A shielded hot-wire probe has been developed which permits the determination of mean velocities, rms velocities, and other turbulence parameters in highly turbulent flow fields and in rapidly reversing flows. The instantaneous velocity vector in the flow field may point in any direction. The shield is a small disk with a hole in its center. Two wires are placed close and parallel to each other inside the hole and normal to the axis of the hole. The effect of the thermal wake of the upstream wire on the downstream wire is used to determine the flow direction instantaneously. Only the thermally undisturbed upstream signals pass through the gate of an amplifier and are further processed. The sign of one of the signals is inverted by the amplifier. The probe has been tested in air flow in the velocity range from 0.3 m/sec to 1 0.0 m/sec. This corresponds to Reynolds numbers based on the shield outside diameter from 7.4 X 102 to 2.5 X 104.

Flow parameters were measured in a baffled, turbulent, stirred tank agitated by a six-blade, disk style turbine. The working fluid was air. Mean and fluctuating velocities were measured between the blades of the impeller with a probe mounted on the spinning impeller. Mean velocities, turbulent velocities, one-dimensional energy spectra, and Eulerian autocorrelation functions were measured in the impeller stream by using the shielded hot-wire anemometer of Gunkel et al. (1971) which permits the measurement of turbulence parameters in flows of very high turbulence intensity. Reliable impeller pumping capacities were obtained yielding Q r a d / N D 3 = 1.0 at the impeller periphery. An energy balance on a control volume containing the impeller and the impeller stream showed that the energy put into the tank via the impeller appeared as a net efflux of kinetic energy leaving the control volume. Therefore, most of the energy input to the tank is dissipated in the bulk of the tank. SCOPENo progress in the understanding of mixing operations in stirred tanks can be achieved without a better picture of the flow phenomena in stirred tanks. The main objectives of this study were: to measure flow parameters in a turbulent stirred tank, from them to determine how the energy put into the tank was dissipated, and then to derive theoretically supported scale-up procedures for operations in stirred tanks. The achievement of this last objective is of most immediate importance for practical applications.Previous studies on the flow phenomena in the impeller stream of a stirred tank have reported mean velocities, turbulent velocities, one-dimensional energy spectra, and correlation functions (Kim and Manning, 1964;Bowers, 1965;Cutter, 1966; Sat0 et al., 1967;Mujumdar et al., 1970;Rao and Brodkey, 1972;Cho et al., 1971). The main shortcoming of these studies is the poor precision of the experimental techniques which were not suitable for the high turbulence intensities (up to Svo)found in stirred tanks. Nevertheless, Cutter (1966) concluded that 70% of the energy put into the tank was dissipated within the impeller and the impeller stream, and only 30y0 was dissipated in the bulk of the tank. In the first part of the present paper, accurate flow parameters are reported in the impeller stream from a six-blade, dipk style turbine. An energy balance is then used to determine the amount of energy dissipated in the impeller and the impeller stream. CONCLUSIONS A N D SIGNIFICANCEA very complete picture of the flow pattern in the neighborhood of a six-blade, disk style turbine impeller has been obtained. For the first time velocities between the blades of a rotating impeller have been measured. These measurements indicated that four vortices are present between each pair of blades, two above and two below the disk.Mean velocity profiles in the impeller stream showed a jet like behavior, with the impeller stream entraining fluid as it traveled from the periphery of the impeller to the tank wall. Integration of the velocity profiles yielded ...

O r a d p r e sFig. A2. Velocities and angles used for calculating of the energy flux through control surface 1. tropic at any z in the impeller stream at s = 7 cm: Incorporating these simplifications and neglecting fluctuating velocities raised to the power 3, we get 11 = nrlp j'Ila [ ( ~sres + ~v r e s u2r,~) COST -2 T J r e s K s s i n 7 dz (A16)The flux of kinetic energy through control surface 2 was determined similarly by assuming that uraa was negligible and that the flow was isotropic: r e s , a t + m r e s , a t y z r e s , a t ) c0s-C-2f7res,at&es,at sin 71 rdr (A17) CTres,,t is the sum of the velocity components v,, and ntan, and ure7,,,t is the fluctuating velocity in direction of Ures,at. The -/ Fig. A3. Velocities and angles used for calculating the energy flux through control surface 2.angles and velocity components are shown in Figure A3. All the terms in Equations (AlG) and (A17) were obtained from measured velocities. The control surfaces were set at s = 7 cin and z2 = t 3.75 cm for the data presented in Tahle 2 . Part II. T h e Bulk of the TankTurbulence parameters were measured in the bulk of turbulent stirred tanks of 45.7 and 91.4 cm diameter with air as the working fluid. Three types of turbine impellers were studied ranging in diameter from 22.8 to 45.7 cm. The turbulence in the bulk of the tank was essentially homogeneous and isotropic. The normalized one-dimensional energy spectra and the Eulerian autocorrelation functions were approximately the same throughout the tank and for all tanks, impellers, and operating conditions. The space averaged turbulent velocities were correlated by using the turbulent energy equation. A transformation of the measured spectra from the frequency space to the wave number space was accomplished. Integration of the dissipation spectra in the wave number space confirmed that most of the energy input is dissipated in the bulk of the tank through the turbulent motion. The results were extended to low viscosity liquid systems and used to interpret the data on mass transfer from suspended particles.