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Aerospace
Volume 2
Issue 4
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Aerospace, Volume 2, Issue 4 (December 2015) – 5 articles , Pages 555-672

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2749 KiB  
Article
C0 Layerwise Model with Fixed Degrees of Freedom and Variable In- and Out-of-Plane Kinematics by Strain Energy Updating Technique
by Ugo Icardi and Federico Sola
Aerospace 2015, 2(4), 637-672; https://doi.org/10.3390/aerospace2040637 - 17 Nov 2015
Viewed by 5911
Abstract
Physically based zigzag models have the merit of giving accurate stress predictions for laminates and sandwiches keeping fixed the functional degrees of freedom, though at the expense of the introduction of their derivatives. In the present paper, a technique that enables deleting these [...] Read more.
Physically based zigzag models have the merit of giving accurate stress predictions for laminates and sandwiches keeping fixed the functional degrees of freedom, though at the expense of the introduction of their derivatives. In the present paper, a technique that enables deleting these derivatives is developed. The objective is finding a priori corrections of displacements, which make the energy of the model with all the derivatives neglected equivalent to that of its initial counterpart model containing all the derivatives. Numerical applications show that this technique can obtain accurate results, even for strongly asymmetrical lay-ups, keeping low the computational cost. Full article
(This article belongs to the Special Issue Feature Papers in Aerospace)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>(<b>a</b>) Through-the thickness variation of displacement contributions; (<b>b</b>) geometry considered to enforce in-plane continuity.</p> Full article ">Figure 2
<p>Stages of the procedure employed to obtain the equivalent C<sup>0</sup> model.</p> Full article ">Figure 3
<p>Exact solution and through-the-thickness distribution of: (<b>a</b>) normalized transverse shear stress; and (<b>b</b>) normalized in-plane displacement by the OM Model [<a href="#B55-aerospace-02-00637" class="html-bibr">55</a>] and by the present EM Model for a laminated beam.</p> Full article ">Figure 4
<p>Exact solution and through-the-thickness distribution of: (<b>a</b>) normalized transverse shear stress; (<b>b</b>) normalized transverse stress; (<b>c</b>) normalized in-plane displacement; and (<b>d</b>) normalized transverse displacement by the OM Model [<a href="#B55-aerospace-02-00637" class="html-bibr">55</a>] and by the present EM model for a sandwich beam with damaged upper face.</p> Full article ">Figure 4 Cont.
<p>Exact solution and through-the-thickness distribution of: (<b>a</b>) normalized transverse shear stress; (<b>b</b>) normalized transverse stress; (<b>c</b>) normalized in-plane displacement; and (<b>d</b>) normalized transverse displacement by the OM Model [<a href="#B55-aerospace-02-00637" class="html-bibr">55</a>] and by the present EM model for a sandwich beam with damaged upper face.</p> Full article ">Figure 5
<p>Exact solution and through-the-thickness distribution of: (<b>a</b>) normalized transverse shear stress and (<b>b</b>) normalized in-plane displacement by the model [<a href="#B73-aerospace-02-00637" class="html-bibr">73</a>] and by the present EM model for a sandwich plate.</p> Full article ">Figure 6
<p>Normalized transverse shear stress by the present EM Model and by the 3D FEM [<a href="#B72-aerospace-02-00637" class="html-bibr">72</a>] for a cantilever beam.</p> Full article ">Figure 7
<p>Lay-ups and fiber orientation considered.</p> Full article ">Figure 8
<p>Normalized transverse shear stress by the OM Model and by the present EM Model for a simply-supported double core sandwich beam with spatially variable stiffness faces.</p> Full article ">Figure 9
<p>Sandwich beam with step variation of fiber orientation: non-dimensional in-plane variation of (<b>a</b>) in-plane stress and (<b>b</b>) in-plane stress gradient.</p> Full article ">
763 KiB  
Article
Acoustic Radiation by 3D Vortex Rings in Air
by Fedor V. Shugaev, Dmitri Y. Cherkasov and Oxana A. Solenaya
Aerospace 2015, 2(4), 627-636; https://doi.org/10.3390/aerospace2040627 - 6 Nov 2015
Cited by 1 | Viewed by 5506
Abstract
Acoustic radiation emitted by three-dimensional (3D) vortex rings in air has been investigated on the basis of the unsteady Navier–Stokes equations. Power series expansions of the unknown functions with respect to the initial vorticity which is supposed to be small are used. In [...] Read more.
Acoustic radiation emitted by three-dimensional (3D) vortex rings in air has been investigated on the basis of the unsteady Navier–Stokes equations. Power series expansions of the unknown functions with respect to the initial vorticity which is supposed to be small are used. In such a manner the system of the Navier–Stokes equations is reduced to a parabolic system with constant coefficients at high derivatives. The initial value problem is as follows. The vorticity is defined inside a toroid at t = 0. Other gas parameters are assumed to be constant throughout the whole space at t = 0. The solution is expressed by multiple integrals which are evaluated with the aid of the Korobov grids. Density oscillations are analyzed. The results show that the frequency band depends on the initial size of the vortex ring and its helicity. The presented data may be applied to the study of a flow in a wake region behind an aerodynamic body. Full article
(This article belongs to the Special Issue Recent Advances in Aeroacoustics)
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Graphical abstract
Full article ">Figure 1
<p>Density oscillations for the case of no helicity.</p> Full article ">Figure 2
<p>Density oscillations for the case of present helicity.</p> Full article ">Figure 3
<p>Density oscillations at the final stage of the process (no helicity).</p> Full article ">Figure 4
<p>Density oscillations at the final stage of the process (helicity is present).</p> Full article ">Figure 5
<p>Density oscillations inside the initial vortex ring (no helicity).</p> Full article ">Figure 6
<p>Density oscillations inside the initial vortex ring (helicity is present).</p> Full article ">
2417 KiB  
Article
Optimization of Variable Stiffness Laminates and Sandwiches Undergoing Impulsive Dynamic Loading
by Ugo Icardi and Federico Sola
Aerospace 2015, 2(4), 602-626; https://doi.org/10.3390/aerospace2040602 - 23 Oct 2015
Cited by 2 | Viewed by 6251
Abstract
This paper, which deals with variable stiffness composites, is aimed at showing the effects of optimization on the response characteristics and stress fields of these materials. A new optimization technique that has recently been developed is used to find spatially variable distributions of [...] Read more.
This paper, which deals with variable stiffness composites, is aimed at showing the effects of optimization on the response characteristics and stress fields of these materials. A new optimization technique that has recently been developed is used to find spatially variable distributions of stiffness properties at any point, which minimize the interlaminar stresses without significant stiffness loss. After solving the Euler–Lagrange equations obtained by the strain energy extremization with varying the stiffness properties, curvilinear paths of fibres are found in closed form that modify natural frequencies, improve dynamic response and aid in recovery of critical interlaminar stresses. In the current version of the optimization technique, a more realistic description of the optimized shear coefficients is provided in order to accurately describe local effects. As a structural model, a zig-zag model with variable through-the-thickness kinematics is adopted, which is able to adapt itself to variations in solutions, thus providing accurate results from constitutive equations. This model is adopted because an accurate description of strain energy is mandatory for an effective application of the optimization procedure proposed. The numerical results show that the optimization procedure effectively recovers the stress concentrations while simultaneously improving the dynamic response of laminates and sandwiches. Full article
(This article belongs to the Special Issue Adaptive/Smart Structures and Multifunctional Materials with Application to Morphing Aircraft)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Lay-ups considered for the local optimization of a sandwich beam.</p> Full article ">Figure 2
<p>Lay-ups considered for the optimization of the laminated plate and in-plane distributions of the optimized stiffness coefficients.</p> Full article ">Figure 3
<p>Non dimensional deflection time history for a simply-supported sandwich plate (<math display="inline"> <semantics> <mrow> <msub> <mi>L</mi> <mi>x</mi> </msub> <mo>=</mo> <msub> <mi>L</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.6096</mn> <mtext> m</mtext> <mo>,</mo> <mtext> </mtext> <mi>h</mi> <mo>=</mo> <mn>29.21</mn> <mtext> mm</mtext> </mrow> </semantics> </math>) subjected to (<b>a</b>) triangular pulse loading, (<b>b</b>) step pulse loading, and (<b>c</b>) constant pulse loading; (<b>d</b>) Non dimensional deflection time history for different orders of expansion.</p> Full article ">Figure 4
<p>Non dimensional deflection time history for different length to thickness ratios.</p> Full article ">Figure 5
<p>Non-dimensional deflection time history for all the optimized configurations.</p> Full article ">Figure 6
<p>Lay-ups considered for the optimization of the sandwich plate.</p> Full article ">Figure 7
<p>Non-dimensional deflection time history for all the optimized configurations.</p> Full article ">Figure 8
<p>Lay-ups considered for the local optimization of the laminated beam.</p> Full article ">Figure 9
<p>Through the thickness variation of (<b>a</b>) transverse displacement, (<b>b</b>) in-plane stress, (<b>c</b>) transverse shear stress, and (<b>d</b>) transverse normal stress for the optimization of a laminated plate.</p> Full article ">Figure 10
<p>Through the thickness variation of (<b>a</b>) transverse displacement, (<b>b</b>) in-plane stress, (<b>c</b>) transverse shear stress, and (<b>d</b>) transverse normal stress.</p> Full article ">
1459 KiB  
Article
East–West GEO Satellite Station-Keeping with Degraded Thruster Response
by Stoian Borissov, Yunhe Wu and Daniele Mortari
Aerospace 2015, 2(4), 581-601; https://doi.org/10.3390/aerospace2040581 - 29 Sep 2015
Cited by 8 | Viewed by 13045
Abstract
The higher harmonic terms of Earth’s gravitational potential slowly modify the nominal longitude of geostationary Earth orbit (GEO) satellites, while the third-body presence (Moon and Sun) mainly affects their latitude. For this reason, GEO satellites periodically need to perform station-keeping maneuvers, namely, east–west [...] Read more.
The higher harmonic terms of Earth’s gravitational potential slowly modify the nominal longitude of geostationary Earth orbit (GEO) satellites, while the third-body presence (Moon and Sun) mainly affects their latitude. For this reason, GEO satellites periodically need to perform station-keeping maneuvers, namely, east–west and north–south maneuvers to compensate for longitudinal and latitudinal variations, respectively. During the operational lifetime of GEO satellites, the thrusters’ response when commanded to perform these maneuvers slowly departs from the original nominal impulsive behavior. This paper addresses the practical problem of how to perform reliable east–west station-keeping maneuvers when thruster response is degraded. The need for contingency intervention from ground-based satellite operators is reduced by breaking apart the scheduled automatic station-keeping maneuvers into smaller maneuvers. Orbital alignment and attitude are tracked on-board during and in between sub-maneuvers, and any off nominal variations are corrected for with subsequent maneuvers. These corrections are particularly important near the end of the lifetime of GEO satellites, where thruster response is farthest from nominal performance. Full article
(This article belongs to the Special Issue Feature Papers in Aerospace)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>East–west (E–W) station-keeping deadband of a GEO satellite.</p> Full article ">Figure 2
<p>Phase trajectory of the GEO E–W station-keeping using a stable thruster under <math display="inline"> <mrow> <mover accent="true"> <mi>λ</mi> <mo>¨</mo> </mover> <mo>&lt;</mo> <mn>0</mn> </mrow> </math>.</p> Full article ">Figure 3
<p>Simple control scheme near the stable node with <math display="inline"> <mrow> <mover accent="true"> <mi>λ</mi> <mo>¨</mo> </mover> <mo>&lt;</mo> <mn>0</mn> </mrow> </math>.</p> Full article ">Figure 4
<p>Simple control scheme using incorrect thrust near the unstable node with <math display="inline"> <mrow> <mover accent="true"> <mi>λ</mi> <mo>¨</mo> </mover> <mo>&lt;</mo> <mn>0</mn> </mrow> </math>.</p> Full article ">Figure 5
<p>Ideal cycle of the E–W station-keeping operation.</p> Full article ">Figure 6
<p>Example of five loops of the operation ring of E–W station-keeping.</p> Full article ">Figure 7
<p>Thruster response at the beginning of its lifetime.</p> Full article ">Figure 8
<p>Thruster response at the end of its lifetime.</p> Full article ">Figure 9
<p>Momentum-biased wheel configuration.</p> Full article ">Figure 10
<p>Thruster output of longitudinal station-keeping (westward) defined in the body frame.</p> Full article ">Figure 11
<p>Possible thruster setup for a GEO satellite.</p> Full article ">Figure 12
<p>Momentum wheel (MW) rotation rate.</p> Full article ">Figure 13
<p>Yaw evolution.</p> Full article ">Figure 14
<p>Nominal thruster workflow.</p> Full article ">Figure 15
<p>Modified workflow for degraded thruster performance.</p> Full article ">Figure 16
<p>Illustration of the workflow.</p> Full article ">
6081 KiB  
Article
CFD Study of an Annular-Ducted Fan Lift System for VTOL Aircraft
by Yun Jiang, Bo Zhang and Tao Huang
Aerospace 2015, 2(4), 555-580; https://doi.org/10.3390/aerospace2040555 - 29 Sep 2015
Cited by 22 | Viewed by 23803
Abstract
The present study aimed at assessing a novel annular-ducted fan lift system for VTOL aircraft through computational fluid dynamics (CFD) simulations. The power and lift efficiency of the lift fan system in hover mode, the lift and drag in transition mode, the drag [...] Read more.
The present study aimed at assessing a novel annular-ducted fan lift system for VTOL aircraft through computational fluid dynamics (CFD) simulations. The power and lift efficiency of the lift fan system in hover mode, the lift and drag in transition mode, the drag and flight speed of the aircraft in cruise mode and the pneumatic coupling of the tip turbine and jet exhaust were studied. The results show that the annular-ducted fan lift system can have higher lift efficiency compared to the rotor of the Apache helicopter; the smooth transition from vertical takeoff to cruise flight needs some extra forward thrust to overcome a low peak of drag; the aircraft with the lift fan system enclosed during cruise flight theoretically may fly faster than helicopters and tiltrotors based on aerodynamic drag prediction, due to the elimination of rotor drag and compressibility effects on the rotor blade tips; and pneumatic coupling of the tip turbine and jet exhaust of a 300 m/s velocity can provide enough moment to spin the lift fan. The CFD results provide insight for future experimental study of the annular-ducted lift fan VTOL aircraft. Full article
(This article belongs to the Special Issue Feature Papers in Aerospace)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>The momentum model of the ducted lift fan system.</p> Full article ">Figure 2
<p>(<b>a</b>) The annular-ducted lift fan system and the aircraft with the annular duct opened; (<b>b</b>) the lift fans; (<b>c</b>) the top front view of the aircraft with the annular duct system enclosed by upper aperture and lower louvers; (<b>d</b>) the lift fan and its tip turbine in a gas chamber. The upper wall of the chamber has been removed to expose the tip turbine inside.</p> Full article ">Figure 3
<p>(<b>a</b>) Volume mesh of the annular-ducted lift fan system in the central plane for the hover and transition mode study. Different colors show different blocks; (<b>b</b>) surface mesh on the surface of the aircraft and the symmetry plane for the aerodynamic drag study; (<b>c</b>) volume mesh in the central plane of the gas chamber for the tip turbine study.</p> Full article ">Figure 4
<p>(<b>a</b>) Three-dimensional swirling streamlines in front of the central plane of the helicopter in hover mode; (<b>b</b>) the rotor tip vortex in the central plane of the helicopter.</p> Full article ">Figure 5
<p>Streamlines in the central plane of the generic fan-in-wing configuration at an angle of attack of 20°. Freestream velocity <span class="html-italic">U</span> = 30 m/s, and fan speed <span class="html-italic">N</span> = 21,000 rpm.</p> Full article ">Figure 6
<p>Lift and drag coefficients as a function of the angle of attack for <span class="html-italic">U</span> = 30 m/s and <span class="html-italic">N</span> = 21,000 rpm. The experimental data come from Thouault [<a href="#B3-aerospace-02-00555" class="html-bibr">3</a>].</p> Full article ">Figure 7
<p>Comparison of computed and experimental data for the NACA-0012 airfoil at <span class="html-italic">M</span> = 0.7 and <span class="html-italic">Re</span> = 9 × 10<sup>6</sup>. (<b>a</b>) Lift <span class="html-italic">vs.</span> angle of attack; (<b>b</b>) lift <span class="html-italic">vs.</span> drag polar; (<b>c</b>) pressure coefficient distribution at <span class="html-italic">z</span> = 1 and α = 1.55°. The experimental data come from Harris [<a href="#B17-aerospace-02-00555" class="html-bibr">17</a>].</p> Full article ">Figure 7 Cont.
<p>Comparison of computed and experimental data for the NACA-0012 airfoil at <span class="html-italic">M</span> = 0.7 and <span class="html-italic">Re</span> = 9 × 10<sup>6</sup>. (<b>a</b>) Lift <span class="html-italic">vs.</span> angle of attack; (<b>b</b>) lift <span class="html-italic">vs.</span> drag polar; (<b>c</b>) pressure coefficient distribution at <span class="html-italic">z</span> = 1 and α = 1.55°. The experimental data come from Harris [<a href="#B17-aerospace-02-00555" class="html-bibr">17</a>].</p> Full article ">Figure 8
<p>(<b>a</b>) Three-dimensional streamlines in front of the central plane in hover mode; (<b>b</b>) surface streamlines in the central plane of the aircraft; (<b>c</b>) static pressure on the upper surface of the fans, duct, fuselage and peripheral wing; (<b>d</b>) pressure contour inside the annular-ducted lift fan system.</p> Full article ">Figure 8 Cont.
<p>(<b>a</b>) Three-dimensional streamlines in front of the central plane in hover mode; (<b>b</b>) surface streamlines in the central plane of the aircraft; (<b>c</b>) static pressure on the upper surface of the fans, duct, fuselage and peripheral wing; (<b>d</b>) pressure contour inside the annular-ducted lift fan system.</p> Full article ">Figure 9
<p>Computed time-averaged net drag and lift-to-aircraft weight ratio at different angles of attack in transition mode. The lift was maintained equal to the weight of the aircraft through the change of the rotational speed of the fans.</p> Full article ">Figure 10
<p>The aircraft attitudes and streamlines in the central plane of the aircraft in transition mode. The lift was maintained equal to the weight of the aircraft by adjusting the fan rotational speeds. (<b>a</b>) Angle of attack α = 0°, freestream speed <span class="html-italic">U</span> = 20 m/s, fan speeds <span class="html-italic">N</span> = +108, −117 rpm; (<b>b</b>) angle of attack α = −21°, <span class="html-italic">U</span> = 10 m/s, fan speeds <span class="html-italic">N</span> = +122, −121 rpm; (<b>c</b>) angle of attack α = 15°, <span class="html-italic">U</span> = 20 m/s, fan speeds <span class="html-italic">N</span> = +91, −97 rpm.</p> Full article ">Figure 11
<p>(<b>a</b>) Streamlines in the central plane of the aircraft in cruise mode; (<b>b</b>) pressure coefficient in the central plane of the aircraft at speed of 0.7 Ma.</p> Full article ">Figure 12
<p>The computed drag (the engines were not considered) of the aircraft increases with cruise speed at different angles of attack.</p> Full article ">Figure 13
<p>Rhombic-shaped annular-ducted lift fan aircraft.</p> Full article ">Figure 14
<p>(<b>a</b>) Velocity vector in the central plane of the gas chamber when the tip turbine was still; (<b>b</b>) enlarged view of velocity vectors; (<b>c</b>) enlarged view of velocity vectors when the tip turbine rotated at a speed <span class="html-italic">n</span> = 120 rpm; (<b>d</b>) pressure contour in the central plane of the chamber; (<b>e</b>) the enlarged view of pressure on the turbine blades to show the pressure difference on two sides of the blades.</p> Full article ">Figure 14 Cont.
<p>(<b>a</b>) Velocity vector in the central plane of the gas chamber when the tip turbine was still; (<b>b</b>) enlarged view of velocity vectors; (<b>c</b>) enlarged view of velocity vectors when the tip turbine rotated at a speed <span class="html-italic">n</span> = 120 rpm; (<b>d</b>) pressure contour in the central plane of the chamber; (<b>e</b>) the enlarged view of pressure on the turbine blades to show the pressure difference on two sides of the blades.</p> Full article ">Figure 14 Cont.
<p>(<b>a</b>) Velocity vector in the central plane of the gas chamber when the tip turbine was still; (<b>b</b>) enlarged view of velocity vectors; (<b>c</b>) enlarged view of velocity vectors when the tip turbine rotated at a speed <span class="html-italic">n</span> = 120 rpm; (<b>d</b>) pressure contour in the central plane of the chamber; (<b>e</b>) the enlarged view of pressure on the turbine blades to show the pressure difference on two sides of the blades.</p> Full article ">
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