Walls and Windows: Characterization for CFD

Walls, windows, doors, and other exterior elements influence system performance by absorbing and transferring energy. The impact these components have can be characterized mathematically as simulation inputs and material properties, rather than explicitly representing their detailed geometry. This decreases simulation complexity and runtime without a loss in the results fidelity.

The characterization method will be determined by the analysis scope.  Walls, windows, doors, and other exterior elements are accounted for with film coefficient boundary conditions or homogenous volumes with effective conductivities. 

Film coefficients are boundary conditions that represent U-factors (also known as thermal conductance), which are the inverse of R-values (also known as thermal resistance). 

Effective conductivities are a single thermal conductivity value that represents the conductivity of multiple elements.

U-Factors

In Simulation CFD, U-factors can be applied directly as film coefficient boundary conditions.  Film coefficients are used when detailed output of a system’s exterior surroundings are not required.  For example, the wake of wind behind a building is not important to an analysis of an interior office space; in this instance a film coefficient would be used to represent the exterior walls and exterior air domain without explicitly modeling them.


An internal air volume with film coefficients defined can replace externally facing components such as walls and windows. 
1: Internal air
2: Walls
3: Windows
4: External air
U: Film coefficients defined on internal air volume surfaces

U-factors can be given by manufacturers (for direct input as a film coefficient) or derived mathematically:

U = 1/(Ri  + R1 + R2 + … Ro)

Where:

Ri = The resistivity of the inside air convecting to the inside surface of the wall (solved in Simulation CFD)

R1, R2= Resistivity of each component of the wall.

Ro = The resistivity of the outdoor air convecting to the outside surface of the wall

A film coefficient representing the U-factor of a construction element can be derived with material properties and physical dimensions.

The thermal resistances are used to derive the U-factor that will be applied in Simulation CFD.

Thermal Resistence of construction element=Length/Conductivity*Area

Thermal Resistence to exterior heat transfer= 1/Heat Transfer Rate*Area

(1) Air volume  (2) Construction element (brick wall) (3) External environment

(1) Air volume

(2) Construction element (brick wall)

(3) External environment

For example, in the following pair of simulations, results from a simulation with an explicitly modeled brick wall are compared to results that come from a U-factor applied as a film coefficient to the air volume.

The U-factor derivation below assumes a 3.5 inch brick wall, conductivity of .72 W/m-K and an external heat transfer rate of 5 W/m^2-K (typical natural convection value).  This equates to a U-factor of ~3 W/m^2-K that is applied to the external air domain as a film coefficient to replace the explicitly modeled brick wall.

The top image depicts temperature results for a simulation with air and an explicitly modeled brick wall.  The bottom image depicts an equivalent simulation with air and a U-factor applied as a film coefficient to represent the brick wall.

The top image depicts temperature results for a simulation with air and an explicitly modeled brick wall.

The bottom image depicts an equivalent simulation with air and a U-factor applied as a film coefficient to represent the brick wall.


XY plot taken from left to right for both analyses along the dashed line in upper image. The bottom row plot confirms identical temperatures across both analyses.

XY plot taken from left to right for both analyses along the dashed line in upper image. The bottom row plot confirms identical temperatures across both analyses.

Deriving U-factors for common construction elements is usually avoided by the use of common values provided by component manufacturers.  Several common components and values are found below:

Location U (BTU/hr-ft^2-R) U (W/m^2-K)
Natural Convection 1.76 10
Wall - wood studs, R13 Insulation .08 .45
Window, single glass 1.1 6.24
Window, double glass, ¼ air space .59 3.36
Window, triple glass .39 2.21
Door, 1” wood .64 3.64

Film coefficients are the preferred method to account for externally facing construction elements when the external air domain is not critical to the simulation. 

Effective Conductivities

Conduction through thin layers of glass panes and gas (e.g., argon) of a window (left) can be more simply modeled by calculating an equivalent thermal resistance and applying it to a single volume (right).

Conduction through thin layers of glass panes and gas (e.g., argon) of a window (left) can be more simply modeled by calculating an equivalent thermal resistance and applying it to a single volume (right).

When construction elements (walls, windows, and doors) are not represented with film coefficients, a homogenous characterization can be used for Simulation CFD to solve the heat transfer rates and temperature gradients around and through the elements.

A single homogenous volume with an effective conductivity can be used to represent a layered construction or network of elements, rather than explicitly modeling the individual components. 

For example, mathematically representing a multi-pane, gas-filled window as a single volume is preferred over modeling each individual component.

In most instances the effective conductivity or thermal resistance of a system is provided by manufacturers.  Deriving the effective conductivity, if not readily found, is done by calculating the thermal resistance of each component and combining the values with physical dimensions.

Thermal Resistence of each Element = Length/Conductivity*Area

The effective conductivity is used in Simulation CFD as the conductivity material property for a single volume representing the system, and can be calc*ulated as follows:

Ke=Ae/Le (R1+R2 + Rn)

The effective conductivity is used in Simulation CFD as the conductivity material property for a single volume representing the system, and can be calculated as follows:

Where:

Ke = Effective conductivity of the characterized element

Le = Thickness of the characterized element

Ae = Area of the characterized element

R1,2,n = Thermal resistance of respective element 
 
Characterizing elements in this manner effectively accounts for their influence and allows Simulation CFD to solve for their thermal gradients and heat transfer rates.
 

Windows

Windows may contain numerous panes of glass, gas, trim, and framing details that are unnecessary to model in simulation.  Replacing these details with a single volume with an effective conductivity will adequately capture the influence of this system.


Left: Detailed window model containing window panes, trim, and framing.
Right: Single volume with an effective conductivity material property defined in Simulation CFD 

Walls

Walls are composed of multiple elements such as framing, insulation, and fascias that are unnecessary to model in Simulation CFD.  They can be characterized as a homogenous volume with an effective conductivity.


Left: Wall composed of framing, insulation, and facias.
Right: A single volume with an effective conductivity defined in Simulation CFD.

Summary

Exterior and interior construction elements such as walls, windows, and doors can be characterized with film coefficients or homogeneous volumes with effective conductivities.  Representing these construction elements with boundary conditions and simple volumes greatly reduces simulation complexity and run time without sacrificing results fidelity.