Large Eddy Simulation of Supersonic Twin-Jet Impingement Using a Fifth-Order WENO Scheme
Toh, Hoong Thiam
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A three-dimensional flow field produced by supersonic twin-jet impingement is studied using a large eddy simulation (LES). The numerical model consists of two parallel axisymmetric jets of diameter 𝐷*, 3𝐷* apart, issuing from a plane which is at a distance H*=4𝐷* above the ground. The jet diameter 𝐷*, mean velocity 𝑊ₒ*, mean density 𝜌ₒ* and mean temperature 𝑇ₒ* at the jet center in the exit plane are used as reference values. The Mach number and Reynolds number of the jets are M=1.5 and Re=550,000, respectively. This model is closely related to the experimental setup of Elavarasan et al.(Elavarasan et al., 2000). The three-dimensional time-dependent compressible Navier-Stokes equations are solved using the method of lines. The convective terms are discretized using a fifth-order WENO scheme, whereas the viscous terms are discretized using a fourth-order central-differencing scheme. A low-storage five-stage fourth-order Runge-Kutta scheme is used to advance the solution in time. Code verification is achieved by comparison with flat-plate boundary-layer linear stability analysis, and computational data by Bendiks et al. (Bendiks et al., 1999). for a compressible turbulent round jet. Instantaneous flow, mean flow and Reynolds stresses for the twin-jet impingement are presented and discussed. The results reveal the existence of flapping behavior in the fountain. The flapping fountain is the vortical structure formed by the alternating merging of a primary vortex tube with a secondary vortex tube induced by the neighboring primary vortex tube. The nondimensional period of flapping is found to be 7𝐷*/𝑊ₒ*. High unsteadiness and strong interaction between the fountain and the jets are also observed. Due to the high diffusion and spreading rate of the fountain, the interaction between the fountain and the jets is only significant up to a height which is less than 3𝐷*. It is found that the mean peak velocity in the fountain is 0.40406 𝑊ₒ* and it occurs at 0.536607𝐷* from the ground. The suitability of the fifth-order WENO scheme to simulate turbulent flow field with embedded shocks is also demonstrated by its capability to capture unsteady shock waves in the impingement regions.
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