An Energy Assessment for Liquids in a Filled Precessing Spherical Cavity

1973 ◽  
Vol 40 (4) ◽  
pp. 851-856 ◽  
Author(s):  
J. P. Vanyo
Keyword(s):  
Energy Dissipation ◽  
Turbulent Flows ◽  
Spherical Cavity ◽  
Fluid Motion ◽  
Analytical Models ◽  
Physical Parameters ◽  
Energy Assessment ◽  
Analytical Approximations ◽  
Dissipation Rates ◽  
Direct Applicability

Experimental results and analytical approximations for energy dissipation due to liquids in a filled precessing spherical cavity are presented. The range of physical parameters include kinematic viscosities from 1 to 1000 centistokes, half coning angles from 5/8 to 10 deg, precession speeds from 0.15 to 200 rpm, and spin speeds (relative to the precessing frame) of from 7.5–900 rpm. These parameters and the associated energy dissipation rates, as low as 10−4 watts, place the results in the region of direct applicability to spinning satellite stability problems. A dimensionless parameter related to an Ekman number is used to correlate energy dissipation rates with laminar, intermediate, and fully turbulent flows. The reduced data are integrated with data from other sources and used to develop equations in dimensionless form for the experimental and analytical results. The results, while not defining details of fluid motion, place experimental bounds on the integrated shear stress at the cavity wall for analytical models.

Measurement of Energy Dissipation in a Liquid-Filled, Precessing, Spherical Cavity

1971 ◽  
Vol 38 (3) ◽  
pp. 674-682 ◽  
Author(s):  
J. P. Vanyo ◽  
P. W. Likins
Keyword(s):  
Energy Dissipation ◽  
Spherical Cavity ◽  
Mechanical Energy ◽  
Rigid Sphere ◽  
Analytical Approximations ◽  
Constant Rate ◽  
Experimental Apparatus ◽  
Half Angle ◽  
Analytical Estimation ◽  
Order Of Magnitude

Methods are described for the experimental measurement and analytical estimation of the losses of mechanical energy in a spinning and precessing spherical cavity filled with fluid. Test results are presented and correlated with analytical estimates based on two different mathematical models of the system. The experimental apparatus is a gimbaled mechanism which constrains a rigid body with a spherical cavity to spin about an axis through the cavity center at a constant rate ψ˙, while the spin axis cones about an inertially fixed axis at a constant rate φ˙ with a constant conical half angle θ. Measurements of current required by motors which maintain the constancy of ψ˙ and φ˙ provide a measure of the energy losses in the fluid in the steady state, after suitable dry test calibrations. Experimental results are presented for a 22-cm-dia cavity containing fluids of kinematic viscosities of 1 and 20 centistokes, with θ ranging from 5–30 deg, ψ˙ ranging from 60–1000 rpm, and φ˙ ranging from −400 to +600 rpm. Analytical approximations are developed on the basis of (a) a variation of the oscillating flat-plate solution, and (b) a rigid interior sphere of fluid idealization. The rigid sphere method gives energy dissipation rates that are generally valid over most of the important range of parameters, while the oscillating surface solution is generally an order of magnitude too low in its predictions of energy dissipation.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

DIMENSIONLESS PHYSICAL-MATHEMATICAL MODELING OF TURBULENT NATURAL CONVECTION

2021 ◽  
Vol 20 (3) ◽  
pp. 37
Author(s):  
S. A. Verdério Júnior ◽  
V. L. Scalon ◽  
S. R. Oliveira ◽  
P. C. Mioralli ◽  
E. Avellone
Keyword(s):  
Mathematical Modeling ◽  
Natural Convection ◽  
Turbulent Flows ◽  
Convection Heat Transfer ◽  
Thermal Engineering ◽  
Physical Parameters ◽  
Problem Situation ◽  
Dimensionless Numbers ◽  
Turbulent Natural Convection ◽  
Cooling Coils

Natural convection heat transfer is present in the most diverse applications of Thermal Engineering, such as in electronic equipment, transmission lines, cooling coils, biological systems, etc. The correct physical-mathematical modeling of this phenomenon is crucial in the applied understanding of its fundamentals and the design of thermal systems and related technologies. Dimensionless analyses can be applied in the study of flows to reduce geometric and experimental dependence and facilitate the modeling process and understanding of the main influence physical parameters; besides being used in creating models and prototypes. This work presents a methodology for dimensionless physical-mathematical modeling of natural convection turbulent flows over isothermal plates, located in an “infinite” open environment. A consolidated dimensionless physical-mathematical model was defined for the studied problem situation. The physical influence of the dimensionless numbers of Grashof, Prandtl, and Turbulent Prandtl was demonstrated. The use of the Theory of Dimensional Analysis and Similarity and its application as a tool and numerical device in the process of building and simplifying CFD simulations were discussed.

Behaviour in flow: perspectives on the distribution and dispersion of meroplanktonic larvae in the water column

2001 ◽  
Vol 58 (1) ◽  
pp. 86-98 ◽  
Author(s):  
Anna Metaxas
Keyword(s):  
Water Column ◽  
Turbulent Flows ◽  
Larval Dispersal ◽  
Spatial Scales ◽  
Fluid Motion ◽  
Benthic Boundary Layer ◽  
Larval Distribution ◽  
Physical Measurements ◽  
Marine Benthic Invertebrates

For marine benthic invertebrates with meroplanktonic larvae, the relative importance of hydrodynamics and swimming behaviour in determining larval dispersal in the water column, particularly at small spatial scales, has not been determined. In the field, larval aggregations recorded at physical and biological discontinuities in the water column were attributed to hydrodynamics. Similar aggregations obtained in the absence of flow in the laboratory indicate a potentially significant role of behaviour. At large spatial scales, larval distribution in the plankton is mainly regulated by horizontal advection. However, the ability of larvae to behaviourally regulate their position at scales of micrometres to metres when exposed to turbulent fluid motion in the water column, as evidenced in the benthic boundary layer, is unknown. Evaluation of swimming in turbulent flows in the water column is an intriguing area of research, which involves several constraints. In the field, quantification of behaviour is limited by low success in tracking larvae and lack of appropriate observational tools. In the laboratory, the generation and quantification of flow regimes that are representative of those in the field remains a challenge. An approach that integrates biological and physical measurements within realistic ranges is necessary to advance our understanding of larval dispersal.

scholarly journals In pursuit of giants

2020 ◽  
Vol 644 ◽  
pp. A144
Author(s):  
D. Donevski ◽  
A. Lapi ◽  
K. Małek ◽  
D. Liu ◽  
C. Gómez-Guijarro ◽  
...  
Keyword(s):  
Star Formation ◽  
Galaxy Evolution ◽  
Galaxy Formation ◽  
Main Sequence ◽  
Stellar Mass ◽  
Starburst Galaxies ◽  
Analytical Models ◽  
Physical Parameters ◽  
Star Forming ◽  
Galaxy Populations

The dust-to-stellar mass ratio (Mdust/M⋆) is a crucial, albeit poorly constrained, parameter for improving our understanding of the complex physical processes involved in the production of dust, metals, and stars in galaxy evolution. In this work, we explore trends of Mdust/M⋆ with different physical parameters and using observations of 300 massive dusty star-forming galaxies detected with ALMA up to z ≈ 5. Additionally, we interpret our findings with different models of dusty galaxy formation. We find that Mdust/M⋆ evolves with redshift, stellar mass, specific star formation rates, and integrated dust size, but that evolution is different for main-sequence galaxies than it is for starburst galaxies. In both galaxy populations, Mdust/M⋆ increases until z ∼ 2, followed by a roughly flat trend towards higher redshifts, suggesting efficient dust growth in the distant universe. We confirm that the inverse relation between Mdust/M⋆ and M⋆ holds up to z ≈ 5 and can be interpreted as an evolutionary transition from early to late starburst phases. We demonstrate that the Mdust/M⋆ in starbursts reflects the increase in molecular gas fraction with redshift and attains the highest values for sources with the most compact dusty star formation. State-of-the-art cosmological simulations that include self-consistent dust growth have the capacity to broadly reproduce the evolution of Mdust/M⋆ in main-sequence galaxies, but underestimating it in starbursts. The latter is found to be linked to lower gas-phase metallicities and longer dust-growth timescales relative to observations. The results of phenomenological models based on the main-sequence and starburst dichotomy as well as analytical models that include recipes for rapid metal enrichment are consistent with our observations. Therefore, our results strongly suggest that high Mdust/M⋆ is due to rapid dust grain growth in the metal-enriched interstellar medium. This work highlights the multi-fold benefits of using Mdust/M⋆ as a diagnostic tool for: (1) disentangling main-sequence and starburst galaxies up to z ∼ 5; (2) probing the evolutionary phase of massive objects; and (3) refining the treatment of the dust life cycle in simulations.

scholarly journals Multi-Physical Design and Resonant Controller Based Trajectory Tracking of the Electromagnetically Driven Fast Tool Servo

Actuators ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 28
Author(s):  
Imran Hussain ◽  
Wei Xia ◽  
Dongpo Zhao ◽  
Peng Huang ◽  
Zhiwei Zhu
Keyword(s):  
Natural Frequency ◽  
Trajectory Tracking ◽  
Voice Coil Motor ◽  
Diamond Turning ◽  
Analytical Models ◽  
Physical Parameters ◽  
Fast Tool Servo ◽  
Element Analysis ◽  
Loop Control ◽  
Resonant Controller

In this paper, a voice coil motor (VCM) actuated fast tool servo (FTS) system is developed for diamond turning. To guide motions of the VCM actuator, a crossed double parallelogram flexure mechanism is selected featuring totally symmetric structure with high lateral stiffness. To facilitate the determination of the multi-physical parameters, analytical models of both electromagnetic and mechanical systems are developed. The designed FTS with balanced stroke and natural frequency is then verified through the finite element analysis. Finally, the prototype of the VCM actuated FTS is fabricated and experimentally demonstrated to achieve a stroke of ±59.02 μm and a first natural frequency of 253 Hz. By constructing a closed-loop control using proportional–integral–derivative (PID) controller with the internal-model based resonant controller, the error for tracking a harmonic trajectory with ±10 μm amplitude and 120 Hz frequency is obtained to be ±0.2 μm, demonstrating the capability of the FTS for high accuracy trajectory tracking.

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