Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

The motion generated by a rising particle in a rotating fluid – numerical solutions. Part 2. The long container case

2002 ◽  
Vol 454 ◽  
pp. 345-364 ◽  
Author(s):  
E. MINKOV ◽  
M. UNGARISH ◽  
M. ISRAELI
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Rotating Fluid ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Theory And Experiments ◽  
Taylor Column

Numerical finite-difference results from the full axisymmetric incompressible Navier–Stokes equations are presented for the problem of the slow axial motion of a disk particle in an incompressible, rotating fluid in a long cylindrical container. The governing parameters are the Ekman number, E = ν*/(Ω*a*2), Rossby number, Ro = W*/(Ω*a*), and the dimensionless height of the container, 2H (the scaling length is the radius of the particle, a*; Ω* is the container angular velocity, W* is the particle axial velocity and ν* the kinematic viscosity). The study concerns the flow field for small values of E and Ro while HE is of order unity, and hence the appearance of a free Taylor column (slug) of fluid ‘trapped’ at the particle is expected. The numerical results are compared with predictions of previous analytical approximate studies. First, developed (quasi-steady-state) cases are considered. Excellent agreement with the exact linear (Ro = 0) solution of Ungarish & Vedensky (1995) is obtained when the computational Ro = 10−4. Next, the time-development for both an impulsive start and a start under a constant axial force is considered. A novel unexpected behaviour has been detected: the flow field first attains and maintains for a while the steady-state values of the unbounded configuration, and only afterwards adjusts to the bounded container steady state. Finally, the effects of the nonlinear momentum advection terms are investigated. It is shown that when Ro increases then the dimensionless drag (scaled by μ*a*W*) decreases, and the Taylor column becomes shorter, this effect being more pronounced in the rear region (μ* is the dynamic viscosity). The present results strengthen and extend the validity of the classical drag force predictions and therefore the issue of the large discrepancy between theory and experiments (Maxworthy 1970) concerning this force becomes more acute.

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.

scholarly journals Numerical study of the thermosolutal convection in a 3-D cavity submitted to cross gradients of temperature and concentration

2019 ◽  
Vol 23 (3 Part B) ◽  
pp. 1923-1933
Author(s):  
Meriem Ouzaouit ◽  
Btissam Abourida ◽  
Lahoucine Belarche ◽  
Hicham Doghmi ◽  
Mohamed Sannad
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stokes Equations ◽  
Numerical Study ◽  
Thermosolutal Convection ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Conservation Of Momentum ◽  
Prandtl Numbers

This study is a contribution to the numerical study of the thermosolutal convection in a 3-D porous cavity filled with a binary fluid submitted to cross gradients of temperature and concentration. The Navier-Stokes equations, mass and energy governing the physical problem are discretized by the finite volume method. The equations of conservation of momentum coupled with the continuity equation are solved using the SIMPLEC algorithm, then the obtained system is solved using the implicit alternating directions method. The numerical simulations, presented here, correspond to a wide range of thermal Rayleigh number (103< Ra < 106) and buoyancy ratio (1 < N < 12). The Lewis and Prandtl numbers were fixed respectively at 5 and 0.71 and the sections dimension ? = D / H = 0.4. The temperature distribution, the flow pattern and the average heat and mass transfer are examined. The obtained results show significant changes in terms of heat and mass transfer, by proper choice of the governing parameters.

Effects of Distance Between Pads on the Inlet Pressure Build-Up on Pad Bearings

2002 ◽  
Vol 124 (3) ◽  
pp. 506-514 ◽  
Author(s):  
Jong-Soo Kim ◽  
Kyung-Woong Kim
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Results ◽  
Loss Coefficient ◽  
Inlet Pressure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Lubricating Film ◽  
Wide Range

Full Navier-Stokes equations are solved numerically for a cavity region between two consecutive pads and a parallel lubricating film. Numerical solutions are obtained for a wide range of Reynolds number and various values of a distance between pads. Numerical results show that the inlet pressure build-up is significantly affected by Reynolds number and the distance between two adjacent pads. A new formula is derived of loss coefficient with Reynolds number and a distance factor, for using it in an extended Bernoulli equation, on the basis of numerical results. Experiments are conducted to investigate the validity of the formula of loss coefficient proposed by authors.

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.

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