency when Re=570, P=1 andl=10mm

Frequency

t/T

f00.125

0.25

0.375

0.50.6250.75

0.875

0.09861222220

10.1027

122222010.1071

122222010.1120

122222010.1173

1222220

10.1232

1222220

10.12971222223

10.1369122222

3

10.1449122222

3

10.1540122222

3

10.1643122222

3

10.1760

122223

3

10.1895

1222233

10.2053112223

3

10.2240112223310.2464

1122233

10.2738112223

3

10.3080112223

3

10.3520112223

3

10.41071122333

10.49281122333

10.61601122333

1

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Characteristics of flow patterns under pulsatile flow with same oscillatory fractionin the grooved channel

Table 2 Stable and unstable state of flow patterns during a pulsating cycle for different frequency and groove length when Re=300
and P=1groove
lengthFrequency

l8

1214t/T

f00.125

0.25

0.375

0.5

0.625

0.75

0.875

0.065

111111010.130111223010.324

111123

3

10.0651122

120

10.1301122230

10.324

1

11123

3

10.0651222220

10.1301222230

10.324

1

122

3

3

3

14. Conclusions
In this paper, experimental researches are conducted to explore the characteristics of the pulsatile flow in thegrooved channel. The main conclusions are obtained as follows:(1) The flow mixing intensity of the pulsatile flow in the grooved channel belongs to the deceleration phase isbetter than that during the acceleration phase, and the instability of the flow enhances with t/T during the deceleration
phase.
(2) As the frequency increases, the onset of the unstable flow state is postponed, but the pulsatile flow patternof “3” state starts to appear and advance gradually. The flow mixing intensity of the mainstream and the recirculationvortex increases as pulsatile frequency.
(3) As the increase of groove length, the onset of the unstable state gradually advances, the duration of theunstable state augments and the instability of the flow enhances.
Acknowledgment
This study is sponsored by the National Key R&D Program of china(2019YFB1504301) , the cooperative
Research Program of IOES (No. 19A02) and the National Natural Science Foundation of China (No. 11972105).
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[4] Y.B. Junxiu PAN, Hirofumi ARIMA, Yasuyuki IKEGAMI. Characteristics of pulsatile flow with the reverse
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[5] F. Zhang, Y. Bian, Y. Liu, et al. Experimental and numerical analysis of heat transfer enhancement and flow

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Yunijie YANG, Youngning BIAN, Hirofumi ARIMA and Yasuyuki IKEGAMIcharacteristics in grooved channel for pulsatile flow. International Journal of Heat and Mass Transfer 2019; 141:1168-80.
[6] Y.B. Faming Sun, Hirofumi Arima, Yasuyuki Ikegami, Xinsheng Xu. Strength characteristics of the selfsustained wave in grooved channels with different groove length. Heat Mass Transfer 2010; 46: 1229-37.