Transient internal waves produced by a moving body in a tank of density-stratified fluid

1973 ◽  
Vol 61 (3) ◽  
pp. 465-480 ◽  
Author(s):  
E. W. Graham
Keyword(s):  
Steady State ◽  
Surface Waves ◽  
Internal Waves ◽  
Stratified Fluid ◽  
The Body ◽  
Wave System ◽  
Similarity Parameter ◽  
Steady State Condition ◽  
Towing Tank ◽  
Moving Body

The internal waves produced by a moving body are generally longer in the direction of motion than the corresponding surface waves. This difference is accentuated when the density variation is slight and the body velocity is large in which case a very long towing tank may be required for the simulation of a steady-state condition. The following theoretical study of transient waves is intended as a step in relating test conditions and requisite towing-tank sizes.A source–sink pair travelling for a finite time is used to represent the restricted motion of a body in a tank. The approximate length and volume of the body are fixed, but its precise shape (somewhat irregular and slightly time dependent) is assumed to be of secondary importance and is not calculated here. The density-stratified fluid is assumed to have a constant Brunt–Väisälä frequency.A solution in the form of a triple sum over the tank eigenfunctions applies quite generally for the internal wave system (neglecting surface waves and the potential-flow-type solution near the body). Examples covering the large-scale structure of the flow field have been solved for two values of an approximate similarity parameter. The value of the similarity parameter indicates how closely steady-state conditions are approached. The first (larger) value chosen produces a well-defined quasi-steady state near the body with transient fluctuations of the order of ± 10%. The second (smaller) value gives a poorly defined quasisteady state with fluctuations of the order of ±50%. More elaborate studies varying the tank length, width and depth could be made by programming the calculations.The effect of a collapsing wake has not been considered here, but might possibly be treated by similar methods.

Motion of an axisymmetric body in a rotating stratified fluid confined between two parallel planes

1969 ◽  
Vol 38 (4) ◽  
pp. 833-842 ◽  
Author(s):  
D. V. Krishna ◽  
L. V. Sarma
Keyword(s):  
Steady State ◽  
Oblate Spheroid ◽  
Vertical Axis ◽  
Vertical Gradient ◽  
Steady State Solution ◽  
Stratified Fluid ◽  
Axisymmetric Body ◽  
The Body ◽  
Homogeneous Fluid ◽  
Axis Of Rotation

We consider here the flow due to the oscillation of a slender oblate spheroid in a non-homogeneous, rotating fluid confined between two parallel planes which are perpendicular to the (vertical) axis of rotation. The direction of oscillation of the spheroid is perpendicular to the axis of rotation. By solving a set of dual integrals the steady-state solution is obtained in the two cases when the plates are at an infinite distance from the body and when they are at a large but finite distance. The singular or discontinuous surfaces observed in the case of homogeneous fluid are absent here. Also, the steady-state velocity is no longer independent of the distance along the axis of rotation. The velocity has now a vertical gradient, an important feature in the case of stratified fluid. It is also found that the presence of the plane boundaries increases the force on the body.

scholarly journals Computational Performance of Disparate Lattice Boltzmann Scenarios under Unsteady Thermal Convection Flow and Heat Transfer Simulation

Computation ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 65
Author(s):  
Aditya Dewanto Hartono ◽  
Kyuro Sasaki ◽  
Yuichi Sugai ◽  
Ronald Nguele
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Natural Convection ◽  
Lattice Boltzmann ◽  
Numerical Results ◽  
Convection And Heat Transfer ◽  
Steady State Condition ◽  
Physical Systems ◽  
Flow And Heat Transfer ◽  
Computational Performance

The present work highlights the capacity of disparate lattice Boltzmann strategies in simulating natural convection and heat transfer phenomena during the unsteady period of the flow. Within the framework of Bhatnagar-Gross-Krook collision operator, diverse lattice Boltzmann schemes emerged from two different embodiments of discrete Boltzmann expression and three distinct forcing models. Subsequently, computational performance of disparate lattice Boltzmann strategies was tested upon two different thermo-hydrodynamics configurations, namely the natural convection in a differentially-heated cavity and the Rayleigh-Bènard convection. For the purposes of exhibition and validation, the steady-state conditions of both physical systems were compared with the established numerical results from the classical computational techniques. Excellent agreements were observed for both thermo-hydrodynamics cases. Numerical results of both physical systems demonstrate the existence of considerable discrepancy in the computational characteristics of different lattice Boltzmann strategies during the unsteady period of the simulation. The corresponding disparity diminished gradually as the simulation proceeded towards a steady-state condition, where the computational profiles became almost equivalent. Variation in the discrete lattice Boltzmann expressions was identified as the primary factor that engenders the prevailed heterogeneity in the computational behaviour. Meanwhile, the contribution of distinct forcing models to the emergence of such diversity was found to be inconsequential. The findings of the present study contribute to the ventures to alleviate contemporary issues regarding proper selection of lattice Boltzmann schemes in modelling fluid flow and heat transfer phenomena.

Continuous determination of the volume of a space in a non steady state condition

1974 ◽  
Vol 36 (1) ◽  
pp. 59-66
Author(s):  
Oscar A. Gómez-Poviña ◽  
Carmen Sainz de Calatroni ◽  
Susana Orden de Puhl ◽  
Mariano J. Guerrero
Keyword(s):  
Steady State ◽  
State Condition ◽  
Steady State Condition ◽  
Continuous Determination

Generation of long subharmonic internal waves by surface waves

2016 ◽  
Vol 106 ◽  
pp. 12-26 ◽  
Author(s):  
Navid Tahvildari ◽  
James M. Kaihatu ◽  
William S. Saric
Keyword(s):  
Surface Waves ◽  
Internal Waves

Internal-inertia waves in a fluid of variable depth

1973 ◽  
Vol 73 (1) ◽  
pp. 205-213 ◽  
Author(s):  
W. D. McKee
Keyword(s):  
Exact Solutions ◽  
Surface Waves ◽  
Internal Waves ◽  
Vertical Velocity ◽  
General Problem ◽  
Three Dimensional ◽  
Variable Depth ◽  
Internal Inertia ◽  
Perturbation Pressure ◽  
Rotating Stratified Fluid

AbstractWaves in a rotating, stratified fluid of variable depth are considered. The perturbation pressure is used throughout as the dependent variable. This proves to have some advantages over the use of the vertical velocity. Some previous three-dimensional solutions for internal waves in a wedge are shown to be incorrect and the correct solutions presented. A WKB analysis is then performed for the general problem and the results compared with the exact solutions for a wedge. The WKB solution is also applied to long surface waves on a rotating ocean.

An Approach for Snaky Well Productivity under Steady-State Condition

2006 ◽  
Author(s):  
Zhilin Qi ◽  
Zhimin Du ◽  
Baosheng Liang ◽  
Yong Tang ◽  
Shouping Wang ◽  
...  
Keyword(s):  
Steady State ◽  
State Condition ◽  
Well Productivity ◽  
Steady State Condition

Modeling the performance of biodegradation of textile wastewater using polyurethane foam sponge cube as a supporting medium

2010 ◽  
Vol 62 (12) ◽  
pp. 2801-2810 ◽  
Author(s):  
Yen-Hui Lin
Keyword(s):  
Steady State ◽  
Polyurethane Foam ◽  
Textile Wastewater ◽  
Pilot Scale ◽  
Biofilm Reactor ◽  
Column Test ◽  
Steady State Condition ◽  
Suspended Biomass ◽  
The Government ◽  
Carbon Dioxide Co2

A pilot-scale fixed-biofilm reactor (FBR) was established to treat textile wastewater to evaluate the feasibility of replacing conventional treatment processes that involve activated sludge and coagulation units. A kinetic model was developed to describe the biodegradation of textile wastewater by FBR. Batch kinetic tests were performed to evaluate the biokinetic parameters that are used in the model. FBR column test was fed with a mean COD of 692 mg/L of textile wastewater from flow equalization unit. The influent flow rate was maintained at 48.4 L/h for FBR column test. Experimental data and model-predicted data for substrate effluent concentration (as COD), concentration of suspended biomass in effluent and the amount of carbon dioxide (CO2) produced in the effluent agree closely with each other. Microscopic observations demonstrated that the biofilm exhibited a uniform distribution on the surface of polyurethane foam sponge. Under a steady-state condition, the effluent COD from FBR was about 14.7 mg COD/L (0.0213 Sb0), meeting the discharge standard (COD < 100 mg/L) that has been set by the government of Taiwan for textile wastewater effluent. The amount of biofilm and suspended biomass reached a maximal value in the steady state when the substrate flux reached a constant value and remained maximal. Approximately 33% of the substrate concentration (as COD) was converted to CO2 during biodegradation in the FBR test. The experimental and modeling schemes proposed in this study could be employed to design a full-scale FBR to treat textile wastewater.

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