Form and skin drag contributions to power consumption for the pitched‐blade turbine

Abstract

The determination of power consumption of rotating impellers in an agitated tank has primarily relied on traditional dimensional analysis concepts and correlations. Another traditional approach based on form and skin drag is also possible in determining the power consumption occurring in mixing. This approach, however, appears to have been neglected in the literature on mixing.Traditionally, power number correlations for turbulent flow usually appear as = K pN3D5 where the constant, K, is dependent on the type of impeller. Power can also be written as a drag force times a velocity:where the velocity, U , is related to impeller tip speed or ND. The drag force is usually expressed as function of a drag coefficient, the projected area (which is proportional to D2), fluid density, and velocity asThe total drag force is a sum of skin and form drag forces. The force arising from skin drag is simply 1 2where T , is the wall (or blade) shear stress. The force arising from form drag can be expressed as trailing vortex systems have a low pressure core that coalesces sparged gas to form gas cavities behind the impeller blades. These low-pressure vortex regions may contribute substantially to the form drag contribution of the power. The second objective of this paper is to investigate the possible interrelationship between vortex systems and power consumption for the pitched-blade turbine. This investigation includes a study of the effects of the addition of winglets and fins (added to the impeller blades in the vicinity of the vortex systems) on power consumption.The impeller used in this study was a 45" pitched-blade turbine with four blades. The flows, which may be of importance, are shown in Figure 1 and exist as boundary layers on both the front and back sides of the impeller blades, a wake behind the blade, and a vortex system on the impeller blade tip. However, visual observation studies (Yuan et al., 1980) using neutrally buoyant tracer particles of the flow through the impeller indicate that the wake region behind the blade is not significant, the flow resembling a boundary layer.For the calculation of the skin drag in this work, the boundary layers shown in Figure 1 were assumed to be turbulent on both sides of the impeller blade. It was further assumed that the boundary layers were turbulent, since the impeller Reynolds numbers indicated turbulent conditions in the tank. This, however, was not a critical assumption for the outcome of this study, and a standard correlation was used to calculate skin drag. The calculation of the form drag portion of the power required experimental determination of the pressure drop occurring across the blade. having a projected area A . The drag coefficient in Eq. incorpotaps, 2.4 mm in dia,, on the front and back sides of the blade, as shown in rates both skin and form drag contributions to the drag force. The objective of this paper, in part, is to investigate the contributions of skin and form drag to the power that is transferred from a in mixing has demonstrated the importance ...

Experimental studies of ventilated cavities in a channel

“…Pressure was measured in gassed conditions over the blade. The drag force was calculated as reported by Tay and Tatterson (1985). Sovran et al (1978) reported a drag coefficient of 1.98 for long straight blades placed in unconstricted flow.…”

“…With negative pressure behind the blade, the sparged gas tries to occupy the entire negative pressure zone. The pres- sure coefficient (C P ) at particular point 'P' was calculated as (Tay and Tatterson, 1985) C P = P P /(0.5 L V 2 F ). Fig.…”

“…This difficulty was circumvented by designing and constructing a transparent acrylic channel. The correspondence between the rotational frame of impeller and the one-directional flow of channel is based on the simplified assumptions put forth by Tay and Tatterson (1985). The rotational effect of the impeller gives rise to the velocity with tangential, radial and axial components.…”

Trailing vortices around a 45° pitched‐blade impeller

“…Hockey and Nouri (1996) employed a six-blade 60" PBT and measured mean and rms velocities in the bulk flow and around the turbine using ensemble-averaged and angle-resolved LDA techniques, respectively, and reported a peak velocity of 0.55 Ali et al (1981) observed that only a single trailing vortex was formed at the trailing edge of a four-blade 45" PBT, while Kresta and Wood (1993a) reported that a trailing vortex extending over approximately 20% of the blade was formed at the lower tip of the blade and a smaller one at the top corner of the blade. Tay and Tatterson (1985) reported that the flow over a PBT blade contains boundary layers on the front and back of the blade, a wake behind the blade, and a trailing vortex on the blade tip. However, they indicated that the wake region behind the blade was not significant and the flow resembles a boundary layer.…”

“…The trailing vortices formed behind the blades have a low-pressure core. These low-pressure regions do not contribute to the drag portion of the power consumption of the impeller (Tay and Tatterson, 1985), but may coalesce sparged gas to form gas cavities behind the blades. The trailing vortices have been identified as very important for ligament and sheet production in liquid-liquid dispersion, as shown by Ali et al (1981) and Sheu et a1 (1982), who emphasized that the trailing vortex system is the major flow mechanism responsible for dispersion.…”