Pressure equalization 9

Roof mounted solar arrays can be considered a double layer system – with the roof as the inner layer and the modules as the outer layer just as roof pavers are. The external (upper) surface and cavity (lower surface of the modules) are exposed to wind flow since there is a void beneath the roof and the underside of the modules. Pressure equalization is a wind loading process that can occur; with the cavity pressure partially approaching that on the upper (external) surface of the array. Perfect pressure equalization is unlikely in practice (since it could only happen for static, uniform, external pressures), however, net pressures on roof-mounted pavers have been found to be less that what would be expected on the bare roof due to this process (Bienkiewicz and Endo, 2009). As such, pressure equalization can play a crucial role in reducing the (net) design wind loads for the outer layer of double layer systems (see Bienkiewicz and Endo, 2009 for roof pavers and Kopp, 2014 for tilted solar installations on flat roofs). The process of pressure equalization is not limited to roof pavers and solar modules, but also impacts cladding systems such as curtain walls, brick veneer or vinyl siding walls, and rainscreen walls (Kumar, 2000).

Rainscreens are used to protect structures from rain infiltration. The systems employ (at least) two layers with a cavity of air in between outer (cladding layer) and an interior layer; the outer one is an air-permeable rainscreen and the inner layer is an air barrier. The outer layers work together to protect the structure with the rainscreen deflecting the majority of the rain and the cavity between the layers providing drainage for any water that does penetrate. Kumar (2000) noted that Pressure Equalized Rainscreens (PER) can be designed to reduce the wind loads on the screen (outer layer) through deliberate venting, openings designed to ensure rapid equalization. The total venting area, in

addition to the dimensions of both the cavity and the vented openings, are key design parameters. Small, deep vents lead to laminar flow, with turbulent flow associated with vents that are large in cross-section, yet shallow in depth (Cook, 1990). Smaller cavities require less airflow to achieve equalization and thus yield a faster response time – important when designing for the short duration peaks across the rainscreen (Kumar, 2000).

While vents are beneficial in ensuring pressure equalization for rainscreens, a similar statement can be made regarding gaps for loose-laid pavers. As previously mentioned, Kind and Wardlaw (1982) found that the inclusion of gaps between individual paver elements could actually prevent the failure when performing blow-off tests. This indicates that resistance to failure of individual pavers was increased when the pavers were not flush with one another but separated by an air gap. In 1991, Okada and Okabe tested failure wind speeds of paver systems with two different cavity depths. They found that a cavity depth (not loose-laid, but mounted with an offset from the roof) resulted in lower failure wind speeds due to relatively poorer pressure equalization. Thus, while gaps are beneficial, relatively large cavity depths are detrimental to pressure equalization, consistent with the discussion on pavers in section 1.4 where pressure equalization is noted to be improved with higher values of G/H.

While large cavity depths may not be optimal with respect to increasing pressure equalization, they are a required component of dual-layer wall or roof systems which have many uses in the design and construction industries. As such, a number of research studies have highlighted methods to maximize pressure equalization by modifying the cavity.

Kumar (2000) noted that continuous cavities are not always efficient and that compartmentalization improves pressure equalization. He notes that pressure

equalization is highly dependent on the spatially-varying, external, pressure variations. Dividing the cavity into compartments can reduce the external pressure gradients and reduce cross-flow between adjacent cavities, improving pressure equalization and

around the corner of buildings which can experience large pressure gradients, in fact Morrison and Hershfield Ltd (1990) went so far as to say that compartmentalization is absolutely necessary at the corners of buildings when studying a vinyl siding clad wood- framed wall. Introducing small compartments in these regions can reduce the pressure drop across the outer surface as well as the volume of air required for equalization, reducing the response time of the cavity pressures (Kumar, 2000). Larger compartments can be used in the interior region of a building façade where the external pressure

gradients are smaller.

Another way to increase the pressure equalization would be to increase the flow resistance in the cavity. Gerhardt and Janser (1994) noted that increasing the flow resistance within the cavity by adding batten or wire nets has a similar effect to compartmentalization, improving the pressure equalization and reducing the net wind loading on the outer layer.

A number of studies have contributed to theoretical models based on the Helmholtz principle, standard gas law and mass continuity to predict cavity pressures based on external pressures (for a selection see Holmes, 1979; Kumar and Van Schijndel, 1998, 1999; and Latta, 1973).

Oh and Kopp (2014, 2015) conducted wind tunnel studies to characterize cavity pressures in a double-layer system and developed an analytical model, validated with experimental results. Their analytical model was developed noting the many similarities between the double-layer systems of wall systems (rainscreens) and solar arrays. Their parameter, φ, is the ratio of cavity flow pressure drop to the orifice flow pressure drop. φ is dependent on a number of parameters including the G/H ratio as well as the Reynolds number, such that

(1)

where fH is the friction coefficient through the cavity, L is the module length, ft is the

friction loss through the orifice or gap, t is the module thickness and the CL is the orifice

loss coefficient. Equation 1 was developed based on a model with a single cavity with a gap before and after the module, limiting the flow to one direction. The friction losses through the orifice are significantly lower than the total loss coefficient, allowing the simplification of Equation 2, yielding,

. 2

where Lc is an effective cavity length, ReH is the cavity Reynolds number. A φ value

greater than order (1) indicates that cavity flow dominates such that the cavity pressure distribution is liner in nature. Alternatively, when the orifice (gap) flow dominates, the cavity pressure distribution is uniform and yields a φ value less than order (1). The parameter is thought to be robust since the values were found to be order of magnitudes larger or smaller than the transition point between the different flow mechanisms. It is

unclear how the equations to evaluate φ could be used to predict the cavity flow of systems with multiple cavities, multi-directional flows, or even how to precisely define the effective cavity length.