Application of particle image velocimetry measurement technique to study pulsating flow in a rod bundle channel

Journal Pre-proofs Application of Particle Image Velocimetry Measurement Technique to Study Pulsating Flow in a Rod Bundle Channel Peiyao Qi, Xing Li, Feng Qiu, Shouxu Qiao, Sichao Tan, Xiaoyu Wang PII: DOI: Reference:

S0894-1777(19)31603-6 https://doi.org/10.1016/j.expthermflusci.2020.110047 ETF 110047

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Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

24 September 2019 14 January 2020 14 January 2020

Please cite this article as: P. Qi, X. Li, F. Qiu, S. Qiao, S. Tan, X. Wang, Application of Particle Image Velocimetry Measurement Technique to Study Pulsating Flow in a Rod Bundle Channel, Experimental Thermal and Fluid Science (2020), doi: https://doi.org/10.1016/j.expthermflusci.2020.110047

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Application of Particle Image Velocimetry Measurement Technique to Study Pulsating Flow in a Rod Bundle Channel Peiyao Qia, Xing Lib, Feng Qiua, Shouxu Qiaoa,*, Sichao Tan a,*, Xiaoyu Wangc a Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering

University, Harbin 150001, PR China b Wuhan Second Ship Design and Research Institute, Wuhan, Hubei 430205, China c

Science and Technology on Reactor System Design Technology Laboratory, Nuclear Power Institute of China, Chengdu 610041, PR China.

Abstract: The flow rate of the primary coolant in a nuclear reactor will fluctuate during accident conditions or in floating reactors that are affected by inertial forces in the ocean. These fluctuations may have a substantial impact on heat transfer by the primary coolant in the reactor. In the current research, the flow field distribution and turbulence structure at different planes of a 5 × 5 rod bundle under pulsating flow conditions were measured using phase-locked particle image velocimetry and matching index refractive. The local ensemble-averaged velocity and root-mean-square (RMS) component distributions of different pulsating flow phases were obtained from the measurement results. This experimental study covered a pulsation period T range of 3 – 7 s and an imposed pulsation amplitude Au range of 0.31 – 0.65. For quasi-steady, intermediate-frequency, and high-frequency pulsating flows, the ensemble-averaged velocity of different phases and the distribution of velocity amplitude modulation in different subchannels were studied. Moreover, the phase shifts of the velocity modulation amplitude and RMS components of the rod bundle channel relative to the imposed pulsating flow with different pulsation parameters (Au, T) were also analyzed. Results for the rod bundle channel under the pulsating flow condition and for a conventional channel were compared; the discrepancies and agreements are discussed in detail. These research results can help to understand pulsating flow in a rod bundle channel better, and the experimental results can provide reference and validation data for numerical simulations. Keywords: Experimental; Pulsating flow; Rod bundle channel; PIV; Turbulence

Nomenclature General symbols

Greek letters

Au

Pulsatile velocity amplitude, (-)

D

Rod diameter, (m)

Dh

Hydraulic diameter, (m)



g

Gravity acceleration, (m/s2)

α*

Dimensionless acceleration, (-)

P

Rod pitch, (m)

ν

Kinetic viscosity, (m2/s)

Q

Flow rate, (m3/h)

σ

Uncertainty parameter, (-)

Re

Reynold number, (-)

S

Stokes number, (-)

St

Turbulence stokes number, (-)

ta

Time-averaged value

T

Pulsatile period, (s)

st

Steady-state value

vb

Cross-section mean velocity, (m/s)

b

bulk flow

ω

𝜔′

Pulsatile frequency, (-) Dimensionless frequency, (-) Density, (kg/m3)

Subscripts

1. Introduction The fuel assembly is one of the most important components of a nuclear reactor, as the operation and safety of the reactor are directly influenced by the thermal-hydraulic characteristics of the fuel assembly. During unsteady transients, such as in accident scenarios or in a floating reactor subject to inertial forces from ocean movement. The flow rate of the primary coolant will fluctuate, which can result in unique flow and heat transfer characteristics [1–3]. Consequently, studying the flow and heat transfer mechanisms of fuel assemblies under unsteady conditions is essential to improve the system performance and reduce the risk of accidents. Two methods are mainly used to study the thermal-hydraulic characteristics of a system with fluctuating flow rate. One is to install an experimental device on the rolling mechanism to simulate ocean movement conditions and generate periodic flow fluctuations in the system [2,4–6]. The other is to create unsteady or pulsating inlet flow rate by using a reciprocating pump [7–9] or by adjusting the rotational speed of the pump [10,11]. The author’s group has previously researched the thermal-hydraulic characteristics of periodic flow fluctuations under oceanic conditions [12–14]. As direct measurement of the flow field in the rolling channel is difficult, most of the research focused on the analysis of pressure drop and heat transfer parameters. Considering the requirements of flow field measurement, the current research used the second method to generate pulsating flow.

Researchers have performed pioneering studies on flow field distribution in pulsating flow. Richardson and Tyler [15] and Uchida [16] proved the existence of the annular effect of velocity, showing both experimentally and theoretically that the peak velocity of the cross-section appears near the wall, in oscillating flow. Ohmi and Iguch [17] classified pulsating flow into quasi-steady, intermediate, and inertia-dominant regions based on the Womersley number, which is a dimensionless frequency, ( w '=R ( / ) ), representing the ratio of transient inertial force to viscous force [18]. They concluded that the time-average friction factor in the quasi-steady region is consistent with the steady-state, while the time-average friction factors in the intermediate and inertia-dominant regions are larger than the steady-state friction factors corresponding to same time-averaged Reynolds number. Cheng [19] and Telionis [20] performed the theoretical study and concluded that the annular effect is more prominent when the pulsation frequency is high, whereas the velocity distribution resembles a parabolic shape when the frequency is low. Shemer [21] and He [22] studied the radial distribution of the velocity modulation amplitude. They found that the maximum amplitude of the velocity modulation appears at the center of the pipe for low-frequency pulsations. When the pulsation frequency is high, the maximum amplitude of the velocity modulation occurs near the wall, and the turbulence in the pipe center is almost stable (that is, it does not fluctuate), which is called a freezing phenomenon in the core region. The ensemble-averaged turbulent fluctuations in pulsating flow have also been investigated. Ohmi [7] and Fishler [23] used hot-wire anemometry to measure the instantaneous radial velocity in a circular pipe. They proposed that a turbulent spot bursts out in the half-cycle of deceleration, and disappears in the half-cycle of acceleration owing to the increase in inertial force and re-lamination. Trip [24] also concluded that the turbulent intensity of the cross-section decreases with increasing flow rate. Tu [25] focused on the local instantaneous velocity and found that the amplitude of turbulence intensity near the wall is larger than in the pipe center. Ohmi and Iguch [17] and He [22] measured the root-mean-square (RMS) velocity of pulsating flow in a circular pipe using laser doppler anemometry (LDA). They found that the RMS velocity always responds first near the channel wall and then propagates toward

the center. The pulsating flow discussed previously is mostly in simple geometries such as circular or square channels. In the matrix arrangement of rod bundles, the coolant flows axially along the subchannels, but adjacent subchannels are connected by gaps; because of the large velocity gradient, complex cross-flows develop between adjacent subchannels [26,27]. The cross-flow can greatly improve the mixing of the coolant and therefore improve the heat transfer. Consequently, investigations of flow characteristics in rod bundle channels have been intense for decades. However, measurement locations for the traditional intrusive measurement methods are limited in rod bundles because of the complexity of the flow channels. In addition, such methods inevitably disturb the flow [28–30], which limits their application in rod bundle channels. With the development of nonintrusive instantaneous measurement techniques, LDA and particle image velocimetry (PIV) have been widely applied in rod bundle channels [31–34]. Hassan [35,36] successfully used the fluorinated ethylene propylene (FEP) and water as matching index refractive (MIR) combination to achieve full-field measurement by PIV in rod bundle channels. Childs [37] proposed new MIR combination obtained a kind of convergence of average full field was independent of measurement plane depth relative to camera view window. The MIR technique can minimize the optical distortion caused by differences in refractive index, thereby significantly improving the understanding of the flow field and turbulence structure in rod bundle channels. The previous studies have revealed flow characteristics in rod bundle channels. First, the tighter bundle structure causes the coolant to be more affected by the viscosity near the rod, such that the velocity distribution is quite different from that in simple channels. Second, the geometric asymmetry and non-uniformity of the shear stress distribution result in turbulence anisotropy in the rod bundle channel [38,39]. In addition, the flow field in the rod bundle channel becomes more complicated when the flow is unsteady. In typical unsteady flow, pulsating flow can be regarded as a combination of steady flow and oscillating flow. Flow parameters, such as pressure and velocity change periodically. Compared to a steady flow, pulsation flow is affected by the pulsation frequency, the pulsating amplitude, and the time-averaged Reynolds number, which undoubtedly increases the difficulty of investigations.

To summarize, the acceleration and deceleration of fluid caused by flow fluctuation can alter the flow field and turbulence structure. However, limited studies have been performed on the pulsating flow field in rod bundle channels. The present study is driven by an interest in the fluid mechanics of pulsating flow in rod bundles, in particular, the flow field and turbulence intensity in subchannels, which may have a substantial impact on heat transfer in the reactor. In recent years, the authors have studied the flow structure in a rod bundle channel under steady-state conditions [40] and the influence of pulsating flow on friction factor [41]. As an extension of this work, the current research focuses on examining the flow field distribution and turbulence structure of unsteady flow in rod bundle channels with a visualization method. First, the difference in velocity distribution between pulsating flow (acceleration and deceleration phases) and steady flow was analyzed. Next, the effects of different pulsating flow parameters (pulsation period and amplitude) on the velocity modulation amplitude were studied, and are explained here in terms of the local velocity phase shift relative to the imposed pulsating flow. The effects of different pulsation parameters on local and spatially averaged turbulence characteristics in the rod bundle channel are also discussed. MIR and proper orthogonal decomposition (POD) background removal techniques were used to improve the accuracy of the results. The results of the current study can provide a reference for verifying the numerical simulation results of pulsating flow in rod bundle channels.

2. Experimental apparatus and measurement techniques 2.1 Flow facility and test section A schematic diagram of the experimental setup is shown in Fig. 1. The apparatus consisted of a water tank, power system, data acquisition system, pump, control system and vertical rod bundle channel. The water tank was equipped with heaters and coolers to ensure that the temperature of the experimental fluid remained constant. The system loop had open circulation to ensure that the experimental pressure was nearatmospheric. Deionized water with 1% Sodium chloride is used as an experimental working fluid. According to the measurement of an Abbe refractometer, the refractive index of 1% sodium chloride solution is 1.3376 at 20 ℃, which is very close to that of the FEP tube (1.338). And because of the low concentration, its physical properties change little. (the density of 1% sodium chloride solution is 1.005, and the

corresponding density of deionized water is 0.9982). A honeycomb structure flow straightener device is installed in the lower chamber of the fuel rod bundle channel to ensure a uniform flow of the entrance flow. During the experiment, working fluid flows out of the centrifugal pump, enters the test section through various control valves and electromagnetic flowmeters in the pipeline, and finally returns to the water tank to complete the cycle.

Fig. 1. Schematic diagram of 5 × 5 rod bundle test loop A test section with a 5 × 5 arrangement of rod bundle was built to simulate a typical pressurized-water reactor (PWR) rod bundle channel, as shown in Fig. 2 (a). The blue arrow on the left of Fig. 2 (a) represents the direction of fluid flow corresponding to the y-coordinate direction. The flow channel is made of polished transparent plexiglass channel with 8mm thickness. The length of the channel is 1100 mm, and the flow area is 65 × 65 mm2. The pitch (P) is 12.6 mm, and the rod diameter (D) is 9.5 mm. The other geometric parameters of the test section are summarized and tabulated in Table 1. Two none-mixing spacer grids with springs and dimples, arranged at 100 mm and 1000 mm from the channel entrance, were used to fix the rod location and prevents vibration. The schematic diagram of the spacer grid is shown in Fig. 2 (b). The PIV measurement window is positioned at 600 mm (about 61.7 Dh) downstream of the nonmixing spacer grid. To ensure that the measurement area had fully developed flow, the velocity distribution at different distances (61.7 Dh ,70 Dh, where Dh is the hydraulic

diameter) downstream of the spacer grid was measured. As shown in Fig. 3, the velocity distributions in the two measured regions were in good agreement, and the measurement area was therefore considered to have fully developed flow. To achieve the visualization in the rod bundle channel, the rods are made of the 0.35 mm thickness FEP material. As a result, the optical distortion caused by the difference in materials can be neglected in the visualization experiment [35]. Besides, the small FEP material thickness can ensure good transparency of the rod. Table 1 Test section parameters

Parameter Rod inner diameter (mm) Rod external diameter (mm) Rod Length (mm) Hydraulic diameter (mm) Rod refractive index P/D (pitch/diameter) W/D (wall/diameter)

Value 8.9 9.5 1100 9.752 1.338 1.326 1.268

Fig. 2. Detail of the rod bundle channel and coordinate system.

(a)

(b)

Fig. 3. Velocity distribution at various distances downstream of spacer grid; (a) plane A1, (b) plane B1 The control method of pulsating flow is as follows: The digital signal generated by the control system was converted into the analog signal recognized by the converter through the D/A port of the Printed Circuit Boards (PCB) circuit. The converter was connected to the centrifugal pump. The voltage of the analog signal 0-10 V corresponds to the frequency of the converter (0-50 HZ) so that analog. Thus, the centrifugal pump can adjust the flow rate through different rotational speeds through the voltage of 0-10 V. The periodic change of pump speed can be realized by using a sinusoidal wave signal generating program through frequency converter. It should be noted that the loop flow is affected by driving force and loop resistance, and the relationship between the driving force and pump speed is non-linear. Therefore, it is necessary to carefully adjust the controller in the test to obtain the required experimental conditions. The time constant of the flowmeter was 100 ms, which is enough for measurement of the pulsating flow with a minimum period of 3 s. Fig. 4 shows the instantaneous flow measured by the flowmeter. The expected results of the input control system are in good agreement with the measured results, with a maximum error of less than 5%.

Fig. 4 Accuracy verification for pulsating flow 2.2 Measurement technique A PIV system with a phase-triggering device was used to measure the flow field in the pulsating flow, as shown by the red dotted closure in Fig. 1. The tracer particles used in the PIV experiment were polyamide seeding particles (PSP) with an average diameter dp = 10 μm. The density ratio of PSP as compared to water

p /  f = 1.03.

According to the relaxation time of particles in fluid defined by Melling [42], Eq.(1) is used to describe the response time τp of particles in the working fluid.

p 

(  p - f )d p2 18 f

(1)

The response time τp of the tracer particle was calculated to be much less than 0.001 s. Therefore, the particle well represents the characteristics of the pulsating flow. A 20 W continuous laser with a wavelength of 532 nm was used to illuminate the PIV window, and the laser sheet thickness is 1.2 mm. The transistor-transistor logic (TTL) signal generated by the function generator was used to control the high-speed charge-coupled device (CCD) camera (Photron Fastcam SA1, with 1024 × 1024 pixels resolution) to record the moving particles in the test section. PIV measurements were performed at planes A1, A2, and B1, as labeled in Fig. 2(c). The size of plane A was 65 mm × 65 mm, that of plane B was 34.5 mm × 34.5 mm. The velocity components u and v represented the transverse and the axial flow direction, respectively. The size of the first interrogation window used to compute the cross-correlation function was 64 × 64 pixels, and the final one was 16 × 16 pixels with a 50% overlap. The sizes of the windows

corresponding to plane A and B were 0.51 mm × 0.51 mm and 0.27 mm × 0.27 mm. Considering the large velocity gradient in the rod bundle channel, the adaptive interrogation method [43] with variable interrogation window size and shape was used for cross-correlation analysis. Fig. 5 (a) and (c) show the original images of planes A and B captured by the highspeed camera. The brighter area in the image indicates the FEP rod. Although the refractive index of the FEP rod was close to that of working fluid, the rods still absorbed more energy than the surrounding water, such that the original image had intense background noise. The non-uniform background affected the accuracy of the calculation results. In this study, POD-based background removal [44] and image enhancement techniques [45] are used to improve image quality. POD-based background removal is a pre-processing algorithm proposed for PIV analysis, which can eliminate the background noise with large intensity, gradients, and time oscillation. In Fig. 5 (b) and (d) images, the FEP rods can hardly be distinguished after the background removal.

(a)

(b)

(c)

(d)

Fig. 5. Comparison of original and post-processing images; (a) original image of plane A1, (b) post-processing of A1, (c) original image of B1, and (d) post-processing of B1 For pulsating flow, the PIV trigger mechanism was used to accurately acquire the flow field in different phases of the cycle by using phase-locked technology; that is, the PIV system always captured the flow field information at fixed phase angle. As schematically shown in Fig. 6, 20 phases (every 18o) were investigated in each pulsation cycle. The ensemble-averaged velocity can be obtained by averaging the velocity fields of the same phase in many cycles. The phase-locked PIV process was as follows: the sinusoidal voltage signal was output to the frequency converter through the computer control system to cause the centrifugal pump to generate a sinusoidal fluctuation pulsating flow. Besides, this voltage signal also outputted to the in house made sinusoidal square-wave conversion circuit, to convert the sinusoidal signal into the square wave signal with the same period and the duty ratio of 50%. This signal was externally triggered into the pulse generator (agilent33220A), which causes the signal generator to output a TTL signal with an amplitude of 5 V and phase adjustment at the same frequency. The TTL signal was used to trigger the image capturing by a highspeed CCD camera. Phase 1 and phase 11 were the phases with the maximum positive and negative accelerations, respectively. Phase 6 and phase 16 were the phases of maximum and minimum velocity, respectively, and their acceleration was smallest.

Fig. 6. Phases of PIV measurement in pulsating flow 2.3 Experiment condition and data processing The instantaneous cross-sectional mean velocity vb can be expressed by finite Fourier expansions. In the current study, the mean velocity of the sinusoidal fluctuations could be approximated by the first harmonics, as shown in Eq (2).

v b = v b ,ta   v b s i n ( t    1 )

(2)

where vb,ta is the time-averaged velocity of a cycle in the pulsating flow, Δvb is the amplitude of the cross-sectional mean velocity, ω is the angular frequency, t is the measured time, and defined as

1 is the phase angle. the pulsation velocity amplitude Au is

A u   v b / v b , ta

Table 2 lists the experimental conditions and measurement locations used in the current study. For all experimental conditions, the time-averaged Reynolds number (Reta) remained constant at 7940. The Reta is defined as Reta  (vb,ta  Dh ) / , the hydraulic diameter Dh is 9.75 mm. And the kinematic viscosity υ is 8.92 × 10-7 m2/s estimated at 20oC. The pulsating amplitudes (Au) are of 31.25% and 65%. The pulsating periods of the flow are 3 s, 4 s, and 7 s, which correspond to the non-dimensional frequency parameter

+ ( v / u2 ) are 0.000865, 0.000649 and 0.000371,

respectively. The calculation process of friction velocity u ( =  w /  ) is as follows: The friction resistance factor λ of the rod bundle channel is calculated by the empirical relation by Cheng [46] and Qi [11], and then the wall shear stress  w  (vb /8) is 2

calculated according to the λ, and finally get u . The conditions are represented by the case name in the first column of the table. For example, PA2T4A65 is a pulsating flow

at the A2 with a period of 4 s, and a pulsation amplitude of 65%. This study involved 15 cases. Table 2 Experiment cases Position

Case PA1(A2,B1)T3A31.25

Amplitude (%)

vb,ta (m/s)

Reta (-)

T (s)

St(-)

ω+(-)

α* (-)

31.25

3

0.4396

0.000865

0.0351

4

0.3297

0.000649

0.0248

4

0.3297

0.000649

0.0517

PA1(A2,B1)T4A31.25

Plane

31.25

PA1(A2,B1)T4A65

A1(A2,

65

PA1(A2,B1)T7A31.25

B1)

31.25

7

0.1884

0.000371

0.0142

65

7

0.1884

0.000371

0.0296

PA1(A2,B1)T7A65

0.724

7940

As the velocity varies periodically, the instantaneous velocity component in each direction can be decomposed into the three parts as given in Eq. (3).

f (xi , t)  f (xi )  f '(xi , t)  f ''(xi , t) where

(3)

f (xi ) is the mean velocity for one or more periods, f ’(xi,t) is the velocity

fluctuation caused by turbulence, and f ’’(xi,t) is the periodic component. The phaseaveraged velocity field (at phase index m) can be calculated from the ensemble-average using Eq. (4).

1 N  F (x i , m )   f (x i , m , n) N n 1

(4)

where  represents the phases, and n is the number of cycles. In addition, the sum of the periodic component and mean velocity from Eq. (5) is the phase-averaged velocity . Thus,

f (xi ,t)  F(xi ,)  f '(xi ,t)

(5)

The turbulent fluctuating velocity component in the pulsating flow of each phase can be calculated using Eq. (6). f '(x i ,  ) 

1 N

N

 ( F (x ,  )  f (x ,  , n)) n 1

i

i

2

(6)

The ideal case for phase averaging is to use enough periodic velocity fields to achieve sufficient convergence. However, due to the storage and post-processing capability, limited periodic velocity fields are available and feasible for processing. Scholars have different opinions on the number of cycle samples needed for processing the phase average velocity. Trip [24] used 50 cycles when using PIV to study the effect of pulsating flow on the transition in a circular pipe; Joel [47] considers that 250 periodic

samples can converge well when he was studying the turbulence characteristics of pulsating flow. Mao and Jaworski [48] studied the turbulent flow characteristics of the oscillating flow in a parallel plate structure. They conclude that although the results of 1000 periodic samples can converge well, the results of 100 periodic averages can also represent the results of the most flow fields. The convergence of each result from the ensemble-average method is calculated to test the number of cycles required. The residual used is similar to that used in the numerical simulation. M  i , j (  in, j   in,j1 ) 2 M

  (n)  RPIV

(  i , j  in, j ) M

2

(7)

n where  i , j represents the computed results from the average of n images at the (i,j)

coordinates, M represents the total number of nodes. Fig. 7 shows the residual convergence results for the velocity and the fluctuating velocity at different planes and different flow conditions. It can be seen that the residuals of velocity and fluctuation velocity reduce to less than 5% at around 200 and 500 periodic samples, respectively. Considering the accuracy and the data processing power, 500 periodic samples were selected for post-processing in the current study.

Fig. 7. PIV data convergence results The uncertainty analysis is performed using the ITTC-recommended procedures and guidelines proposed by Nishio [49]. According to Eq. (9), the factors affecting the uncertainty of PIV measurement are the magnification factor (α, mm/pixel) identified through calibration, the displacement of particle images (ΔX, mm), the time interval between successive images (Δt, s), and the error (δu) caused by other factors. u=  (  X /  t )   u

(8)

Based on the above estimation method, the maximum experimental uncertainty of the PIV measurement in the current study is listed in Table 3. As can be seen, the maximum combined uncertainty of the current experiment is 35.2 mm/s, which is less than 5% for the current research. Table 3 Uncertainty analysis Uncertainty parameter

Standard uncertainty

Sensitive coefficient

Uncertainty(mm/s)

Magnification factor α Displacement of images ΔX Interval of images Δt Experiment Δu Combined uncertainty

0.0001517[mm/pixel]

22676.3[pixel/s] 253.6[mm/(pixel·s)] 4000000[mm/s2] 1

3.44 35 0.03 1.65 35.2

0.138 [pixel] 7.5 ns 1.65 mm/s

3. Results and discussion To better illustrate the influence of pulsating flow on the flow field of different subchannels of the rod bundle channel, different types of subchannels are named as shown in Fig. 8. For the subchannel naming convention, the first letter I or G represents the inner or gap subchannel, and the second letter L, R or C represents the left, right or center subchannel, respectively. The first subscript represents different planes, that is, 2 and 1 are planes A2 and A1, and B is plane B1; the second subscript represents the number of subchannels of the same type. For example, IR21 is the first internal channel on the right of Plane A2.

Fig. 8. Naming convention for coolant subchannels in rod bundle channel 3.1 Steady-state flow characteristics The velocity distribution in the rod bundle channel under steady-state condition is first introduced as a basis for analysis. For the steady-state, PIV measurements were performed at Reynolds numbers of 2870, 5520, 7965, 10570 and 13525. The

dimensionless axial velocities at different Reynolds numbers at planes A and B are shown in Fig. 9. In the figures, the measured velocities are normalized by the steadystate cross-sectional averaged velocity, vb,st, which is calculated from the electromagnetic flowmeter measurement. Fig. 9 (a) indicates that the normalized velocity at plane B1 decreases with increasing Reynolds number. The enlarged area in Fig. 9 (a) shows that the flow boundary at the rod surface becomes thinner with increasing Reynolds number, that is, the thin layer with a large velocity gradient near the surface appears to approach the rod surface gradually. This indicates that, with increasing flow velocity, the influence of the wall viscosity force on the fluid decreases gradually. The axial distributions of the velocities normalized by the bulk velocity at planes A1 and A2 are shown in Fig. 9 (b) and (c). The velocity of the inner subchannel is higher than that of the gap subchannel because the viscous effect is less significant in the inner subchannel owing to the greater distance to the rod surface compared to the gap subchannel. A comparison of velocity distributions at different Reynolds numbers at plane A shows that the normalized velocity in each subchannel decreases with increasing of Reynolds number and that the difference between the central subchannel and wall subchannels decreases gradually. The cause is believed to be the viscous effects, as discussed previously. The nonuniformity of the velocity distribution caused by the viscous effect decreases as the velocity increases. It should be noted that the measured velocity in the rod bundle is not exactly symmetric. This may be caused by the uncertainties of the rods during installation. However, these slight asymmetry does not affect the analysis of the results.

(a)

(b)

(c)

Fig. 9 Velocity distributions with different Reynolds numbers under steady-state conditions; (a) plane B1, (b) plane A1, and (c) plane A2 3.2 Velocity characteristics of pulsating flow To visually compare the flow field distributions with different pulsation phases in the rod bundle channel, six representative phases in a pulsation period were selected for analysis and comparison. Among them, the  1/  11,  5/  7,  17 /  15 pairs (as shown in Fig. 6) have the same acceleration magnitudes but opposite acceleration slopes.  1 and  11 are the phases of maximum acceleration in each pulsation period.

Fig. 10 (a) to (c) show the normalized axial velocity distributions at planes A1, A2, and B1 in different phases for a pulsation period of 4s, average Reynolds number of 7940 and amplitude of 31.25%. In Fig. 10 (a) and (b), the velocity distributions in phases  5 and  7, and in  15 and  17 almost overlap with each other, which indicates that the acceleration and deceleration do not have much effect on velocity distribution in these phases.

However, the velocity distributions in phases  1 and  11 differ greatly because of the opposite acceleration rates. This is believed to be caused by different effects of the relatively large acceleration on the flow: the acceleration of the fluid causes the velocities in sub-channels near the channel wall (IL2(1)3, GL2(1)2, IR2(1)3, GR2(1)2) to be greater than during the deceleration at the corresponding flow rate, whereas the opposite phenomenon occurs in subchannels far from the channel wall, i.e., the velocities in subchannels far from the wall are smaller in  1 than in  11. A comparison of velocity profiles at different phases reveals that the magnitude of the acceleration determines the difference in velocity distribution. A greater acceleration rate creates a high velocity near the wall, but a low velocity in the channels away from the wall. This phenomenon is similar to the annular effect in a circular pipe during oscillating flow [16,22]; that is, the influence of wall viscous forces on quasi-steady-state flow causes the maximum velocity to appear at the center of the pipe. For oscillating flow with high frequency, the peak velocity appears near the wall, while the velocity at the pipe center decreases. The pulsating flow examined in the current study can be regarded as the superposition of the oscillating flow and the steady flow. Moreover, the velocity distribution of pulsating flow is close to that of stable component, because the stable component is large and dominate the flow. The velocity change in the rod bundle channel is more obvious only when the acceleration is high. In recent years, the author has studied the variation of instantaneous friction factor with flow rate in a pulsating flow in a rod bundle channel [11]; with the fluid acceleration, the instantaneous friction factor was found to be more significant than the steady-state friction factor, whereas the reversed occurs with deceleration. The PIV flow field measurement results in the current study show that this is precisely because when pulsating flow accelerates, the fluid velocity gradient near the wall increases, thereby increasing the wall shear stress. Fig. 10 (c) indicates that the dimensionless velocity distributions at plane B and plane A with different phases are similar. The velocity distributions at the same Reynolds number differ only when the acceleration is significant. The dimensionless velocity of the acceleration phase is higher than that of the deceleration phase in the near-wall subchannel (GRB3, GRB2), and the velocity difference in the GRB3 channel is more prominent.

(a)

(b)

(c) Fig. 10 Velocity distributions for different phases with pulsating flow; (a) plane A1, (b) plane A2, and (c) plane B1 Fig. 11 (a) shows the profiles of normalized pulsation velocity amplitudes for pulsation periods between 3 s and infinity (quasi-steady flow) in the rod bundle channel. The pulsation amplitude in the gap sub-channel is smaller than that in the adjacent inner sub-channel. Moreover, for the quasi-steady-state flow, behavior in the subchannel near the wall is similar to that in the center region of the channel. As the pulsation frequency increases, the pulsation velocity amplitude decreases gradually, especially in the center region of the channel, and the minimum pulsation amplitude appears in the center of the channel. This may be because the flows in the channel center respond to the imposed pulsating flow more slowly compared to the flows near the channel wall. However, the pulsation amplitude near the channel wall behaves in the opposite manner, that is, the pulsation amplitude increases with increasing pulsation frequency.

Some scholars [21,25] have studied the local velocity amplitude distribution of the pulsating flow in a circular tube and reached similar conclusions, i.e., the fluid in the tube center cannot adequately respond to the imposed pulsation with increasing frequency, resulting in a smaller amplitude of the velocity modulation. In addition, they found that the amplitude of velocity modulation in the central region remains constant when the pulsation period is decreased from 4 s to 2 s (Corresponding dimensionless time T* from 1.13 to 0.56), and the central region area increases with decreasing pulsation period. In the present study of the pulsating flow in the rod bundle channel, however, without similar phenomenon was found. The reason will be discussed in the following sections. Fig. 11 (b) shows the distribution of local velocity amplitude modulation at the planes A1 and A2. The local amplitude distribution at plane A1 is similar to that in plane A2. The central region of the channel with higher pulsation frequency has a smaller amplitude, and the subchannel near the channel wall has a larger amplitude. The difference is that, for the same pulsation frequency, the amplitude at plane A1 is larger than that at plane A2. A reasonable explanation is that plane A2 is farther away from the wall of the rod bundle channel. Therefore, the distribution of the pulsation velocity amplitude modulation under the pulsating flow condition is inferred to be concave,that is, the velocity amplitude modulation near the wall is larger, whereas at the center it is smaller. Fig. 11 (c) shows the distribution of local velocity amplitude with different imposed pulsating flow amplitudes. Comparison of the different amplitudes with the same pulsation frequency shows that, when the fluid velocity amplitude is larger, it hardly affects the difference in amplitude modulation between the center region of the channel and the subchannel near the wall. This observation is consistent with those of earlier studies in a pipe [22]. However, the large amplitude modulation in the rod bundle channel reduces the local amplitude difference between the adjacent gap and inner subchannels, which differs from the research results for the pipe.

(a)

(b)

(c)

Fig. 11. Influence of different pulsating flow parameters on local amplitude of velocity modulation; (a)effect of frequency, (b)effect of recording position, and (c)effect of velocity modulation of amplitude

Fig. 12 shows the profiles of the local ensemble-averaged velocity relative to the phase shift of the imposed pulsating flow for different pulsation periods, and amplitudes and at different planes. For the pulsating flow with higher frequency (T = 3 s, 4 s), the velocity phase shift distribution is characterized by a velocity response near the wall is faster than the imposed pulsation, and by a more significant phase advance closer to the wall. In the subchannel away from the wall, the phase advance gradually decreases and eventually lags the imposed pulsation. Furthermore, the inner subchannel phase shift lags that of the gap subchannel. Shemer [21] and He [22] found similar phenomena when they studied the phase shifts of pulsating flow in conventional channels such as circular tubes and rectangular channels, that is, the phase of velocity in the center of the channel lagged behind that of the fluid near the wall. However, their results showed that the phase lag at the center of the channel remains almost constant with increasing pulsation frequency, but no similar phenomenon was found in the rod bundle channel.

Ramaprian and Tu [50] proposed the Stokes layer thickness

 = 2v / 

( = uτ/ω in

turbulence) and Stokes number S  R /  of pulsating flow to characterize the effects of fluid viscosity, pulsation frequency, and channel size. With increasing pulsating frequency, the Stokes layer becomes thinner, limiting the viscous effect concentrated in the region near the wall, where the fluid is mainly affected by the imposed axial pressure gradient and the viscous effect. The fluid far away from the wall is less affected by the viscous force and is mainly affected by the imposed axial pressure gradient and the inertial force. Under the influence of inertial force, the fluid in the central region of the pipe lags the fluid near the wall. The rod bundle channel has not only the channel wall but also the rod surface. The Stokes layer near the wall exists almost everywhere in the channel, and therefore the pulsating flow can affect most locations in the rod bundle channel. As the gap sub-channel is closer to the rod surface where the Stokes layer exists, and the viscous effect is concentrated, the phase is advanced relative to the inner sub-channel. In addition, the Stokes layer becomes thinner with increasing frequency, leading to a decrease in a phase advance. The profile of the velocity phase under the large pulsation period condition (T = 7 s) is entirely different from that under the small pulsation period conditions (T = 3 s and 4 s) at high frequencies. Between the GL(R)22 and IL(R)23 subchannels, the phase of the velocity lags with the imposed pulsation. It first increases and then decreases when approaching the channel wall. The phase lag near the wall causes the phase shift of the gap subchannel to lag that of the inner subchannel. Similar phenomena have been reported by Shemer [21] and He [22]. Their research results showed that the phase increases with low-frequency pulsating flow approach the wall, and a certain degree of phase lag occurs when near the wall. Comparison of A1 and A2 for 3 s periods shows that the phase of A2 slightly lags that of A1. This is because plane A1 is closer to the wall of the channel. In fact, the results of phase shift distribution also confirm the results of velocity modulation amplitude mentioned previously. For the pulsating flow with higher frequency, the phase lag in the center region of the rod bundle channel lags the wall, which makes the central region unable to respond to the imposed pulsation, resulting in a smaller amplitude of velocity modulation in the central region. Comparison of the pulsating flow with different amplitudes in Fig. 12 at a pulsation

period of 7 s, shows that changing the amplitude has little effect on the phase shift of the flow field in the rod bundle channel. This may be because the penetration depth of the pulsation in the viscous is independent of the pulsation amplitude, and therefore pulsation amplitude does not have a significant effect on velocity phase shift.

Fig. 12. Phase shift of velocity modulation relative to imposed flow pulsation.

3.3 Turbulence quantities The fluctuation velocity components at different phases or the rod bundle channel are calculated from Eq. (6) in Section 2.2. Fig. 13 shows the distribution of the dimensionless fluctuation velocity component with a period of 4 s and an amplitude of 0.3125 at a typical phase. The general behaviors of u'/vb and v'/vb are similar. At phases with small acceleration or deceleration rates, such as the  5/  7, and  15/  17 pairs, the profiles of the normalized fluctuating velocity almost overlap with each other although they are in the opposite phases. However, at phases with larger acceleration/deceleration rates, such as  1 and  11, the normalized fluctuating velocity at the deceleration phase is obviously larger than that at the acceleration phase, which indicates that acceleration will affect the distribution of the fluctuating velocity component. Furthermore, for the same velocity, the difference in the fluctuation velocity between the acceleration and deceleration phases in the gap subchannel is larger than that in the inner subchannel.

(a)

(b)

Fig. 13 RMS component distribution at different phases; (a)u'/vb component, and (b)v'/vb component

To further analyze the influence of pulsating flow on the statistical turbulence information in the rod bundle channel, the area-averaged velocity information was estimated with Eq. (9).

ku 

1 u '( x, y )dA A  A

(9)

Where, u’(x,y) represents the velocity or fluctuation velocities at position (x,y) and A is the cross-section area. Fig. 14(a) shows the plots of the area-averaged dimensionless fluctuation velocity component overtime for a period of 3s and amplitude of 0.3125 in plane A2. ku/vb and kv/ vb behave similarly, that is they gradually decrease during the acceleration phase, reach a minimum, and finally increase at the end of the acceleration phase. TRIP [24] and Tu [25] found a similar variation trend for the fluctuation velocity in the circular tube. However, their study did not separate the variation of u' and v' turbulent fluctuation component. Fig. 14(b) shows the variation of fluctuation velocity with the different phase in pulsating flow. The turbulence caused by the pulsating flow first responds to the axial fluctuation component, which indicates the response times of the two fluctuation components are different in the rod bundle channel.

(b)

(a)

Fig. 14 Plot of area-averaged component as a function of phase in a cycle (a) dimensionless fluctuation velocity (b) fluctuation velocity To analyze the influence of different pulsation parameters on the fluctuation velocity component, the variation of ku was plotted against the Reynolds number for different flow conditions, as shown in Fig. 15. Also plotted in the figure by a purple line is the turbulence fluctuation velocity in the steady flow. The comparison indicates that the acceleration causes ku to be less than the steady-state value and that the deceleration is reversed. For pulsating flows with the same amplitude, the deviations between acceleration and deceleration fluctuation velocity components increase with increasing frequency at the same Reynolds number. For pulsating flows with the same period, this deviation increases as the amplitude increases. It can be concluded that both frequency and amplitude affect the ku to deviate from the steady-state value. From the perspective of pulsating flow acceleration, it can be concluded that the deviation of the turbulence intensity component from the steady-state value under pulsating flow conditions should be related to fluid acceleration. The author used a fitted dimensionless acceleration α* to obtain a formula that can predict the average resistance coefficient for pulsating flow. The dimensionless acceleration α* is defined as 4A  '  = u Re ta

2

*

(10)

The physical meaning of this expression is the interaction of three pulsation parameters: Reta, Au,

' . The dimensionless acceleration α* for each case is listed in

Table 2. The deviation of the turbulent component from the steady-state value increases with increasing α*. Base on the definition of α*, the dimensionless acceleration becomes zero when the amplitude or frequency approaches zero, the and turbulent component then equals the steady-state value accordingly.

Fig. 15. Plot of area-averaged fluctuation velocity component as a function of Re in cycle Fig. 16 shows the phase shifts of u' and v' modulation relative to the imposed pulsation under different experimental conditions. The profiles of the fluctuation velocity phase shifts for u' and v' are similar. The phase shifts are small in gap subchannels and near the channel wall, but large in inner subchannels. This indicates that the turbulent component in pulsating flow is generated in the near-wall region and gradually propagates toward the central region. This also explains why the turbulence response at plane A1 is faster than at plane A2, as shown in the figure, as plane A1 is closer to the channel wall. The phase difference between the center region and the near-wall region increases with increasing frequency, and the overall phase difference also increases. In addition, the turbulence response of u' lags behind that of v'. This phenomenon is like that obtained by previous scholars in simple geometric channels [22,51]. A reasonable explanation is that the change of axial velocity results in the change of v', and the generation of u' is to redistribute turbulent kinetic energy through the effect of pressure, which makes u' lag behind v' [22]. In addition, comparison between the fourth and fifth  u' and  v' profiles shows that the pulsation amplitude hardly affects the phase shift.

Fig. 16. Phase shift relative to imposed flow pulsation of fluctuation velocity. (a)  u', and (b)  v'

4. Conclusion In this study, the characteristics of pulsating flow in a 5 × 5 rod bundle channel were studied using the PIV technique. The distributions of ensemble-averaged velocity and RMS components at different pulsation phases were obtained by combining phaselocked PIV and refractive index matching techniques. The effects of the pulsating frequency and pulsating amplitude on the phase shifts of the velocity modulation amplitude and RMS components relative to the imposed pulsating flow were analyzed and compared to results from an earlier study. Typical conclusions can be drawn as follows: Under steady-state conditions, the velocity in the rod bundle channel is affected by near-wall viscosity and varies with the type of the gap and inner subchannels. As the mainstream flow rate increases, the thin layer with a large velocity gradient near the wall gradually becomes thinner and appears to approaches the wall. Moreover, the viscous force of the rod bundle gradually weakens its influence on the fluid, and overall velocity distribution in the channel tends to be uniform. The velocity distribution is changing in rod bundle channel under pulsating flow. When the fluid is in the acceleration phase, the fluid velocity and the velocity gradient near the channel wall becomes larger, and the velocity near the central region becomes smaller. The larger velocity gradient near the wall causes the instantaneous friction factor in the acceleration phase of the pulsating flow be larger than the corresponding steady-state value. The velocity modulation amplitude is larger near the wall region in high-frequency

pulsating flow, and the local modulation amplitude in the central region gradually decreases as pulsation frequency increases. The phase shift of the central region lags the wall region in high-frequency pulsating flow. This makes the central region of the high-frequency pulsation channel unable to respond in time to imposed pulsation, therefore the velocity modulation amplitude of the central region remains small. The phase shift of the pulsating flow velocity modulation amplitude is different from the circular tube, in which the phase shift is close to zero in the core region. This is because both rod surfaces and channel walls exist in the rod bundle channel, which make the Stokes layer cover most of the area in the channel such so that the pulsating flow can affect most of the area. The dimensionless RMS velocity components gradually decrease as the fluid accelerates, and gradually increase as the fluid decelerates. Moreover, the deviation of the turbulent components from the steady-state value are proportional to the dimensionless acceleration α*. In addition, a certain phase difference occurs between the RMS components and the imposed pulsating flow, and u' lags behind v'. The RMS phase shift distribution indicates that the turbulent flow initially occurs near the wall and propagates away from the wall region. With increasing frequency, the phase shift lag of the turbulent flow and the imposed pulsating flow increases. The results of current research can help to better understand the pulsating flow in the rod bundle channel. Finally, the experimental results can provide validations for the numerical simulation.

Acknowledgement This work is financially supported by National Key R&D Program of China (2017YFE0106200), Heilongjiang Provincial Natural Science Foundation of China (JQ2019A001), National Natural Science Foundation of China (11905039), and Special Financial of Heilongjiang Postdoc (002150830602).

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Highlights 1. The experimental data of pulsating flow in rod bundle channel with different phases are provided by phase-locked PIV and MIR. 2. The effects of acceleration and deceleration of pulsating flow on velocity distribution and turbulence characteristics in different subchannel are analyzed. 3. The effects of different parameters of pulsating flow on the velocity amplitude modulation, phase shift and RSM are analyzed. 4.The propagation of pulsating flow in rod bundle channel is discussed.

Conflict of Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Application of Particle Image Velocimetry Measurement Technique to Study Pulsating Flow in a Rod Bundle Channel”.

Author Contribution Statement Peiyao Qi: Designed and carried out experiments, Methodology, Data curation, Writing- Original draft preparation. Xing Li, Qiu feng: Carried out experiments, Analyzed data Sichao Tan, Shouxu Qiao: Supervision, Review & Editing. Xiaoyu Wang: Investigation.