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At least 19 records

Finite element simulation of temperature dependent free surface flows

The method of Engelman and Sani (1984) for a finite-element simulation of incompressible surface flows with a free and/or moving fluid interface, such as encountered in crystal growth and coating and polymer technology, is extended to temperature-dependent flows, including the effect of temperature-dependent surface tension. The basic algorithm of Saito and Scriven (1981) and Ruschak (1980) has been generalized and implemented in a robust and versatile finite-element code that can be employed with relative ease for the simulation of free-surface problems in complex geometries. As a result, the costly dependence on the Newton-Raphson algorithm has been eliminated by replacing it with a quasi-Newton iterative method, which nearly retains the superior convergence properties of the Newton-Raphson method.

Engelman, M. S.↗

Finite element solutions of free surface flows

A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.

Zarda, P. R.↗

Continuation in a parameter - Experience with viscous and free surface flows

The results of modifications in continuation methods applied to obtain solutions to the Navier-Stokes systems of equations for incompressible, two-dimensional, steady flows are reported. It is shown that parameter continuation permits prediction of accurate, initial estimates for iterative processing of nonlinear finite difference and finite element equations of motions. The new parameter steps are derived from values of the preceding parameter steps. The accuracy of the estimates is ensured with appropriate choices of the step size. The continuation predictor/iterative corrector is demonstrated to trace the branches of parameter space along which steady flow states are found, and techniques are available for tracing multiply branching paths. The techniques are applied to solving the Navier-Stokes equations for flow through a rotating square channel, the formation of a falling liquid curtain, and gyrostatic equilibria of rotating cylindrical drops.

Kheshgi, H. S.↗

Distribution of resistive body-force in curved free-surface flow

The customary procedure for including resistive effects in turbulent hydraulic and stratified atmospheric flows is to integrate the empirically-known boundary shears over the entire wetted boundary of a thin fluid slab. A resistive body-force is then assumed to exist everywhere in each slab to replace the boundary shearing force. For the classical Saint-Venant (1871) model, this body-force can be shown to have a constant distribution in the vertical direction, and therefore can be evaluated for use in the momentum differential equation. In the newer Dressler theory (1978), however, for unsteady flow over curved beds, it is proved here that a constant body-force distribution is not possible. Its variable distribution is determined as well as its magnitude for use in the curved-flow equations. This variable distribution acts to produce an equal resultant in every thin layer of fluid parallel to the bed in an angular wedge over the curved channel bed. The new curved-flow equations are therefore extended to include resistive effects.

Sivakumaran, N. S.↗

Computational and theoretical analysis of free surface flow in a thin liquid film under zero and normal gravity

The results of a numerical computation and theoretical analysis are presented for the flow of a thin liquid film in the presence and absence of a gravitational body force. Five different flow systems were used. Also presented are the governing equations and boundary conditions for the situation of a thin liquid emanating from a pressure vessel; traveling along a horizontal plate with a constant initial height and uniform initial velocity; and traveling radially along a horizontal disk with a constant initial height and uniform initial velocity.

Faghri, Amir↗

Application of the methods of gas dynamics to water flows with free surface I : flows with no energy dissipation

The application is treated in sufficient detail to facilitate as much as possible its application by the engineer who is less familiar with the subject. The present work was undertaken with two objects in view. In the first place, it is considered as a contribution to the water analogy of gas flows, and secondly, a large portion is devoted to the general theory of the two-dimensional supersonic flows.

Preiswerk, Ernst↗

RIPPLE - A new model for incompressible flows with free surfaces

A new free surface flow model, RIPPLE, is summarized. RIPPLE obtains finite difference solutions for incompressible flow problems having strong surface tension forces at free surfaces of arbitrarily complex topology. The key innovation is the continuum surface force model which represents surface tension as a (strongly) localized volume force. Other features include a higher-order momentum advection model, a volume-of-fluid free surface treatment, and an efficient two-step projection solution method. RIPPLE's unique capabilities are illustrated with two example problems: low-gravity jet-induced tank flow, and the collision and coalescence of two cylindrical rods.

Kothe, D. B.↗

An experimental study of free surface deformation in oscillatory thermocapillary flow

Free surface deformation of a test fluid induced by steady and oscillatory thermocapillary flow in a small cylindrical container (diameter = 4.8 mm) is studied experimentally. The fluid (2 Cs oil) is heated by a cylindrical wire (diameter = 0.48 mm) placed along the centerline of the cylinder. The relative displacement and oscillation frequency of free surface are measured in a radial cross-section for various applied temperature differences. It is found that the amplitude of the free surface height oscillations is large near the heater and the cold wall and relatively small in the middle part. The frequency of the free surface oscillations is same as the frequency of the temperature oscillations. Based on these data, the free surface motion during oscillations is delineated.

Lin, Jianlian↗

Computing Incompressible Flows With Free Surfaces

RIPPLE computer program models transient, two-dimensional flows of incompressible fluids with surface tension on free surfaces of general shape. Surface tension modeled as volume force derived from continuum-surface-force model, giving RIPPLE both robustness and accuracy in modeling surface-tension effects at free surface. Also models wall adhesion effects. Written in FORTRAN 77.

Kothe, D.↗

Project JOVE

The goal of this project is to investigate new areas of research pertaining to free surface-interface fluids mechanics and/or microgravity which have potential commercial applications. This paper presents an introduction to ferrohydrodynamics (FHD), and discusses some applications. Also, computational methods for solving free surface flow problems are presented in detail. Both have diverse applications in industry and in microgravity fluids applications. Three different modeling schemes for FHD flows are addressed and the governing equations, including Maxwell's equations, are introduced. In the area of computational modeling of free surface flows, both Eulerian and Lagrangian schemes are discussed. The state of the art in computational methods applied to free surface flows is elucidated. In particular, adaptive grids and re-zoning methods are discussed. Additional research results are addressed and copies of the publications produced under the JOVE Project are included.

Lyell, M. J.↗

Numerical simulation of fluid flow and heat transfer in a thin liquid film over a stationary and rotating disk and comparison with experimental data

In the first section, improvements in the theoretical model and computational procedure for the prediction of film height and heat-transfer coefficient of the free surface flow of a radially-spreading thin liquid film adjacent to a flat horizontal surface of finite extent are presented. Flows in the presence and absence of gravity are considered. Theoretical results are compared to available experimental data with good agreement. In the presence of gravity, a hydraulic jump is present, isolating the flow into two regimes: supercritical upstream from the jump and subcritical downstream of it. In this situation, the effects of surface tension are important near the outer edge of the disk where the fluid experiences a free fall. A region of flow separation is present just downstream of the jump. In the absence of gravity, no hydraulic jump or separated flow region is present. The variation of the heat-transfer coefficient for flows in the presence and absence of gravity are also presented. In the second section, the results of a numerical simulation of the flow field and associated heat transfer coefficients are presented for the free surface flow of a thin liquid film adjacent to a horizontal rotating disk. The computation was performed for different flow rates and rotational velocities using a 3-D boundary-fitted coordinate system. Since the geometry of the free surface is unknown and dependent on flow rate, rate of rotation, and other parameters, an iterative procedure had to be used to ascertain its location. The computed film height agreed well with existing experimental measurements. The flow is found to be dominated by inertia near the entrance and close to the free surface and dominated by centrifugal force at larger radii and adjacent to the disk. The rotation enhances the heat transfer coefficient by a significant amount.

Faghri, Amir↗

Numerical and experimental analysis of a thin liquid film on a rotating disk related to development of a spacecraft absorption cooling system

The numerical and experimental analysis of a thin liquid film on a rotating and a stationary disk related to the development of an absorber unit for a high capacity spacecraft absorption cooling system, is described. The creation of artificial gravity by the use of a centrifugal field was focused upon in this report. Areas covered include: (1) One-dimensional computation of thin liquid film flows; (2) Experimental measurement of film height and visualization of flow; (3) Two-dimensional computation of the free surface flow of a thin liquid film using a pressure optimization method; (4) Computation of heat transfer in two-dimensional thin film flow; (5) Development of a new computational methodology for the free surface flows using a permeable wall; (6) Analysis of fluid flow and heat transfer in a thin film in the presence and absence of gravity; and (7) Comparison of theoretical prediction and experimental data. The basic phenomena related to fluid flow and heat transfer on rotating systems reported here can also be applied to other areas of space systems.

Faghri, Amir↗

Application of the Analogy Between Water Flow with a Free Surface and Two-dimensional Compressible Gas Flow

The theory of hydraulic analogy, that is, the analogy between water flow with a free surface and two-dimensional compressible gas flow and the limitations and conditions of the analogy are discussed. A test run was made using the hydraulic analogy as applied to the flow about circular cylinders at various diameters at subsonic velocities extending to the super critical range. The apparatus and techniques used in this application are described and criticized. Reasonably satisfactory agreement of pressure distributions and flow fields existed between water and airflow about corresponding bodies. This agreement indicated the possibility of extending experimental compressibility research by new methods.

Orlin, W James↗

Application of the Analogy Between Water Flow with a Free Surface and Two-Dimensional Compressible Gas Flow

The theory of the hydraulic analogy -- that is, the analogy between water flow with a free surface and two-dimensional compressible gas flow -- and the limitations and conditions of the analogy are discussed. A test was run using the hydraulic analogy as applied to the flow about circular cylinders of various diameters at subsonic velocities extending into the supercritical range. The apparatus and techniques used in this application are described and criticized. Reasonably satisfactory agreement of pressure distributions and flow fields existed between water and air flow about corresponding bodies. This agreement indicated the possibility of extending experimental compressibility research by new methods.

Orlin, W James↗

Three-Dimensional, Multi-Phase Unsteady Flow of Water Undergoing Multiple Flow Regimes (Free Surface, Droplet, and Fluid Film)

Upgrades to the Mobile Launcher Rainbird nozzles were implemented for the Artemis II launch to increase water flow rates and improve the mobile launcher deck water coverage while minimizing the water throw distance to avoid impacting the Space Launch System (SLS) rocket nozzles. This analysis describes the use of a three-dimensional, multi-phase, free surface transient computational fluid dynamics (CFD) model to simulate the water flowing out through the Rainbird nozzle and ensure compliance with current Artemis requirements. Flow rates, pressures, velocities, nozzle throw distances and coverage areas were analyzed to ensure that system requirements are met. The completed results were used to make necessary modifications to the Ignition Overpressure Protection and Sound Suppression (IOP/SS) system Rainbird design by reshaping the nozzle used in the system.

CFD↗

Implementation of nonreflective boundary condition at the outflow boundary

Numerical techniques for the solution of free surface flows about a disturbance on or near a free surface were developed. Any disturbance moving on or near a liquid surface generates surface waves that propagate away from the disturbance. The potential flow problems in which the evolution of free surface waves is the principal phenomenon of interest are considered. The distinct feature of these problems is that the position of the surface is also unknown and is to be determined as part of the solution. Two boundary conditions are required at the free surface since there are two unknown functions there, the free surface height and the potential function. The required boundary conditions are satisfied by the kinematic condition which states that no flow can cross the surface and the dynamic condition which matches the fluid pressure to the pressure acting on the surface through Bernoulli's equation.

Hall, D. R.↗

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Chen, Yen-Sen↗