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

2016 ◽  
Author(s):  
Peter Forsyth ◽  
David R. H. Gillespie ◽  
Matthew McGilvray ◽  
Vincent Galoul
Keyword(s):  
Particle Size ◽  
Random Walk ◽  
Low Temperature ◽  
Gas Turbine ◽  
Pipe Flow ◽  
Particle Deposition ◽  
Integration Time ◽  
Time Step ◽  
Particulate Deposition ◽  
Continuous Random Walk

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.

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

2017 ◽  
Author(s):  
Peter Forsyth ◽  
David R. H. Gillespie ◽  
Matthew McGilvray
Keyword(s):  
Numerical Simulation ◽  
Random Walk ◽  
Gas Turbine ◽  
Particle Deposition ◽  
Solid Phase ◽  
Numerical Models ◽  
Dynamic Mesh ◽  
Bulk Fluid ◽  
Mesh Morphing ◽  
Continuous Random Walk

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.

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

2020 ◽  
Author(s):  
Nikul Vadgama ◽  
Marios Kapsis ◽  
Peter Forsyth ◽  
Matthew McGilvray ◽  
David R. H. Gillespie
Keyword(s):  
Random Walk ◽  
Particle Tracking ◽  
Gas Turbines ◽  
Complex Flow ◽  
Time Step ◽  
Design Studies ◽  
Turbulent Statistics ◽  
Continuous Random Walk ◽  
Simple Flows ◽  
Accelerating Flows

Abstract 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.

Phase transformation and Raman spectra in BaTiO3 nanocrystals

2002 ◽  
Vol 718 ◽  
Author(s):  
Jian Yu ◽  
X. J. Meng ◽  
J.L. Sun ◽  
G.S. Wang ◽  
J.H. Chu
Keyword(s):  
Particle Size ◽  
Phase Transformation ◽  
Low Temperature ◽  
Long Range ◽  
Lattice Expansion ◽  
Inversion Symmetry ◽  
Range Interaction ◽  
Cooperative Phenomena ◽  
Long Range Interaction ◽  
Hydrothermal Methods

AbstractIn this paper, size-induced ferroelectricit yweakening, phase transformation, and anomalous lattice expansion are observed in nanocrystalline BaTiO3 (nc-BaTiO3) deriv ed b y low temperature hydrothermal methods, and they are w ellunderstood using the terms of the long-range interaction and its cooperative phenomena altered by particle size in covalen t ionic nanocrystals. In cubic nc-BaTiO3, five modes centerd at 186, 254, 308, 512 and 716 cm-1 are observed Raman active in cubic nanophase, and they are attributed to local rhombohedral distortion breaking inversion-symmetry in cubic nanophase. The254 and 308 cm-1 modes are significantly affected not only by the concentration of hydroxyl defects, but also their particular configuration. And the 806 cm-1 modes found to be closely associated with OH - absorbed on grain boundaries.

scholarly journals A Numerical Study of the Effect of Particle Size on Particle Deposition on Turbine Vanes and Blades

2021 ◽  
Vol 13 (5) ◽  
pp. 168781402110178
Author(s):  
Zhengang Liu ◽  
Weinan Diao ◽  
Zhenxia Liu ◽  
Fei Zhang
Keyword(s):  
Particle Size ◽  
Particle Deposition ◽  
Numerical Study ◽  
Stokes Number ◽  
Capture Efficiency ◽  
Particle Capture ◽  
Factors Affecting ◽  
Pressure Surface ◽  
Deposition Area ◽  
Turbine Vanes

Particle deposition could decrease the aerodynamic performance and cooling efficiency of turbine vanes and blades. The particle motion in the flow and its temperature are two important factors affecting its deposition. The size of the particle influences both its motion and temperature. In this study, the motion of particles with the sizes from 1 to 20 μm in the first stage of a turbine are firstly numerically simulated with the steady method, then the particle deposition on the vanes and blades are numerically simulated with the unsteady method based on the critical viscosity model. It is discovered that the particle deposition on vanes mainly formed near the leading and trailing edge on the pressure surface, and the deposition area expands slowly to the whole pressure surface with the particle size increasing. For the particle deposition on blades, the deposition area moves from the entire pressure surface toward the tip with the particle size increasing due to the effect of rotation. For vanes, the particle capture efficiency increases with the particle size increasing since Stokes number and temperature of the particle both increase with its size. For blades, the particle capture efficiency increases firstly and then decreases with the particle size increasing.

scholarly journals The Influence of an Integration Time Step on Dynamic Calculation of a Vehicle-Track-Bridge under High-Speed Railway

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 431
Author(s):  
Junjie Ye ◽  
Hao Sun
Keyword(s):  
High Speed ◽  
Coupled Model ◽  
Short Wave ◽  
Integration Time ◽  
Vertical Acceleration ◽  
Dynamic Calculation ◽  
Time Step ◽  
High Speed Railway ◽  
Track Irregularity ◽  
Track Bridge

In order to study the influence of an integration time step on dynamic calculation of a vehicle-track-bridge under high-speed railway, a vehicle-track-bridge (VTB) coupled model is established. The influence of the integration time step on calculation accuracy and calculation stability under different speeds or different track regularity states is studied. The influence of the track irregularity on the integration time step is further analyzed by using the spectral characteristic of sensitive wavelength. According to the results, the disparity among the effect of the integration time step on the calculation accuracy of the VTB coupled model at different speeds is very small. Higher speed requires a smaller integration time step to keep the calculation results stable. The effect of the integration time step on the calculation stability of the maximum vertical acceleration of each component at different speeds is somewhat different, and the mechanism of the effect of the integration time step on the calculation stability of the vehicle-track-bridge coupled system is that corresponding displacement at the integration time step is different. The calculation deviation of the maximum vertical acceleration of the car body, wheel-sets and bridge under the track short wave irregularity state are greatly increased compared with that without track irregularity. The maximum vertical acceleration of wheel-sets, rails, track slabs and the bridge under the track short wave irregularity state all show a significant declining trend. The larger the vibration frequency is, the smaller the range of integration time step is for dynamic calculation.

scholarly journals Low temperature synthesis and characterization of Mn3O4 nanoparticles

2007 ◽  
Vol 5 (1) ◽  
pp. 169-176 ◽  
Author(s):  
Abdülhadi Baykal ◽  
Yüksel Köseoğlu ◽  
Mehmet Şenel
Keyword(s):  
Particle Size ◽  
Infrared Spectroscopy ◽  
Low Temperature ◽  
Synthesis And Characterization ◽  
Low Temperature Synthesis ◽  
Temperature Synthesis ◽  
X Ray ◽  
Peak Broadening ◽  
Mn3o4 Nanoparticles

AbstractHeating hydrous manganese (II) hydroxide gel at 85 °C for 12 hours produces Mn3O4 nanoparticles. They were characterized by X-ray powder diffraction (XRD) and infrared spectroscopy (FTIR). The particle size estimated from the SEM and X-ray peak broadening is approximately 32 nm, showing them to be nanocrystalline. EPR measurements confirm a typical Mn2+signal with a highly resolved hyperfine structure.

On the age distribution of a Markov chain

1978 ◽  
Vol 15 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain, obtained by restarting the original chain at a fixed state after each absorption. The limiting age, A(j), is the weak limit of the time given Xn = j (n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems for A (J) (J → ∞) are given for these examples.

A chemically intercooled gas turbine cycle for recovery of low-temperature thermal energy

Energy ◽  
2006 ◽  
Vol 31 (10-11) ◽  
pp. 1554-1566 ◽  
Author(s):  
Hongguang Jin ◽  
Hui Hong ◽  
Ruixian Cai
Keyword(s):  
Low Temperature ◽  
Gas Turbine ◽  
Thermal Energy ◽  
Gas Turbine Cycle
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