Prandtl number scaling of natural convection of an inclined flat plate due to uniform surface heat flux

A new scaling analysis has been performed for the unsteady natural convection boundary layer under a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages including a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as numerical results. Earlier scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings performed very well with Rayleigh number and aspect ratio dependency. In this study, a new Prandtl number scaling has been developed using a triple-layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the new scaling performs considerably better than the previous scaling.

Sensing properties of e-beam evaporated nanostructured pure and iron-doped tungsten oxide thin films

Gas sensing properties of nanostructured pure and iron-doped WO3 thin films are discussed. Electron beam evaporation technique has been used to obtain nanostructured thin films of WO3 and WO3:Fe with small grain size and porosity. Atomic force microscopy has been employed to study the microstructure. High sensitivity of both films towards NO2 is observed. Doping of the tungsten oxide film with Fe decreased the material resistance by a factor of about 30 when exposed to 5 ppm NO2. The high sensitivity is attributed to an improved microstructure of the films obtained through e-beam evaporation technique, and subsequent annealing at 300oC for 1 hour.

Performance testing of road bridge deck containing flat rail wagons

A road bridge containing disused flatbed rail wagons as the primary deck superstructure was performance tested in a low volume, high axle load traffic road in Queensland, Australia; some key results are presented in this paper. A fully laden truck of total weight 28.88 % of the serviceability design load prescribed in the Australian bridge code was used; its wheel positions were accurately captured using a high speed camera and synchronised with the real‐time deflections and strains measured at the critical members of the flat rail wagons. The strains remained well below the yield and narrated the existence of composite action between the reinforced concrete slab pavement and the wagon deck. A three dimensional grillage model was developed and calibrated using the test data, which established the structural adequacy of the rail wagons and the positive contribution of the reinforced concrete slab pavement to resist high axle traffic loads on a single lane bridge in the low volume roads network.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

Can partial coherence interferometry be used to determine retinal shape?

Purpose: To determine likely errors in estimating retinal shape using partial coherence interferometric instruments when no allowance is made for optical distortion. Method: Errors were estimated using Gullstrand’s No. 1 schematic eye and variants which included a 10 D axial myopic eye, an emmetropic eye with a gradient-index lens, and a 10.9 D accommodating eye with a gradient-index lens. Performance was simulated for two commercial instruments, the IOLMaster (Carl Zeiss Meditec) and the Lenstar LS 900 (Haag-Streit AG). The incident beam was directed towards either the centre of curvature of the anterior cornea (corneal-direction method) or the centre of the entrance pupil (pupil-direction method). Simple trigonometry was used with the corneal intercept and the incident beam angle to estimate retinal contour. Conics were fitted to the estimated contours. Results: The pupil-direction method gave estimates of retinal contour that were much too flat. The cornea-direction method gave similar results for IOLMaster and Lenstar approaches. The steepness of the retinal contour was slightly overestimated, the exact effects varying with the refractive error, gradient index and accommodation. Conclusion: These theoretical results suggest that, for field angles ≤30º, partial coherence interferometric instruments are of use in estimating retinal shape by the corneal-direction method with the assumptions of a regular retinal shape and no optical distortion. It may be possible to improve on these estimates out to larger field angles by using optical modeling to correct for distortion.

Numerical method for predicting the elastic lateral distortional buckling moment of a mono-symmetric beam with web openings

When used as floor joists, the new mono-symmetric LiteSteel beam (LSB) sections require web openings to provide access for inspections and various services. The LSBs consist of two rectangular hollow flanges connected by a slender web, and are subjected to lateral distortional buckling effects in the intermediate span range. Their member capacity design formulae developed to date are based on their elastic lateral buckling moments, and only limited research has been undertaken to predict the elastic lateral buckling moments of LSBs with web openings. This paper addresses this research gap by reporting the development of web opening modelling techniques based on an equivalent reduced web thickness concept and a numerical method for predicting the elastic buckling moments of LSBs with circular web openings. The proposed numerical method was based on a formulation of the total potential energy of LSBs with circular web openings. The accuracy of the proposed method’s use with the aforementioned modelling techniques was verified through comparison of its results with those of finite strip and finite element analyses of various LSBs.

Member moment capacities of mono-symmetric LiteSteel beam floor joists with web openings

Recently developed cold-formed LiteSteel beam (LSB) sections have found increasing popularity in residential, industrial and commercial buildings due to their light weight and cost-effectiveness. Another beneficial characteristic is that they allow torsionally rigid rectangular flanges to be combined with economical fabrication processes. Currently, there is significant interest in the use of LSB sections as flexural members in floor joist systems. When used as floor joists, these sections require openings in the web to provide access for inspection and other services. At present, however, there is no design method available that provides accurate predictions of the moment capacities of LSBs with web openings. This paper presents the results of an investigation of the buckling and ultimate strength behaviour of LSB flexural members with web openings. A detailed fine element analysis (FEA)-based parametric study was conducted with the aim of developing appropriate design rules and making recommendations for the safe design of LSB floor joists. The results include the required moment capacity curves for LSB sections with a range of web opening combinations and spans and the development of appropriate design rules for the prediction of the ultimate moment capacities of LSBs with web openings.

Numerical study of cold-formed steel beam subject to lateral-torsional buckling

The use of cold-formed steel members as structural columns and beams in residential, industrial and commercial buildings has increased significantly in recent times. This study is focused on the use of cold-formed steel sections as flexural members subject to lateral-torsional buckling. For this purpose a finite element model of a simply supported lipped channel beam under uniform bending was developed, validated using available numerical and experimental results, and used in a detailed parametric study. The moment capacity results were then compared with the predictions from the current ambient temperature design rules in the cold-formed steel structures codes of Australia, New Zealand, North America and Europe. European design rules were found to be conservative while Australian and American design rules were unsafe. This paper presents the results of the numerical study, the comparison with the current design rules and the new proposed design rules.

Design of LiteSteel Beam floor joists with web opening using an equivalent web thickness method

The LiteSteel Beam (LSB) is an innovative cold-formed steel hollow flange section. When used as floor joists, the LSB sections require holes in the web to provide access for various services. In this study a detailed investigation was undertaken into the elastic lateral distortional buckling behaviour of LSBs with circular web openings subjected to a uniform moment using finite element analysis. Validated ideal finite element models were used first to study the effect of web holes on their elastic lateral distortional buckling behaviour. An equivalent web thickness method was then proposed using four different equations for the elastic buckling analyses of LSBs with web holes. It was found that two of them could be successfully used with approximate numerical models based on solid web elements with an equivalent reduced thickness to predict the elastic lateral distortional buckling moments.

Modified beam theories for bending properties of nanowires considering surface/intrinsic effects and axial extension effect

Several studies of the surface effect on bending properties of a nanowire (NW) have been conducted. However, these analyses are mainly based on theoretical predictions, and there is seldom integration study in combination between theoretical predictions and simulation results. Thus, based on the molecular dynamics (MD) simulation and different modified beam theories, a comprehensive theoretical and numerical study for bending properties of nanowires considering surface/intrinsic stress effects and axial extension effect is conducted in this work. The discussion begins from the Euler-Bernoulli beam theory and Timoshenko beam theory augmented with surface effect. It is found that when the NW possesses a relatively small cross-sectional size, these two theories cannot accurately interpret the true surface effect. The incorporation of axial extension effect into Euler-Bernoulli beam theory provides a nonlinear solution that agrees with the nonlinear-elastic experimental and MD results. However, it is still found inaccurate when the NW cross-sectional size is relatively small. Such inaccuracy is also observed for the Euler-Bernoulli beam theory augmented with both contributions from surface effect and axial extension effect. A comprehensive model for completely considering influences from surface stress, intrinsic stress, and axial extension is then proposed, which leads to good agreement with MD simulation results. It is thus concluded that, for NWs with a relatively small cross-sectional size, a simple consideration of surface stress effect is inappropriate, and a comprehensive consideration of the intrinsic stress effect is required.

Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.

The 3D kinematics of the single leg flat and decline squat

Background: Pre-participation screening is commonly used to measure and assess potential intrinsic injury risk. The single leg squat is one such clinical screening measure used to assess lumbopelvic stability and associated intrinsic injury risk. With the addition of a decline board, the single leg decline squat (SLDS) has been shown to reduce ankle dorsiflexion restrictions and allowed greater sagittal plane movement of the hip and knee. On this basis, the SLDS has been employed in the Cricket Australia physiotherapy screening protocols as a measure of lumbopelvic control in the place of the more traditional single leg flat squat (SLFS). Previous research has failed to demonstrate which squatting technique allows for a more comprehensive assessment of lumbopelvic stability. Tenuous links are drawn between kinematics and hip strength measures within the literature for the SLS. Formal evaluation of subjective screening methods has also been suggested within the literature. Purpose: This study had several focal points namely 1) to compare the kinematic differences between the two single leg squatting conditions, primarily the five key kinematic variables fundamental to subjectively assess lumbopelvic stability; 2) determine the effect of ankle dorsiflexion range of motion has on squat kinematics in the two squat techniques; 3) examine the association between key kinematics and subjective physiotherapists’ assessment; and finally 4) explore the association between key kinematics and hip strength. Methods: Nineteen (n=19) subjects performed five SLDS and five SLFS on each leg while being filmed by an 8 camera motion analysis system. Four hip strength measures (internal/external rotation and abd/adduction) and ankle dorsiflexion range of motion were measured using a hand held dynamometer and a goniometer respectively on 16 of these subjects. The same 16 participants were subjectively assessed by an experienced physiotherapist for lumbopelvic stability. Paired samples t-tests were performed on the five predetermined kinematic variables to assess the differences between squat conditions. A Bonferroni correction for multiple comparisons was used which adjusted the significance value to p = 0.005 for the paired t-tests. Linear regressions were used to assess the relationship between kinematics, ankle range of motion and hip strength measures. Bivariate correlations between hip strength measures and kinematics and pelvic obliquity were employed to investigate any possible relationships. Results: 1) Significant kinematic differences between squats were observed in dominant (D) and non-dominant (ND) end of range hip external rotation (ND p = <0.001; D p = 0.004) and hip adduction kinematics (ND p = <0.001; D p = <0.001). With the mean angle, only the non-dominant leg observed significant differences in hip adduction (p = 0.001) and hip external rotation (p = <0.001); 2) Significant linear relationships were observed between clinical measures of ankle dorsiflexion and sagittal plane kinematic namely SLFS dominant ankle (p = 0.006; R2 = .429), SLFS non-dominant knee (p = 0.015; R2 = .352) and SLFS non-dominant ankle (p = 0.027; R2 = .305) kinematics. Only the dominant ankle (p = 0.020; R2 = .331) was found to have a relationship with the decline squat. 3) Strength measures had tenuous associations with the subjective assessments of lumbopelvic stability with no significant relationships being observed. 4) For the non-dominant leg, external rotation strength and abduction strength were found to be significantly correlated with hip rotation kinematics (Newtons r = 0.458 p = 0.049; Normalised for bodyweight: r = 0.469; p = 0.043) and pelvic obliquity (normalised for bodyweight: r = 0.498 p = 0.030) respectively for the SLFS only. No significant relationships were observed in the dominant leg for either squat condition. Some elements of the hip strength screening protocols had linear relationships with kinematics of the lower limb, particularly the sagittal plane movements of the knee and ankle. Strength measures had tenuous associations with the subjective assessments of lumbopelvic stability with no significant relationships being observed; Discussion: The key finding of this study illustrated that kinematic differences can occur at the hip without significant kinematic differences at the knee as a result of the introduction of a decline board. Further observations reinforce the role of limited ankle dorsiflexion range of motion on sagittal plane movement of the hip and knee and in turn multiplanar kinematics of the lower limb. The kinematic differences between conditions have clinical implications for screening protocols that employ frontal plane movement of the knee as a guide for femoral adduction and rotation. Subjects who returned stronger hip strength measurements also appeared to squat deeper as characterised by differences in sagittal plane kinematics of the knee and ankle. Despite the aforementioned findings, the relationship between hip strength and lower limb kinematics remains largely tenuous in the assessment of the lumbopelvic stability using the SLS. The association between kinematics and the subjective measures of lumbopelvic stability also remain tenuous between and within SLS screening protocols. More functional measures of hip strength are needed to further investigate these relationships. Conclusion: The type of SLS (flat or decline) should be taken into account when screening for lumbopelvic stability. Changes to lower limb kinematics, especially around the hip and pelvis, were observed with the introduction of a decline board despite no difference in frontal plane knee movements. Differences in passive ankle dorsiflexion range of motion yielded variations in knee and ankle kinematics during a self-selected single leg squatting task. Clinical implications of removing posterior ankle restraints and using the knee as a guide to illustrate changes at the hip may result in inaccurate screening of lumbopelvic stability. The relationship between sagittal plane lower limb kinematics and hip strength may illustrate that self-selected squat depth may presumably be a useful predictor of the lumbopelvic stability. Further research in this area is required.

Analysis of Cone-Beam CT using prior information

Treatment plans for conformal radiotherapy are based on an initial CT scan. The aim is to deliver the prescribed dose to the tumour, while minimising exposure to nearby organs. Recent advances make it possible to also obtain a Cone-Beam CT (CBCT) scan, once the patient has been positioned for treatment. A statistical model will be developed to compare these CBCT scans with the initial CT scan. Changes in the size, shape and position of the tumour and organs will be detected and quantified. Some progress has already been made in segmentation of prostate CBCT scans [1],[2],[3]. However, none of the existing approaches have taken full advantage of the prior information that is available. The planning CT scan is expertly annotated with contours of the tumour and nearby sensitive objects. This data is specific to the individual patient and can be viewed as a snapshot of spatial information at a point in time. There is an abundance of studies in the radiotherapy literature that describe the amount of variation in the relevant organs between treatments. The findings from these studies can form a basis for estimating the degree of uncertainty. All of this information can be incorporated as an informative prior into a Bayesian statistical model. This model will be developed using scans of CT phantoms, which are objects with known geometry. Thus, the accuracy of the model can be evaluated objectively. This will also enable comparison between alternative models.

An investigation into factors affecting electron density calibration for a megavoltage cone-beam CT system

There is a growing interest in the use of megavoltage cone-beam computed tomography (MV CBCT) data for radiotherapy treatment planning. To calculate accurate dose distributions, knowledge of the electron density (ED) of the tissues being irradiated is required. In the case of MV CBCT, it is necessary to determine a calibration-relating CT number to ED, utilizing the photon beam produced for MV CBCT. A number of different parameters can affect this calibration. This study was undertaken on the Siemens MV CBCT system, MVision, to evaluate the effect of the following parameters on the reconstructed CT pixel value to ED calibration: the number of monitor units (MUs) used (5, 8, 15 and 60 MUs), the image reconstruction filter (head and neck, and pelvis), reconstruction matrix size (256 by 256 and 512 by 512), and the addition of extra solid water surrounding the ED phantom. A Gammex electron density CT phantom containing EDs from 0.292 to 1.707 was imaged under each of these conditions. The linear relationship between MV CBCT pixel value and ED was demonstrated for all MU settings and over the range of EDs. Changes in MU number did not dramatically alter the MV CBCT ED calibration. The use of different reconstruction filters was found to affect the MV CBCT ED calibration, as was the addition of solid water surrounding the phantom. Dose distributions from treatment plans calculated with simulated image data from a 15 MU head and neck reconstruction filter MV CBCT image and a MV CBCT ED calibration curve from the image data parameters and a 15 MU pelvis reconstruction filter showed small and clinically insignificant differences. Thus, the use of a single MV CBCT ED calibration curve is unlikely to result in any clinical differences. However, to ensure minimal uncertainties in dose reporting, MV CBCT ED calibration measurements could be carried out using parameter-specific calibration measurements.