Scaling laws of flow structures around geometrically similar fire whirls

Abstract

This paper discusses the scaling laws of the flow structures around geometrically similar fire whirls, an insight that will be necessary when applying laboratory-scale data to real-scale fire whirls in urban or wildland fires. A fixed-frame-type fire-whirl generator is used to form geometrically similar fire whirls of three different scales. A particle image velocimetry (PIV) technique is used to measure the tangential (rotational) and the radial velocity components around the fire whirls. Scaling analysis is then conducted to derive two pi numbers, namely, the Reynolds number and the Froude number. Measured tangential velocity distributions are nearly uniform in the vertical direction when the height from the floor is greater than ~1 cm, where the velocity profiles are found to be well correlated using the Froude number, suggesting that viscosity plays only a minor role. Near the floor, on the other hand, the magnitude of tangential velocity is reduced, leading to an enhanced radial inflow toward the flame, a phenomenon similar to the Ekman layer. This inflow layer pushes the flame toward the fuel surface, increasing the heat input from the flame to the fuel and hence the burning rate. It is found that the Froude number can also correlate the radial velocity distributions near the floor.