Chapter 26. Alphanumeric Reporting FLUENT provides tools for computing and reporting integral quantities at surfaces and boundaries. These tools enable you to find the mass flow rate and heat transfer rate through boundaries, the forces and moments on boundaries, and the area, integral, flow rate, average, and mass average (among other quantities) on a surface or in a volume. In addition, you can print histograms of geometric and solution data, set reference values for the calculation of nondimensional coefficients, and compute projected surface areas. You can also print or save a summary report of the models, boundary conditions, and solver settings in the current case. These features are described in the following sections. Section 26.1: Reporting Conventions Section 26.2: Fluxes Through Boundaries Section 26.3: Forces on Boundaries Section 26.4: Projected Surface Area Calculations Section 26.5: Surface Integration Section 26.6: Volume Integration Section 26.7: Histogram Reports Section 26.8: Reference Values Section 26.9: Summary Reports of Case Settings Reporting tools for the discrete phase are described in Section 19.13. c Fluent Inc. November 28, 2001 26-1
Alphanumeric Reporting 26.1 Reporting Conventions For 2D problems, FLUENT computes all integral quantities per unit depth. For axisymmetric problems, all integral quantities are computed for an angle of 2π radians. 26.2 Fluxes Through Boundaries For selected boundary zones, you can compute the following quantities: The mass flow rate through a boundary is computed by summing the dot product of the density times the velocity vector and the area projections over the faces of the zone. The total heat transfer rate through a boundary is computed by summing the total heat transfer rate, q = q c + q r, over the faces, where q c is the convective heat transfer rate and q r is the radiation heat transfer rate. The computation of the heat transfer through the face depends on the specified boundary condition. For example, the conduction heat transfer on a constant-temperature wall face would be the product of the thermal conductivity with the dot product of the area projection and the temperature gradient. For flow boundaries, the total heat transfer rate is the flow rate of the conserved quantity. Depending on the models that are being used, the total heat transfer rate may include the convective flow of sensible or total enthalpy, diffusive flux of energy, etc. The radiation heat transfer rate through a boundary is computed by summing the radiation heat transfer rate q r over the faces. The computation of the radiation heat transfer depends on the radiation model used. For example, you might use flux reporting to compute the resulting mass flow through a duct with pressure boundaries specified at the inlet and exit. 26-2 c Fluent Inc. November 28, 2001
26.2 Fluxes Through Boundaries Flux Reporting with Particles and Volumetric Sources Note that the reported mass and heat balances address only flow that enters or leaves the domain through boundaries; they do not include the contributions from user-defined volumetric sources or particle injections. For this reason, a mass or heat imbalance may be reported. To determine if a solution involving a discrete phase is converged, you can compare this imbalance with the change in mass flow or heat content computed in the particle tracking summary report. The net flow rate or heat transfer rate reported in the Flux Reports panel should be nearly equal to the Change in Mass Flow or Heat Content in the summary report generated from the Particle Tracks panel. 26.2.1 Generating a Flux Report To obtain a report of mass flow rate, heat transfer rate, or radiation heat transfer rate on selected boundary zones, use the Flux Reports panel (Figure 26.2.1). Report Fluxes... The steps for generating the report are as follows: 1. Specify which flux computation you are interested in by selecting Mass Flow Rate, Total Heat Transfer Rate, orradiation Heat Transfer Rate under Options. 2. In the Boundaries list, choose the boundary zone(s) on which you want to report fluxes. If you want to select several boundary zones of the same type, you can select that type in the Boundary Types list instead. All of the boundaries of that type will be selected automatically in the Boundaries list (or deselected, if they are all selected already). Another shortcut is to specify a Boundary Name Pattern and click Match to select boundary zones with names that match the specified pattern. For example, if you specify wall*, all boundaries whose names begin with wall (e.g., wall-1, wall-top) will be selected c Fluent Inc. November 28, 2001 26-3
Alphanumeric Reporting Figure 26.2.1: The Flux Reports Panel automatically. If they are all selected already, they will be deselected. If you specify wall?, all boundaries whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 3. Click on the Compute button. The Results list will display the results of the selected flux computation for each selected boundary zone, and the box below the Results list will show the summation of the individual zone flux results. Note that the fluxes are reported exactly as computed by the solver. Therefore, they are inherently more accurate than those computed with the Flow Rate option in the Surface Integrals panel (described in Section 26.5). 26-4 c Fluent Inc. November 28, 2001
26.3 Forces on Boundaries 26.3 Forces on Boundaries You can compute and report the forces along a specified vector and the moments about a specified center for selected wall zones. This feature can be used, for example, to report aerodynamic coefficients such as lift, drag, and moment coefficient for an airfoil calculation. 26.3.1 Computing Forces and Moments The forces on a wall zone are computed by summing the dot product of the pressure and viscous forces on each face with the specified force vector. In addition to the actual pressure, viscous, and total forces, the associated force coefficients are also computed, using the reference values specified in the Reference Values panel (as described in Section 26.8). The force coefficient is defined as force divided by 1 2 ρv2 A,whereρ, v, and A are the density, velocity, and area explicitly specified in the Reference Values panel. Finally, the summations of the pressure, viscous, and total forces for all the selected wall zones are presented in both dimensional form and as nondimensional coefficients. The moment vector about a specified center is computed by summing the product of the force vectors for each face with the moment vector i.e., summing the forces on each face about the moment center. In addition to the actual components of the pressure, viscous, and total moment, the moment coefficients are also printed. The moment coefficient is defined as the moment divided by the product of the reference dynamic pressure, reference area, and the reference length. Finally, the summations of the pressure, viscous, and total moments for all the selected wall zones are presented in both dimensional form and as nondimensional coefficients. To reduce round-off error, a reference pressure (also specified in the Reference Values panel) is used to normalize the cell pressure for computation of the pressure force. For example, the net pressure force vector is computed as the vector sum of the individual force vectors for each face: n F p = (p p ref )Aˆn (26.3-1) = n paˆn + p ref n Aˆn (26.3-2) c Fluent Inc. November 28, 2001 26-5
Alphanumeric Reporting where n is the number of faces, A is the area of the face, and ˆn is the unit normal to the face. This normalization has implications when computing total force coefficients for open domains. For closed domains, the additional term introduced by the reference pressure cancels, but for open domains the pressure normalization introduces a net force equivalent to the product of the projected area of the missing portion of the domain and the specified reference pressure. 26.3.2 Generating a Force or Moment Report To obtain a report for selected wall zones of forces along a specified vector or moments about a specified center, use the Force Reports panel (Figure 26.3.1). Report Forces... Figure 26.3.1: The Force Reports Panel The steps for generating the report are as follows: 1. Specify which type of report you are interested in by selecting Forces or Moments under Options. 26-6 c Fluent Inc. November 28, 2001
26.4 Projected Surface Area Calculations 2. If you choose a force report, specify the X, Y, andz components of the Force Vector along which the forces will be computed. If you choose a moment report, specify the X, Y, andz coordinates of the Moment Center about which the moments will be computed. 3. In the Wall Zones list, choose the wall zone(s) on which you want to report the force or moment information. A shortcut that may be useful if you have a large number of wall zones is to specify a Wall Name Pattern and click Match to select wall zones with names that match the specified pattern. For example, if you specify out*, all walls whose names begin with out (e.g., outer-wall-top, outside-wall) will be selected automatically. If they are all selected already, they will be deselected. If you specify out?, all walls whose names consist of out followed by a single character will be selected (or deselected, if they are all selected already). 4. Click on the Print button. In the console (text) window, the pressure, viscous (if appropriate), and total forces or moments, and the pressure, viscous, and total force or moment coefficients along the specified force vector or about the specified moment center will be printed for the selected wall zones. The summations of the coefficients and the forces or moments for all selected wall zones will be printed at the end of the report. 26.4 Projected Surface Area Calculations You can use the Projected Surface Areas panel (Figure 26.4.1) to compute an estimated area of the projection of selected surfaces along the x, y, or z axis (i.e., onto the yz, xz, orxy plane). Report Projected Areas... The procedure for calculating the projected area is as follows: 1. Select the Projection Direction (X, Y, or Z). 2. Choose the surface(s) for which the projected area is to be calculated in the Surfaces list. c Fluent Inc. November 28, 2001 26-7
Alphanumeric Reporting Figure 26.4.1: The Projected Surface Areas panel 3. Set the Min Feature Size to the length of the smallest feature in the geometry that you want to resolve in the area calculation. (You can just use the default value to start with, if you are not sure of the size of the smallest geometrical feature.) 4. Click on Compute. The area will be displayed in the Area box and in the console window. 5. To improve the accuracy of the area calculation, reduce the Min Feature Size by half and recompute the area. Repeat this step until the computed Area stops changing (or you reach memory capacity). This feature is available only for 3D domains. 26-8 c Fluent Inc. November 28, 2001
26.5 Surface Integration 26.5 Surface Integration You can compute the area or mass flow rate, or the integral, areaweighted average, flow rate, mass-weighted average, sum, facet average, facet maximum, facet minimum, vertex average, vertex minimum, and vertex maximum for a selected field variable on selected surfaces in the domain. These surfaces are sets of data points created by FLUENT for each of the zones in your model, or defined by you using the methods described in Chapter 24. Since a surface can be arbitrarily positioned in the domain, the value of a variable at each data point is obtained by linear interpolation of node values. For some variables, these node values are computed explicitly by the solver. For others, however, only cell-center values are computed, and the node values are obtained by averaging of the cell values. These successive interpolations can lead to small errors in the surface integration reports. (Chapter 27 provides information on which variables have computed node values.) Example uses of several types of surface integral reports are given below: Area: You can compute the area of a velocity inlet zone, and then estimate the velocity from the mass flow rate: v = ṁ (26.5-1) ρa Area-weighted average: You can find the average value on a solid surface, such as the average heat flux on a heated wall with a specified temperature. Mass average: You can find the average value on a surface in the flow, such as average enthalpy at a velocity inlet. Mass flow rate: You can compute the mass flow rate through a velocity inlet zone, and then estimate the velocity from the area, as described above. Flow rate: To calculate the heat transfer rate through a surface, you can calculate the flow rate of enthalpy. c Fluent Inc. November 28, 2001 26-9
Alphanumeric Reporting Integral: You can use integrals for more complex calculations, which may involve the use of the Custom Field Function Calculator panel, described in Section 27.5, to calculate a function that requires integral computations (e.g., swirl number). 26.5.1 Computing Surface Integrals Area The area of a surface is computed by summing the areas of the facets that define the surface. Facets on a surface are either triangular or quadrilateral in shape. n da = A i (26.5-2) Integral An integral on a surface is computed by summing the product of the facet area and the selected field variable, such as density or pressure. Each facet is associated with a cell in the domain. If the facet is the result of an isovalue cut through 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 used 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. n φda = φ i A i (26.5-3) Area-Weighted Average The area-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and facet area by the total area of the surface: 26-10 c Fluent Inc. November 28, 2001
26.5 Surface Integration 1 A φda = 1 n φ i A i (26.5-4) A Flow Rate The flow rate of a quantity through a surface is computed by summing the product of density and the selected field variable with the dot product of the facet area vector and the facet velocity vector: φρ v da n = φ i ρ i v i A i (26.5-5) Mass Flow Rate The mass flow rate through a surface is computed by summing the product of density with the dot product of the facet area vector and the facet velocity vector: ρ v da n = ρ i v i A i (26.5-6) Mass-Weighted Average The mass-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and the absolute value of the dot product of the facet area and momentum vectors by the summation of the absolute value of the dot product of the facet area and momentum vectors (surface mass flux): φρ v d A ρ v d A = n φ i ρ i vi A i n ρ i vi A i (26.5-7) c Fluent Inc. November 28, 2001 26-11
Alphanumeric Reporting Sum The sum of a specified field variable on a surface is computed by summing the value of the selected variable at each facet: Facet Average n φ i (26.5-8) The facet average of a specified field variable on a surface is computed by dividing the summation of the cell values of the selected variable at each facet by the total number of facets: n φ i n (26.5-9) Facet Minimum The facet minimum of a specified field variable on a surface is the minimum cell value of the selected variable on the surface. Facet Maximum The facet maximum of a specified field variable on a surface is the maximum cell value of the selected variable on the surface. Vertex Average The vertex average of a specified field variable on a surface is computed by dividing the summation of the node values of the selected variable at each node by the total number of nodes: n φ i n (26.5-10) 26-12 c Fluent Inc. November 28, 2001
26.5 Surface Integration Vertex Minimum The vertex minimum of a specified field variable on a surface is the minimum node value of the selected variable on the surface. Vertex Maximum The vertex maximum of a specified field variable on a surface is the maximum node value of the selected variable on the surface. 26.5.2 Generating a Surface Integral Report To obtain a report for selected surfaces of the area or mass flow rate or the integral, flow rate, sum, facet maximum, facet minimum, vertex maximum, vertex minimum, or mass-, area-, facet-, or vertex-averaged quantity of a specified field variable, use the Surface Integrals panel (Figure 26.5.1). Report Surface Integrals... The steps for generating the report are as follows: 1. Specify which type of report you are interested in by selecting Area, Integral, Area-Weighted Average, Flow Rate, Mass Flow Rate, Mass-Weighted Average, Sum, Facet Average, Facet Minimum, Facet Maximum, Vertex Average, Vertex Minimum, orvertex Maximum in the Report Type drop-down list. 2. If you are generating a report of area or mass flow rate, skip to the next step. Otherwise, use the Field Variable drop-down lists to select the field variable to be used in the surface integrations. First, select the desired category in the upper drop-down list. You can then select a related quantity from the lower list. (See Chapter 27 for an explanation of the variables in the list.) 3. In the Surfaces list, choose the surface(s) on which to perform the surface integration. If you want to select several surfaces of the same type, you can select that type in the Surface Types list instead. All of the surfaces c Fluent Inc. November 28, 2001 26-13
Alphanumeric Reporting Figure 26.5.1: The Surface Integrals Panel of that type will be selected automatically in the Surfaces list (or deselected, if they are all selected already). Another shortcut is to specify a Surface Name Pattern and click Match to select surfaces with names that match the specified pattern. For example, if you specify wall*, all surfaces whose names begin with wall (e.g., wall-1, wall-top) will be selected automatically. If they are all selected already, they will be deselected. If you specify wall?, all surfaces whose names consist of wall followed by a single character will be selected (or deselected, if they are all selected already). 4. Click on the Compute button. Depending on the type of report you have selected, the label for the result will change to Area, Integral, 26-14 c Fluent Inc. November 28, 2001
26.6 Volume Integration Area-Weighted Average, Flow Rate, Mass Flow Rate, Mass-Weighted Average, Sum of Facet Values, Average of Facet Values, Minimum of Facet Values, Maximum of Facet Values, Average of Surface Vertex Values, Minimum of Vertex Values, ormaximum of Vertex Values, as appropriate. Note the following items: Mass averaging weights toward regions of higher velocity (i.e., regions where more mass crosses the surface). Flow rates reported using the Surface Integrals panel are not as accurate as those reported with the Flux Reports panel (described in Section 26.2). The facet and vertex average options are recommended for zeroarea surfaces. 26.6 Volume Integration The volume, sum, volume integral, volume-weighted average, mass integral, and mass-weighted average can be obtained for a selected field variable in selected cell zones in the domain. Example uses of the different types of volume integral reports are given below: Volume: You can compute the total volume of a fluid region. Sum: You can add up the discrete-phase mass or energy sources to determine the net transfer from the discrete phase. You can also sum user-defined sources of mass or energy. Volume integral: For quantities that are stored per unit volume, you can use volume integrals to determine the net value (e.g., integrate density to determine mass). Volume-weighted average: You can obtain volume averages of mass sources, energy sources, or discrete-phase exchange quantities. c Fluent Inc. November 28, 2001 26-15
Alphanumeric Reporting Mass integral: You can determine the total mass of a particular species by integrating its mass fraction. Mass-weighted average: You can find the average value (such as average temperature) in a fluid zone. 26.6.1 Computing Volume Integrals Volume The volume of a surface is computed by summing the volumes of the cells that comprise the zone: n dv = V i (26.6-1) Sum The sum of a specified field variable in a cell zone is computed by summing the value of the selected variable at each cell in the selected zone: Volume Integral n φ i (26.6-2) A volume integral is computed by summing the product of the cell volume and the selected field variable: n φdv = φ i V i (26.6-3) Volume-Weighted Average The volume-weighted average of a quantity is computed by dividing the summation of the product of the selected field variable and cell volume by the total volume of the cell zone: 26-16 c Fluent Inc. November 28, 2001
26.6 Volume Integration Mass-Weighted Integral 1 V φdv = 1 V n φ i V i (26.6-4) The mass-weighted integral is computed by summing the product of density, cell volume, and the selected field variable: n φρdv = φ i ρ i V i (26.6-5) Mass-Weighted Average The mass-weighted average of a quantity is computed by dividing the summation of the product of density, cell volume, and the selected field variable by the summation of the product of density and cell volume: φρdv n φ i ρ i V i = ρdv n ρ i V i (26.6-6) 26.6.2 Generating a Volume Integral Report To obtain a report for selected cell zones of the volume or the sum, volume integral, volume-weighted average, mass-weighted integral, or massweighted average quantity of a specified field variable, use the Volume Integrals panel (Figure 26.6.1). Report Volume Integrals... The steps for generating the report are as follows: 1. Specify which type of report you are interested in by selecting Volume, Sum, Volume Integral, Volume-Average, Mass Integral, or Mass-Average under Options. 2. If you are generating a report of volume, skip to the next step. Otherwise, use the Field Variable drop-down lists to select the field c Fluent Inc. November 28, 2001 26-17
Alphanumeric Reporting Figure 26.6.1: The Volume Integrals Panel variable to be used in the integral, sum, or averaged volume integrations. First, select the desired category in the upper drop-down list. You can then select a related quantity from the lower list. (See Chapter 27 for an explanation of the variables in the list.) 3. In the Cell Zones list, choose the zones on which to compute the volume, sum, volume integral, volume-weighted average, mass integral, or mass-averaged quantity. 4. Click on the Compute button. Depending on the type of report you have selected, the label for the result will change to Total Volume, Sum, Total Volume Integral, Volume-Weighted Average, Total Mass- Weighted Integral, ormass-weighted Average, as appropriate. 26-18 c Fluent Inc. November 28, 2001
26.7 Histogram Reports 26.7 Histogram Reports In FLUENT, you can print geometric and solution data in the console (text) window in histogram format or plot a histogram in the graphics window. Graphical display of histograms and the procedures for defining a histogram are discussed in Section 25.8.7. The number of cells, the range of the selected variable or function, and the percentage of the total number of cells in the interval will be reported, as in the example below: 0 cells below 1.195482 (0 %) 2 cells between 1.195482 and 1.196048 (4.1666667 %) 1 cells between 1.196048 and 1.196614 (2.0833333 %) 0 cells between 1.196614 and 1.19718 (0 %) 0 cells between 1.19718 and 1.197746 (0 %) 2 cells between 1.197746 and 1.198312 (4.1666667 %) 1 cells between 1.198312 and 1.198878 (2.0833333 %) 6 cells between 1.198878 and 1.199444 (12.5 %) 9 cells between 1.199444 and 1.20001 (18.75 %) 25 cells between 1.20001 and 1.200576 (52.083333 %) 2 cells between 1.200576 and 1.201142 (4.1666667 %) 0 cells above 1.201142 (0 %) To generate such a printed histogram, use the Solution Histogram panel. Report Histogram... Follow the instructions in Section 25.8.7 for generating histogram plots, but click on Print instead of Plot to create the report. c Fluent Inc. November 28, 2001 26-19
Alphanumeric Reporting 26.8 Reference Values You can control the reference values that are used in the computation of derived physical quantities and nondimensional coefficients. These reference values are used only for postprocessing. Some examples of the use of reference values include the following: Force coefficients use the reference area, density, and velocity. In addition, the pressure force calculation uses the reference pressure. Moment coefficients use the reference length, area, density and velocity. In addition, the pressure force calculation uses the reference pressure. Reynolds number uses the reference length, density, and viscosity. Pressure and total pressure coefficients use the reference pressure, density, and velocity. Entropy uses the reference density, pressure, and temperature. Skin friction coefficient uses the reference density and velocity. Heat transfer coefficient uses the reference temperature. Turbomachinery efficiency calculations use the ratio of specific heats. 26.8.1 Setting Reference Values To set the reference quantities used for computing normalized flow-field variables, use the Reference Values panel (Figure 26.8.1). Report Reference Values... You can input the reference values manually or compute them based on values of physical quantities at a selected boundary zone. The reference values to be set are Area, Density, Enthalpy, Length, Pressure, Temperature, Velocity, dynamic Viscosity, and Ratio Of Specific Heats. For 2D problems, an additional quantity, Depth, can also be defined. This value 26-20 c Fluent Inc. November 28, 2001
26.8 Reference Values Figure 26.8.1: The Reference Values Panel c Fluent Inc. November 28, 2001 26-21
Alphanumeric Reporting will be used for reporting fluxes and forces. (Note that the units for Depth are set independently from the units for length in the Set Units panel.) If you want to compute reference values from the conditions set on a particular boundary zone, select the zone in the Compute From dropdown list. Note, however, that depending on the boundary condition used, only some of the reference values may be set. For example, the reference length and area will not be set by computing the reference values from a boundary condition; you will need to set these manually. To set the values manually, simply enter the value for each under the Reference Values heading. 26.8.2 Setting the Reference Zone If you are solving a flow involving multiple reference frames or sliding meshes, you can plot velocities and other related quantities relative to the motion of a specified reference zone. Choose the desired zone in the Reference Zone drop-down list. Changing the reference zone allows you to plot velocities (and total pressure, temperature, etc.) relative to the motion of different zones. See Chapter 9 for details about postprocessing of relative quantities. 26-22 c Fluent Inc. November 28, 2001
26.9 Summary Reports of Case Settings 26.9 Summary Reports of Case Settings You may sometimes find it useful to get a report of the current settings in your case. In FLUENT, you can list the settings for physical models, boundary conditions, material properties, and solver controls. This report allows you to get an overview of your current problem definition quickly, instead of having to check the settings in each panel. 26.9.1 Generating a Summary Report To generate a summary report you will use the Summary panel (Figure 26.9.1). Report Summary... Figure 26.9.1: The Summary Panel The steps are as follows: 1. Select the information you would like to see in the report (Models, Boundary Conditions, Solver Controls, and/or Material Properties) in the Report Options list. 2. To print the information to the FLUENT console window, click on the Print button. To save the information to a text file, click on the Save... button and specify the filename in the resulting Select File dialog box. c Fluent Inc. November 28, 2001 26-23
Alphanumeric Reporting 26-24 c Fluent Inc. November 28, 2001