Integrals in FLUENT
Purpo : This document describes various Integral tools available in FLUENT and illustrates their usage.
Introduction
Interpreting the solution is an important task in CFD simulation. In most of the engineering applications we are interested in gross or average effects such as force exerted on a surface, total mass flow rate, etc. However, this information is not a standard part of the CFD solution data t, which contains primary solution variables. We frequently perform various integration operations to extract derived quantities from the primary variables. For efficient postprocessing, FLUENT provides veral integration options. This document describes each of the operations with a few examples.
1. Integration Operations
FLUENT, being a finite volume solver, divides the computational domain into a number of control volumes called cells .
Each cell is defined by a t of grid points (or nodes), a cell center, and the faces that bound the cell (s
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ee Figure 1.1). The solver data is available at cell center, node position, and at the face center.
Figure 1.1 Cell nomenclature
Cell Values
Solver data available at the cell center is referred as cell values . In Figure 1.1, the cell center is shown by a black dot. In this document cell values are denoted by subscript c (, nc c φ).
Facet Values
Solver data available at the face center is referred as facet values. In Figure 1.1, face center is shown by a red dot. In this document facet values are denoted by subscript f (, nf f φ).
Node Values
pomegranateSolver data available at the nodes is referred as node values . In Figure 1.1, nodes are shown by a black star. In this document node values are denoted by subscript n (, nn n φ).
Generally, integration involves accessing the solver data and summing over all grid points, cell center, and the faces as per integral type.
Figure 1.1 explains one such example , wherein the surface compris of 26 facets and total surface area is calculated as:
Total surface area (A ) = ∫
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nf
i i
A
overturedA 1
where, is the area of i th face and i varies from 1 to 26 i A
Similarly, the area-weighted average of a quantity is calculated as:
tiktok怎么读Area-weighted average of ∫∑===nf
i i fi
f A A dA A 111φφφ
where,A is the total surface area and fi φis value of φ at i th face.
寻找伴郎2. Surface Integration
dreddNote: Each facet is associated with a cell in the domain. If the facet is the result of an isovalue cut thr
ough the cell, the field variable assigned to the facet is the associated cell value. If the facet is on a boundary surface, an interpolated face value is ud for the integration instead of the cell value. This is done to improve the accuracy of the calculation and to ensure that the result matches the boundary conditions specified on the boundary and the fluxes reported on the boundary.
3. Volume Integration
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Notes:
come on1.FLUENT stores most variables in cells. For postprocessing, the entire region contained within the cell has this
value. A surface cell value is the value of the cell that has been intercted by a surface facet or line, or that contains a surface point. Since surface facets and lines are created from the interction of isovalues and the existing grid cells, this is a unique definition. On a boundary, the cell value is the value in the cell adjacent to the boundary. For details refer to Section 30.1.1 of the FLUENT6.3 Ur’s Guide.
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2.The interior facets on a zone surface are associated with two cells (c0 and c1). The values of a specified variable
on such facets are computed as the average of the two cell values of the lected variable. The boundary facet values of a specified field variable on a zone surface are computed from the boundary condition provided by the ur. For details refer to Section 30.1.3 of the FLUENT6.3 Ur’s Guide.
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3.Node values are explicitly defined or obtained by weighted averaging of the cell data. Various boundary
conditions impo values of field variables at the domain boundaries, so grid node values on the boundary zones are obtained by simple averaging of the adjacent boundary face data. In addition, for veral variables (e.g., node coordinates) explicit node values are available at all nodes. For details refer to Section 30.1.2 of the FLUENT6.3 Ur’s Guide.
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4.For 2D problems, by default, facet area is the area of the face formed by extruding the edge by a unit depth in the
z-direction. Similarly, cell volume is the volume formed by extruding the 2D face by a unit depth in the z-direction. This z-direction depth can be modified in the Reference Value panel. For details refer to Section
29.10.1 of the FLUENT6.3 Ur’s Guide.
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5.For axi-symmetric problems, facet area is the area of the annular face formed by rotating the edge about an axis
through the entire 2п-radian slice (and not through a 1-radian slice). Similarly, cell volume is volume formed by rotating the 2D face about axis through the entire 2п-radian slice.illusions
The detailed procedure for generating integrals is available at:
Reporting Alphanumeric Data /fluent6326/doc/ori/html/ug/node1190.htm
Product Version:FLUENT6.3 onward
Authors:Jayesh Mutyal and Kapil Sahu
