Tangential velocity measurement

Now imagine first that the swirling fluid has an infinite viscosity (behaves like a solid body). Hence, no shearing motion exists between fluid layers at different radii. In this case fluid elements at all radial positions are forced to have the same angular velocity. The angular velocity, f2, is measured in radians per unit of time, usually seconds, and therefore has units s . It equals ve/r, with v the tangential velocity, measured in m/s. Swirl with constant O is called forced vortex flow or solid-body rotation ... 

Here vq is the measured tangential velocity profile at time t and (ve,steady) is the value at steady-state. Both intensity indices have a value of unity at f = 0, and approach zero as t approaches infinity. Figure 4.5.15 shows the variation of the intensity indices with average strain, for an outer cylinder velocity of 0.05 cm s 1. These plots indicate that the mixing process occurs in two stages, where the velocity profile develops only after the droplet concentration profile is essentially uniform. It can be seen that 1 decays to zero at approximately 100 strain units, whereas Iv shows that the steady-state velocity profile is reached only when y ps 400. From Figure 4.5.14 it can be seen that when y = 115, flow is detected... 

Laboratory measurements on hydrocylones have shown that, in the primary vortex, the relation between tangential velocity ut and radius r, is approximately of the form ... 

FIGURE 4M (a) Left Measured and predicted tangential velocities in a 75-nun hydro-( lone right measured and predicted axial velocities in a 75-nun hydrocydone. (b) Predicted fluid streamlines and particle tirgectories in a 75-nim hydrocyclone. 

The flow pattern of the vortex in the secondary combustion chamber was measured with a Laser Doppler Velocimeter (LDV). The profile measurements were performed at various feed rates and air settings as well as different hardware configurations. The LDV measured the axial and tangential velocity vectors of the flow in the hot flame simultaneously. 

An estimate of the time available for growth, Tp, may be obtained from the dense-phase tangential velocity Uijj (equal to r, dijjfdd, with ijj the angle measured from the vertical) at the bubble-emulsion interface ... 

The predicted profiles of mean radial and tangential velocities at the impeller center plane are compared with the experimental data measured by PIV and LDA in Fig. 10.8. A similar comparison for turbulent kinetic energy is shown in Fig. 10.9. 

Less experimental work has been performed for axial impellers. Kresta and Wood [48] performed LDV measurements of mean and fluctuating radial, axial and tangential velocities in cylindrical tanks with a 45 -pitched, four blade turbine at 400 rpm. A review of experimental investigations of turbulent flow in closed and free-surface unbaffled tanks stirred by radial impellers can be found in Ciofalo et al [12]. 

Fig. 7.28. Measured and simulated radial profiles of the tangential velocity component at the axial level of the disc.

One application of the solutions (4-55)-(4-61) is to evaluate the effect of viscous dissipation in the use of a shear rheometer to measure the viscosity of a Newtonian fluid. In this experiment, we subject the fluid in a thin gap between two plane walls to a shear flow by moving one of the walls in its own plane at a known velocity and then measuring the shear stress produced at either wall (by measuring the total tangential force and dividing by the area). In the absence of viscous dissipation, the velocity profile is linear and the shear rate is simply given by the tangential velocity U divided by the gap width d. Now, the constitutive equation, (2-87), for an incompressible Newtonian fluid applied to this simple flow situation takes the form... 

Laser Doppler Velocimetry measurements were performed on a TARS in a cold-flow test rig that simulates an identical hot combustion rig. Axial and tangential velocity mapping of the flow in different cross-sectional planes and along a centerline streamwise plane revealed several important flow structures in the triple annular swirling flow with co-swirling and counter-swirling cases. An axisym-metric recirculation zone was formed in the center of the flow, but the outer... 

The effect of polymer solutions, ejected at very small flow rates at the tip of a finite span hydrofoil, on the inception and extent of tip vortex cavitation is investigated. The results show that the dessinent cavitation numbers are significantly reduced by polymer additives as compared with those in pure water. Moreover, for operating conditions well below critical, the presence of polymer in the vortex core results in the nearly complete elimination of the vapour cavity. These effects can be interpreted on the basis of a modification of the velocity field due to the viscoelastic properties of the polymer solutions. L.D.A. measurements indicate a large decrease of the tangential velocity component in the transition region between the inner solid body rotation co.e and the outer potential vortex flow. Also, a change of the slope of the velocity within the core is observed. 

The tangential velocities weremeasured at a station. 20 m downstream from the tip of the wing. This distance was selected because it was expected that the whole fluid has been set in rotation as a result of the roll-un at the tip and that vortex diffusion was still limited [7]. Measurements were conducted, for non cavitating conditions, at a free stream velocity of 5 m/s, two incidence angles, 5 and 10°, and five ejection conditions. 

The net effect of the two lateral walls of the test section on the non centered vortex is to induce a maximum radial velocity of 0.15 m/s directed upwards. Because of the tangential velocity the polymer will fill up an increasingly larger circular area when convected downstream. The maximum radius occupied by the polymer at the measuring station will be 0.62 mm, comparable to the dimensions where velocity modifications occur. 

It follows, therefore, that tangential velocity distributions at low solids concentrations can be estimated from simple measurements of radial static pressure. This was the idea behind the early studies of tangential velocity distributions in clean liquid flow. Driessen was the first to derive an expression relating the tangential velocity, Vt, to the radial pressure distribution by assuming the radial velocity component negligible in relation to the tangential component, so that... 

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