Solution of the Radiative Integral Transfer Equations in Rectangular Absorbing, Emitting, and Anisotropically Scattering Homogeneous Medium

2004 ◽  
Vol 126 (1) ◽  
pp. 137-140 ◽  
Author(s):  
Zekeriya Altac¸ ◽  
Mesut Tekkalmaz

Radiative integral transfer equations for a rectangular absorbing, non-emitting, and linearly anisotropically scattering homogeneous medium are solved numerically for the incident energy and the net heat flux components using the method of “singularity subtraction.” A benchmark problem is chosen as a rectangular homogeneous cold participating medium which is subject to externally uniform diffuse radiation on the bottom wall. The solutions for the incident energy and net heat flux components for selected points for a square domain are provided in tabular form for benchmarking purposes.

2020 ◽  
Vol 55 (4) ◽  
pp. 477-493
Author(s):  
Gyundo Pak ◽  
Jae-Hyoung Park ◽  
Seok-Joon Lee ◽  
Young-Gyu Park ◽  
You-Soon Chang

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
James D. Heidmann ◽  
Srinath Ekkad

A novel turbine film-cooling hole shape has been conceived and designed at NASA Glenn Research Center. This “antivortex” design is unique in that it requires only easily machinable round holes, unlike shaped film-cooling holes and other advanced concepts. The hole design is intended to counteract the detrimental vorticity associated with standard circular cross-section film-cooling holes. This vorticity typically entrains hot freestream gas and is associated with jet separation from the turbine blade surface. The antivortex film-cooling hole concept has been modeled computationally for a single row of 30 deg angled holes on a flat surface using the 3D Navier–Stokes solver GLENN-HT. A blowing ratio of 1.0 and density ratios of 1.05 and 2.0 are studied. Both film effectiveness and heat transfer coefficient values are computed and compared to standard round hole cases for the same blowing rates. A net heat flux reduction is also determined using both the film effectiveness and heat transfer coefficient values to ascertain the overall effectiveness of the concept. An improvement in film effectiveness of about 0.2 and in net heat flux reduction of about 0.2 is demonstrated for the antivortex concept compared to the standard round hole for both blowing ratios. Detailed flow visualization shows that as expected, the design counteracts the detrimental vorticity of the round hole flow, allowing it to remain attached to the surface.


Author(s):  
Chia Hui Lim ◽  
Graham Pullan ◽  
Peter Ireland

Turbine design engineers have to ensure that film cooling can provide sufficient protection to turbine blades from the hot mainstream gas, while keeping the losses low. Film cooling hole design parameters include inclination angle (α), compound angle (β), hole inlet geometry and hole exit geometry. The influence of these parameters on aerodynamic loss and net heat flux reduction is investigated, with loss being the primary focus. Low-speed flat plate experiments have been conducted at momentum flux ratios of IR = 0.16, 0.64 and 1.44. The film cooling aerodynamic mixing loss, generated by the mixing of mainstream and coolant, can be quantified using a three-dimensional analytical model that has been previously reported by the authors. The model suggests that for the same flow conditions, the aerodynamic mixing loss is the same for holes with different α and β but with the same angle between the mainstream and coolant flow directions (angle κ). This relationship is assessed through experiments by testing two sets of cylindrical holes with different α and β: one set with κ = 35°, another set with κ = 60°. The data confirm the stated relationship between α, β, κ and the aerodynamic mixing loss. The results show that the designer should minimise κ to obtain the lowest loss, but maximise β to achieve the best heat transfer performance. A suggestion on improving the loss model is also given. Five different hole geometries (α = 35.0°, β = 0°) were also tested: cylindrical hole, trenched hole, fan-shaped hole, D-Fan and SD-Fan. The D-Fan and the SD-Fan have similar hole exits to the fan-shaped hole but their hole inlets are laterally expanded. The external mixing loss and the loss generated inside the hole are compared. It was found that the D-Fan and the SD-Fan have the lowest loss. This is attributed to their laterally expanded hole inlets, which lead to significant reduction in the loss generated inside the holes. As a result, the loss of these geometries is ≈ 50% of the loss of the fan-shaped hole at IR = 0.64 and 1.44.


Author(s):  
Yu Zou ◽  
Xiulan Huai ◽  
Fang Xin ◽  
Zhixiong Guo

Molecular dynamics simulations are carried out to study the thermal and mechanical phenomena of ultra-high heat flux conduction induced by ultrafast laser heating in thin Si films. Nanoscale Si films with various depths in heat flux direction are treated as a semi-infinite model for the study of ultrafast heat conduction. A distribution of internal heat source is applied to simulate the absorption of the laser energy in films and the induced temperature distribution. Stress distribution and the evolution of the displacement are calculated. Thermal waves are observed from the development of temperature distribution in the heat flux direction, though the average temperature of the simulated Si films increases monotonically. The average stress shows periodic oscillations. The time development of strain has the same trend as the average stress, and the net heat flux shows the same trend as the stress at different depths of the Si films in the direction of heat flux. This reveals a close relationship between stress and net heat flux in the Si films in the process of ultrafast laser heating.


2007 ◽  
Vol 20 (13) ◽  
pp. 3190-3209 ◽  
Author(s):  
Lisan Yu ◽  
Xiangze Jin ◽  
Robert A. Weller

Abstract This study investigated the accuracy and physical representation of air–sea surface heat flux estimates for the Indian Ocean on annual, seasonal, and interannual time scales. Six heat flux products were analyzed, including the newly developed latent and sensible heat fluxes from the Objectively Analyzed Air–Sea Heat Fluxes (OAFlux) project and net shortwave and longwave radiation results from the International Satellite Cloud Climatology Project (ISCCP), the heat flux analysis from the Southampton Oceanography Centre (SOC), the National Centers for Environmental Prediction reanalysis 1 (NCEP1) and reanalysis-2 (NCEP2) datasets, and the European Centre for Medium-Range Weather Forecasts operational (ECMWF-OP) and 40-yr Re-Analysis (ERA-40) products. This paper presents the analysis of the six products in depicting the mean, the seasonal cycle, and the interannual variability of the net heat flux into the ocean. Two time series of in situ flux measurements, one taken from a 1-yr Arabian Sea Experiment field program and the other from a 1-month Joint Air–Sea Monsoon Interaction Experiment (JASMINE) field program in the Bay of Bengal were used to evaluate the statistical properties of the flux products over the measurement periods. The consistency between the six products on seasonal and interannual time scales was investigated using a standard deviation analysis and a physically based correlation analysis. The study has three findings. First of all, large differences exist in the mean value of the six heat flux products. Part of the differences may be attributable to the bias in the numerical weather prediction (NWP) models that underestimates the net heat flux into the Indian Ocean. Along the JASMINE ship tracks, the four NWP modeled mean fluxes all have a sign opposite to the observations, with NCEP1 being underestimated by 53 W m−2 (the least biased) and ECMWF-OP by 108 W m−2 (the most biased). At the Arabian Sea buoy site, the NWP mean fluxes also have an underestimation bias, with the smallest bias of 26 W m−2 (ERA-40) and the largest bias of 69 W m−2 (NCEP1). On the other hand, the OAFlux+ISCCP has the best comparison at both measurement sites. Second, the bias effect changes with the time scale. Despite the fact that the mean is biased significantly, there is no major bias in the seasonal cycle of all the products except for ECMWF-OP. The latter does not have a fixed mean due to the frequent updates of the model platform. Finally, among the four products (OAFlux+ISCCP, ERA-40, NCEP1, and NCEP2) that can be used for studying interannual variability, OAFlux+ISCCP and ERA-40 Qnet have good consistency as judged from both statistical and physical measures. NCEP1 shows broad agreement with the two products, with varying details. By comparison, NCEP2 is the least representative of the Qnet variabilities over the basin scale.


2012 ◽  
Vol 249-250 ◽  
pp. 443-451
Author(s):  
Jing Zhou Zhang ◽  
Xiao Ming Tan ◽  
Xing Dan Zhu

A three-dimensional numerical study on the flow and heat transfer characteristics over a rotating disk with bottom wall subjected to uniform heat flux was conducted with the use of RNG k- turbulent model. And some experiments were also made for validation. The effects of rotating angular speed and pin configuration on the temperature maps and convective heat transfer characte-ristics on rotating surface are analyzed. As the increase of rotating velocity, the impingement of pumping jet on the centre of rotating disk became stronger and the transition from laminar to turbu-lent occurred at the outer radius of rotating disk, which resulted in heat transfer enhancement. The pins on the disk made the pumping action of a rotating disk weaker. Simultaneously, they also acted as disturbing elements to the cyclone flow near the rotating disk surface, which made the overall heat transfer to be enhanced. Under the same extend areas of different pins, needle pin has higher convective heat transfer capacity than the discrete ring pin.


1995 ◽  
Vol 13 (10) ◽  
pp. 1047-1053 ◽  
Author(s):  
N. C. Wells

Abstract. Estimates of the components of the surface heat flux in the Western Equatorial Pacific Ocean are presented for a 22-day period, together with a critical analysis of the errors. It is shown that the errors in latent heat, and solar and longwave radiation fluxes, dominate the net heat flux for this period. It is found that the net heat flux into the ocean over the 22-day period is not significantly different from zero. It is also demonstrated that because of the variability in daily averaged values of solar radiation and the latent heat of evaporation, a large number of independent flux measurements will be required to determine with confidence the climatological net heat flux in this region. The variability of latent fluxes over the 22-day period suggest that climatological estimates based on monthly mean observations may lead to a significant underestimate of the latent heat flux.


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