Analytical Tools and Method for Modeling Transport Processes in Fluids

Abstract

An improved computer implemented method for modeling transport processes in fluids is disclosed. The method is adapted to model gas flow including dilute gas flow at high Knudsen numbers. Instead of modeling based on using an infinitesimal fluid element of a continuous medium, the method approximates fluid flow as a model gas flow. The method is based on assuming that each of a plurality of particles, which compose the model gas, travels with a probability between any of two points in space occupied by the model gas by following a ballistic trajectory governed by a law of motion in free space and treating each of the plurality of ballistic particles as a property carrier transporting one or more of mass, momentum, and energy between the points of consecutive collisions. The major steps of the method are indicated in the accompanying flow chart. The method also delivers a new basis for prediction of dynamic evolution of the model gas system by considering a pre-established or known dynamic history of the system during a pre-initial period.

Description

TECHNICAL FIELD[0001]The present invention relates to an improvement of the computer implemented method for modeling transport processes in fluids.BACKGROUND ART[0002]Computational Fluid Dynamics (CFD) is used mainly for analytical predictions of the fluid transport properties, including velocity, heat transfer coefficient, and pressure; still, CFD has many challenges. One challenge is that the users must select the appropriate models to characterize their specific problem. However, errors due to uncertainty in the formulation of the model and often intentional simplification of the model may diminish the usefulness of the results of the computations. Also, errors in the modeling of the fluids are disturbed with the choice of the governing equations to be solved and models for the fluid properties. The sources of uncertainty in physical models are listed by Mehta, U. B. 1996, “Guide to Credible Computer Simulations of Fluid Flows,” AIAA Journal of Propulsion and Power 12, 5, 940-948...

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Benefits of technology

[0022]Moreover, the improved method will be applicable even in values of Knudsen number equal to or higher than 10, which is a molecular beam region. Improvement by increasing the operable range of Knudsen numbers is of great importance for the CFD method and will expand horizons of CFD applications in the industry and in the technological processing. Finally, both Simulation 1 and Simulation 2 demonstrate improvement from the prior art, which consists of the capability to produce useful results by much lower computational resources.

[0024]The method offers a basis for a new generation of a Computational Fluid Dynamics analysis processes since modeling of the fluid system evolution can be based not only on the established initial conditions at the initial time for the fluid system but also on the pre-established dynamic history of the fluid system at a period preceding the initial time, thus increasing certainty and accuracy of prediction of the fluid system evolution for extended period of time. The method advances a new generation of a Computational Fluid Dynamics analysis processes by a significant decrease of physical modeling errors due to uncertainty in the formulation of the model and deliberate simplifications of the model. The method creates potentially much lower discretization errors since the flow problem can be formulated by direct application of integral or integro-differential equations, thus decreasing errors occurred from the representation of the governing flow differential equations and other physical models as algebraic expressions in a discrete domain of space and time. A new generation of Computational Fluid Dynamics software products, which are based on the disclosed analytical tools and method, are anticipated having capability to modeling gases from the continuum flow regime (Kn<0.01) to the rarefied and free molecular flow regime (Kn>10), considerably higher accuracy of prediction, and lower computation cost.

Problems solved by technology

Computational Fluid Dynamics (CFD) is used mainly for analytical predictions of the fluid transport properties, including velocity, heat transfer coefficient, and pressure; still, CFD has many challenges.

One challenge is that the users must select the appropriate models to characterize their specific problem.

However, errors due to uncertainty in the formulation of the model and often intentional simplification of the model may diminish the usefulness of the results of the computations.

Also, errors in the modeling of the fluids are disturbed with the choice of the governing equations to be solved and models for the fluid properties.

The general major disadvantage of any existing or available on market CFD software consists of using an infinitesimal fluid element viewed as a continuous medium, to which fundamental physical principles are applied.

This approach is in a contradiction with the molecular or particle nature, thus providing a source of significant uncertainty in interpreting the results of modeling and calculations.

Disadvantageously, this approach does not consider the dynamic behavior of the fluid system in times earlier than initial time, t0, which actually affects the behavior of the fluid system in times following the initial time.

Also, the balance equations can only describe fluid flow approximately mostly because of the inability to determine the functional distribution for viscous stress forces and the rate of heat addition and viscous dissipation.

Thus, although the conservation laws correctly describe the fluid within a control volume located remotely in a fluid flow, they do not take into consideration the molecular nature of the fluid.

As a general limitation, microscopic or bulk analysis allows the treatment of a collection of free particles as a continuum where collisional mean free path, λf, is much lower than the macroscopic length scale L of the system.

However, the classical continuum approach cannot be applied to situations when the length scale of the system is of the same order or less as compared to the collisional mean free path.

At the current state of the art, specifying the boundary conditions is one of the most difficult parts of the analysis.

The limitation that the NS equations are valid for Kn<0.01 reduces the fields of CFD applications significantly.

Specifically, the CFD method is inapplicable for modeling of dilute or rarefied gases.

It is not useful for simulations microelectronics and nanoelectronics low-pressure processing and plasma processing.

It does not simulate a gas flow properly in microchannels in micromechanical systems (MEMS) applications.

This method is enormously complicated and restricted because of the limitation of the available computational approaches for modeling real physical systems.

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