Theoretical analysis of perching and hovering maneuvers

Unsteady aerodynamic phenomena are encountered in a large number of modern aerospace and non-aerospace applications. Leading edge vortices (LEVs) are of particular interest because of their large impact on the forces and performance. In rotorcraft applications, they cause large vibrations and torsional loads (dynamic stall), affecting the performance adversely. In insect flight however, they contribute positively by enabling high-lift flight. Identifying the conditions that result in LEV formation and modeling their effects on the flow is an important ongoing challenge. Perching (airfoil decelerates to rest) and hovering (zero freestream velocity) maneuvers are of special interest. In earlier work by the authors, a Leading Edge Suction Parameter (LESP) was developed to predict LEV formation for airfoils undergoing arbitrary variation in pitch and plunge at a constant freestream velocity. In this research, the LESP criterion is extended to situations where the freestream velocity is varying or zero. A point-vortex model based on this criterion is developed and results from the model are compared against those from a computational fluid dynamics (CFD) method. Abstractions of perching and hovering maneuvers are used to validate the low-order model's performance in highly unsteady vortex-dominated flows, where the time-varying freestream/translational velocity is small in magnitude compared to the other contributions to the velocity experienced by the leading edge region of the airfoil. Time instants of LEV formation, flow topologies and force coefficient histories for the various motion kinematics from the low-order model and CFD are obtained and compared. The LESP criterion is seen to be successful in predicting the start of LEV formation and the point-vortex method is effective in modeling the flow development and forces on the airfoil. Typical run-times for the low-order method are between 30-40 seconds, making it a potentially convenient tool for control/design applications

Phen­yl(3-methyl-1-phenyl­sulfonyl-1H-indol-2-yl)methanone

In the title compound, C22H17NO3S, the N atom of the indole ring system deviates by 0.031 (3) Å from a least-squares plane fitted through all nine non-H ring atoms. The geometry around the S atom can be described as distorted tetra­hedral. As a result of the electron-withdrawing character of the phenyl­sulfonyl groups, the N—Csp 2 bond lengths are longer than the typical mean value for N atoms with a planar configuration

Hydrophilic nanoparticles stabilising mesophase curvature at low concentration but disrupting mesophase order at higher concentrations

Silica nanoparticles form aggregates at mesophase domain boundaries, which may suppress or promote curvatures depending on the nanoparticle concentration.</p

tert-Butyl 3-[2,2-bis­(ethoxy­carbon­yl)­vinyl]-2-methyl-1H-indole-1-carboxyl­ate

In the title compound, C22H27NO6, the indole ring system is planar and the ethoxy­carbonyl chains adopt extended conformations. In the crystal, inversion dimers linked by pairs of C—H⋯O hydrogen bonds occur, resulting in R 2 2(16) dimers, which are inter­linked into a chain propagating along the a axis by π–π stacking inter­actions [centroid–centroid distance 3.5916 (9) Å]

2,5-Dimethyl-1-phenyl­sulfonyl-1H-pyrrole-3,4-dicarbaldehyde

In the title compound, C14H13NO4S, the mean planes of the pyrrole and phenyl rings form a dihedral angle of 88.7 (1)°. The aldehyde groups are slightly twisted from the pyrrole plane. In the crystal structure, mol­ecules are linked into a three-dimensional framework by C—H⋯O hydrogen bonds

Phen­yl(1-phenyl­sulfonyl-1H-indol-2-yl)methanone

The asymmetric unit of the title compound, C21H15NO3S, contains two crystallographically independent mol­ecules. As a result of the electron-withdrawing character of the phenyl­sulfonyl groups, the N—Csp 2 bond lengths are slightly longer than the anti­cipated value of approximately 1.35 Å for N atoms with planar configurations. Both unique S atoms have a distorted tetra­hedral configuration. In each mol­ecule, the indole ring system is essentially planar (r.m.s. deviations for all non-H atoms of 0.020 and 0.023 Å). In one mol­ecule, the indole ring system makes dihedral angles of 65.7 (8) and 73.4 (8)°, respectively, with the benzene and phenyl rings [62.2 (7) and 72.1 (7)°, respectively, in the other mol­ecule]

Diethyl 2-[(5-meth­oxy-2-methyl-1-phenyl­sulfonyl-1H-indol-3-yl)methyl­ene]malonate

In the title compound, C24H25NO7S, the sulfonyl-bound phenyl ring is approximately perpendicular to the indole ring system [dihedral angle = 87.72 (5)°]. The methyl group of one of the ester units is disordered over two positions with occupancies of 0.527 (13) and 0.473 (13). An intra­molecular C—H⋯O hydrogen bond is observed. In the crystal structure, mol­ecules are linked into a ribbon structure running along the c axis by inter­molecular C—H⋯O hydrogen bonds and C—H⋯π inter­actions involving the pyrrole ring

3-Ethyl-5-(4-meth­oxy­phen­oxy)-2-(pyridin-4-yl)-3H-imidazo[4,5-b]pyridine

In the title compound, C20H18N4O2, the imidazopyridine fused ring system is almost perpendicular to the benzene ring [dihedral angle = 87.6 (5)°]. The pyridine ring makes a dihedral angle of 35.5 (5)° with the mean plane of the imidazopyridine fragment. The crystal structure is stabilized by an aromatic π–π stacking inter­action between the phenyl rings of neighbouring mol­ecules [centroid–centroid distance = 3.772 (2) Å, inter­planar distance = 3.546 (2) Å and slippage = 1.286 (2) Å]

Analysis of model rotor blade pressures during parallel interaction with twin vortices

This paper presents and provides analysis of unsteady surface pressures measured on a model rotor blade as the blade experienced near parallel blade vortex interaction with a twin vortex system. To provide a basis for analysis, the vortex system was characterized by hot-wire measurements made in the interaction plane but in the absence of the rotor. The unsteady pressure response resulting from a single vortex interaction is then presented to provide a frame of reference for the twin vortex results. A series of twin vortex interaction cases are then presented and analyzed. It is shown that the unsteady blade pressures and forces are very sensitive to the inclination angle and separation distance of the vortex pair. When the vortex cores lie almost parallel to the blade chord, the interaction is characterized by a two-stage response associated with the sequential passage of the two cores. Conversely, when the cores lie on a plane that is almost perpendicular to the blade chord, the response is similar to that of a single vortex interaction. In all cases, the normal force response is consistent with the distribution of vertical velocity in the flow field of the vortex system. The pitching moment response, on the other hand, depends on the localized suction associated with the vortex cores as they traverse the blade chord