• Turbulent Liquid Atomization
• Advanced Numerical Methods for Complex Reacting Turbulent Flows
• Advanced Numerical Methods for Multiphase Flows
• Lagrangian and Eulerian Spary Modeling
• Gas-solid Risers
• Turbulent Spray Combustion
• Electrohydrodynamic Atomization

Turbulent Liquid Atomization

In most energy conversion systems, fuel is injected in liquid form. Atomization of the liquid fuel, or the process by which a coherent liquid flow disintegrates into droplets, represents one of the key challenges that remain to be tackled to make predictive simulations possible. Because atomization governs the size of the fuel droplets, and therefore their subsequent evaporation rate, it will have far-reaching repercussions on many aspects of the combustion process, for example pollutant formation. However, the inherent multi-physics and multi-scale nature of this process limits both experimental and numerical investigations.

The animation shows the turbulent atomization of a liquid jet at Re=3000 and We=2000. For this simulation, a spectrally refined level set approach is used to track the interface geometry, and ghost fluid is used to model surface tension forces and to account for the discontinuous material properties between the phases.

This simulation was conducted on 70 million grid points using 512 processors for two days. Such numerical studies can help better understand the fundamental physical processes behind atomization, ultimately allowing the development of accurate atomization models for LES.

Advanced Numerical Methods for Complex Reacting Turbulent Flows

Large eddy simulation (LES) has been shown to be highly suited for the computation of the strongly unsteady phenomena that occur in combustion devices. Still, LES of multi-physics problems is a young research field, and especially in the areas of multiphase flows and combustion, the required models are often non-existent or lack the desired accuracy. Contrarily to direct numerical simulation (DNS) where all flow scales are resolved, LES separates turbulent flow fields into large-scale resolved and small-scale unresolved components by a spatial filtering procedure, and models the unresolved components. Even resolving only the large-scale turbulence significantly improves the accuracy of flow predictions compared to Reynolds averaged approaches (RANS), while greatly reducing the computational cost in comparison to DNS.

Previous work aiming at extending high order fully conservative numerical algorithms to complex reacting turbulent flows ultimately led to the development of an efficient multi-physics DNS/LES code of arbitrary accuracy, called NGA. This code has been used in numerous DNS and LES studies including liquid atomization, spray dynamics, spray combustion, premixed, partially-premixed, and non-premixed turbulent jets and combustion in technical devices, such as large-scale furnaces, internal combustion engines, and aircraft engine afterburners. Such a tool provides a unique platform on which physical phenomena can be studied through detailed simulations, and new LES models can be developed and tested. Future development will include an implicit compressible formulation, moving immersed Boundaries, and multi-block/overset grids capabilities. NGA is routinely run on hundreds of cores and solved very large and complex problems using millions of grid cells. The largest simulations have used over 10,000 cores to simulate a diesel jet with over 1 billion grid cells.

Advanced Numerical Methods for Multiphase Flows

Because primary atomization represents a challenge for experimentalists, numerical modeling should provide a much needed alternative. However, numerical studies of primary atomization have also been very sparse. To simulate two-phase flows, various techniques have been developed, that all enjoy some benefit and suffer from limitations. Because no clear gold standard has emerged on how to conduct a numerical simulation of complex two-phase flows, the number of direct numerical studies of primary atomization remains limited. Several key issues remain, such as the discontinuous nature of the flow properties across the phase-interface, the singularity of the surface tension forces, and the very large range of scales involved in atomization.

The second order version of NGA was modified using the Ghost Fluid Method (GFM) to handle the discontinuous density and the surface tension force in a sharp manner, and the Continuum Surface Force (CSF) method was used to account for the jump in the viscous stresses within an semi-implicit formulation. Such a methodology provides a fast, robust, and accurate way of handling multiphase flows. Combining methods tailored for turbulence with state-of-the-art multiphase models in the context of a fully semi-implicit time integration is a unique feature of the present work. Three new numerical schemes for interface transport and representation were designed, providing substantial improvements over existing methods in terms of mass conservation, robustness, and accuracy: the Accurate Conservative Level Set (ACLS) method, the Spectrally Refined Interface (SRI) approach, and the quadrature-free Discontinuous Galerkin (DG) approach. Future work will be required to further improve the overall accuracy and robustness of such methods. In addition, current approaches are not capable of handling mass and heat transfer processes.

The SRI method was recently improved with several key modifications. First, the number of quadrature points is allowed to vary from cell to cell, enabling the sub-cell resolution to be adapted to the interface topology. Two strategies for adaptive refinement were combined, namely refinement based on the distance from the phase-interface, and refinement based on the local front curvature. The curvature is computed from the sub-cell quadrature data, allowing to achieve up to third order convergence, which was found to virtually eliminate spurious currents. The new adaptive SRI scheme (ASRI) is easier to implement, and is shown to be more accurate and computationally efficient than the original SRI approach. For a range of Reynolds and Weber numbers, ASRI was found to give very accurate results, even with a limited resolution (20 cells per diameter), as shown in the bottom left image of the figure collage below. Because of its excellent accuracy for interface description and transport, the ASRI strategy constitutes a method of choice for highly detailed numerical simulations of turbulent breakup. Current work is being done on developing a quadrature-free DG level set scheme to accurately and robustly capture the interface. DG allows for a high-order representation of the interface topology without using large stencils. As a result, DG will be an excellent candidate for very large simulations on thousands of processors where communication amongst processors can become costly.

Droplet moving in quiescent gas with a density ratio of one billion

Also recently introduced is the concept of GFM applied to the velocity field and within the Navier-Stokes equations, thereby formally allowing for discontinuous velocities. This approach remains robust in the presence of high density ratios without relying on numerical dissipation, known to be detrimental to turbulence simulation. In addition, this approach allows for an implicit temporal integration of the Navier-Stokes equations while maintaining a sharp description of all discontinuities, including the one found in the viscous term. The figure to the right show a a droplet moving in quiescent gas with a density ratio of one billion in the absence of viscous and surface tension forces. Because of the large density ratio, the aerodynamic forces caused by the gas on the liquid droplet are negligible, and the drop should not deform as it moves through the gas.

Lagrangian and Eulerian Spary Modeling

Sprays and other dispersed-phase systems can be described by a kinetic equation containing terms for spatial transport, acceleration, and particle processes (such as evaporation or collisions). In principle, the kinetic description is valid from the dilute (non-collisional) to the dense limit. However, its numerical solution in multi-dimensional systems is intractable due to the large number of independent variables. As an alternative, Lagrangian methods "discretize" the density function into "parcels" that are simulated using Monte-Carlo methods.

While quite accurate, as in any statistical approach, Lagrangian methods require a relatively large number of parcels to control statistical noise, and thus are computationally expensive. A less costly alternative is to solve Eulerian transport equations for selected moments of the kinetic equation. However, it is well known that in the dilute limit, Eulerian methods have great difficulty describing correctly the moments as predicted by a Lagrangian method. A two-point quadrature-based Eulerian moment closure was developed and tested for the Williams spray equation. It was shown that this method can successfully handle highly non-equilibrium flows (e.g., impinging particle jets, jet crossing, particle rebound off walls, and homogeneous isotropic turbulence) that heretofore could not be treated with the Eulerian approach. This approach will be the basis of future Eulerian model development, and will need to be extended to multiple-point quadrature, evaporation, collisions. Future work will also include the development of an LES formulation.

Gas-solid Risers

Gas-particle flows in vertical risers are used in many industries including gasification/pyrolysis for biofuel conversion, coal combustion, and fluid catalytic cracking. Experimental studies have shown riser flows to be unsteady with large solid-volume fraction fluctuations. Regions of densely-packed particles, referred to as clusters and streamers form, which greatly affect the overall flow behavior and mixing properties. A Eulerian-Lagrangian approach is used to simulate riser flows and better understand the cluster formation. The gas phase is solved on an Eulerian grid while each particle is tracked individually.

The first image shows a 3D simulation of the flow destabilizing (10.2 million particles, Re=1, Fr=55.5), along with a 2D cross section of the flow at a later time to convey particle clustering. The simulation was conducted on 4 million grid points using 512 processors for approximately one week. The second image shows instantaneous gas volume fraction of the flow with and without collisions.

Turbulent Spray Combustion

In gas turbine engines, liquid fuel must first evaporate before it can be consumed by combustion. Hence, liquid atomization and vaporization is of paramount importance in combustion systems, and governs how fuel is supplied to the flame. A key element in predicting the complex behavior of gas turbine engines is therefore accurately modeling spray evaporation. Indeed, in reacting multi-phase flows the combustion process is intricately linked to spray evaporation. The energy required by the phase change is provided by the heat of combustion, and the fuel consumed by the flame comes from liquid vaporization creating a complex sub-filtered mixing field.

A complex flame structure including premixed and diffusion combustion regions has been observed in preliminary simulations, which confirms the need for an adequate partially premixed combustion model. Results of preliminary studies have shown that typical gaseous combustion models may not be able to adequately describe multi-phase reacting flows. The scalar dissipation rate appears to be significantly modified by the presence of the spray, and this should be reflected in the combustion model.

Electrohydrodynamic Atomization

Over the past decade, there has been considerable interest in controlling the emissions from small engines in the size range of 200 cm³ or smaller. Fuel injection schemes may reduce the incidence of pollutant emissions. However, the cost of implementation is a barrier to large scale adoption. The cost of fuel injection is driven by both the need to pump the fuel to the injection pressure and to add parts for the injector head. One approach to small-scale fuel injection is to capitalize upon the benefits of electrohydrodynamics (EHD) and enhance fuel atomization. There are many possible benefits to EHD aided atomization for combustion, such as smaller droplets, wider spray cone, and the ability to control or "tune" the spray for improved performance.

Electrohydrodynamic flows and sprays have drawn increasing interest in recent years, yet key questions regarding the complex interactions among electrostatic charge, electric fields, and the dynamics of atomizing liquids remain unanswered. Direct numerical simulations (DNS) of realistic liquid break-up are challenging due to the computational expense involved. High-fidelity numerical simulations should be able to provide some assistance in answering questions about the fundamentals and dynamics of EHD.

Recently, the NGA code has been adapted with an EHD module to explore EHD atomization. A ghost fluid method (GFM) approach is employed to solve for the electric potential Poisson equation in a sharp, accurate and robust manner. EHD boundary and jump conditions are implemented using a similar methodology, and subsequently used to solve the pressure Poisson equation. Electric charge is modeled in the bulk, with an initial assumption of no surface charge. This assumption corresponds to a regime of high electric Reynolds number, Re_e=τ_e/τ_f, where τ_e is the charge relaxation time scale and τ_f is the fluid advection time scale. We will use this new module to perform large-scale, high fidelity DNS simulations of EHD atomization.