This study aims to obtain the relationship between density and compressive strength of foamed concrete. Foamed concrete is a preferred building material due to the low density of its concrete. In foamed concrete, the compressive strength reduces with decreasing density. Generally, a denser foamed concrete produces higher compressive strength and lower volume of voids. In the present study, the tests were carried out in stages in order to investigate the effect of sand–cement ratio, water to cement ratio, foam dosage, and dilution ratio on workability, density, and compressive strength of the control foamed concrete specimen. Next, the test obtained the optimum content of processed spent bleaching earth (PSBE) as partial cement replacement in the foamed concrete. Based on the experimental results, the use of 1:1.5 cement to sand ratio for the mortar mix specified the best performance for density, workability, and 28-day compressive strength. Increasing the sand to cement ratio increased the density and compressive strength of the mortar specimen. In addition, in the production of control foamed concrete, increasing the foam dosage reduced the density and compressive strength of the control specimen. Similarly with the dilution ratio, the compressive strength of the control foamed concrete decreased with an increasing dilution ratio. The employment of PSBE significantly influenced the density and compressive strength of the foamed concrete. An increase in the percentage of PSBE reduced the density of the foamed concrete. The compressive strength of the foamed concrete that incorporated PSBE increased with increasing PSBE content up to 30% PSBE. In conclusion, the compressive strength of foamed concrete depends on its density. It was revealed that the use of 30% PSBE as a replacement for cement meets the desired density of 1600 kg/m3, with stability and consistency in workability, and it increases the compressive strength dramatically from 10 to 23 MPa as compared to the control specimen. Thus, it demonstrated that the positive effect of incorporation of PSBE in foamed concrete is linked to the pozzolanic effect whereby more calcium silicate hydrate (CSH) produces denser foamed concrete, which leads to higher strength, and it is less pore connected. In addition, the regression analysis shows strong correlation between density and compressive strength of the foamed concrete due to the R2 being closer to one. Thus, production of foamed concrete incorporating 30% PSBE might have potential for sustainable building materials.
The paper is focused on the study of the solidification process of pure metals, in which the solidification front is smooth. It has the shape of a surface separating liquid from solid in three dimensional space or a curve in 2D. The location and topology of moving interface change over time and its velocity depends on the values of heat fluxes on the solid and liquid side of it.Such a formulation belongs to a group called Stefan problems. A mathematical model of the Stefan problem is based on differential equations of heat conduction and interface motion. This system of equations is supplemented by appropriate initial and boundary conditions as well as the continuity conditions at the solidification interface. The solution involves the determination of temporary temperature field and interface position. Typically, it is impossible to obtain the exact solution of such problem. This paper presents a mathematical model for the two-dimensional problem. The equation of heat conduction is supplemented with Dirichlet and Neumann boundary conditions. Interface motion is described by the level set equation which solution is sought in the form of temporary distribution of the signed distance function. Zero level of the distance field coincides with the position of the front. Values of the signed distance function obtained from the level set equation require systematic reinitialization.Numerical model of the process based on the finite element method (FEM) is also presented. FEM equations are derived and discussed. The explicit time integration scheme is proposed. It helps to avoid solving the system of equations during each time step. The reinitialization procedure of the signed distance function is described in detail. Examples of numerical analysis of the solidification process of pure copper within the complex geometry are presented. Results obtained from the use of constant material properties are compared with those obtained from the use of temperature dependent properties.Keywords: Pure Metal, Stefan Problem, Sharp Interface, Solidification, Finite Element Method, Level Set Method W pracy skupiono się na badaniu procesu krzepnięcia czystych metali, podczas którego front krzepnięcia pozostaje płaski. W przypadku trójwymiarowym jest on powierzchnią oddzielającą ciecz od ciała stałego, w przypadku dwuwymiarowym ma postać krzywej. Położenie i topologia frontu krzepnięcia zmienia się w czasie, a prędkość przemieszczania zależy od różnicy wartości strumieni cieplnych po stronie ciała stałego i cieczy.Takie sformułowanie klasyfikuje opisywane zjawisko w grupie tzw. zagadnień Stefana. Model matematyczny tego procesu stanowią równania różniczkowe przewodnictwa ciepła oraz ruchu powierzchni międzyfazowej. Układ ten uzupełniają odpowiednie warunki brzegowe, początkowe oraz warunki ciągłości na froncie. Jego rozwiązanie polega na wyznaczeniu chwilowych pól temperatury oraz położenia frontu. Najczęściej nie da się uzyskać rozwiązania tak sformułowanego problemu w sposób dokładny. W pracy zaprezentowano model matematyczny zagadni...
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