Steady-state Heat Balance Equation Research Articles

Development and Processing of Thermal-Hydraulic Model for GFR 2400 Fast Reactor Design and NESTLE Coupled Transient Code

Abstract The paper investigates the influence of the used thermal-hydraulic approximations on the coupled calculations of gas-cooled fast reactor design (hereby GFR 2400). The NESTLE code is used as coupled simulation tool and solves the multigroup neutron diffusion equation by the finite difference method that is internally coupled with a thermal-hydraulic subchannel code. The in-house developed tempin code and the computational fluid dynamics (CFD) code fluent (from ANSYS code system, Canonsburg, PA) are used to prepare the thermal-hydraulic data for the GFR 2400 calculations. The tempin code solves the steady-state heat balance equation with flowing coolant in triangular lattice cell together with temperature dependent thermal-hydraulic properties of the fuel, cladding, and coolant. Based on the calculated fuel bundle temperature distributions by the tempin code, the thermal-hydraulic material properties (approximations) suitable for the NESTLE coupled code are processed for the GFR 2400 design. The influence of the constant and radial heat generation term within the fuel pin is studied within the paper. The performance of the NESTLE code with thermal-hydraulic approximations processed by both (tempin and fluent) methods is compared with the findings of the GoFastR project. Moreover, both the thermal-hydraulic approximations were compared for one steady-state and one transient state, related to the rapid withdrawal of one control rod assembly from the core. Changes in thermal-hydraulic distributions are described and visualized in the paper.

Integrating Dynamic Line Rating in Security Constrained Optimal Power Flow Considering Wind Power Generation. (Dept. E )

Traditional optimal power flow (OPF) problem is solved considering static line rating (SLR) of the transmission lines which are constant values of power flow limits. This led to underutilization of the network and higher locational marginal prices (LMPs). Dynamic line rating (DLR) is one of the active solutions to enhance ampacity for overhead transmission lines (OHTL), especially with the penetration of high wind power without investing in an additional transmission line network. This paper investigates the effect of integrating the DLR on power dispatch with uncertainty levels due to renewable energy sources (RES) generation. The model propose is a multi-period security-constrained OPF based on particle swarm optimization (SCOPF/PSO) that takes into consideration the steady-state heat-balance equation (SS-HBE) of the OHTL and the ramp-up time of generation units. The problem is a multi-objective optimization one; the main objective is to maximize the social welfare (SW) by minimizing total system operation cost and maximizing the revenue from the energy consumers, whereas the second objective is to minimize the thermal emissions. To demonstrate the effectiveness of the proposed model, a case study is applied to the modified IEEE 30-bus test system. The results expound on the effectiveness of the proposed approach.

Application of direct collocation method in short-term line ampacity calculation

Commonly for the calculation of line ampacity (rating) the steady-state heat balance equation is used. In this paper a novel method for the calculation of line ampacity is developed. This method is based on the definition of an optimal control problem and its solution represents the line ampacity in the desired time range. The solution of the defined optimal control problem is obtained by applying the direct collocation method. In this manner the short-term line ampacity is obtained by solving a nonlinear programming problem. Nowadays, many algorithms and hardware implementations are available for solving similar nonlinear programming problems. Thus, the usage of this method is suitable for simplifying the calculation of the short-term line ampacity in contemporary dynamical line rating systems. Finally, the developed is compared with existing methods for the short-term line ampacity calculation and the advantages and the disadvantages of each method are discussed. At the end of the paper for a 240/40mm2 aluminium steel-reinforced conductor, the methods are tested on several cases and the results compared. The effectiveness of each method is checked by simulating the conductor non-steady-state heat balance equation with the obtained results for the line ampacities. From the obtained results it is proven that the developed method effectively calculates the short-term line ampacity, and at the same time simplifies the calculation process. This paper is recommended for researchers focused in the field of dynamical rating systems.

Optimal power flow in distribution network considering spatial electro‐thermal coupling effect

The conductor resistance changes in accordance with the conductor temperature, in turn the line thermal capacity limit and power flow are influenced by its spatial characteristics of line routes and surrounding weather conditions. In light of the significant difference of spatial characteristics of line routes and weather conditions in different regions covered by distribution network, a novel optimal power flow (OPF) model in distribution network considering spatial electro-thermal coupling effect is proposed to integrate heat transfer constraints and electro-thermal coupling constraints into normal distribution network operation constraints. To address the computational complexity of the proposed model, the line thermal capacity limit is calculated firstly using the spatial steady-state heat balance equation. Then, a genetic algorithm combined with an extended back/forward sweep method is presented to solve the distribution system OPF problem, in which the heat balance equation is embedded in the forward sweep stage of the power flow calculation. Consequently, line temperatures, resistances, and power flows are dynamically updated during the iterative procedure. A 14-bus system with nine regions shows that the spatial electro-thermal coupling effect has a significant impact on the result of power flow and the optimal dispatch of the distributed generation in the distribution network.

Indirect Method of the Critical Parameters of Frank-Kamenetskii Equations in Spontaneous Combustion Theory

The steady state heat balance equation in Frank-Kamenetskii model is one of the basic models of spontaneous combustion. For a non-uniform temperature exothermic reaction system met the Arrhenius law, the reaction heat term of the heat balance equation can be described by a simple nonlinear term. The simplified spontaneous theoretical model equation is a typical bifurcation problem. The governing equation of bifurcation points is generally Nonlinear Ill-posed Equation. To solve this kind of equation, usually we divide it into three steps to complete: regularization, difference and iterative. Homotopy-Newton hybrid method is a typical direct method to solve it. However, this direct method for a specific problem, deterministic and convergence of solutions are not guaranteed. In this paper, a kind of effective indirect method is introduced. This shooting method by control parameter can effectively improve the convergence.

Mathematical Model to Predict Solids Content of Water Treatment Residuals during Drying

Dewatering and drying of residuals are extremely energy intensive processes, which are necessary to reduce the quantity of wet residuals produced from the water and wastewater treatment operations. Meteorological conditions are a major factor in the drying of residuals, which can greatly affect the drying period. A mathematical model is developed for the process of drying of water treatment residuals. A steady-state heat-balance equation is applied for a control volume of residuals that takes into account the heat transfer by radiation, convection, and evaporation. The mathematical model was validated using drying experiments conducted in a wind tunnel as well as other experiments conducted in an open environment equipped with a weather monitoring station. Good agreement was obtained between model predictions and experimental observations. The model can be used to predict the drying time of a given application of water treatment residuals with the knowledge of meteorological conditions.

A measurement technique for hemispherical total emissivity using feedback-controlled pulse current heating

A new measurement technique for hemispherical total emissivity of electrical conductors at high temperatures (above 1500 K) which uses feedback-controlled pulse heating has been developed. In this technique, a specimen is heatedrapidly in vacuum by resistive self-heating up to a preset high temperature in a short time (about 200 ms), and then is maintained at that temperature under brief steady-state conditions (about 500 ms). In order to achieve fast feedback temperature control, a computer-controlled system with a solid-state switch, which regulates the current through the specimen, is employed. The radiance temperature of the specimen is measured with a high-speed radiation thermometer. In order to determine the true temperature, the normal spectral emissivity of the specimen is measured with a laser ellipsometer. Hemispherical total emissivity is determined at the plateau of temperature by the use of a steady-state heat balance equation based on the Stefan-Boltzmann law. Preliminary experiments were conducted on strip-shaped specimens of tantalum and molybdenum in the temperature range approximately 1900 to 2800 K.

Hemispherical total emissivity of niobium, molybdenum, and tungsten at high temperatures using a combined transient and brief steady-state technique

The hemispherical total emissivity of three refractory metals, niobium, molybdenum, and tungsten, was measured with a new method using a combined transient and brief steady-state technique. The technique is based on rapid resistive self-heating of a solid cylindrical specimen in vacuum up to a preset high temperature in a short time (about 200 ms) and then keeping the specimen at that temperature under steady-state conditions for a brief period (about 500ms) before switching off the current through the specimen. Hemispherical total emissivity is determined at the temperature plateau from the data on current through the specimen, the voltage drop across the middle portion of the specimen, and the specimen temperature using the steady-state heat balance equation based on the Stefan–Boltzmann law. Temperature of the specimen is determined from the measured surface radiance temperature and the normal spectral emissivity; the latter is obtained from laser polarimetric measurements. Experimental results on the hemispherical total emissivity of niobium (2000 to 2600 K), molybdenum (2000 to 2700 K), and tungsten (2000 to 3400 K) are reported.

A combined transient and brief steady-state technique for measuring hemispherical total emissivity of electrical conductors at high temperatures: Application to tantalum

A new method for measuring hemispherical total emissivity of electrically conducting materials at high temperatures (above 1500 K) using a feedback-controlled pulse-heating technique has been developed. The technique is based on rapid resistive self-heating of a solid cylindrical specimen in vacuum up to a preset high temperature in a short time (about 200 ms) and then keeping the specimen at that temperature under steady-state conditions for a brief period (about 500 ms) before switching off the current through the specimen. The specimen is maintained at constant temperature with a feedback control system which controls the current through the specimen. The computer-controlled feedback system operates a solid-state switch (composed of field-effect transistors). The sensing signal for the feedback is provided by a high-speed optical pyrometer. Hemispherical total emissivity is determined at the temperature plateau from the data on current through the specimen, the voltage drop across the middle portion of the specimen, and the specimen temperature using the steady-state heat balance equation based on the Stefan-Boltzmann law. The true temperature of the specimen is determined from the measured radiance temperature and the normal spectral emissivity: the latter is obtained from laser polarimetric measurements. The experimental quantities are measured and recorded every 0.2 ms with a 12-bit digital oscilloscope. To demonstrate the feasibility of the technique, experiments were conducted on a tantalum specimen in the temperature range 2000 to 2800 K. The results on hemispherical total emissivity are presented and are compared with the data given in the literature.

Multiple solutions in hollow geometries in the theory of thermal ignition

Following Burnell et al., the dimensionless form of the steady state heat balance equation for material undergoing an exothermic reaction over the symmetrical N-dimensional unit sphere is u″(r) + (N − 1)r −1u′(r) + λe −( 1 u ) = 0 . The parameter λ is held constant so that the solution structure is dependent on the bifurcation parameter U appearing in the boundary condition u(1) = U. In previous papers we discussed the existence of multiple solutions for both class A (slab, infinite cylinder, and sphere) and nonclass A geometries and showed that multiple solutions (of multiplicity greater that three) occur for 2 < N < 12. In this paper, we present numerical results for some hollow geometries which indicate that similar solution structure to that of previous cases is preserved and that the multiplicity of solutions does not always depend on the size of the hollow region.