Material selection for high temperature applications

In this paper several materials have been evaluated in order to select the best suitable alloy for the production of a gas turbine transition piece. These components are exposed to complex thermal stresses and different damages, each of them requiring particular characteristics of the material. The procedure described takes into account the variability of requirements with some parameters, in particular temperature and service time. Due to the high value of temperature and the constraint of ductility, the choice of material has been limited to superalloys and stainless steels. A comparison between several alloys has been carried out on the basis of constraints and requirements previously determined. Using a suitable objective function, the method allows ranking materials in order to find the alloy which maximize component’s performance.     

A pulsed-wire technique for velocity and temperature measurements in natural convection flows

A pulsed-wire probe based on the use of one or two parallel wires, capable of measuring the velocity and the temperature in natural convection flows is described. These measurements are based on the analysis of the relaxation response of a pulsing wire, submitted to a very short electrical pulse. The analysis of the temperature variation on an optional second receiver wire, gives information about the velocity direction. The implementation simplicity of this probe, its good spatial precision, the lack of thermal contamination of the flow, as well as the possibility of obtaining simultaneous velocity and temperature measurements, allow the integration of the device in a multi-point measurement network, capable to deliver thermal and dynamic cartographies of unsteady convection flows.     

A proposal for thermal conductivity standards with special respect to convection and radiation effects

The influence of convection and especially radiation on measured liquid thermal conductivities is discussed for steady state methods and the transient hot wire method. New radiation and convection free thermal conductivity data are given for a mixture of 90% toluene and 10% ethanol, and for mono-, di-, and triethyleneglycol. The glycols are suitable as thermal conductivity standards for steady state methods and the transient hot wire method.

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Ein Vorschlag für Wärmeleitfähigkeitsstandards unter besonderer Berücksichtigung der Konvektion und Strahlung

Zusammenfassung Für stationäre Meßmethoden und für die instationäre Hitzdrahtmethode wird der Einfluß der Konvektion und der Strahlung auf die gemessene Wärmeleitfähigkeit von Flüssigkeiten diskutiert. Neue strahlungs- und konvektionsfreie Wärmeleitfähigkeitswerte werden für ein Gemisch aus 90% Toluol und 10% Ethanol und für Mono-, Diund Triethylenglycol angegeben. Die Glycole sind als Wärmeleitfähigkeitsstandard sowohl für stationäre Methoden als auch für die instationäre Hitzdrahtmethode geeignet.

     

Grey-body surface radiation coupled with conduction and convection for general geometries

This paper presents a numerical technique for the simulation of the effects of grey-diffuse surface radiation on the temperature field of fluid flows using FIDAP, a general purpose incompressible, viscous fluid code. The radiating surface relationships assume a non-participating medium, constant surface temperature and heat fluxes at the discretized elemental level. The technique involves the decoupling of energy and radiation exchange equations. A concept of macrosurfaces, each containing a number of radiating boundary surfaces, is introduced. These boundary macroelements then carry the information from the radiating boundary into the fluid regime. A number of simulations illustrating the algorithm are presented.     

The mathematical modelling of thermal radiation in high temperature fluidized bed

The aim of this study is composed of two parts. One of them is to calculate the radiation heat flux and the other is to determine the overall heat transfer coefficient for the gas-fluidized bed. The radiative heat transfer model is developed for predicting the total heat transfer coefficients between submerged surfaces and fluidized beds for several working temperatures. The role of radiation heat transfer in the overall heat transfer process at an immersed surface in a gas-fluidized bed at high temperatures is investigated. Analytical results are compared with the previously done experiments and a good agreement between the two, is obtained.

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Bestimmung der Wärmeübertragungs-Koeffizienten in Gas-Wirbelschichten

Zusammenfassung Diese Untersuchung besteht aus folgenden zwei Teilen: 1. Kalkulation des Radiationswärmeübergangs in Gas-Wirbelschichten. 2. Bestimmung des Wärmeübergangs-Koeffizienten in Gas-Wirbelschichten. Dieses Radiationswärmeübergangsmodell wurde entwickelt, um die Wärmeübertragungs-Koeffizienten zwischen der eingetauchten Oberfläche und der Wirbelschicht bei verschiedener Wärme schätzungsweise zu bestimmen. Es wurde das Verhältnis der Radiationswärmeübertragung in Gas-Wirbelschichten zum totalen Wärmeübergang untersucht. Die Meßwerte wurden mit theoretischen Resultaten verglichen.

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Nomenclature c (x) specific heat capacity of packet [J/kg K] - c _p specific heat capacity of particle [J/kg K] - c _pg specific heat capacity of gas [J/kg K] - d _p average diameter of the bed particles [m] - f ₀ the fraction of time that a unit surface exposed to the bubble phase - 1–f ₀ the fraction of time that a unit surface exposed to the packet phase - g acceleration due to gravity [m/s²] - h _b heat transfer coefficient for the surface in contact with bubble [W/m² K] - h _bc conduction heat transfer coefficient for the surface/bubble [W/m²K] - h _br radiation heat transfer coefficient for the surface/bubble [W/m²K] - h _p heat transfer coefficient for the surface in contact with packet [W/m²K] - h _pc conduction heat transfer coefficient for the surface/packet [W/m² K] - h _pr radiation heat transfer coefficient for the surface/packet [W/m² K] - h _T total heat transfer coefficient between bed and surface [W/m² K] - k ⁰ thermal conductivity of the emulsion phase for fixed bed [W/m K] - k(x) thermal conductivity of packet [W/m K] - k _e the logarithmic mean of conductivity for first layer in packet [W/m K] - k _g the logarithmic mean of conductivity for the first layer in packet [W/m K] - K extinction coefficient [1/m] - m mass [kg] - n number of layers - p air pressure [pa] - q _pc mean local conduction heat transfer for packet [kW/m²] - q _pr mean local radiation heat transfer for packet [kW/m²] - Q _p average heat flux during packet contact with surface [kW/m²] - Q _b average heat flux during bubble contact with surface [kW/m²] - R gas constant [287.04 J/kg K] - t time [s] - t _g residence time for gas bubble [s] - t _k residence time for packet [s] - T temperature [K] - T _b bed temperature [K] - T _W surface temperature [K] - V _mf minimum fluidization velocity [m/s] - v _t terminal velocity [m/s] - x distance [m] Greek symbols t time increment - x thickness of the layer - emissivity - thermal diffusivity [m²/s] - (x) voidage of fluidized bed - _mf void ratio of the bed at minimum fluidization - ₀ voidage of fixed bed - _g dynamic viscosity of gas [kg/m s] - _g kinematic viscosity of gas [m²/s] - (x) density of packet [kg/m³] - _p density of particles [kg/m³] - _g density of gas [kg/m³] - Stefan-Boltzmann constant [5.66·10^–8 W/m²K⁴] - geometric shape factor for particles Dimensionless numbers Ar Archimedes numberAr=g d _p ³ ( _p – _g ) _g / _g ² - Nu Nusselt numberNu=h·d/k - Re Reynolds numberRe=d _p ·V _mf / _g - Pr Prandtl numberPr=C _{pg g} /k _g      

A comparison of theory and experiment for high density,high temperature germanium spectra

This paper compares results from theoretical predictions to experimental emission data from germanium obtained on the HELEN laser at AWE. The aim of the comparison was to test opacity predictions of highly stripped, medium Z elements, a regime which has received relatively little attention due the difficulty of achieving conditions near LTE at high temperatures. The data show emission from the 2p–3d and 2s–3p transitions from a layer of germanium buried in plastic and heated by the HELEN CPA beam. Predictions of spectra constructed using data generated by the grasp2K atomic structure code coupled to Saha–Boltzman population dynamics were compared to the experimental emission. It was found that the grasp2K calculations match the position of all the features in the experiment well, but non-LTE effects in the experiment make it unreasonable to expect a match to line strengths. Two opacity codes, CASSANDRA and DAVROS, were benchmarked against the grasp2K simulations. It was shown that the major difference in the two opacity codes is due to different approaches to calculating total ion energies. For this reason the DAVROS line positions are significantly more accurate than those of CASSANDRA.     

Buoyancy-dominated laminar convection and radiation transfer in rod arrays

Laminar combined free and forced convection together with radiation transfer in flow of steam at 68 bar through rods in triangular and square arrays have been investigated numerically. The pitch to diameter ratio has been varied from 1.2 to 2.0. Heat transfer results have been obtained for both up and down forced flow influenced by bouyancy with and without the effects of variable thermophysical fluid properties. The Rosseland diffusion approximation has been used for radiative transfer. First- and second-orde r density changes have been investigated.     

Combined natural convection and radiation in a vertical annulus

This paper presents a numerical study of the effects of thermal radiation on the heat transfer of steady natural convection in a participating fluid contained inside a cylindrical annulus. The fluid absorbs and emits radiation energy. Uniform temperature difference is imposed across the inner and outer cylinder walls. The radiation part of the problem is treated by using the two-dimensional P-1 approximation. The numerical calculations were executed using the PROJECTION algorithm with a power law scheme. The analysis are performed for Rayleigh number ranging from 10⁴ to 10⁶, aspect ratio varying between 2 and 10, and the radius ratio ranging from 1.25 to 10 for N=0.1, 1, and X where N is the conduction-to-radiation parameter. The thermal radiation greatly influences the flow field and temperature distribution inside the enclosure for different aspect ratio and radius ratios. Those results are presented vividly by the streamlines and isotherms. Based on the results, the average Nusselt number is correlated by a relation of the form N¥ˆ=a+b ln A and N¥ˆ=c+d exp(m-/e). The coefficients for various N are tabulated. Zusammenfassung Ziel der numerischen Studie ist es, die Einflüsse der Wärmestrahlung auf den Wärmeübergang durch stationäre, natürliche Konvektion an ein, in einem zylindrischen Ringraum befindlichen Fluid zu bestimmen, das Strahlungsenergie absorbiert und emittiert. Innere und äußere Zylinderwand werden auf unterschiedlichen, aber konstanten Temperaturen gehalten. Der Strahlungstransport wird mittels der zweidimensionalen P-1-Approximation erfaßt; die numerischen Berechnungen erfolgten unter Verwendung des PROJECTION-Algorithms nach einem Potenzgesetzschema. Die Untersuchung erstreckt sich auf Rayleigh-Zahlen von 10⁴ bis 10⁶, auf Seitenverhältnisse von 2 bis 10 und auf Radienverhältnisse von 1,25 bis 10. Der Leitungs/Strahlungs-Parameter N hatte die Werte 0,1-1,0 und X. Die Wärmestrahlung hat im Variationsbereich des Seiten-und des Radienverhältnisses großen Einfluß auf das Strömungsverhalten und die Temperaturverteilung im Ringspalt, was sich sehr gut durch Stromlinien-und Isothermenfeld-Darstellungen belegen läßt. Die Resultate stützen Berechnungsgleichungen für die gemittelte Nusselt-Zahl der Form N¥ˆ=a+b ln A und N¥ˆ=e+d exp(-/e). Die einzelnen Koeffizienten sind für verschiedene N-Werte in Tabellen zusammengestellt.     

A model for universal spatial variations of temperature fluctuations in turbulent Rayleigh-Bénard convection

We propose a theoretical model for spatial variations of the temperature variance σ~2( z, r)( z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection(RBC).Adapting the "attached-eddy" model of shear flow to the plumes of RBC, we derived an equation for σ~2 which is based on the universal scaling of the normalized RBC temperature spectra. This equation includes both logarithmic and power-law dependences on z/λ_(th), where λ_(th) is the thermal boundary layer thickness. The equation parameters depend on r and the Prandtl number Pr, but have only an extremely weak dependence on the Rayleigh number Ra Thus our model provides a near-universal equation for the temperature variance profile in turbulent RBC.     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

A new fabrication process for a flexible skin with temperature sensor array and its applications

This paper reports a novel technique for fabrication of a flexible skin with a temperature sensor array (40×1 sensors). A simplified MEMS technology using platinum resistors as sensing materials, which are sandwiched between two polyimide layers as flexible substrates is developed. The two polyimide layers are deposited on top of a thin aluminum layer, which serves as a sacrificial layer such that the flexible skin can be released by metal etching and peeled off easily. The flexible skin with a temperature sensor array has a high mechanical flexibility and can be handily attached on a highly curved surface to detect tiny temperature distribution inside a small area. The sensor array shows a linear output and has a sensitivity of 7.5mV/℃ (prior to amplifiers) at a drive current of 1 mA. To demonstrate its applications, two examples have been demonstrated, including measurement of temperature distribution around a micro heater of a micro PCR (polymerase chain reaction) chip for DNA amplification and detection of separation point for flow over a circular cylinder. The development of the flexible skin with a temperature sensor array may be crucial for measuring temperature distribution on any curved surface in the fields of aerodynamics, space exploration, auto making and biomedical applications etc.     

Non-LTE radiation transport in high radiation plasmas

A primary goal of numerical radiation transport is obtaining a self-consistent solution for both the radiation field and plasma properties, which requires consideration of the coupling between the radiation and the plasma. The different characteristics of this coupling for continuum and line radiation have resulted in two separate sub-disciplines of radiation transport with distinct emphases and computational techniques. LTE radiation transfer focuses on energy transport and exchange through broadband radiation, primarily affecting temperature and ionization balance. Non-LTE line transfer focuses on narrowband radiation and the response of individual level populations, primarily affecting spectral properties. Many high energy density applications, particularly those with high-Z materials, incorporate characteristics of both these regimes. Applications where the radiation fields play an important role in the energy balance and include strong line components require a non-LTE broadband treatment of energy transport and exchange.We discuss these issues and present a radiation transport treatment which combines features of both approaches by explicitly incorporating the dependence of material properties on both temperature and radiation fields. The additional terms generated by the radiation dependence do not change the character of the system of equations and can easily be added to a numerical transport implementation. A numerical example from a Z-pinch application demonstrates that this method improves both the stability and convergence of the calculations. The information needed to characterize the material response to radiation is closely related to that used by the linear response matrix (LRM) approach to near-LTE simulation, and we investigate the use of the LRM for these calculations.     

Laminar forced convection in vertical pipes exposed to external natural convection and external radiation: uncoupled/lumped solution

This paper is concerned with the laminar forced convection flow in a vertical pipe exposed to either natural convection or simultaneous natural convection and thermal radiation external to the pipe. An uncoupled/lumped formulation enabled the determination of the mean bulk temperature distribution of the internal flow and the total rate of heat transfer. Average values for both internal and external Nusselt numbers have been taken from standard correlations reported in the literature, leading to the calculation of an effective average Nusselt number, which controls the thermal interaction process. Typical results for a selected combination of internal and external fluids are discussed at length and they compared favorably with others based on a conjugate/numerical formulation. This formulation necessitated a finite difference methodology where information was transferred between the two flows (internal and external), via their respective heat transfer coefficients. On the other hand, attention was focused on the uncoupled/lumped formulation in order to examine in detail the effects of the thermal boundary conditions, and consequently the important role of radiation as an enhancing heat transfer mechanism.     

Effect of radiation on natural convection in an L-shaped corner

An experimental investigation of the interaction of surface radiation and natural convection in an L shaped corner is presented. Parametric studies to explore the influence of surface emissivity and aspect ratio on the total heat transfer rate from the isothermal vertical wall of the L corner, have been carried out. For an L corner with highly polished walls, the present experimental results are compared with results available in literature, and are found to be in good agreement. A new semi-experimental method for solving this class of problems is discussed, and a correlation for estimating the total Nusselt number is proposed. It is found that surface radiation has a significant effect on the total heat transferred from the vertical wall of the L-shaped corner. Received: 18 February 1999/Accepted: 21 July 1999