Analytical Equilibrium Swirling Inflow Conditions for Computational Fluid Dynamics
T HE specification of swirling inflow conditions is an integral and important part of computational fluid dynamics (CFD) of swirling flows, which are complex flows with many practical applications [1], for instance, in turbulent combustion [2]. To specify a swirling velocity profile with a desired swirl number in a traditional CFDanalysis based on aReynolds-averagedNavier–Stokes (RANS) modeling approach is not an easy task, which becomes even more difficult in advanced CFD approaches such as direct numerical simulation (DNS) or large-eddy simulation (LES). DNS or LES of spatially inhomogeneous turbulent flows requires turbulent inflow boundary conditions [3], which may be generated either from an auxiliary simulation, from a proper orthogonal decomposition and linear stochastic estimation [4], from a digital filter reproducing specified statistical data [5], or simply taken as the mean velocity profile with superimposed fluctuations [6], which is essentially a perturbed inflow. With the presence of swirling, inflow conditions are difficult to specify. For RANS-based CFD, an appropriate mean velocity profile is needed. For DNS and LES, apart from the mean velocity profile, information on an appropriate “turbulent” component is needed as well. Pierce and Moin [7] developed a method for generating equilibrium swirling inflow conditions, which represents a logical, idealized starting point for generating swirling velocity profiles. In their method, the swirling inflow is obtained numerically by solving for the flow driven by fictitious axial and azimuthal body forces, where the axial body force represents themean pressure gradient that drives the physical flow. The azimuthal body force is not physically producible and may be thought of as existing only to overcome drag from the walls. This technique was used in LES of a coaxial jet combustor and good agreement with the experimental data was observed [7]. The method can be regarded as an effective and simple means of generating realistic swirling inflow conditions. In this study, efforts have beenmade to derive an analytical formof the equilibrium swirling inflow conditions. The analytical swirling inflow is easy to implement, as it does not require solving for the flow numerically [7]. The particular forms of the analytical equilibrium swirling velocity profiles have been obtained for swirling annular and round jets, which can be directly applied in the specification of swirling inflow conditions for RANS approaches and further explored for the specification of swirling inflow conditions for DNS and LES, regardless of the turbulent component needed in the timedependent simulations. A desired swirl number at the inflow can also be conveniently achieved by adjusting a constant.