The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

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VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high–Reynolds number, massively separated flows remains, for which DES is convincingly more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES). This review discusses compelling examples, noting the visual and quantitative success of DES. Its principal weakness is its response to ambiguous grids, in which the wall-parallel grid spacing is of the order of the boundary-layer thickness. In some situations, DES on a given grid is then less accurate than RANS on the same grid or DES on a coarser grid. Partial remedies have been found, yet dealing with thickening boundary layers and shallow separation bubbles is a central challenge. The nonmonotonic response of DES to grid refinement is disturbing to most observers, as is the absence of...

Detached-Eddy Simulation

Traditional geotechnical analyses for landslides involve failure prediction (i.e. onset of failure) and the design of structures that can safely withstand the applied loads. The analyses provide limited information on the post-failure behaviour. Modern numerical methods are able to simulate large mass movements and there is an opportunity to utilise such methods to evaluate the risks of catastrophic damage if a landslide occurs. In this paper, various large-deformation analysis methods are introduced and their applicability for solving landslide problems is discussed. Since catastrophic landslides often involve seepage forces, consideration of the coupled behaviour of soil and pore fluid is essential. Two approaches to model soil–pore fluid coupling in large-deformation analysis using the material point method (MPM) are introduced. An example simulation is presented for each approach; one on a model levee failure and the other on a natural cut slope failure (the Selborne experiment conducted by Cooper and co-workers in 1998). In the levee failure case, MPM simulation was able to capture a complex failure mechanism including the development of successive shear bands. The simulation was also able to predict excess pore pressure generation during the failure propagation and the subsequent consolidation stage. The simulations demonstrated the importance of the dilation characteristics of soil as well as changes in geometry for the post-failure behaviour. In the Selborne case, MPM was able to simulate the progressive failure of brittle, overconsolidated clay. The evolution of shear stresses along the failure surface was also captured by the MPM. The changes in the pore pressure and the actual shape of the failure surface were simulated by the MPM. The importance of accurately modelling the shear band within the MPM framework is highlighted.

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Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method

This paper presents a review of erosion and deposition research in turbomachines and the associated degradation in engine performance caused by particulate matter ingestion Parameters affecting surface material losses as a result of erosion and development of experimental and analytical approaches to predict flowpath erosion and deposition are discussed Tests results that quantify the effects of temperature, impact particle composition, impact velocity and angle, and surface material composition are reviewed along with particle restitution data (ratios of rebound to impact velocities and angles) Development and application of models using these data to calculate surface erosion in turbomachinery are described These models predict particle trajectories in turbomachinery passages to determine impact rates, impact velocities, impact angles and uses the experimentally-obtained erosion data to calculate material losses Literature on the effects of erosion on turbomachine performance and life is surveyed Mechanisms of particle delivery and attachment upon arrival at turbomachine flowpath surfaces are also discussed along with experiential models that have been developed to predict surface deposit buildup Delivery to turbine surfaces can occur as a result of inertial flight, as for erosion, but also through transport mechanisms involving turbulence, Brownian diffusion, and thermophoresis The particle size range, where each of these mechanisms is dominant for delivery to surfaces, is described The history and experience of developing models that use these mechanisms to quantify particle delivery rates to turbine flow path surfaces is discussed, along with the use of sticking fraction data to determine the amount of material retained on the surfaces after delivery and the resulting deposit buildup rates Finally, factors that control whether extreme rates of deposition can occur in turbomachinery are described

Erosion and Deposition in Turbomachinery

https://research.birmingham.ac.uk/portal/files/53643809/APEN2017.pdf

Performance-based health monitoring, diagnostics and prognostics for condition-based maintenance of gas turbines: A review

This paper presents the results of a combined experimental and computational research program to investigate turbine vane and blade material surface deterioration caused by solid particle impacts. Tests are conducted in the erosion wind tunnel for coated and uncoated blade materials at various impact conditions. Surface roughness measurements obtained prior and subsequent to the erosion tests are used to characterize the change in roughness caused by erosion. Numerical simulations for the three-dimensional flow field and particle trajectories through a low-pressure gas turbine are employed to determine the particle impact conditions with stator vanes and rotor blades using experimentally based particle restitution models. Experimental results are presented for the measured blade material/coating erosion and surface roughness. The measurements indicate that both erosion and surface roughness increase with impact angle and particle size. Computational results are presented for the particle trajectories through the first stage of a low-pressure turbine of a high bypass turbofan engine. The trajectories indicate that the particles impact the vane pressure surface and the aft part of the suction surface. The impacts reduce the particle momentum through the stator but increase it through the rotor. Vane and blade surface erosion patterns are predicted based on the computed trajectories and the experimentally measured blade coating erosion characteristics.

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Turbine Blade Surface Deterioration by Erosion

Detached Eddy Simulations are performed for unsteady three-dimensional supersonic turbulent flow over an open L/D = 5 cavity at free-stream Mach number of 1.19. Numerical results are obtained from the explicit solution and Shear-Stress-Transport based simulations using the 3 rd order Roe scheme. Computational results are presented for the unsteady vortex and shock structures. The acoustic response of the cavity is presented in the form of pressure fluctuations and sound pressure level spectra. The computational results are compared to existing experimental data and to results obtained from twodimensional Reynolds Averaged Navier Stokes with algebraic turbulence model.

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Detached eddy simulations of supersonic flow over cavity

This paper presents a methodology for three dimensional numerical simulations of super cooled water droplet trajectories through aeroengine rotating mac hinery Both flow and droplets’ governing equations are formulated and solved in the reference frame of rotating blades A Eulerian -Lagrangian approach is used for the continuous and discrete phases with one -way interaction model to simulate the aerodynami c effects on the three -dimensional particle trajectories A flux -based collection efficiency model is proposed for internal flows to enable the calculation of the amount of water that impinges the rotating and stationary blade surfaces The methodology is applied to a transonic fan rotor and the computational results for the 3D flow field is compared with available experimental data The computed droplet trajectories, rotor blade impingement locations, and the corresponding water collection efficiency are p resented and compared for different droplet sizes

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Numerical simulations of ice droplet trajectories and collection efficiency on aero - engine rotating machinery

This paper presents computational results for two DES (Detached Eddy Simulation), one hybrid RANS (Reynolds Averaged Navier-Stokes)/ LES (Large Eddy Simulation) and some preliminary results from PANS (Partially Averaged Navier-Stokes) turbulence for simulation of unsteady separated turbulent flows. The models are implemented in a full 3-D Navier Stokes solver and are based on the twoequation k-e model. The formulations of each model are presented and results are analyzed for subsonic flow over a Backward Facing Step (BFS). Simulations are carried out using a 3 rd order Roe scheme. A comparative assessment is made between the predictions from the DES, hybrid and PANS models. The predicted results are compared with the available experimental data for skin-friction coefficient, and different turbulent quantities. The three-dimensionality of the flow field and the separated fine scale structures are presented through the Q iso-surfaces.

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DES, Hybrid RANS/LES and PANS Models for Unsteady Separated Turbulent Flow Simulations

This paper presents a parametric study of ice accretion on a high bypass turbofan engine booster rotor. Both flow and droplets' governing equations are formulated and solved in the reference frame of the rotating blades. A Eulerian-Lagrangian approach is used for the continuous and discrete phases with one-way interaction model to simulate momentum and energy exchange on the droplets and their effects on the three-dimensional droplet trajectories. The flux-based collection efficiency is calculated for the rotor blade at 60%, 70%, 80%, 90% and 100% engine design speed. A quasi-3D analysis of the ice accretion over the rotor blade is conducted based on the computed flow characteristics using the code LEWICE. Results are presented for the ice shape variation along the span, inlet temperature and rotor speeds. The highest accumulation was predicted on the blade pressure side leading edge near the hub and increased with reduced rotor speed and flow temperature.

Kaushik Das

Papers

Turbine Blade Surface Deterioration by Erosion

Detached eddy simulations of supersonic flow over cavity

Numerical simulations of ice droplet trajectories and collection efficiency on aero - engine rotating machinery

DES, Hybrid RANS/LES and PANS Models for Unsteady Separated Turbulent Flow Simulations

Ice Shape Prediction For Turbofan Rotating Blades