One of the useful features in ANSYS Fluent is the solar load model. This capability can be used to calculate the effective radiation load based on the position on the earth’s surface (latitude and longitude), the model orientation with respect to North, the time of day, the season, and established conditions for clear or cloudy weather. The applications are widespread, but readily apparent are calculations of radiative heating on automotive cabins and buildings.
Two options are available for the solar load model; solar ray tracing or discrete ordinates. Solar ray tracing is coupled to Fluent by computing heat fluxes from incident solar radiation using a ray tracing and shading algorithm, and then applies the calculated heat flux on element faces of semi-transparent walls. Solar ray tracing presents less computational overhead than discrete ordinates, as it calculates the solar loads once at the beginning of a steady-state simulation. However, it uses some simplifying assumptions to do so (another example of the accuracy/solution time tradeoff that simulation analysts often encounter). It does not calculate the emission from surfaces, and the reflecting component of the incident load is distributed uniformly across all participating surfaces rather than retained locally at the surfaces reflected to. However, solar ray tracing can be coupled with one of the supported radiation models (P-1, Rosseland, Surface-to-Surface) if surface emission effects are important.
The discrete ordinates method is coupled to Fluent by calculating radiation heat fluxes on semi-transparent walls. The discrete ordinates approach directly calculates the irradiation flux as a boundary condition for the solution of the radiative transfer equation.
A key part of the Solar Load Model in Fluent is the Solar Calculator, which calculates the solar beam direction and irradiation for a known time and position. The Solar Calculator inputs are displayed in Figure 1, followed by an explanation of each.
Figure 1 – Solar Calculator Panel for Fluent’s Solar Load Model
The inputs for the Solar Calculator are:
· Global position (latitude, longitude, and time zone). The time zone is measured as a plus or minus from Greenwich Mean Time (GMT).
· Starting date and time
· Orientation of the model with respect to North/East
· Solar irradiation method
· Sunshine factor
There are two choices for the irradiation method; Fair Weather Conditions (ASHRAE) and Theoretical Maximum (NREL). These methods are similar, but the Fair Weather Conditions method applies greater attenuation on the radiative load. The sunshine factor is simply a linear multiplier that allows the incident load to be reduced in order to account for cloud cover. Once the irradiation and solar beam direction are known, they are applied as inputs to the solar ray tracing algorithm or the discrete ordinates method.
After selecting the appropriate input conditions for the Flatiron Solar Calculator, you can click “Apply” to generate the irradiation and solar beam direction information. This information is printed to the Fluent TUI (text user interface) window, and typically looks something like:
Sun Direction Vector: X: -0.0722563, Y: 0.799654, Z: -0.596097
Sunshine Fraction: 1
Direct Normal Solar Irradiation (at Earth’s surface) [W/m^2]: 1327.15
Diffuse Solar Irradiation – vertical surface: [W/m^2]: 105.195
Diffuse Solar Irradiation – horizontal surface [W/m^2]: 113.693
Ground Reflected Solar Irradiation – vertical surface [W/m^2]: 117.495
Figure 2 – Printed result in the Fluent interface after applying the Solar Calculator
This information is printed so that it can be used in the specification of boundary conditions. The Solar Load Model (for both Ray Tracing and Discrete Ordinates) applies a calculated solar flux on semi-transparent surfaces only, so if there are opaque surfaces in the model, the solar load will have to be applied as a boundary condition on the opaque surfaces explicitly.
The explicit application of the solar load to the opaque surfaces in the model requires the calculation of the heat flux on that surface. The solar load is a vector quantity applied to the model along the “Sun Direction Vector” (Figure 2). The incident solar load on a particular surface will be the component of this vector projected into the direction of the local surface normal vector. The result of the projection is then multiplied by the “Direct Normal Solar Irradiation” shown in the printed output in Figure 2. This value represents the heat flux which must be applied as a boundary condition on the opaque surfaces of the model. Intuitively, if the result of the dot product between the “Sun Direction Vector” and the unit normal on the surface is a negative scalar, then the surface in question is not irradiated by the sun.
The Solar Load Model is applied to calculate the load on a simple model of two solid aluminum blocks subjected to solar heating in Phoenix on a summer day at 1 pm with an ambient temperature of 100 degrees Fahrenheit (see Figure 3). The view in Figure 3 is from the South (positive y direction).
Figure 3 – Simple geometry for coupled thermal and fluid solution with solar loading
The grid contains ~200e3 cells, and uses hex elements to resolve the interior of the blocks and tetra elements to resolve the air volume of the surroundings. Inflation layers are used at the interfaces between the air volume and the solids. The solar loads on each surface and contributions from natural convection (in the form of heat transfer coefficients) are applied as heat flux conditions on the walls of the aluminum blocks. In this case, the Solar Calculator is used to get the sun direction vector and applied load, which are applied as individual boundary conditions. The Solar ray tracing and the coupling of the Solar Load model with the radiation models is not utilized in this example, primarily because the boundaries on which the solar loads are applied are all opaque, and the re-radiation of energy is not accounted for. The coupled solver with pseudo-transient relaxation is applied for the solution of the momentum, energy, and turbulence equations. A few representative plots are shown in Figure 4 a-c.
(a) (b) (c)
Figure 4 – Simulation results: (a) Temperature contours on aluminum blocks; (b) Temperature contours in a plane; (c) Vertical velocity contours in a plane
In summary, the Solar Load Model in Fluent presents a way to easily calculate details about the solar heat flux conditions given a certain geographical location, season, and time of day. Furthermore, Fluent’s Solar Load model has the capability to resolve the physics associated with solar heating of transparent media and re-radiation problems.