Rockets/landers arrive on the Moon with supersonic speed and impact lunar regolith. There is no reliable software to computationally simulate in an effective way the supersonic plumes escaping from these rockets/devices. A Large Eddy Simulation (LES) model and hybrid WENO (weighted essentially non-oscillatory) scheme numerical method were developed to address this problem.
Large Eddy Simulations of supersonic turbulent jets are carried out to understand their structure and quantify their turbulent characteristics. The LES uses a dynamic Smagorinsky model supplemented by the Yoshizawa model to model the sub-grid terms. The numerical method is a hybrid scheme in which a fifth-order WENO scheme is combined with a fourth-order central-difference scheme. A Runge-Kutta third-order scheme is used for time integration. Simulations are performed for supersonic jets having Reynolds numbers 1500, 3700, and 7900, and Mach numbers of 1.4 and 2.1. The Reynolds number value is observed to play a role in the transition to turbulence, but once transition has been achieved, it has a subdued effect above a threshold value.
The results of the simulations showed that turbulent structures in the transition region are more coherent, and the potential core is longer when the jet Mach number is higher; a larger potential core leads to a slower downstream velocity decay. The rms (root mean square) velocities are biased in the axial direction, as expected. In the fully turbulent downstream regions, the computed Reynolds stress is higher for a larger Mach number jet. Peak pressure fluctuations are observed to occur about half a jet diameter radially away from the centerline of the jet, and this location is found to be independent of both Reynolds and Mach numbers. The pressure-velocity correlations and the turbulent kinetic energy profiles are also investigated along the centerline and radial directions, and it is found that the peak turbulent kinetic energy in the axial directions occurs at the same location as the maximum pressure fluctuations.
The pressure-velocity correlations are primarily negative. For the fully developed turbulence jets, the pressure-radial velocity correlation is null at the centerline, and decreases to a minimum a short distance away from the centerline after which it again increases, exhibits a local peak, and then asymptotes to zero. This non-monotonic behavior is attributed to the radial expansion of the jet close to the centerline followed by fluid entrainment into the jet at larger radial locations. The pressure-axial velocity correlation is non-zero at the center line, reaches a minimum radially farther away than the pressure-radial velocity correlation counterpart, and thereafter increases and asymptotes to zero. The pressure-axial velocity correlation has the largest negative value for an intermediate Reynolds number. Thus, viscous effects have a nonmonotonic effect on the pressure-velocity fluctuation extrema.
This work was done by Josette Bellan of Caltech and Kaushik Balakrishnan for NASA's Jet Propulsion Laboratory. This software is available for license through the Jet Propulsion Laboratory, and you may request a license here. NPO-49812