Influence of Ship Motion on Flow Field over Modified Simple Frigate Shapes

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Key Laboratory of Unsteady Aerodynamics and Flow Control，Ministry of Industry and Information Technology，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China

Abstract: When the frigate moves forward，due to the ship motion such as pitching and rolling，the flow over the flight deck becomes very complex，which may seriously threaten the taking off and landing of the ship-borne helicopter. The flow fields over the different modified simple frigate shape（SFS）models，consisting of the hangar and flight deck，were numerically studied by changing the ratio of hangar height and length in the static state and pitching state. For different models，the contours of velocity and pressure above the flight deck，as well as the variations of velocity components of the observation points and line in static state and pitching state were compared and analyzed. The results show that the size of recirculation zone and the location of the reattachment point have distinct differences for diverse models，and reveal the tracks of recirculation zone’s center and reattachment position in a pitching period. In addition，the velocity components at two observation positions also change periodically with the periodic motion. Furthermore，the deviations of the velocity components in static state and pitching state are relatively large，therefore，the flow fields in static state cannot be used to simulate that in pitching state correctly.

Key words：computational fluid dynamics；simple frigate shape；ship airwake；pitching；recirculation zone

0 Introduction

Air passing through the ship’s superstructure causes the formation of a region of disturbed flow over the flight deck due to a combination of its for?ward speed and the prevailing wind，which is known as the ship airwake［1］. The flight deck is the main site for the ship-borne helicopter operations over the sea，and the flow over the deck is signifi?cantly affected by natural wind， superstructure shape and ship motion. When the frigate moves for?ward，the ship airwake appears in the rear of the hangar，accompanying with the flow separation，backflow and vortex. Meanwhile，due to the differ?ent wind over deck（WOD）and movement such as heaving，pitching and rolling，the flow over the flight deck becomes very complex，which may seri?ously threaten the taking off and landing of the shipborne helicopter. Therefore，there must be a clear understanding of the characteristics of the ship air?wake over the flight deck.

In the early years，the wind tunnel model test and in situ experiment were main methods to study the ship airwake over the flight deck. In 1992，since the previous simulator was based on a faulty air?wake database，which was based on a uniform ve?locity profile and very low turbulence，Healey at?tempted to correct this situation by making three-di?mensional hot-wire anemometer measurements of the airwake properties of a stationary l/141-scale model ship in a simulated atmospheric boundary lay?er［2］. In 2014，Bardera-Mora presented the main re?sults of the ship airwake simulation performed on a frigate ship model in a low-speed wind tunnel by par?ticle image velocimetry（PIV）［3］. Moreover，wind velocity measurements on board above the flight deck were also carried out by a sonic anemometer and results were compared with these obtained in wind tunnel tests. The results show that the turbu?lence intensity levels measured on board are lower than these measured in the wind tunnel tests. These differences can be probably due to differences in the boundary layer parameters （velocity profile and spectrum）. However，these two methods require lots of manpower and resources，and are also very time consuming. In the recent years，the computa?tional fluid dynamics（CFD）method has been grad?ually developed and widely used to research the ship airwake over the flight deck. The unsteady flow field of an LHA-class U.S. Navy ship was simulat?ed numerically by Polsky in 2002［4］，and the results were compared well with both wind tunnel and in si?tu experiment data. The research on the airwake simulation for a Navy destroyer DDG-81 was per?formed by Woodson and Ghee in 2005［5］，which in?dicated that the CFD methods could successfully simulate ship airflow. Later，Thornber et al. studied two different Royal Navy ships for fourteen different wind angles with implicit large eddy simulation（ILES）［6］. The study for evaluating the aerodynam?ic impact of ship superstructures on helicopter opera?tions was performed by K??ri? et al. in 2013［7］.Compared to the baseline ship geometry，all the ship modifications，particularly the side-flap and the notch modification，can significantly reduce rootmean-square forces and moments. Lately，Watson et al. performed the computational and experimental modeling study of the unsteady airflow over the United Kingdom’s new aircraft carrier HMS Queen Elizabeth［8］. Their full-scale CFD results showed reasonable agreement with the small scale experi?ment results，suggesting that the full-scale CFD method is at least as representative of the full-scale situation as the small-scale experiment. Therefore，the CFD method can be used to simulate the flow field over the large ship and offer correct flow data for pilots.

Under the auspices of the technical co-opera?tion programmer（TTCP），a collaborative ship air?wake modeling activity was set up to develop a ship airwake validation database［9］. Therefore，the sim?ple frigate shape（SFS） and its updated version SFS2 shown in Fig.1 were created to provide an easy research on the ship airwake. The simple SFS is a highly simplified ship geometry，which was cre?ated originally by a ship airwake modeling working group within TTCP. Later，the National Research Council of Canada（NRC）performed a series of wind tunnel experiments on both geometries［10-11］.The steady-state ship airwake over the SFS was al?so numerically studied with commercial software Fluent［12］，which showed that the general features of the flow compare reasonably well between the ex?perimental data and predicted data. Syms used the Lattice-Boltzmann method to investigate the flow to?pology on and off the surface of the SFS［13］. Be?cause of the ability in capturing the turbulent struc?tures for massively separated flow，the detached-ed?dy simulation（DES）turbulence model［14］，as well as its improved versions delayed DES（DDES）［15］and improved DDES（IDDES）［16］，becomes a popu?lar turbulence model for the ship airwake research?es. In 2010，Forrest et al. numerically studied the ship airwake of the SFS2 and a Royal Navy Type 23 Frigate with DES method［1］. Comparisons of DES results and wind tunnel data showed good agreement，which indicated that the DES method can be used to simulate the ship airwake. Zhao et al.employed the entropy-based detached-eddy simula?tion（SDES） method to simulate the airwake on SFS model，and concluded that SDES could accu?rately predict airwake［17］. Li et al. found that both large-eddy simulation（LES）result and DES result all well match the experimental result［18］. More?over，they found that both LES and DES methods are superior to RANS method in simulating ship air?wake. The DDES method was used to compute the unsteady ship airwake on the SFS2 as well as the Canadian Patrol Frigate，and the results were well compared with the experimental results［19］. Lately，a parametric study，employing IDDES with the shear stress transport（SST）k?ωturbulence model，was conducted by varying the hangar length to find the optimal afterbody model with minimal recircula?tion zone behind the hangar，and the optimal after?body model was obtained［20］.

Fig.1 Schematic of SFS and its updated version SFS2

However，most of the researches on the flow fields of SFS and SFS2 were based on the motion?less state，without considering the ship motion caused by the sea waves. In this paper，the flow fields over the modified SFS models with different hangar’s geometries were numerically simulated in both static state and motion state. The purpose of this study is to investigate the effect of the motion state and different hangar’s geometries on the flow fields over the helideck.

1 Numerical Method

Since the inflow Mach number is less than 0.3，thus the flow around the ship can be treated as the incompressible flow. The incompressible flow gov?erning equations are

whereVis the velocity vector，ρthe density of the air，dV/dtthe material derivative ofV，pthe static pressure，andFthe viscous force vector. The com?mercial CFD solver FLUENT was used for the nu?merical simulation，employing RANS with thek?εturbulence model for closure. The coupling of the pressure and velocity was handled using semi-implic?it method for pressure-linked equation（SIMPLE）algorithm and the time discretization was performed implicitly using a second-order accurate scheme with dual time stepping.

The dynamic mesh method was used to deform the mesh thus to simulate the ship’s motion. The spring-based smoothing，used in this paper，is one of the dynamic mesh updated method，where the edges between any two mesh nodes are idealized as a network of interconnected springs. The initial spacings of the edges before any boundary motion constitute the equilibrium state of the mesh. A dis?placement at a given boundary node will generate a force proportional to the displacement along all the springs connected to the node. Using Hook’s Law，the force on a mesh node can be written as

where ?xiand ?xjare the displacements of nodeiand its neighborj.niis the number of neighboring nodes connected to nodei，andkijthe spring con?stant between nodeiand its neighborj.

The spring constant for the edge connecting nodesiandjis defined as

wherekfacis the value for spring constant factor. At equilibrium，the net force on a node due to all the springs connected to the node must be zero. This condition results in an iterative equation such that

wheremis the iteration number.

Since the displacements are known at all the boundaries （after boundary node positions have been updated），Eq.（5）is solved using a Jacobi sweep on all interior nodes. At convergence，the po?sitions are updated such that

2 Model and Grid

The SFS is a representative case of the study on the flow over the ship flight deck，since it has a simplified geometry containing the hangar，bridge（funnel/mast）and flight deck（shown in Fig.1）.The configuration used in this study was shown in Fig.2. It is a modified SFS model named MSFS without the bridge on the hangar，which also can be regarded as the simplified afterbody of frigate. Some preliminary tests were undertaken with and without the bridge，and their results found that the bridge has relatively little effect on the aft flow field［21］.Therefore，the bridge on the SFS was removed in this paper for convenience.

Fig.2 Schematic of MSFS geometry model

The multi-block structured grid of the MSFS was shown in Fig.3，and the enlarged view of grid was shown at the top right corner of graph. The ve?locity inlet boundary is in front of the flow field，and the velocity magnitude of the freestream is 10 m/s.The pressure outlet boundary is in the rear. The width of the hangar is set toB，the height isH，and the length isL，whereB= 0.1 m，H=0.05 m.Ris defined asH/Land the total lengthLtotal=12H. In this paper，by changing the height-length ratioR，the flow fields of different MSFS models for a head?wind were numerically studied in the static state and motion state（pitching and rolling），respectively.For convenience，the MSFS models withR=1∶1，R=1∶3 andR=1∶6 are namedM1，M3 andM6，respectively.

Fig.3 Schematic of grid at the central section

3 Verification Process

To verify the numerical method，the numerical simulation results of the SFS2 model were com?pared with experimental data. The normalized veloc?ity components along a lateral line were shown in Fig.4，whereU，V，Wdenote longitudinal velocity in theXdirection，lateral velocity in theYdirection and vertical velocity in theZdirection，respectively.The lateral position is normalized by the ship beam.The results in this study are consistent with the nu?merical results of Li et al.［18］，which are also used the RANS turbulent model. For the both RANS re?sults，the velocity components are well matched with the experimental data［1］except the longitudinal velocity near the center of the line. The reason for this discrepancy is that the velocity fluctuation be?hind the hangar is averaged by RANS model.Though there is a discrepancy between experiment data and RANS results，Reddy et al. have demon?strated the feasibility of the numerical simulation of ship airwake with RANSk?εturbulence model［12］.

Fig.4 Comparison of experiment data and RANS results

In order to verify the rationality and indepen?dence of the grid，the flow field of MSFS3 with ap?proximately 2.6 million，6 million and 11.5 million grid cells were numerically simulated and compared.

In Fig.5，the result was shown by plotting lim?iting streamlines（skin-friction lines）on the deck surface of the MSFS3. The limiting streamlines are the streamlines close to the surface，which can pro?vide a lucid description of the flow topology. It can be clearly seen that the reattachment line on the deck surface is like a parabola. The recirculation zone is on its left side and the red line passes its apex. It also can be observed that the locations of the reattachment lines for different grids are basical?ly same.

Fig.5 Limiting streamlines on MSFS deck surface

As can be seen from Table 1，for three differ?ent grids，the force coefficients in the same direction have only slight differences，which means that the calculation results are basically the same for differ?ent grids. Therefore，the coarse grid was used in this paper to improve the computational efficiency.

Table 1 Force coefficients of different directions for dif?ferent grids

4 Result and Analysis

The numerical simulations were performed on the flow field of the different MSFS models in static state and pitching state in current study，respective?ly. The contours of velocity and pressure as well as the streamlines were compared and analyzed. Fur?thermore，the quantitative analysis of velocity com?ponents at the observation points and the observa?tion line above the deck for different models was giv?en. The positions of two observation pointsP0andP1，colored in white and black，were shown in Fig.6.P0is located in the longitudinal central sec?tion andP1is on the left side ofP0，and they are both at 1/2 hangar height.The observation line（col?ored in red）and three different maps were shown in Fig.7. The line is parallel toYdirection and passes throughP0andP1.

Fig.6 Schematic of observation points

Fig.7 Schematic of observation line and maps

4.1 Static state

The numerical simulations of the flow fields over the MSFS models with different height-length ratios（R=1∶1，1∶3，1∶6，respectively）in the stat?ic state were carried out first，and the characteristics of the flow fields over the deck were analyzed and compared.

As seen in Fig.8，when the incoming flow pass?es the edge of MSFS front wall，the upstream recir?culation zoneAand downstream recirculation zoneCwith a clockwise rotation are formed due to the flow separation. The shear layer and the center of re?circulation zone are located in the low speed area（colored in blue）. After the flow reaches the down?stream wall， the reattachment zone is formed.Meanwhile，the flow is divided into two parts. One part flows downstream and the other part goes up?stream. When encountering the hangar door，it flows along the hangar door. After bypassing the edge of hangar door，a small upstream recirculation zoneBwith an anticlockwise rotation is generated forM1 andM3 models.

Fig.8 Contours of velocity and streamlines at Map_Y

For different models，the structures of flow fields have obvious discrepancy. There are two small upstream recirculation zones and one large downstream recirculation zone for theM1 andM3 models，while there are only two distinct recircula?tion zones for theM6 model，including one up?stream recirculation zoneAand one downstream re?circulation zoneC. With the increment ofL，the up?stream recirculation zoneAincreases，while the downstream recirculation zoneCshrinks. The rea?son is that when the hangar length increases，there is enough space to form a large recirculation zone up?stream，and more backflow is attached to the up?stream wall，making the kinetic energy of the flow reduced due to the skin-friction. Consequently，the downstream recirculation zone becomes smaller be?cause there is less energy to drive the flow to cycle in the downstream recirculation zone.

Fig.9 shows the flow structures for different models at horizontal plane Map_Z. Due to the head?wind and symmetrical geometry，the flow fields on the left side and right side of different MSFS models are symmetrical. Similar to the contours of velocity and streamlines at Map_Y，on the one side of the MSFS，there are also two small upstream recircula?tion zones and one large downstream recirculation zone forM1 andM3 models，and only two distinct recirculation zones forM6 model. With the increase ofL，the upstream recirculation zoneDincreases，too，while the downstream recirculation zoneFshrinks.

Fig.9 Contours of velocity and streamlines at Map_Z

The pressure distributions are diverse for differ?ent models in Fig.10. As can be seen that the down?stream high pressure area（colored in yellow）inM6 is closer to the hangar door and the upstream low pressure area（colored in blue）is larger than that inM1. The downstream reattachment position is af?fected by high pressure area. Therefore，the size of downstream recirculation zone is limited by the loca?tion of high static pressure area.

Fig.10 Contours of pressure and streamlines at Map_Y

The limiting streamline distributions on the downstream wall were given in Fig.11，and the left end is the location of hangar door. The locations of the reattachment lines for different models are di?verse. However，the reattachment line on the deck surface for each model is all like a parabola. The re?circulation zone is on its left side and the red line passes its apex. The length of downstream recircula?tion zone forM6 is denoted byLd，and the result shows that the length of downstream recirculation zone forM1 andM3 is about 3.45Ldand 2.75Ld，re?spectively. For a ship-borne helicopter，it is condu?cive to take off and land on the flight deck with smaller downstream recirculation zone. Consequent?ly，theM6 model can offer a valuable reference for the design of the frigate superstructure.

Fig.11 Streamlines distribution on downstream wall

It is worth noting that the flow field over the flight deck forM6 can be approximated to that over a backward-facing step（BFS）with a closed recircu?lation zone bounded by an unsteady shear layer［22］，which can be seen in Fig.12［23］. For the sake of a clear description of the three-dimensional recircula?tion zone，a schematic of flow field over the MSFS was presented in Fig.13［24］. The recirculation zone behind the hangar appears when flow rounds the hangar. The appearance of the lateral flow from the two sides of the hangar leads to the three-dimension?al flow structure over the flight deck and the appear?ance of the horseshoe vortex.

Fig.12 Flow field over backward facing step[23]

Fig.13 Flow field over simplified frigate afterbody[24]

The differences of vertical velocity for diverse MSFS models should be attracted attention while the ship-borne helicopter is operating over the deck，because the distributions of vertical velocity can in?fluence the helicopter’s safety. The distributions of velocity components at the observation line for dif?ferent models were plotted in Figs.14—16，whereU，V，Wdenote longitudinal velocity，lateral ve?locity and vertical velocity， respectively. The curves of longitudinal velocity are axisymmetric for different models. It is worth noting that the sign of longitudinal velocity is almost positive except two sides forM1 andM3，meaning that the observation line is mainly located in the recirculation zone and the longitudinal velocity is the largest at the center forM1 andM3. However，the sign of longitudinal velocity is almost negative except the center forM6，meaning that the observation line is located outside the recirculation zone and the longitudinal velocity is the smallest at the center. It can be found that the distributions of lateral velocity are centrally symmetric for different models in Fig.15. In Fig.16，the downwash appears at the center and the upwash occurs on the two sides forM1 andM3. However，the observation line is only located in the downwash forM6.

Fig.14 Distributions of longitudinal velocity at observation line

Fig.15 Distributions of lateral velocity at observation line

Fig.16 Distributions of vertical velocity at observation line

4.2 Pitching state

In the real sea conditions，due to the random?ness of the sea waves，the motion of the ship is more complex，which is generally irregular motion.However，some scholars assumed that the motion of the ship is simple harmonic motion to study the calculation method of the ship/helicopter operation limits envelope［25?26］. Therefore，the simple harmon?ic motion model was established in this paper for the MSFS models.

In the pitching state，the flow fields over differ?ent models were numerically simulated. The period of pitching motion is 2 s，the maximum pitching an?gle is about 5°，and the function of pitching motion is

whereωyis the angular velocity of the rotation around theYaxis，and the unit is rad/s. In this pa?per，A=0.274，T=2 s，θ=0. The results of nu?merical simulation for different models in the third period were shown as follows.

The contours of velocity and streamlines at Map_YforM1 model in pitching state were shown in Fig.17. The black points and grey points denote the center of recirculation zone and the reattachment position on the downstream wall，respectively. The tracks of their movements were illustrated in the pic?ture. TheM1 reaches the maximum pitching angle atT/4，and there is a big downstream recirculation zone similar to the flow field in the static state. TheM1 model returns to its initial position atT/2 and the center of recirculation zone as well as the reat?tachment position gradually moves downstream. As the aft part ofM1 is gradually sinking，the recircula?tion zone over the deck enlarges obviously. More?over，the center of recirculation zone and reattach?ment position are moving toward the end of the deck until 3T/4. At the end of a period，theM1 model re?turns initial position，and the center of recirculation zone as well as reattachment position is moving up?stream. It can also be observed that the structure of flow fields atT/2 is basically the same to that atT.

Fig.17 Contours of velocity and streamlines at Map_Y for M1 model in pitching state

For theM3 model，the tracks of the center of recirculation zone and reattachment position in a pitching period are similar to that ofM1 model，as shown in Fig.18.

Fig.18 Contours of velocity and streamlines at Map_Y for M3 model in pitching state

However，there are some differences in the pitching flow fields forM6 compared withM1 andM3. AtT/4，there are two big recirculation zones（upstream recirculation zone and downstream recir?culation zone）over the hangar and flight deck，re?spectively. As the rear of theM6 model is gradually sinking，the upstream recirculation zone is moving downstream while the downstream recirculation zone is moving upstream. Eventually，these two re?circulation zones are merged into one as shown in 3T/4. WhenM6 model returns to initial position atT，the center of the merged recirculation zone is moving upstream. The location of the reattachment position is slightly moving upstream at first，then moving downstream and finally moving back to its origin in a pitching period，as shown in Fig.19.

Fig.19 Contours of velocity and streamlines at Map_Y for M6 model in pitching state

Due to the three-dimensional characteristics of the model and flowfield，a clear description of the three-dimensional streamlines behind the hangar at different time was shown in Fig.20，where the streamlines were colored in velocity magnitude.Not?ing that the dominant structures of 3-D streamlines for different models are similar，therefore the 3-D streamlines forM3 were only presented here. It can be seen that the streamlines behind the hangar ap?pear like a spiral shape，and keep rotating to form the recirculation zone. Compared with Fig.18，the recirculation zone also enlarges obviously as the aft part ofM3 is gradually sinking. The motion tracks of the center of recirculation zone and reattachment position in a pitching period are similar.

Fig.20 Schematic of 3-D streamlines for M3

In order to analyze the influence of pitching mo?tion on the flow fields quantitatively，the velocity components at observation points in pitching state were shown in Figs.21—23. For each model the sign of longitudinal velocity is positive，indicating that the observation pointP0is in the backflow of re?circulation zone all the time. However，the direction of longitudinal velocity at observation pointP1is changing when MSFS is pitching，because the shear layer is swing back and forth at this point.When the point is located in the shear layer，the lon?gitudinal velocity is close to 0. Noticeably，the lon?gitudinal velocity at both observation points changes periodically，and the period is 2 s，which is the same as the period of the pitching motion. The varia?tions of the longitudinal velocity are similar forM1 andM3 models，and the range of their variations is larger compared withM6 model.

Since the observation pointP0is located in the central section and the MSFS models are symmetri?cal，the lateral velocity fluctuates slightly and is around 0 with the pitching motion. Differently，due to the observation pointP1is not located in the cen?tral section，the lateral velocity has periodic fluctua?tion obviously，and the period is also 2 s.

In Fig.23（a），the direction of the vertical ve?locity is changing in a pitching period forM6 mod?el，indicating that the upwash and downwash areas are produced alternately at observation pointP0.However，forM1 andM3 models，P0is in the downwash area all the time and the variations of the vertical velocity are basically the same. As seen in Fig.23（b），for three different models，the upwash and downwash areas are produced alternately at ob?servation pointP1，which is different fromP0. Simi?larly，the vertical velocity at these two observation points changes periodically with the periodic pitch?ing motion，and the period is 2 s. In addition，the variations of the vertical velocity are similar forM1 andM3 models.

Fig.21 Curves of longitudinal velocity at different observa?tion points in pitching state

Fig.23 Curves of vertical velocity at different observation points in pitching state

From the above RANS results，the periodicity of flowfield for the pitching state can be captured.For the further verification，the DES turbulence model was used in the same pitching state，due to its ability in capturing the turbulent structures for massively separated flow. The accuracy of DES is sufficient for investigating the ship airwake，and the results show better consistency with experimental data［1，17-19］. In pitching state，the vertical velocity at the observation pointP0forM6 obtained from the RANS and DES methods was compared in Fig.24.The red line denotes the RANS results，and the blue line denotes the DES results. It can be found that there is obvious vertical velocity fluctuation in the DES results，so the Fast Fourier Transform was used to filter the fluctuation，and the green line denotes the filtered results. Compared with the RANS results， the vertical velocity with DES changes periodically，and the period is also about 2 s. In addition，the variations of the vertical veloci?ty are similar for RANS and DES results. Conse?quently，it is reasonable to simulate the ship air?wake for the ship motion case with RANS method.

Fig.24 Comparison of RANS and DES results in pitching state for M6

The standard deviations of velocity compo?nents at the observation points in different models were given in Table 2 and Table 3. In Table 2，the fluctuation of longitudinal velocity at the observation pointP0forM1 is larger than others. The fluctua?tion of the vertical velocity forM6 model is relative?ly large，while the lateral velocity in each model is almost unchanged. Compared withP0，the standard deviation of the velocity components atP1is larger except the vertical velocity forM6，and the most ob?vious discrepancy exist in the lateral velocity. It also can be found in Table 3 that the standard deviations of three velocity components are the largest inM1，which means the flow field over theM1 model is more turbulent.

Table 2 Standard deviation of velocity components at observation point P0 in pitching state m/s

Table 3 Standard deviation of velocity components at observation point P1 in pitching state m/s

4.3 Comparisons of two states

To further analyze the differences of flow fields over the deck between pitching and static state when the MSFS model is located on the horizontal posi?tion，the comparisons of velocity components at ob?servation pointP0for these two states were given in Table 4 and Table 5. The subscripts“s”and“p”de?note the static state and pitching state. During a pitching period，the MSFS model returns to hori?zontal position for two time atT/2 andT，and the subscripts“m”and“e”denote the middle of a period and the end of a period. Therefore，Us，Upm，Upemean the longitudinal velocity in static state，pitch?ing state atT/2 andT，respectively.?denotes the deviation of the velocity components between two states，which is defined by │(Upx-Us)/Upx│，andxcan be substituted by“e”and“m”.

Table 4 Comparisons of longitudinal velocity at P0 be?tween pitching and static states

Table 5 Comparisons of vertical velocity at P0 between pitching and static states

When different models are located on the hori?zontal position，the velocity components have obvi?ous divergence in different states. The longitudinal velocity in static state is lower than that in pitching state，especially forM6 model，the larger deviation between two states is 93.8% atT/2 and 94.4% atT. The reason is that in static state the observation point is located in the shear layer ofM6，where the longitudinal velocity is very low. While theM6 mod?el is in pitching motion，the recirculation zone be?hind the hangar is moving and increasing with the pitching motion. Therefore，the observation point is located in the backflow of the recirculation zone，where the velocity is larger. The smallest deviation occurs inM3 model，and the deviation between two states is 18.9% atT/2 and 7% atT.

The lateral velocity of the observation pointP0approximates to 0 in static state and pitching state for different models，due to the pointP0is located in the central section and the MSFS models are sym?metrical，which is consistent with that in Fig.15 and Fig.22.

Fig.22 Curves of lateral velocity at different observation points in pitching state

The comparisons of vertical velocity atP0be?tween pitching and static states were shown in Ta?ble 5. The vertical velocity in static state is lower than that at the end of a pitching period. The largest deviation between two states appears inM6 model，and the deviation is 175.1% atT/2 and 74.5% atT.It is noteworthy that the signs of vertical velocity atT/2 in pitching state and static state are opposite，therefore，the deviation is more than 100%，which has the serious effect on the ship-borne helicopter because the rotor-aerodynamic force is sensitive to the upwash and downwash. The smallest deviation between two states occurs inM1 model，and the de?viation is 17.4% atT/2 and 35.8% atT，which is relatively large and cannot be neglected for the shipborne helicopter’s safe operations over the deck.Furthermore，due to the unsteady characteristics of the instantaneous flow fields in the motion state，the velocity components atT/2 andTin the pitching motion is different for the same MSFS model，though the MSFS models are both located on the horizontal position at these two moments.

From Fig.25 to Fig.27，the comparisons of ve?locity components distributions on observation line for these two states were given to analyze the dis?crepancy of flow fields over the deck. LetS，PmandPedenote the static state，pitching state atT/2 andT，respectively. As shown in Fig.25，for theM1 model，the largest deviation of longitudinal velocity between two states appears at the center of the ob?servation line. It is noteworthy that the deviation of the longitudinal velocity on the whole line between static state and pitching state atT/2 is the largest.Furthermore，the longitudinal velocity in static state is smaller than that in pitching state，and it is largest atT/2 in pitching state. Similarly，the largest devia?tion of longitudinal velocity between two states ap?pears at the center for theM3 model. However，near two sides of the deck，the deviation is very small，indicating that the longitudinal velocity near the sides of deck is not affected seriously by the pitching motion. For theM6 model，the largest de?viation of longitudinal velocity between these two states is also appearing at the center area，however，the deviation on the whole line between static state and pitching state atTmoment is the largest，which is different fromM1 andM3.

Fig.25 Comparisons of longitudinal velocity distributions at observation line for different models

In Fig.26，for different models，the lateral ve?locity at center of the observation line is close to 0，and the deviation between two states is equal to 0，too. Nevertheless，the lateral velocity except the center has obvious deviation between two states，es?pecially near two sides of the deck forM6.

Fig.26 Comparisons of lateral velocity distributions at observation line for different models

The comparisons of vertical velocity distribu?tions are given in Fig.27. For bothM1 andM3 mod?els，the downwash velocity in the pitching state atTis higher when -0.20.3，there are both upwash and downwash in the static state，however，the upwash is only appearing in the end of a pitching period and the downwash is only appearing in the middle of a pitching period. Differently，for theM6 model，the deviation of the vertical velocity between different states is very large，except the area nearY/B=±0.25. Particularly，at two different moments in the pitching state，the largest deviation of vertical velocity is appearing near the two sides of the deck，though the decks at two moments are both located on the same position.

Fig.27 Comparisons of vertical velocity distributions at observation line for different models

5 Conclusions

In the current study，the numerical calculations of the unsteady flow fields over different MSFS models were carried out in the static state and pitch?ing state，respectively，with the emphasis on the in?fluence of ship motion on the flow fields over the flight deck. The following conclusions were ob?tained by comparing and analyzing the contours of velocity and streamlines，as well as the quantitative results.

（1） For different models，the structures of flow fields have obvious discrepancy. With the in?crease ofL，the downstream recirculation zone is decreasing，which is conducive to take off and land on the deck for the ship-borne helicopter.

（2）The moving tracks of recirculation zone’s center and reattachment position in a pitching period are similar inM1 andM3 models，while are differ?ent from that inM6 model.

（3）Except the lateral velocity atP0，the veloci?ty components at the observation points change peri?odically with the periodic pitching motion for the three models，and the period is equal to the pitching period.

（4）By comparing the deviations of the velocity components in static state and pitching state when the MSFS is located on the horizontal position，the results show that the flow field in static state is quite different from the pitching state. Therefore，the ef?fect of ship motion cannot be neglected in analyzing ship airwake.