Volume of fluid vof method for dynamics of free boundaries in dating, volume of fluid method
Traditional VOF methods define a concentration function, C, to denote materials.
The issue always distills down to the unique tracking and resolving of multiple interfaces in a computational cell. This iterative cycle is continued until a set of convergence criteria are achieved based on residuals and iterative value changesand then the time step is complete and the variable fields velocity, pressure, temperature, etc.
As discussed above, at least a single set of conservation equations is still required to resolve the flow field dynamics, i. The fluid materials of the microgrid cells disposed in a grid location can be determined using modular arithmetic when using unique identifiers which are prime numbers.
A macrogrid including control volumes is created on a computational domain in which N materials and their interfaces are to be tracked. A method for tracking cells in a fluid dynamics computation comprising: The top layer is partially trapped in the upper left hand corner eddy with the balance following the primary circulation cell.
For the purpose of simplicity, an example utilizing three separate materials will be described.
An exemplary embodiment of a method for tracking N fluid materials and their interfaces, made in accordance with the present invention, is shown in a flowchart in FIG. A microgrid cell methodology is embedded on a regular macrogrid to subdivide and then tag fluid materials in a computational system preferably using a prime numbering algorithm.
This choice of material is preferably overridden if a microcell exceeds a predetermined momentum criteria, i. Specifically, the algorithm exploits the concept of modular arithmetic until a solution of 0 is calculated.
Of course, the computational grid selection must be chosen with prudence. If no material is advected into an interim array location, then the value remains as "1" and indicates that void is present. It is still yet another object to provide a method for tracking N materials and their associated interfaces by uniquely identifying and tracking, with a single concentration function C, N fluid materials wherein N may be 2 or greater.
This process of iteratively determining new fluid fractions in the control volumes, solving equations of fluid motion to arrive at new velocity fields, advecting microcells in fluid vision accommodating iol power vision reviews with the newly derived velocity fields, and then reallocating the microcells to comport with constraints such as conservation of momentum and conservation of mass is repeated over many time steps to simulate the fluid flow.
Further references indicate height functions are implemented where a reference line or plane is chosen in the computational domain Nichols and Hirt, Numerical experiments verify that an increase in microgrid mesh while maintaining the original computational mesh yields more refined results with a minimal increase in computational expense.
Utilizing the same shading scheme as depicted in FIG. N may be 2 or more materials. A prime number generator is utilized in this preferred embodiment that will create enough unique primes to delineate every material in the simulation.
This time step is chosen because it shows adequate detail of all the eddy features. If this is not possible, a mass error is accrued and through the progress of a calculation, the total mass error is determined and used as a gauge to evaluate the overall simulation accuracy.
N N In stepequations of fluid motion are solved for each of the macrogrid control volumes to arrive at a velocity field for each of the control volumes as well as other conserved variables such as pressure, turbulent kinetic energy, and temperature.
From these volume fractions, average parameters needed to solve equations of fluid motion can be readily derived. Because the algorithm employs an additive and collective response measure to the effect of velocity over multiple time steps, the more coarse the microgrid cell refinement is, the less immediate physical response one can see in areas of relatively low velocity.
In this interpretation, C, although called a concentration function, acts as the fluid fraction of material 1 or 2 in any given cell.
Step includes applying initial and boundary conditions to the macrogrid and control volumes. Volume of fluid method - wikipedia This problem originates from excessive diffusion of the transport equation.
The different methods for treating VOF can be roughly divided into three categories, namely the donor-acceptor formulation, higher order differencing schemes and line techniques. These locations correspond to a micr ocellular void and a sum of their number gives a maximum number of overlap sites that subsequently sizes a caching array.
In this situation, the excess primes are stripped step from the microgrid cells using modular arithmetic and then placed into the caching array, while one copy is left behind to fill the location. These equations rely upon principles of conservation of mass, conservation of momentum, and conservation of energy to derive velocity fields across each of the control volumes during each time step of the simulation.
Those skilled in the art of computational fluid dynamics modeling and simulation will appreciate that models can be made employing, by way of example and not limitation, other boundary and initial conditions such as symmetry planes, inflow and outflow boundaries, constant pressure surfaces, and an initial mean velocity and density distribution applied to the fluid materials.
The above described computational fluid dynamic methods fail to provide a method which can readily handle explicit or implicit tracking of the interface between three or more generally immiscible fluid materials.
Again, those skilled in the art will realize that many other alternative reallocation procedures or algorithm could be used to rearrange the overlapping microgrid cells and voids to establish a microgrid having a single fluid material or microcell in each microgrid location, as was the case in the initial microgrid cell arrangement shown in FIG.
Each microgrid cell reacts to its associated local control volume or macrogrid velocity conditions and may subsequently be displaced to another control volume after movement is rectified.
The macrogrid and control volumes are initialized with initial and boundary conditions representative of the problem to be solved. Methods have been employed previously which have attempted to track two interfaces or three materials in a computational fluid simulation. The user can define how many times these small adjustments will be tolerated before an "interfacial bump", for lack of a better description, is implemented.
Volume of fluid method This scheme formed a basis for the compressive differencing schemes. In step,the remaining voids are evaluated using maximum material gradient condition, momentum considerations and material content of the caching array.
In the original VOF-article by Hirt, a donor-acceptor scheme was employed. Also, while the overall response of the system at coarse micromesh is good, it may be noted that interfacial smoothness and subtle feature resolution is increased with the refinement of the microgrid.
Again the steps may be taken as described in steps a, b or c. What happens is this: In this way, a prime representation of the system is built.
In step b, the needed prime from the closest neighbor is extracted and a void is created in a new location. Once again, the microgrid is scanned for cells that contain more than one prime or different materials. Similarly, the microgrid cells in the control volumes may also move in the y- and z- directions, if a 3 dimensional model were used.
The prime NOT replaced in the once mixed cell is then redistributed to a next best location. Using a randomizer, the starting location for the scan is moved in step c. Similarly, a cell may receive two copies of the same material e.
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