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Solar and Environmental Loading on Buildings
This house model demonstrates how HVAC designers can evaluate building designs using TAI's WinTherm and RadTherm codes. These heat transfer design codes evaluate solar loading, multiple bounce radiation exchange, interaction with the terrain, shadows, wind, rain, and interior/exterior convection. In the future, the code will also model transparent objects such as windows and perform interior energy balances. |
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Model Setup
In the figure below, the different colors denote the assignment of thermal properties and boundary conditions. The mesh for the house consists of 1802 elements. We used fewer elements in the meshes for the terrain and surrounding buildings (569 elements for the terrain, 12 elements each for the surrounding buildings) because we were not interested in calculating the temperature gradients across these objects. The primary purpose of the trees and surrounding buildings is to cast shadows. All of these ancillary objects contribute to the radiation exchange between the house and its environment.
A HVAC design must account for various meteorological factors: wind speed/ direction, cloud cover, rain, and solar irradiance. RadTherm and WinTherm include all these factors into the heat transfer calculation. By assigning a weather file to the problem, the user provides the sky, wind, and air temperature information needed for a very detailed and realistic simulation. Weather files contain the data displayed in the column to the right.
Both RadTherm and WinTherm employ an accurate solar model to calculate the sun position and intensity as a function of latitude, longitude, date, and time of day. The sky temperature and solar readings (explained below) account for environmental radiation exchange. The code uses the air temperature and wind speed and direction to calculate environmental convection on the external portions of the house.
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Weather File Data
- Latitude (Degrees North)
- Longitude (Degrees West)
- Elevation above Sea Level (Meters)
- Date: DDMMYY (Day, Month, Year)
- Time (Seconds)
- Wind Speed in Knots
- Wind Direction (from North to East) in Degrees
- Air Temperature in degrees C
- Relative Humidity in %
- Barometric Pressure in Millibars
- Pyrheliometer Reading (Direct Solar Beam) in W/m2
- Pyranometer Reading (Total Solar on Horizontal) in W/m2
- Diffuse Solar Component in W/m2
- Broadband Effective Sky Temperature in degrees C
- Sensor Band Effective Sky Temperature in degrees C
- Cloud cover in tenths (0 = clear, 10 = total overcast)
- Rain Rate in mm/hr
- Rain Temperature in degrees C (dew point will override this value)
- Solar Zenith Angle (from Vertical to Horizontal) in Degrees
- Solar Azimuth Angle (from North to East) in Degrees
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Radiation Exchange
SOLAR LOADING
The user assigns surface conditions to the house's roof and sides. To each surface, the user assigns an absorptivity, the fraction of incoming solar energy that the surface absorbs. The absorptivity can be calculated by integrating the product of the spectral solar radiance striking the surface by the spectral emissivity (or 1.0-reflectance) of the surface. Aspen gray, shown to the right, has an absorptivity of 82.2% or 0.822.
The source for this data is http://www.fsec.ucf.edu/~bdac/pubs/crr670/.
A compilation of relevant roof surface properties materials is provided here.
The absorptivity property determines the amount of incident solar energy absorbed. The magnitude of incident solar energy is the combination of the following:
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Direct Solar Irradiance
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Diffuse Solar Irradiance
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Reflected Solar
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- Measured by pyrheliometer (W/m^2)
- Short wavelength
- Depends on angle of incidence
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- Not to be confused with thermal skyshine or sky temperature which is long wavelength
- No direct components
- Measured by a shadow band pyranometer (W/m^2) with correction for diffuse shaded portion
- Short wavelength
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- Total solar (direct + diffuse) reflected from the surroundings.
- Measured by downlooking pyranometer (W/m^2)
- Short wavelength
- Depends on orientation
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Radiation From Other Parts
Each element has a view factor to the background, sky, and other elements. The total radiation will be the net result of emitted radiant energy, incoming solar radiance, and incoming radiant energy (reflected or emitted from other elements). The software automatically accounts for multiple bounce reflections.
The energy that each element emits and absorbs from other elements is dependant on the surfaces' emissivity values. Radiant energy is emitted according to the Stephan-Boltzmann equation. Since the elements are not transparent, whatever is not absorbed is reflected. The emissivity for Aspen Gray is 0.91. The surface setup dialog is shown to the right.
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Convection Exchange
There are two types of convection utilized in the house model: environmental (wind) and fluid film. For film convection, the user directly specifies the convection coefficient. The environmental convection algorithm calculates the convection coefficient based on wind direction and wind speed. The wind convection model also accounts for the heat transfer due to rain.
We selected the film convection model to simulate the regulated temperature inside the house. We obtained the needed convection coefficients from the ASHRAE Handbook. The handbook lists resistance (R) values for a variety of surfaces. The convection coefficient (h) is the reciprocal of the resistance value. For the inside of the roof, we used the ASHRAE value for a 45° sloped roof and calculated a convection coefficient of 1.6 Btu/hr-ft^2-°R. For the inside of the vertical walls, we used a value of 1.6393 Btu/hr-ft^2-°R.
The outside of the walls, the terrain, and the tree are all subjected to environmental convection. Environmental convection is computed by calculating the direction of the wind relative to each element and the temperature difference between the air and the element. For the tree, an area multiplier of 3 is used to model the higher surface area due to leaves and to simulate the effects of evapotranspiration. This makes the tree very responsive to changes in air temperature and wind. It should also be noted that the rain-rate causes a conduction from the portion of a part subjected to wind convection. In the case of rain, the software calculates conduction from the rain layer to the underlying surface.
Conduction
The primary interest in conduction is in the house walls. We used anisotropic conduction because conduction through the roof and walls is significantly different than conduction along these surfaces. Heat travels easier along the wood or plaster layers composing the interior and exterior surfaces of the wall than through the insulation between the layers. We modeled the walls as three layered parts. The outer layer represents siding or shingles; the middle layer models the insulation, rafters, and all internal components; while the inner layer represents gypsum board.
To calculate the thermal properties of the wall and roofing materials, we took thickness and resistance values from the ASHRAE Handbook and backed out the conductivity values. We carefully assigned a realistic thickness to each part. Lastly we adjusted the middle layer of the walls and roof to account for the combined properties (material density and specific heat) of insulation, rafters, and other internal components.
The three layer setup along with convection is shown below:
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Roof Construction
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1. Inside wall surface (film convection)
2. Gypsum wallboard (back layer)
3. Nominal rafter (middle layer)
4. Fiber insulation (middle layer)
5. Plywood sheathing (middle layer)
6. Permeable felt building membrane (middle layer)
7. Asphalt shingle roofing (front layer)
8. Outside surface (wind convection) |
Thermal Model
Note: the middle material consists of an anisotropic conducting, lumped property middle material
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