Studies on the impact of external fire on the lye of the shelter housing

Purpose: The presented article presents a numerical analysis carried out to determine the impact of an external fire taking place on the surface of the ground on the level of stress of the trench shelter casing protected by a layer of soil. Design/methodology/approach: Numerical analysis was carried out in two stages. In the first stage, a quasi-stationary distribution of the initial temperature in the centre of the ground and the shelter casing was sought. In the second stage of the analysis, the effect of the fire was considered according to the profile of time changes in the temperature of the shelter object. Findings: We assume that the trench shelter is in an oblong shape, and the fire extends over a vast area. The area surrounding the shelter casing was treated as a material with average constant thermodynamic values. Research limitations/implications: The process related to heating and cooling the enclosure was described on the basis of the Fourier equation on heat conduction in terms of the heterogeneous nature of the material, primer and concrete. Practical implications: The use of the trench shelter model as a research element in the design of special objects. Originality/value: The methods of non-stationary temperature flow through the ground and the shelter casing used, allows for a very realistic indication of how the housing will behave under the influence of high temperature caused by an external fire. The article can be useful for designers who design underground shelters.

Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source

We derived a semianalytical solution for the time-dependent temperature distribution in a three-layered laterally infinite scattering and absorbing slab illuminated by an obliquely incident collimated beam of light. The light propagation was modeled by the low-order $$P_1$$ P 1 and $$P_3$$ P 3 approximations to the radiative transfer equation with closed form expressions for eigenvalues and eigenvectors, yielding a quickly computable solution, while the heat conduction was modeled by the Fourier equation. The solution was compared to a numerical solution using a Monte Carlo simulation for the light propagation and an FEM method for the heat conduction. The results showed that using the $$P_3$$ P 3 solution for the light propagation offers a large advantage in accuracy with only a moderate increase in calculation time compared to the $$P_1$$ P 1 solution. Also, while the $$P_3$$ P 3 solution is not a very good approximation for the spatially resolved absorbance itself, its application as a source term for the heat conduction equation does yield a very good approximation for the time-dependent temperature.

Uncertainty Relations in Hydrodynamics

The qualitative behaviors of uncertainty relations in hydrodynamics are numerically studied for fluids with low Reynolds numbers in 1+1 dimensional system. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys. Lett. A 382, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schrödinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

Uncertainty Relations in Hydrodynamics

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

Numerical validation of a method determining thermal diffusivity based on a measurement of a temperature profile

The knowledge of dynamic thermal properties of building elements is necessary to investigate temperature and heat flux changes in natural daily and annual cycles. The basic dynamic parameter is thermal diffusivity. A method for determining its value for real objects has been proposed. This method is based on measuring the temperature in the element’s volume and on assuming that the obtained results meet the Fourier equation. Validation by a numerical experiment was made. The wall of the building with known thermal parameters was assumed and the temperature distribution was calculated over time in the process of non-stationary heat exchange. From the results, the diffusivity value was calculated and compared with the data entered into the model. Validations were performed for several accuracy of the temperature value and for two forms of function which approximated the temperature values obtained from calculation. A preliminary analysis of errors has been carried out. Keywords: measurements of thermal diffusivity, temperature distribution in a building element, approximation, heat transfer

Semi-Analytical Model for Heat and Mass Transfer Evaluation of Vapor Bubbling

Multi-stage refrigeration systems cover a wide range of possibilities and are diffusing more and more. The idea that inspired this work derived from the need to have a tool to model the energy behavior of the intercooler inside a multi-stage refrigeration system. In this work, a semi-analytical model of a single bubble, injected into the liquid of an intercooler of a multi-stage system, has been developed. The developed model is a set of equations derived from the Fourier equation for heat conduction in defined conditions and includes the effects of sensible and latent heat. The vapor bubble is supposed to be injected in the saturated liquid contained in a tank at a defined depth, at an intermediate pressure. The model has been implemented in Matlab and the results show the influence of the liquid surface tension, the injection depth and the thermal diffusivity of the vapor. The model developed here is a useful low-cost tool for evaluating heat transfer optimization of a separator/intercooler of a multi-stage refrigeration system.

Numerical Analysis on Velocity and Temperature of the Fluid in a Blast Furnace Main Trough

The main trough is a part of the blast furnace process for hot metal and molten slag transportation from the tap hole to the torpedo, and mechanical erosion of the trough is an important reason for a short life of a campaign. This article employed OpenFoam code to numerically study and analyze velocity, temperature and wall shear stress of the fluids in the main trough during a full tapping process. In the code, a three-dimensional transient mass, momentum and energy conservation equations, including the standard k-ε turbulence model, were developed for the fluid in the trough. Temperature distribution in refractory is solved by the Fourier equation through conjugate heat transfer with the fluid in the trough. Change velocities of the fluid during the full tapping process are exactly described by a parabolic equation. The investigation results show that there are strong turbulences at the area of hot metal’s falling position and the turbulences have influence on velocity, temperature and wall shear stress of the fluid. With the increase of the angle of the tap hole, the wall shear stress increases. Mechanical erosion of the trough has the smallest value and the campaign of the main trough is estimated to expand over 5 days at the tap hole angle of 7°.

Mixing Versus Stirring

Mixing is the operation by which a system evolves under stirring from one state of simplicity—the initial segregation of the constituents—to another state of simplicity—their complete uniformity. Between these extremes, patterns emerge, possibly interact, and die sooner or later. This review summarizes recent developments on the problem of mixing in its lamellar representation. This point of view visualizes a mixture as a set of stretched lamellae, or sheets, possibly interacting with each other. It relies on a near-exact formulation of the Fourier equation on a moving substrate and allows one to bridge the spatial structure and evolution of the concentration field with its statistical content in a direct way. Within this frame, one can precisely describe both the dynamics of the concentration levels in a mixture as a function of the intensity of the stirring motions at the scale of a single lamella and the interaction rule between adjacent lamellae, thus offering a detailed representation of the mixture content, its structure, and their evolution in time.

Heat transport solutions in rectangular shields using harmonic polynomials.

The search for the temperature field in a two-dimensional problem is common in building physics and heat exchange in general. Both numerical and analytical methods can be used to obtain a solution. Here a method of initial functions, the basics of which were given by W.Z. Vlasov i A.Y. Lur’e were adopted. Originally MIF was used for analysis of the loads of a flat elastic medium. Since then it was used for solving concrete beams, plates and composite materials problems. Polynomial half-reverse solutions are used in the theory of a continuous medium. Here solutions were obtained by direct method. As a result, polynomial forms of the considered temperature field were obtained. The Cartesian coordinate system and rectangular shape of the plate were assumed. The governing are the Fourier equation in steady state . Boundary conditions in the form of temperature (τ(x),t(y)) or/and flux (p(x), q(y)) can be provided. The solution T(x, y) were assumed in the form of an infinite power series developed in relation to the variable y with coefficients Cn depending on x. The assumed solution were substituted into Fourier equation and after expanding into Taylor series the boundary condition for y = 0 and y=h were taken into account. Form this condition a coefficients Cn can be calculated and therefore a closed solution for temperature field in plate.