Deformation Process of a Water Droplet Impinging on a Solid Surface

1995 ◽  
Vol 117 (3) ◽  
pp. 394-401 ◽  
Author(s):  
Natsuo Hatta ◽  
Hitoshi Fujimoto ◽  
Hirohiko Takuda
Keyword(s):  
Solid Surface ◽  
Central Region ◽  
Deformation Process ◽  
Stokes Equations ◽  
Liquid Droplet ◽  
Navier Stokes ◽  
Maximum Diameter ◽  
Navier Stokes Equations ◽  
First Case ◽  
Practical Standpoint

This paper is concerned with numerical simulations of the deformation behavior of a liquid droplet impinging on a flat solid surface, as well as the flow field inside the droplet. In the present situation, the case where a droplet impinges on the surface at room temperature with a speed in the order of a few [m/s], is treated. These simulations were performed using the MAC-type solution method to solve a finite-differencing approximation of the Navier-Stokes equations governing an axisymmetric and incompressible fluid flow. For the first case where the liquid is water, the liquid film formed by the droplet impinging on the solid surface flows radially along it and expands in a fairly thin discoid-like shape. Thereafter, the liquid flow shows a tendency to stagnate at the periphery of the circular film, with the result that water is concentrated there is a doughnut-like shape. Subsequently, the water begins to flow backwards toward the center where it accumulates in the central region. For the second case where a n-heptane droplet impinges the surface, the film continues to spread monotonically up to a maximum diameter and there is no recoiling process to cause a backwards flow towards the central region. In this study the whole deformation process was investigated from numerical as well as experimental points of view. We find that the results obtained by the present mathematical model give fairly good agreement with the experimental observations. The effects of the viscous stresses and the surface tension on the deformation process of the droplets are estimated and discussed from a practical standpoint.

scholarly journals A class of exact solutions of equations for plane steady motion of incompressible fluids of variable viscosity in presence of body force

2018 ◽  
Vol 7 (3) ◽  
pp. 77
Author(s):  
Mushtaq Ahmed ◽  
Waseem Ahmed Khan ◽  
S M. Shad Ahsen
Keyword(s):  
Exact Solutions ◽  
Body Force ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Steady Motion ◽  
Incompressible Fluids ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Case

This paper determines a class of exact solutions for plane steady motion of incompressible fluids of variable viscosity with body force term in the Navier-Stokes equations. The class consists of stream function  characterized by equation , in polar coordinates ,  where ,  and  are continuously differentiable functions, derivative of  is non-zero but double derivative of  is zero. We find exact solutions, for a suitable component of body force, considering two cases based on velocity profile. The first case fixes both the functions ,  and provides viscosity as function of temperature. Where as the second case fixes the function , leaves  arbitrary and provides viscosity and temperature for the arbitrary function . In both the cases, we can create infinite set of expressions for streamlines, viscosity function, generalized energy function and temperature distribution in the presence of body force.  

scholarly journals Toward coherently representing turbulent wall-flow dynamics

2013 ◽  
Vol 734 ◽  
pp. 1-4 ◽  
Author(s):  
J. C. Klewicki
Keyword(s):  
Solid Surface ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Flow Dynamics ◽  
Coherent Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Formation And Evolution ◽  
Wall Flow ◽  
Turbulent Wall

AbstractThe complex dynamics of turbulent flow in the vicinity of a solid surface underlie numerous scientifically important processes, and pose persistently daunting challenges in many engineering applications. Since their discovery decades ago, coherent motions have presented a tantalizing prospective opportunity for constructing descriptions of wall-flow dynamics using only a relatively small number of elements. The veracity and reliability of such representations are, however, ultimately tied to their basis in the Navier–Stokes equations. In this regard, the study by Sharma & McKeon (J. Fluid Mech., vol. 728, 2013, pp. 196–238) constitutes an important contribution, as it not only provides insights regarding the mechanisms underlying wall-flow coherent motion formation and evolution, but does so within a Navier–Stokes framework.

SLIDING FRICTION IN VISCOUS HYDRODYNAMICS: THE ROUGH SURFACE AS VORTICITY SOURCE

1989 ◽  
Vol 03 (05) ◽  
pp. 393-397
Author(s):  
H. DEKKER
Keyword(s):  
Friction Coefficient ◽  
Viscous Fluid ◽  
Rough Surface ◽  
Solid Surface ◽  
Sliding Friction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Source ◽  
Viscous Hydrodynamics

Basset’s collective friction coefficient for a viscous fluid flowing past a rough solid surface is obtained — analytically — as an intrinsic consequence of the Navier-Stokes equations by treating the surface as a source of vorticity.

A LATTICE BOLTZMANN METHOD FOR COMPUTATION OF AEROACOUSTIC INTERACTION

2007 ◽  
Vol 18 (04) ◽  
pp. 463-472 ◽  
Author(s):  
E. W. S. KAM ◽  
R. C. K. LEUNG ◽  
R. M. C. SO ◽  
X. M. LI
Keyword(s):  
Stokes Equations ◽  
Scattering Problem ◽  
Relaxation Times ◽  
Short Wave ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Bgk Model ◽  
Navier Stokes Equations ◽  
First Case ◽  
Boltzmann Method

This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.

scholarly journals On Fluid Flow Field Visualization in a Staggered Cavity: A Numerical Result

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 226 ◽  
Author(s):  
Khalil Ur Rehman ◽  
Nabeela Kousar ◽  
Waqar A. Khan ◽  
Nosheen Fatima
Keyword(s):  
Fluid Flow ◽  
Stokes Equations ◽  
Mathematical Formulation ◽  
Navier Stokes ◽  
Line Graphs ◽  
Navier Stokes Equations ◽  
Boundary Constraints ◽  
Numerical Result ◽  
First Case ◽  
Contour Plots

In this paper we have considered a staggered cavity. It is equipped with purely viscous fluid. The physical design is controlled through mathematical formulation in terms of both the equation of continuity and equation of momentum along with boundary constraints. To be more specific, the Navier-Stokes equations for two dimensional Newtonian fluid flow in staggered enclosure is formulated and solved by well trusted method named finite element method. The novelty is increased by considering the motion of upper and lower walls of staggered cavity case-wise namely, in first case we consider that the upper wall of staggered cavity is moving and rest of walls are kept at zero velocity. In second case we consider that the upper and bottom walls are moving in a parallel way. Lastly, the upper and bottom walls are considered in an antiparallel direction. In all cases the deep analysis is performed and results are proposed by means of contour plots. The velocity components are explained by line graphs as well. The kinetic energy examination is reported for all cases. It is trusted that the findings reported in present pagination well serve as a helping source for the upcoming studies towards fluid flow in an enclosure domains being involved in an industrial areas.

Analytical and numerical aspects of the electromagnetic stirring induced by alternating magnetic fields

1981 ◽  
Vol 102 ◽  
pp. 405-430 ◽  
Author(s):  
Y. R. Fautrelle
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Uniform Magnetic Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Case ◽  
Special Cases ◽  
Alternating Magnetic Fields

The dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder in a uniform magnetic field parallel to the axis. Neglecting the motion effects in Maxwell's equations, the problem is conveniently decoupled into electromagnetic and dynamic parts. Using either analytical or numerical solutions of the electromagnetic equations, the electromagnetic forces are calculated and introduced in the motion equations. In the first case, asymptotic solutions of the Navier–Stokes equations valid for high frequencies are calculated and compared with numerical solutions obtained for the same geometry. The second case has been studied numerically, and the solutions are presented and interpreted.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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