CDF Report Using a Phoenics Program (Lab Report Sample)

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06 November 2015
CDF report using a PHOENICS program
Task 1
Question 1
Question 2
In PHOENICS, a dependent variable is the subject in a conservation equation, while the auxiliary variable constitutes the constant as derived from a case algebraic equation. Examples of dependent PHOENIC variables include pressure, enthalpy, volume fractions, temperature and displacements among others. On the other hand, case examples of auxiliary variables include density, diffusivity, velocity, or gravitational forces among others.
Question 3
A problem geometry constitutes of either scalar or vector quantities. Conceptually speaking, scalar quantities constitute one-dimensionally measurable quantities such as temperature, velocity, absorptivity, compressibility, or weight. On the other hand, a geometric vector consists of multi-dimensional quantities, which often constitute both magnitude and direction of orientation. Examples of vector quantities include vector resolute and displacements.
Question 4
Vector quantities are often computed in reference to cells staggered with respect to particular scalar cells. Primarily, these constitute the V cell, the U cell and the Scalar cell. On the other hand, a scalar and by extension, vector quantities are also referenced by a unique index of the form (IX, IY, IZ). However, it should be noted that scalars are stored at the central points of six-sided cells, with the value of the particular scalar being assumed to be typical for the entire cell. Conversely, vectors are stored at the central points of the six faces created within the IX, IY and IZ cell nomenclature.
Question 5
In PHOENICS, grids constitute cells that are topographically made of Cartesian brick elements, and, hence may include three types of grid. These are: 1) Cartesian grids; 2) cylindrical-polar grids; and, 3) Orthogonal (or) non-orthogonal body fitted grids. Despite the grid type exhibited by the PHOENICS, the grid distribution may be non-uniform for all the coordinates or coordinate directions. However, cylindrical-polar coordinates should have the X (or I), Y (or J) and the Z (or K) orientations. In such instances, the X-coordinates are always angular, and the Y-coordinate radial, while the Z-coordinates are always axial in direction.
Question 6
The basic form of balance equation used in CDF codes assumes that:
Outflow from a cell = inflow to the cell – net source within the cell
Question 7
The generalized form of single-phase conservation equation solved in CDF codes takes the form: , where,
r is the density, υ the vector velocity, Γφ diffusion exchange coefficient, and, ѕφ the source term.
Question 8
Particular examples of the single-phase conservation equation are the momentum equation, the enthalpy and the continuity equations among others.
Question 9
The finite volume form of the equation takes the form:  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image659.gif" \* MERGEFORMATINET 
. By continuity,
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image657.gif" \* MERGEFORMATINET 
, where vt and v1 are turbulent and laminar viscosities consecutively. In the neighbor link, a’s take the form:
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image661.gif" \* MERGEFORMATINET 
 of the convention diffusion transient.
Question 10
In CFD codes, auxiliary equations are used to close the equation set. With CFD equations being highly non-linear, the auxiliary equation set provides for the thermodynamic properties, as well as defines the transport properties, the source terms and the interphase transport features of the CFD problem in question.
Question 11
Differential equations used in CFD computations must be supplemented through diverse boundary conditions before they can be successfully solved. In practice, these boundary conditions define the fluid or heat flow problem as necessary to convey the required information on the amount of fluid that enters a domain. The CFD boundary conditions used in PHOENICS include several variants such as a fixed value, fixed flux rate as well as linear and non-linear components.
Question 12
In PHOENICS, boundary conditions are often represented as linearized sources to the cells adjacent to various boundaries. Here, the boundary conditions take the form:  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image662.gif" \* MERGEFORMATINET 

Where, aBC is the ‘coefficient’ and  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image663.gif" \* MERGEFORMATINET 
termed as the ‘value’. Here, aBC is summed with the aP and aBC  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image663.gif" \* MERGEFORMATINET 
 on the right hand side of the  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image665.gif" \* MERGEFORMATINET 
 equation. Therefore,
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image666.gif" \* MERGEFORMATINET 

Question 13
In PHOENICS, fixed value boundary conditions are introduced by making the aBC very big. This results in the following:
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image667.gif" \* MERGEFORMATINET 

On the other hand, flux boundary conditions are introduced by making aBC very small and setting aBC  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image663.gif" \* MERGEFORMATINET 
 at the required flux level. The latter results in the following:
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image669.gif" \* MERGEFORMATINET 

Question 14
By default, all domain edges used in PHOENICS are impervious to flow, adiabatic and frictionless.
Question 15
The finite volume form of the equation takes the form:  INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image659.gif" \* MERGEFORMATINET 
. By continuity,
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image657.gif" \* MERGEFORMATINET 
, where vt and v1 are turbulent and laminar viscosities consecutively. In the neighbor link, a’s take the form:
 INCLUDEPICTURE "/phoenics/d_polis/d_lecs/general/image661.gif" \* MERGEFORMATINET 
 of the convention diffusion transient.
Question 16
In CFD, there are specific boundary conditions that must be set relating to where and possibly when the boundary is to be set as well as the values of T, V and C. As such, the settings to be made relate to the fixed value, the fixed source (flux), the linear boundary conditions, the wall conditions, particular general sources, inflows and outflows as well as non-linear boundary conditions.
Question 17
Turbulent flows often exhibit particular general properties including:
Irregular flow – turbulent flows are often random, and have less deterministic features
Rapid mixing and increased momentum, heat and mass transfer rates attributable to the high diffusivity attributable to the turbulent flow
Turbulent flows will always occur at high Reynolds numbers
Turbulent flows are also rotational in nature. As a consequence, they have non-zero vorticity.
With the kinetic energy associated with the viscous shear stress in the material in motion, the kinetic energy is converted to heat. As a result, the process can be said to be highly dissipative.
Question 18
Direct numerical simulation is a CFD technique for which Navier-Stokes equations are solved numerically without the use or reference to any turbulence model.
Question 19
Question 20
Question 21
Question 22
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