Generally one considers ``driving rain'' as rain that is carried (driven) by wind. A synonym is ``wind-driven rain''. Here, we will use a more restricted definition: driving rain (or wind-driven rain) is rain that is carried by wind and driven onto building envelopes. Usually we will look at building envelopes which are vertical, although rain distribution on roofs is affected by wind too.
Because wind always plays a role in formation and distribution of rain, the quantities and physical concepts described in the previous section 2.2 also apply for driving rain (yet sometimes slightly adapted).
The general model of driving rain used in this study takes the trajectories of raindrops into account. In reality, every individual drop has its individual drop trajectory. Moreover, the lifetime of a drop is affected by drop interaction (collision and breakup) and the environment (wind and evaporation). The model takes only the influence of the wind into account. This is sketched in figure 2.12 for raindrops of one particular size. From the discussion in section 2.2.3 we expect that the trajectories of raindrops will also be affected by the turbulence in the wind. The turbulent dispersion of raindrops will imply that raindrops starting at the same point will follow different paths (figure 2.12).
The driving rain amount per drop size in relation to the reference rain
amount per drop size is characterised by a catch ratio :
The reference of in eq. 2.26 is taken in the wind flow undisturbed by individual buildings or other obstacles. The reference is preferably taken at the site itself and then the model applies for the second step in our general two-step approach (figure 1.1).
The driving rain intensity on the building envelope is:
The catch ratio (and eventually the driving rain intensity) depends on the following factors:
The model can be elaborated into a numerical model. This will be done in chapter 6 (CFD simulations). Similar numerical models were described in the literature, e.g.: [Bookelmann and Wisse 1992], [Choi 1993], [Karagiozis and Hadjisophocleous 1996], [van Mook et al. 1997], [Sankaran and Paterson 1995a], [Hangan and Surry 1998] and [Blocken and Carmeliet 2000a]. However, the cited authors (except for [Sankaran and Paterson 1995a]) did not take the turbulent dispersion of raindrops into account: the trajectories were calculated according to the mean wind field. In chapter 6 we will study the differences resulting from calculations with or without turbulent drop dispersion.
In the practice of driving rain measurements, raindrop spectra have
never been measured, and raindrop trajectories are not determined.
Based on the integral rain quantities, one correlates the driving rain
intensity with the horizontal rain intensity, i.e. the reference in the
undisturbed wind flow, by means of their ratio:
1. Vertical rain intensity
Some authors try to distinguish several factors in the driving rain
ratio. The first step is to define a vertical rain intensity
[mm h], i.e. the rain intensity through a vertical
plane in the undisturbed wind flow. It is
assumed to be related to the reference wind speed and horizontal rain
intensity in the following way:
[Lacy 1965] calculated
and as follows: he assumed that the ratio of vertical and horizontal
rain intensities is equal to the ratio of wind speed and terminal
velocity of drops of median size ():
He gives an empirical relationship between and
which he deducted from data presented by [Laws and
Substituting eq. 2.32 in eq. 2.30 yields the desired
[Lacy 1965] showed also that calculated values of (eq. 2.33) agree quite well with measurements of for 75 storms with driving rain that occurred during 1948-1963 in Garston (UK). Only rain storms of more than 10 hours were taken into account; the time interval of the measurements was not specified. Measurements of [Künzel 1994] at Holtzkirchen (DE) yielded a value for of about 0.2.
With the quantities defined in section 2.2.4, one
can express the vertical rain intensity [mm h] in
terms of the reference wind speed [m s] and the
integral of the raindrop mass concentration spectrum (i.e. the liquid
water content [kg m]):
To investigate the validity of the model of Lacy (eq. 2.29) for several given raindrop spectra, we combine equations 2.29 and 2.34, yielding , and plot for . Figure 2.13 shows this plot for raindrop spectra of [Marshall and Palmer 1948] and [Ulbrich 1983] (compare with figure 2.10). In figure 2.14 is plotted for Best spectra according to parameters given by [Best 1950] and according to the measurements in the Netherlands of [Wessels 1972] (cf. figure 2.11). These figures show that parameter becomes constant for larger , but for rain intensities below 1 mm h can increase up to 0.4. Moreover, rainfall with larger drops will yield a lower value of . Applying the data of [Wessels 1972], we find that ranges from 0.2 to 0.35. The generally measured value 0.22 (i.e. at the lower part of the mentioned range) might originate from the sensitivity of free-standing driving rain gauges, which is often low for low rain intensities and for rainfall with mainly small drops.
2. Driving rain intensity
The second step is to relate vertical rain intensity to driving rain
The obstruction factor is meant to reflect the building geometry, surrounding topology and façade position. It ranges from 0.1 to 2. Examples for values of are found in [Lacy 1965], [Frank 1973], [Lacy 1977], [Brown 1988], [Henriques 1992] and [Künzel 1994].
Finally, we conclude that both the coefficient and the obstruction factor depend on the raindrop spectrum. So, they are interdependent. It is probably better to merge the two coefficients into one coefficient ( ).
© 2002 Fabien J.R. van Mook