Consideration Heat Research Articles

Set-valued solutions for non-ideal detonation

The existence and structure of a steady-state gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consideration frictional and heat losses between the gas and the particles. A new formulation of the governing equations is introduced that eliminates the difficulties with numerical integration across the sonic singularity in the reactive Euler equations. With the new algorithm, we find that when the sonic point disappears from the flow, there exists a one-parameter family of solutions parameterized by either pressure or temperature at the end of the reaction zone. These solutions (termed “set-valued” here) correspond to a continuous spectrum of the eigenvalue problem that determines the detonation velocity as a function of a loss factor.

Modeling the burnout of solid polydisperse fuel under the conditions of external heat transfer

A self-similar burnout mode of solid polydisperse fuel is considered taking into consideration heat transfer between fuel particles, gases, and combustion chamber walls. A polydisperse composition of fuel is taken into account by introducing particle distribution functions by radiuses obtained for the kinetic and diffusion combustion modes. Equations for calculating the temperatures of particles and gases are presented, which are written for particles average with respect to their distribution functions by radiuses taking into account the fuel burnout ratio. The proposed equations take into consideration the influence of fuel composition, air excess factor, and gas recirculation ratio. Calculated graphs depicting the variation of particle and gas temperatures, and the fuel burnout ratio are presented for an anthracite-fired boiler.

Effects of Packaging and Heat Transfer Kinetics on Drug-Product Stability During Storage Under Uncontrolled Temperature Conditions

To predict the stability of pharmaceutical preparations under uncontrolled temperature conditions accurately, a method to compute the average reaction rate constant taking into account the heat transfer from the atmosphere to the product was developed. The average reaction rate constants computed with taken into consideration heat transfer (κ(re) ) were then compared with those computed without taking heat transfer into consideration (κ(in) ). The apparent thermal diffusivity (κ(a) ) exerted some influence on the average reaction rate constant ratio (R, R = κ(re) /κ(in) ). In the regions where the κ(a) was large (above 1 h(-1) ) or very small, the value of R was close to 1. On the contrary, in the middle region (0.001-1 h(-1) ), the value of R was less than 1.The κ(a) of the central part of a large-size container and that of the central part of a paper case of 10 bottles of liquid medicine (100 mL) fell within this middle region. On the basis of the above-mentioned considerations, heat transfer may need to be taken into consideration to enable a more accurate prediction of the stability of actual pharmaceutical preparations under nonisothermal atmospheres.

A Mathematical Model for Carbothermic Reduction of Dust-Carbon Composite Agglomerates

Recycling iron–bearing dust from steel mills has gained a considerable attention in the past two decades to recover the valuable metals in dust while improving the sustainability of steel production. As a method for extracting the metals from dust, the reduction of dust–carbon composite agglomerates using a rotary hearth furnace (RHF) has been practiced in the steel industry. The use of low–grade carbonaceous reductants, such as low–rank coal and waste plastic, is of steelmakers’ interest to further enhance the waste recycling using the RHF process. However, applying these materials as reductants has proven to be a challenging task since the impact of the released volatile gas from such reductants on reduction reactions is not predictable. In addition, the reduction kinetics of dust pellet in RHF is more complicated than the reaction behaviour of sintered ore in blast furnace due to the higher furnace temperature, faster reduction and rapid gas evolution inside the agglomerate. To predict the reaction behaviour of the dust–carbon composite in RHF, a mathematical model was developed. The model takes into consideration heat and mass transfer as well as the reduction reaction of iron and zinc oxides, gasification of carbon and release of volatiles. The simulated behaviour of a dust pellet by the proposed model provides beneficial information to promote recycling an expanded range of waste materials in the RHF process. The modelling approach and calculation results are discussed in the present paper.

Computational thermodynamic analysis of compression ignition engine

This paper presents diesel engine simulation taking into consideration heat transfer and variable specific heats. A dual Weibe function is used to model the heat release. It was found that early injection timing leads to higher levels of pressure and temperature in the cylinder. Also, it was found that BMEP is more sensitive to equivalence ratio than to engine speed. Higher values of equivalence ratio lead to lower thermal efficiency even an increase in the value of BMEP was revealed. For medium engine speeds between 2000 and 3000, it was found that the optimum equivalence ratio is between 0.5 and 0.7. However, for low engine speeds the optimum equivalence ratio was around 0.35. For high engine speeds the thermal efficiency was almost independent of equivalence ratios higher than 0.4.

Development and simulation of a hydrogen storage unit using metal hydrides

This paper presents a hydrogen storage system using metal hydrides for a Combined Heat and Power CHP) system. Hydride storage technology has been chosen due to project specifications: high volumetric capacity, low pressures (<3.5 bar) and low temperatures (<75 °C: fuel cell temperature). During absorption, heat from hydride generation is dissipated by fluid circulation. An integrated plate-fin type heat exchanger has been designed to obtain good compacity and to reach high absorption/desorption rates. At first, the storage system has been tested in accordance with project specifications (absorption/desorption 3.5/1.5 bar). Then, the hydrogen charge/discharge times have been decreased to reach system limits. System design has been used to simulate thermal and mass comportment of the storage tank. The model is based on the software Fluent. We take in consideration heat and mass transfers in the porous media and a convective flow for cooling/heating the system during absorptions/desorptions. The hydride thermal and mass comportment has been integrated in the software. The heat and mass transfers experimentally obtained have been compared to results calculated by the model.

Woodpecker cavity aeration: a predictive model

We studied characteristics of the Syrian woodpecker (Dendrocopos syriacus) cavities in the field and a laboratory model, and rates of gas exchange in the laboratory. Night temperature of occupied cavities is 4.3 degrees C higher than empty ones, representing energy savings of approximately 24%. Oxygen conductance (GNO2) of an empty cavity is 7.1 ml[STPD] (Torr h)(-1), and is affected by winds at velocities up to 0.8 m/s. Day and night body temperatures were 42.0 and 40.1 degrees C, respectively. Steady-state O2 consumption rates (MO2) were 3.49 +/- 0.49 and 2.53 +/- 0.26 ml[STPD] (g h)(-1) during day and night respectively -- higher than predicted by allometry. A mathematical model describing PO2 in a cavity, taking into consideration MO2, GNO2, heat convection and wind speed, from the moment birds inhabit it, was developed. It shows that on the average, one woodpecker staying in its cavity at night does not encounter hypoxic conditions. However, in nest cavities with below the average GNO2, with more inhabitants (e.g. during the breeding season), hypoxia may become a problem.

Optimization of shape and functional structure of buildings as well as heat source utilisation. Partial problems solution

The aim of the paper is to present rational methods of multicriteria optimization of the shape and structure of energy-saving buildings, as well as optimization of heat sources taking into account the energy criteria. Mathematical model describing heat losses and gains in a building during the heating season was selected and refined. It takes into consideration heat losses through walls, roof, floor and transparent partitions as well as heat gains due to insolation across transparent partitions. Particular attention was paid to a more detailed description of heat gains due to solar radiation, depending on the position of partitions relative to their north–south axis and the degree of their use. The problem of multicriteria optimization of individual homes and blocks of flats was formulated on the basis of the following criteria: • minimum construction costs, including cost of materials, erection, heating installations together with the cost of heat sources, • minimum seasonal demand of heating energy, • minimum of pollution emitted by heat sources installed in the building. The following were accepted as the global optimization criteria allowing to find the preferred solution: • minimum building construction costs and its running costs over N-years’ period together with minimum environment pollution during that period, • minimum distance from the point belonging to the compromise set to the ideal point. The method of solving the above formulated problem consists in decomposing it into three part-problems: • optimization of internal partitions of the building, • optimization of the shape of building, • optimization of heat sources. Part-problems must be co-ordinated subsequently.

Pulverized coal char combustion: the effect of particle size on burner performance

A two-dimensional, two-phase combustion model of pulverized coal char is presented in this paper. It is of particular importance to reveal the controlling mechanisms, through prediction of the diffusion and reaction rates and to evaluate the effect of initial coal-particle size on the performance of the burner. The partial differential equations of conservation of mass, momentum, energy and chemical species are solved taking into consideration turbulent flow, interphase mass and heat transfer, radiative heat transfer and operational conditions such as coal feed and primary and secondary air. The equations are integrated with the finite volume methods and are solved for the flow field, temperature field of gaseous and solid phases and the concentration of reactants and products. The results are compared with experimental data from the literature and the comparison is satisfactory.

Prediction of coal-water slurry dispersion in a fluidized bed combustor

Coal-water slurry (CWS) injection in a fluidized bed leads to formation of three carbon phases: aggregates (A phase), tiny carbon deposits on individual bed particles (S phase), and carbon fines (F phase). The mechanism by which CWS is dispersed in a bubbling fluidized bed is analyzed by considering fundamental aspects and key stages underlying interaction of a CWS spray with hot bed solids. A mathematical model has been developed for the formation rates of carbon phases inside the jet zone from the fixed carbon injected with CWS. The model, which takes into consideration fluid dynamics, heat, and mass transfer of the jetting region, has a predictive character and uses no adjustable parameter. A key role is played by the submodel that predicts the rate of CWS deposition on sand particles entrained by the jet. Results show that the formation rates of the three carbon phases can be controlled by adjusting injection conditions. The mathematical model may complement a code aimed at predicting and controlling combustion efficiency of CWS in actual fluidized bed boilers. Model predictions are compared with experimental results obtained by Miccio et al. [8]. In spite of the complexity of the phenomena, the general trends of the predicted and experimental results as a function of injection conditions are the same. The agreement between the model and experimental results is not always satisfactory, but it tends to be better under injection conditions leading to generation of finer CWS droplets. Reasons for the discrepancies are discussed thoroughly.

Using non-linear χ2 fit in flash method

The paper presents a data reduction method for determination of thermal diffusivity in flash method. It is based on non-linear χ 2 fit to a model which takes into consideration heat losses. The advantage of the method is that it does not need a knowledge of base line and is suitable for data disturbed by noise and mains hum. A comparison with some other data reduction methods is given.

Bipolar nickel-metal hydride battery for hybrid vehicles

Hybrid electric vehicles are receiving increased interest as an approach to decrease vehicle pollution, dependence, and consumption of liquid petroleum and meet forthcoming Government vehicle emission standards. A number of schemes are under consideration (heat engine battery, fuel cell battery, peaking battery, inner-city battery, etc.). The success of any of the approaches will be dependent on battery capabilities, i.e., power, density, life, and cost. The nickel-metal hydride system appears to be the most promising of the candidate battery chemistries. Preliminary designs and analysis have been prepared and are presented for various configurations. Initial performance characterization tests are presented. It is concluded that a bipolar package arrangement for the Ni-MH chemistry appears most suited for the hybrid vehicle application considered. >

都市の熱環境制御手法に関する研究 （第２報）

Urbanization induces the increase of energy consumption in cities. It also alters the land use and cover in urban areas. Combination of these changes results in the temperature increase in cities, and thereby cause the increasing demand of energy required for air conditioning especially in summer. Thus, it is imperative to reexamine the physical structure of the cities with a view to alleviating the heat-island phenomena caused by urbanization. For this purpose, this study aims to establish the relationship between the urban thermal structure and the parameters specifying the land use pattern of the area under consideration (albedo, roughness length, relative humidity, and heat capacity). The analysis is based on an energy budget model. For Fukuoka City area, surface temperature estimated by the model is compared with the infrared surface temperatures data obtained from satellites (NOAA). A relatively good correlation was found between them, but further analysis must be made to achieve a better agreement.

Theory of the hypersonic viscous shock layer at high Reynolds numbers and intensive injection of foreign gases: PMM vol. 38, n≗ 6, 1974, pp. 1015–1024

The hypersonic flow around smooth blunted bodies in the presence of intensive injection from the surface of these is considered. Using the method of external and internal expansions the asymptotics of the Navier-Stokes equations is constructed for high Reynolds numbers determined by parameters of the oncoming stream and of the injected gas. The flow in the shock layer falls into three characteristic regions. In regions adjacent to the body surface and the shock wave the effects associated with molecular transport are insignificant, while in the intermediate region they predominate. In the derivation of solution in the first two regions the surface of contact discontinuity is substituted for the region of molecular transport (external problem). An analytic solution of the external problem is obtained for small values of parameters ε 1 = ρ ∞ ρs ∗ and δ = ρ ω ∗ 1 2 ν ω ∗ ρ ∞ 1 2 ν ∞ , in the form of corresponding series expansions in these parameters. Asymptotic formulas are presented for velocity profiles, temperatures, and constituent concentration across the shock layer and, also, the shape of the contact discontinuity and of shock wave separation. The derived solution is compared with numerical solutions obtained by other authors. The flow in the region of molecular transport is defined by equations of the boundary layer with asymptotic conditions at plus and minus infinity, determined by the external solution (internal problem). A numerical solution of the internal problem is obtained taking into consideration multicomponent diffusion and heat exchange. The problem of multicomponent gas flow in the shock layer close to the stagnation line was previously considered in [1] with the use of simplified Navier-6tokes equations. The supersonic flow of a homogeneous inviscid and non-heat-conducting gas around blunted bodies in the presence of subsonic injection was considered in [2–7] using Euler's equations. An analytic solution, based on the classic solution obtained by Hill for a spherical vortex, was derived in [2] for a sphere on the assumption of constant but different densities in the layers between the shock wave and the contact discontinuity and between the latter and the body. Certain results of a numerical solution of the problem of intensive injection at the surface of axisymmetric bodies of various forms, obtained by Godunov's method [3], are presented. Telenin's method was used in [4] for numerical investigation of flow around a sphere; the problem was solved in two formulations: in the first, flow parameters were determined for the whole of the shock layer, while in the second this was done for the sutface of contact discontinuity, which was not known prior to the solution of the problem, with the pressure specified by Newton's formula and flow parameters determined only in the layer of injected gases. The flow with injection over blunted cones was numerically investigated in [5] by the approximate method proposed by Maslen. The flow in the shock layer in the neighborhood of the stagnation line was considered in [6, 8], and intensive injection was investigated by methods of the boundary layer theory in [8–12].

Reaction zone and stability of gaseous detonations

Many experiments have been performed by various authors to measure the “thickness” of the reaction zone of gaseous detonations, i.e., the extension of the region where the main part of the chemical reaction takes place. These experiments have shown that at an initial pressure of 1 atmos the zone was too narrow to be resolved. Only in spinning detonations using modes close to the fundamental can one obtain a measure of the reaction time. Both spin and the dependence of the detonation velocity on the flow of the burned gas seem to be closely related to the mechanism of stabilization of a detonation. If the reaction rate is increased, rather high modes of fundamental spin frequency can be detected, which seem to disappear in very long tubes. This indicates a rather strong coupling between the burned gas and the reaction zone, the source of energy. The energy involved in the spin vibrations was found to decrease with increasing mode (frequency roughly proportional to n −1 ). The dependence of the detonation velocity on the flow conditions in the burned gas, also obtained experimentally, points at the coupling between reaction zone and flow in the burned gas. The end of the zone, in which the energy release which propagates the detonation takes place, lies in a region where chemical reaction is not yet finished. Using the conditions for flow through Mach-number 1, while taking into consideration heat addition, change of the effective tube area by boundary layer and the influence of expansion waves from the wall etc., and applying it to the velocity deficit of the real detonation, one can get an estimate of the state of chemical reaction at the area where M =1. This area seems to be rather sensitive to disturbances. In order to investigate the chemical reaction in the main part of the reaction zone, low pressure detonations were used. In overdriven detonations, where the stabilization effects mentioned above are rather unimportant, the reaction zone was fairly smooth. The conditions of normal detonations had to be chosen very carefully in order to obtain regular signals. In some hydrocarbon-O 2 systems, density gradients were determined. In the system H 2 −O 2 −N 2 density gradients, temperatures, OH-concentrations etc. were measured. The temperatures at the “end of the reaction” zone agreed with calculated temperatures within the limits of experimental error. Density, temperature and OH-concentration distribution correspond in principle to the model of Doering, von Neumann and Zeldovich. The chemical reaction, immediately following the shock front in H 2 −O 2 −N 2 mixtures could be described using the known kinetic data of the H 2 −O 2 reaction.

Temperatures in Polar Ice Caps

DECREASE in temperature with depth which was first observed by Sorge1 in the top 20 m. of ice at Eismitte in Greenland has since been confirmed for much deeper strata there2,3 and in Antarctica4,5. Sorge thought that the negative temperature gradient could have been created by a secular rise in air temperature. Independent evidence exists for such a trend in Greenland but not in Antarctica6. Moreover, the much greater depth to which a steady decrease in temperature in the ice has now been traced would require a surface warming extending over very long periods. In these circumstances it seems necessary to consider first the effects of the warming of the ice-cap surface connected with the decrease in its height during the outward movement of the ice. By geometrical reasoning Robin7 deduced that in the absence of heat conduction this movement (of velocity v) coupled with a net surface accumulation v leads to the temperature gradient: where α is the surface slope and λ the vertical gradient of the annual mean air temperature along the ice cap surface. A more complete treatment of the problem, taking into consideration heat conduction as well as advective temperature changes, now shows the relation (1) to have a deeper significance.