Effect of head swing motion on hydrodynamic performance of fishlike robot propulsion*

Dan XIA （夏丹）， Wei-shan CHEN （陳維山）， Jun-kao LIU （劉軍考）， Ze WU （吳澤）

1. School of Mechanical Engineering， Southeast University， Nanjing 211189， China， E-mail: dxia@seu.edu.cn

2. State Key Laboratory of Robotics and System， Harbin Institute of Technology， Harbin 150001， China

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Effect of head swing motion on hydrodynamic performance of fishlike robot propulsion*

Dan XIA （夏丹）1， Wei-shan CHEN （陳維山）2， Jun-kao LIU （劉軍考）2， Ze WU （吳澤）1

1. School of Mechanical Engineering， Southeast University， Nanjing 211189， China， E-mail: dxia@seu.edu.cn

2. State Key Laboratory of Robotics and System， Harbin Institute of Technology， Harbin 150001， China

This paper studies the effect of the head swing motion on the fishlike robot swimming performance numerically. Two critical parameters are employed in describing the kinematics of the head swing: the leading edge amplitude of the head and the trailing edge amplitude of the head. Three-dimensional Navier-Stokes equations are used to compute the viscous flow over the robot. The user-defined functions and the dynamic mesh technology are used to simulate the fishlike swimming with the head swing motion. The results reveal that it is of great benefit for the fish to improve the thrust and also the propulsive efficiency by increasing the two amplitudes properly. Superior hydrodynamic performance can be achieved at the leading edge amplitudes of0.05L（Lis the fish length） and the trailing edge amplitudes of0.08L. The unsteady flow fields clearly indicate the evolution process of the flow structures along the swimming fish. Thrust-indicative flow structures with two pairs of pressure cores in a uniform mode are generated in the superior performance case with an appropriate head swing， rather than with one pair of pressure cores in the case of no head swing. The findings suggest that the swimming biological device design may improve its hydrodynamic performance through the head swing motion.

fishlike swimming， head swing motion， hydrodynamic performance， biological device design

Introduction

Aquatic animals have evolved with very excellent propulsive performance through water. Recently，the bio-inspired propulsion system imitating the way of fish swimming has been widely applied in the autonomous underwater vehicle （AUV） design［1-3］. The rapid development of the AUV， such as the fishlike robot， has inspired the hydrodynamics study on the swimming mechanism for fish. In recent years， numerous simulations and experiments have provided a wealth of data in terms of both the swimming mechanics and the wake flow structure［4-10］. In addition to the mechanisms of the swinging head， the other various swimming mechanisms， such as the flapping foil， the oscillating caudal fin and the undulating pectoral fins， were widely reported in literature［5-10］. The inspiration for the present study comes from the phenomenon of the dolphin swimming with a head swing behavior of large amplitude［11，12］. As compared with the previous studies of other swimming mechanisms， the head swing problem for the fishlike propulsion is still unclear. And the hydrodynamics behind the head swing motion is far from being well understood.

A great deal of experimental studies for the fishlike swimming were carried out. Review papers［13-16］presented a summary of recent developments in visualization experiments. Read et al.［13］performed experiments on an oscillating foil to assess its performance in producing a large thrust. Hover and Triantafyllou［14］compared the swimming performance of four foils and confirmed that the saw tooth foil produces the highest thrust. The recent studies of the hydrodynamics of oscillating foils［15，16］also help to gain an understanding of the fishlike swimming mechanisms. Floch et al.［15］，Lauder and Drucker［16］indicated that the fish produces the thrust by accelerating the water through the movement of their body and appendages， and the power losscan be reduced through the morphological design， the phased kinematics and behaviors. Although some insights into the fish swimming mechanisms are obtained from these studies， further investigations of this theme are needed， such as the swimming mechanism in the head swing problem， which has not been fully studied by previous researchers.

Numerical simulations of the fishlike swimming were also carried out［17-20］. Zhu et al.［17］highlighted the flow structures around the fishlike swimming and presented a vortex control method to improve the efficiency. Liao et al.［18］revealed a thrust jet by studying the rainbow trout swimming. Tang and Lu［19］carried out a numerical study on the self-propulsion of the 3-D flapping flexible plate. The recent studies of the hydrodynamics around the foils［20］also help to gain an understanding of the swimming mechanisms. To some extent， these studies produced some important results and shed new light into the hydrodynamics of the fishlike swimming. However， most of these studies focused on simulating a number of different swimming modes or their flow regimes， but a specific investigation of the effect of the head swing motion on the hydrodynamics for the fishlike swimming is not seen in the literature.

The objective of this work is to provide some insights into the hydrodynamics of the fishlike robot swimming with the head swing motion and to explore the flow features of different head swing laws. The head swing motion cannot be realized by purely experimental means， mainly because it is very difficult to carry out controlled experiments in which the governing parameters can be systematically varied. However， such insights can be obtained by combining the numerical simulation and the controlled numerical experiments. This paper employs the 3-D Navier Stokes equations to solve the flow over the fishlike robot with the head swing motion. Two aspects will be studied:（1） the effects of the head swing motion on the thrust and the propulsive efficiency， and （2） the effects of the head swing motion on evolving the flow structure near the robot.

Fig.1 Physical model of the fishlike robot

1. Physical model and kinematics

1.1 Physical model

In this paper， we use a fishlike robot prototype developed by the State Key Laboratory of Robotics and System as the virtual swimmer. The physical model and the kinematics of the swimmer is an imitation of the shape and the movement of a small tuna. However， the true shape of the biological tuna has still not been described accurately to be used as a direct input to the physical model. Therefore， we use the curve fitting method to describe the shape of the fishlike robot， whose physical model is shown in Fig.1. We define the coordinate system in the frame （x， y， z）where x-axis，y -axis， and z-axis are along the longitudinal， transverse and spanwise directions respectively. The fishlike robot has symmetricalxyand xzplanes over the profile， which is composed of head，body and caudal fin. The 3-D size of the robotx×y× z is 0.20 m×0.025 m×0.05 m.

Fig.2 Physical model of the swimming domain

Figure 2 shows the physical model of the swimming domain， which is a 2 m×0.5 m×0.5 m cubic tank filled with water. The fishlike robot is placed 0.2 m from the outlet plane in the x-axis direction and centered in they -axis and the z-axis directions. The domain width of 0.5 m and the height of 0.5 m are large enough for the robot realizing the swimming motion. A uniform grid with constant spacing of 0.01Lis used to discretize the swimming domain enclosing the fish， including 5×106cells.

1.2 Kinematics

The kinematics of the fishlike robot is selected to resemble the tuna motion observed in a live tuna， but variations are also introduced to investigate the effect of the head swing motion. In general， the kinematics of the robot has two basic components: the head and body， represented by a 2-D flexible spline curve and the caudal fin described by an oscillating foil［4，20］. The origin of the spline curve coincides with the mass center of the robot. In this sense， the spline head and body is responsible for the caudal fin's heave and the caudalfin's own rotation is responsible for its pitch. The spline head and body are treated as a traveling wave expressed as

where yb（x， t）is the instant transverse displacement of the head and body，A（ x）is the amplitude function，ωis the wave frequency，kis the wave number，denoted ask=2π/λ， andλis the wave length.

Here we assume that the robot length is unchanged during the traveling wavy motion. To model the head swing and the body undulation， the amplitude A（ x）is approximated by a quadratic polynomial

where C0，C1，C2are the envelope amplitude coefficients. To represent the kinematics in detail， we use the amplitude of the leading edge of the headAh， the amplitude of the trailing edge of the headA0， and the amplitude of the caudal peduncular joint Ab. The matrix connecting the envelope amplitude coefficients and the motion amplitudes can then be given as

where xh，x0are the position of the leading edge and the trailing edge of the head， as shown in Fig.1，xbis the position of the tail peduncle. They describe in detail the mathematical underpinnings of the method chosen to control the head swing motion.

The head swing motion of a swimming robot is not easy to describe precisely. In this work， a simplification is made. As shown in Eq.（3）， a matrix equation based on the swing amplitudes and the envelope coefficients are employed to represent the shape of the fish profile. We employ two critical parameters in describing the head swing motion: the leading edge amplitudeAhand the trailing edge amplitude A0. The effect of altering each parameter on the overall kinematics of the robot is best displayed in Fig.3. In these plots， starting with a single case of no head swing，each parameter is individually altered to highlight its effect on the overall kinematics.

For the caudal fin， it can be simplified as an oscillating foil， which moves at a specific combination of the pitch and heave motions［4，20］. The instant transverse displacement ycf（t ）and the angular displacement θ（t）are given as

where Abis the heave amplitude of the caudal peduncular joint，Lbis the length of the body segments，θmaxis the pitch amplitude of the caudal fin， and? is the phase angle， by which the heave leads to the pitch.

Fig.3 Kinematics of the fishlike robot

The present work for each case of the fishlike robot swimming is based on the following parameters:（f =2 Hz，Ab=0.08L，αmax=20o，?=90o）. The results of the robot swimming with no head swing can be used as a reference case for other head swing cases. To investigate the effect of the head swing on the hydrodynamics， two variables ofAhand A0are examined. After our tests， it is indicated that the effect of the changes in the amplitude of the leading edge of the head becomes very weak whenAh＞0.08L. Therefore， the amplitude variables ofAhand A0here range from0Lto0.08L in an interval of0.02L.

2. Numerical method

2.1 Governing equations

The objective of this work is to investigate the effect of the head swing motion on the thrust and thepropulsive efficiency of the fishlike robot swimming. We consider a 3-D incompressible flow over the robot undergoing a steady forward motion. The equations governing the motion of a viscous fluid are the 3-D Navier-Stokes equations given by

whereu is the fluid velocity vector，ρis the density，p is the pressure，μis the dynamic viscosity and?is the gradient operator. To solve the equations in a domain containing the robot， a no-slip condition is imposed on the moving interface with the fluid velocityand the fish velocityas

In our simulation， the motion of the fishlike robot is in turn described by the Newton's equations of motion as

whereF and MZare the fluid force and torque acting on the fish，mis the fish massis the swimming acceleration，andare the angular velocity and the angular acceleration， and IZis the inertial moment about the yaw axis. The feedback of the torque is limited to the yaw direction to simplify the computations. The fluid forceF and the torque MZare computed as follows:

2.2 Numerical method

The Navier-Stokes equations here are discretized using a finite volume method: a second-order Crank-Nicolson scheme is applied for the unsteady term， a second-order upwind scheme is used for the convective term and a second-order central differencing scheme is used for the diffusion term. The pressure velocity coupling of the continuity equation is achieved using the SIMPLE algorithm. The solution of the Newton's motion equation for the fish is implemented by using the user-defined function. The coupling procedure is implemented using an improved staggered integration algorithm［10，20］. The mesh grids are locally refined near the fish and the wake region. To capture the movement of the fishlike robot in the 3-D domain，a dynamic mesh technique is used. At each updated time instant， the grids around the robot are regenerated and smoothed using the regridding and smoothing methods. The tail beat periodT is divided into 200 time steps， i.e.，?t=T/200. To ensure the grid quality updated at each time-step， a small time-step size is required depending on the tail-beat frequency.

2.3 Performance parameters

Several parameters are used to quantify the swimming performance. The drag force acting on the robot and the power needed for it to be propelled are relevant in this work. The total drag force consists of a viscous drag and a pressure drag. As shown in Fig.1，the viscous drag and the pressure drag per unit area can then be expressed as

whereU is the swimming velocity of the robot. The input power required for the robot swimming consistsof two parts. One is the lateral power PS， required to produce the lateral oscillation， and is defined as

The other is the thrust power， needed to overcome the drag， and is defined as PD=-FDU. Thus， the input powerPTcan be obtained by PT=PS+PD. Considering the fishlike propulsion subject to a net thrust （i.e.，CD＜0）， we further introduce the propulsive efficiency defined as

Fig.4 Time history of the hydrodynamic force and its pressure and viscous components from the present work compared with the results of Dutsch et al.［21］

2.4 Numerical validation

To validate our numerical method in predicting the forces and the flow structures， we simulate the case of a cylinder starting to oscillate in the horizontal direction in the fluid initially at rest. The resulting flow for this case provides a stable vortex shedding with two fixed stagnation points on the front and the back of the cylinder. The detailed studies were reported in Dutsch et al.［21］. The translational motion of the cylinder is given by a harmonic oscillation. We choose the case for validation with the same parameters as used in Dutsch et al.［21］where both the experimental and numerical results were reported. The numerical computations are found to yield sufficiently accurate force information. Figure 4 compares the calculated total hydrodynamic force and its pressure and viscous components with the reported results［21］. It is clear that they are in good agreement. Figure 5 shows the calculated instantaneous contours of the pressure and the vorticity field at four different phase angles of the oscillatory cylinder motion. The flow structures reflect the vortex formation during the forward and backward motions， which is dominated by two counter-rotating vortices. The computed results agree with the Dutsch et al.'s computational results［21］， which are not shown here but were reported clearly in their paper.

Fig.5 Contours of pressure and vorticity at four different phase angles （please see Fig.6 in Dutsch et al.［21］）

3. Results and discussions

In this section， we analyse the effect of the head swing on the yielding fishlike swimming by varying the amplitudes of Ahand A0， while keeping the amplitude ofAbunchanged. The aim is to ensure the motion of the caudal fin unchanged during the variations ofAhand A0.

It is noted that the fishlike robot is in a free swimming， not fixed at a position. When the robot swims at a steady speed， the performance parameters defined in Section 2.3 over time are in accordance with the sinusoidal variation. In other words， the average values of them are always zero. Therefore， they could not be used to explore the variation of the performance parameters with different head swing laws of the robot. On the other hand， the instant maximum values of these parameters can be used to study the effect of the head swing motion on the hydrodynamics performance instead of the averages of them. Therefore， the following parameters are referred to the instant maximumvalues， not the average values.

Fig.6 Variations of performance parameters as functions of A0

3.1 Effect of trailing edge amplitude of head A0

To discuss the effect of the trailing edge amplitude A0more directly， we assume that the leading amplitude Ahis fixed to zero. Figure 6（a） plots the variations of the drag coefficients CDP，CDFand CDas functions of A0. It can be seen that both CDPand CDdecrease quickly with the increase of A0， while CDFalmost keeps constant. Under this condition， the swimming profile is shown in Fig.3（b）. Comparison of these cases with no head swing case reveals that it is of great benefit for the fishlike robot to generate a thrust by increasing A0while keeping Ahinvariable. Both CDPand CDare always negative in these cases，thus the thrust force is generated.

Figure 6（b） plots the variation of the powersPD，PTand the efficiencyηwith respect to A0. As A0increases，PDincreases slowly， and PTincreases slowly first and then more quickly. The trend ofηis increasing quickly first until a turning point and then slowly. Comparison of these cases with no head swing case reveals that it is favorable for the fishlike robot to realize a high efficiency by increasing A0. However，closer inspection shows that the increases of the thrust and the propulsive efficiency with larger A0are at the expense of the high input power PT.

3.2 Effect of leading edge amplitude of head Ah

To study the effect of the leading edge amplitude Ah， we assume that the trailing amplitude A0is fixed to zero. Figure 7（a） shows the variations of the drag coefficientsCDP，CDFand CDas functions of Ah. It is observed that the CDPand CDincrease as Ahincreases， while CDFalmost keeps constant. In this regard， the swimming profile of the robot is shown in Fig.3（c）. It is important to note that it is of no benefit for the fishlike robot to generate the thrust by only increasingAhwhile keeping A0invariable.

Fig.7 Variations of performance parameters as functions of Ah

Figure 7（b） plots the variation of the powers PD，PTand the efficiency ηwith respect to Ah. As Ahincreases，PDdecreases slowly， and PTdecreases somewhat first and then increases a lot. Therefore， it is observed thatηwill decrease quickly with the increase of Ah. Comparison of these cases with no head swing case shows that it is unfavorable for the fishlike robot to realize a high efficiency by increasingAhwhile keeping A0invariable.

Fig.8 Variations of parameters as functions of A0and Ah

3.3 Effect of A0and Ah

Figures 8（a）-8（c） plot the variations of the drag coefficients CDP，CDFand CDas functions of Ahand A0. It is observed that CDP，CDFand CDvary more sensitively to A0than to Ah. For a fixed Ah，as A0increases， CDPand CDdecrease rapidly while CDFincreases somewhat. But they see no obvious changes as Ahincreases. Therefore， in the first consideration，A0is better than Ahfor the thrust generation. Closer inspection reveals that the minimum drag，namely， the maximum thrust occurs atAh=0.06L and A0=0.08L ， while the minimum thrust occurs at Ah=0.08Land A0=0L. Thus， it is indicated that the fishlike robot swimming with an appropriate amplitude for the head swing is of benefit to reduce the drag and improve the thrust.

Figures 8（d）-8（f） plot the variations of the powers PD，PTand the efficiencyηwith respect to Ahand A0. Similarly， it can be seen that PDand PTvary more sensitively to A0than to Ah. For a fixed Ah， as A0increases，PDand PTincrease significantly，while they do not see obvious changes as Ahincreases. Closer inspection shows that the maximum thrust power occurs atAh=0.06Land A0=0.08L， while the minimum input power occurs atAh=0.04LandA0=0.08L . Another common feature is thatηincreases quickly first and then slowly as A0increases. The optimum efficiency occurs at Ah=0.05Land A0=0.08L. Thus， it is reasonably revealed that the fishlike robot swimming with an appropriate amplitude for the head swing is beneficial to save the input power and increase the propulsive efficiency.

Fig.9 Evolution of pressure contours at Ah=0L，A0=0L

3.4 3-D flow structures

The aim of this work is to explore the mechanism of the fishlike robot swimming with the head swing motion. The robot is specified to swim with a same movement of the tail but a different movement of the head. As we all know， the vorticity shedding is concentrated in the tail portion of the fish during the swimming. In this work， in all cases， we have similar vorticity contours. Since the vorticity contours are similar，they can not be used to reflect the effects of the different head swing motions on the flow structures around the tail region. Therefore， we can make a hypothesis that the effects of the head swing motion on generating the thrust and the input power are related to the pressure distribution around the fishlike robot. In order to provide evidence for this hypothesis， it is insightful to examine the flow structures. The pressure contours are shown for four representative cases in Fig.3.

Fig.10 Evolution of pressure contours at Ah=0L ，A0=0.08L

Figure 9 plots the pressure distribution contours generated by the swimming robot with no head swing（as shown in Fig.3（a））. It is noted that there is always a high pressure core in front of the robot head throughout a half cycle. When the robot is on the left limit position shown in Fig.9， a low pressure core is on the left side of the tail， while a high pressure core is on the right side. It can be concluded that the robot experiences a drag at this time. The drag appears because the local forward pressure differential around the tail is smaller than the backward pressure differential on the front of the head. As the robot travels to the mid-point，the low pressure core on the left side gradually moves to the tail， and a new low pressure core is formed on the right side. The imbalances of the pressure differe-ntial around the fishlike robot lead to either the increase or the decrease of the drag. As the robot travels to the right limit position， the drag gradually deceases as a result of the wake formed by the shedding of the low pressure core from the trailing edge of the robot. A notable feature is that only one pair of pressure cores occurs on the different sides of the robot during the stroke. As the robot returns to its left limit position，the flow structures mirror the pattern observed in Fig.9. Previous studies of oscillating foils show very similar flow pattern［10，13，17，20］.

Figure 10 plots the pressure distribution contours generated by the swimming robot in the case of Ah= 0，A0=0.08Las shown in Fig.3（b） over one half cycles. Since Ahis zero， it can be seen that a high pressure core is always existed in front of the robot head. This pattern is the same as the pattern observed in the case of no head swing. When the robot is on the right limit position， a high pressure core is on the left side of the tail， while a low pressure core is on the right side. It can be deduced that the robot experiences a thrust at this time. This thrust appears because the local forward pressure differential on the tail is larger than the backward pressure differential on the front of the head. As the robot travels to the mid-point， another high pressure core is formed on the right side near the head and then gradually moves to the central portion，while another new low pressure core is formed on the left side. It will lead to a forward pressure differential to generate the thrust at the anterior portion. As the robot travels to the left limit position， the high pressure core and the low pressure core at the anterior portion gradually move to the tail. Meanwhile， another high pressure core and another low pressure core at the tail portion gradually move to the trailing edge and then shed off. A notable feature is that two pairs of the pressure cores are found to coexist in a uniform mode around the robot. These behaviors are nicely consistent with previous findings for foils［13，15］.

Figure 11 plots the pressure distribution contours generated by the swimming robot in the case of Ah= 0.08L，A0=0L as shown in Fig.3（c）. Since Ahis 0.08L， it can be seen that both a high pressure core and a low pressure core are always coexisted on the different sides in front of the head. This feature will result in an invariable backward pressure gradient at the fore portion and yield a standing drag. When the robot is at its left limit position， a low pressure core is on the left side near the tail. As the robot travels to the mid-point， the low pressure core gradually moves to the trailing edge， and another low pressure core on the right side near the head disappears along the surface. As the robot travels to its right limit position， the drag gradually deceases as a result of the wake formed by the shedding of the low pressure core from the trailing edge of the caudal fin. Meanwhile， at the fore portion，the high pressure core dissipates from the left side and appears on the right side. During the right stroke， the backward pressure gradient at the fore portion near the head yields a standing drag effect， while the gradually moving pressure core at the tail portion produces an alternative thrust effect. A key factor is that two pairs of the pressure cores are found to coexist in a reverse mode around the robot. Therefore， it is determined by a comparison of the drag effect of the head and the thrust effect of the tail for the robot to generate a thrust or a drag. As the robot returns to its left limit position， the pressure contours around the robot mirror the pattern observed in the right stroke.

Fig.11 Evolution of pressure contours at Ah=0.08L，A0=0L

Figure 12 plots the pressure distribution contours generated by the swimming robot in the case of Ah= 0.05L，A0=0.08Las shown in Fig.3（d）. It is clearly observed that the effect of the head swing motion on determining the nature of the local pressure distributions along the robot surface is evident. It can be obse-rved that the forward positive pressure differences between the left and right sides of the robot achieve the maximum in this case. An important feature is that two pairs of pressure cores in a uniform mode coexist around the robot over the full cycle. During the left stroke， a negative drag， namely， a positive thrust is always produced since the left and right sides of the robot are analogous to the pressure and suction regions. Although the profile of the robot is inverted at the right stroke， the signs of the drag are consistent with those at the left stroke.

Fig.12 Evolution of pressure contours at Ah=0.05L，A0= 0.08L

Compared to the robot swimming with no head swing shown in Fig.9， it is apparent that the head swing of the robot helps the pressure differentials generated by the head motion to produce the positive thrust throughout a swimming cycle. With respect to the robot swimming with only changing either Ahor A0presented in Fig.10 and Fig.11， it is obvious from Fig.12 that the head swing motion of the robot with varying both Ahand A0assists the vortex core in moving more smoothly from the leading edge to the trailing edge of the robot. Comparing the swimming behaviors of the robot in this case， it is noted that a similar feature is observed in dolphins， which beat their heads in the wake of other moving bodies when swimming.

4. Discussion

Comparing the above results， a remarkable difference between them is that two pairs of the pressure cores in a uniform mode coexist around the robot over the full cycle in some cases with the head swing， rather than only one pair of them in no head swing case. Not only the pressure differential due to one pair of pressure cores around the tail generates a thrust， but also the other pair of pressure cores located at the head can produce a thrust. Thus， for the fishlike robot propulsion， a standing thrust effect must be realized owing to the additive contributions of the two pressure differentials.

5. Conclusions

（1） The effect of varying A0on the propulsive performance is found more significant than varying Ah. As A0increases， the thrust increases and the input power increases slowly first and then quickly. Thus，the trend ofηis increasing quickly first and then slowly. And the thrust-indicative flow structures with two pairs of pressure cores in a uniform mode are observed coexisting around the robot.

（2） As Ahincreases， the thrust decreases while the input power increases， thus，ηwill decrease quickly. The drag-indicative flow structures with two pairs of pressure cores in a reverse mode are observed around the robot.

（3） Based on the understanding of the effect of the variation of Ahor A0respectively， we further deal with the simultaneous variation of Ahand A0. When the thrust increases at a larger A0， the appropriate value of Ahwill reduce the drag of the backward pressure differential further and thus decrease the input power by weakening the adverse pressure gradient around the head.

（4） It is revealed that the fishlike robot can be optimized to increase the thrust， minimize the input power and improve the propulsive efficiency by an appropriate head swing motion. The findings of this paper suggest that fish， dolphin， and aquatic animals may benefit the hydrodynamic characteristic by the head swing motion.

Acknowledgements

This work was supported by the State Key Laboratory of Robotics and System （HIT） （Grant No. SKLRS 2011-ZD-03）.

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10.1016/S1001-6058（16）60668-6

April 6， 2015， Revised July 18， 2015）

* Project supported by the National Natural Science Foundation of China （Grant Nos. 51205060， 51405080）.

Biography: Dan XIA （1982-）， Male， Ph. D.，

Associate Professor

2016，28（4）:637-647