Development and Validation of a Continuous Random Walk Model for Particle Tracking in Accelerating Flows

Stochastic particle tracking models coupled to RANS fluid simulations are frequently used to simulate particulate transport and hence predict component damage in gas turbines. In simple flows the Continuous Random Walk (CRW) model has been shown to model particulate motion in the diffusion-impaction regime significantly more accurately than Discrete Random Walk implementations. To date, the CRW model has used turbulent flow statistics determined from DNS in channels and experiments in pipes. Robust extension of the CRW model to accelerating flows modelled using RANS is important to enable its use in design studies of rotating engine-realistic geometries of complex curvature. This paper builds on previous work by the authors to use turbulent statistics in the CRW model directly from Reynolds Stress Models (RSM) in RANS simulations. Further improvements are made to this technique to account for strong gradients in Reynolds Stresses in all directions; improve the robustness of the model to the chosen time-step; and to eliminate the need for DNS/experimentally derived statistical flow properties. The effect of these changes were studied using a commercial CFD solver for a simple pipe flow, for which integral deposition prediction accuracy equal to that using the original CRW was achieved. These changes enable the CRW to be applied to more complex flow cases. To demonstrate why this development is important, in a more complex flow case with acceleration, deposition in a turbulent 90° bend was investigated. Critical differences in the predicted deposition are apparent when the results are compared to the alternative tracking models suitable for RANS solutions. The modified CRW model was the only model which captured the more complex deposition distribution, as predicted by published LES studies. Particle tracking models need to be accurate in the spatial distribution of deposition they predict in order to enable more sophisticated engineering design studies.

Efficient simulation of bubble dispersion and resulting interaction

In this work, an efficient model for simulating bubble dispersion and coalescence due to turbulence is developed in the Euler-Lagrange framework. The primary liquid phase is solved on the Euler grid with the RANS turbulence model. Bubble motion is computed with the force balance equations. One-way coupling between two phases is assumed and the framework is designed for the computation of disperse bubbly flows at low Eötvös number. The turbulent dispersion of the dispersed phase is reconstructed with the continuous random walk (CRW) model. Bubble-bubble collisions and coalescence are accounted for deterministically. To accelerate the time-consuming search for potential collision partners in dense bubbly flows, the sweep and prune algorithm is employed, which can be utilized in arbitrary mesh types and sizes. Validation against experiments of turbulent pipe flows demonstrates that the one-way coupled EL-CRW dispersion model can well reproduce the bubble distribution in a typical dense bubbly pipe flow. Good agreement of the bubble size distribution at the pipe outlet between the simulation and the experiment is obtained.

Development and Applications of a Coupled Particle Deposition Dynamic Mesh Morphing Approach for the Numerical Simulation of Gas Turbine Flows

The presence and accretion of airborne particulates, including ash, sand, dust, and other compounds, in gas turbine engines can adversely affect performance and life of components. Engine experience and experimental work has shown that the thickness of accreted layers of these particulates can become large relative to the engine components on which they form. Numerical simulation to date, using a variety of flow coupling models, has largely ignored the effects of resultant changes in the passage geometry due to the build-up of deposited particles. This paper will focus on updating the boundaries of the flow volume geometry by integrating the deposited volume of particulates on the solid surface. Numerical models of small particulate turbulent motion and stick/bounce models are developed and integrated within commercial software to perform 3D fluid simulations to capture the deposition behaviour. The technique is implemented using a novel, coupled deposition-dynamic mesh morphing approach to the simulation of particulate-laden flows using RANS modelling of the bulk fluid, and Lagrangian-based particulate tracking. On an iterative basis the calculated particle deposition distributions are used to modify the surface topology by altering the locations of surface nodes. The mesh, continuous phase solution, and particle tracking are then recalculated, from which the mesh is again modified. The sensitivity to the modelling time steps employed is explored. This mesh morphing technique is further refined through the application of the particle stick-bounce model of Bons et al. [1] and the Continuous Random Walk model. An impingement geometry case is used to assess the validity of the technique, and a passage with film cooling holes is interrogated. The paper illustrates that for engine realistic levels of internal deposition this can lead to a significant disparity in the local aerodynamic flow field. Modelling of several internal flow fields have been investigated to illustrate the use of the technique. Differences are seen for all of the sticking and solid phase motion models employed. Notably, there are real discrepancies in using commercial and bespoke models. At small solid particle sizes considerable disparity is observed between the discrete and continuous random walk modelling approaches, while the position and level of accretion is altered through the use of a non-isotropic stick and bounce model.

Validation and Assessment of the Continuous Random Walk Model for Particle Deposition in Gas Turbine Engines

Threats to engine integrity and life from deposition of environmental particulates that can reach the turbine cooling systems (i.e. <10 micron) have become increasing important within the aero-engine industry, with an increase of flight paths crossing sandy, tropical storm-infested, or polluted airspaces. This has led to studies in the turbomachinery community investigating environmental particulate deposition, largely applying the Discrete Random Walk (DRW) model in CFD simulations of air paths. However, this model was conceived to model droplet dispersion in bulk flow regimes, and therefore has fundamental limitations for deposition studies. One significant limitation is an insensitivity to particle size in the turbulent deposition size regime, where deposition is strongly linked to particle size. This is highlighted within this study through comparisons to published experimental data. Progress made within the wider particulate deposition community has recently led to the development and application of the Continuous Random Walk (CRW) model. This new model provides significantly improved predictions of particle deposition seen experimentally in comparison to the DRW for low temperature pipe flow experiments. However, the CRW model is not without its difficulties. This paper highlights the sensitivities within the CRW model and actions taken to alleviate them where possible. For validation of the model at gas turbine conditions, it should be assessed at engine-representative conditions. These include high-temperature and swirling flows, with thermophoretic and wall-roughness effects. Thermophoresis is a particle force experienced in the negative direction of the temperature gradient, and can strongly effect deposition efficiency from certain flows. Previous validation of the model has centred on low temperatures and pipe flow conditions. Presented here is the validation process which is currently being undertaken to assess the model at gas turbine-relevant conditions. Discussion centres on the underlying principles of the model, how to apply this model appropriately to gas turbine flows and initial assessment for flows seen in secondary air systems. Verification of model assumptions is undertaken, including demonstrating that the effect of boundary layer modelling of anisotropic turbulence is shown to be Reynolds-independent. The integration time step for numerical solution of the non-dimensional Langevin equation is redefined, showing improvement against existing definitions for the available low temperature pipe flow data. The grid dependence of particle deposition in numerical simulations is presented and shown to be more significant for particle conditions in the diffusional deposition regime. Finally, the model is applied to an engine-representative geometry to demonstrate the improvement in sensitivity to particle size that the CRW offers over the DRW for wall-bounded flows.

Kinetic study of the heterogeneous photocatalysis of porous nanocrystalline TiO2 assemblies using a continuous random walk simulation

The Monte Carlo continuous time random walk method was used to study the photocatalytic kinetics of nanocrystalline TiO2 materials in this research.

LES Sub-Grid Diffusion for Lagrangian Particles

A continuous random walk (CRW) turbulent diffusion model was developed for Lagrangian particles within flow fields simulated by hybrid RANS/LES methodologies. For RANS flow-fields, the conventional time-scale and length-scale constants were determined by the turbulence intensity and dissipation values computed by the single-phase solver with a k-ω (Menter SST) model and subsequent comparison with turbulent particle diffusion experimental results of Snyder & Lumley (1971). This allowed validation against data for four particle types ranging from hollow glass to copper shot in grid-generated turbulence. The stochastic diffusion model was then extended to utilize the Nichols-Nelson k-ω hybrid RANS-LES turbulence model in a more complex turbulent flow resulting from the unsteady, three dimensional wake of a cylinder at Mach number of 0.1 and Reynolds number (ReD) of 800. The gas flow was computed with a 5th-order upwind-biased scheme. Throughout the wake, the sub-grid random walk model yielded good predictions of particle diffusion as compared with DNS. Also, these results indicate that crossing trajectory effects and inertia-based drift corrections are critical to handling a variety of particle Stokes numbers as well as regions of non-homogeneous turbulence, even when most of the kinetic energy is captured with the resolved-scales of an LES approach.