Nondegeneracy of optimality conditions in control problems for a radiative–conductive heat transfer model

This paper presents results of numerical simulations of various processes that demonstrate phase change heat transfer at high heat fluxes using the level-set method. The model used for the purpose has been first validated for the growth of an evaporating bubble in infinite medium, and fim boiling in 2D and 3D. It has then been applied to simulate the nucleation and departure of a single bubble from a solid body subject to conductive heat transfer. Unlike our previous investigations where phase change induced evaporation rate was incorporated like a sub-grid scale heat transfer model applied to the triple contact line, the present work reports simulations with direct phase change modelling by integrating energy fluxes at the interface. The effect of the conductive heat transfer in the solid from which the bubble departs is also taken into account. Comparison with visual images suggests that accounting for conjugate heat transfer is important to capturing micro-hydrodynamics in nucleate boiling, at least qualitatively.

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How Does Concrete Affect Evaporation of Cryogenic Liquids: Evaluating Liquefied Natural Gas Plant Safety

ASCE-ASME J Risk and Uncert in Engrg Sys Part B Mech Engrg ◽

10.1115/1.4030947 ◽

2015 ◽

Vol 2 (1) ◽

Author(s):

Alfonso Ibarreta ◽

Ryan J. Hart ◽

Nicolas Ponchaut ◽

Delmar “Trey” Morrison ◽

Harri Kytömaa

Keyword(s):

Heat Transfer ◽

Natural Gas ◽

Evaporation Rate ◽

The United States ◽

Cryogenic Liquid ◽

Liquefied Natural Gas ◽

Conductive Heat Transfer ◽

Transfer Model ◽

Conductive Heat ◽

Substrate Properties

With the impending natural gas boom in the United States, many companies are pursuing Department of Energy (DOE) approval for exporting liquefied natural gas (LNG), which is a cryogenic liquid. The next decade also promises to demonstrate growth in LNG-fueled fleets of vehicles and marine vessels, as well as growth in other natural gas uses. The future expansion in the LNG infrastructure will lead to an increased focus on managing the risks associated with spills of LNG. Risk analysis involving LNG spill scenarios and their consequences requires determining the size of resulting ignitable flammable vapor clouds. This in turn depends strongly on the rate of evaporation of the spilled LNG. The evaporation of a cryogenic LNG spill (and thus the flammable vapor cloud hazard) can be quite a complex process, and it is primarily controlled by the rate of spreading of the pool and by the transient conductive heat transfer from the ground to the spilled liquid. Radiative and convective heat transfer are also present, but the conductive heat transfer rate dominates in the evaporation of a cryogenic liquid spilled into a trench or sump initially at ambient temperature. The time-dependent evaporation rate can be calculated using a variety of models, such as the built-in model in PHAST Det Norske Veritas (DNV) or other proprietary models that account for pool spreading, heat conduction within the substrate, and phase change. Trenches and sumps used to contain LNG spills are normally lined with various types of concrete, including insulated or aerated concrete. The authors have found that for a cryogenic liquid, the choice of thermal properties for concrete can greatly affect the source term. This paper presents a sensitivity study of the effects of substrate properties on the evaporation rate of LNG. The study will look at the dependence for a range of sump diameters. The PHAST model results will be compared to results obtained using an in-house shallow water equation (SWE) liquid propagation and heat transfer model. The results of the paper will provide guidance for the selection of substrate properties during modeling as well as a comparison of the relative evaporation rates expected for different surfaces, such as regular concrete and insulated concrete.

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How Does Concrete Affect Evaporation of Cryogenic Liquids: Evaluating LNG Plant Safety

Volume 15: Safety, Reliability and Risk; Virtual Podium (Posters) ◽

10.1115/imece2013-65318 ◽

2013 ◽

Author(s):

Alfonso Ibarreta ◽

Ryan J. Hart ◽

Nicolas Ponchaut ◽

Delmar (Trey) Morrison ◽

Harri Kytömaa

Keyword(s):

Heat Transfer ◽

Natural Gas ◽

Evaporation Rate ◽

Shallow Water Equation ◽

Sensitivity Study ◽

Cryogenic Liquid ◽

Conductive Heat Transfer ◽

Transfer Model ◽

Conductive Heat ◽

Substrate Properties

With the impending natural gas boom in the U.S., many companies are pursuing DOE approval for exporting liquefied natural gas (LNG), which is a cryogenic liquid. The next decade also promises to demonstrate growth in LNG-fueled fleets of vehicles and marine vessels, as well as growth in other natural gas uses. The future expansion in the LNG infrastructure will lead to an increased focus on managing the risks associated with spills of LNG. Risk analysis involving LNG spill scenarios and their consequences requires the determination of the size of resulting ignitable flammable vapor clouds. This in turn depends strongly on the rate of evaporation of the spilled LNG. The evaporation of a cryogenic LNG spill (and thus the flammable vapor cloud hazard) can be quite a complex process, and it is primarily controlled by the rate of spreading of the pool and by the transient conductive heat transfer from the ground to the spilled liquid. Radiative and convective heat transfer are also present, but the conductive heat transfer rate dominates in the evaporation of a cryogenic liquid spilled into a trench or sump initially at ambient temperature. The time dependent evaporation rate can be calculated using a variety of models, such as the built-in model in PHAST (DNV) or other proprietary models that account for pool spreading, heat conduction within the substrate, and phase change. Trenches and sumps used to contain LNG spills are normally lined with various types of concrete, including insulated or aerated concrete. We have found that for a cryogenic liquid, the choice of thermal properties for concrete can greatly affect the source term. In this work, we perform a sensitivity study of the effects of substrate properties on the evaporation rate of LNG. The study will look at the dependence for a range of sump diameters. The PHAST model results will be compared to results obtained using an in-house Shallow Water Equation (SWE) liquid propagation and heat transfer model. The results of this work will provide guidance for the selection of substrate properties during modeling; as well as a comparison of the relative evaporation rates expected for different surfaces, such as regular concrete and insulated concrete.

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A Heat Transfer Model to Predict Temperature Distribution in Stored Wheat

Journal of Agricultural and Marine Sciences [JAMS] ◽

10.24200/jams.vol5iss2pp85-90 ◽

2000 ◽

Vol 5 (2) ◽

pp. 85

Author(s):

A.M.S. AI-Amri ◽

S.K. Abbouda

Keyword(s):

Heat Transfer ◽

Initial Moisture Content ◽

Ambient Air ◽

Storage Conditions ◽

Heat Transfer Model ◽

Weather Data ◽

Transfer Model ◽

Conductive Heat ◽

Stored Wheat ◽

Grain Temperature

The combined convective and conductive heat transfer model which previously developed by Abbouda er al. (1992) was applied in this study to simulate the temperatures of wheat grain during storage process using input data of initial grain temperatures, ambient air temperatures, wind speeds and thermal properties of grain, bin structure and soil. The local weather data used in the model were obtained from the meteorological station of King Faisal University at Al-Ahsa Province of Saudi Arabia. Experimental data showed that, bin size and initial moisture content affected the grain temperature differences between the top surface and the bottom of the bin. The average grain temperature followed the trend of the ambient air temperature with a time delay. Predicted and measured grain temperatures were in close agreement for a test period of one year. Results indicated that the model and the parameter values used in the model are applicable for predicting temperature of stored wheat under static storage conditions.

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Numerical Study of the Thermal Model on High Uniformity Temperature Test Platform

MATEC Web of Conferences ◽

10.1051/matecconf/201925603003 ◽

2019 ◽

Vol 256 ◽

pp. 03003

Author(s):

Zijuan Wang ◽

Ying Zhou ◽

Han Xiao ◽

Shao Jingyi

Keyword(s):

Heat Transfer ◽

Surface Temperature ◽

Numerical Study ◽

Radiation Heat Transfer ◽

Heat Transfer Model ◽

Transfer Model ◽

Conductive Heat ◽

Temperature Uniformity ◽

Test Platform ◽

Background Temperature

The surface temperature uniformity of a test platform with an effective test area of 600 mm × 600 mm was numerically studied. The conductive heat transfer model for the test platform and the device under test (DUT) installed on the surface was established in the present work, as well as the radiation heat transfer model from the platform surface to the background temperature. The platform surface was divided into 5 or 9 regions where heated independently to make the surface temperature consistent. The temperature uniformity of these two partition designs was compared. The result shows that the 9 regions design has higher temperature uniformity at both target temperatures of -10°C and +45°C.

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Modelling and Simulation Heat Transfer in Wheat Stored in a Simulated Sealed Pit

International Journal of Food Engineering ◽

10.1515/1556-3758.1308 ◽

2012 ◽

Vol 8 (4) ◽

Author(s):

Brian C. Stenning

Keyword(s):

Heat Transfer ◽

Finite Difference ◽

Input Data ◽

Storage Period ◽

Conductive Heat Transfer ◽

Wall Material ◽

Transfer Model ◽

Conductive Heat ◽

Short Period ◽

Grain Temperature

Abstract A mathematical model was developed to predict the change of temperature distribution with time in the radial and axial directions in a simulated sealed cylindrical pit. The finite difference method was used in the model to calculate the conductive heat transfer. The model can predict the grain temperatures in the pit during the storage period using input data of initial grain temperature, storage time and number of spatial elements in both radial and axial directions. Other input data include the finite difference spatial increment in both directions, the finite time increment, temperatures of soil surrounding the pit and the physical properties of grain, pit wall material and surrounding soil. To validate the model, predicted temperatures were compared with measured data for wheat of Apollo variety being stored in a simulated sealed pit for a period of 70 days. The wheat was stored in a cylindrical mild steel tank with 0.6 m in both diameter and height. The initial grain temperature was 15°C. Both measured and predicted wheat temperatures attained equilibrium state within a short period of storage (2 to 6 days) and the equilibrium was maintained throughout the experiment period. The conductive heat transfer model predicted the grain temperatures accurately and within the bounds of the experimental error. The standard error of estimate between measured and predicted was 0.12°C -0.25°C.

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