Effects of scaling on numerical modeling of a transverse jet into supersonic cross flows

Supersonic combustion using transverse sonic injection into the supersonic stream is investigated numerically. A threedimensional dual-mode scramjet combustor configuration with significant upstream interaction was selected to provide an understanding of key features of upstream interaction, and to identify physical and numerical issues relating to modeling of dual-mode configurations. The numerical analysis was performed with vitiated air at freestream Mach number of 2.5 using hydrogen as the sonic injectant. The results are presented for a three-dimensional (% scale) geometry. Comparisons are made with experimental results. Results show that numerical modeling using a scaled geometry provides good agreement with experimental results for dual mode combustion of this configuration. This study supports the argument that numerical scaling is usetil in simulating dual-mode scramjet combustor flow-fields and could provide an excellent convergence acceleration technique for dualmode simulations. L INTRODUCTION Recently many studies have been conducted in response to the increased interest in the development of dual mode combustion systems.‘-” It has been found that an optimal combustor design utilizes transverse fuel injection downstream of a rearward-facing step. The step has several purposes: to isolate the inlet boundary layer from the pressure rise generated in the combustion chamber, to improve species mixing, and to create recirculation regions to sustain combustion. Many numerical and experimental studies have been conducted to investigate transverse injection into such a complex flowfield’-“. However, the physics of this flow field are not yet tilly understood. Until recently, the numerical research was limited to two-dimensional models due to the complexities of the physics of the flow and the limitation on computer resources. Recently, Matsuo et al.’ and Mizobuchi et al6 presented numericalexperimental studies to investigate turbulence temperature fluctuations in a scramjet combustion chamber. They * Graduate Research Assistant, Associate Member ASME ** Associate Professor, Member AAIA ’ Manager, Hyper X Program, NASA Langley Research Center, Hampton, VA 23681 ” Eminent Professor/Scholar, AX4 Associate Fellow (c)1999 American Institute of Aeronautics & Astronautics concluded that the treatment of turbulence modeling is the key to an accurate computational scheme. Essential to the design of the scramjet engine is a detailed understanding of the complex flowfield in different regions of the combustion system. Constraints on system size and weight have created a need to improve technology for designing and analyzing such systems. Faster processors and efficient numerical techniques are essential. However, often it is the physical I . dimensions of the problem that, in requiring a fine mesh, consume so much computational time. In such cases, it is the responsibility of ,CFD modelers to understand how physical problems can be scaled to utilize computational space more efficiently. Also, the results from scaled geometry could be used to accelerate the convergence of full,scale geometry simulations. It is well known that for many systems it is possible to scale ~ physical dimensions and governing equations to give non-dimensional results. Unfortunately, few studies have been conducted on the scaling of mixing and reacting flows. The complexities of the 1 turbulence, mixing, and chemical reaction i make scaling of this problem an interesting task. The objective of this computational study is to numerically investigate a threedimensional dual-mode scramjet combustor configuration with significant upstream ’ interaction. This simulation is undertaken to provide an understanding of key features of upstream interaction, physical and numerical issues. In particular, this paper presents a report on the work in progress for an investigation into geometrical scaling of , numerical models where mixing and combustion are of primary concern. The combustion chamber is numerically modeled using a simplified l/d scale three-dimensional model. Numerical results are compared with experimental data. THEORETICAL MODEL The physical model under investigation, transverse hydrogen jet injection into supersonic air flow in a scramjet combustion engine, is shown Fig. 1. The freestream inlet height is 32 mm and the inlet channel is 200 mm long. There are 3.2 mm steps on the upper and lower walls of the chamber. The walls are then parallel over 96 mm. Finally, the chamber expands at 1 .? degree angle. The jets are located 12.8 mm downstream of the steps on the upper and lower walls. The jet injection holes are of 4 mm diameter, five on the lower wall and four on the upper wall. The distance between the injection hole centers is 32mm The governing equations for this problem are Navier-Stokes equations and species continuity equations. AnRNGkepsilon turbulence model is used. A simple one step kinetic model is employed. For the present study, the compressible, unstructured code, RAMPANT, is used to investigate the characteristics of the three-dimensional model of the scramjet combustion chamber. This code uses first/second order finite volume discretization method and a coupled implicit (Block Gauss-Seidel) solver. Further details of the numerical methods used in RAMPANT can be found in Ref. 10. Before using a full-scale model with combustion, it is necessary to simplify the model to investigate certain aspects of the code. As shown in Fig 1, the computational domain is simplified to encompass half of the upper and half of the lower jet (using the symmetry condition for these planes). To conserve computational time the possibility of scaling the problem is also investigated. An analysis of a % scale simplified threedimensional model of the combustion (c)1999 American Institute of Aeronautics & Astronautics chamber is performed. Mesh cells are concentrated around the walls, particularly in the region near the jets.