1ＯＴＥＣ
Vol. 28（2023），1 ～ 8Experimentally and Numerically Analysis of Flow Behaviors in
Grooved Channels for Pulsatile FlowZhichao XU*1, Gang CAO*1, Yongning BIAN*2 and Hirofumi ARIMA*3*1,2

School of Ocean Science and Technology, Dalian University of Technology, 116024, China*3

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

Abstract
In this paper, the flow behaviors in the rectangular grooved channel which is the basic unit of the plate heat exchanger
is investigated. Under the action of the pulsating flow field, the flow characteristics and flow structure in different lengthsof grooved channels are analyzed experimentally and numerically. The instantaneous pulsating flow rate is monitored byan electromagnetic flowmeter to analyze the change rule of the pulsation ratio of the pulsating flow in the experiment,
and the overall pressure drop in the grooved channel is monitored by a differential transducer. Furthermore, the flow isvisualized by the aluminum dust method. It is seen that the flow visualization method matched well with the numericalsimulation results. In the grooved channels with different groove lengths, the pulsation ratio of the flow is influenced
obviously by the frequency of pulsation. It can be observed that the actual pulsation ratio of the pulsating flow decreases
with increasing frequency. In addition, it can be revealed that there is a phase difference between the curves of flow rate
and pressure drop with time, and the magnitude of the phase difference is related to the pulsation frequency and the groove
length.
Keywords: Grooved channel, Numerical simulation, Aluminum dust method, Real pulsation ratio, Phase difference

1.Introduction
Ocean thermal energy conversion (OTEC) is an essential method for utilizing ocean thermal energy. The basic
principle of Ocean Thermal Energy Conversion (OTEC) is to use the warm water (26-28°C) on the ocean surface to heatand vaporize the work fluid in the circulating system, and the resulting steam drives the turbine to rotate and generate
electricity. Deep cold seawater (4-6°C) condenses the exhaust gas into a liquid again and a thermodynamic cycle iscompleted (Weiming Liu et al., 2020).
In the ocean thermal energy conversion cycle, the high-efficiency plate heat exchanger is a crucial equipment. To
study the plate heat exchanger, the rectangular groove channel is the basic unit. (Han Huang et al., 2018) carried out
numerical and experimental studies on the grooved channel with different groove lengths and determined the groove
length 𝑙𝑙𝑙𝑙 = 4𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 for the maximum value of the heat transfer coefficient. (Fengge Zhang et al., 2019) studied the heattransfer efficiency of the grooved channel with different pulsation frequencies, and the results showed that the heat transfer
efficiency increases with the increase of frequency, especially the smaller the amplitude of pulsation flow the better theheat transfer effect is at the low frequency. (Junxiu Pan et al., 2020) studied the heat transfer efficiency of grooved
channels with different pulsation ratios. The maximum heat transfer enhancement factor is 2.74 when the pulsation ratiois 1.4, which suggests that the pulsating flow with reverse flow can increase the heat transfer.

2. Numerical simulation and experiment
2.1 Experimental settings

Date of Manuscript Acceptance 2023.12.28
E-mail of corresponding author: ybian@dlut.edu.cn*2Zhichao XU, Gang CAO, Yongning BIAN and Hirofumi ARIMA

The experimental setup is depicted in Fig. 2.1 (a) below. Water is utilized as the working medium and all experiments
are conducted at room temperature. The water tank is used for water storage and the water as the working medium is sent
to the test section by a centrifugal pump. The volumetric flow rate of water is adjusted by a control valve. The pulsating
flow in the experiment is obtained utilizing a piston pump, which is driven by a servo motor. The flow rate of the masswas measured by an electromagnetic flowmeter with a measurement error of 1 𝑚𝑚𝑚𝑚/𝑠𝑠. The total differential pressure in
the test section was measured by a micro-pressure manometer with a measurement error of 0.065 𝑘𝑘𝑘𝑘𝑘𝑘. In addition, theflow visualization was done by using the aluminum dust method to observe the flow structure of the fluid in the groove.
The photographing system is shown in Fig. 2.1 (b) below. Aluminum dust particles with a diameter of about 40 𝜇𝜇𝜇𝜇
are injected into the circulating pipeline. The flow lines in the observation section can be observed through the reflectionof the aluminum dust on the light source. Since the instantaneous velocity flow field repeats periodically after the fully
developed section, the groove of the 20th cycle was chosen as the observation section in this experiment. A cold lightsheet was used as the light source, and the flow lines in the groove were photographed with a light-controlled digital
camera.

澳(a) Diagram of the experimental system.

(b) Diagram of the photographing system.

Fig.2.1 Experimental system and Photographing system.
The structure of the groove is shown in Fig. 2.2 below. ℎ∗ , 𝑓𝑓 ∗ , and 𝑡𝑡 ∗ are the characteristic length, the frequency ofthe pulsating flow, and the time, respectively, and in this paper 𝑙𝑙 ∗ = 8, 10, 12, and the physical quantities are labelledwith "*" in the upper right corner to indicate that they are dimensioned values.

Fig.2.2 Structure of the grooved channel.
The average velocity at the inlet of the grooved channel is:

u*s = Qs* / (2W *h* ) 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 (1)where Qs* is the volume flow rate of the constant flow.
As suggested by (Faming Sun et al., 2010), the characteristic velocity of the pulsatile flow 𝑢𝑢𝑚𝑚 ∗ is calculated by：*um= 3 / 2 u*s 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳 澳澳 澳 (2)The net Reynolds number is calculated as：* *Res =  *umh / *

where 𝜇𝜇 ∗ and 𝜌𝜌∗ are the viscosity and density of water, respectively.

(3)

Experimentally and Numerically Analysis of Flow Behaviors in Grooved Channels for Pulsatile Flow3

The amplitude 𝑄𝑄0 ∗ of the pulsating flow volume flow rate is:Q0* = 2 f *s* ( D*2p / 4) 澳(4)where 𝑠𝑠 ∗ is the stroke of the piston pump and the diameter of the piston 𝐷𝐷𝑝𝑝 ∗ = 50 mm.
The pulsation ratio 𝑃𝑃 is the ratio of the amplitude of the pulsating flow volume flow rate to the net flow rate:

P = Q0* / Qs* 澳(5)The instantaneous volume flow rate 𝑄𝑄𝑖𝑖 ∗ is:

(6)

Qi* =
Qs* + Q0* sin(2 f *t* ) =Qs*[1 + P sin(2 f *t* )] 澳

2.2 Numerical simulation methodAccording to (Adachi and Uehara, 2001b), it was shown that the instantaneous velocity field repeats periodically inthe fully developed region. The flow reaches the fully developed state at the 9th groove from the inlet boundary.
Considering that the current research situation is also in this flow state, a model consisting of 25 basic units of typicalrectangular grooves was used. A structured grid was used in this study as shown in Fig. 2.3. It should be explained thatan extended straight pipe was added at the exit of the fluted channel in order to minimize the influence of the exit boundaryon the flow inside the groove.

Fig.2.3 Schematic of the grid in the grooved channel.
In this study, the finite volume method (FVM) numerical method is used to investigate the flow characteristics andheat transfer characteristics in the grooved channel. The commercial software ANSYS Fluent is used for the numericalsimulation of the flow procedure. The Reynolds number 𝑅𝑅𝑅𝑅 = 500 was chosen for the numerical simulation, which islower than the critical Reynolds number 𝑅𝑅𝑅𝑅𝑐𝑐 = 604 (Faming Sun et al., 2010), which indicates that the flow state in theflow path is still laminar during the pulsation period. Therefore, the laminar flow model is chosen for this simulation. The
coupling of pressure and velocity is performed using the SIMPLE algorithm. The solution is considered to be converged
when the normalized residuals reach 10−8 for the energy equation and 10−6 for the continuity and velocity equations.
The boundary conditions at the inlet of the flow channel were set as velocity inlet and pulsation flow was realized throughthe prepared UDF, the outlet was set as pressure outlet, the upper and lower walls of the groove were set as constanttemperature and set as the no-slip wall.
The grooved channel was modelled using a dimensionless method, where each physical quantity was dimensioned
as:
*
**
*
*
x =x* / h* , y = y* / h* , u =u* / um, v =v* / v*m , p = p* / (  *u*2m ), T =(T − Tin ) / (Tw − Tin ) 澳(7)Where 𝑢𝑢∗ is the flow rate in the horizontal coordinate direction, 𝑣𝑣 ∗ is the flow rate in the vertical coordinate
direction, 𝑝𝑝∗ is the pressure difference, 𝑇𝑇 ∗ is the temperature of the local work material, 𝑇𝑇𝑤𝑤 ∗ is the temperature of thewall of the recessed channel, and 𝑇𝑇𝑖𝑖𝑖𝑖 ∗ is the inlet temperature of the work material.
Then the dimensionless governing equations can be written as:u v(8)澳
+=0澳
x y

4Zhichao XU, Gang CAO, Yongning BIAN and Hirofumi ARIMAStuuup   2u  2u+u +v=− +(+)澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳澳tx
yx Re x 2 y 2Stv
v
v
p   2 v  2 v+u +v =− +(+)澳澳澳澳澳澳澳澳澳澳澳txyy Re x 2 y 2St

T
T
T
  2T  2T+u+ v=(+)澳澳澳澳澳澳澳澳澳澳澳tx
y RePr x 2 y 2Where 𝑃𝑃𝑃𝑃 is the Prandtl number.
𝑆𝑆𝑆𝑆 number (Strouhal number) is calculated as:*St = f *h* / um澳

澳 (9)澳

澳 (10)澳

(11)

3. Results and discussions
3.1 Numerical simulation results
澳When 𝑝𝑝 = 1.4, 𝑅𝑅𝑅𝑅 = 500, 𝑆𝑆𝑆𝑆 = 0.1765 , the flow structure images inside the fully developed groove at eight
moments in the numerical simulation are compared with the experimental images, as shown in Fig. 3.1 below.

Fig.3.1 Comparison between numerical and experimental vortex structure.

Experimentally and Numerically Analysis of Flow Behaviors in Grooved Channels for Pulsatile Flow

Fig.3.1 Continued.

5

6Zhichao XU, Gang CAO, Yongning BIAN and Hirofumi ARIMA

It can be observed that the vortex structure inside the groove in the numerical simulation results matches the vortexstructure in the experiments at different moments well within a pulsation period, which proves that the numerical method
adopted in this paper is reasonable and correct. Therefore, the numerical simulation method can be applied in different
structural grooved channels.

3.2 Experimental results and discussions
3.2.1 The practical pulsation ratio
In the experiments, the practical pulsation ratio of the pulsation flow is not the same as the set pulsation ratio P.
Therefore, the relationship between the actual and set values of the pulsation ratio is analyzed in depth. Define 𝑂𝑂𝑓𝑓 toreflect the real amplitude of the pulsation flow in the experiment, and its calculation formula is:

Of =

Qe*
Qs*

(12)

澳澳Where 𝑄𝑄𝑒𝑒 ∗ is the maximum value of pulsating flow in the experiments.
The 𝑂𝑂𝑓𝑓 at different 𝑆𝑆𝑆𝑆 numbers for groove lengths 𝑙𝑙 ∗ = 8, 10, 12 with 𝑅𝑅𝑅𝑅 = 375 and pulsation ratios 𝑝𝑝 = 0.6,1.0, 1.4 have been analyzed respectively, as shown in Figs. 3.2. It can be observed that 𝑂𝑂𝑓𝑓 decreases gradually with theincrease of the 𝑆𝑆𝑆𝑆 number, which can indicate that the gap between the practical and theoretical values of the pulsation
ratio increases with the increase of pulsation frequency. Therefore, the actual pulsation ratio is closer to the set value ofthe pulsation ratio when the experiment is carried out under low-frequency conditions. Where from the figure, the groove
length has less effect on the practical pulsating ratio.
Re=375,P=0.6
1.0Re=375,P=1.0

1.0Re=375,P=1.4

1.0

0.8

0.8

0.60.000OfOfOf

0.8

l*=8mml*=10mm
l*=12mm0.001

0.6

l*=8mml*=10mm
l*=12mm

0.60.002

St0.003

0.004

0.4

0.00150.0030(a)l*=8mml*=10mm
l*=12mm0.4

St0.00450.00600.20.002

(b)

0.004

St

0.006

0.008

0.010

(c)

Fig.3.2 Practical pulsation ratio of experimental data.

3.2.2 The phase difference
In the experiments, there is a significant phase difference between the instantaneous flow curve and the pressure
drop curve, as shown in Fig. 3.3 below, and it varies with the experimental conditions.
10.23 10.55

2.81 3.15

200

Qi
ΔP

0.3

Qi(ml/s)

ΔP(kPa)

0.2

100

0.1

005t(s)100.0
15

Fig.3.3 Phase difference between flow rate and pressure drop.

7

Experimentally and Numerically Analysis of Flow Behaviors in Grooved Channels for Pulsatile Flow

The phase difference ∆𝜑𝜑 is defined as the difference in acquisition time corresponding to the extreme values of thepressure drop and flow curves, with the expression:=()360° tP − tQi f 澳(13)The phase difference for different pulsation ratios and different 𝑆𝑆𝑆𝑆 numbers for groove lengths 𝑙𝑙 ∗ = 8, 10, 12 at
𝑅𝑅𝑅𝑅 = 375 have been analyzed, as shown in Fig. 3.4. Overall, the phase difference for different pulsation ratios decreases
with the increase of pulsation frequency, but it tends to decrease and then increases in the case of pulsation ratio 𝑝𝑝 = 1.4.
With the increase in frequency, the peak of the pressure drop will be ahead of the peak of the flow wave, forming anegative phase difference. It is also found that at different frequencies, the phase difference is always the largest for groove
length 𝑙𝑙 ∗ = 12 and always the smallest for 𝑙𝑙 ∗ = 8, so it can be concluded that the magnitude of the phase difference is
not only related to the frequency but also to the length of the groove.
3030

Re=375,P=1.0

Re=375,P=0.630

1515-15l*=8mm
l*=10mm
l*=12mm

Δφ(°)

Δφ(°)

Δφ(°)

1500-15Re=375,P=1.4l*=8mm
l*=10mm
l*=12mm0l*=8mm
l*=10mm
l*=12mm-15-30-30
0.000

0.001

0.002

St(a)

0.003

0.004

0.00150.0030St0.0045

0.0060-30(b)

0.002

0.004

0.006

St

0.008

0.010

(c)

Fig.3.4 Phase difference of experimental data.

4. Conclusions
In this paper, a combination of experimental and numerical simulation is used to investigate the grooved channel
under a pulsating flow field. The following main conclusions can be drawn.
(1) The vortex structure post-processing image obtained by the numerical simulation method matches well with theexperimental flow visualization vortex structure image, which indicates that the numerical simulation method used in thisstudy is reasonable, and this method can be applied to different structures in the grooved channel.
(2) The experimental results show that the groove structure has less influence on the real pulsation ratio, and the gap
between the real pulsation ratio and the theoretical pulsation ratio increases with the increase of pulsation frequency.
(3) From the experiments, the magnitude of the phase difference decreases with the increase of pulsation frequency,and the peak of the pressure drop will be ahead of the peak of the flow wave, forming a negative phase difference. Thelonger the length of the groove the larger the phase difference.

Acknowledgments
This study is sponsored by the National Key R&D Program of China (2019YFB1504301), and the Cooperative
Research Program of IOES (No. 23A13).

8Zhichao XU, Gang CAO, Yongning BIAN and Hirofumi ARIMA

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