Lift, coefficient

The original work by NACA and NASA is the basis on which most modern axial-flow compressors are designed. Under NACA, a large number of blade profiles were tested. The test data on these blade profiles is published. The cascade data conducted by NACA is the most extensive work of its kind. In most commercial axial-flow compressors NACA 65 series blades are used. These blades are usually specified by notation similar to the following 65-(18) 10. This notation means that the blade has a lift coefficient of 1.8, a profile shape 65, and a thickness/chord ratio of 10%. The lift coefficient can be directly related to the blade camber angle by the following relationship for 65 series blades ... 

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

Labyrinth piston, 49 Labyrinth seal leakage, 532 Lantern ring, 74 Lapping block set, 335 Lateral critical speeds, 384 Leakage, seal, 532, 533, 534 Leland-Mueller rule, 26 Lift coefficient, 226 Liquid... 

At flow speeds well below the speed of sound, the lift coefficient depends only on the shape and orientation (angle of attack) of the body ... 

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

Engineers commonly use dimensionless ratios such as the Reynolds number and the lift coefficient to help understand complex experimental data, organize equations and model building, and relate model testing in a wind tunnel to that of a prototype flight. This kind of analysis is called dimensional analysis because it uses the dimensional nature of important variables to derive dimensionless parameters that determine the scaling properties of a physical system. 

In financial matters, a similar technique, ratio analysis, is used to judge whether a company is healthy witli respect to industry standards. In ratio analysis most of die quantities compared are quantities of money, so the ratio of one quantity of money to another quantity of money is, by definition, a new dimensionless ratio (like die Reynolds number or lift coefficient), and these financial ratios can be used to compare businesses in similar industries or businesses (in engineering, such comparison is referred to as dynamic similitude). 

Terminology used here is as given in Fig. 5.1, showing the variation of computed lift coefficient C , with time for an impulsive start of the flow past a cylinder. It is noted that the amplitude of the lift variation always attains the same value (not shown here) and the corresponding time period is given by T = 27r/o e, irrespective of the method used for the computation, provided the same grid is used for these calculations. 

Figure 5.3 Variation of Saturation amplitude of lift coefficient with Reynolds number.

Basset force coefficient Transversal lift coefficient Eulerian quantity at node n ... 

Figure 104. Lifting coefficient 6 for the balls in a tube mill as a function of drum loading...

The lifting coefficient d can be estimated from results obtained for ball charges in tube mills (Figure 104 ). For the typical granulation drum loadings of ( = 0.1 to 0.3, 6 is approximately constant. 

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. 

In aircraft calculations the drag coefficient of a wing usually is based on the wing s horizontal surface rather than on the area perpendicular to the flow. In addition, aeronautical engineers define a lift coefficient Q with exactly the same form as EqJ 6.53. In the equation F stands for the upward force of the air exerted on an airplane s wings, A stands for the horizontal wing surface, and Cj is replaced with C,. 

To illustrate this point, one must look at the derivative of drag with respect to chord length. We wish to treat velocity, area, and lift coefficient as constants, so the span must be a function of aspect ratio. Using the definition for aspect ratio and defining the average chord length c =A/b, we obtain... 

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