To study the effects of aerodynamic loads on the aerodynamic characteristics of stationary and azimuthally rotating antennas, wind tunnel force tests are conducted using solid and porous plate antennas. The variation of aerodynamic coefficient with azimuth angle is obtained when the antenna is stationary and azimuthal rotation, and the results are compared with those from numerical simulations. The variation in the aerodynamic coefficients with respect to the azimuth angle is found to be sinusoidal for both the solid and porous plate antennas rotating in azimuth. Compared with the antenna stationary, quantitative analysis indicates that the rotational motion increases the maximum value and root mean square of the aerodynamic coefficient. For solid plate antenna, |_{x}|_{_max}, |_{my}|_{_max}, and |_{mz}|_{_max} increase by 41.6%, 15.0%, and 47.3%, respectively; _{x_rms}, _{my_rms}, and _{mz_rms} increase by 19.0%, 20.0%, and 19.1%, respectively. For porous plate antenna, |_{x}|_{_max}, |_{my}|_{_max}, and |_{mz}|_{_max} increase by 30.6%, 71.4%, and 40.9%, respectively; _{x_rms}, _{my_rms}, and _{mz_rms} increase by 22.9%, 50%, and 20%, respectively. The wind tunnel tests verify the feasibility of using numerical simulations to obtain the flow field results. By analyzing the surface pressure coefficient and vortex core track distribution, the effects of azimuthal rotation on the aerodynamic characteristics of the antenna are further clarified.

The aerodynamic load of large-scale rotating radar antennas is constantly changing. Thus, it is necessary to consider not only the aerodynamic characteristics of the antenna at rest but also the aerodynamic characteristics of rotating radar antennas in terms of the rigidity and strength of the antenna structure and the servo system [

The difference in the aerodynamic characteristics of radar antennas under static and rotating conditions mainly depends on the antenna type and the rotation parameters [

In studies on the aerodynamic characteristics of radar antennas, numerical simulations can provide more flow field details than wind tunnel tests [

Research on the aerodynamic characteristics of radar antennas using numerical simulations not only considers the surface pressure and aerodynamic coefficient. As the radar antenna rotates, the resulting vortex structure affects the aerodynamic characteristics of the antenna. Gumusel et al. [

In general, there are several problems to be solved regarding the aerodynamic characteristics of radar antennas in azimuthal rotation. In terms of wind tunnel tests, the limitations of the related dynamic force measurement test conditions mean that existing research contents focus on the aerodynamic characteristics of the antenna at rest, while the aerodynamic characteristics of antenna rotation have rarely been studied. Without knowing the difference between them, it is impossible to design a reasonable and effective antenna servo system or to investigate the wind resistance performance. Regarding numerical simulations, the shape, boundary conditions, and material properties need to be simplified, which will have a certain impact on the simulation results. Additionally, the existing numerical simulation results for radar antennas in azimuthal rotation lack the support of wind tunnel test data. As the semiempirical formula only applies to specific antenna shapes, it has significant limitations in practical engineering applications, and its accuracy needs to be verified by wind tunnel tests.

In this study, the aerodynamic characteristics of solid and porous plate antennas are obtained using a wind tunnel dynamic force test platform, and the quantitative differences of aerodynamic characteristics between the stationary and azimuthal rotation of antenna are analyzed. The variations in the antenna aerodynamic coefficients with azimuth angle are thus obtained. By comparing the wind tunnel test results with those from numerical simulations, the feasibility of using numerical methods to analyze the structure distribution of the surrounding pressure field and vorticity field when the antenna is stationary and rotating is verified. Comparing the differences in the flow fields then reveals the effect of the rotation on the aerodynamic characteristics of antennas.

Experiments were carried out in the NH-2 wind tunnel at the Laboratory of Aerodynamics at Nanjing University of Aeronautics and Astronautics. The NH-2 wind tunnel is a closed-circuit, low-speed wind tunnel with a test section measuring 3 m (width) × 2.5 m (height) × 6 m (length). The wind tunnel has a 2.89 : 1 contraction ratio, a flow velocity range of 0–93 m/s, and a turbulence intensity range of 0.10–0.14%.

The radar antenna model for the test has three parts: a plate antenna, rod, and elevation angle adjustment mechanism. Since the solid type and porous type are the two most commonly used plate antennas that can rotate in azimuth, two types of plate antenna models are considered in this study: a solid plate and a porous plate. The antenna models are shown in Figures

Radar antenna model in wind tunnel test section. (a) Solid plate; (b) porous plate; (c) definition of models.

Test model details.

Antenna type | Elevation angle (°) | Porosity rate (%) | Blocking rate (%) | |
---|---|---|---|---|

Solid plate | 25 | 0 | 0 | <2.5 |

Porous plate | 32 | 0 | 38 | <2.5 |

The radar antenna is mounted on a six-component box strain balance, which is connected to the base below the wind tunnel test section by a DD motor, as indicated in Figure

Wind tunnel dynamic force measurement test platform. (a) Overall driving and model connection method; (b) motion control and data acquisition system.

The strain-gage balance provides six-component force data, which are converted into the load signal using the balance formula in the AIAA strain-gage standard [

In the wind tunnel static force test, the sampling aerodynamic load is collected at a sampling frequency of 1 kHz over a sample collection time of 4 s. The data are then averaged to give the mean aerodynamic force. The test is carried out in a uniform flow of 25 m/s for the porous plate and 28 m/s for the solid plate. The radar antennas are tested at azimuth angles ranging from 0 to 180° in intervals of 5°.

To study the effects of radar antenna rotation on the aerodynamic characteristics, dynamic test data are also measured. The dynamic wind moment is related to the dimensionless parameter of reduced frequency

The output signal of the balance is mixed with vibration noise in the system. The raw data are filtered using a 4th-order Butterworth low-pass filter, and the cut-off frequency is set to 5 Hz [

Raw and filtered voltage data of the balance output as a function of time (the zero-point reference set has been deducted). (a) Δ_{x}–_{my}–

The reference system uses the wind axis system, as shown in Figure

Reference system of strain balance (wind axis system).

In designing a radar antenna servo system that has sufficient structural rigidity, there are five significant aerodynamic forces and moments: drag (_{x}), lateral force (_{z}), rolling moment (_{x}), azimuth moment (_{y}), and pitching moment (_{z}). The force and moment data of the radar antenna are expressed in dimensionless form using a drag coefficient _{x} = _{x}/(0.5 × ^{2}×_{z} = _{z}/(0.5 × ^{2} × S), rolling moment coefficient _{mx} = _{x}/(0.5 × ^{2} × _{my} = _{y}/(0.5 × ^{2} × _{mz} = _{z}/(0.5 × ^{2} ×

Computational fluid dynamics (CFD) software is used to simulate the antenna flow field distribution. Numerical simulations are carried out for the solid plate antenna and the porous plate antenna.

The continuity equation and momentum equations are_{ij} is the Reynolds stress tensor; _{i} and _{j} are the velocity components in the _{i} and _{j} directions, respectively; _{i} contains other related source terms of the model, such as porous medium and user-defined source terms.

The shear-stress transport k-

The dissipation rate equation is

The computational domain and antenna model are established on a 1 : 1 scale with respect to the wind tunnel test section and the antenna test model size. The antenna model is positioned in the middle of the computational domain, 150°C from both the entrance and exit, and the blockage rate of the model is less than 2%. Simulations are performed with a uniform inflow (28 m/s for solid plate antenna; 25 m/s for porous plate antenna) corresponding to the flow velocity in the wind tunnel tests. As shown in Figure

Computational domain and mesh division. (a) Computational domain; (b) mesh division around the model.

CFD mesh-independence verification for

Mesh number | 16 million | 8 million | 4 million |
---|---|---|---|

_{x} | 2.33 | 2.34 (0.4%) | 2.33 (0%) |

_{z} | −1.24 | −1.23 (0.8%) | −1.25 (−0.8%) |

_{mx} | −0.87 | −0.87 (0%) | −0.87 (0%) |

_{my} | 0.11 | 0.11 (0%) | 0.10 (−9%) |

_{mz} | 1.53 | 1.54 (0.7%) | 1.54 (0.7%) |

The numerical simulations are divided into two parts: steady numerical simulations and unsteady numerical simulations. In the steady numerical simulations, the antenna azimuth angle ^{−4} and the aerodynamic coefficient remains stable; for unsteady simulations, observe the change of the aerodynamic coefficient value with the calculation step. When it shows a stable periodic change, continue to calculate multiple rotation cycles to obtain the CFD result with a stable periodic change of the aerodynamic coefficient with respect to time. The aerodynamic coefficient components decomposed by the model in the wind axis system, that is, _{x}, _{z}, _{mx}, _{my}, and _{mz}, are monitored and recorded. As the antenna model is symmetric about the XOY plane, the mean, maximum, and root mean square (RMS) values of the steady aerodynamic coefficients of the antenna are the same in the ranges

Figure _{x} and _{mz} appear near _{x} and _{mz} near _{x} and _{mz} when the antenna is located at the maximum windward position (

Wind tunnel test results and numerical simulation results of aerodynamic coefficient with respect to the azimuth angle when the antenna is at rest (solid plate, _{x} − _{z} − _{mx} − _{my} − _{mz} −

Under the effect of wind loading, accurate acquisition of the maximum and RMS value of the antenna aerodynamic coefficient is particularly important for antenna servo system design and to ensure structural stiffness and strength. Larger peak values of the aerodynamic coefficients will place higher requirements on the ability of the servo system to resist variable loads, and the volume and weight of the servo motor will increase accordingly. These parameters ultimately determine the reliability and energy consumption of the equipment [

Figure _{x} and _{my} do not attain the maximum values at the maximum windward region of the antenna, and _{z}, _{mx}, and _{my} are not equal to zero. Note that, except for _{my}, the peak values of the aerodynamic coefficients are overestimated by the numerical method, whereas the RMS values of the aerodynamic coefficients are underestimated. With the exception of the RMS of _{x}, the simulation results for the aerodynamic coefficient RMS values are slightly smaller than the test results.

Wind tunnel test results and numerical simulation results of aerodynamic coefficient with respect to azimuth angle when the antenna rotates in azimuth (solid plate, _{x} − _{z} − _{mx} − _{my} − _{mz} −

There are some differences in the peak values given by the numerical simulations and the wind tunnel tests. This is because the turbulence model cannot accurately express the pressure of vortices and only provides the statistical characteristics of this quantity [

Figure

Wind tunnel test results and numerical simulation results of aerodynamic coefficients with respect to the azimuth angle when the antenna is stationary and azimuthal rotation (solid plate), (a) _{x} − _{z} − _{mx} − _{my} − _{mz} −

Table _{x}_mean|, |_{my}_mean|, and |_{mz}_mean| increase by 12.4%, 500%, and 13.3%, respectively; |_{x}|_max, |_{my}|_max, and |_{mz}|_max increase by 41.6%, 15.0%, and 47.3%, respectively; _{x}_rms, _{my}_rms, and _{mz}_rms increase by 19.0%, 20.0%, and 19.1%, respectively. Therefore, changing from a static antenna to azimuthal rotation places a greater wind load on the whole structure. Moreover, the radar antenna is subject to a periodic alternating load for a long time, which will reduce the service life of the servo motor and increase the shutdown rate of the radar antenna.

The mean, maximum, and RMS values of aerodynamic coefficients for the solid plate antenna when the antenna is stationary and azimuthal rotation (the direction is not included in these results).

Solid plate | Exp. | |||
---|---|---|---|---|

Mean | Maximum | RMS | ||

Stationary | _{x} | 0.89 | 1.37 | 1.00 |

_{z} | 0.02 | 1.01 | 0.64 | |

_{mx} | 0.00 | 0.73 | 0.45 | |

_{my} | 0.01 | 0.20 | 0.10 | |

_{mz} | 0.60 | 0.93 | 0.68 | |

Azimuthal rotation | _{x} | 1.00 | 1.94 | 1.19 |

_{z} | 0.06 | 1.12 | 0.67 | |

_{mx} | 0.09 | 0.77 | 0.47 | |

_{my} | 0.06 | 0.23 | 0.12 | |

_{mz} | 0.68 | 1.37 | 0.81 |

When the antenna is stationary, the aerodynamic coefficients _{x} and _{mz} have positive peaks at _{z} and _{mx} have positive peaks at _{my}. However, the rotation motion will lead to some advance or lag in the azimuthal position corresponding to the peak aerodynamic coefficient of the solid plate antenna. Therefore, the effect of the aerodynamic load on the aerodynamic characteristics of radar antennas with azimuthal rotation cannot be ignored. Otherwise, it would be very difficult to design a lightweight antenna servo system and transmission mechanism under the premise of ensuring stability, flexibility, safety, reliability, and a long service life [

As the size and range of application of radar antennas increase, the vibrations caused by wind loading as the antenna rotates have an increasingly prominent effect on their stability and electrical performance. For a rotating radar antenna, the wind load changes periodically, which will lead to periodic vibrations of the antenna and periodic changes in the aerodynamic coefficients. Jin and Xu [

In Figure

Schematic diagram of pressure monitoring points on the surface of a solid plate antenna (red region represents the windward side of the antenna, blue region represents the leeward side of the antenna, and rotation is counterclockwise).

Figure

Pressure coefficients of the surface monitoring points with respect to azimuth angle when the solid plate antenna is stationary,

Nephogram diagram of pressure distribution on the front and back of the antenna. (a)–(d) The front of the antenna; (e)–(h) the back of the antenna. (a)

Figure

Pressure coefficients of the surface monitoring point with respect to azimuth angle when the solid plate antenna rotates,

Figure

Vorticity nephogram and pressure isosurface nephogram (black solid line represents positive pressure value, black dotted line represents negative pressure value, and color cloud images represent vorticity), (a)

It can be seen from Figure _{my} is great than zero. By

From the perspective of quantitative analysis, the surface pressure coefficients of monitoring points A1–A3 and B1–B3 change greatly with the azimuth angle, with

As the pressure in a vortex is lowest at its core and increases with distance from the core, the position distribution of the vortices will affect the aerodynamic coefficient of the antenna by affecting the pressure distribution around and on its surface. Therefore, analysis of the vortex core positions in the flow field can reveal the formation mechanism of different pressure distributions and reveal the differences in aerodynamic characteristics between static and rotating antennas [

Figure

Vortex core track and static pressure YOZ multisection pressure nephogram distribution with azimuth angle. (a)

Vortex cores track at four instantaneous positions for the solid plate antenna. The wind is blowing from right to left. (a)–(d) Stationary and (e)–(h) azimuthal rotation. (a)

As the pressure is proportional to the distance from the vortex core, the distribution of vortex cores around the antenna has a large effect on the surface pressure. In Figure

Designs that increase the porosity rate of the radar antenna can reduce the weight of the servo system and decrease the wind loading on the antenna, thus reducing both design costs and energy consumption. The aerodynamic characteristics of the porous plate antenna at rest and azimuthal rotation are studied, and the effects of azimuthal rotation on its aerodynamic characteristics are analyzed.

Figure _{x} and _{mz} appear at _{z} and _{mx} appear at

Wind tunnel test results and numerical simulation results of aerodynamic coefficient with respect to the azimuth angle when the antenna is at rest (porous plate, _{x} − _{z} − _{mx} − _{my} − _{mz} −

Figure _{my} at

Wind tunnel test results and numerical simulation results of aerodynamic coefficient with respect to azimuth angle when the antenna rotates in azimuth (porous plate, _{x} − _{z} − _{mx} − _{my} − _{mz} −

Figure

Wind tunnel test results and numerical simulation results of aerodynamic coefficients with respect to the azimuth angle when the antenna is stationary and azimuthal rotation (porous plate). (a) _{x} − _{z} − _{mx} − _{my} − _{mz} −

Table _{x}_mean|, |_{my}_mean|, and |_{mz}_mean| increase by 17.6%, 300%, and 14.8%, respectively; |_{x}|_max, |_{my}|_max, and |_{mz}|_max increase by 30.6%, 71.4%, and 40.9%, respectively; _{x}_rms, _{my}_rms, and _{mz}_rms increase by 22.9%, 50%, and 20%, respectively. The results show that the aerodynamic coefficients _{x} and _{mz} have negative peaks at _{z} and _{mx} have positive peaks at

The mean, maximum, and RMS values of aerodynamic coefficients for the porous plate antenna when the antenna is stationary and azimuthal rotation (the direction is not included in these results).

Porous plate | Exp. | |||
---|---|---|---|---|

Mean | Maximum | RMS | ||

Stationary | _{x} | 0.74 | 1.24 | 0.83 |

_{z} | 0.07 | 0.57 | 0.32 | |

_{mx} | 0.02 | 0.20 | 0.11 | |

_{my} | 0.01 | 0.07 | 0.04 | |

_{mz} | 0.27 | 0.44 | 0.30 | |

Azimuthal rotation | _{x} | 0.87 | 1.62 | 1.02 |

_{z} | 0.11 | 0.67 | 0.36 | |

_{mx} | 0.05 | 0.30 | 0.17 | |

_{my} | 0.04 | 0.12 | 0.06 | |

_{mz} | 0.31 | 0.62 | 0.36 |

In Figure

Schematic diagram of pressure monitoring points on the surface of the porous plate antenna. Red region represents the windward side of the antenna, blue region represents the leeward side of the antenna, and rotation is counterclockwise.

Figure

Pressure coefficients of the surface monitoring points with respect to azimuth angle when the porous plate antenna is stationary,

Figure

Pressure coefficient of the surface monitoring points with respect to azimuth angle as the porous plate antenna rotates,

Figure

Vortex cores track at four instantaneous positions for the porous plate antenna; the wind is blowing from right to left. (a)–(d) Stationary; (e)–(h) azimuthal rotation. (a)

To analyze the effect of the vortex core positions on the aerodynamic coefficient of the antenna, the region with the highest density of vortex cores around the antenna is roughly illustrated by the blue squares in Figure

In this study, the aerodynamic characteristics of a solid plate antenna and a porous plate antenna at rest and during azimuthal rotation have been studied by means of wind tunnel force tests. The variation in the aerodynamic coefficients with respect to the azimuth angle during the antenna is stationary and during azimuthal rotation were then analyzed. Besides, the numerical simulation results corresponding to the working conditions of the wind tunnel test are given. The rationality of the numerical simulation method used in this paper was verified through comparisons with the wind tunnel test results. The pressure and vortex in the flow field are given, the effect of the rotation distribution on the aerodynamic characteristics of the antenna is revealed, and the simulation results provide a reference for analyzing the flow field structure of radar antennas.

A comparison of the wind tunnel test data for the aerodynamic coefficients over one rotation period showed that significant differences occur in the aerodynamic characteristics of the antenna relative to the azimuth angle when the antenna is stationary and when the antenna azimuth rotates. The mean, maximum, and RMS values of the aerodynamic coefficients were found to increase to different extents. The mean, maximum, and RMS values of the drag coefficient, azimuth moment coefficient, and pitching moment coefficient all increase by more than 10% when the antenna is a solid plate; when the antenna is a porous plate, they all increase by more than 14.5%.

The numerical simulation results show that the aerodynamic characteristics of the antenna are highly correlated with the relative position of the vortex cores in the flow field, and the surface pressure of the antenna decreases as the distance to the vortex cores decreases. For the solid plate antenna, the vortex cores in the flow field around the antenna mainly affect the magnitude and distribution of the pressure on the leeward side of the antenna; for the porous plate antenna, the vortex cores in the surrounding flow field have a greater impact on the pressure on the leeward side of the antenna and on the windward side of the antenna. In addition, there are scattered and discontinuous vortex core tracks around the antenna. This track has little effect on the surface pressure of the antenna, so the continuity of the vortex core tracks near the antenna has a high correlation with the aerodynamic characteristics.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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