Estimation of Convective Extreme Events over Germany based on Large Scale Parameters

Strong convective events can produce extreme precipitation, hail, lightning or gusts, potentially inducing severe socio-economic impacts. These events have a relatively small spatial extension and, in most cases, a short lifetime. In this study, a model is developed for estimating convective extreme events based on large scale conditions. It is shown that strong convective events can be characterized by a Weibull distribution of radar-based rainfall with a low shape and high scale parameter value. A radius of 90km around a station reporting a convective situation turned out to be suitable. A methodology is developed to estimate the Weibull parameters and thus the occurrence probability of convective events from large scale atmospheric instability and enhanced near-surface humidity, which are usually found on a larger scale than the convective event itself. Here, the probability for the occurrence of extreme convective events is estimated from the KO-index indicating the stability, and relative humidity at 1000hPa. Both variables are computed from ERA-Interim reanalysis. In a first version of the methodology, these two variables are applied to estimate the spatial rainfall distribution and to estimate the occurrence of a convective event. The developed method shows significant skill in estimating the occurrence of convective events as observed at synoptic stations, lightning measurements, and severe weather reports. In order to take frontal influences into account, a scheme for the detection of atmospheric fronts is implemented. While generally higher instability is found in the vicinity of fronts, the skill of this approach is largely unchanged. Additional improvements were achieved by a bias-correction and the use of ERA-Interim precipitation. The resulting estimation method is applied to the ERA-Interim period (1979-2014) to establish a ranking of estimated convective extreme events. Two strong estimated events that reveal a frontal influence are analysed in detail. As a second application, the method is applied to GCM-based decadal predictions in the period 1979-2014, which were initialized every year. It is shown that decadal predictive skill for convective event frequencies over Germany is found for the first 3-4 years after the initialization.

Scaling of natural convection of an inclined flat plate : sudden cooling condition

The natural convection boundary layer adjacent to an inclined plate subject to sudden cooling boundary condition has been studied. It is found that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh-Bénard instability if the Rayleigh number exceeds a certain critical value. A scaling relation for the onset of instability of the boundary layer is achieved. The scaling relations have been developed by equating important terms of the governing equations based on the development of the boundary layer with time. The flow adjacent to the plate can be classified broadly into a conductive, a stable convective or an unstable convective regime determined by the Rayleigh number. Proper scales have been established to quantify the flow properties in each of these flow regimes. An appropriate identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is also presented in this study. Different flow regimes based on the stability of the boundary layer have been discussed with numerical results.

Effects of corrugation frequency and aspect ratio on natural convection within an enclosure having sinusoidal corrugation over a heated top surface

Natural convection of a two-dimensional laminar steady-state incompressible fluid flow in a modified rectangular enclosure with sinusoidal corrugated top surface has been investigated numerically. The present study has been carried out for different corrugation frequencies on the top surface as well as aspect ratios of the enclosure in order to observe the change in hydrodynamic and thermal behavior with constant corrugation amplitude. A constant flux heat source is flush mounted on the top sinusoidal wall, modeling a wavy sheet shaded room exposed to sunlight. The flat bottom surface is considered as adiabatic, while the both vertical side walls are maintained at the constant ambient temperature. The fluid considered inside the enclosure is air having Prandtl number of 0.71. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results in terms of isotherms, streamlines and average Nusselt numbers are obtained for the Rayleigh number ranging from 10^3 to 10^6 with constant physical properties for the fluid medium considered. It is found that the convective phenomena are greatly influenced by the presence of the corrugation and variation of aspect ratios.

Mixed convection laminar flow along a horizontal plate subject to streamwise sinusoidal surface temperature

Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

Modeling heat and mass transfer process during convection drying of fruit

Fruit drying is a process of removing moisture to preserve fruits by preventing microbial spoilage. It increases shelf life, reduce weight and volume thus minimize packing, storage, and transportation cost and enable storage of food under ambient environment. But, it is a complex process which involves combination of heat and mass transfer and physical property change and shrinkage of the material. In this background, the aim of this paper to develop a mathematical model to simulate coupled heat and mass transfer during convective drying of fruit. This model can be used predict the temperature and moisture distribution inside the fruits during drying. Two models were developed considering shrinkage dependent and temperature dependent moisture diffusivity and the results were compared. The governing equations of heat and mass transfer are solved and a parametric study has been done with Comsol Multiphysics 4.3. The predicted results were validated with experimental data.

Nucleation experiments in a microgravity environment

A simple experimental apparatus is described in which a wide variety of vapor phase nucleation studies of refractory materials could be performed aboard NASA's KC-135 Research Aircraft. The chief advantage of a microgravity environment for these studies is the expected absence of thermally driven convective motions in the gas. The absence of convection leads to much more accurate knowledge of both the temperature distribution in the system and the time evolution of the refractory vapor concentration as a function of distance from the crucible.The evolution of the apparatus will be described as more experience is gained with the microgravity environment. Such experiments will be used to prepare for similar ones carried out aboard either the shuttle or Space Station where considerably longer duration experiments are possible.

Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Fractal dimension of dried foods : a correlation between microstructure and porosity

The quality of dried food is affected by a number of factors including quality of raw material, initial microstructure, and drying conditions. The structure of the food materials goes through deformations due to the simultaneous effect of heat and mass transfer during the drying process. Shrinkage and changes in porosity, microstructure and appearance are some of the most remarkable features that directly influence overall product quality. Porosity and microstructure are the important material properties in relation to the quality attributes of dried foods. Fractal dimension (FD) is a quantitative approach of measuring surface, pore characteristics, and microstructural changes [1]. However, in the field of fractal analysis, there is a lack of research in developing relationship between porosity, shrinkage and microstructure of different solid food materials in different drying process and conditions [2-4]. Establishing a correlation between microstructure and porosity through fractal dimension during convective drying is the main objective of this work.

Effect of cell wall properties of plant tissue on porosity and shrinkage of dried apple

In this study cell wall properties; moisture distribution, stiffness, thickness and cell dimension have been taken into consideration. Cell wall stiffness dependent on complex combination of plant cell microstructures, composition and water holding capacity of the cell. In this work, some preliminary steps taken by investing cell wall properties of apple in order to predict change of porosity and shrinkage during drying. Two different types of apple cell wall characteristic were investigated to correlate with porosity and shrinkage after convective drying. A scanning electron microscope (SEM), 2N Intron, a pyncometer and image J software were used in order to measure and analyze cell characteristics, water dynamics, porosity and shrinkage. Cell stiffness of red delicious apple was found higher than granny smith apples. A significant relationship has found between cell wall characteristics and both heat and mass transfer. Consequently, evolution of porosity and shrinkage noticeably influenced during convective drying by the nature of cell wall. This study has brought better understanding of porosity and shrinkage of dried food stuff in microscopic (cell) level and would provide better insight to attain energy effective drying process and quality food stuff.

Total heat transfer measurements on a flight investigation of reentry environment model

Stagnation-point total heat transfer was measured on a 1:27.7 model of the Flight Investigation of Reentry Environment II flight vehicle. Experiments were performed in the X1 expansion tube at an equivalent flight velocity and static enthalpy of 11 km/s and 12.7 MJ/kg, respectively. Conditions were chosen to replicate the flight condition at a total flight time of 1639.5 s, where radiation contributed an estimated 17-36% of the total heat transfer. This contribution is theorized to reduce to <2% in the scaled experiments, and the heating environment on the test model was expected to be dominated by convection. A correlation between reported flight heating rates and expected experimental heating, referred to as the reduced flight value, was developed to predict the level of heating expected on the test model. At the given flow conditions, the reduced flight value was calculated to be 150 MW/m2. Average stagnation-point total heat transfer was measured to be 140 ± 7% W/m2, showing good agreement with the predicted value. Experimentally measured heat transfer was found to have good agreement of between 5 and 15% with a number of convective heating correlations, confirming that convection dominates the tunnel heating environment, and that useful experimental measurements could be made in weakly coupled radiating flow

Multiscale coupling and multiphysics approaches in earth sciences : applications

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtoseconds to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth’s core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth’s surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults. A particular interesting case is discussed in detail, where out of the fluid dynamic solution, ductile compaction bands appear which are akin and can be confused with their brittle siblings. The main difference is that they require the factor time and also a much lower driving forces to emerge. These low stress solutions cannot be obtained on short laboratory time scales and they are therefore much more likely to appear in nature than in the laboratory. We finish with a multiscale description of a seminal structure in the Swiss Alps, the Glarus thrust, which puzzled geologists for more than 100 years. Along the Glarus thrust, a km-scale package of rocks (nappe) has been pushed 40 km over its footwall as a solid rock body. The thrust itself is a m-wide ductile shear zone, while in turn the centre of the thrust shows a mm-cm wide central slip zone experiencing periodic extreme deformation akin to a stick-slip event. The m-wide creeping zone is consistent with the THM feedback length scale of solid mechanics, while the ultralocalised central slip zones is most likely a fluid dynamic instability.

Heat transfer measurements on the first experimental layer of the FIRE II reentry vehicle in expansion tubes

The present study focused on simulating a trajectory point towards the end of the first experimental heatshield of the FIRE II vehicle, at a total flight time of 1639.53s. Scale replicas were sized according to binary scaling and instrumented with thermocouples for testing in the X1 expansion tube, located at The University of Queensland. Correlation of flight to experimental data was achieved through the separation, and independent treatment of the heat modes. Preliminary investigation indicates that the absolute value of radiant surface flux is conserved between two binary scaled models, whereas convective heat transfer increases with the length scale. This difference in the scaling techniques result in the overall contribution of radiative heat transfer diminishing to less than 1% in expansion tubes from a flight value of approximately 9-17%. From empirical correlation's it has been shown that the St √Re number decreases, under special circumstances, in expansion tubes by the percentage radiation present on the flight vehicle. Results obtained in this study give a strong indication that the relative radiative heat transfer contribution in the expansion tube tests is less than that in flight, supporting the analysis that the absolute value remains constant with binary scaling.

Numerical simulation of idealised three-dimensional downburst wind fields

Convective downburst wind storms generate the peak annual gust wind speed for many parts of the non-cyclonic world at return periods of importance for ultimate limit state design. Despite this there is little clear understanding of how to appropriately design for these wind events given their significant dissimilarities to boundary layer winds upon which most design is based. To enhance the understanding of wind fields associated with these storms a three-dimensional numerical model was developed to simulate a multitude of idealised downburst scenarios and to investigate their near-ground wind characteristics. Stationary and translating downdraft wind events in still and sheared environments were simulated with baseline results showing good agreement with previous numerical work and full-scale observational data. Significant differences are shown in the normalised peak wind speed velocity profiles depending on the environmental wind conditions in the vicinity of the simulated event. When integrated over the height of mid- to high rise structures, all simulated profiles are shown to produce wind loads smaller than an equivalent 10 m height matched open terrain boundary layer profile. This suggests that for these structures the current design approach is conservative from an ultimate loading standpoint. Investigating the influence of topography on the structure of the simulated near-ground downburst wind fields, it is shown that these features amplify wind speeds in a manner similar to that expected for boundary layer winds, but the extent of amplification is reduced. The level of reduction is shown to be dependent on the depth of the simulated downburst outflow.

Heat transfer analysis of viscous incompressible fluid by combined natural convection and radiation in an open cavity

The effect of radiation on natural convection of Newtonian fluid contained in an open cavity is investigated in this study. The governing partial differential equations are solved numerically using the Alternate Direct Implicit method together with the Successive Over Relaxation method. The study is focused on studying the flow pattern and the convective and radiative heat transfer rates are studied for different values of radiation parameters namely, the optical thickness of the fluid, scattering albedo, and the Planck number. It was found that in the optically thin limit, an increase in the optical thickness of the fluid raises the temperature and radiation heat transfer of the fluid. However, a further increase in the optical thickness decreases the radiative heat transfer rate due to increase in the energy level of the fluid, which ultimately reduces the total heat transfer rate within the fluid.