scholarly journals A higher-order numerical analysis to study the flow physics and to optimize the design of a short-dwell blade coaters for higher efficiency

2021 ◽  
Vol 2090 (1) ◽  
pp. 012053
Author(s):  
Bapuji Sahoo ◽  
Bikash Mahato ◽  
T. V. S. Sekhar
Keyword(s):  
Amplification Factor ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Material Design ◽  
Navier Stokes ◽  
Contour Plot ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
Runge Kutta Method ◽  
Spatial Derivatives

Abstract Blade coaters are most commonly used for coating of paper and paperboard with higher efficiency. The efficiency of short-dwell blades coaters depends on many factors such as the properties of the coating material, design of the coating reservoir, the types of flow behaviour taking place inside the reservoir, etc. In this work, we have proposed an optimal design of the reservoir to improve the efficiency of short-dwell coaters. The reservoir has been modeled as flow inside a two-dimensional rectangular cavity. Incompressible Navier-Stokes equations in primitive variable formulation have been solved to obtain the flow fields inside the cavity. Spatial derivatives present in the momentum, and continuity equations are evaluated using a sixth-order accurate compact scheme whereas the temporal derivatives are calculated using the fourth-order Runge-Kutta method. The actual rate of convergence of the numerical scheme has been discussed in detail. In addition, the accuracy and stability of the used numerical method are also analysed in the spectral plane with the help of amplification factor and group velocity contour plot. The obtained numerical solutions have been validated with the existing literature. Four different aspect ratio cases (L/H = 3/4,4/3,4/5 and 5/4) have been considered for the simulations including the case of square cavity. It has been observed that L/H = 5/4 case provides best results among all others.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

An investigation on the instability of a flexible liquid-filled rotor

2019 ◽  
Vol 234 (2) ◽  
pp. 165-172
Author(s):  
Guangding Wang ◽  
Huiqun Yuan ◽  
Hongyun Sun
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Coupling Model ◽  
Frequency Equation ◽  
Rotor System ◽  
System Stability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
The Stability

In this paper, the stability of a flexible rotor partially filled with liquid is investigated. On the basis of the Navier-Stokes equations for the incompressible flow, a two-dimensional analytical model is developed for fluid motion. Applying the perturbation method, the linearized Navier-Stokes and continuity equations of fluid particles are obtained. Using the boundary conditions of fluid motion, the fluid forces exerted on the rotor are calculated. According to the established fluid-structure coupling model of the rotor system, the whirling frequency equation, which is applied to determine the stability of the system, is derived. The analysis results of the system stability are compared with the theoretical ones reported in the previous study. Good agreement is shown between the results of the present analysis and the literature results. The influences of the main parameters on the dynamic stability of the rotor system are discussed.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

Reliability of Convective Diffusion Process in Stenosis Blood Vessels

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
R.K. Saket ◽  
Anil Kumar
Keyword(s):  
Mass Transport ◽  
Diffusion Process ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Wall Stress ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Equations ◽  
Recirculation Flow ◽  
Convection Diffusion Equation

This paper presents a convective dominated reliable diffusion process in an axi-symmetric tube with a local constriction simulating a stenos artery considering the porosity effects. The investigations demonstrate the effects of wall shear stress and recirculation flow on the concentration distribution in the vessels lumen and on wall mass transfer keeping the porosity in view. The flow is governed by the incompressible Navier-Stokes equations for Newtonian fluid in porous medium. The convection diffusion equation has been used for the mass transport. The effect of porosity is examined on the velocity field and wall stress. The numerical solutions of the flow equations and the coupled mass transport equations have been obtained using a finite difference method. This paper explains the reliable effects of flow porosity on the mass transport.

Numerical Modeling of Flow Over a Dam Spillway

2006 ◽  
Author(s):  
Iraj Saeedpanah ◽  
M. Shayanfar ◽  
E. Jabbari ◽  
Mohammad Haji Mohammadi
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Iterative Solution ◽  
Free Surface Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
Water Jets ◽  
Pressure Fields ◽  
Good Agreement

Free surface flows are frequently encountered in hydraulic engineering problems including water jets, weirs and around gates. An iterative solution to the incompressible two-dimensional vertical steady Navier-Stokes equations, comprising momentum and continuity equations, is used to solve for the priori unknown free surface, the velocity and the pressure fields. The entire water body is covered by a unstructured finite element grid which is locally refined. The dynamic boundary condition is imposed for the free surface where the pressure vanishes. This procedure is done continuously until the normal velocities components vanish. To overcome numerical errors and oscillations encountering in convection terms, the SUPG (streamline upwinding Petrov-Galerkin) method is applied. The solution method is tested for different discharges onto a standard spillway geometries. The results shows good agreement with available experimental data.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

Turbulent Flow Velocity Between Rotating Co-Axial Disks of Finite Radius

1989 ◽  
Vol 111 (3) ◽  
pp. 333-340 ◽  
Author(s):  
J. F. Louis ◽  
A. Salhi
Keyword(s):  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Finite Radius ◽  
Navier Stokes Equations ◽  
Rotating Cavity ◽  
Tangential Wall ◽  
Frictional Forces

The turbulent flow between two rotating co-axial disks is driven by frictional forces. The prediction of the velocity field can be expected to be very sensitive to the turbulence model used to describe the viscosity close to the walls. Numerical solutions of the Navier–Stokes equations, using a k–ε turbulence model derived from Lam and Bremhorst, are presented and compared with experimental results obtained in two different configurations: a rotating cavity and the outflow between a rotating and stationary disk. The comparison shows good overall agreement with the experimental data and substantial improvements over the results of other analyses using the k–ε models. Based on this validation, the model is applied to the flow between counterrotating disks and it gives the dependence of the radial variation of the tangential wall shear stress on Rossby number.

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