Drag force coefficient

The drag force coefficient in Eqs. (4.5) and (4.6), CD, depends on the flow regime, as has been described in Chapter 2 the relationships between CD and the Reynolds... 

The drag force coefficient used was taken from Gibilaro et al [51]. Prom (10.100) and (10.101) a derived coefficient was defined by ... 

FIGURE 4.53 Dependence of the drag force coefficient,/, on the dimensionless distance, (a) For surfactant concentrations above the CMC at different surface viscosities, (b) For different values of tlie surface elasticity, the effects of surface viscosities and the viscosity of drop phase are neglected. 

The sectional buffeting lift, moment and drag forces are expressed in terms of steady average lift, twist and drag force coefficients Cj, and C, respectively, as... 

The drag force is exerted in a direction parallel to the fluid velocity. Equation (6-227) defines the drag coefficient. For some sohd bodies, such as aerofoils, a hft force component perpendicular to the liquid velocity is also exerted. For free-falling particles, hft forces are generally not important. However, even spherical particles experience lift forces in shear flows near solid surfaces. 

L = lift force D = drag force Cl = lift coefficient Cd = drag coefficient A = surface area p = fluid density V = fluid velocity... 

Two coefficients have been defined. Cl and Co, relating velocity, density, area, and lift or drag forces. These coefficients can be calculated from wind-tunnel tests and plotted as shown in Figure 7-6b versus the angle of attack... 

The resistance to liquid flow aroimd particles may be presented by an equation similar to the viscosity equation but with considering the void fraction. Recall that the shear stress is expressed by the ratio of the drag force, R, to the active surface, K27td. The total sphere surface is Ttd and Kj is the coefficient accoimting for that part of the surface responsible for resistance. Considering the influence of void fraction as a function 2( ). we obtain ... 

The life and drag characteristics of a body in a flow are almost always given in terms of Cl and rather than the forces themselves, because the force coefficients are a more fundamental index of the aerodynamic properties. 

The force of aerodynamic drag opposing foiward motion of the vehicle depends on its drag coefficient (Cj), its frontal area (A,), the air density (p), and the velocity of the wind with respect to the vehicle. In still air, this velocity is simply the vehicle velocity (V.). If driving into a headwind of velocity V , however, the wind velocity with respect to the vehicle is the sum of these two. Multiplying the aerodynamic drag force by vehicle velocity provides the aerodynamic power requirement (PJ. 

The drag coefficient for an antomohile body is typically estimated from wind-tunnel tests. In the wind tunnel, the drag force acting on a stationaiy model of the vehicle, or the vehicle itself, is measured as a stream of air is blown over it at the simulated vehicle speed. Drag coefficient depends primarily on the shape of the body, but in an actual vehicle is also influenced by other factors not always simulated in a test model. 

Drag coefficient Cd c - Fd Cd 1PV2A Fd =drag force A = area normal to flow (Drag stress)/ ( momentum flux) External flows... 

Here V represents the local volume of a computational cell and Va the volume of particle a. The 5-function ensures that the drag force acts as a point force at the (central) position of this particle. In Eq. (42), [ > is the momentum transfer coefficient, which will be discussed in more detail in Section III.D. The gas phase density p is calculated from the ideal gas law ... 

In previous work, we have mainly used the DPM model to investigate the effects of the coefficient of normal restitution and the drag force on the formation of bubbles in fluidized beds (Hoomans et al., 1996 Li and Kuipers, 2003, 2005 Bokkers et al., 2004 Van der Floef et al., 2004), and not so much to obtain information on the constitutive relations that are used in the TFMs. In this section, however, we want to present some recent results from the DPM model on the excess compressibility of the solids phase, which is a key quantity in the constitutive equations as derived from the KTGF (see Section IV.D.). The excess compressibility y can be obtained from the simulation by use of the virial theorem (Allen and Tildesley, 1990). 

As a matter of fact, one may think of a multiscale approach coupling a macroscale simulation (preferably, a LES) of the whole vessel to meso or microscale simulations (DNS) of local processes. A rather simple, off-line way of doing this is to incorporate the effect of microscale phenomena into the full-scale simulation of the vessel by means of phenomenological coefficients derived from microscale simulations. Kandhai et al. (2003) demonstrated the power of this approach by deriving the functional dependence of the singleparticle drag force in a swarm of particles on volume fraction by means of DNS of the fluid flow through disordered arrays of spheres in a periodic box this functional dependence now can be used in full-scale simulations of any flow device. 

---