Material characterisation and numerical modelling of gypsum plasterboards in fire

The fire resistance characteristic of LSF wall systems mainly depends on the protective linings in use, commonly gypsum plasterboards. However, unclassified boards with varying composition and more notably with ambiguous thermal properties are increasingly becoming available in the market. Therefore a study was undertaken with an aim to set minimum standards for fire protective boards used in LSF wall applications. This paper presents the details of this study based on material characterisation and finite element thermal modelling of the most commonly used fire protective board, gypsum plasterboards, to address these critical issues related to fire safety design. In the material characterisation phase of this study, thermal properties of three different gypsum plasterboards manufactured in Australia were measured, analysed and compared. Subsequently, it proposes a thermal property based “k-factor” capable of giving an overall measure of the fire performance of boards, so that it can be used in appropriately classifying fire protective boards. As it is not known how this factor relates to the overall fire performance of LSF wall systems, numerical models were also developed and used to simulate the performance of LSF walls exposed to the standard fire. Finally, a correlation between time-temperature profiles from numerical analyses and calculated k-factors was established.

Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

Tax principles and tax harmonization under imperfect competition: A cautionary example

This paper shows that under imperfect competition, the welfare effects of indirect tax harmonization may depend crucially on whether taxes are levied by the destination or the origin principle. In a standard model of imperfect competition, while harmonization always makes at least one country better off, and may be Pareto-improving, when taxes are levied under the destination principle (which currently applies in the European Union), harmonization of origin-based taxes (as recently proposed by the European Commission) is certain to be Pareto-worsening when the preferences in the two countries are identical, and is likely to be so even when they differ.

Stationary crack tip fields in elastic-plastic solids: an overview of recent numerical simulations

In this paper, an overview of some recent numerical simulations of stationary crack tip fields in elastic-plastic solids is presented. First, asymptotic analyses carried out within the framework of 2D plane strain or plane stress conditions in both pressure insensitive and pressure sensitive plastic solids are reviewed. This is followed by discussion of salient results obtained from recent computational studies. These pertain to 3D characteristics of elastic-plastic near-front fields under mixed mode loading, mechanics of fracture and simulation of near-tip shear banding process of amorphous alloys and influence of crack tip constraint on the structure of near-tip fields in ductile single crystals. These results serve to illustrate several important features associated with stress and strain distributions near the crack tip and provide the foundation for understanding the operative failure mechanisms. The paper concludes by highlighting some of the future prospects for this field of study.

Numerical Study of Heat Transfer From Pin-Fin Heat Sink Using Steady and Pulsated Impinging Jets

This paper investigates numerically the heat transfer characteristics of confined slot jet impingement on a pin-fin heat sink. A variety of pin-fin heat sinks is investigated, and the resulting enhancement of heat transfer studied. The distribution of heat transfer coefficient on the top surface of the base plate and that along the fin height are examined. Both steady and pulsated jets are studied. It is observed that for a steady jet impingement on a pin-fin heat sink, the effective heat transfer coefficient increases with fin height, leading to a corresponding decrease in base plate temperature for the same heat flux. In the case of pulsated jets, the influence of pulse frequency and the Reynolds number is examined, and their effect on the effective heat transfer coefficient is studied.

A numerical study of projectile impact on thin aluminium plates

This article deals with a simulation-based Study of the impact of projectiles on thin aluminium plates using LS-DYNA by modelling plates with shell elements and projectiles with solid elements. In order to establish the required modelling criterion in terms of element size for aluminium plates, a convergence Study of residual velocity has been carried Out by varying mesh density in the impact zone. Using the preferred material and meshing criteria arrived at here, extremely good prediction of test residual velocities and ballistic limits given by Gupta et al. (2001) for thin aluminium plates has been obtained. The simulation-based pattern of failure with localized bulging and jagged edge of perforation is similar to the perforation with petalling seen in tests. A number Of simulation-based parametric studies have been carried out and results consistent with published test data have been obtained. Despite the robust correlation achieved against published experimental results, it would be prudent to conduct one's own experiments, for a final correlation via the present modelling procedure and analysis with the explicit LS-DYNTA 970 solver. Hence, a sophisticated ballistic impact testing facility and a high-speed camera have been used to conduct additional tests on grade 1100 aluminium plates of 1 mm thickness with projectiles Of four different nose shapes. Finally, using the developed numerical simulation procedure, an excellent correlation of residual velocity and failure modes with the corresponding test results has been obtained.

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.

A numerical study of the effect of loading conditions on tubular hydroforming

In this work, the mechanics of tubular hydroforming under various types of loading conditions is investigated. The main objective is to contrast the effects of prescribing fluid pressure or volume flow rate, in conjunction with axial displacement, on the stress and strain histories experienced by the tube and the process of bulging. To this end, axisymmetric finite element simulations of free hydroforming (without external die contact) of aluminium alloy tubes are carried out. Hill’s normally anisotropic yield theory along with material properties determined in a previous experimental study [A. Kulkarni, P. Biswas, R. Narasimhan, A. Luo, T. Stoughton, R. Mishra, A.K. Sachdev, An experimental and numerical study of necking initiation in aluminium alloy tubes during hydroforming, Int. J. Mech. Sci. 46 (2004) 1727–1746] are employed in the computations. It is found that while prescribed fluid pressure leads to highly non-proportional strain paths, specified fluid volume flow rate may result in almost proportional ones for the predominant portion of loading. The peak pressure increases with axial compression for the former, while the reverse trend applies under the latter. The implication of these results on failure by localized necking of the tube wall is addressed in a subsequent investigation.

Concrete-filled double skin tube columns subjected to lateral impact loading: Experimental and numerical study

This research treats the lateral impact behaviour of composite columns, which find increasing use as bridge piers and building columns. It offers (1) innovative experimental methods for testing structural columns, (2) dynamic computer simulation techniques as a viable tool in analysis and design of such columns and (3) significant new information on their performance which can be used in design. The research outcomes will enable to protect lives and properties against the risk of vehicular impacts caused either accidentally or intentionally.

Numerical Simulation of Groundwater Flow with Gradually Increasing Heterogeneity due to Clogging

Well injection replenishes depleting water levels in a well field. Observation well water levels some distance away from the injection well are the indicators of the success of a well injection program. Simulation of the observation well response, located a few tens of meters from the injection well, is likely to be affected by the effects of nonhomogeneous medium, inclined initial water table, and aquifer clogging. Existing algorithms, such as the U.S. Geological Survey groundwater flow software MODFLOW, are capable of handling the first two conditions, whereas time-dependent clogging effects are yet to be introduced in the groundwater flow models. Elsewhere, aquifer clogging is extensively researched in theory of filtration; scope for its application in a well field is a potential research problem. In the present paper, coupling of one such filtration theory to MODFLOW is introduced. Simulation of clogging effects during “Hansol” well recharge in the parts of western India is found to be encouraging.

Numerical studies on channel formation and growth during solidification: Effect of process parameters

In the present work, solidification of a hyper-eutectic ammonium chloride solution in a bottom-cooled cavity (i.e. with stable thermal gradient) is numerically studied. A Rayleigh number based criterion is developed, which determines the conditions favorable for freckles formation. This criterion, when expressed in terms of physical properties and process parameters, yields the condition for plume formation as a function of concentration, liquid fraction, permeability, growth rate of a mushy layer and thermophysical properties. Subsequently, numerical simulations are performed for cases with initial and boundary conditions favoring freckle formation. The effects of parameters, such as cooling rate and initial concentration, on the formation and growth of freckles are investigated. It was found that a high cooling rate produced larger and more defined channels which are retained for a longer durations. Similarly, a lower initial concentration of solute resulted in fewer but more pronounced channels. The number and size of channels are also found to be related to the mushy zone thickness. The trends predicted with regard to the variation of number of channels with time under different process conditions are in accordance with the experimental observations reported in the literature.

Towards the Use of Radar Winds in Numerical Weather Prediction

Numerical weather prediction (NWP) models provide the basis for weather forecasting by simulating the evolution of the atmospheric state. A good forecast requires that the initial state of the atmosphere is known accurately, and that the NWP model is a realistic representation of the atmosphere. Data assimilation methods are used to produce initial conditions for NWP models. The NWP model background field, typically a short-range forecast, is updated with observations in a statistically optimal way. The objective in this thesis has been to develope methods in order to allow data assimilation of Doppler radar radial wind observations. The work has been carried out in the High Resolution Limited Area Model (HIRLAM) 3-dimensional variational data assimilation framework. Observation modelling is a key element in exploiting indirect observations of the model variables. In the radar radial wind observation modelling, the vertical model wind profile is interpolated to the observation location, and the projection of the model wind vector on the radar pulse path is calculated. The vertical broadening of the radar pulse volume, and the bending of the radar pulse path due to atmospheric conditions are taken into account. Radar radial wind observations are modelled within observation errors which consist of instrumental, modelling, and representativeness errors. Systematic and random modelling errors can be minimized by accurate observation modelling. The impact of the random part of the instrumental and representativeness errors can be decreased by calculating spatial averages from the raw observations. Model experiments indicate that the spatial averaging clearly improves the fit of the radial wind observations to the model in terms of observation minus model background (OmB) standard deviation. Monitoring the quality of the observations is an important aspect, especially when a new observation type is introduced into a data assimilation system. Calculating the bias for radial wind observations in a conventional way can result in zero even in case there are systematic differences in the wind speed and/or direction. A bias estimation method designed for this observation type is introduced in the thesis. Doppler radar radial wind observation modelling, together with the bias estimation method, enables the exploitation of the radial wind observations also for NWP model validation. The one-month model experiments performed with the HIRLAM model versions differing only in a surface stress parameterization detail indicate that the use of radar wind observations in NWP model validation is very beneficial.

Exploiting ground-based measurements of the Global Positioning System for numerical weather prediction

Data assimilation provides an initial atmospheric state, called the analysis, for Numerical Weather Prediction (NWP). This analysis consists of pressure, temperature, wind, and humidity on a three-dimensional NWP model grid. Data assimilation blends meteorological observations with the NWP model in a statistically optimal way. The objective of this thesis is to describe methodological development carried out in order to allow data assimilation of ground-based measurements of the Global Positioning System (GPS) into the High Resolution Limited Area Model (HIRLAM) NWP system. Geodetic processing produces observations of tropospheric delay. These observations can be processed either for vertical columns at each GPS receiver station, or for the individual propagation paths of the microwave signals. These alternative processing methods result in Zenith Total Delay (ZTD) and Slant Delay (SD) observations, respectively. ZTD and SD observations are of use in the analysis of atmospheric humidity. A method is introduced for estimation of the horizontal error covariance of ZTD observations. The method makes use of observation minus model background (OmB) sequences of ZTD and conventional observations. It is demonstrated that the ZTD observation error covariance is relatively large in station separations shorter than 200 km, but non-zero covariances also appear at considerably larger station separations. The relatively low density of radiosonde observing stations limits the ability of the proposed estimation method to resolve the shortest length-scales of error covariance. SD observations are shown to contain a statistically significant signal on the asymmetry of the atmospheric humidity field. However, the asymmetric component of SD is found to be nearly always smaller than the standard deviation of the SD observation error. SD observation modelling is described in detail, and other issues relating to SD data assimilation are also discussed. These include the determination of error statistics, the tuning of observation quality control and allowing the taking into account of local observation error correlation. The experiments made show that the data assimilation system is able to retrieve the asymmetric information content of hypothetical SD observations at a single receiver station. Moreover, the impact of real SD observations on humidity analysis is comparable to that of other observing systems.

On the mechanical behavior of compacted pack ice : A theoretical and numerical investigation

Pack ice is an aggregate of ice floes drifting on the sea surface. The forces controlling the motion and deformation of pack ice are air and water drag forces, sea surface tilt, Coriolis force and the internal force due to the interaction between ice floes. In this thesis, the mechanical behavior of compacted pack ice is investigated using theoretical and numerical methods, focusing on the three basic material properties: compressive strength, yield curve and flow rule. A high-resolution three-category sea ice model is applied to investigate the sea ice dynamics in two small basins, the whole Gulf Riga and the inside Pärnu Bay, focusing on the calibration of the compressive strength for thin ice. These two basins are on the scales of 100 km and 20 km, respectively, with typical ice thickness of 10-30 cm. The model is found capable of capturing the main characteristics of the ice dynamics. The compressive strength is calibrated to be about 30 kPa, consistent with the values from most large-scale sea ice dynamic studies. In addition, the numerical study in Pärnu Bay suggests that the shear strength drops significantly when the ice-floe size markedly decreases. A characteristic inversion method is developed to probe the yield curve of compacted pack ice. The basis of this method is the relationship between the intersection angle of linear kinematic features (LKFs) in sea ice and the slope of the yield curve. A summary of the observed LKFs shows that they can be basically divided into three groups: intersecting leads, uniaxial opening leads and uniaxial pressure ridges. Based on the available observed angles, the yield curve is determined to be a curved diamond. Comparisons of this yield curve with those from other methods show that it possesses almost all the advantages identified by the other methods. A new constitutive law is proposed, where the yield curve is a diamond and the flow rule is a combination of the normal and co-axial flow rule. The non-normal co-axial flow rule is necessary for the Coulombic yield constraint. This constitutive law not only captures the main features of forming LKFs but also takes the advantage of avoiding overestimating divergence during shear deformation. Moreover, this study provides a method for observing the flow rule for pack ice during deformation.

On the behaviour of some physical parameterization methods in high-resolution numerical weather prediction models

Modern-day weather forecasting is highly dependent on Numerical Weather Prediction (NWP) models as the main data source. The evolving state of the atmosphere with time can be numerically predicted by solving a set of hydrodynamic equations, if the initial state is known. However, such a modelling approach always contains approximations that by and large depend on the purpose of use and resolution of the models. Present-day NWP systems operate with horizontal model resolutions in the range from about 40 km to 10 km. Recently, the aim has been to reach operationally to scales of 1 4 km. This requires less approximations in the model equations, more complex treatment of physical processes and, furthermore, more computing power. This thesis concentrates on the physical parameterization methods used in high-resolution NWP models. The main emphasis is on the validation of the grid-size-dependent convection parameterization in the High Resolution Limited Area Model (HIRLAM) and on a comprehensive intercomparison of radiative-flux parameterizations. In addition, the problems related to wind prediction near the coastline are addressed with high-resolution meso-scale models. The grid-size-dependent convection parameterization is clearly beneficial for NWP models operating with a dense grid. Results show that the current convection scheme in HIRLAM is still applicable down to a 5.6 km grid size. However, with further improved model resolution, the tendency of the model to overestimate strong precipitation intensities increases in all the experiment runs. For the clear-sky longwave radiation parameterization, schemes used in NWP-models provide much better results in comparison with simple empirical schemes. On the other hand, for the shortwave part of the spectrum, the empirical schemes are more competitive for producing fairly accurate surface fluxes. Overall, even the complex radiation parameterization schemes used in NWP-models seem to be slightly too transparent for both long- and shortwave radiation in clear-sky conditions. For cloudy conditions, simple cloud correction functions are tested. In case of longwave radiation, the empirical cloud correction methods provide rather accurate results, whereas for shortwave radiation the benefit is only marginal. Idealised high-resolution two-dimensional meso-scale model experiments suggest that the reason for the observed formation of the afternoon low level jet (LLJ) over the Gulf of Finland is an inertial oscillation mechanism, when the large-scale flow is from the south-east or west directions. The LLJ is further enhanced by the sea-breeze circulation. A three-dimensional HIRLAM experiment, with a 7.7 km grid size, is able to generate a similar LLJ flow structure as suggested by the 2D-experiments and observations. It is also pointed out that improved model resolution does not necessary lead to better wind forecasts in the statistical sense. In nested systems, the quality of the large-scale host model is really important, especially if the inner meso-scale model domain is small.