Direct numerical simulation of the near field dynamics of a rectangular reactive plume

Abstract

Spatial direct numerical simulation (DNS) is used to study the near field dynamics of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field, which interact with the flame and temporally create localized holes within the reaction zone in which no chemical reactions take place. The interaction between density gradients and gravity plays a major role in the vorticity generation of the buoyant plume. At the downstream of the reactive plume, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional (3D) vortex interactions. Analysis of energy spectra shows that the spatially developing reactive plume has a tendency of transition to turbulence under the effects of combustion-induced buoyancy. The buoyancy effects are found to be very important to the formation, development, interaction, and breakdown of vortices in reactive plumes. In contrast with the relaminarization effects of chemical exothermicity via viscous damping and volumetric expansion on non-buoyant jet diffusion flames, the tendency towards transition to turbulence in reactive plumes is greatly enhanced by the buoyancy effects.

Introduction

As an efficient technique of passive flow control, jets in non-circular configurations, such as elliptic, rectangular, square and triangular geometries, are encountered in various engineering applications such as combustors, cooling of energy conversion devices, and exhaust of aerospace vehicles. Non-circular jets have attracted an extensive research interest in recent years, both experimentally (e.g. Ho and Gutmark, 1987; Hertzberg and Ho, 1995; Zhang, 2000) and numerically (e.g. Miller and Madnia, 1995; Grinstein and Kailasanath, 1995; 1996; Grinstein and DeVore, 1996; Wilson and Demuren, 1998). Recently, the topic has been reviewed by Gutmark and Grinstein (1999).

In a broad range of practical applications, buoyancy due to density inhomogeneity under the influence of gravity plays a major role in the flow development of non-circular jets. The density inhomogeneity can result from inhomogeneities in temperature, differences in concentration of chemical species, changes in material phase, and many other effects in the flow field. Buoyancy effects are especially important to low-speed combustion applications, such as fires. However, buoyancy effects have not been taken into consideration in the existing numerical studies of non-circular jets (Miller and Madnia, 1995; Grinstein and Kailasanath, 1995, Grinstein and Kailasanath, 1996; Grinstein and DeVore, 1996; Wilson and Demuren, 1998).

Free jets and plumes in open-boundary domains with buoyancy effects usually consist of a strongly buoyant near field and a turbulent, weakly buoyant far field. In the near field, the most prominent feature of buoyant jets and plumes is that the large vortical structures dominate the flow field of both reacting and non-reacting flows (e.g. Cetegen and Ahmed, 1993; Katta et al., 1994; Lingens et al., 1996; Cetegen et al., 1998; Maxworthy, 1999; Jiang and Luo, 2000a). The mechanism leading to the formation of these vortical structures is believed to be an absolute flow instability (Lingens et al., 1996; Maxworthy, 1999; Jiang and Luo, 2000c), which is different from that of non-buoyant jets. It was dentified (Jiang and Luo, 2000c) that the evolution of vortices in buoyant jets and plumes does not rely on the spatial amplification of external perturbations applied at the flow boundary but on the interactions between the density gradients and gravity.

The near field dynamics of buoyant jets and plumes, such as the formation and transport of vortices and laminar to turbulent flow transition, still has not been fully understood. In general, theoretical analysis is not able to deal with such complicated flow patterns. Experimental measurements of the flow field are difficult to reach a high level of detail and accuracy, especially for reacting flows. By using experimental techniques, it is also hard to investigate the mechanisms involved in the physical problem due to the coupling among combustion, buoyancy, and flow turbulence. For the study of the near field dynamics including flow transition, the conventional numerical simulations based on Reynolds averaging are not suitable either. Advanced numerical techniques, such as direct numerical simulation (DNS), provide a possibility to get a better understanding of the physical problem.

Numerical studies on buoyant jets and plumes in non-circular configurations especially those concerning combustion-induced buoyancy effects are very scarce in the literature. Previous studies on buoyant jets and plumes by the present authors (Jiang and Luo, 2000a, Jiang and Luo, 2000b, Jiang and Luo, 2000c) were limited to axisymmetric and planar configurations. However, three-dimensional effects are important in many applications and 3D simulations are essential to the understanding of flow transition. In this study, a fully 3D simulation is performed for a buoyant rectangular plume with an aspect ratio of 2:1. The plume considered is unsteady, viscous, reacting flow with temperature-dependent viscosity. A global, one-step reaction governed by temperature-dependent, finite-rate Arrhenius kinetics is used to represent the chemistry.

In the context of DNS, most simulations reported in the literature are temporal simulations (Moin and Mahesh, 1998) with the imposition of periodic boundaries in at least one direction, which are computationally less demanding. However, it is not possible to simulate buoyant non-circular jets and plumes in a temporal way because the buoyancy acceleration in the streamwise direction and the non-parallel effects due to flow entrainment through the side boundaries are significant in the near field. Therefore, a spatial DNS is necessary to simulate buoyant jets and plumes. To restrict the computational costs, the spatial DNS in this study is focused on the near field of the rectangular plume, which provides detailed information about the early stage of the spatial development of the flow field.

DNS results are presented mainly for a rectangular reactive plume in this paper, but some results from the simulation of a rectangular non-reactive thermal plume are also included to highlight their differences. The rest of the paper is organized as follows. Section 2 first presents the governing equations for the flow field, and then introduces the numerical methods and boundary conditions for the spatial DNS of open-boundary buoyant flows. Section 3 is a discussion of the simulation results from a comparative study of rectangular reactive and non-reactive plumes. The analysis of results is based on both instantaneous and time-averaged flow quantities. Finally, conclusions are drawn in Section 4.