Flow of Granular Material through Rotating Cylinders: Modelling Transients

2000 ◽  
Vol 627 ◽  
Author(s):  
Richard J. Spurling ◽  
John F. Davidson ◽  
David M. Scott
Keyword(s):  
Steady State ◽  
Granular Material ◽  
Dynamic Model ◽  
Solid Body ◽  
Flow Rate ◽  
Rotational Speed ◽  
Transport Model ◽  
Volumetric Flow Rate ◽  
Body Motion ◽  
Angle Of Repose

ABSTRACTGranular material, fed continuously into the top of a slowly rotating, slightly inclined cylinder, forms a moving bed. Much of the bed rotates with the cylinder in solid body motion. When particles reach the surface of the bed, they move rapidly down it, and are absorbed once more into the solid body motion. Such cylinders are used in calcining, pharmaceutical manufacture, and drying. A steady state transport model, applicable when the bed depth varies slowly along the cylinder, has existed for around 50 years. The bed surface is considered locally flat, and particles in it fall along the line of steepest descent, inclined to the horizontal at the angle of repose. There is reasonable agreement with experiment.We propose a quasi-steady state dynamical model, in which the steady state model is coupled with a volume balance across an axial element. The model takes the form of a nonlinear diffusion equation which was solved numerically. The parameters of the dynamic model are the dimensions of the cylinder and outlet dam, the inclination of the axis of the cylinder, its rotational speed, the angle of repose of the granular material and its feed volumetric flow rate: the dynamic model has no free parameters. Experiments were conducted using sand, mean particle size 490 μm, in a perspex tube of length 1 m, radius 0.0515 m, lined with sandpaper, with a feed end dam of height 0.029 m, and with no exit dam, or an exit dam of height 0.0105 m. With the system initially in steady state, step changes in feed flow rate, rotational speed or axis inclination were imposed, and the resulting discharge flow rate and bed depth axial profile measured as functions of time. Good agreement is found between model and experiment.

scholarly journals Validation of the generalized model of two-phase thermosyphon loop based on experimental measurements of volumetric flow rate

2016 ◽  
Vol 37 (3) ◽  
pp. 109-138 ◽  
Author(s):  
Henryk Bieliński
Keyword(s):  
Steady State ◽  
Flow Rate ◽  
Vertical Section ◽  
Volumetric Flow Rate ◽  
Working Fluid ◽  
Two Phase ◽  
Generalized Model ◽  
Flow Models ◽  
Theoretical Predictions ◽  
The One

AbstractThe current paper presents the experimental validation of the generalized model of the two-phase thermosyphon loop. The generalized model is based on mass, momentum, and energy balances in the evaporators, rising tube, condensers and the falling tube. The theoretical analysis and the experimental data have been obtained for a new designed variant. The variant refers to a thermosyphon loop with both minichannels and conventional tubes. The thermosyphon loop consists of an evaporator on the lower vertical section and a condenser on the upper vertical section. The one-dimensional homogeneous and separated two-phase flow models were used in calculations. The latest minichannel heat transfer correlations available in literature were applied. A numerical analysis of the volumetric flow rate in the steady-state has been done. The experiment was conducted on a specially designed test apparatus. Ultrapure water was used as a working fluid. The results show that the theoretical predictions are in good agreement with the measured volumetric flow rate at steady-state.

Numerical and experimental investigation of flow phenomena in rotating step-holes for direct-spray-cooled electric motors

2020 ◽  
pp. 146808742091804
Author(s):  
Christopher Beck ◽  
Jürgen Schorr ◽  
Harald Echtle ◽  
Jasmin Verhagen ◽  
Annette Jooss ◽  
...  
Keyword(s):  
Flow Rate ◽  
Electric Motor ◽  
Rotational Speed ◽  
High Speed ◽  
High Efficiency ◽  
Volumetric Flow Rate ◽  
Dielectric Fluid ◽  
Electric Motors ◽  
Test Environment ◽  
Operating Points

Despite their high efficiency, electric motors are thermally limited in some operating points by several types of losses. Whenever temperature–critical components threaten to overheat, the performance is reduced for component protection (derating). The use of a suitable cooling concept may reduce the derating. The design of efficient cooling concepts of electric motors in traction drives with increased power densities is challenging, caused by the fact that the heat releases in the components vary considerably with the operating point. One option to reduce the temperatures is to place the heat sinks close to heat sources. Therefore, direct spray cooling with nozzles located in the rotor shaft is often used for cooling the end windings. The dielectric fluid (e.g. oil) is introduced into the mainly air-filled interior of the electric motor. In the following study, the behavior of the jet in the rotating step-holes at different volumetric flow rates is examined. To carry out the investigation, a new test rig and a novel optically accessible electric motor were designed. In this specifically designed test environment, the shape of the jets of different operating points is investigated by direct high-speed visualization. The cinematography setup is made of a four-light-emitting diode system in combination with a high-speed camera. A combined approach of experiment and simulation is used to find basic mechanisms of spray formation produced by rotating step-holes. Depending on the volumetric flow rate and the rotational speed, the direction of the oil jet gets more curved in relation to the rotating nozzle after exiting the small bore. If the deflection is large, the jet impinges on the wall of the large bore before reaching the end of the nozzle. The jet formation at the exit of the step-hole is mainly driven by the divergent forces in the liquid caused by impingement and the counteracting Coriolis force. Depending on the volumetric flow rate with constant rotational speed, different cross-sectional shapes of the jet at the exit are observed. These characteristic shapes can be grouped as a round undisturbed jet, strands with a connecting lamella and a C-shaped cross-section.

A Simplified Dynamic Model for the Analysis of the Slider Off-Track Motion Due to Head-Disk Interactions

2007 ◽  
Author(s):  
Yanhui Yuan ◽  
Shao Wang
Keyword(s):  
Steady State ◽  
Dynamic Model ◽  
Rotational Speed ◽  
Hard Disk Drives ◽  
Hard Disk ◽  
Degree Of Freedom ◽  
Force Function ◽  
Transverse Displacement ◽  
Disk Drives ◽  
Rotational Mode

The slider off-track motion is a growing concern for hard disk drives with higher densities. In the present study, a five-degree-of-freedom model was developed for the analysis of the slider off-track motion. The situations of a slider in contact with a single bump and multiple bumps were studied. For a single bump, the excitation to the transverse displacement of the slider is close to an impulse. However, for multiple bumps in a sequence, the excitation gives an effect of a step force function with its plateau value dependent on the circumferential spacing of the bumps, and the rotational speed of the disk. In the case of a bump spacing of 50 μm and a rotational speed of 7200 rpm, the transverse displacement may reach a steady-state of more than 1 μm within 10 ms. The off-track motion of the slider is dominated by the rotational mode of the actuator arm and the sway mode of the suspension, and is very weakly affected by other modes.

Deviations Due to Non-Newtonian Influences Within a Miniature Viscous Disk Pump

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Phil Ligrani ◽  
Hui Jiang ◽  
Benjamin Lund ◽  
Jae Sik Jin
Keyword(s):  
Newtonian Fluid ◽  
Flow Rate ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Sucrose Concentration ◽  
Pure Water ◽  
Pressure Rise ◽  
Volumetric Flow Rate ◽  
Newtonian Flow ◽  
Newtonian Behavior

A miniature viscous disk pump (VDP) is utilized to characterize and quantify non-Newtonian fluid deviations due to non-Newtonian influences relative to Newtonian flow behavior. Such deviations from Newtonian behavior are induced by adding different concentrations of sucrose to purified water, with increasing non-Newtonian characteristics as sucrose concentration increases from 0% (pure water) to 10% by mass. The VDP consists of a 10.16 mm diameter disk that rotates above a C-shaped channel with inner and outer radii of 1.19 mm, and 2.38 mm, respectively, and a channel depth of 200 μm. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Within the present study, experimental data are given for rotational speeds of 1200–2500 rpm, fluid viscosities of 0.001–0.00134 Pa s, pressure rises of 0–220 Pa, and flow rates up to approximately 0.00000005 m3/s. The theory of Flumerfelt is modified and adapted for application to the present VDP environment. Included is a new development of expressions for dimensionless volumetric flow rate, and normalized local circumferential velocity for Newtonian and non-Newtonian fluid flows. To quantify deviations due to the magnitude non-Newtonian flow influences, a new pressure rise parameter is employed, which represents the dimensional pressure rise change at a particular flow rate and sucrose concentration, as the flow changes from Newtonian to non-Newtonian behavior. For 5% and 10% sucrose solutions at rotational speeds of 1200–2500 rpm, this parameter increases as the disk dimensional rotational speed increases and as the volumetric flow rate decreases. Associated magnitudes of the pressure difference parameter show that the fluid with the larger sucrose concentration (by mass) produces significantly larger differences between Newtonian and non-Newtonian fluid flow, for each value of dimensional volumetric flow rate. For each disc rotational speed, compared to Newtonian data, dimensional pressure rise variations with dimensional volumetric flow rate, which are associated with the non-Newtonian data, are generally lower when compared at a particular volumetric flow rate. Agreement with analytic results, for any given flow rate, rotational speed, and flow passage height, validates the shear stress model employed to represent non-Newtonian behavior, as well as the analytic equations and tools (based upon the Navier–Stokes equations) which are employed to predict measured behavior over the investigated range of experimental conditions.

Miniature Single-Disk Viscous Pump (Single-DVP), Performance Characterization

2005 ◽  
Vol 128 (3) ◽  
pp. 602-610 ◽  
Author(s):  
Danny Blanchard ◽  
Phil Ligrani ◽  
Bruce Gale
Keyword(s):  
Flow Rate ◽  
Rotational Speed ◽  
Pressure Rise ◽  
Volumetric Flow Rate ◽  
Outer Radius ◽  
Fluid Viscosity ◽  
Pump Chamber ◽  
Inner Radius ◽  
Viscous Pump ◽  
Single Disk

The development and testing of a rotating single-disk viscous pump are described. This pump consists of a 10.16mm diameter spinning disk, and a pump chamber, which are separated by a small gap that forms the fluid passage. The walls of the pump chamber form a C-shaped channel with an inner radius of 1.19mm, an outer radius of 2.38mm, and a depth of 40, 73, 117, or 246μm. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Experimental flow rate and pressure rise data are obtained for rotational speeds from 100to5000rpm, fluid chamber heights from 40to246μm, flow rates from 0to4.75ml∕min, pressure rises from 0to31.1kPa, and fluid viscosities from 1to62mPas. An analytical expression for the net flow rate and pressure rise, as dependent on the fluid chamber geometry, disk rotational speed, and fluid viscosity, is derived and found to agree with the experimental data. The flow rate and pressure rise of the pump vary nearly linearly with rotational speed. The volumetric flow rate does not change significantly with changes in fluid viscosity for the same rotational speed and pumping circuit. Advantages of the disk pumps include simplicity, ease of manufacture, ability to produce continuous flow with a flow rate that does not vary significantly in time, and ability to pump biological samples without significant alteration or destruction of cells, protein suspension, or other delicate matter.

The pumping characteristics of screw rotors. I. The theory of calculation of the pumping capacity of screw rotors

1987 ◽  
Vol 52 (2) ◽  
pp. 357-371 ◽  
Author(s):  
František Rieger
Keyword(s):  
Present State ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Screw Rotor ◽  
Screw Rotors

This paper summarizes the present state of the theory of calculation of the pumping capacity of screw rotors. The calculation starts from the equation for the volumetric flow rate of the flow between two unconfined plates modified by correction coefficients obtained from the relationships for the flow rate in simpler geometrical configurations to which the screw rotor may be, under certain circumstances, reduced.

Pahoehoe and aa in Hawaii: volumetric flow rate controls the lava structure

1990 ◽  
Vol 52 (8) ◽  
pp. 615-628 ◽  
Author(s):  
Scott K Rowland ◽  
George PL Walker
Keyword(s):  
Flow Rate ◽  
Volumetric Flow Rate

Simultaneous Measuring Method for Both Volumetric Flow Rates of Air-Water Mixture Using a Turbine Flowmeter

1996 ◽  
Vol 118 (1) ◽  
pp. 29-35 ◽  
Author(s):  
K. Minemura ◽  
K. Egashira ◽  
K. Ihara ◽  
H. Furuta ◽  
K. Yamamoto
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Volumetric Flow Rate ◽  
Oil Field ◽  
Liquid Density ◽  
Water Mixture ◽  
Rotor Speed ◽  
Flow Rates ◽  
Field Development ◽  
Turbine Flowmeter

A turbine flowmeter is employed in this study in connection with offshore oil field development, in order to measure simultaneously both the volumetric flow rates of air-water two-phase mixture. Though a conventional turbine flowmeter is generally used to measure the single-phase volumetric flow rate by obtaining the rotational rotor speed, the method proposed additionally reads the pressure drop across the meter. After the pressure drop and rotor speed measured are correlated as functions of the volumetric flow ratio of the air to the whole fluid and the total volumetric flow rate, both the flow rates are iteratively evaluated with the functions on the premise that the liquid density is known. The evaluated flow rates are confirmed to have adequate accuracy, and thus the applicability of the method to oil fields.

Development of Cooling System for a Large Area at High Heat Flux by Using Flow Boiling in Narrow Channels

2009 ◽  
Author(s):  
Shinichi Miura ◽  
Yukihiro Inada ◽  
Yasuhisa Shinmoto ◽  
Haruhiko Ohta
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flow Rate ◽  
Mass Velocity ◽  
Cooling System ◽  
Volumetric Flow Rate ◽  
High Heat ◽  
High Heat Flux ◽  
Gap Size ◽  
Heated Channel

Advance of an electronic technology has caused the increase of heat generation density for semiconductors densely integrated. Thermal management becomes more important, and a cooling system for high heat flux is required. It is extremely effective to such a demand using flow boiling heat transfer because of its high heat removal ability. To develop the cooling system for a large area at high heat flux, the cold plate structure of narrow channels with auxiliary unheated channel for additional liquid supply was devised and confirmed its validity by experiments. A large surface of 150mm in heated length and 30mm in width with grooves of an apex angle of 90 deg, 0.5mm depth and 1mm in pitch was employed. A structure of narrow rectangular heated channel between parallel plates with an unheated auxiliary channel was employed and the heat transfer characteristics were examined by using water for different combinations of gap sizes and volumetric flow rates. Five different liquid distribution modes were tested and their data were compared. The values of CHF larger than 1.9×106W/m2 for gap size of 2mm under mass velocity based on total volumetric flow rate and on the cross section area of main heated channel 720kg/m2s or 1.7×106W/m2 for gap size of 5mm under 290kg/m2s were obtained under total volumetric flow rate 4.5×10−5m3/s regardless of the liquid distribution modes. Under several conditions, the extensions of dry-patches were observed at the upstream location of the main heated channel resulting burnout not at the downstream but at the upstream. High values of CHF larger than 2×106W/m2 were obtained only for gap size of 2mm. The result indicates that higher mass velocity in the main heated channel is more effective for the increase in CHF. It was clarified that there is optimum flow rate distribution to obtain the highest values of CHF. For gap size of 2mm, high heat transfer coefficient as much as 7.4×104W/m2K were obtained at heat flux 1.5×106W/m2 under mass velocity 720kg/m2s based on total volumetric flow rate and on the cross section area of main heated channel. Also to obtain high heat transfer coefficient, it is more useful to supply the cooling liquid from the auxiliary unheated channel for additional liquid supply in the transverse direction perpendicular to the flow in the main heated channel.

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