Galaxy number counts at second order: an independent approach

Next generation surveys will be capable of determining cosmological parameters beyond percent level. To match this precision, theoretical descriptions should look beyond the linear perturbations to approximate the observables in large scale structure. A quantity of interest is the Number density of galaxies detected by our instruments. This has been focus of interest recently, and several efforts have been made to explain relativistic effects theoretically, thereby testing the full theory. However, the results at nonlinear level from previous works are in disagreement. We present a new and independent approach to computing the relativistic galaxy number counts to second order in cosmological perturbation theory. We derive analytical expressions for the full second order relativistic observed redshift, for the angular diameter distance and for the volume spanned by a survey. Finally, we compare our results with previous works which compute the general distance-redshift relation, finding that our result is in agreement at linear order

Burning dynamics and in-depth flame spread of wood cribs in large compartment fires

Wood cribs pervade the fire research literature as the chosen fuel load for testing within the built environment. As such, the underpinning knowledge of fire behaviour in compartments was developed from experiments using wood cribs in small compartments. Despite the apparent incomparability of porous fuel-beds such as cribs to real solid fuels in the built environment, the role of the fuel mass transfer number (“B-Number”) in defining the compartment fire dynamics has received little attention. In the case of large open-plan compartments, the burning processes are strongly dependant on the relationship of the fuel nature and compartment geometry. To address these limitations, the physical processes in-depth and external to a spreading wood crib fire in a compartment are examined. A theory to couple these processes to a compartment is proposed and analogised into the classical “Emmons problem”, leading to a definition of a total mass transfer number for a wood crib. Comparing the theory against data from a large-scale experiment shows that the wood crib approximates steady-state burning in two regimes: a fuel-bed-controlled regime and a momentum-controlled regime. The fuel-bed-controlled regime occurs when the burning and spread rates are governed by the processes internal to the crib, and the fire behaviour is therefore defined by the crib geometry. This regime is characterised by a fire that travels or grows slowly, with small external heat fluxes. The momentum-controlled regime occurs when the fire is fully-developed and the external heat fluxes are very large. Burning rates are controlled by the residence time, with the compartment fire dynamics defined by complex transport processes associated with the momentum-driven flows external to the crib. Transitions from the fuel-bed-controlled regime to the momentum-controlled regime are driven by accelerations in the flame spread rate along the surface of the crib leading to additional energy input mechanism that is used to raise the in-depth flame spread rate of the crib. It is hypothesised that the burning mechanisms of fuels with large mass transfer numbers, such as non-charring plastics, diverge significantly from wood cribs, and therefore extrapolating test data from wood cribs fires in compartments to real fuels must be done with extreme caution. Thus, the nature of the fuel is an important and unavoidable consideration when studying the fire dynamics of large open-plan compartments

Mechanisms of flame spread and burnout in large enclosure fires

Knowledge of the first principles defining fire behaviour in large enclosures remains limited despite their common use in modern tall buildings. The evolution of a fire in large enclosures can be defined by the relationship between the flame front and burnout velocities (VS/VBO). This relationship can be classified into three distinct fire spread modes being Mode 1 (VS/VBO → ∞), Mode 2 (VS/VBO > 1), and Mode 3 (VS/VBO ≈ 1). The mechanisms governing flame spread and burnout are investigated using four full-scale enclosure fire experiments with high porosity wood cribs with similar enclosure geometries. Flame and burnout front positions and velocities are estimated using video data. Velocities are affected by the heat feedback from the enclosure and smoke layer to the fuel. The spread velocity shows two regimes, a minimum external heat flux above which there is surface spread (q''s,min) and a heat flux that defines the onset of very rapid flame spread ((q''rs,crit)). A phenomenological model is developed to help identify the underlying mechanisms controlling the transition between the different spread modes. Both the model and data show that for wood cribs, the dependence of the burnout front velocity to the external radiation is weak, whereas the dependence of the flame spread velocity to the external and flame heat flux is strong. A transition from Mode 3 (VS/VBO ≈ 1) to Mode 2 (VS/VBO > 1) occurs with increasing external heat fluxes above q''s,min. The transition to Mode 1 (VS/VBO → ∞) is further defined once (q''rs,crit) is attained due to a sudden increase in the flame heat flux by changing the ventilation condition, or by significant increases in the external heat flux from the enclosure

Upward Flame Spread for Fire Risk Classification of High-Rise Buildings

External fire spread has the potential to breach vertical compartmentation and violate the fire safety strategy of a building. The traditional design solution to this has been the use of non-combustible materials and spandrel panels but recent audits show that combustible materials are widespread and included in highly complex systems. Furthermore, most jurisdictions no longer require detailing of spandrel panels under many different circumstances. These buildings require rapid investigation using rational scientific methods to be able to adequately classify the fire risk. In this work, we use an extensive experimental campaign of material-scale data to explore the critical parameters driving upward flame spread. Two criteria are outlined using two different approaches. The first evaluates the time to ignition and the time to burnout to assess the ability for a fire to spread, and can be easily determined using traditional means. The second evaluates the preheated flame length as the critical parameter driving flame spread. A wide range of cladding materials are ranked according to these criteria to show their potential propensity to flame spread. From this, designers can use conservative approaches to perform fire risk assessments for buildings with combustible materials or can be used to aid decision-making. Precise estimates of flame spread rates within complex façade systems are not achievable with the current level of knowledge and will require a substantial amount of work to make progress

Influence of heating conditions and initial thickness on the effectiveness of thin intumescent coatings

The study presented herein shows an experimental methodology aimed at analysing the effectiveness of intumescent coatings through detailed characterisation of their thermo-physical response for a range of heating conditions and applied initial dry film thickness (DFT). Steel plates coated with a commercial solvent-based thin intumescent coating were exposed to well-defined and highly-repeatable heating conditions in accordance with the H-TRIS test method. Experimental results emphasise that the swelling process and the resulting swelled thickness govern the thermo-physical response of intumescent coatings, thus their effectiveness. During swelling, the coated steel asymptotically tends to the temperature range 300–350 °C, regardless of the heating condition or DFT. Thermo-gravimetric analysis demonstrates that the coating undergoes the swelling reaction at this temperature range. Once the swelling process is completed, the steel temperature increases above 350 °C. The steel temperature acts as an indicator of the swelling process, as the reaction occurs near the steel-coating interface. The intumescent coating swells and insulates the steel substrate by displacing the already-swelled coating towards the direction of the heat source. Aiming at predicting the swelling of intumescent coatings, empirical correlations are derived: the swelling rate is governed by the heating conditions and the maximum swelled thickness is governed by the initial DFT

A simplified correction method for thermocouple disturbance errors in solids

When a thermocouple is embedded in a material of lower thermal conductivity, under certain heating or cooling conditions, the presence of the thermocouple can distort the surrounding temperature field. As a result, the measured temperatures may be very different to the ‘undisturbed’ temperatures that would exist without the thermocouple. This study presents the results of a sensitivity analysis of key factors influencing this thermal disturbance. A series of heat transfer models and accompanying experiments are used to demonstrate the effects of thermocouple geometry, contact conditions, thermal properties, and heating regime on the temperature measurement error. These tailored finite element models were validated against experiments on vermiculite insulation board, which confirmed the accuracy of the models in simulating the thermal disturbance for inert heating conditions. Also, a simplified version of the finite element model was used to calculate the thermal disturbance error for a number of conditions, and subsequently to predict a range of corrected temperatures for the experimental measurements. This correction method was found to greatly improve the accuracy of the results for inert heating conditions. Since the method does not account for the effects of moisture in heat transfer, a creep of uncorrected errors could be observed

Understanding fire growth for performance based design of bamboo structures

This paper analyses the different parameters governing fire growth and presents the results obtained for laminated bamboo samples produced from the species Phyllostachys pubescens “Moso”. Parameters such as critical heat flux, temperature for ignition, thermal inertia, mass loss rate and heat release rates are studied herein. Last, the ignition parameters of laminated bamboo are contrasted against the available information on bamboo and commonly used timber products. Results show that overall, laminated bamboo show higher critical heat flux for ignition, ignition temperature, and thermal inertia when compared to timber species

Overcoming risk assessment limitations for potential fires in a multi-occupancy building

Decision-making under risk has been a key issue in systems with a potential for major losses such as chemical process industries (Bhopal - 1984, Toulouse - 2001) or high occupancy buildings (World Trade Center - 2001, Grenfell Tower - 2017). For the past decades, engineering disciplines have supported risk management decision-making through the implementation of risk assessments using quantitative approaches. The popularity of this approach relates to the quantitative definition of risk given by Kaplan in 1981, who decomposed risk into a set of scenarios, probability of occurrence and consequences. Recently, research on quantitative risk assessments (QRA) has reported key limitations on identifying the set of scenarios and estimating their probability of occurrence. These limitations may lead to uncertainties of up to three orders of magnitude that affect the QRA’s ability of delivering reliable information to stakeholders. This research uses an alternative definition of risk and applies it to a case study of a multi-occupancy building in the event of a fire. The proposed approach quantifies the maximum damage potential (MDP) of the system when all the active safety measures are allowed to fail, even those with low failure frequencies. The system’s MDP is compared to its maximum allowable damage (MAD), which is previously defined by the stakeholders. This approach allows defining design modifications and operational rules aiding the development of the building’s fire safety strategy. Finally, a comparison between the obtained results and a typical QRA is used to comment on the suitability of the proposed approach when evaluating risk in complex systems

A Review and Analysis of the Thermal Exposure in Large Compartment Fire Experiments

Developments in the understanding of fire behaviour for large open-plan spaces typical of tall buildings have been greatly outpaced by the rate at which these buildings are being constructed and their characteristics changed. Numerous high-profile fire-induced failures have highlighted the inadequacy of existing tools and standards for fire engineering when applied to highly-optimised modern tall buildings. With the continued increase in height and complexity of tall buildings, the risk to the occupants from fire-induced structural collapse increases, thus understanding the performance of complex structural systems under fire exposure is imperative. Therefore, an accurate representation of the design fire for open-plan compartments is required for the purposes of design. This will allow for knowledge-driven, quantifiable factors of safety to be used in the design of highly optimised modern tall buildings. In this paper, we review the state-of-the-art experimental research on large openplan compartment fires from the past three decades. We have assimilated results collected from 37 large-scale compartment fire experiments of the open-plan type conducted from 1993 to 2019, covering a range of compartment and fuel characteristics. Spatial and temporal distributions of the heat fluxes imposed on compartment ceilings are estimated from the data. The complexity of the compartment fire dynamics is highlighted by the large differences in the data collected, which currently complicates the development of engineering tools based on physical models. Despite the large variability, this analysis shows that the orders of magnitude of the thermal exposure are defined by the ratio of flame spread and burnout front velocities (VS / VBO), which enables the grouping of open-plan compartment fires into three distinct modes of fire spread. Each mode is found to exhibit a characteristic order of magnitude and temporal distribution of thermal exposure. The results show that the magnitude of the thermal exposure for each mode are not consistent with existing performance-based design models, nevertheless, our analysis offers a new pathway for defining thermal exposure from realistic fire scenarios in large open-plan compartments