Open design of high pressure ratio radial-inflow turbine for academic validation

Computational Fluid Dynamics (CFD) simulations are widely used in mechanical engineering. Although achieving a high level of confidence in numerical modelling is of crucial importance in the field of turbomachinery, verification and validation of CFD simulations are very tricky especially for complex flows encountered in radial turbines. Comprehensive studies of radial machines are available in the literature. Unfortunately, none of them include enough detailed geometric data to be properly reproduced and so cannot be considered for academic research and validation purposes. As a consequence, design improvements of such configurations are difficult. Moreover, it seems that well-developed analyses of radial turbines are used in commercial software but are not available in the open literature especially at high pressure ratios. It is the purpose of this paper to provide a fully open set of data to reproduce the exact geometry of the high pressure ratio single stage radial-inflow turbine used in the Sundstrand Power Systems T-100 Multipurpose Small Power Unit. First, preliminary one-dimensional meanline design and analysis are performed using the commercial software RITAL from Concepts-NREC in order to establish a complete reference test case available for turbomachinery code validation. The proposed design of the existing turbine is then carefully and successfully checked against the geometrical and experimental data partially published in the literature. Then, three-dimensional Reynolds-Averaged Navier-Stokes simulations are conducted by means of the Axcent-PushButton CFDR CFD software. The effect of the tip clearance gap is investigated in detail for a wide range of operating conditions. The results confirm that the 3D geometry is correctly reproduced. It also reveals that the turbine is shocked while designed to give a high-subsonic flow and highlight the importance of the diffuser.

Computational fluid dynamics simulation and turbomachinery code validation of a high pressure ratio radial-inflow turbine

The present study explores reproducing the closest geometry of a high pressure ratio single stage radial-inflow turbine applied in the Sundstrans Power Systems T-100 Multipurpose Small Power Unit. The commercial software ANSYS-Vista RTD along with a built in module, BladeGen, is used to conduct a meanline design and create 3D geometry of one flow passage. Carefully examining the proposed design against the geometrical and experimental data, ANSYS-TurboGrid is applied to generate computational mesh. CFD simulations are performed with ANSYS-CFX in which three-dimensional Reynolds-Averaged Navier-Stokes equations are solved subject to appropriate boundary conditions. Results are compared with numerical and experimental data published in the literature in order to generate the exact geometry of the existing turbine and validate the numerical results against the experimental ones.

Large-Eddy Simulation of physiological pulsatile non-newtonian flow in a channel with double constriction

Physiological pulsatile flow in a 3D model of arterial double stenosis, using the modified Power-law blood viscosity model, is investigated by applying Large Eddy Simulation (LES) technique. The computational domain has been chosen is a simple channel with biological type stenoses. The physiological pulsation is generated at the inlet of the model using the first four harmonics of the Fourier series of the physiological pressure pulse. In LES, a top-hat spatial grid-filter is applied to the Navier-Stokes equations of motion to separate the large scale flows from the subgrid scale (SGS). The large scale flows are then resolved fully while the unresolved SGS motions are modelled using the localized dynamic model. The flow Reynolds numbers which are typical of those found in human large artery are chosen in the present work. Transitions to turbulent of the pulsatile non-Newtonian along with Newtonian flow in the post stenosis are examined through the mean velocity, wall shear stress, mean streamlines as well as turbulent kinetic energy and explained physically along with the relevant medical concerns.

Numerical simulation of red blood cells' deformation using SPH method

A numerical simulation method for the Red Blood Cells’ (RBC) deformation is presented in this study. The two-dimensional RBC membrane is modeled by the spring network, where the elastic stretch/compression energy and the bending energy are considered with the constraint of constant RBC surface area. Smoothed Particle Hydrodynamics (SPH) method is used to solve the Navier-Stokes equation coupled with the Plasma-RBC membrane and Cytoplasm- RBC membrane interaction. To verify the method, the motion of a single RBC is simulated in Poiseuille flow and compared with the results reported earlier. Typical motion and deformation mechanism of the RBC is observed.

Deformation of a single red blood cell in a microvessel

Red blood cells (RBCs) are the most common type of cells in human blood and they exhibit different types of motions and deformed shapes in capillary flows. The behaviour of the RBCs should be studied in order to explain the RBC motion and deformation mechanism. This article presents a numerical simulation method for RBC deformation in microvessels. A two dimensional spring network model is used to represent the RBC membrane, where the elastic stretch/compression energy and the bending energy are considered with the constraint of constant RBC surface area. The forces acting on the RBC membrane are obtained from the principle of virtual work. The whole fluid domain is discretized into a finite number of particles using smoothed particle hydrodynamics concepts and the motions of all the particles are solved using Navier--Stokes equations. Minimum energy concepts are used to simulate the deformed shape of the RBC model. To verify the model, the motion of a single RBC is simulated in a Poiseuille flow and the characteristic parachute shape of the RBC is observed. Further simulations reveal that the RBC shows a tank treading motion when it flows in a linear shear flow.

Fluid registration of diffusion tensor images using information theory

We apply an information-theoretic cost metric, the symmetrized Kullback-Leibler (sKL) divergence, or $J$-divergence, to fluid registration of diffusion tensor images. The difference between diffusion tensors is quantified based on the sKL-divergence of their associated probability density functions (PDFs). Three-dimensional DTI data from 34 subjects were fluidly registered to an optimized target image. To allow large image deformations but preserve image topology, we regularized the flow with a large-deformation diffeomorphic mapping based on the kinematics of a Navier-Stokes fluid. A driving force was developed to minimize the $J$-divergence between the deforming source and target diffusion functions, while reorienting the flowing tensors to preserve fiber topography. In initial experiments, we showed that the sKL-divergence based on full diffusion PDFs is adaptable to higher-order diffusion models, such as high angular resolution diffusion imaging (HARDI). The sKL-divergence was sensitive to subtle differences between two diffusivity profiles, showing promise for nonlinear registration applications and multisubject statistical analysis of HARDI data.

The impact of wall shear stress and pressure drop on the stability of the atherosclerotic plaque

Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The mechanism of blood flow and plaque rupture in stenotic arteries is still not fully understood. A three dimensional rigid wall model was solved under steady state conditions and unsteady conditions by assuming a time-varying inlet velocity profile to investigate the relative importance of axial forces and pressure drops in arteries with asymmetric stenosis. Flow-structure interactions were investigated for the same geometry and the results were compared with those retrieved with the corresponding 2D cross-section structural models. The Navier-Stokes equations were used as the governing equations for the fluid. The tube wall was assumed hyperelastic, homogeneous, isotropic and incompressible. The analysis showed that the three dimensional behavior of velocity, pressure and wall shear stress is in general very different from that predicted by cross-section models. Pressure drop across the stenosis was found to be much higher than shear stress. Therefore, pressure may be the more important mechanical trigger for plaque rupture other than shear stress, although shear stress is closely related to plaque formation and progression.

Simulation of the interaction between blood flow and atherosclerotic plaque

It has been well accepted that over 50% of cerebral ischemic events are the result of rupture of vulnerable carotid atheroma and subsequent thrombosis. Such strokes are potentially preventable by carotid interventions. Selection of patients for intervention is currently based on the severity of carotid luminal stenosis. It has been, however, widely accepted that luminal stenosis alone may not be an adequate predictor of risk. To evaluate the effects of degree of luminal stenosis and plaque morphology on plaque stability, we used a coupled nonlinear time-dependent model with flow-plaque interaction simulation to perform flow and stress/strain analysis for stenotic artery with a plaque. The Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations for the fluid. The Ogden strain energy function was used for both the fibrous cap and the lipid pool. The plaque Principal stresses and flow conditions were calculated for every case when varying the fibrous cap thickness from 0.1 to 2mm and the degree of luminal stenosis from 10% to 90%. Severe stenosis led to high flow velocities and high shear stresses, but a low or even negative pressure at the throat of the stenosis. Higher degree of stenosis and thinner fibrous cap led to larger plaque stresses, and a 50% decrease of fibrous cap thickness resulted in a 200% increase of maximum stress. This model suggests that fibrous cap thickness is critically related to plaque vulnerability and that, even within presence of moderate stenosis, may play an important role in the future risk stratification of those patients when identified in vivo using high resolution MR imaging.

The Influence of Farm Management on NSW Rural Property Income and Total Average Annual Returns

The importance of agriculture in many countries has tended to reduce as their economies move from a resource base to a manufacturing industry base. Although the level of agricultural production in first world countries has increased over the past two decades, this increase has generally been at a less significant rate compared to other sectors of the economies. Despite this increase in secondary and high technology industries, developed countries have continued to encourage and support their agricultural industries. This support has been through both tariffs and price support. Following pressure from developing economies, particularly through the World Trade Organisation (WTO), GATT Uruguay round and the Cairns Group developed countries are now in various stages of winding back or de-coupling agricultural support within their economies. A major concern of farmers in protected agricultural markets is the impact of a free market trade in agricultural commodities on farm incomes, profitability and land values. This paper will analyse both the capital and income performance of the NSW rural land market over the period 1990-1999. This analysis will be based on several rural land use classifications and will compare the total return from rural properties based on the farm income generated by both the average farmer and those farmers considered to be in the top 20% of the various land use areas. The analysis will provide a comprehensive overview of rural production in a free trade economy.

Characteristics of sustainable entrepreneurship : some early explorations from the CAUSEE study

Principal Topic: For forward thinking companies, the environment may represent the ''biggest opportunity for enterprise and invention the industrial world has ever seen'' (Cairncross 1990). Increasing awareness of environmental and sustainability issues through media including the promotion of Al Gore's ''An Inconvenient Truth'' has seen increased awareness of environmental and sustainability issues and increased demand for business processes that reduce detrimental environmental impacts of global development (Dean & McMullen 2007). The increased demand for more environmentally sensitive products and services represents an opportunity for the development of ventures that seek to satisfy this demand through entrepreneurial action. As a consequence, increasing recent market developments in renewable energy, carbon emissions, fuel cells, green building, and other sectors suggest an increasing importance of opportunities for environmental entrepreneurship (Dean and McMullen 2007) and increasingly important area of business activity (Schaper 2005). In the last decade in particular, big business has sought to develop a more ''sustainability/ green friendly'' orientation as a response to public pressure and increased government legislation and policy to improve environmental performance (Cohen and Winn 2007). Whilst much of the literature and media is littered with examples of sustainability practices of large firms, nascent and young sustainability firms have only recently begun generating strong research and policy interest (Shepherd, Kuskova and Patzelt 2009): not only for their potential to generate above average financial performance and returns owing to a greater popularity and demand towards sustainability products and services offerings, but also for their intent to lessen environmental impacts, and to provide a more accurate reflection of the ''true cost'' of market offerings taking into account carbon and environmental impacts. More specifically, researchers have suggested that although the previous focus has been on large firms and their impact on the environment, the estimated collective impact of entries and exits of nascent and young firms in development is substantial and could outweigh the combined environmental impact of large companies (Hillary, 2000). Therefore, it may be argued that greater attention should be paid to nascent and young firms and researching sustainability practices, for both their impact in reducing environmental impacts and potential higher financial performance. Whilst acknowledging this research only uses the first wave of a four year longitudinal study of nascent and young firms, it can still begin to provide initial analysis on which to continue further research. The aim of this paper therefore is to provide an overview of the emerging literature in sustainable entrepreneurship and to present some selected preliminary results from the first wave of the data collection, with comparison, where appropriate, of sustainable and firms that do not fulfil this criteria. ''One of the key challenges in evaluating sustainability entrepreneurship is the lack of agreement in how it is defined'' (Schaper, 2005: 10). Some evaluate sustainable entrepreneurs simply as one category of entrepreneurs with little difference between them and traditional entrepreneurs (Dees, 1998). Other research recognises values-based sustainable enterprises requiring a unique perspective (Parrish, 2005). Some see the environmental or sustainable entrepreneurship is a subset of social entrepreneurship (Cohen & Winn, 2007; Dean & McMullen, 2007) whilst others see it as a separate, distinct theory (Archer 2009). Following one of the first definitions of sustainability developed by the Brundtland Commission (1987) we define sustainable entrepreneurship as firms which ''seek to meet the needs and aspirations of the present without compromising the ability to meet those of the future''. ---------- Methodology/Key Propositions: In this exploratory paper we investigate sustainable entrepreneurship using Cohen et al.'s (2008) framework to identify strategies of nascent and young entrepreneurial firms. We use data from The Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE). This study shares the general empirical approach with PSED studies in the US (Reynolds et al 1994; Reynolds & Curtin 2008). The overall study uses samples of 727 nascent (not yet operational) firms and another 674 young firms, the latter being in an operational stage but less than four years old. To generate the sub sample of sustainability firms, we used content analysis techniques on firm titles, descriptions and product descriptions provided by respondents. Two independent coders used a predefined codebook developed from our review of the sustainability entrepreneurship literature (Cohen et al. 2009) to evaluate the content based on terms such as ''sustainable'' ''eco-friendly'' ''renewable energy'' ''environment'' amongst others. The inter-rater reliability was checked and the Kappa's co-efficient was found to be within the acceptable range (0.746). 85 firms fulfilled the criteria given for inclusion in the sustainability cohort. ---------- Results and Implications: The results for this paper are based on Wave one of the CAUSEE survey which has been completed and the data is available for analysis. It is expected that the findings will assist in beginning to develop an understanding of nascent and young firms that are driven to contribute to a society which is sustainable, not just from an economic perspective (Cohen et al 2008), but from an environmental and social perspective as well. The CAUSEE study provides an opportunity to compare the characteristics of sustainability entrepreneurs with entrepreneurial firms without a stated environmental purpose, which constitutes the majority of the new firms created each year, using a large scale novel longitudinal dataset. The results have implications for Government in the design of better conditions for the creation of new business, firms who assist sustainability in developing better advice programs in line with a better understanding of their needs and requirements, individuals who may be considering becoming entrepreneurs in high potential arenas and existing entrepreneurs make better decisions.

Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

Exponential asymptotics with multiple stokes lines

When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.