A second degree approximation for the calculation of the transfer function coefficients for heat conduction through walls

Calculation of the conduction transfer function coefficients using a state space representation requires the transient governing differential equation to be discretized in space by the use of finite difference or finite element methods, in order to obtain a set of first order differential equations. The use of FEM to discretize the media gives an additional advantage due to it is possible to use a higher order approximation of the dependent variable, which gives us a better accuracy with less elements. In this paper, the transient heat flow problem is tackled using a quadratic finite element. The variational formulation for the governing differential equation is developed, the Ritz approximation to construct the finite element formulation is used and the approximation functions are presented using a normalized local coordinate system for elements with three equally spaced nodes for the one-dimensional problem. The 2D transient problem is presented using a rectangular 8 node element. Results with 1, 2 and 3 three-node elements are compared with the ASHRAE conduction transfer functions for the 3, 5, 6, 8 and 32 wall groups and a 2D-example is given.     

Coupling analysis of finite element and finite volume method for the design and construction of FPSO crane

The aim of this study is to establish a procedure for systematic design and performance evaluation of an offshore platform (FPSO; Floating, Production, Storage and Offloading) crane using a computational approach. Coupling analyses of the finite element and finite volume methods, which are applicable for ensuring robust design under the consideration of nonlinear environmental effects, were carried out. In order to investigate the effects of dynamic loading, the boundary conditions of an offshore platform crane having a lifting capacity of 100 tons were studied. In the finite volume method, a series of analyses were carried out using the computational fluid dynamics code, FLUENT. The crane's weight, maximum lifting load, calculated wind pressure and boundary conditions such as the inclination of the deck due to the extreme roll motion of FPSO were also considered in the finite element analyses using the commercial code, MSC/NASTRAN. Deformation, stress distribution, as well as fatigue life estimation were conducted under the unified computational environment. An advanced procedure for evaluating design concept validation was proposed for the application of FPSO design and construction.     

A new stable finite volume method for predicting thermal performance of a whole building

Discretised governing equations involving only temperatures and heat fluxes at both surfaces of a solid wall layer were obtained by combining a new stable finite volume scheme for the two inner nodes of the wall layer with the surface diffusion equations (discretised by third order equations). The finite volume scheme for the inner nodes of the layer is proved to be stable with its truncation error being O(Δx⁴,Δx²Δt²)$O(\mathrm{\Delta }{x}^4,\mathrm{\Delta }{x}^2\mathrm{\Delta }{t}^2)$. A special analytical solution for a solid wall was used to evaluate different schemes for the inner nodes, showing that the new proposed scheme performs better than all other schemes for time steps of 3600 and 600 s. Finally, this scheme was used to simulate a whole house and the predicted zonal air temperature, and surface temperatures agreed well with measured values.     

A criterion for the assessment of the reliability of ASHRAE conduction transfer function coefficients

This paper presents a new mathematical approach, which, when applied to conduction transfer functions (CTFs) of a multi-layered wall, is able to predict the reliability of building simulations. This new procedure can be used to identify the best set of CTF coefficients, which are a critical point at the core of the ASHRAE calculation methodology founded on the transfer function method. To evaluate the performance of different CTF coefficient sets, the authors performed a large number of thermal simulations on the multi-layered walls included in the ASHRAE Handbook, volume fundamentals, and on other walls typical of Mediterranean building heritage. Those data were employed to test an algorithm able to assess the reliability of the simulations. The numerical results show that it is possible to select the optimal number of coefficients on the basis of the size of the poles of a CTF. The proposed criterion, which employs a pole threshold value, is highly accurate, fast and easy to integrate in the most diffuse building simulation tools.     

框架—剪力墙结构的地震响应有限元分析方法

进行了框架—剪力墙结构的地震响应有限元分析,从强度和变形两方面来检验框架—剪力墙结构的安全和抗震可靠度;通过对结构进行模态分析,得出了结构的抗剪承载能力和储备,该方法对框架—剪力墙结构体系的分析设计具有一定的指导意义。     

Structural reliability analysis for implicit performance functions using artificial neural network

The Monte-Carlo simulation (MCS), the first-order reliability methods (FORM) and the second-order reliability methods (SORM), are three reliability analysis methods that are commonly used for structural safety evaluation. The MCS requires the calculations of hundreds and thousands of performance function values. The FORM and SORM demand the values and partial derivatives of the performance function with respect to the design random variables. Such calculations could be time-consuming or cumbersome when the performance functions are implicit. Such implicit performance functions are normally encountered when the structural systems are complicated and numerical analysis such as finite element methods has to be adopted for the prediction.To address this issue, this paper presents three artificial neural network (ANN)-based reliability analysis methods, i.e. ANN-based MCS, ANN-based FORM, and ANN-based SORM. These methods employ multi-layer feedforward ANN technique to approximate the implicit performance functions. The ANN technique uses a small set of the actual values of the implicit performance functions. Such a small set of actual data is obtained via normal numerical analysis such as finite element methods for the complicated structural system. They are used to develop a trained ANN generalization algorithm. Then a large number of the values and partial derivatives of the implicit performance functions can be obtained for conventional reliability analysis using MCS, FORM or SORM. Examples are given in the paper to illustrate why and how the proposed ANN-based structural reliability analysis can be carried out. The results have shown the proposed approach is applicable to structural reliability analysis involving implicit performance functions. The present results are compared well with those obtained by the conventional reliability methods such as the direct Monte-Carlo simulation, the response surface method and the FORM method 2.     

Reliability analysis of laterally loaded piles using response surface methods

Response surface methods have been applied to the reliability analysis of laterally loaded piles. Beam elements and a series of discrete springs are used to model the pile–soil system. The pile head displacement and the maximum bending moment in the piles are used as the performance criteria in this study. It is shown in the illustrative example that the CDF and PDF curves of the pile head displacement and the maximum bending moment in the pile obtained from the proposed methods are in good agreement with Monte Carlo simulation. The failure probabilities of the pile under specified performance criteria, the probabilistic responses of the pile-soil system, and the effect of pile-soil parameters to the failure probability of the pile are also studied.     

Estimation of thermophysical properties using natural signal analysis with heat and moisture transfer model

Conduction heat transfer through opaque envelope components characterizes the thermal performance of buildings and its consequences in terms of energy consumption and thermal comfort. A building envelope can be thermally described by two parameters: thermal conductivity (λ) and heat capacity (ρ·c). Estimating these thermal properties in situ allows the characterization of real building elements considering different aspects, such as thermal behavior under specific weather conditions, quality variability in materials, local construction technologies and material deterioration. This paper presents a method to estimate the thermal conductivity and volumetric heat capacity of a homogeneous element using a non-destructive test considering natural oscillations. Surface temperature and heat flow are measured in a concrete sample (with known thermal properties) and the data is treated with a signal processing technique. Estimation is carried out with a heat and moisture transfer model. Measurements were performed on six separate days under different sky conditions within a period of one month, to determine the importance of solar radiation as a heat source. Results gave acceptable estimates (average inaccuracy of 10-14%) of both thermophysical properties.     

Theoretical performance assessment of an integrated photovoltaic and earth air heat exchanger greenhouse using energy and exergy analysis methods

In this paper, a simplified mathematical model develops to study round the year effectiveness of photovoltaic/thermal (PV/T) and earth air heat exchanger (EAHE) integrated with a greenhouse, located at IIT Delhi, India. The solar energy application through photovoltaic system and earth air heat exchanger (EAHE) for heating and cooling of a greenhouse is studied with the help of this simplified mathematical model. Calculations are done for four types of weather conditions (a, b, c and d types) in New Delhi, India. The paper compares greenhouse air temperatures when it is operated with photovoltaic/thermal (PV/T) during daytime coupled with earth air heat exchanger (EAHE) at night, with air temperatures when it is operated exclusively with photovoltaic/thermal system (PV/T) and earth air heat exchanger (EAHE), for 24 h. The results reveal that air temperature inside the greenhouse can be increased by around 7-8 °C during winter season, when the system is operated with photovoltaic (PV/T), coupled with earth air heat exchanger (EAHE) at night. From the results, it is seen that the hourly useful thermal energy generated, during daytime and night, when the system is operated with photovoltaic (PV/T) coupled with earth air heat exchanger (EAHE), is 33 MJ and 24.5 MJ, respectively. The yearly thermal energy generated by the system has been calculated to be 24728.8 kWh, while the net electrical energy savings for the year is 805.9 kWh and the annual thermal exergy energy generated is 1006.2 kWh.     

Three-dimensional nonlinear analysis for the coupled problem of the heat transfer of the surrounding rock and the heat convection between the air and the surrounding rock in cold-region tunnel

According to the basic theories of heat transfer, geocryology and fluid mechanics, taking the coupled problem of the heat transfer of the rock surrounding the tunnel and the heat convective between the air in the tunnel and the rock surrounding the tunnel into account, three-dimensional calculating model of the coupled problem are presented. The finite element formulae of this problem are obtained by Galerkin’s method, and the computer program of the finite element is compiled. Using the program, three-dimensional nonlinear analyses for the coupled problem of the heat transfer of the rock surrounding the tunnel and the heat convective between the air in the tunnel and the rock surrounding Fenghuo mountain tunnel on the Qinghai–Tibet Railway are made. The agreement between the calculated results and the in-situ observed data is seen to be very good. The calculated results illustrate that the freezing–thawing situation of the rock surrounding the tunnel can correctly be predicted even if the air temperature distribution along the tunnel is unknown. In thus way, the large cost of in-situ observation for the air temperature in the tunnel can be saved.     

Pillar design by combining finite element methods, neural networks and reliability: a case study of the Feng Huangshan copper mine, China

This paper presents a mine pillar design approach by combining finite element methods (FEMs), neural networks (NN) and reliability analysis. This practical approach is presented by examining an actual cylindrical mine pillar in a copper mine and taking into account uncertainties in ore pillar material parameters including modulus, Poisson's ratio, density and uniaxial compressive strength. The ore pillar had to be able to safely and effectively support a drilling room that occupied an open space of 3.8 m high and 55 m long and 20 m wide and at a depth of 360 m below ground surface. Three-dimensional FEM was used to simulate the mining operations and to estimate average pillar compressive stress at each operation step. A pillar performance function was established in implicit form taking into account pillar strength and pillar dimension. NN was incorporated in the FEM to substantially reduce the number of finite element calculations in establishment of the relationship between pillar compressive stress and basic random variables. Trained NN was then used to generate a database for the implicit performance function. The database was used to determine the reliability index and failure probability for each trial pillar diameter. Relationship between pillar reliability index and each of the coefficients of variation of the basic random variables was used for optimal design of pillar diameter. The optimal pillar design was used in the mining construction and functioned well.     

Estimation of seismic active earth pressure on reinforced retaining wall using lower bound limit analysis and modified pseudo-dynamic method

Present study estimates seismic active earth pressure on the reinforced retaining wall by combining the lower bound finite element limit analysis and the modified Pseudo-dynamic method. A series of parametric analyses are performed by varying seismic acceleration coefficient, time period of seismic loading, soil friction and dilation angles, reinforcement spacing, length of reinforcement, soil-reinforcement interface, damping ratio of soil, soil-wall interface, wall inclination, and ground inclination. Maximum active earth pressure is exerted when natural time period of reinforced soil matches with the time period of an earthquake. Reinforcement is found to be effective in terms of reducing active earth pressure significantly on the wall subjected to seismic loading. Effectiveness of reinforcement depends upon two factors, namely vertical spacing and soil-reinforcement interface friction angle. For relatively smaller reinforcement spacing, soil-reinforcement behaves like a composite block, which helps to constraint stresses within a small area behind the wall. Maximum tensile resistance is developed when fully rough interface condition is assumed between soil and reinforcement layer. Failure patterns are provided to understand the behaviour of reinforced retaining wall under different time of seismic loading.     

Thermal performance of a naturally ventilated building using a combined algorithm of probabilistic occupant behaviour and deterministic heat and mass balance models

This study explores the role of occupant behaviour in relation to natural ventilation and its effects on summer thermal performance of naturally ventilated buildings. We develop a behavioural algorithm (the Yun algorithm) representing probabilistic occupant behaviour and implement this within a dynamic energy simulation tool. A core of this algorithm is the use of Markov chain and Monte Carlo methods in order to integrate probabilistic window use models into dynamic energy simulation procedures. The comparison between predicted and monitored window use patterns shows good agreement. Performance of the Yun algorithm is demonstrated for active, medium and passive window users and a range of office constructions. Results indicate, for example, that in some cases, the temperature of an office occupied by the active window user in summer is up to 2.6 °C lower than that for the passive window user. A comparison is made with results from an alternative behavioural algorithm developed by Humphreys [H.B. Rijal, P. Tuohy, M.A. Humphreys, J.F. Nicol, A. Samuel, J. Clarke, Using results from field surveys to predict the effect of open windows on thermal comfort and energy use in buildings, Energy and Buildings 39 (7) (2007) 823-836.]. In general, the two algorithms lead to similar predictions, but the results suggest that the Yun algorithm better reflects the observed time of day effects on window use (i.e. the increased probability of action on arrival).