Pitching moment

About: Pitching moment is a research topic. Over the lifetime, 3213 publications have been published within this topic receiving 38721 citations.

The Estimation of Normal-Force, Drag, and Pitching-Moment Coefficients for Blunt-Based Bodies of Revolution at Large Angles of Attack

Abstract: : A method is developed which accurately predicts for blunt-based bodies of revolution the normal force coefficient and the pitching moment coefficient for angles of attack far beyond the range of potential theory. It is based on the principle of superposition of the results of potential theory and the viscous force on a cylindrical body due to the transverse component of flow. In contrast to previously used methods, the viscous cross force is assumed not to be in a steady state, but in a transient development along the body. The method is compared with experimental data for both subsonic and supersonic flows and with both laminar and turbulent axial boundary layers. The method is also useful for extrapolation of small-yaw data to large yaws and to different Reynolds numbers. The results presented have been applied only in the range M = 0 to M = 2.87 and for a limited range of Reynolds numbers.

RANS-based Aerodynamic Shape Optimization Investigations of the Common Research Model Wing

Abstract: The aerodynamic shape optimization of transonic wings requires Reynolds-averaged Navier–Stokes (RANS) modeling due to the strong nonlinear coupling between airfoil shape, wave drag, and viscous effects. While there has been some research dedicated to RANS-based aerodynamic shape optimization, there has not been an benchmark case for researchers to compare their results. In this investigations, a series of aerodynamic shape optimizations of the Common Research Model wing defined for the Aerodynamic Design Optimization Workshop are presented. The computational fluid dynamics solves Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. The drag coefficient at the nominal flight condition is minimized subject to lift, pitching moment and geometric constraints. A multilevel acceleration technique is used to reduce the computational cost. A total of 768 shape design variables are considered, together with a grid with 28.8 million cells. The drag coefficient of the optimized wing is reduced by 8.5% relative to the baseline. The single-point design has a sharp leading edge that is prone to flow separation at off-design conditions. A more robust design is achieved through a multipoint optimization, which achieves more reliable performance when lift coefficient and Mach number are varied about the nominal flight condition. To test the design space for local minima, randomly generated initial geometries are optimized, and a flat design space with multiple local minima was observed.

Experimental investigation of side-jet steering for supersonic and hypersonic missiles

Abstract: An experimental investigation of the interaction between a side jet and the external flow is presented. The experiments were carried out in three different wind tunnels at supersonic and hypersonic Mach numbers ranging from 2 to 10. The model used in all the experiments consisted of a cylindrical body and various ogival nose sections, and had no lifting surfaces. The single sonic jet nozzle was located on the lee side of the cylindrical center body section with respect to a positive angle of attack. Several nozzle shapes and jet injection angles were examined. Forces and moments were measured directly in all the experiments, and surface pressure surveys were taken in some supersonic experiments. The results reveal a small jet force amplification at supersonic and hypersonic Mach numbers around zero angle of attack. Significant amplification because of positive angle of attack was noted at hypersonic speeds. The injection nozzle shape and vector angle can have a noticeable effect on the magnitude of the jet force amplification, especially at hypersonic speeds. In addition, the interaction gives rise to a significant pitching moment that may be utilized to produce an additional aerodynamic control force.

Aerodynamic loads on airfoil with trailing-edge flap pitching with different frequencies

Abstract: Unsteady aerodynamic loads on NACA 0012 airfoil with a trailing-edge flap were measured in wind tunnel and calculated from a simple theoretical model. The airfoil model of 0.18 m chord length used in wind-tunnel test was oscillating in pitch about an axis located at 35% chord length from the airfoil leading edge. The length of trailingedge flap was 22.6% of airfoil chord. The flap was also deflecting harmonically, but with frequency different from airfoil pitching motion. The influence of phase delay between airfoil angle of incidence and flap deflection at the beginning of the motion was considered. The theoretical method used for calculation of unsteady airfoil loads is based on two-dimensional, inviscid, incompressible flow model at subsonic Mach numbers. The expressions for unsteady aerodynamic loads calculations on the airfoil and on the flap were obtained in a closed form using distribution of flow velocity potential along the airfoil chord and along the flap length. Lift and aerodynamic moment measured in the wind tunnel were compared with results of calculations. The correlation between experimental and theoretical results is adequate.

A predictive quasi-steady model of aerodynamic loads on flapping wings

Abstract: Quasi-steady aerodynamic models play an important role in evaluating aerodynamic performance and conducting design and optimization of flapping wings. The kinematics of flapping wings is generally a resultant motion of wing translation (yaw) and rotation (pitch and roll). Most quasi-steady models are aimed at predicting the lift and thrust generation of flapping wings with prescribed kinematics. Nevertheless, it is insufficient to limit flapping wings to prescribed kinematics only since passive pitching motion is widely observed in natural flapping flights and preferred for the wing design of flapping wing micro air vehicles (FWMAVs). In addition to the aerodynamic forces, an accurate estimation of the aerodynamic torque about the pitching axis is required to study the passive pitching motion of flapping flights. The unsteadiness arising from the wing’s rotation complicates the estimation of the centre of pressure (CP) and the aerodynamic torque within the context of quasi-steady analysis. Although there are a few attempts in literature to model the torque analytically, the involved problems are still not completely solved. In this work, we present an analytical quasi-steady model by including four aerodynamic loading terms. The loads result from the wings translation, rotation, their coupling as well as the added-mass effect. The necessity of including all the four terms in a quasi-steady model in order to predict both the aerodynamic force and torque is demonstrated. Validations indicate a good accuracy of predicting the CP, the aerodynamic loads and the passive pitching motion for various Reynolds numbers. Moreover, compared to the existing quasi-steady models, the presented model does not rely on any empirical parameters and thus is more predictive, which enables application to the shape and kinematics optimization of flapping wings.