Krishnan Mahesh

Large-eddy simulation of swirling particle-laden flows in a coaxial-jet combustor

Abstract Large-eddy simulation (LES) of particle-laden, swirling flow in a coaxial-jet combustor is performed. A mixture of air and lightly loaded, spherical, glass-particles with a prescribed size-distribution enters the primary jet, while a swirling stream of air flows through the annulus. The incompressible, spatially filtered Navier–Stokes equations are solved on unstructured grids to compute the turbulent gas-phase. A Lagrangian formulation and an efficient particle-tracking scheme on unstructured meshes is developed to compute the dispersed phase. The particles are treated as point sources and influence the gas phase only through momentum-exchange terms. The particle-dispersion characteristics are examined in detail; in particular, the dependence of particle trajectories and residence times upon particle sizes is emphasized. The mean and turbulent quantities for the gas and particle phases are compared to experimental data and good agreement is obtained. The LES results are significantly more accurate than the Reynolds-averaged Navier–Stokes equation (RANS) predictions of the same problem. Insight into the two-phase swirling flows is obtained through the residence-times and particle velocity-diameter correlations.

Study of trajectories of jets in crossflow using direct numerical simulations

This paper studies the trajectories and near field of round jets in crossflow. Incompressible direct numerical simulations are performed at velocity ratios of 1.5 and 5.7 and the effects of jet velocity profile and boundary layer thickness on the jet trajectory are examined. The ‘ rd ’ scaling used at present (Margason 1993) does not contain any information on these parameters, and trajectories scaled by rd do not collapse. The trajectory is strongly influenced by the near field which depends on both the jet velocity profile and the crossflow boundary layer. A length scale is proposed to describe the near field of the jet. An analytical expression is proposed for this length scale which is a measure of the relative inertia of the jet and the crossflow. Incorporating this length scale significantly improves the scaling of the trajectories.

The influence of entropy fluctuations on the interaction of turbulence with a shock wave

Direct numerical simulation and inviscid linear analysis are used to study the interaction of a normal shock wave with an isotropic turbulent field of vorticity and entropy fluctuations. The role of the upstream entropy fluctuations is emphasized. The upstream correlation between the vorticity and entropy fluctuations is shown to strongly influence the evolution of the turbulence across the shock. Negative upstream correlation between u ′ and T ′ is seen to enhance the amplification of the turbulence kinetic energy, vorticity and thermodynamic fluctuations across the shock wave. Positive upstream correlation has a suppressing effect. An explanation based on the relative effects of bulk compression and baroclinic torque is proposed, and a scaling law is derived for the evolution of vorticity fluctuations across the shock. The validity of Morkovins hypothesis across a shock wave is examined. Linear analysis is used to suggest that shock-front oscillation would invalidate the relation between u rms and T rms , as expressed by the hypothesis.

Large-Eddy Simulation of Reacting Turbulent Flows in Complex Geometries

Large-eddy simulation (LES) has traditionally been restricted to fairly simple geometries. This paper discusses LES of reacting flows in geometries as complex as commercial gas turbine engine combustors. The incompressible algorithm developed by Mahesh et al. (J. Comput. Phys., 2004, 197, 215-240) is extended to the zero Mach number equations with heat release. Chemical reactions are modeled using the flamelet/progress variable approach of Pierce and Moin (J. Fluid Mech., 2004, 504, 73-97). The simulations are validated against experiment for methane-air combustion in a coaxial geometry, and jet-A surrogate/air combustion in a gas-turbine combustor geometry.

Direct numerical simulation of round turbulent jets in crossflow

Direct numerical simulation is used to study a round turbulent jet in a laminar crossflow. The ratio of bulk jet velocity to free-stream crossflow velocity is 5.7 and the Reynolds number based on the bulk jet velocity and the jet exit diameter is 5000. The mean velocity and turbulent intensities from the simulations are compared to data from the experiments by Su & Mungal (2004) and good agreement is observed. Additional quantities, not available from experiments, are presented. Turbulent kinetic energy budgets are computed for this flow. Examination of the budgets shows that the near field is far from a state of turbulent equilibrium – especially along the jet edges. Also – in the near field – peak kinetic energy production is observed close to the leading edge, while peak dissipation is observed toward the trailing edge of the jet. The results are used to comment upon the difficulty involved in predicting this flow using RANS computations. There exist regions in this flow where the pressure transport term, neglected by some models and poorly modelled by others, is significant. And past the jet exit, the flow is not close to established canonical flows on which most models appear to be based.

The interaction of an isotropic field of acoustic waves with a shock wave

Moores (1954) inviscid linear analysis of the interaction of a shock wave with a plane acoustic wave is evaluated by comparison to computation. The analysis is then extended to study the interaction of an isotropic field of acoustic waves with a normal shock wave. The evolution of fluctuating kinetic energy, sound level and thermodynamic fluctuations across the shock wave are examined in detail. The interaction of acoustic fluctuations with the shock is notably different from that of vortical fluctuations. The kinetic energy of the acoustic fluctuations decreases across the shock wave for Mach numbers between 1.25 and 1.8. For Mach numbers exceeding 3, the kinetic energy amplifies by levels that significantly exceed those found in the interaction of vortical fluctuations with the shock. Upon interacting with the shock wave, the acoustic waves generate vortical fluctuations whose contribution to the far-field kinetic energy increases with increasing Mach number. The level of sound increases across the shock wave. The rise in the sound pressure level across the shock varies from 5 to 20 dB for Mach number varying from 1.5 to 5. The fluctuations behind the shock wave are nearly isentropic for Mach number less than 1.5, beyond which the generation of entropy fluctuations becomes significant.

Modeling the effect of shock unsteadiness in shock/turbulent boundary-layer interactions

Reynolds-averaged Navier-Stokes (RANS) methods often cannot predict shock/turbulence interaction correctly. This may be because RANS models do not account for the unsteady motion of the shock wave that is inherent in these interactions. Previous work proposed a shock-unsteadiness correction that significantly improves prediction of turbulent kinetic energy amplification across a normal shock in homogeneous isotropic turbulence. We generalize the modification to shock-wave/turbulent boundary-layer interactions and implement it in the κ-e, κ-ω, and Spalart-Allmaras models. In compression-comer flows, the correction decreases the turbulent kinetic energy amplification across the shock compared to the standard κ-e and κ-w models. This results in improved prediction of the separation shock location, delayed reattachment, and slower recovery of the boundary layer on the ramp. For the Spalart-Allmaras model, the modification amplifies eddy viscosity across the shock, moving the separation location closer to the experiment.

Upstream entrainment in numerical simulations of spatially evolving round jets

Direct numerical simulation is used to study the effect of entrainment near the inflow nozzle on spatially evolving round jets. Inflow entrainment is obtained by providing a buffer region upstream of the inflow nozzle. Simulations are performed at Reynolds numbers of 300 (laminar) and 2400 (turbulent), respectively. Simulations without the inflow buffer are contrasted to those with the buffer region. The potential core is seen to close earlier in the presence of inflow entrainment. As a result, near-field turbulent intensities and pressure fluctuations on the jet centerline are noticeably affected. It is suggested that inflow entrainment results in an effective co-flow, whose effect on the volumetric flow rate near the inflow nozzle is appreciable for both laminar and turbulent jets. When plotted in similarity variables, the far-field solutions with and without inflow entrainment agree well with each other, and experiment. The results suggest the importance of allowing for inflow entrainment in simulations of turbulent jets, particularly for studies where near-field behavior is important.

Direct numerical simulation of passive scalar transport in transverse jets

Direct numerical simulation is used to study passive scalar transport and mixing in a round turbulent jet, in a laminar crossflow. The ratio of the jet velocity to that of the crossflow is 5.7, the Schmidt number of the scalar is 1.49, and the jet-exit Reynolds number is 5000. The scalar field is used to compute entrainment of the crossflow fluid by the jet. It is shown that the bulk of this entrainment occurs on the downstream side of the jet. Also, the transverse jet entrains more fluid than a regular jet even when the jet has not yet bent into the crossflow. The transverse jets enhanced entrainment is explained in terms of the pressure field around the jet. The acceleration imposed by the crossflow deforms the jet cross-section on the downstream side, which sets up a pressure gradient that drives downstream crossflow fluid toward the jet. The simulation results are used to comment on the applicability of the gradient-diffusion hypothesis to compute passive scalar mixing in this flow field. Computed values of the eddy diffusivity show significant scatter, and a pronounced anisotropy. The near field also exhibits counter gradient diffusion.

Dynamics and mixing of vortex rings in crossflow

Direct numerical simulation is used to study the effect of crossflow on the dynamics, entrainment and mixing characteristics of vortex rings issuing from a circular nozzle. Three distinct regimes exist, depending on the velocity ratio (ratio of the average nozzle exit velocity to free-stream crossflow velocity) and stroke ratio (ratio of stroke length to nozzle exit diameter). Coherent vortex rings are not obtained at velocity ratios below approximately 2. At these low velocity ratios, the vorticity in the crossflow boundary layer inhibits roll-up of the nozzle boundary layer at the leading edge. As a result, a hairpin vortex forms instead of a vortex ring. For large stroke ratios and velocity ratio below 2, a series of hairpin vortices is shed downstream. The shedding is quite periodic for very low Reynolds numbers. For velocity ratios above 2, two regimes are obtained depending upon the stroke ratio. Lower stroke ratios yield a coherent asymmetric vortex ring, while higher stroke ratios yield an asymmetric vortex ring accompanied by a trailing column of vorticity. These two regimes are separated by a transition stroke ratio whose value decreases with decreasing velocity ratio. For very high values of the velocity ratio, the transition stroke ratio approaches the ‘formation number’. In the absence of trailing vorticity, the vortex ring tilts towards the upstream direction, while the presence of a trailing column causes it to tilt downstream. This behaviour is explained. In the absence of crossflow, the trailing column is not very effective at entrainment, and is best avoided for optimal mixing and entrainment. However, in the presence of crossflow, the trailing column is found to contribute significantly to the overall mixing and entrainment. The trailing column interacts with the crossflow to generate a region of high pressure downstream of the nozzle that drives crossflow fluid towards the vortex ring. There is an optimal length of the trailing column for maximum downstream entrainment. A classification map which categorizes the different regimes is developed.