A Study of the Nusselt-Rayleigh and Sherwood-Rayleigh Number Relations for Water Undergoing Free-Surface Natural Convection

2007 ◽  
Author(s):  
S. M. Bower ◽  
J. R. Saylor
Keyword(s):  
Free Surface ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Power Law ◽  
Fluid Layer ◽  
Power Laws ◽  
Surface Boundary ◽  
Free Surface Boundary Condition ◽  
Transfer Case ◽  
Solid Plate

An experimental study is presented of the Nusselt-Rayleigh and Sherwood-Rayleigh number relations for water undergoing free-surface natural convection, which is natural convection beneath an air/water interface. The focus of this work is on the Nu-Ra relationship. This relationship is typically studied using the traditional Rayleigh-Be´nard convection experiment where a fluid layer is bounded above and below by solid plates of different, but constant, temperatures. Hence, the boundary conditions are of the no-slip, constant-temperature type. Power laws are typically used in these studies to correlate the Nu-Ra data, and existing studies have given power law exponents that are usually close to 1/3. The experimental data obtained in this study yields a power law relation of the form: Nu=(0.0016)Ra0.328(1) for 107 < Ra < 1011. This result is surprising in that the effect of the free-surface boundary condition on the power law exponent is quite small when compared to the solid plate case. However, the prefactor in Eq. (1) is significantly smaller than for the solid plate case. The Sh-Ra data obtained in this study are also fit to a power law, giving: Sh=(0.0019)Ra0.329(2) where Sh is the dimensionless mass transfer coefficient for evaporation. The exponent of this power law differs from that which has been observed by prior researchers. However, the prior research on evaporation that utilizes this form for scaling the data is considerably smaller than for the heat transfer case. Possible explanations for the observed behavior are presented.

SPLASH Free-Surface Flow Code Methodology for Hydrodynamic Design and Analysis of IACC Yachts

1993 ◽  
Author(s):  
Bruce S. Rosen ◽  
Joseph P. Laiosa ◽  
Warren H. Davis ◽  
David Stavetski
Keyword(s):  
Free Surface ◽  
High Performance ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Surface Boundary ◽  
Induced Drag ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
America’S Cup ◽  
Areas Of Interest

A unique free-surface flow methodology and its application to design and analysis of IACC yachts are discussed. Numerical aspects of the inviscid panel code and details of the free-surface boundary condition are included, along with enhancements developed specifically for the '92 America's Cup defense. Extensive code validation using wind tunnel and towing tank experimental data address several areas of interest to the yacht designer. Lift and induced drag at zero Froude number are studied via a series of isolated fin/bulb/winglet appendages. An isolated surface piercing foil is used to evaluate simple lift/free­surface interactions. For complete IACC yacht models, upright wave resistance is investigated, as well as lift and induced drag at heel and yaw. The excellent correlation obtained for these cases demonstrates the value of this linear free-surface methodology for use in designing high performance sailing yachts.

scholarly journals Investigation of Free Surface Damping Models With Applications to Gap Resonance Problems

2017 ◽  
Author(s):  
Kevin Markeng ◽  
Torgeir Vada ◽  
Zhi Yuan Pan
Keyword(s):  
Free Surface ◽  
Energy Dissipation ◽  
Resonance Problem ◽  
Surface Boundary ◽  
Flow Solver ◽  
3 Dimensional ◽  
Energy Devices ◽  
Dissipation Term ◽  
Free Surface Boundary Condition ◽  
Damping Model

In this paper two methods for modelling the damping in a narrow gap are investigated. The first method is called the Pressure Damping Model. This method has been used in studies of wave energy devices. An attractive feature of this model is that the modified input is directly related to the energy dissipation in the gap, which means that if this dissipation is estimated the input to the model can be obtained directly. The idea of the method is to add a pressure input in the gap to suppress the resonant motion. A challenge with the method is that it contains a non-linear term. The second method is the Newtonian Cooling damping model. The method is based on introducing a dissipation term in the free surface boundary condition. This dissipation term contains a coefficient which is not directly related to the energy dissipation. Hence this method is not so easy to relate directly to the estimated energy dissipation. An advantage with this method is that it is linear and hence can be expected to be more robust. In the first part of the paper a 2-dimensional problem is investigated using both methods. In addition to the numerical performance and robustness, much focus is put on investigation of the energy balance in the solution, and we attempt to relate both models to the energy dissipation in the gap. In the second part the Newtonian cooling method is implemented in a 3-dimensional potential flow solver and it is shown that the method provides a robust way to handle the resonance problem. The method will give rise to a modified set of equations which are described. Two different problems are investigated with the 3D solver. First we look at a side-by-side problem, where the 3D results are also compared with 2D results. Finally, the moonpool problem is investigated by two different 3D solvers, a classical Green’s function based method and a Rankine solver. It is also shown how this damping model can be combined with a similar model on the internal waterplane to remove irregular frequencies.

scholarly journals Natural Convection Experiments in a Liquid-Saturated Porous Medium Bounded by Vertical Coaxial Cylinders

1983 ◽  
Vol 105 (4) ◽  
pp. 795-802 ◽  
Author(s):  
D. C. Reda
Keyword(s):  
Natural Convection ◽  
Surface Temperature ◽  
Fluid Layer ◽  
Saturated Porous Medium ◽  
Outer Cylinder ◽  
Power Input ◽  
Surface Boundary ◽  
Measured Temperature ◽  
Heater Surface ◽  
Numerical Predictions

An experimental effort is presently underway to investigate natural convection in liquid-saturated porous media utilizing a geometry and hydrodynamic/thermal boundary conditions relevant to the problem of nuclear-waste isolation in geologic repositories. During the first phase of this research program, detailed measurements were made of the steady-state thermal field throughout an annular test region bounded by a vertical, constant-heat-flux, inner cylinder and a concentrically placed, constant-temperature, outer cylinder. An overlying, constant-pressure fluid layer was utilized to supply a permeable upper surface boundary condition. Results showed the heater surface temperature to increase with increasing vertical distance due to the buoyantly driven upflow. The measured temperature difference (ΔT) between the average heater surface temperature and the constant outer-surface temperature was found to be progressively below the straight-line/conduction-only solution for ΔT versus power input, as the latter was systematically increased. Comparisons between measured results and numerical predictions obtained using the finite element code MARIAH showed very good agreement, thereby contributing to the qualification of this code for repository-design applications.

Coupled Dynamic Analysis of a Moored Spar Platform in Time Domain

2010 ◽  
Author(s):  
M. D. Yang ◽  
B. Teng
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Dynamic Analysis ◽  
Time Domain ◽  
Surface Boundary ◽  
Spar Platform ◽  
Mooring Lines ◽  
Coupled Dynamic Analysis ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

A time-domain simulation method is developed for the coupled dynamic analysis of a spar platform with mooring lines. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary condition, and Stokes perturbation procedure is then used to establish corresponding boundary value problems with time-independent boundaries. A higher order boundary element method is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by 4th order Adams-Bashforth-Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. For the mooring-line dynamics, a geometrically nonlinear finite element method using isoparametric cable element based on the total Lagrangian formulation is developed. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring lines are solved simultaneously using Newmark method. Numerical results including motions and tensions in the mooring lines are presented.

scholarly journals Free-Surface Effects on Interaction of Multiple Ships Moving at Different Speeds

2019 ◽  
Vol 63 (4) ◽  
pp. 251-267 ◽  
Author(s):  
Zhi-Ming Yuan ◽  
Liang Li ◽  
Ronald W. Yeung
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Present Article ◽  
Hydrodynamic Interaction ◽  
Surface Effects ◽  
Superposition Method ◽  
Surface Boundary ◽  
Gravitational Acceleration ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

Ships often have to pass each other in proximity in harbor areas and waterways in dense shipping-traffic environment. Hydrodynamic interaction occurs when a ship is overtaking (or being overtaken) or encountering other ships. Such an interactive effect could be magnified in confined waterways, e.g., shallow and narrow rivers. Since Yeung published his initial work on ship interaction in shallow water, progress on unsteady interaction among multiple ships has been slow, though steady, over the following decades. With some exceptions, nearly all the published studies on ship-to-ship problem neglected free-surface effects, and a rigid-wall condition has often been applied on the water surface as the boundary condition. When the speed of the ships is low, this assumption is reasonably accurate as the hydrodynamic interaction is mainly induced by near-field disturbances. However, in many maneuvering operations, the encountering or overtaking speeds are actually moderately high (Froude number Fn > 0.2, where <inline-graphic xlink:href="josr10180089inf1.tif"/>, U is ship speed, g is the gravitational acceleration, and L is the ship length), especially when the lateral separation between ships is the order of ship length. Here, the far-field effects arising from ship waves can be important. The hydrodynamic interaction model must take into account the surface-wave effects. Classical potential-flow formulation is only able to deal with the boundary value problem when there is only one speed involved in the free-surface boundary condition. For multiple ships traveling with different speeds, it is not possible to express the free-surface boundary condition by a single velocity potential. Instead, a superposition method can be applied to account for the velocity field induced by each vessel with its own and unique speed. The main objective of the present article is to propose a rational superposition method to handle the unsteady free-surface boundary condition containing two or more speed terms, and validate its feasibility in predicting the hydrodynamic behavior in ship encountering. The methodology used in the present article is a three-dimensional boundary-element method based on a Rankine-type (infinite-space) source function, initially introduced by Bai and Yeung. The numerical simulations are conducted by using an in-house‐developed multibody hydrodynamic interaction program “MHydro.” Waves generated and forces (or moments) are calculated when ships are encountering or passing each other. Published model-test results are used to validate our calculations, and very good agreement has been observed. The numerical results show that free-surface effects need to be taken into account for Fn > 0.2.

A Second-Order Theory for the Potential Flow About Thin Hydrofoils

1984 ◽  
Vol 28 (01) ◽  
pp. 55-64
Author(s):  
Colen Kennell ◽  
Allen Plotkin
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Potential Flow ◽  
Order Theory ◽  
Wave Drag ◽  
Second Order ◽  
The Body ◽  
Surface Shape ◽  
Surface Boundary ◽  
Free Surface Boundary Condition

This research addresses the potential flow about a thin two-dimensional hydrofoil moving with constant velocity at a fixed depth beneath a free surface. The thickness-to-chord ratio of the hydrofoil and disturbances to the free stream are assumed to be small. These small perturbation assumptions are used to produce first-and second-order subproblems structured to provide consistent approximations to boundary conditions on the body and the free surface. Nonlinear corrections to the free-surface boundary condition are included at second order. Each subproblem is solved by a distribution of sources and vortices on the chord line and doublets on the free surface. After analytic determination of source and doublet strengths, a singular integral equation for the vortex strength is derived. This integral equation is reduced to a Fredholm integral equation which is solved numerically. Lift, wave drag, and free-surface shape are calculated for a flat plate and a Joukowski hydrofoil. The importance of free-surface effects relative to body effects is examined by a parametric variation of Froude number and depth of submergence.

A time-splitting method on a nonstaggered grid in curvilinear coordinates for implicit simulation of non-hydrostatic free-surface flows

2007 ◽  
Vol 34 (1) ◽  
pp. 99-106 ◽  
Author(s):  
M Javan ◽  
M M Namin ◽  
S A.A. Salehi Neyshabouri
Keyword(s):  
Free Surface ◽  
Moving Boundary ◽  
Control Volume ◽  
Splitting Method ◽  
Free Surface Flows ◽  
Curvilinear Coordinates ◽  
Surface Boundary ◽  
Surface Flows ◽  
Free Surface Boundary Condition ◽  
Time Splitting

The numerical solution of flows with a freely moving boundary is of great importance in practical application such as ship hydrodynamics. Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady and steady free-surface flows on a nonstaggered grid in curvilinear coordinates, using a non-hydrostatic pressure distribution. In this model, Reynolds equation and the kinematic free-surface boundary condition are solved simultaneously, so that the water-surface elevation can be integrated into the solution and solved for, together with the velocity and pressure field. In computational space, the Cartesian velocity components and the pressure are defined at the center of a control volume, while the volume fluxes are defined at the midpoint on their corresponding cell faces. Detailed numerical results are presented for the wave generation above an obstacle and resonant motion standing wave. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply.Key words: free-surface simulation, nonstaggered grid, time-splitting method, unsteady flow, turbulent flow.

Zero Speed Rankine-Kelvin Hybrid Method With a Cylinder Control Surface

2015 ◽  
Author(s):  
Hui Li ◽  
Hao Lizhu ◽  
Huilong Ren ◽  
Xiaobo Chen
Keyword(s):  
Free Surface ◽  
Green Function ◽  
Hybrid Method ◽  
Exterior Domain ◽  
Control Surface ◽  
Surface Boundary ◽  
Rankine Source ◽  
Free Surface Boundary Condition ◽  
Interior Domain ◽  
The Green Function

The solution of hydrodynamic problem with forward speed still has some well-known problems such as high oscillation and slow convergence of the wave term when using a moving and oscillating source as the Green function. Recently, Ten and Chen (2010) has come up with a new method to benefit the merits of both the Rankine source and moving and oscillating source by taking a hemisphere as the control surface which separates the fluid region into two domains, but some troubles have been induced in the process of solution. Therefore, in this paper, a cylindrical surface instead of a hemisphere is selected to be the control surface to make the solution easy, and in this method, the control surface isn’t divided into panels. In the interior domain near the ship, the Rankin Green function is used to simplify the calculation. In the exterior domain some distance from the ship, there is no panels representing the free surface by using the Green function which satisfy the free surface boundary condition. The whole fluid region matches by the condition that the velocity potentials and their normal derivatives in the interior domain and exterior domain are equal on the control surface separately. In this paper, we have validated the Rankine-Kelvin hybrid method is applicable by adopting it to solve the zero speed problem in this work.

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