Development of accurate, robust liquid equations of state for multi-phase CFD simulations with a modified AUSM+-up scheme

Eight equations of state (EOS) have been evaluated for the simulation of compressible liquid water properties, based on empirical correlations, the principle of corresponding states and thermodynamic relations. The IAPWS-IF97 EOS for water was employed as the reference case. These EOSs were coupled to a modified AUSM+-up convective flux solver to determine flow profiles for three test cases of differing flow conditions. The impact of the non-viscous interaction term discretisation scheme, interfacial pressure method and selection of low-Mach number diffusion were also compared. It was shown that a consistent discretisation scheme using the AUSM+-up solver for both the convective flux and the non-viscous interfacial term demonstrated both robustness and accuracy whilst facilitating a computationally cheaper solution than discretisation of the interfacial term independently by a central scheme. The simple empirical correlations gave excellent results in comparison to the reference IAPWS-IF97 EOS and were recommended for developmental work involving water as a cheaper and more accurate EOS than the more commonly used stiffened-gas model. The correlations based on the principles of corresponding-states and the modified Peng-Robinson cubic EOS also demonstrated a high degree of accuracy, which is promising for future work with generic fluids. Further work will encompass extension of the solver to multiple dimensions and to account for other source terms such as surface tension, along with the incorporation of phase changes. © 2013.

CFD modeling of single-phase flow in a packed bed with MRI validation

Computational fluid dynamics (CFD) simulations are becoming increasingly widespread with the advent of more powerful computers and more sophisticated software. The aim of these developments is to facilitate more accurate reactor design and optimization methods compared to traditional lumped-parameter models. However, in order for CFD to be a trusted method, it must be validated using experimental data acquired at sufficiently high spatial resolution. This article validates an in-house CFD code by comparison with flow-field data obtained using magnetic resonance imaging (MRI) for a packed bed with a particle-to-column diameter ratio of 2. Flows characterized by inlet Reynolds numbers, based on particle diameter, of 27, 55, 111, and 216 are considered. The code used employs preconditioning to directly solve for pressure in low-velocity flow regimes. Excellent agreement was found between the MRI and CFD data with relative error between the experimentally determined and numerically predicted flow-fields being in the range of 3-9%. © 2012 American Institute of Chemical Engineers (AIChE).

Development of realistic liquid equations of state for multi-phase CFD modelling

Several equations of state (EOS) have been incorporated into a novel algorithm to solve a system of multi-phase equations in which all phases are assumed to be compressible to varying degrees. The EOSs are used to both supply functional relationships to couple the conservative variables to the primitive variables and to calculate accurately thermodynamic quantities of interest, such as the speed of sound. Each EOS has a defined balance of accuracy, robustness and computational speed; selection of an appropriate EOS is generally problem-dependent. This work employs an AUSM+-up method for accurate discretisation of the convective flux terms with modified low-Mach number dissipation for added robustness of the solver. In this paper we show a newly-developed time-marching formulation for temporal discretisation of the governing equations with incorporated time-dependent source terms, as well as considering the system of eigenvalues that render the governing equations hyperbolic.

Multi-dimensional conditional moment closure modelling applied to a heavy-duty common-rail diesel engine

A multi-dimensional combustion code implementing the Conditional Moment Closure turbulent combustion model interfaced with a well-established RANS two- phase flow field solver has been employed to study a broad range of operating conditions for a heavy duty direct-injection common-rail Diesel engine. These conditions include different loads (25%, 50%, 75% and full load) and engine speeds (1250 and 1830 RPM) and, with respect to the fuel path, different injection timings and rail pressures. A total of nine cases have been simulated. Excellent agreement with experimental data has been found for the pressure traces and the heat release rates, without adjusting any model constants. The chemical mechanism used contains a detailed NOx sub-mechanism. The predicted emissions agree reasonably well with the experimental data considering the range of operating points and given no adjustments of any rate constants have been employed. In an effort to identify CPU cost reduction potential, various dimensionality reduction strategies have been assessed. Furthermore, the sensitivity of the predictions with respect to resolution in particular relating to the CMC grid has been investigated. Overall, the results suggest that the presented modelling strategy has considerable predictive capability concerning Diesel engine combustion without requiring model constant calibration based on experimental data. This is true particularly for the heat release rates predictions and, to a lesser extent, for NOx emissions where further progress is still necessary. © 2009 SAE International.

Water droplet flow paths and droplet deposition in low pressure steam turbines

The complex three-dimensional two-phase flow in a low pressure steam turbine is investigated with comprehensive numerical flow simulations. In addition to the condensation process, which already takes place in the last stages of steam turbines, the numerical flow model is enhanced to consider the drag forces between the droplets and the vapour phase. The present paper shows the differences in the flow path of the phases and investigates the effect of an increasing droplet diameter. For the flow simulations a performance cluster is used because of the high effort for such multi-momentum two-phase flow calculations. In steam turbines the deposition of small water droplets on the stator blades or on parts of the casing is responsible for the formation of large coarse water droplets and these may cause additional dissipation as well as damage due to blade erosion. A method is presented that uses detailed CFD data to predict droplet deposition on turbine stator blades. This simulation method to detect regions of droplet deposition can help to improve the design of water removal devices. © Springer-Verlag Berlin Heidelberg 2013.

Coupled deformation-flow analysis for methane hydrate production by depressurized wells

A formulation for coupled flow-deformation analysis of methane-hydrate extraction problems is presented. By assuming that the hydrate does not flow, a two phase flow formulation is considered, based on Darcy's law and capillary pressure relation. The formulation is implemented in the finite difference code FLAC. The code was used to investigate the stability of a methane extraction well by depressurizing the well. © 2005 Taylor & Francis Group, London.

Poroelastic indentation analysis for hydrated biological tissues

Indentation techniques are employed for the measurement of mechanical properties of a wide range of materials. In particular, techniques focused at small length-scales, such as nanoindentation and AFM indentation, allow for local characterization of material properties in heterogeneous materials including natural tissues and biomimetic materials. Typical elastic analysis for spherical indentation is applicable in the absence of time-dependent deformation, but is inappropriate for materials with time-dependent responses. Recent analyses for the viscoelastic indentation problem, based on elastic-viscoelastic correspondence, have begun to address the issue of time-dependent deformation during an indentation test. The viscoelastic analysis has been shown to fit experimental indentation data well, and has been demonstrated as useful for characterization of viscoelasticity in polymeric materials and in hydrated mineralized tissues. However, a viscoelastic analysis is not necessarily sufficient for multi-phase materials with fluid flow. In the current work, a poroelastic analysis-based on fluid motion through a porous elastic network-is used to examine spherical indentation creep responses of hydrated biological materials. Both analytical and finite element approaches are considered for the poroelastic Hertzian indentation problem. Modeling results are compared with experimental data from nanoindentation of hydrated bone immersed in water and polar solvents (ethanol, methanol, acetone). Baseline (water-immersed) bone responses are characterized using the poroelastic model and numerical results are compared with altered hydration states due to polar solvents. © 2007 Materials Research Society.

Characteristics of blood flow in microchannels and relevant impact on modelling blood behaviour in biochip separators

This paper reports a perspective investigation of computational modelling of blood fluid in microchannel devices as a preparation for future research on fluid-structure interaction (FSI) in biofluid mechanics. The investigation is carried out through two aspects, respectively on physical behaviours of blood flow in microchannels and appropriate methodology for modelling. The physics of blood flow is targeted to the challenges for describing blood flow in microchannels, including rheology of blood fluid, suspension features of red blood cells (RBCs), laminar hydrodynamic influence and effect of surface roughness. The analysis shows that due to the hyperelastic property of RBC and its comparable dimension with microchannels, blood fluid shows complex behaviours of two phase flow. The trajectory and migration of RBCs require accurate description of RBC deformation and interaction with plasma. Following on a discussion of modelling approaches, i.e. Eulerian method and Lagrangian method, the main stream modelling methods for multiphase flow are reviewed and their suitability to blood flow is analysed. It is concluded that the key issue for blood flow modelling is how to describe the suspended blood cells, modelled by Lagrangian method, and couple them with the based flow, modelled by Eulerian method. The multiphase flow methods are thereby classified based on the number of points required for describing a particle, as follows: (i) single-point particle methods, (ii) mutli-point particle methods, (iii) functional particle methods, and (iv) fluid particle methods. While single-point particle methods concentrate on particle dynamic movement, multipoint and functional particle methods can take into account particle mechanics and thus offer more detailed information for individual particles. Fluid particle methods provide good compromise between two phases, but require additional information for particle mechanics. For furthermore detailed description, we suggest to investigate the possibility using two domain coupling method, in which particles and base flow are modelled by two separated solvers. It is expected that this paper could clarify relevant issues in numerical modelling of blood flow in microchannels and induce some considerations for modelling blood flow using multiphase flow methods. © 2012 IEEE.

Unsteady numerical study of wet steam flow in a low pressure steam turbine

In steam power plants condensation already starts in the flow path of the low pressure part of the steam turbine, which leads to a complex three-dimensional two-phase flow. Wetness losses are caused due to thermodynamic and mechanical relaxation processes during condensation and droplet transport. The present investigation focuses on the unsteady effects due to rotor-stator interaction on the droplet formation process. Results of unsteady three dimensional flow simulations of a two-stage steam turbine are presented, whereby this is the first time that non-equilibrium condensation is considered in such simulations. The numerical approach is based on RANS equations, which are extended by a wet steam specific nucleation and droplet growth model. Despite the use of a high performance cluster the unsteady simulation has a considerably high simulation time of approximately 60 days by use of 48 CPUs. © Springer-Verlag Berlin Heidelberg 2012.

High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

In this article, we detail the methodology developed to construct arbitrarily high order schemes - linear and WENO - on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set. © 2012 Global-Science Press.