Application of Computer Simulation to the VО2 Synthesis Process Optimization

As the CVD technique becomes more and more important in both industry and academia, it is necessary to predict the behavior of such elusive systems to understand the relationship between the system variables. The systems can be understood and predicted by using three tools: theory analysis, experiment, and simulation. However, due to the highly complex flow conditions in CVD reactors, it is not possible to manually calculate or even depict the properties of the flow, for example, the flow rates, the precursor concentrations, velocity profiles, temperature distributions. On the other hand, computational fluid dynamics (CFD) is the computational method that can potentially be used to improve the efficiency of existing operating systems as well as the design of new systems. It provides a qualitative and, occasionally, quantitative analysis of flowing fluids in relation to the fluids’ surroundings. Using CFD, flow regimes in CVD reactors can be accurately simulated to give a more meticulous view of a reactor’s regional behavior that is difficult to observe by experiment. Computer algorithms are being used to envisage flow features on the basis of a set of conservation equations for mass, momentum, and energy in a flow geometry of interest, such as ID, 2D, or 3D, together with subsidiary sets of equations reflecting the problem in question.

Accompanied by the increase in computational power, software development, and distributed knowledge, CFD simulation becomes more and more important. Compared with the experiment, fluid dynamic phenomena simulation through CFD software has the advantage of low cost, less consumption of time, safer procedures, and better accuracy. Because APCVD is the most commonly used CVD system, the simulation and model for this CVD technique is the best established. Therefore, the CFD simulation of the APCVD system will be the focus in this section.

Governing Equations of Computational Fluid Dynamics Modeling

CFD simulations were performed in the software Ansys Fluent, which uses the finite volume method for solving equations in momentum, mass, and energy. Fluid motion within a fluid is described by the Navier-Stokes equations. More details of the numerical algorithm and procedures can be found in the user's guide of Ansys Fluent. The transport behavior of gas depends on the degree of rarefaction, expressed by the Knudsen number Kn = A/L, the ratio of the mean free path of molecules Л, and a typical length scale of the smallest detail of interest within the reactor, L. The mean free path, according to the kinetic gas theory, is described by Ref. [1].

where T is the gas temperature, p is the reactor pressure, kB is the Boltzmann constant, and о is the collision diameter. In the case of the APCVD V02 deposition system, all tryouts were used at atmospheric pressure and temperatures between 300°C and 750°C with nitrogen as the carrier gas (

In CFD analysis, the domain is divided into a finite number of elements. The following steps are used to solve a general CFD simulation problem:

  • 1. Provide an outline of the geometrical domain.
  • 2. Divide the domain into nonoverlapping grid cells or control volumes.
  • 3. Assign the physical and chemical phenomena.
  • 4. Define material (build in library or new assignment) and fluid properties.
  • 5. Specify boundary conditions that occur within the geometrical domain.

Consequently, the physical and chemical phenomena are described by the equations of mass transport, momentum, heat, and concentration of chemical genera involved in the CVD process.

The mass conservation equation is referred to as the continuity equation in continuum mechanics, identifying the net accumulation of mass in any fluid element, and is equal to the net rate of flow of mass into the fluid element.

where p is the average density of the fluid, v is the flow velocity vector field in the fluid, (x, y) are the 2DS spatial coordinates, and tis time.

The momentum conservation equation in an inertial (nonaccelerating) is given by:

where p is the density of the fluid, и is the speed, r indicates the tensor forces associated with the rate of shear, p is the dynamic viscosity, 8 is the identity matrix, and T is the temperature.

The equations for thermal energy are given below.

where p is the density of the fluid, и is the speed, r refers to the tensor forces associated with the rate of shear, p is the dynamic viscosity, 8 is the identity matrix, T is the temperature, h is the thermodynamic enthalpy, Se is the term of power generation, /?j is the reaction rate for the component j, A is the thermal conductivity, cPii is the specific heat at constant pressure, Д HR is the change in enthalpy of the reaction, P is the pressure, and R is the universal gas constant.

If the fluid is incompressible (p = 0) and inviscid (д = 0), then the Navier-Stokes equations become the Euler equations, as seen below.

And by inserting the vector identity, it becomes

Assuming the external force field has a potential on combining the Eqs. (8.5-8.7), we will get

The solution of the above equations gives results such as the distribution of velocity and temperature profiles of the elements for the geometry of the components. While using these equations, the domain of the part to be simulated is discretized or meshed into control volumes or areas (3D or 2D shapes) of micro- or nanodimensions. It is obvious that these volumes or areas represent the actual or scaled (up or down) part, which will be used under the same conditions as those of the experimental procedure.

The fluid boundaries in the simulations considered are the walls of each part, the bottom, and the free surface of the fluid. On the walls, the boundary condition is that the velocity of the flow at the wall is zero in the normal direction of the wall.

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