By Warren J. Keegan, Sandra E. Moriarty, Thomas R. Duncan
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In laminar ﬂow, the ﬂuid moves under the inﬂuence of an axial pressure gradient and the individual ﬂuid layers act on each other with shear stress proportional to the velocity gradient. Because there is no pressure gradient in the lateral direction, the ﬂow is streamlined, which by deﬁnition means that for each streamline, the velocity is constant. 1). 9) restates the ﬁrst Reynolds’ experimental characterization indicating that for laminar ﬂows in conduits and pipes, the ﬂow rate is proportional to the ﬁrst power of the pressure drop per unit length.
5 Schematic diagram of the effect of swirl on jet aerodynamics. CRZ, central recirculation zone; ERZ, external recirculation zone. 40 Rotary Kilns combustion systems. The centrifugal effect of the swirling jet induces a reduced pressure along the axis close to the burner and an increased pressure further downstream resulting in an axial recirculation eddy. 34) The nozzle ﬂux of angular momentum L_ 0 and the ﬂux of linear momentum G_ 0 might be calculated as L_ 0 ¼ 2pr Zr0 ð! u! 35) 0 G_ 0 ¼ 2p Zr0 À 2Á P þ r!
One important estimate is the distance at which a particle in a particle-laden jet will travel before coming to rest. 8% of its initial value. 40) where m and rp are the mass and radius of the particle, respectively, and m is the dynamic viscosity of the surrounding ﬂuid. , 1967). However, if the particles were ﬁner, for example, 40 mm in size, then the range would only be 30 cm, which would have a damping effect on the jet due to turbulent energy transfer. The relaxation time is a measure of the shortest timescale of turbulence to which the particle could respond.