Pitching Moment Research Articles

Aerodynamic Characteristics of a Z-Shaped Folding Wing

Z-shaped folding wings have the potential to enhance the flight performance of an aircraft, contingent upon its mission requirements. However, the current scope of research on unmanned aerial vehicles (UAVs) with Z-shaped folding wings primarily focuses on the analysis of their folding structure and aeroelasticity-related vibrations. Computational fluid dynamics methods and dynamic meshing are employed to examine the folding process of Z-shaped folding wings. By comparing the steady aerodynamic characteristics of Z-shaped folding wings with those of conventional wings, this investigation explores the dynamic aerodynamic properties of Z-shaped folding wings at varying upward folding speeds. The numerical findings reveal that the folding of Z-shaped folding wings reduces the lift-to-drag ratio, yet simultaneously diminishes the nose-down pitching moment, thereby augmenting maneuverability. Concerning unsteady aerodynamics, the transient lift and drag coefficients of the folded wing initially increase and subsequently decrease as the folding angle increases at small angles of attack. Likewise, the nose-down pitching moment exhibits the same pattern in response to the folding angle. Additionally, the aerodynamic coefficients experience a slight decrease during the initial half of the folding process with increasing folding speed. Once the wing reaches approximately 40°~45° of folding, there is an abrupt change in the transient aerodynamic coefficients. Notably, this abrupt change is delayed with higher folding speeds, eventually converging to similar values across different folding speeds.

Efficient Global Aerodynamic Shape Optimization of a Full Aircraft Configuration Considering Trimming

Most existing aerodynamic shape optimization (ASO) studies do not take the balanced pitching moment into account and thus the optimized configuration has to be trimmed to ensure zero pitching moment, which causes additional drag and reduces the benefit of ASO remarkably. This article proposes an efficient global ASO method that directly enforces a zero pitching moment constraint. A free-form deformation (FFD) parameterization combing Laplacian smoothing method is implemented to parameterize a full aircraft configuration and ensure sufficiently smooth aerodynamic shapes. Reynolds-averaged Navier–Stokes (RANS) equations are solved to simulate transonic viscous flows. A surrogate-based multi-round optimization strategy is used to drive ASO towards the global optimum. To verify the effectiveness of the proposed method, we adopt two design optimization strategies for the NASA Common Research Model (CRM) wing–body–tail configuration. The first strategy is to optimize the configuration without considering balance of pitching moment, and then manually trim the optimized configuration by deflecting the horizontal tail. The second one is to directly enforce the zero pitching moment constraint in the optimization model and take the deflection angle of the horizontal tail as an additional design variable. Results show that: (1) for the first strategy, about 4-count drag-reducing benefits would be lost when manually trimming the optimal configuration; (2) the second strategy can achieve 3.2-count more drag-reducing benefits than the first strategy; (3) compared with gradient-based optimization (GBO), surrogate-based optimization (SBO) is more efficient than GBO for ASO problems with around 80 design variables, and the benefit of ASO achieved by SBO is comparable to that obtained by GBO.

Effects of pitch angle on a near free surface underwater vehicle

Simulations of an underwater vehicle were conducted to investigate the effects of steady pitch angle, Froude number, and submergence depth. A shallow submerged (D* = 1.1) to a deeply submerged (D* = 6.6) SUBOFF was investigated over a range of steady pitch angles and Froude numbers. Results show that proximity to the free surface causes increased resistance, heave and pitch moment and that free surface effects diminish rapidly with increased submergence depth. Even though D* = 3.3 is typically quoted as being the deeply submerged threshold, free surface effects can still be observed especially at large pitch angles. At pitch angle, asymmetry can be seen between the pressure distribution of the upper and lower surfaces of the SUBOFF, with a phase shift of the hydrodynamic forces and moments. At smaller pitch angles, the changes in hydrodynamic forces and moments stay relatively linear at an offset from zero degrees. At larger pitch angles, the hydrodynamic forces and moments become non-linear due to crossflow separation and air entrainment over the bow/stern. Additionally, the potential of the stern planes to cope with free surface effects were investigated, showing the safety threshold with respect to Froude number, submergence depth, and hull pitch angle.

Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

Forebody Articulation at High Angles of Incidence

An experimental investigation was carried out to understand the effect of forebody articulation on the aerodynamic characteristics and the flowfield development over a slender body at high angles of incidence. The experiments were carried out at the Florida A&M University and Florida State University low-speed wind tunnel over a range of forebody deflection (, , and ) and flow conditions. The results show that a positive forebody deflection increases the normal-force coefficient, whereas a negative forebody deflection decreases the normal-force coefficient at high angles of incidence. Pitching moment characteristics showed that all forebody deflections tested produce a pitching moment despite minimal normal force at low angles of incidence. Lateral aerodynamic characteristics showed that the side-force onset angle does not solely depend on the semi-apex angle of the forebody (as predicted for axisymmetric slender bodies), and the role of the forebody-to-aftbody transition geometry in initiating vortex asymmetry is equally important. The particle image velocimetry results show that a positive forebody deflection increases the size, strength, and circulation of the vortices developing on the body, leading to an increase in aerodynamic forces and moments. The flowfield development for a negative forebody deflection is dominated by secondary shear-layer vortices originating from the forebody to aftbody junction.

Flight Load Calculation Using Neural Network Residual Kriging

Flight load calculation, an important step in aircraft design and optimization, typically involves millions of computations and requires significant computing resources and time. Improving the efficiency of flight load calculations while maintaining accuracy is therefore of great significance for shortening research and development cycles. This study investigated and compared multiple algorithms, including the neural network model, the Kriging surrogate model, and the neural network residual Kriging (NNRK) model, for flight load analysis. The accuracies of all models were confirmed through evaluation, with NNRK being the most efficient, making it highly suitable for flight load analysis. The flight load data of a civil aircraft, including the total weight, the center of gravity, the pitch moment of inertia, the altitude, the Mach number, the airspeed, the velocity pressure, the pitch rate, the load factor, and the angle of attack as input parameters, were used as sample data to establish models, for predicting wing loads under different flight conditions. The accuracies of all regressions were confirmed through evaluation, with NNRK being the most efficient. The flight load calculation shows that NNRK can significantly improve analysis efficiency and provide new insights into efficient and comprehensive flight load analysis.

High-fidelity modelling of lift-based wave energy converters in a numerical wave tank

This work presents the development of a numerical model for the investigation of lift-based wave energy converter (lift-WEC) hydrodynamics. The developed model, based on the RANS equation, is validated regarding its ability to replicate foil-flow interaction in various conditions based on experimental references from literature. Limitations of the numerical model are discussed, such as the overprediction of stall angles at low Reynolds numbers and the possibility of artificial rotor ventilation near the free surface. Within the range of relevant operating conditions for a lift-WEC, the model is found to replicate experimental results with good accuracy. Subsequently, a particularity of the cyclorotor WEC concept is investigated: Load measurements in calm water showed positive tangential forces, apparently indicating the generation of thrust in the absence of external energy sources. Numerical simulations reveal that this is the result of a significant azimuthal shift of the hydrodynamic load centre for non-zero pitch and that the consideration of foil pitch moments is required in order to obtain accurate shaft torque predictions. The hydrodynamic coefficients of the cyclorotor foils are compared with coefficients obtained for symmetrical foils in straight flight. It is shown that the assumption of similarity, which is often applied when modelling these devices in semi-analytical tools, is only valid for small angles of attack.

Performance analysis and flow mechanism of channel wing considering propeller slipstream

The development of the Urban Air Mobility concept has proposed stringent requirements for the fixed-wing vehicle’s Short/Vertical Take-Off and Landing (S/VTOL) performance. With its lift-enhancing impact, the channel wing, can improve aircraft low-speed performance and Short Take-Off and Landing (STOL) capability. It is critical for the performance analysis and flow mechanism study of a channel wing that considers the influence of propeller slipstream to guide the design of S/VTOL aircraft. The law and mechanism for the effect of the enclosing angle of the arc wing, the phase angle of the propeller, the tip clearance, the rotational speed and the chordwise position of the propeller on the channel wing are explored utilizing the quasi-steady multi reference frame method. A channel wing with a larger enclosing angle has a better ability to enhance lift and reduce drag using propeller slipstream. The effect of propeller phase angle on channel wing aerodynamic forces is periodic and weak. Increasing propeller rotational speed is helpful to enhance lift and resist flow separation for channel wing. It can reduce drag for tractor configuration but increase drag for pusher configuration. However, the nose-down pitching moment of a channel wing will grow dramatically, making longitudinal trimming in aircraft layout design challenging.

Robotic Hummingbird Axial Dynamics and Control near Hovering: A Simulation Model

After a short overview of the COLIBRI project, this paper considers the cycle-averaged flight dynamics of a flapping-wing robot near hovering, taking advantage of the weak coupling between the roll and pitch axes. The system is naturally unstable; it needs to be stabilized actively, which requires an attitude reconstruction. Due to the flapping of the wings, the system is subject to a strong periodic noise at the flapping frequency and its higher harmonics; the resulting axial forces and pitch moments are characterized from experimental data. The flapping noise propagates to the six-axis Inertial Measurement Unit (IMU) consisting of three accelerometers and three gyros. The paper is devoted to attitude reconstruction in the presence of flapping noise representative of flight conditions. Two methods are considered: (i) the complementary filter based on the hovering assumption and (ii) a full-state dynamic observer (Kalman filter). Unlike the complementary filter, the full-state dynamic observer allows the reconstruction of the axial velocity, allowing us to control the hovering without any additional sensor. A numerical simulation is conducted to assess the merit of the two methods using experimental noise data obtained with the COLIBRI robot. The paper discusses the trade-off between noise rejection and stability.

Numerical and Experimental Investigation on Nosebleed Air Jet Control for Hypersonic Vehicle

A new idea of nosebleed air jets with strong coupled internal and external flow is put forward using the lateral jet control principle to improve the maneuverability and fast reaction capabilities of hypersonic vehicles. The hypersonic vehicle’s nose stagnant high-pressure and high-temperature gas is utilized as the drive source for long-term jet control. The significant coupled jet interaction of the internal and external flow changes the aerodynamic characteristics. As a result, the structure is basic and does not rely on any external source to achieve flight attitude control. The complicated flow characteristics of the nosebleed jet in supersonic crossflow surrounding the vehicle were numerically and experimentally investigated. The jet interaction characteristics and the aerodynamic characteristic changes generated by the nosebleed air jet are verified by comparing the flow field with and without the jet. Results indicate that the nosebleed air jet alters the center-of-pressure coefficient, which is subsequently coupled with the interference aerodynamic force. This results in a variation in pitch moment. The jet decreases the pitching moment coefficient when compared with the case without a jet. It is probable that combining nosebleed air jets with model centroid adjustment yields an optimal trim angle of attack.

Comparative analysis of closed-form expressions and other commonly used seakeeping methods

Closed-form expressions (CFE) are semi-analytical transfer functions for ship wave-induced responses based only on main ship particulars. They are useful in an early stage of ship design and situations when hull lines for seakeeping analysis are not available. As the accuracy of CFE remains an open subject, the aim of the present study is to quantify the frequency independent model error (FIME) of CFE. Measured transfer functions of the heave, pitch, and vertical wave bending moment at midship for 13 ships are acquired from literature, together with calculated transfer functions using the strip theory and the 3D panel method, where several speeds and heading angles are available. FIME is determined by comparing transfer functions calculated by CFE, strip theory, and 3D panel codes with model-scale experiments. Multivariate linear regression analysis is performed for three seakeeping methods to indicate a dependence of FIME on the main parameters of the analysis. Dispersion of the FIME around the regression line is determined, enabling a relative comparison of the uncertainty of seakeeping methods of different complexity. The results of this study may improve the practical applicability of CFE and provide an uncertainty quantification of commonly used seakeeping methods, which is important for probability-based applications.

Influence of differential longitudinal cyclic pitch on flight dynamics of coaxial compound helicopter

The Differential Longitudinal Cyclic Pitch (DLCP) in coaxial compound helicopter is found to be useful in mitigating low-speed rotor interactions and improving flight performance. The complex mutual interaction is simulated by a revised rotor aerodynamics model, where an improved Blade Element Momentum Theory (BEMT) is proposed. Comparisons with the rotor inflow distributions and aircraft trim results from literature validate the accuracy of the model. Then, the influence of the DLCP on the flight dynamics of the aircraft is analysed. The trim characteristics indicate that a negative DLCP can reduce collective and differential collective inputs in low speed forward flight, and the negative longitudinal gradient is alleviated. Moreover, a moderate DLCP can reduce the rotor and total power consumption by 4.68% and 2.9%, respectively. As DLCP further increases, the increased propeller power and unbalanced thrust allocation offset the improvement. In high-speed flight, DLCP does not improve the performance except for extra lateral and heading stick displacements. In addition, the tip clearance is degraded throughout the speed envelope due to the differential pitching moment and the higher thrust from the lower rotor. Meanwhile, the changed rotor efficiency and induced velocity alter low-speed dynamic stability and controllability. The pitch and roll subsidences are slightly degraded with the DLCP, while the heave subsidence, dutch roll and phugoid modes are improved. Lastly, the on-axis controllability, including collective, differential collective pitch, longitudinal and lateral cyclic pitches, varies with DLCP due to its effect on rotor efficiency and inflow distribution. In conclusion, a reasonable DLCP is recommended to adjust the rotor interaction and improve aircraft performance, and further to alter the flight dynamics and aerodynamics of aircraft.

An Improved Emergency Blow Theoretical Model for Naval Submarine Blowing System and Experimental Verification

_ An improved emergency blow model is proposed, which is based on the traditional emergency blow model and takes into account the influence of compressed air overflows from flood holes in the later stage of blowing. In order to verify the prediction accuracy of the improved emergency blow model for tank blowing, the full-scale model experiment of tank blowing was conducted to investigate the effects of air source volume, air source initial pressure, and flood holes diameters on blowing. The process of air release from bottle and main ballast tank drainage can be accurately simulated by the improved emergency blow model, and the prediction error of tank air peak pressure is shown to be <10%. Additionally, it is found that the air source volume has no effect on the tank’s air peak pressure or tank drainage rate. By analyzing the dynamic characteristics of tank air pressure, it is found that the dynamic change trend of air pressure differs between flood holes with small and large diameters. In the small diameter conditions, the air pressure reaches the maximum when the compressed air just enters the tank; however, under large diameter conditions, the peak pressure comes before the accumulated air pressure is released. The experiment and simulation demonstrate that increasing the area of the flood holes has a decreasing effect on the amount of air accumulated in the tank, and that the decreasing effect becomes more pronounced as the air source initial pressure increases. Introduction To carry out military operations, submarines are deployed both underwater and close to the open surface. About 170 submarines have sunk since they were originally created as a result of an accident, such as a fire, explosion, malfunction, grounding, or collision (Park & Kim 2017). Submarines run the risk of losing safety control in these critical situations. The best method of self-rescue is emergency floating to the surface to prevent bottoming or going deeper than allowed (Liu et al. 2009). A key factor in emergency rising to the water’s surface is the compressed air blowing mechanism. In such an operation, supplying air to the main ballast tank and blowing out ballast water should be used to achieve positive buoyancy or recover a positive pitching moment, which can be used to restore the safe depth of the submarine. Emergency blow is the term used to describe the process of directly supplying air to the main ballast tank without using a high-pressure valve column. The emergency blow is explored in this work because its influence is significantly greater than that of usual blowing, or traditional blowing.

The Effect of a Linear Free Surface Boundary Condition on the Steady-State Wave-Making of Shallowly Submerged Underwater Vehicles

Near-surface simulation methods for shallowly submerged underwater vehicles are necessary for the population of a variety of free-surface-affected, coefficient-based maneuvering and seakeeping models. Simulations vary in complexity and computational costs, often sacrificing accuracy for simplicity and speed. One particular simplifying assumption, the linearization of the free surface boundary conditions, is explored in this study by comparing the steady-state wave-making characteristics of a shallowly submerged prolate spheroid using two different simulation methods at several submergence depths and forward speeds. Hydrodynamic responses are compared between a time-domain boundary element method that makes use of a linearized free surface boundary condition and an inviscid, volume of fluid Reynolds-Averaged Navier–Stokes computational fluid dynamics code that imposes no explicit free surface boundary condition. Differences of up to 22.6%, 32.5%, and 33.3% are found in the prediction of steady state surge force, heave force, and pitch moment, respectively. The largest differences between the two simulation methods arise for motions occurring at small submergences and large wave-making velocities where linear free-surface assumptions become less valid. Nonlinearities that occur in such cases are revealed through physical artifacts such as wave steepening, wave breaking, and high-energy waves. A further examination of near-surface viscous forces reveals that the viscous drag on the vessel is depth dependent due to the changing velocity profile around the body.

Study on fast prediction method of hydrodynamic load of floating horizontal axis tidal current turbine with pitching motion under free surface

The floating horizontal-axis tidal current turbine (HATCT) moves with the floating carrier while rotating, resulting in a change in its relative inflow velocity at any time. If the rotating speed of the HATCT is fixed, the HATCT cannot work at the optimum tip speed ratio, resulting in the failure to achieve the optimum power generation efficiency. Therefore, this paper proposes a control strategy for the rotating speed of the HATCT, and obtains the hydrodynamic loads of the HATCT with variable speed rotation and pitching motion under free surface conditions based on the CFD method. Compared with the hydrodynamic load of the HATCT under the same situation but with fixed speed control, the variable speed control can effectively improve the power coefficient of the HATCT, but the load fluctuation in terms of the inflow direction load, power, and pitch moment coefficients are more significant than those with fixed speed control. On this basis, according to the variation law of the damping coefficient with pitch period, pitch amplitude, and tip speed ratio, the hydrodynamic load prediction method of the HATCT with pitching motion is established. The validity of this prediction method is verified by comparing the results with those of CFD calculation.

The cubic pitching moment coefficient of spin-stabilized projectiles

This technical note presents a feasible method to effectively predict the cubic pitching moment coefficient for spin-stabilized projectiles. First, a surrogate model for predicting the cubic moment coefficient is constructed by using the Kriging method to relevant published data of several typical spin-stabilized projectiles. The result of a wind tunnel test validates the accuracy of the Kriging prediction, implying that this prediction model complements the current research literature. Second, the global sensitivity analysis combined with this prediction model is used to assess the effect of the shape parameters of spin-stabilized projectiles on the cubic pitching moment coefficient. As a result, the relationship between the shape parameters and the nonlinear pitching moment coefficient is preliminarily explored. The results of an example show that the cylindrical part length, the head shape parameter and the nose length have greater influence, whereas the boat-tail length has the weakest influence.

Computational Fluid Dynamics Modeling Analysis of a Martian Rotorcraft With Individual Blade Control

Abstract Computational fluid dynamics (CFD) analysis was conducted on a proposed blade root-actuated individual blade control (IBC) system for future Martian rotorcraft. IBC offers many potential benefits to rotary-winged exploration of Mars, including precision control of rotor blade forces. This study seeks to provide an estimate of rotor blade force and system power as a basis for concept feasibility analysis and experimental prototyping. ansys fluent was used to compute blade pitching moment, lift, and drag under various feathering waveforms, amplitudes, biases, and frequencies. It is determined that the rapid feathering characteristic of IBC has a non-negligible impact on blade forces. It is also found that actuators with power ratings on the order of 101 W are likely sufficient for blade actuation on Martian rotorcraft.

Effect of a Secondary Injection on the Performance of Three-Dimensional Over-under TBCC Exhaust Nozzles

A numerical simulation is used to investigate the flow field characteristics of a three-dimensional over-under turbine-based combined cycle circular-to-rectangular transition exhaust nozzle when only the turbojet flowpath is in operation. The effect on the exhaust nozzle performance of there being a secondary injection on the ramp of the expansion section of the turbojet flow path is then examined. Finally, the impact of variations in the secondary injection design parameters is further investigated. The results show that a secondary injection can improve the exhaust nozzle's performance by reducing the axial force on the inner wall of the flow path. However, changes in flight status can undermine this improvement. Under the baseline operating condition, a secondary injection with a larger angle and close to the ramp outlet can produce a more significant improvement in nozzle performance. In this study, the axial thrust coefficient, lift and pitch moment of the nozzle can be improved by a maximum of 9.312%, 66.007% and 10.975%, respectively.

Dynamic Analysis of Underwater Torpedo during Straight-Line Navigation

Torpedoes play an irreplaceable role in naval warfare; therefore, it is significant to study the dynamic response of the direct navigation of torpedoes. In order to study the dynamic response of torpedoes under different Munk moment coefficients, the dynamic equation of torpedoes is established based on the momentum theorem and the momentum moment theorem. The linear motion mathematical model of torpedoes is obtained. The relationship between the torpedo and the Munk moment coefficient is derived. The straight-line motion model of the torpedo under different Munk moments is established, and the dynamic properties of the space motion of the torpedo are analyzed. It is found that the Munk moment coefficient increase will lead to an increase in the deflection of the torpedo’s direct motion on each degree of freedom, and the Munk moment coefficient is related to the additional mass matrix. During the design of the torpedo, the added mass should be reduced by changing the shape of the torpedo as much as possible so as to reduce the pitch moment, yaw, and roll moments of the torpedo.

HLPW-4: Wall-Modeled Large-Eddy Simulation and Lattice–Boltzmann Technology Focus Group Workshop Summary

A summary of the nine submissions to the Wall-Modeled Large-Eddy Simulation and Lattice–Boltzmann (WMLESLB) Technical Focus Group (TFG) at the 4th High lift Prediction Workshop is provided. The focus of this TFG was to assess the current capabilities of WMLES and LB methods on a complex high-lift configuration across a wide range of angles of attack. Analysis of the submitted data suggests that >250 M spatial degrees of freedom are needed to accurately predict pitching moments at high angles of attack due to large pressure gradients present on the outboard slat and main element for α>17° (corrected for free-air). While some scatter is reported in pitching moment coefficient at the low-angles of attack (α<11°), excellent agreement is observed between submissions near the CL,max state. Objective superiority of WMLES methods over Reynolds-averaged Navier–Stokes (RANS) can be seen in terms of lack of excess outboard separation; a majority of the WMLES and LB submissions predict wedge-shaped separation patterns consistent with the experimental oil flow. The in-tunnel simulations show excellent agreement with the experiment in terms of a) integrated loads, b) surface flow-topology, and c) mechanism for the onset of inboard stall. Further evidence is provided to demonstrate both qualitative and quantitative superiority of the WMLES submissions over RANS.