Generalized IBL models for gravity-driven flow over inclined surfaces

Abstract In this investigation we propose several generalized first-order integral-boundary-layer (IBL) models to simulate the two-dimensional gravity-driven flow of a thin fluid layer down an incline. Various cases are considered and include: isothermal and non-isothermal flows, flat and wavy bottoms, porous and non-porous surfaces, constant and variable fluid properties, and Newtonian and non-Newtonian fluids. A numerical solution procedure is also proposed to solve the various model equations. Presented here are some results from our numerical experiments. To validate the generalized IBL models comparisons were made with existing results and the agreement was found to be reasonable.

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Viscous Thin-Film Flow Over a Round-Crested Weir

Journal of Fluids Engineering ◽

10.1115/1.2823522 ◽

1999 ◽

Vol 121 (3) ◽

pp. 673-677 ◽

Cited By ~ 11

Author(s):

Kenneth J. Ruschak ◽

Steven J. Weinstein

Keyword(s):

Empirical Equation ◽

Film Flow ◽

Flow Profile ◽

Thin Film Flow ◽

Order Ordinary Differential Equation ◽

First Order ◽

Entire Flow ◽

Gravity Driven ◽

Gravity Driven Flow ◽

The Relationship

Gravity-driven flow over a round-crested weir is analyzed for viscous flow. An equation for the entire flow profile is obtained by simplifying the equations for slowly varying film thickness, assuming a velocity profile, and integrating across the film. Solution of the resulting first order, ordinary differential equation requires a boundary condition generated at a critical point of the flow, beyond which waves cannot propagate upstream. Results for the relationship between head and flow rate are consolidated on a dimensionless master curve represented by an empirical equation.

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EFFECT OF FLOCCULATING AGENTS ON DRAG IN GRAVITY-DRIVEN FLOW SYSTEMS

International Journal of Fluid Mechanics Research ◽

10.1615/interjfluidmechres.2017015534 ◽

2017 ◽

Vol 44 (4) ◽

pp. 339-347

Author(s):

M. K. S. V. Raghav ◽

Ravi Teja ◽

Chirravuri Subbarao

Keyword(s):

Flow Systems ◽

Gravity Driven ◽

Gravity Driven Flow

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Drag reduction using mixed solutions of hydrotrope and surfactant in gravity driven flow systems

i-manager’s Journal on Future Engineering and Technology ◽

10.26634/jfet.8.3.2218 ◽

2013 ◽

Vol 8 (3) ◽

pp. 22-27

Author(s):

M. Venkata Ramana ◽

◽

Ch. V. Subbarao ◽

P. V. Gopal singh ◽

Krishna Prasad K.M.M ◽

...

Keyword(s):

Drag Reduction ◽

Mixed Solutions ◽

Flow Systems ◽

Gravity Driven ◽

Gravity Driven Flow

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Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions

Fractal and Fractional ◽

10.3390/fractalfract5010015 ◽

2021 ◽

Vol 5 (1) ◽

pp. 15

Author(s):

Misir J. Mardanov ◽

Yagub A. Sharifov ◽

Yusif S. Gasimov ◽

Carlo Cattani

Keyword(s):

Integral Equation ◽

Integral Boundary Conditions ◽

Contraction Mapping Principle ◽

Boundary Problems ◽

Integral Boundary ◽

Multipoint Problem ◽

First Order ◽

Banach Contraction ◽

First Time ◽

Banach Contraction Mapping Principle

This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem (SFPT) on the integral equation, we can show that the solution of the multipoint problem exists and it is unique.

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Portable analyzer for continuous monitoring of sulfur dioxide in gas stream based on amperometric detection and stabilized gravity-driven flow

Sensors and Actuators B Chemical ◽

10.1016/j.snb.2015.11.008 ◽

2016 ◽

Vol 225 ◽

pp. 24-33 ◽

Cited By ~ 5

Author(s):

Mohamed A.R.A. Alnaqbi ◽

Muna S. Bufaroosha ◽

Mohamed H. Al-Marzouqi ◽

Sayed A.M. Marzouk

Keyword(s):

Sulfur Dioxide ◽

Continuous Monitoring ◽

Amperometric Detection ◽

Gravity Driven ◽

Portable Analyzer ◽

Gravity Driven Flow

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Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

International Journal of Rotating Machinery ◽

10.1155/s1023621x98000074 ◽

1998 ◽

Vol 4 (2) ◽

pp. 73-90 ◽

Cited By ~ 19

Author(s):

Peter Vadasz ◽

Saneshan Govender

Keyword(s):

Rayleigh Number ◽

Porous Layer ◽

Temperature Fields ◽

Wave Number ◽

Marginal Stability ◽

Two Dimensional ◽

Wide Range ◽

Gravity Driven ◽

Gravity Driven Flow ◽

The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

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The Interplay of Permeability and Fluid Properties as a First Order Control of Heat Transport, Venting Temperatures and Venting Salinities at Mid-Ocean Ridge Hydrothermal Systems

Frontiers in Geofluids ◽

10.1002/9781444394900.ch10 ◽

2011 ◽

pp. 132-141

Author(s):

T. Driesner

Keyword(s):

Heat Transport ◽

Hydrothermal Systems ◽

First Order ◽

Mid Ocean Ridge ◽

Fluid Properties ◽

Ocean Ridge

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Modeling Gas-Liquid Head Performance of Electrical Submersible Pumps

Risk and Reliability and Evaluation of Components and Machinery ◽

10.1115/pvp2004-3006 ◽

2004 ◽

Cited By ~ 2

Author(s):

Datong Sun ◽

Mauricio Prado

Keyword(s):

Petroleum Industry ◽

Nuclear Industry ◽

Two Phase ◽

Liquid Model ◽

Electrical Submersible Pumps ◽

Pump Head ◽

Fluid Properties ◽

Interfacial Characteristic ◽

Model Equations ◽

Shock Loss

This study presents a new gas-liquid model to predict Electrical Submersible Pumps (ESP) head performance. The newly derived approach based on gas-liquid momentum equations along pump channels has improved the Sachdeva model [1, 2] in the petroleum industry and generalized the Minemura model [3] in the nuclear industry. The new two-phase model includes novel approaches for wall frictional losses for each phase using a gas-liquid stratified assumption and existing correlations, a new shock loss model incorporating rotational speeds, a new correlation for drag coefficient and interfacial characteristic length effects by fitting the model results with experimental data, and an algorithm to solve the model equations. The model can predict pressure and void fraction distributions along impellers and diffusers in addition to the pump head performance curve under different fluid properties, pump intake conditions, and rotational speeds.

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