Lift and drag

After a fragment has attained a certain initial velocity, the forces acting upon it during flight are those of gravity and fluid dynamics. Fluid-dynamic forces are subdivided into drag and lift components. The effects of these forces depend on the fragment s shape and direction of motion relative to the wind. 

The simplest relationship for calculating fragment range neglects drag and lift forces. Vertical and horizontal range, and z, then depend upon initial velocity and initial trajectory angle Oj ... 

Drag and lift coefficients for rotating spheres. All data plotted are for smooth spheres. 

C Define frontal area of a body subjected to external flow. When is it appropriate to use the fronial area in drag and lift calculations ... 

The CSF and CSS based versions of the VOF method have been used to calculate improved estimates of the single particle drag and lift coefficients and for simulating breakage and coalescence of dispersed flows containing a few fluid particles [49, 218, 50, 141, 18]. 

Swanson [145] reviewed the investigations of the Magnus force, and presented experimental drag and lift coefficients for an infinite, rotating cylinder at different Reynolds numbers and velocity ratios. For velocity ratios less than 0.55, and Reynolds numbers between 12.8 x 10 and 50.1 x 10 the cylinder would experience negative lift. 

Clift et al [22] summarized the measurements of drag and lift on rotating spheres, and concluded that the phenomena involved are so complex that drag and lift forces on rotating spheres should be determined experimentally. 

Dandy and Dwyer [30] computed numerically the three-dimensional flow around a sphere in shear flow from the continuity and Navier-Stokes equations. The sphere was not allowed to move or rotate. The drag, lift, and heat flux of the sphere was determined. The drag and lift forces were computed over the surface of the sphere from (5.28) and (5.33), respectively. They examined the two contributions to the lift force, the pressure contribution and the viscous contribution. While the viscous contribution always was positive, the pressure contribution would change sign over the surface of the sphere. The pressure... 

Lee and Borner [88] used LDA measurements to characterize the suspension turbulent flow to enable the calculation of the drag and lift forces. The results were in fair agreement with the measurements of Lee and Durst [89]. 

To summarize, no firm conclusions regarding the impact of free stream turbulence on the drag and lift force coefficients can be drawn analyzing the available data. More detailed experiments are obviously needed to better understand the affect of turbulence on the drag and lift force coefficients. 

Kariyasaki proposed to calculate the lift force from a balance of buoyancy, gravity, drag and lift, hence ... 

As can be seen from Eq. (5.100), the virtual-mass force reduces the drag and lift forces by a factor of 1 /y. The buoyancy force is not modified because we have chosen to define it in terms of the effective volume Vpy. We remind the reader that the mesoscale acceleration model for the fluid seen by the particle A j must be consistent with the mesoscale model for the particle phase A p in order to ensure that the overall system conserves momentum at the mesoscale. (See Section 4.3.8 for more details.) As discussed near Eq. (5.14) on page 144, this is accomplished in the single-particle model by constraining the model for Apf given the model for Afp (which is derived from the force terms introduced in this section). Thus, as in Eqs. (5.98) and (5.99), it is not necessary to derive separate models for the momentum-transfer terms appearing in Apf. 

The beach profile (Figure 2.9) is the product of the oscillatory onshore and offshore motions of its constituent materials affected by the waves and the wave-induced currents. Granular particles on the seabed can be dislodged and suspended in the water column by a combination of drag and lift forces. These forces on the particles are exerted by bott-tom shear stresses developed by either the wave velocity exceeding a threshold value or the occurrence of turbulence. Once the particles are in the water column, they are kept in suspension longer than in subaerially wind-blown conditions because of a combination... 

In order to compare the drag and lift forces of detachment, let us now express the drag in a form corresponding to Eq. (X.38) ... 

The mobilizing moment induced by the drag, lift, and inertia forces. The correction factor for the moments induced by the drag and lift forces (KOcd and KOcl ) area is obtained as the ratio of describing the changes of both surface areas (As and At) and lever arms (r and Vs) of the drag and lift forces Fd and Fl. The correction factor KOcm is obtained as the ratio of lever arms Vsn of the inertia force with and without deformation effect. 

The value of the drag and lift coefficients are determined by the shape of the flying ob-... 

We have so far described drag and lift forces acting on a suspended particle. There are, however, additional hydrodynamic forces, such as Basset history, Faxen correction, and virtual mass effects that act on the particles. Some of these forces could become important especially for the particles suspended in a liquid. The general equation of motion of a small spherical particle suspended in fluid as obtained by Maxey and Riley is given as... 

Solids pickup from the vessel base is achieved by a combination of the drag and lift forces of the moving fluid on the solid particles and the bursts of turbulent eddies originating from the bulk flow in the vessel. This is clearly evident in... 

The CSF and CSS based versions of the VOF method have been used to calculate improved estimates of the single particle drag and lift coefficients and for simulating breakage and coalescence of dispersed flows containing a few fluid particles [20, 53, 54, 150, 232]. A third variant of the VOF method calculates the interface tension force by the CSS method and perform an independent PLIC reconstruction of the interface to improve the design of the advection schemes. In this way the tailored advection discretization schemes prevent numerical smoothing of the interface [160]. 

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