AN EMBEDDED BOUNDARY FORMULATION FOR LARGE-EDDY SIMULATION OF TURBULENT FLOWS INTERACTING WITH MOVING BOUNDARIES

A non-boundary-conforming formulation for simulating transitional and turbulent flows with complex geometries and dynamically moving boundaries on fixed orthogonal grids is developed. The underlying finite-difference solver for the filtered incompressible Navier-Stokes equations in both Cartesian and cylindrical coordinates is based on a second-order fractional step method on staggered grid. To satisfy the boundary conditions on an arbitrary immersed interface, the velocity field at the grid points near the interface is reconstructed locally without smearing the sharp interface. The complications caused by the Eulerian grid points emerging from a moving solid body into the fluid phase are treated with a novel ``field-extension'' strategy. To treat the two-way interactions between the fluid and structure, a strong coupling scheme based on Hamming's fourth-order predictor-corrector method has been developed. The fluid and the structure are treated as elements of a single dynamical system, and all of the governing equations are integrated simultaneously, and iteratively in the time-domain. A variety of two and three-dimensional fluid-structure interaction problems of increasing complexity have been considered to demonstrate the accuracy and the range of applicability of the method. In particular, forced vibrations of a rigid circular cylinder including the harmonic in-line vibrations in a quiescent fluid and the transverse vibrations in a free-stream, and the vortex-induced vibrations of an elastic cylinder with one and two degrees of freedom in a free-stream are presented and compared with reference simulations and experiments. Three-dimensional DNS and LES of fluid flows involving stationary complex geometries include the flow past a sphere at $Re=50 \sim 1,000$, the transitional flow past an airfoil with a $10^\circ$ attack angle at $Re=10,000$. Then, the turbulent flow over a traveling wavy wall at $Re=10,170$ are simulated are compared with the detailed DNS using body-fitted grid in the literature. Finally, the simulation of the transitional flow past a prosthetic mechanical heart valve with moving leaflets at $Re=4,000$ has been performed. All results are in good agreement with the available reference data

Direct numerical simulation of a turbulent flow over an axisymmetric hill

Direct numerical simulation (DNS) of a turbulent flow over an axisymmetric hill has been carried out to study the three-dimensional flow separation and reattachment that occur on the lee-side of the geometry. The flow Reynolds number is ReH = 6500, based on free-stream quantities and hill height (H). A synthetic inflow boundary condition, combined with a data feed-in method, has been used to generate the turbulent boundary layer approaching to the hill. The simulation has been run using a typical DNS resolution of Dxþ ¼ 12:5; Dzþ ¼ 6:5, and Dyþ1 ¼ 1:0 and about 10 points in the viscous sublayer. It was found that a separation bubble exists at the foot of the wind-side of the hill and the incoming turbulent boundary layer flow undergoes re-laminarization process around the crest of the hill. These lead to a significant flow separation at the lee-side of the hill, where a very large primary separation bubble embedded with a smaller secondary separations have been captured. The present low-Re simulation reveals some flow features that are not observed by high-Re experiments, thus is useful for future experimental studies

Protostellar Outflow Evolution in Turbulent Environments

The link between turbulence in star formatting environments and protostellar jets remains controversial. To explore issues of turbulence and fossil cavities driven by young stellar outflows we present a series of numerical simulations tracking the evolution of transient protostellar jets driven into a turbulent medium. Our simulations show both the effect of turbulence on outflow structures and, conversely, the effect of outflows on the ambient turbulence. We demonstrate how turbulence will lead to strong modifications in jet morphology. More importantly, we demonstrate that individual transient outflows have the capacity to re-energize decaying turbulence. Our simulations support a scenario in which the directed energy/momentum associated with cavities is randomized as the cavities are disrupted by dynamical instabilities seeded by the ambient turbulence. Consideration of the energy power spectra of the simulations reveals that the disruption of the cavities powers an energy cascade consistent with Burgers'-type turbulence and produces a driving scale-length associated with the cavity propagation length. We conclude that fossil cavities interacting either with a turbulent medium or with other cavities have the capacity to sustain or create turbulent flows in star forming environments. In the last section we contrast our work and its conclusions with previous studies which claim that jets can not be the source of turbulence.Comment: 24 pages, submitted to the Astrophysical Journa

Turbulent Fluid Flow Over Aerodynamically Rough Surfaces Using Direct Numerical Simulations

Incompressible turbulent fluid flow in aerodynamically rough channels is investigated using direct numerical simulations. A comprehensive database of simulation data for rough surfaces with different topographical properties has been developed for 17 industrially relevant rough surface samples. It includes numerous commonlyseen industrial rough surfaces such as concrete, graphite, carbon-carbon composite and ground, shotblasted and spark-eroded steel. Other surfaces such as cast, filed and gritblasted steel are also studied, along with replicas of ship propeller surfaces eroded by periods of service. The Reynolds number considered is Reτ = 180, for which the flow is in the transitionally rough regime. A study with variable δ/Sq ratio while keeping S + q constant, where Sq is the root mean squared roughness height, is conducted for one of the samples with the mean profiles showing convergence for δ/Sq >≈ 25. A Reynolds number dependence study is conducted for two of the samples with Reτ up to 720 showing a more complete range up to the fully rough flow regime, allowing the equivalent sandgrain roughness height, ks to be computed. A correlation based on the frontal and wetted roughness area is found to be superior to the surface skewness in predicting ∆U + based on the topographic surface parameters

An embedded boundary approach for simulation of reacting flow problems in complex geometries with moving and stationary boundaries

Many useful engineering devices involve moving boundaries interacting with a reacting compressible flow. Examples of such applications include propulsion systems with moving components such as Internal Combustion (IC) engines, hypersonic propulsive devices such as Oblique Detonation Wave (ODW) engines and solid rocket motors involving regressing propellant surfaces. Computational Fluid Dynamics (CFD) can be effectively employed to study these systems. However, conventional numerical methods face several difficulties related to grid generation, treatment of moving boundaries, lack of adequate grid resolution at an affordable computational cost, and shortcomings in closure models required for Large Eddy Simulation (LES). This thesis demonstrates new accurate numerical models and subgrid closures for LES of problems in non-trivial geometries with moving boundaries. A new high-order adaptive cut-cell based embedded boundary method is developed for viscous flows, which can provide a smooth and accurate reconstruction to predict the near-wall shear stress and pressure distribution. The method can achieve a high order of accuracy even under adverse geometrical constraints such as narrow gaps and sharp corners due to a novel and robust cell clustering algorithm. This algorithm also enforces the stability of the numerical scheme in the presence of arbitrary low volume cells formed in the cell cutting process. Additionally, an extended cell clustering approach, which can achieve exact conservation of mass, momentum, and energy is proposed for moving boundaries. The embedded boundary method is built on a massively parallel framework that performs block structured Adaptive Mesh Refinement (AMR) by interfacing with the BoxLib open source library. This modeling framework is then applied to study fundamental physics in high-speed propulsion systems, for example, shock-turbulence interactions, flame-turbulence interaction, and flame/detonation stabilization in a reacting system. LES using the multilevel subgrid closure for flow and chemistry is used to study flame anchoring in a transverse reacting jet in cross flow. Important mechanisms that stabilize the flame are identified and shown to be consistent with past observations from experiments and using direct numerical simulations (DNS) but obtained here using much coarser grid LES. Finally, to demonstrate the ability of the methodology to simulate moving bodies in a reactive system, DNS of a hypersonic projectile fired into a reacting flow is performed to reveal key effects of pressure on the stabilization of detonation ahead of the projectile.Ph.D

Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations

We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate

Mixing and Demixing Processes in Multiphase Flows With Application to Propulsion Systems

A workshop on transport processes in multiphase flow was held at the Marshall Space Flight Center on February 25 and 26, 1988. The program, abstracts and text of the presentations at this workshop are presented. The objective of the workshop was to enhance our understanding of mass, momentum, and energy transport processes in laminar and turbulent multiphase shear flows in combustion and propulsion environments

A FLUID STRUCTURE INTERACTION STRATEGY WITH APPLICATION TO LOW REYNOLDS NUMBER FLAPPING FLIGHT

In this work a structured adaptive mesh refinement (S-AMR) strategy for fluid-structure interaction (FSI) problems in laminar and turbulent incompressible flows is developed. The Eulerian computational grid consists of nested grid blocks at different refinement levels. The grid topology and data-structure is managed by using the Paramesh© toolkit. The filtered Navier-Stokes equations are evolved in time by means of an explicit second-order projection scheme, where spatial derivatives are approximated with second order central differences on a staggered grid. The level of accuracy of the required variable interpolation operators is studied, and a novel divergence-preserving prolongation scheme for velocities is evolved. A novel direct-forcing embedded-boundary method is developed to enforce boundary conditions on a complex moving body not aligned with the grid lines. In this method, the imposition of no-slip conditions on immersed bodies is done on the Lagrangian markers that represent their wet surfaces, and the resulting force is transferred to the surrounding Eulerian grid points by a moving least squares formulation. Extensive testing and validation of the resulting strategy is done on a numerous set of problems. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used. The grid discontinuities introduced in AMR methods lead to numerical errors in LES, especially if non-dissipative, centered schemes are used. A simple strategy is developed to vary the filter size for filtered variables around grid discontinuities. A strategy based on explicit filtering of the advective term is chosen to effectively reduce the numerical errors across refinement jumps. For all the FSI problems reported, the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time by using a predictor-corrector strategy. Dynamic fluid grid adaptation is implemented to reduce the number of grid points and computation costs. Applications to flapping flight comprise the study of flexibility effects on the aerodynamic performance of a hovering airfoil, and simulation of the flow around an insect model under prescribed kinematics and free longitudinal flight. In the airfoil simulations, it is found that peak performance is located in structural flexibility-inertia regions where non-linear resonances are present