Gaussian Thermal Flux model—I theory

The Gaussian Thermal Flux model is a fast thermal radiation sub-model which operates with minimal input and predicts flux on sloped surfaces for both clear and cloudy days. This paper presents the model's theoretical basis. It is distinguished from empirical models by its detailed two dimensional treatment of clouds, its computation of air layer transmissivity above and below cloud layers and its consideration of cloud height effects. The model improves upon existing flux emissivity and multi-band or line models by being independent of soundings and by its use of gaussian quadrature to speed the numerical integrations. It may be input entirely from standard screen level meteorological measurements.     

Gaussian Thermal Flux model—II validation

The Gaussian Thermal Flux model is a fast thermal radiation sub-model which operates with minimal input and predicts flux on sloped surfaces for both clear and cloudy days. This paper presents the model's theoretical basis. It is distinguished from empirical models by its detailed two dimensional treatment of clouds, its computation of air layer transmissivity above and below cloud layers and its consideration of cloud height effects. The model improves upon existing flux emissivity and multi-band or line models by being independent of soundings and by its use of gaussian quadrature to speed the numerical integrations. It may be input entirely from standard screen level meteorological measurements.     

Global transmissivity and diffuse fraction of solar radiation for clear and cloudy skies as measured and as predicted by bulk transmissivity models

Measurements of cloudiness and of global, direct, and diffuse radiation taken over a 13 mo period at Davis, CA, are analyzed in terms of global transmission (K_t) and diffuse fraction (K_d) for clear sky conditions and for various cloudiness conditions. A number of global transmission clear sky models are compared with observations for ranges of total water column and turbidity and some are found to give representative values for the global radiation at the ground.The dependence of the diffuse fraction on global transmission is found to be best represented by linear formulae—with different dependencies found for clear and cloudy conditions.Global transmission models are also compared with observations for cloudy conditions and found to give representative values of cloud transmissivities if climatological differences in the cloudiness at the measurement site and those sites used to calibrate the cloud models are considered.These results support the use of routine instantaneous surface meteorological data to calculate the most likely instantaneous global and diffuse radiation on a horizontal surface in the absence of any radiation measurements. These calculated irradiances are best used for solar energy system dynamic modeling in which system responses to typical sequences in meteorological conditions are being examined.     

Performance study on the east–west oriented single-axis tracked panel

A theoretical study on the performance of an east–west oriented single-axis tracked panel was originally proposed in this paper. Mathematic expressions applicable for calculating the angle that the tracked panel should rotate by to follow the Sun are derived. The incident angle of sunlight upon the panel as well as the instantaneous increments of solar energy captured by the panel relative to a fixed horizontal surface are then demonstrated graphically. To simulate different operation environments, three kinds of radiation sources will be considered, i.e. the extraterrestrial radiation, global radiation predicted by empirical models under clear sky situation and global radiation observed in Taiwan. Simulation results show that the yearly gains correlate positively with the radiation level, i.e. 21.2%, 13.5% and 7.4% for the extraterrestrial, predicted and observed radiations, respectively, which are far less than those obtained from a north–south oriented single-axis tracked panel. The irradiation increases with the maximum rotation angle of the panel, the benefit of increasing the rotation in overcast environment is not as good as in clear sky, for annual energy collection 45° is recommended. The irradiation received decreases with latitude, but it has a greater gain in higher latitude zone.     

The solar spectrum at typical clear weather days

The solar spectrum in the range of 300 < λ < 1500 nm is given for 5 typical clear weather days. These days are selected to represent typical seasonal conditions in respect to airmass, water vapor, ozone and turbidity. Present data are reviewed and specific conditions are selected. The spectral distribution of the irradiance is given for the direct component, the scattered skylight, the total flux on a horizontal surface and the flux on an inclined surface normal to the direct beam.     

Correcting lateral heat conduction effect in image-based heat flux measurements as an inverse problem

The image deconvolution method is developed, which is coupled with the one-dimensional (1D) analytical inverse method to calculate more accurate heat flux fields by correcting the lateral heat conduction effect in image-based surface temperature measurements. The theoretical foundation is a convolution-type integral equation with a Gaussian filter (kernel) that relates a heat flux field obtained by using the 1D inverse method on a surface to the true heat flux field. The accuracy of this method is evaluated and the standard deviation in the Gaussian filter is determined for different materials through simulations. This method is used to calculate heat flux fields in temperature-sensitive-paint measurements on a 7°-half-angle circular cone at Mach 6 in a short-duration hypersonic wind tunnel. In addition, a simple method is proposed to solve a projection problem associated with image deconvolution for a highly curved developable surface.     

绝热发动机表面瞬态传热的实验研究与解析计算

以绝热发动机燃烧室陶瓷涂层表面的实测瞬态温度和平均热流为边界条件，应用傅里叶数学分析理论，探索出一种确定陶瓷涂层表面局部瞬态热流的数学方法；并结合带陶瓷涂层的２１００型低散热发动机，给出实际计算结果。     

HYPERBOLIC STEFAN PROBLEM WITH APPLIED SURFACE HEAT FLUX AND TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

Abstract

The hyperbolic Stefan problem with an applied surface heat flux and temperature-dependent thermal conductivity is solved numerically for a semi-infinite slab using Mac-Cormack's predictor-corrector method. Solutions are presented for cases where the melt temperature is both below and above the instantaneous jump in surface temperature at time t = O⁺. The interface condition, surface temperature, and internal temperatures are presented for different Stefan numbers and melt temperatures, as well as thermal conductivity both increasing and decreasing with temperature. The results obtained from the hyperbolic solution are compared with those obtained from the parabolic solution.     

Thermocapillary periodic flows

This paper describes experimental investigations of the structure of periodic thermocapillary flows originating from periodic variations of heat flux on a linear source located at a free surface. The periodic flows develop in a plane horizontal layer with adiabatic horizontal surfaces for which the trends in convective flow far from the heat sources are known. The temperature fields are measured at different periods and amplitudes of the change in heat flux. The instantaneous and mean temperature gradients are measured along a free surface and, hence, the friction on the surface. The limits of the propagation of periodic perturbations depending on the amplitude and period of change in loading are found. It is shown that for t₀ < 35 s the thermogravitational forces do not exert a noticeable effect on the propagation of a periodic flow along the free surface.     

On the analysis of an elliptical Gaussian flux image and its equivalent circular Gaussian flux images

For a continuous elliptical Gaussian flux image over the infinite X-Y plane, the parameter relationships between the elliptical Gaussian flux image and the equivalent circular Gaussian flux images are clearly discussed in both mathematical and graphical ways in this paper with respect to the radial power distribution around the image centre (peak flux location in image plane). This paper presents six typical methods (SIGMA-2Mean, SIGMA-1Mean, SIGMA-0Mean in Class One, SIGMA-RPeak, SIGMA-RMean, SIGMA-SqrRMean in Class Two) to give the equivalent circular Gaussian flux images to the elliptical Gaussian flux image, tries to link these circular Gaussian fitting methods to the relevant solar engineering applications, and makes some assessment comments on the elliptical/circular Gaussian modelling in solar mirror optics. By comparing the approximation performance among these six typical fitting methods, it reveals the reason for the 90% intercept over-estimation phenomenon of Francisco J. Collado’s one-point circular Gaussian fitting practice relative to the experimental flux image. The detailed algorithm for automatically finding out the major/minor axes and the image centre of the digital elliptical flux image is also provided in this paper. SIGMA-2Mean and SIGMA-SqrRMean are equivalent for an elliptical flux image, but they are applied in different ways to figure out either the reasonable intercept factor of the experimental flux image on the physical target plane respecting the aperture region of interest, or the power spillage over the limited experimental target plane. At last, this paper introduces the interpolation reconstruction of an elliptical Gaussian flux image over a rectangular domain just based on the boundary pixel values, so it is quite useful for solar engineering, such as fast simulation of a flux image concentrated by a mirror, and also instant approximation of the flux density over the receiver aperture by the linear array of radiometers around the receiver aperture, when the central receiver system is in the normal working state.     

UNSTEADY HEAT TRANSFER FROM A ROTATING DISK WITH SOLIDIFICATION

Abstract

Unsteady heat transfer from an infinite rotating disk when phase change from liquid to solid occurs is investigated numerically. The moving boundary is fixed for all times by a coordinate transformation, and a finite difference method is used to obtain the instantaneous location of the solid-Uquid interface and the heat transfer from the surfaces of solid and liquid. It is observed that the instantaneous heat flux at the surface of the solid can be obtained with sufficient accuracy by measuring the thickness of the solid, or vice versa, When the Prandtl number is varied, the minimum response time of heat transfer in both solid and liquid phases occurs around Pr = 1.     

区域复杂地形晴日太阳辐射估算研究

为改进复杂地形区区域地表接收太阳入射辐射的算法,基于数字高程模型、气象数据与遥感数据,分直接辐射、来自天空的散射辐射及来自周围地形的反射辐射3部分对海河流域2001—2019年区域地表接收的晴日太阳辐射日总量进行估算与分析。经验证,模拟的晴日太阳入射辐射日通量与实测数据吻合度较高,相关系数约为0.9,区域不同地形接收的太阳入射辐射空间差异明显,结果在可接受精度范围内,此估算方法可为山区太阳能的合理利用提供科学基础。     

Formation of a dry spot in a horizontal liquid film heated from below

This study deals with the formation of a dry spot in a non-boiling thin film of ethanol on a horizontal surface upon slowly increasing the heat flux from an embedded nichrome strip. Appreciable thinning of the film occurred prior to rupture, and is associated with the appearance of Bénard-type convective cells. The threshold heat flux for appearance of a dry spot is greater than for disappearance, presumably due to contact angle hysteresis and/or the temperature gradients in the heater strip in the vicinity of the triple interface. A quasi-static stability analysis is given, based upon the equilibrium shape of a semi-infinite drop on a heated surface.     

风冷汽油机缸盖瞬态传热研究

本文介绍了作者在风冷汽油机上所进行的瞬态温度场测量及用表面温度法理论计算的研究结果。作者选 用的实验机型为１６５Ｆ－Ⅲ型风冷汽油机，通过在其缸盖在布置多支ＴＣＳ－Ｋ型薄膜热电偶，利用自行开发的测量系统，实测了在不同运转工况下的温度场。同时，还研究了沉积物对温度测量的影响。在此基础上，运用表面温度法，进行了局部瞬态换热系数的计算，并对结果进行了理论分析。     

Heat extraction efficiency of a concentric glass tubular evacuated collector

The results of detailed measurements and calculations of the properties of Sydney University/Nitto Kohki evacuated collector tubes have been used to develop a formula for the instantaneous heat extraction efficiency η of a collector panel incorporating the evacuated tubes. The instantaneous efficiency depends on ambient temperature, mean fluid temperature in the collector, solar flux and the design of the manifold used to extract heat from the glass absorber tubes. Manifold design determines the mean temperature difference between absorber tube surface and mean fluid temperature for given operating conditions, and strongly affects the efficiency η of a collector panel. Neither changes in the number of evacuated tubes per unit area of collector, nor variations in solar flux, significantly alter the efficiency decrement Δ η₀ associated with a particular manifold design. Calculated efficiencies agree well with experimental results for collector panels incorporating manifolds of various designs. The formula for efficiency η allows detailed analysis of the relative importance of various energy loss mechanisms in a collector.     

Validation of computer models for predicting radiation levels on tilted surfaces

The purpose of this project was to develop a methodology for the validation of computer models used to predict the instantaneous radiation on a tilted surface, given the similar radiation on the horizontal surface. However, the resulting methodology was also used to evaluate algorithms used to predict horizontal radiation from surface and cloud cover statistics as well as the radiation model used in program SOLCOST⁴ which predicts the expected mean daily total radiation for a specific surface and location using primarily the per cent of possible sunshine value.The validation process is three phased. First, measured data have to be collected and evaluated. If the data are questionable, then so will be the final results. Second, the model logic and assumptions must be discussed. If the model gives very accurate results but is very costly to exercise, then its applicability is limited. Third, the statistics of the model calculations versus measured results must be considered. These depict model behavior and any systematic errors. The model validation methodology is presented and illustrated by analyses of four computer models used to predict instantaneous radiation levels on tilted surfaces.     

Experiments on the influence of intake conditions on local instantaneous heat flux in reciprocating internal combustion engines

The present study tries to be a contribution for the development of more precise theoretical models for predicting the dissipation of heat through the combustion chamber walls of reciprocating (internal combustion) IC engines. A fast response thermocouple was embedded in the combustion chamber of a single cylinder engine to measure instantaneous wall temperatures. The heat flux was obtained by solving the one-dimensional transient energy equation with transient boundary conditions using the Fast Fourier Transform. The engine was tested under different operating conditions to evaluate the sensitivity of the measurement procedure to variations of three relevant combustion parameters: injection pressure, air temperature and oxygen concentration at the intake. The local heat flux obtained was compared with other relevant parameters that characterize the thermal behaviour of engines, showing, in most of the cases, correlation among them. The results showed that the instantaneous heat flux through the walls and hence the local wall temperatures are strongly affected by the ignition delay and the start of combustion.     

THE EFFECT OF HEAT FLUX DISTRIBUTION ON THERMOCAPILLARY CONVECTION IN A SIDE-HEATED LIQUID BRIDGE

A numerical analysis is performed on thermocapillary convection in a liquid bridge. The effect of various imposed heat flux distributions on the free surface for axisymmetric liquid bridge flows, in zero gravity, is presented. Constant, polynomial, and different Gaussian profiles are considered, and the resulting velocity and temperature fields are compared. It is shown that a more concentrated heat flux distribution has a significant effect on the hydrodynamics of the liquid bridge. The transition from steady to unsteady flows also depends on the distribution of applied heat flux. The frequency of the oscillation increases with Ma increase.     

A graph-based approach to developing adaptive representations of complex reaction mechanisms

An effective adaptive mechanism reduction approach based on flux graph clustering is proposed in this paper. The instantaneous element flux is quantified and considered as a proxy for describing the reactive propensities of the system. Our underlying hypothesis is that even though particular conditions may be characterized by a multitude of combinations of species mass fraction, T, and P, the essential chemistry, and hence the reaction propensity of the mixture that is active under this family of conditions, is the same. Therefore, we opt to use the instantaneous fluxes through the active reactions as an intrinsic property of the system. Flux graphs are first constructed for the chemical reaction system under numerous conditions aiming at capturing the attainable region. Similarity between flux graphs is quantified through the distances between corresponding vectors, using the cosine coefficient and a novel graph-distance metric taking into account the magnitude of each flux and the activity distribution of different fluxes. A hierarchical clustering algorithm is implemented to group similar instantaneous flux graphs into clusters, and consequently a reduced mechanism is generated for each cluster. A search algorithm is defined afterward to assign a new query point to a particular flux graph cluster, and subsequently the reduced mechanism associated with this cluster is used to describe the system at this time point. Finally, the methodology is demonstrated using n-pentane combustion in an adiabatic plug flow reactor model and a pairwise mixing stirred reactor model.     

Scalar transport in a quasi two-dimensional turbulent wake interacting with a boundary layer

An experimental study of heat transport in the interaction region between the wake of a cylinder and a turbulent boundary layer is presented in this work. The cylinder was placed parallel to a flat plate and normal to the flow. Its position was selected above the boundary layer edge, so that the lower part of the wake was interacting with the boundary layer. Heat was supplied to the boundary layer flow by means of a line heat source. Presence of surface roughness on the cylinder resulted in the deviation of the velocity power spectrum scaling region from the −5/3 power law which is characteristic of three-dimensional turbulence. Point measurements of the instantaneous values of two velocity components and temperature have been taken using hot-wire anemometry. Two turbulent scalar flux components and a Reynolds shear stress component have been obtained directly from the experimental data. Results were assessed in conjunction with the periodic coherent structures in the wake (a von Kármán vortex street) using a phase-averaging technique that provided a clear picture of the heat transport procedures involved.