A simple method for potential flow simulation of cascades

A simple method using a combination of conformal mapping and vortex panel method to simulate potential flow in cascades is presented. The cascade is first transformed to a single body using a conformal mapping, and the potential flow over this body is solved using a simple higher order vortex panel method. The advantage of this method over existing methodologies is that it enables the use of higher order panel methods, as are used to solve flow past an isolated airfoil, to solve the cascade problem without the need for any numerical integrations or iterations. The fluid loading on the blades, such as the normal force and pitching moment, may be easily calculated from the resultant velocity field. The coefficient of pressure on cascade blades calculated with this methodology shows good agreement with previous numerical and experimental results.

Hybrid potential flow-streamtube method for modelling VAWT-flowfield interactions

When designing vertical-axis wind turbines (VAWTs) for deployment in the urban environment, it is desirable to have a low-cost computational model that allows for modelling the coupled interaction of the turbine with the flowfleld. Such a method is presented in this paper, It combines a variation of the multiple streamtube model with a potential method to model flowfleld interactions. A method referred to as "streamtube surgery" is used to couple the influence of the flowfleld with the performance model of the VAWT. This tool is used to explore the instantaneous and cycle-averaged flowflelds of VAWTs. It can also be used to evaluate the influence on performance of multiple VAWTs in dense arrays or to quantify blockage effects of a VAWT in wind tunnel testing.

FastAero – A Precorrected FFT – Fast Multipole Tree Steady and Unsteady Potential Flow Solver

In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping.

Free-surface flow past arbitrary topography and an inverse approach for wave-free solutions

An efficient numerical method to compute nonlinear solutions for two-dimensional steady free-surface flow over an arbitrary channel bottom topography is presented. The approach is based on a boundary integral equation technique which is similar to that of Vanden-Broeck's (1996, J. Fluid Mech., 330, 339-347). The typical approach for this problem is to prescribe the shape of the channel bottom topography, with the free-surface being provided as part of the solution. Here we take an inverse approach and prescribe the shape of the free-surface a priori while solving for the corresponding bottom topography. We show how this inverse approach is particularly useful when studying topographies that give rise to wave-free solutions, allowing us to easily classify eleven basic flow types. Finally, the inverse approach is also adapted to calculate a distribution of pressure on the free-surface, given the free-surface shape itself.

Long range exhaustion-a mathematical model for the axisymmetric air flow of a local exhaust ventilation hood assisted by a turbulent radial jet

Abstract-Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art Banged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air Bow to be reduced and provide a means of identifying and assessing the various parameters that control the air Bow. The mathematical model is formulated in terms of the Stokes steam function, ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained Bow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions. | Mathematical modelling techniques are used to predict the axisymmetric air flow pattern developed by a state-of-the-art flanged exhaust hood which is reinforced by a turbulent radial jet flow. The high Reynolds number modelling techniques adopted allow the complexity of determining the hood's air flow to be reduced and provide a means of identifying and assessing the various parameters that control the air flow. The mathematical model is formulated in terms of the Stokes steam function, Ψ, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained flow is assumed to be an inviscid potential flow. Comparisons made between contours of constant air speed and centre-line air speeds deduced from the model and all the available experimental data show good agreement over a wide range of typical operating conditions.

An experimental and theoretical study of unsteady flow (gust) effects on structures

The gust wind tunnel at IDR, Universidad Politécnica de Madrid (UPM), has been enhanced and the impact of the modification has been characterized. Several flow quality configurations have been tested. The problems in measuring gusty winds with Pitot tubes have been considered. Experimental results have been obtained and compared with theoretically calculated results (based on potential flow theory). A theoretical correction term has been proposed for unsteady flow measurements obtained with Pitot tubes. The effect of unsteady flow on structures and laying bodies on the ground has been also considered. A theoretical model has been proposed for a semi-circular cylinder and experimental tests have been performed to study the unsteady flow effects, which can help in clarifying the phenomenon.

On the two-dimensional theory of incompressible flow over inlets

The linearized solution for the two-dimensional flow over an inlet of general form has been derived, assuming incompressible potential flow. With this theory suction forces at sharp inlet lips can be estimated and ideal inlets can be designed.

Enhancing road safety for young drivers : how Graduate Driver Licensing initiatives can complement "anti-hooning" legislation

Street racing and associated (hooning) behaviours have attracted increasing concern in recent years. While New Zealand and all Australian jurisdictions have introduced “antihooning” legislation and allocated significant police resources to managing the problem, there is limited evidence of the road safety implications of hooning. However, international and Australian data suggests that drivers charged with a hooning offence tend to be young males who are accompanied by one or more peers, and hooning-related crashes tend to occur at night. In this regard, there is considerable evidence that drivers under the age of 25 are over-represented in crash statistics, and are particularly vulnerable soon after obtaining a Provisional licence, when driving at night, and when carrying peer-aged passengers. The similarity between the nature of hooning offenders, offences and crashes, and road safety risks for young drivers in general, suggests that hooning is an issue that may be viewed as part of the broader young driver problem. Many jurisdictions have recently implemented a range of evidence-based strategies to address young driver road safety, and this paper will present Queensland crash and offence data to highlight the potential benefit of Graduated Driver Licensing initiatives, such as night driving restrictions and peer-aged passenger restrictions, to related road safety issues, including hooning. An understanding of potential flow-on effects is important for evaluations of anti-hooning legislation and Graduated Driver Licensing programs, and may have implications for future law enforcement resource allocation and policy development.

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.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

The unsteady laminar compressible boundary-layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer has been studied for all second-order boundary layer effects when the basic potential flow admits selfsimilarity. The solutions for the governing equations are obtained by using an implicit finite-difference scheme. Computations have been carried out for different values of the parameters characterizing the unsteadiness in the free stream velocity, wall temperature, mass transfer rate and variable gas properties. The results are found to be strongly affected by the unsteadiness in the free stream velocity. For large injection rates the second-orderboundary layer effects may prevail over the first-order boundary layer, but reverse is true for suction. The wall temperature and the variation of the density-viscosity product across the boundary layer appreciably change the skin-friction and heat-transfer rates due to second-order boundary-layer effects.

Best practice full-stop: Anticipating the spillover effects of enterprise education

This paper considers the potential flow-on benefits that may arise from the increasing provision of enterprise education. The issue of vulnerability is proposed to be a factor associated with superior learning outcomes. Therefore, this paper aims to highlight the use of student and facilitator vulnerability to increase the capacity for learning in Higher Education. It is argued that students benefit from having to struggle to find their identity within a learning environment. That group work can assist the development of confidence through which improved learning behaviours are adopted. Also, the development of good learning practices in the domain of enterprise education have the potential to aid student learning outcomes in other areas of study. This paper provides another means of valuing the potential gains to be received from enterprise education.