Pitching Moment Coefficient Research Articles

Measurement of aerodynamic force and moment acting on a javelin using a magnetic suspension and balance system

The rules governing the dimensions of the Javelin were substantially changed in 1986. It was considered that this new design guaranteed there was zero pitching moment at 0° angle of attack and that the pitching moment decreased (became negative) with increasing angle of attack. The objective of this study is to investigate if the pitching moment remains always negative (nose-down rotation). To measure accurate aerodynamic forces acting on a Javelin, the world’s largest 1 m magnetic suspension and balance system was used. The magnetic suspension and balance system was able to measure aerodynamic forces without support interference in the wind tunnel. In addition, computational fluid dynamics were carried out to estimate the pitching moment coefficients. It was found that the pitching moment coefficient of a commercially available Javelin becomes positive (nose-up rotation) at lower angles of attack, less than 12°. The pitching moment becomes positive if the upstream side of the center of gravity receives more inflow than the downstream side. This situation can be attained by, for example, increasing the thickness of the upstream side when compared with that of the downstream side.

Refined Aerodynamic Test of Wide-Bodied Aircraft and Its Application

The large dual-channel wide-bodied aircraft has a long range and a high cruise Mach number. Therefore, its aerodynamic design requires a high level of wind tunnel test refinement. Based on the requirements of aerodynamic design for the future wide-bodied aircraft and the characteristics of high-speed wind tunnel tests, the error theory is introduced to analyze the factors affecting the accuracy of the test data. This study carries out a series of research on the improvement of refined aerodynamic test technology in an FL-26 wind tunnel, including design and optimization of the support system of wide-bodied aircraft, model attitude angle measurement, Mach number control accuracy, measurement and control system stability, test data correction and perfection, high-precision force balance and standard model development. In addition, the effect of the standard specification of the refined aerodynamic test is investigated to improve the data quality. The research findings have been applied in the standard model test and subsequent models of wide-bodied aircraft. The results show that when Mach numbers are less than 0.9, the control accuracy of Mach numbers in the FL-26 wind tunnel is smaller than 0.001 and the measurement error of attack angle is smaller than 0.01°. Therefore, it has the ability to correct the data influenced by factors, such as support/wall interference, model deformation, floating resistance and airflow deflection angle. The repeatability accuracy of the standard model’s comparison test shows that the lift coefficient is less than or equal to 0.0012, the drag coefficient is less than or equal to 0.00004, pitching moment coefficient is less than or equal to 0.0004. The bending resolution of the model’s deformation measurement is less than 0.2 mm, and the tensional deformation is smaller than 0.04°. The revised aerodynamic data and model deformation measurement results have good agreement with that of the ETW wind tunnel. The results demonstrate that the improved technology presented in this paper can significantly enhance the refined aerodynamic test of wide-bodied aircraft.

翼列開閉型モーフィング翼のサロゲートモデルに基づく多目的空力最適化と設計情報の抽出

To improve short takeoff and landing performance and stall characteristics of fixed-wing unmanned aerial vehicles, a Multi-Slotted Variable-Camber Morphing Wing was proposed. This airfoil is composed of five components connected, and the aerodynamic characteristics can be adjusted by changing the configuration of each airfoil. In this study, the arrangement of components of the morphing airfoil is optimized aerodynamically by defining 12 design variables, and the obtained Pareto solutions are analyzed to identify essential design variables and components to improve the aerodynamic performance of the entire airfoil. As a result, it was shown that the position of the fourth and fifth components is essential for the lift coefficient, the distance between components is essential for the drag coefficient. Moreover, the position of the second component is essential for the pitching moment coefficient.

A Machine Learning Approach to Predicting Unsteady Transonic Flow of Pitching Airfoils

Abstract A machine learning methodology has been proposed in this paper to study the unsteady transonic aerodynamics in the flutter regime. The methodology is based on a well-established regularization technique, and it compares very well with the data modeling approach proposed recently by the author in the prediction of the lift coefficient, cl, of NACA00 series airfoils over a range of reduced frequency. The present methodology has been extended to the prediction of the airfoil pitching moment coefficient, cpm, also. Just as in the case of the data model proposed earlier, the regularization-based machine learning model is trained on a subset of the considered reduced frequency range and a subset of the NACA00 series airfoils. The model predictions are in good agreement with the computational fluid dynamics (CFD) results, in the reduced frequency range for the selected test NACA00 profiles including those with a thickness typical of supercritical wing sections. The machine learning methodology presented here represents a new technology that can be used in the prediction of transonic flutter aerodynamics of wings using a strip theory approach. This new approach can be coupled with a simple finite element model such as a beam element model offering a rapidly implementable aeroelastic framework for the design of new transonic wings.

Experimental Study of Air-Assisted Rocket System Models for Launching Payloads into a Low Earth Orbit

This paper presents the results of aerodynamic testing of air-launch rocket kit models for launching payloads into a low Earth orbit. The work was performed in a low-speed wind tunnel at the Military University of Technology (MUT, Warsaw, Poland)), using symmetrical airflow. Two carrier aircraft models were tested, i.e., Su-22 and MiG-29 aircraft without launched payloads and with these payloads at a dynamic pressure of q = 500 [Pa] and the range of angles of attack at α = -2828. The values obtained related to the aerodynamic drag coefficient, aerodynamic lift coefficient, pitching moment coefficient and lift to drag ratio, and are given in tabular and graphic forms. The tests were primarily used to validate the numerical results obtained during implementation of the project “Air-assisted rocket system for launching payloads into low Earth orbit - feasibility study”.

Aerodynamic characteristics of store during lateral jet assisted separation from cavity using free drop technique

Aimed at the problem of store separation from internal cavity, this paper innovatively puts forward a separation scheme of using lateral jet to assist store safe separation. The jet ensures that the store is continuously subjected to down head moment during separation, so as to ensure safe separation. The wind tunnel free drop test technique with lateral jet is established, which can ensure that there is no support interference in the motion process of the store and more truly simulate the motion of the store. The feasibility of the new separation scheme is proved by wind tunnel test. The test shows that the new scheme can also change the more dangerous state into a safe state. Through the analysis of the test data, the pitching moment coefficients of the store under different pressures in the high-pressure cylinder are obtained, and the effects of aircraft and cavity on the pitching moment of the store are obtained. The 3 stages of store passing through cavity shock wave are found. The results show that the lateral jet provides the store with continuous head down moment, and makes the store overcome the head up moment caused by the shock wave in front of the cavity, so as to ensure the safety of separation.

Study on a Rapid Aerodynamic Optimization Method of Flying Wing Aircraft for Conceptual Design

Searching for a design scheme satisfying the requirements in aircraft conceptual design can be a time-consuming work because of the multipeak and nonlinearity of the design space. This paper proposed a rapid aerodynamic optimization method for flying wing aircraft conceptual design. This method is aimed at reducing the induced drag at the design point by adjusting the camber and twist angle of spanwise airfoil. Firstly, the mean camber surface of the flying wing aircraft was parameterized. Secondly, the surrogate model was constructed based on the points selected by the optimization Latin square method. Thirdly, the surrogate model combined with a multi-island genetic algorithm was used for the preliminary solution of global optimum, and then, the Nonlinear Programming by Quadratic Lagrangian method combined with a vortex lattice method was used for searching the nearest exact best point from the initial best point. Finally, connecting with manual selection, the optimized flying wing layout scheme was obtained. The optimized results show that the induced drag coefficient is reduced by 10%, the pitching moment coefficient is reduced by an order of magnitude, and the lift drag ratio is increased from 26.3 to 27.3. The proposed optimization method decreases the time cost in aircraft conceptual design while achieving sufficient calculation accuracy. By using this method, the design space can be explored rapidly to search for the best design scheme satisfying the constraints.

Analytical formulas for verification of aerodynamic force and moment computations

In this paper, we derive analytical formulas for the drag, lift, and moment coefficients of a circular cylinder exposed to a fictitious flow defined by analytical functions in two and three dimensions, and demonstrate that these formulas serve as a useful tool for quickly verifying the implementation of force and moment computation algorithms in computational fluid dynamics solvers. Focusing on a typical second-order unstructured-grid solver, we will show that the lift and drag coefficients consist of second-order accurate pressure and first-order accurate viscous force coefficients, and thus it is not always possible to uniquely determine their orders of accuracy although all will be first-order accurate on fine enough grids. For the circular cylinder geometry, the pitching moment coefficient depends only on the viscous stresses and is therefore first-order accurate. In three dimensions, rolling and yaw moments have both pressure and viscous contributions, and therefore they are asymptotically first-order accurate. Viscous contributions to the force and moment coefficients are first-order accurate even for regular grids because the gradient stencil is not symmetric typically at a boundary and any linearly-exact gradient algorithm can be first-order accurate at best; hence, the velocity gradients used to compute the viscous stresses at a wall are first-order accurate. For verification, therefore, it is necessary to verify the pressure and viscous contributions separately; it can be performed rigorously with the analytical formulas presented in this paper.

Nonlinear Aerodynamic Model in Dynamic Ground Effect at High Angles of Attack

This paper focuses on the development of a model to represent the longitudinal aerodynamics of a wing and/or flight vehicle in ground effect when height is a function of time including high angles of attack. A general aerodynamic model of a wing and/or airplane in ground effect that includes high angles of attack was created. The aerodynamic coefficients of wings studied herein were obtained by the unsteady vortex-lattice method with Kirchhoff-based correction (UVLM-K). The wind-tunnel measurements presented in the literature were used to validate the UVLM-K. Then, a rectangular wing was simulated at high angles of attack in takeoff and flare, and the aerodynamic characteristics at different heights above ground were obtained along with the derivatives during these maneuvers. The mathematical model presented herein is capable of modeling unsteady aerodynamic phenomena in ground effect at high angles of attack. When this model was used in the static ground effect, values of equal to or greater than 0.999, 0.981, and 0.993 were obtained for lift, induced drag, and pitching moment coefficients, respectively. In the dynamic ground effect, the model can adjust the aerodynamic coefficient during the maneuvers.

Experimental Study on Dynamic Aerodynamic Characteristics of Different Antenna Aspect Ratios with Reduced Frequency

Radar antennas in the open air are affected by dynamic wind loading during azimuthal scanning. In this state, the acquisition and prediction of the aerodynamic load is the focus of the structure design for the antenna. We performed wind tunnel force tests on flat plate antennas with different aspect ratios. The changes in mean, maximum, and root mean square values of the aerodynamic coefficients relative to the antenna aspect ratio and reduced frequency are given for the first time. The effects of the antenna aspect ratio and reduced frequency on aerodynamic characteristics are analyzed. The experimental results indicate that the magnitude of the azimuthal moment is related to the antenna aspect ratio and the reduced frequency. It is worth noting that the antenna aspect ratio has a significant impact on the mean, maximum, and root mean square values of dynamic aerodynamic coefficients. The mean, maximum, and root mean square values of the rolling moment coefficient, azimuth moment coefficient, and pitching moment coefficient monotonously decrease with the increase in aspect ratio. In addition, the influence of reduced frequency on the dynamic aerodynamic coefficient is closely related to the antenna aspect ratio. Under the same antenna aspect ratio, increasing the reduced frequency will increase the mean, maximum, and root mean square values of the aerodynamic coefficient. For flat plate antennas with different aspect ratios, at the condition of increasing the aspect ratios, the mean, maximum, and root mean square values of aerodynamic coefficients do not change significantly with the change of reduced frequency.

Uncertainty quantification of wind turbine airfoil aerodynamics with geometric uncertainty

An artificial neural network based reduced order model (ROM) is developed to predict the load coefficients and performance of wind turbine airfoils. The model is trained using a representative database of 972 wind turbine airfoil shapes generated by perturbing the design parameters in each of 12 baseline airfoils defining commercially relevant modern wind turbines. The predictions from our ROM show excellent agreement with the CFD data, with a 99th percentile maximum errors of 0.03 in lift-coefficient, 2 in lift-to-drag ratio and 0.002 in pitching moment coefficient. A Monte-Carlo based uncertainty quantification (UQ) and global sensitivity analysis (GSA) framework is developed using this computationally economical ROM. Using UQ, we observed the stall behavior to be very sensitive to geometric uncertainty, with more than 10% deviation in lift coefficient associated to 5% deviation in geometric features. Sobol’s analysis is used to identify the most influencing geometric feature for the stall behavior to be concentrated at the maximum thickness location on the airfoil suction surface.

Low speed aerodynamic characteristics of non-slender delta wing at low angles of attack

Low-speed wind tunnel experiments are conducted to study the aerodynamic performance of a half-span delta wing with 45° leading-edge sweep at subsonic flow regime. The experiments are carried out at a Reynolds number of 8.37 × 105, a free-stream Mach number of 0.1 and angles of attack up to 25°, in steps of 5°. The test model was designed with thirty-two pressure taps fixed on its surfaces (sixteen on each side). Multi-tube manometers were connected to these taps using long tubes to enable recording the pressure readings. Surface pressure distributions and aerodynamic characteristics were calculated at different span-wise locations along the non-dimensional chord-wise distance. Results exhibited that most lift on the studied wing is generated in the region close to the leading edge for all the studied incidence angles. Additional lift is created in the region close to the root chord rather than the tip chord, whereas drag forces increases from tip to root. This can be attributed to the formation of trailing edge vortexes due to the flow separation at the wing leading edge that produces more drag, hence suppressing lift. The study showed also that angle of attack increases the drag coefficient from tip to root, especially at high angle of attack, indicating unfavourable behaviour for manoeuvring. Moreover, the angle of attack increased the pitching moment coefficient up to 10° before it drops sharply until it reaches the tip of the wing model.

Trailing Edge Flap Effects on Dynamic Stall Vortex and Unsteady Aerodynamic Forces on a Pitching Airfoil

This study focuses on the effect of the upward deflection of trailing edge flap (TEF) on the strength and trajectory of dynamic stall vortex (DSV) around a pitching airfoil by means of numerical simulations based on unsteady Reynolds-averaged Navier-Stokes (URANS). The effect of the upward deflection of the TEF on the unsteady aerodynamic forces due to DSV is analyzed. The numerical simulation method for large mesh deformation is constructed. Radial basis function- (RBF-) based mesh deformation algorithm, as well as Laplacian and optimization-based mesh smoothing algorithm, is adopted to ensure the mesh quality in flow field simulations. The results reveal that the upward deflection of the TEF can reduce the peaks of drag and pitching moment coefficients. Although the maximum lift coefficient of the airfoil is slightly reduced, its maximum drag and pitching moment coefficients are significantly reduced by up to 34.8% and 31.8%, respectively. The vorticity transport behavior in a planar control region during the DSV formation and detachment is analyzed. It is found that the TEF can change the development process of the DSV. The upward deflection of the TEF reduces the vorticity flux from the leading edge shear layer, which causes the circulation of the DSV and the translational velocity of the vortex center to decline. The peaks of the unsteady aerodynamic forces on the airfoil induced by the DSV are reduced. The upward deflection of the TEF plays the role of alleviating the pitching moment load. The longer TEF can result in a better control effect. The bigger the upward deflection angle of the TEF, the better its control effect.

Influence of pitching motion on the hydrodynamic performance of a horizontal axis tidal turbine considering the surface wave

A CFD numerical method is established under the wave-current condition, used to analyze the hydrodynamic performance of a horizontal-axis tidal turbine based on floating platform with rotation and pitching motion. The inflow direction load, pitch moment and power coefficients with different depths of the blade tip-immersion, the periods and amplitudes of the pitch, wave heights are obtained. The three coefficients have obvious periodically fluctuated with the pitching and wave frequencies, while the time mean of those have changed little with increasing of the depth of blade tip-immersion, wave height, pitch (wave) period and pitching amplitude. So considering damping and additional mass forces, a load fitting model is established, and the damping and additional mass coefficients are calculated by the least square method. The influence of damping coefficient on the hydrodynamic loads is obvious, while the influence of additional mass coefficient on that can be neglected, and the damping coefficient of inflow direction load coefficient is basically stable. The damping coefficients of the pitching moment and power coefficients fluctuate periodically, but the mean value of damping coefficients keep stable. The research results in this paper are important for studying the coupling motion of the turbine and the floating platform.

Combined effects of inlet airflow temperature and upper expansion angle on the performance of scramjet nozzle

PurposeThe purpose of this paper is to study the combined effects of inlet airflow temperature and the expansion angle of the upper expansion surface (upper expansion angle) on the performance of the scramjet nozzle.Design/methodology/approachThe Spalart-Allmaras turbulence two-dimensional model of the nozzle is established for the study. The influence of inlet airflow temperature on the performance of the nozzle is analyzed by detecting the change of the wall pressure of the nozzle. The three angles are chosen for the upper expansion angle (βb) in the model: 8°, 12° and 16°. The temperature of inlet airflow is 600–1,800 K.FindingsThe study results show that when the βb is 8° and 16°, the wall pressure of the nozzle has a complicated and large fluctuation with the inlet airflow temperature, while the wall pressure has little change as βb is 12°; the thrust coefficient, pitching moment coefficient and lift coefficient of the nozzle fluctuate greatly with the increase of the inlet airflow temperature when βb is 8° and 16°, while the thrust coefficient, pitching moment coefficient and lift coefficient have little fluctuation as βb is 12°.Originality/valueThe study of the combined effects of the inlet airflow temperature and upper expansion angle on the performance of the scramjet nozzle can provide guidance for the design of scramjet nozzles.

Parameterizing Airfoil Shape Using Aerodynamic Performance Parameters

A novel shape parameterization for airfoils (named as PAERO) is proposed to provide design variables related to the aerodynamic characteristics based on the linearized aerodynamic theory. The idea is inspired by the classical thin airfoil theory. Instead of describing the airfoil geometry explicitly, the mean camber line of an airfoil can be implicitly defined by the vortex distribution on the chord line that is expressed by a Fourier series in the thin airfoil theory. The Fourier series is parameterized by the Fourier coefficients specified by users. Within the frame of linearized aerodynamic theory, the first three Fourier coefficients are determined by the angle of attack, lift coefficient, and pitching moment coefficient, naturally providing three aerodynamic performance parameters. Then, the airfoil shape parameterization is completed by further parameterizing the thickness distribution by either the Class-Shape-Transformation method or the B-splines, depending on the specific applications. The test results show that the proposed shape parameterization has the same ability of fitting the existing airfoils as the traditional Class-Shape-Transformation method, but providing more aerodynamic performance parameters that are proved to be highly useful in applications.

A rectangular strut on the expansion ramp of a scramjet thruster for thrust vector control

Cold flow experiments were conducted on a laboratory model of a scramjet thruster consisting of a rectangular strut spanning the width of the expansion ramp of the model. The cross section of the strut was square. The strut was placed at halfway of the ramp length. The experiments were conducted at six different thruster pressure ratios (TPR) i.e., the ratio of inlet total pressure to ambient pressureranging from 5 to 10 at each of six strut heights. The internal wall pressure distributions of the thruster and schlieren images of the flow obtained from experiments were examined. The possibility of using the strut as a supplementary device in the thruster for the control of a hypersonic vehicle which normally employs aerodynamic control was studied. The inlet Mach number of the combustor was 1.8. The thruster model consisted of an isolator, a diverging area combustor and a single expansion ramp. The inlet flow to the thruster was provided by a supersonic nozzle with a rectangular exit of matching dimensions to the rectangular isolator. The diverging combustor was of rectangular cross section, the bottom wall being flat and the upper wall making an inclination of 2.44oto the bottom wall. From the top and bottom wall pressure distributions, two-dimensional internal force coefficients and pitching moment coefficients were calculated and variation of these coefficients with strut height were studied. Larger strut heights caused an increase in side force coefficient at all expansion levels of the ramp nozzle i.e., for all the TPRs employed in the present work (5–10). The variation of pitching moment coefficient with strut height exhibited the similar behavior as that of the side force coefficient. Shifting of strut position from expansion ramp tail end to the ramp mid position did not affect the nature of these variations. These variations were in general nonlinear in nature but the degree of non-linearity varied based on the value of TPR. Larger non linearity in side force coefficient variation was observed at TPRs 5,9 and 10. Larger moment coefficients resulted at lower TPR for the mid ramp position of the strut when compared to ramp tail end position. Large strut heights caused noticeable downward deflection of ramp surface flow. Calculations using the experimental data on wall pressure in the range of strut height variation employed in the present experiments indicate that increments up to 12% in moment coefficient, 20% in side force coefficient and 4% in axial force coefficients were achieved when the strut height was increased to its maximum value (12% of combustor entry section hydraulic diameter). Schlieren images show that the exhaust flow over the expansion ramp suffered a downward deflection and the strut position & height affected the magnitude of the deflection.

Propeller Position Effects over the Pressure and Friction Coefficients over the Wing of an UAV with Distributed Electric Propulsion: A Proper Orthogonal Decomposition Analysis

New propulsive architectures, with high interactions with the aerodynamic performance of the platform, are an attractive option for reducing the power consumption, increasing the resilience, reducing the noise and improving the handling of fixed-wing unmanned air vehicles. Distributed electric propulsion with boundary layer ingestion over the wing introduces extra complexity to the design of these systems, and extensive simulation and experimental campaigns are needed to fully understand the flow behaviour around the aircraft. This work studies the effect of different combinations of propeller positions and angles of attack over the pressure coefficient and skin friction coefficient distributions over the wing of a 25 kg fixed-wing remotely piloted aircraft. To get more information about the main trends, a proper orthogonal decomposition of the coefficient distributions is performed, which may be even used to interpolate the results to non-simulated combinations, giving more information than an interpolation of the main aerodynamic coefficients such as the lift, drag or pitching moment coefficients.

Design, Manufacture and Wind Tunnel Test of a Modular FishBAC Wing with Novel 3D Printed Skins

This paper introduces a new modular Fish Bone Active Camber morphing wing with novel 3D printed skin panels. These skin panels are printed using two different Thermoplastic Polyurethane (TPU) formulations: a soft, high strain formulation for the deformable membrane of the skin, reinforced with a stiffer formulation for the stringers and mounting tabs. Additionally, this is the first FishBAC device designed to be modular in its installation and actuation. Therefore, all components can be removed and replaced for maintenance purposes without having to remove or disassemble other parts. A 1 m span, 0.27 m chord morphing wing with a 25% chord FishBAC was built and tested mechanically and in a low-speed wind tunnel. Results show that the new design is capable of achieving the same large changes in airfoil lift coefficient (approximate ΔCL≈0.55) with a low drag penalty seen in previous FishBAC work, but with a much simpler, practical and modular design. Additionally, the device shows a change in the pitching moment coefficient of ΔCM≈0.1, which shows the potential that the FishBAC has as a control surface.

Unsteady Aerodynamic Modeling and Analysis of Load Distribution for Helicopter Rotor Blades

The complexity of the kinematics and aerodynamics of rotors is a challenging problem for achieving accurate modeling for prediction of rotor loads. The present paper describes an unsteady aerodynamic model based on strip theory for the prediction of local aerodynamic loads on helicopter blades in translational flights. The proposed model accounts aerodynamically for unsteady behavior, poststall, leading-edge suction, and, structurally, local elastic torsion. Also, the local pitching moment coefficient is calculated according to the local parameters of both aerodynamic characteristics and unsteady angle of attack. A case study with published experimental data is selected to validate the model for the same operating conditions. The case is the 7A rotor high-speed test (point 312) performed in the French Space Lab’s (ONERA) S1MA wind tunnel in Modane-Avrieux, France. The proposed model is capable of predicting, qualitatively, the variation in both local normal force and pitching moment coefficients. Computational solver results are compared with experimental results to qualitatively clarify the physical differences between them. The main conclusion is that the proposed model calculations generally reflect the same trends as the test data, providing confidence in the ability to increase the model’s fidelity in calculating the aerodynamic behavior of rotors.