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Auf die Merkliste Drucken Weiterempfehlung. Hardcover Royal Society of Chemistry. Produktbeschreibung Fluid-structure interactions have been well studied over the years but most of the focus has been on high Reynolds number flows, inertially dominated flows where the drag force from the fluid typically varies as the square of the local fluid speed. There are though a large number of fluid-structure interaction problems at low values of the Reynolds number, where the fluid effects are dominated by viscosity and the drag force from the fluid typically varies linearly with the local fluid speed, which are applicable to many current research areas including hydrodynamics, microfluidics and hemodynamics.
Edited by experts in complex fluids, Fluid-Structure Interactions in Low-Reynolds-Number Flows is the first book to bring together topics on this subject including elasticity of beams, flow in tubes, mechanical instabilities induced by complex liquids drying, blood flow, theoretical models for low-Reynolds number locomotion and capsules in flow. The book includes introductory chapters highlighting important background ideas about low Reynolds number flows and elasticity to make the subject matter more approachable to those new to the area across engineering, physics, chemistry and biology.
Ihr Name:. Folgen Sie uns beck-shop. But transitioning between varying types of elements has long been a challenge Figure 6. Meshing a geometry is an essential part of the simulation process, and can be crucial for obtaining the best results in the fastest manner. Lowering the minimum element size in mesh that is computationally taxing is to resolve the flow in the wake.
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To achieve this, additional mesh control entities are introduced in the geometry. These entities are advantageous to normal geometrical entities since they are removed whence they are completely meshed. A smoothing algorithm then smooths the mesh locally in order to minimize gradients in the mesh size. Also, it is easier to introduce a boundary layer mesh when the control entities are removed. Therefore the mesh needs to be quite fine on the airfoils or wing interface so that the fluid motion remains continuous. The mesh used in this model is plotted in figure 6.
The mesh for every airfoil and the tunnel are shown in table 3.
The velocity field is analyzed, in figure 7 shows the von Mises stress in the NACA flapping airfoil and the velocity field for angle of attack 0 at four different times. From figure 7 it is noted that, at all steady flapping oscillating the wake retained approximately the same form. The wake contains lateral jets of fluid, alternating in direction, separated by one or more vortices or a shear layer Figure 7.
Each time the trailing edge changes direction, it sheds a stopstart vortex. As the trailing edge moves to the other side, a low pressure region develops in the posterior quarter of the body, sucking a bolus of fluid laterally. The bolus is shed off the trailing edge, stretching the stopstart vortex into an unstable shear layer, which eventually rolls up into two or more separate, same-sign vortices. This pattern was consistent at all speeds, even though the strength of the lateral jet increased at higher speeds Figure 7.
Also, Wake flow at different speeds and different phases different colors during the trailing edge beat cycle. Black arrows represent flow velocity magnitude and direction. Vorticity is shown in color in the background. The flow around the airfoil is in blue because the low fluid speeds. So, every separation point become a contact point that mean the flow cover the wing and the von Karman vortex street past the airfoils, which will be essentially deformed and influences those stream field. The only separation point can clearly be seen in the trailing edge as shown in figure 7.
In addition, observed a vortex shedding around the trailing edge of both airfoils.
Unsteady fluid-structure interactions of membrane airfoils at low Reynolds numbers | SpringerLink
The behavior of the flow for the pitching airfoil is presented in figure 7. During the down stroke phase the main vortex is shed from the surface and many smaller vortices are generated at the airfoil upper surface as shown in time step 4 in figure 7. The reattachment process is then completed, leading to the latter re circulation zone formation as the vortex shedding displays a periodic behavior.
It is important to note the influence of the lower surface on the flow behavior during the down stroke. As the airfoil pitches down, not only the flow is detaching from the upper surface caused by the vortex shedding, yet the lower surface is acting, in the other direction, producing an upward force and hence reducing the lift. Since the airfoil is symmetric, both surfaces act on the aerodynamic forces generation.
Due to its viscosity the fluid will bend around the airfoil as it sticks on the surface. The difference of speed on the fluid particles of the boundary layer leads to the creation of shear forces that attach the flow and force it to flap in the direction of the slower layer, which is close to the wall, hence the fluid try to wrap around the object.
When the flow is reattached near down stroke, the upper surface again bends the air down in the trailing edge, as expected for a positive attitude incidence. In figure 8 , shows the change in lift and drag forces for NACA flapping airfoil. The change in pressure around the flapping wing produces a force Lift and Drag. These forces evaluated by the difference between the upper surface pressure and the lower surface pressure. The NACA flapping airfoil structure was unique in the deflection because the airfoil did not just flap straight up and down like the other s airfoil.
Figure 8 shows a flapping range plot of the top and bottom portions of the NACA airfoil.
Fluid-Structure Interactions in Low-Reynolds-Number Flows
Since the rear half of the airfoil beyond the fixed domain deflected more than front half of the airfoil, a twisting motion occurred in the flapping of the airfoil. Figure 8 shows deflection measurements taken on a flapping airfoil highlighting the difference in deflection across the airfoil section.
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The initial deflection in the rear half of the airfoil was As flactuation increased, the rear half of the airfoil deflected more than the front half. Measuring the rear half and front half of the airfoil just prior to end of simulation yielded a total deflection of 50 mm and 10 mm, respectively. If the oscillating were able to continue increasing, than the twisting in the NACA airfoil would also increase.
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This twisting phenomenon in the flapping airfoil was also helpful to produce thrust in the simulation of the flapping wing. As shown in figure 9 , the evolution of lift and drag forces for all time for NACA airfoil at 0 deg angle of attack. In other hand the change in lift force larger than in drag force because the oscillating in y direction is larger than x-direction. Also, when angle of attack increase both drag and lift force increase.
In figure 11 shows the oscillation magnitude of trailing edge for both directions x and y.
The trailing edge oscillation in s airfoil completely uncomprehended because the oscillation magnitude in x displacement and y displacement just streight line with magnitude 0 mm. The behavior of trailing edge oscillation in s convex and this airfoil design for laminar flow applications. In addition, in figure 12 the main harmonic oscillation frequencies.
In s airfoil there is no results because uncomprehended behavior in turbulent flow. From the analysis of the lift force and drag force hysteresis loops for the laminar flow results in comparison with turbulent flow results, as shown respectively by figures 12 and 13 , it is possible to observe that the laminar flow results can be addressed with good agreement turbulent flow results for both upstroke and downstroke behavior.
Although the laminar flow results less than turbulent flow, the drag force in laminar flow matched the drag force in turbulent flow results for low Reynolds number regime, as shown by figure The surge of lift force encountered seen in both laminar flow and turbulent flow results cannot be accounted by the flapping airfoil model as well, as in turbulent flow, it is a consequence of the vortex residence at the airfoil upper surface at the end of upstroke phase, presenting a high energy profile due to flow acceleration and vorticity.
As discussed, the downstroke phase has a highly rotational behavior as well, which is not accounted by the laminar flow; hence the hysteresis loops for the flapping airfoil cannot model the flow, differing from the laminar flow and turbulent flow results. The comparison between the laminar flow and turbulent flow computations, the trailing edge displacement for both laminar and turbulent flow shows good agreement in both results as shown in figure The results of trailing edge displacement from turbulent flow, shows that the model can serve as an important tool for the unsteady analysis, rendering fair results with less computational effort than turbulent flow models, for instance.
Both cases displayed misleading results in a minor extent, which is expected due to the two dimensional approach and the material used in this model. The first objective of this paper was to present the preliminary results of a numerical study of the time-varying simulations performed are shown to be closely correlated to the laminar flow simulations developed previously but in three dimensional just reach the steady state.
These simulations enable the progression of the turbulent air flow model to be extended to allow flapping wing to be improved.
The basic sinusoidal wave load process model has been implemented to create multiple velocity magnitude jet flow over a period of 6 seconds. The simulations performed include several flapping beats within this time frame of which the data at each time step closely follow the data gathered from the laminar flow and time-varying turbulence flow models. The second objective was to assess the effect on turbulent mixing of a grid formed by traingular elements with different mesh sizes.