The Vaporization-Condensation Phenomenon in a Linear Heat Wave

1964 ◽  
Vol 4 (02) ◽  
pp. 85-95 ◽  
Author(s):  
Chieh Chu
Keyword(s):  
Liquid Phase ◽  
Temperature Profile ◽  
Gas Phase ◽  
Heat Wave ◽  
Combustion Front ◽  
Wave Process ◽  
Leading Edge ◽  
One Dimensional ◽  
Linear Heat ◽  
Condensation Phenomenon

Chu, Chieh, Member AIME, Sinclair Research, Inc., Tulsa, Okla. Abstract A theoretical investigation has been made of the forward combustion process using a one-dimensional linear mathematical model, taking into consideration the effect of the vaporization-condensation which occurs on the leading edge of the heat wave. This work involves the solution of five coupled partial differential equations. Besides the vaporization-condensation phenomenon, these equations account for conduction, convection, combustion, heat loss, diffusion and bulk fluid flow. For the one-dimensional linear model studied, the vaporization-condensation phenomenon does not induce appreciable change in the temperature at the combustion front; and its primary effect is to create a steam plateau and to increase the length of the heated zone ahead of the combustion front. This effect becomes more pronounced at lower pressures, higher porosities or reduced gas saturations. The peak temperature and the temperature profile on the leading edge of the heat wave stabilize after a certain period. The length of the steam bank remains practically constant, although the length of the water bank increases as the heat wave advances. Introduction The existence of the vaporization-condensation phenomenon in the heat-wave process and the important role played by the phenomenon have been recognized by several investigators. Kuhn and Koch stated that steam plateaus were frequently observed on the temperature records of their experiments. The steam plateaus were attributed primarily to the vaporization and subsequent condensation of the interstitial water existing in the oil sand. Szasz suggested that both lighter hydrocarbons and water are vaporized on the leading edge of the heat wave, carried forward in the gas stream, and then condensed to create banks of oil and water. Martin et al. suggested that the vaporization- condensation phenomenon is one of the main mechanisms of the heat-wave process, along with thermal expansion and viscosity reduction. Wilson et al. reported the existence of a steam plateau several inches in length in their small-scale tube-run experiments. However, this important phenomenon has never been taken into consideration in the numerous theoretical analyses by various authors. The purpose of this work was to study the thermal aspects of a linear heat wave, taking into consideration the vaporization- condensation on the leading edge of the wave, to determine the effect of this phenomenon on the temperature profile of the reservoir, and to investigate how this effect varies when other process variables are changed. THEORY We consider a reservoir of porous medium of cross-sectional area A, extending from x=0 to x=L. This reservoir contains, aside from the solid matrix itself, a gas phase and a "combined liquid phase" which is a combination of two immiscible liquid phases - namely, an oil phase and a water phase. The oil present in the reservoir is assumed to consist of three fractions, a noncondensable gas, a nondistillable residuum, and a vaporizable oil fraction which may be present in both the gas phase and liquid phase. Before the heat-wave process begins, preheating has taken place and has imparted an initial temperature distribution To(x) to the reservoir, At the start of the process, a stream of oxygen-bearing gas is introduced through the face at x=0. This gas supports the combustion of the residual fuel and supplies the heat throughout the process. SPEJ P. 85ˆ

Temperature Predictions and Comparison With Measurements for the Blade Leading Edge and Platform of a 1-1/2 Stage Transonic HP Turbine

2010 ◽  
Author(s):  
R. M. Mathison ◽  
M. B. Wishart ◽  
C. W. Haldeman ◽  
M. G. Dunn
Keyword(s):  
Boundary Condition ◽  
Temperature Profile ◽  
Short Duration ◽  
Computational Models ◽  
Current Model ◽  
Leading Edge ◽  
Inlet Temperature ◽  
Fluid Temperature ◽  
One Dimensional ◽  
Blade Leading Edge

A series of computational predictions generated using FINE/Turbo are compared with data to investigate implementation techniques available for predicting temperature migration through a turbine stage. The experimental results used for comparison are from a one-and-one-half stage turbine operating at design-corrected conditions in a short-duration facility. Measurements of the boundary conditions are used to set up the computational models, and the predicted temperatures are compared to measured fluid temperatures at the blade leading edge and just above the blade platform. Fluid temperature measurements have not previously been available for these locations in a transonic turbine operating at design-corrected conditions, so this represents a novel comparison. Accurate predictions for this short-duration turbine experiment require use of the iso-thermal wall boundary condition instead of an adiabatic boundary condition and accurate specification of the inlet temperature profile all the way to the wall. Predictions using the harmonic method agree with the temperatures measured for the blade leading edge from 65% to 95% span to within 1% normalized temperature data. Agreement over much of the rest of the leading edge is within 5% of the measured value. Comparisons at 5–10% span and for the blade platform show larger differences up to 10%, which indicates that the flow in this region is not fully captured by the prediction. This is not surprising since the purge cavity and platform leading edge features present in the experiment are treated as a smooth hub wall in the current simulation. This work represents a step towards the larger goal of accurately predicting surface heat-flux for the complicated environment of an operational engine as it is reproduced in a laboratory setting. The experiment upon which these computations are based includes realistic complications such as one-dimensional and two-dimensional inlet temperature profiles, a heavily film-cooled vane, and purge cooling. While the ultimate goal is to accurately handle all of these features, the current model focuses on the treatment of a subset of experiments performed for a one-dimensional radial inlet temperature profile and no cooling.

Temperature Predictions and Comparison With Measurements for the Blade Leading Edge and Platform of a 1 1/2 Stage Transonic HP Turbine

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Randall M. Mathison ◽  
Mark B. Wishart ◽  
Charles W. Haldeman ◽  
Michael G. Dunn
Keyword(s):  
Boundary Condition ◽  
Temperature Profile ◽  
Short Duration ◽  
Computational Models ◽  
Current Model ◽  
Leading Edge ◽  
Inlet Temperature ◽  
Fluid Temperature ◽  
One Dimensional ◽  
Blade Leading Edge

A series of computational predictions generated using FINE/TURBO are compared with data to investigate implementation techniques available for predicting temperature migration through a turbine stage. The experimental results used for comparison are from a one-and-one-half stage turbine operating at design-corrected conditions in a short-duration facility. Measurements of the boundary conditions are used to set up the computational models, and the predicted temperatures are compared with measured fluid temperatures at the blade leading edge and just above the blade platform. Fluid temperature measurements have not previously been available for these locations in a transonic turbine operating at design-corrected conditions, so this represents a novel comparison. Accurate predictions for this short-duration turbine experiment require use of the isothermal wall boundary condition instead of an adiabatic boundary condition and accurate specification of the inlet temperature profile all the way to the wall. Predictions using the harmonic method agree with the temperatures measured for the blade leading edge from 65% to 95% span to within 1% normalized temperature data. Agreement over much of the rest of the leading edge is within 5% of the measured value. Comparisons at 5–10% span and for the blade platform show larger differences up to 10%, which indicates that the flow in this region is not fully captured by the prediction. This is not surprising since the purge cavity and platform leading-edge features present in the experiment are treated as a smooth hub wall in the current simulation. This work represents a step toward the larger goal of accurately predicting surface heat-flux for the complicated environment of an operational engine as it is reproduced in a laboratory setting. The experiment upon which these computations are based includes realistic complications such as one-dimensional and two-dimensional inlet temperature profiles, a heavily film-cooled vane, and purge cooling. While the ultimate goal is to accurately handle all of these features, the current model focuses on the treatment of a subset of experiments performed for a one-dimensional radial inlet temperature profile and no cooling.

One-Dimensional Contact Pressure Distribution of Radial Tires in Motion

1995 ◽  
Vol 23 (2) ◽  
pp. 116-135 ◽  
Author(s):  
H. Shiobara ◽  
T. Akasaka ◽  
S. Kagami ◽  
S. Tsutsumi
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Experimental Studies ◽  
Rolling Resistance ◽  
Leading Edge ◽  
Forward Direction ◽  
Contact Pressure Distribution ◽  
Support Ring ◽  
One Dimensional ◽  
Lowered Pressure

Abstract The contact pressure distribution and the rolling resistance of a running radial tire under load are fundamental properties of the tire construction, important to the steering performance of automobiles, as is well known. Many theoretical and experimental studies have been previously published on these tire properties. However, the relationships between tire performances in service and tire structural properties have not been clarified sufficiently due to analytical and experimental difficulties. In this paper, establishing a spring support ring model made of a composite belt ring and a Voigt type viscoelastic spring system of the sidewall and the tread rubber, we analyze the one-dimensional contact pressure distribution of a running tire at speeds of up to 60 km/h. The predicted distribution of the contact pressure under appropriate values of damping coefficients of rubber is shown to be in good agreement with experimental results. It is confirmed by this study that increasing velocity causes the pressure to rise at the leading edge of the contact patch, accompanied by the lowered pressure at the trailing edge, and further a slight movement of the contact area in the forward direction.

Application of Disk Aerators to Recarbonation of Alkaline Wastewater from Wet Gasification of Carbide

1991 ◽  
Vol 24 (7) ◽  
pp. 277-284 ◽  
Author(s):  
E. Gomólka ◽  
B. Gomólka
Keyword(s):  
Carbon Dioxide ◽  
Liquid Phase ◽  
Gas Phase ◽  
Flue Gas ◽  
Carbonic Acid ◽  
Low Cost ◽  
Flue Gases ◽  
Carbon Dioxide Content ◽  
Patent Claim ◽  
Phase Dispersion

Whenever possible, neutralization of alkaline wastewater should involve low-cost acid. It is conventional to make use of carbonic acid produced via the reaction of carbon dioxide (contained in flue gases) with water according to the following equation: Carbon dioxide content in the flue gas stream varies from 10% to 15%. The flue gas stream may either be passed to the wastewater contained in the recarbonizers, or. enter the scrubbers (which are continually sprayed with wastewater) from the bottom in oountercurrent. The reactors, in which recarbonation occurs, have the ability to expand the contact surface between gaseous and liquid phase. This can be achieved by gas phase dispersion in the liquid phase (bubbling), by liquid phase dispersion in the gas phase (spraying), or by bubbling and spraying, and mixing. These concurrent operations are carried out during motion of the disk aerator (which is a patent claim). The authors describe the functioning of the disk aerator, the composition of the wastewater produced during wet gasification of carbide, the chemistry of recarbonation and decarbonation, and the concept of applying the disk aerator so as to make the wastewater fit for reuse (after suitable neutralization) as feeding water in acetylene generators.

Modeling of aerated upflow fixed bed reactors for nitrification

1999 ◽  
Vol 39 (4) ◽  
pp. 85-92 ◽  
Author(s):  
J. Behrendt
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Liquid Phase ◽  
Gas Phase ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Bulk Liquid ◽  
Initial Value ◽  
Fixed Bed Reactors ◽  
Number Of Cells

A mathematical model for nitrification in an aerated fixed bed reactor has been developed. This model is based on material balances in the bulk liquid, gas phase and in the biofilm area. The fixed bed is divided into a number of cells according to the reduced remixing behaviour. A fixed bed cell consists of 4 compartments: the support, the gas phase, the bulk liquid phase and the stagnant volume containing the biofilm. In the stagnant volume the biological transmutation of the ammonia is located. The transport phenomena are modelled with mass transfer formulations so that the balances could be formulated as an initial value problem. The results of the simulation and experiments are compared.

Theoretical analysis of counter-current absorption of a poorly soluble gas based on the PDE-AD model

1986 ◽  
Vol 51 (6) ◽  
pp. 1222-1239 ◽  
Author(s):  
Pavel Moravec ◽  
Vladimír Staněk
Keyword(s):  
Experimental Data ◽  
Liquid Phase ◽  
Gas Phase ◽  
Transfer Functions ◽  
Packed Bed ◽  
Packed Bed Column ◽  
Interfacial Transport ◽  
Gaseous Component ◽  
Poorly Soluble ◽  
Counter Current

Expression have been derived in the paper for all four possible transfer functions between the inlet and the outlet gas and liquid steams under the counter-current absorption of a poorly soluble gas in a packed bed column. The transfer functions have been derived for the axially dispersed model with stagnant zone in the liquid phase and the axially dispersed model for the gas phase with interfacial transport of a gaseous component (PDE - AD). calculations with practical values of parameters suggest that only two of these transfer functions are applicable for experimental data evaluation.

Reesterification of ethyl acetate by propanol catalysed by glycidyl methacrylate copolymers containing sulphonic acid groups

1981 ◽  
Vol 46 (8) ◽  
pp. 1941-1946 ◽  
Author(s):  
Karel Setínek
Keyword(s):  
Liquid Phase ◽  
Ethyl Acetate ◽  
Kinetic Study ◽  
Gas Phase ◽  
Nonlinear Regression ◽  
Kinetic Data ◽  
Glycidyl Methacrylate ◽  
Kinetic Equations ◽  
Methacrylate Copolymers ◽  
Styrene Divinylbenzene

A series of differently crosslinked macroporous 2,3-epoxypropyl methacrylate-ethylenedimethacrylate copolymers with chemically bonded propylsulphonic acid groups were used as catalysts for the kinetic study of reesterification of ethyl acetate by n-propanol in the liquid phase at 52 °C and in the gas phase at 90 °C. Analysis of kinetic data by the method of nonlinear regression for a series of equations of the Langmuir-Hinshelwood type showed that kinetic equations which describe best the course of the reaction are the same as for the earlier studied sulphonated macroporous styrene-divinylbenzene copolymers. Compared types of catalysts differ, however, in the dependence of their activity on the degree of crosslinking of the copolymer used.

Radiolysis of methylcyclopentane. III. Liquid phase mechanism and comparison of cycloalkanes

1968 ◽  
Vol 46 (20) ◽  
pp. 3235-3240 ◽  
Author(s):  
Gordon R. Freeman ◽  
E. Diane Stover
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Bond Cleavage ◽  
Open Chain ◽  
Methyl Substitution ◽  
Product Yields ◽  
Total Ionization ◽  
Gamma Radiolysis ◽  
G Value

The initial yields of the major products of the gamma radiolysis of liquid methylcyclopentane (MCP) at 25° are: G(H2) = 4.2, G(1-methylcyclopentene plus methylenecyclopentane) = 2.7, G(3- plus 4-methyl-cyclopentene) = 1.0, G(open chain hexene) = 1.0, and G(bimethylcyclopentyl) = 0.9. The effects of scavengers on the product yields are reported and the mechanism is discussed.The liquid phase radiolytic decompositions of cyclohexane (CH), methylcyclohexane (MCH), cyclopentane (CP), and MCP are compared. The net amount of C—C bond cleavage is much greater in the five-membered than in the six-membered rings. Methyl substitution on the ring reduces G(H2) by about one unit, mainly because of the formation of a type of ion (QH+) that does not yield hydrogen when neutralized by an electron. The QH+ type ions are formed in MCH and MCP, but not in CH and CP. In all the systems, another type of ion (N+) that does not yield hydrogen when neutralized by an electron is formed with a G value of about unity. The type of ion (PH+) that does yield hydrogen when neutralized by an electron has a G value of 3.4 in CH and CP, but only 2.0 in MCP. It is concluded that G(total ionization) is in the vicinity of 4.4 in the liquid compounds, virtually the same as the gas phase values.

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