Free-molecule flow and surface diffusion through slots and tubes A summary
Free molecule flow and surface diffusion through tubes and two-dimensional slots
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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↗
RIPPLE - A new model for incompressible flows with free surfaces
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Kothe, D. B.↗
Numerical simulation of fluid flow and heat transfer in a thin liquid film over a rotating disk
The results of a numerical simulation of the flow field and associated heat transfer coefficient are presented for the free surface flow of a thin liquid film adjacent to a horizontal rotating disk. The computation has been performed for different flow rates and rotational velocities using a three-dimensional 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 interative procedure had to be used to ascertain its location. The computed film height agreed well with existing experimental measurements. The flow was 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 enhanced the heat transfer coefficient by a significant amount.
Rahman, M. M.↗
New concepts for Reynolds stress transport equation modeling of inhomogeneous flows
The ability to model turbulence near solid walls and other types of boundaries is important in predicting complex engineering flows. Most turbulence modeling has concentrated either on flows which are nearly homogeneous or isotropic, or on turbulent boundary layers. Boundary layer models usually rely very heavily on the presence of mean shear and the production of turbulence due to that mean shear. Most other turbulence models are based on the assumption of quasi-homogeneity. However, there are many situations of engineering interest which do not involve large shear rates and which are not quasi-homogeneous or isotropic. Shear-free turbulent boundary layers are the prototypical example of such flows, with practical situations being separation and reattachment, bluff body flow, high free-stream turbulence, and free surface flows. Although these situations are not as common as the variants of the flat plate turbulent boundary layer, they tend to be critical factors in complex engineering situations. The models developed are intended to extend classical quasi-homogeneous models into regions of large inhomogeneity. These models do not rely on the presence of mean shear or production, but are still applicable when those additional effects are included. Although the focus is on shear-free boundary layers as tests for these models, results for standard shearing boundary layers are also shown.
Perot, J. Blair↗
Modeling of Turbulent Flow in Electromagnetically Levitated Metal Droplets
This article details an effort to improve the understanding and prediction of turbulent flow inside a droplet of molten metal levitated in an electromagnetic field. It is shown that the flow field in a test case, a nickel droplet levitated under microgravity conditions, is in the transitional regime between laminar and turbulent flow. Past research efforts have used laminar, enhanced viscosity, and k-epsilon turbulence models to describe the flow. The method highlighted in our study is the renormalization group (RNG) algorithm. We show that an accurate description of the turbulent eddy viscosity is critical in order to obtain realistic velocity fields, and that the turbulent eddy viscosity cannot be uniform in levitated droplets. The RNG method does not impose isotropic length or time scales on the flow field, thus allowing such nonuniform features to be captured. A number of other materials processing applications exhibit similarly complex flow characteristics, such as highly recirculating, transitional, and free surface flows, for which this modeling approach may prove useful.
Berry, S.↗
Dynamics of electromechanical flow structures.
Free-surface gravity flows and capillary wicking provide examples of flow structures with fluid partially ducted at free surfaces by external forces. Wall-less electromechanical flow structures are developed which have a similar nature, but with polarization forces providing the orientation at free surfaces. Like their mechanical counterparts, these have the ability to ingest liquid or expel vapor through their walls. The structures consist of electrodes running in the flow direction z with slowly varying cross sections in a plane transverse to the flow. A formulation is given of the long-wave nonlinear (principal mode) dynamics, with use made of energy functions to represent a broad class of possible mechanical and electrical structure geometries.
Jones, T. B., Jr.↗
Simulation of three-dimensional liquid sloshing flows using a strongly implicit calculation procedure
A coupled strongly implicit solution strategy for unsteady three-dimensional free surface flows has been developed based on an artificial compressibility formulation for the incompressible Navier-Stokes equations. A pseudotime term has been used in the continuity equation to permit time accurate calculations to be achieved. The scheme appears capable of tracking the free surface reasonably accurately inside a partially-filled spherical container undergoing a general rotating motion characteristic of that experienced by a spin-stabilized satellite. Five different free surface calculations have been presented. Some of the results exhibit an interesting Reynolds number dependent oscillatory behavior which is believed to be physical although no experimental results appears to be available for verification to date.
Chen, K.-H.↗
The flow of a thin liquid film on a stationary and rotating disk. II - Theoretical prediction
The existing theoretical models are improved and a systematic procedure to compute the free surface flow of a thin liquid film is suggested. The solutions for axisymmetric radial flow on a stationary horizontal disk and for the disk rotating around its axis are presented. The theoretical predictions are compared with the experimental data presented in Part I of this report. The analysis shows results for both supercritical and subcritical flows and the flow structure in the vicinity of a hydraulic jump which isolates these two flow types. The detailed flow structure in a hydraulic jump was computed and shown to contain regions of separation including a 'surface roller'. The effects of surface tension are found to be important near the outer edge of the disk where the fluid experiences a free fall. At other locations, the surface tension is negligible. For a rotating disk, the frictional resistance in the angular direction is found to be as important as that in the radial direction.
Rahman, M. M.↗
Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989
Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.
Chung, T. J.↗
Heat transfer to a thin liquid film with a free surface
The numerically computed flow field and heat transfer coefficient are presented for the free surface flow of a thin liquid film in the presence or absence of a gravitational body force. The results of an approximate analysis using the Pohlhausen integral method is also discussed. The flow systems studied here include both plane and radial film flows in the presence or absence of a gravitational body force. The heating conditions include isothermal and uniformly heated surfaces. The transport conditions considered at the free surface are an adiabatic condition and an evaporative free surface maintained at its saturation temperature. The height of the free surface, flow field and heat transfer coefficient, were found to be strongly affected by the gravitational body force. They were also found to depend on the Reynolds number and Froude number of the incoming fluid. In the presence of gravity, a hydraulic jump was found to occur under some flow conditions.
Rahman, M. M.↗
Numerical solution of flow problems using body-fitted coordinate systems
The paper deals with numerically generated boundary-fitted coordinate systems. This procedure eliminates the shape of the boundaries as a complicating factor and allows the flow about arbitrary boundaries to be treated essentially as easily as that about simple boundaries. The technique of boundary-fitted coordinate systems is based on a method of automatic numerical generation of a general curvilinear coordinate system having a coordinate line coincident with each boundary of a general multiconnected region involving any number of arbitrarily shaped boundaries. Once the curvilinear coordinate system is generated, any partial differential system of interest may be solved on the coordinate system by transforming the equations and solving the resulting system in finite-difference approximation on the rectangular transformed plane. Attention is given to the types of boundary-fitted coordinate systems, coordinate system control, operation of the coordinate codes, solution of partial differential equations, application to free-surface flow, and other applications of interest.
Thompson, J. F.↗
Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.
Sidi, A.↗
Quadrature methods for periodic singular and weakly singular Fredholm integral equations
High-accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are subsequently used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Throughout the development the periodic nature of the problem plays a crucial role. Such periodic equations are used in the solution of planar elliptic boundary value problems such as those that arise in elasticity, potential theory, conformal mapping, and free surface flows. The use of the quadrature methods is demonstrated with numerical examples.
Sidi, Avram↗
The Spacelab J mission
This paper describes Spacelab J (SL-J), its mission characteristics, features, parameters and configuration, the unique nature of the shared reimbursable cooperative effort with the National Space Development Agency (NASDA) of Japan and the evolution, content and objectives of the mission scientific experiment complement. The mission is planned for launch in 1991. This long module mission has 35 experiments from Japan as well as 9 investigations from the United States. The SL-J payload consists of two broad scientific disciplines which require the extended microgravity or cosmic ray environment: (1) materials science such as crystal growth, solidification processes, drop dynamics, free surface flows, gas dynamics, metallurgy and semiconductor technology; and (2) life science including cell development, human physiology, radiation-induced mutations, vestibular studies, embryo development, and medical technology. Through an international agreement with NASDA, NASA is preparing to fly the first Japanese manned, scientific, cooperative endeavor with the United States.
Cremin, J. W.↗
Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances
Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.
Liu, Gao-Lian↗
Dynamical Modeling of Surface Tension
In a recent review it is said that free-surface flows 'represent some of the difficult remaining challenges in computational fluid dynamics'. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace's equation by an equivalent volume force. Here, we describe how CSF formulation might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin (1996). This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated. For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin (1996), are discussed.
Brackbill, Jeremiah U.↗
Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials
The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.
Liou, Frank↗