CHF for Uniformly Heated Vertical Tube Under High Pressure Conditions

2002 ◽  
Author(s):  
W. Jaewoo Shim ◽  
Joo-Yong Park
Keyword(s):  
High Pressure ◽  
Mass Flux ◽  
Flow Instability ◽  
Vertical Tube ◽  
Average Error ◽  
New Correlation ◽  
Data Points ◽  
Parameter Ranges ◽  
Two Parameters ◽  
True Mass

In this study, a total of 2,870 high pressure (70 bar ≤ P ≤ 206 bar) data points of critical heat flux (CHF) in uniformly heated round vertical tube for water were collected from 5 different published sources. The data consisted of following parameter ranges: 28.07 ≤ G (mass flux) ≤ 10,565.03 kg/m2s, 1.91 ≤ D (diameter) ≤44.68 mm, 40 ≤L (length) ≤4966 mm, 0.14 ≤qc (CHF) ≤ 9.94 MW/m2, and −0.85 ≤X (exit qualities) ≤ 1.22. With these data a comparative analysis is made on available correlations, and a new correlation is presented. The new high pressure CHF correlation, as in the low and medium pressure cases of earlier studies, comprised of local variables, namely, “true” mass quality, mass flux, tube diameter, and two parameters as a function of pressure only. This study reaffirms our earlier findings that by incorporating “true” mass quality in the local condition hypothesis, the prediction of CHF under these conditions can be obtained quite accurately, overcoming the difficulties of flow instability and buoyancy effects that are inherent in the phenomena. The new correlation predicts the CHF data significantly better than those currently available correlations, with average error 0.12% and rms error 13.52% by the heat balance method.

CHF in Vertical Round Tubes With Uniform Heat Flux

Volume 3 ◽  
2004 ◽  
Author(s):  
W. Jaewoo Shim ◽  
Ji-Su Lee
Keyword(s):  
Heat Flux ◽  
Mass Flux ◽  
World Literature ◽  
Average Error ◽  
Uniform Heat Flux ◽  
New Correlation ◽  
Uniform Heat ◽  
System Pressure ◽  
Data Points ◽  
Parameter Ranges

In recent years it is well known that models based on the local condition hypothesis give significant correlations for the prediction of CHF (Critical Heat Flux), using only few local variables. In this work, a study was carried out to develop a generalized CHF correlation in vertical round tubes with uniform heat flux. For this analysis, a CHF database that composed of over 10,000 CHF data points, which were collected from 12 different sources, was used. The actual data used in the development of this correlation, after the elimination of some questionable data, consisted of 8,951 data points with the following parameter ranges: 0.101 ≤ P (pressure) ≤ 20.679 MPa, 9.92 ≤ G (mass flux) ≤ 18,619.39 kg/m2s, 0.00102 ≤ D (diameter) ≤ 0.04468 m, 0.03 ≤ L (length) ≤ 4.97 m, 0.11 ≤ qc (CHF) ≤ 21.42 MW/m2, and −0.87 ≤ Xe (exit qualities) ≤ 1.58. The result of this work showed that regardless of various flow patterns and regimes that exist in the wide flow conditions, the prediction of CHF can be made accurately with few major local variables: the system pressure (P), tube diameter (D), mass flux of water (G), and true mass flux of vapor (GXt). The new correlation was compared with 5 well-known CHF correlations published in world literature. The new correlation can predict CHF within the root mean square error of 13.44% using the heat balance method with average error of −1.34%.

Analysis for a Generalized CHF Correlation in Uniformly Heated Vertical Round Tubes

2003 ◽  
Author(s):  
W. Jaewoo Shim ◽  
Joo-Yong Park ◽  
Ohyoung Kim
Keyword(s):  
Mass Flux ◽  
Mass Fraction ◽  
Empirical Models ◽  
Data Sets ◽  
Square Root ◽  
System Pressure ◽  
Data Points ◽  
Preliminary Study ◽  
Parameter Ranges ◽  
True Mass

For empirical models based on the local condition hypothesis, few important parameters give significant correlations on the prediction of CHF (Critical Heat Flux). This work is a preliminary study to develop a generalized CHF correlation in uniformly heated vertical round tubes for water. For this analysis, a total of 8,912 CHF data points from 12 different published sources were used. This database consisted of following parameter ranges: 0.101 ≤ P (pressure) ≤ 20.679 MPa, 9.92 ≤ G (mass flux) ≤ 18,619.39 kg/m2s, 0.00102 ≤ D (diameter) ≤ 0.04468 m, 0.03 ≤ L (length) ≤ 4.97 m, 8.5 ≤ L/D ≤ 792.26, −609.33 ≤ Inlet subcooling ≤ 1,655.34 kJ/kg, 0.11 ≤ qc (CHF) ≤ 21.41 MW/m2, and −0.85 ≤ Xe (exit qualities) ≤ 1.58. Five representative CHF data sets at pressure conditions of 0.101, 5.001, 10, 16 and 20 MPa were selected, analyzed, and compared to evaluate the effects of parameters on the CHF. It has revealed that the major variables which influenced the CHF, other than the system pressure (P), were tube diameter (D), mass flux of water (G), and local true mass fraction of vapor (Xt). Square root of GXt and square root of D were the significant parameters that showed strong parametric trends of the data sets. The results of this study have reaffirmed the feasibility that an advanced generalized CHF correlation for uniformly heated vertical round tubes can be found.

Generalized CHF Correlation With Uniform Heat Flux for Annulus

2005 ◽  
Author(s):  
Sung-Woo Lee ◽  
Dong-Kook Kim ◽  
W. Jae-Woo Shim
Keyword(s):  
Heat Flux ◽  
Mass Flux ◽  
World Literature ◽  
Average Error ◽  
Uniform Heat Flux ◽  
Outer Diameter ◽  
Good Prediction ◽  
New Correlation ◽  
Inner Diameter ◽  
True Mass

A new generalized CHF (Critical Heat Flux) correlation was suggested for water flow in uniformly heated Annulur tubes. The parametric ranges of experimental CHF data used for present analysis were as follows: 0.540< P (pressure) < 15.146 MPa, 197.77 < G (mass flux) < 653.52 kg/m2s, I.D (inner diameter) = 9.54 mm, O.D (outer diameter) = 19.4 mm, L (length) = 1.84 m, 75.48 < Inlet subcooling < 358.78 kJ/kg, 490.48 < qc (CHF) < 1775.89 KW/m2, and 0.120 < Xe (exit qualities) < 0.536. The new correlation was based on local condition hypothesis, and therefore consisted of the local variables such as tube diameter, pressure, mass flux of water and true mass fraction of steam. In addition, HBM (Heat Balance Method) that leads to the more accurate prediction of CHF than DSM (Direct Substitution Method) was used in developing the correlation. The new correlation was compared with 5 existing CHF correlations that showed comparatively good prediction in world literature. The new correlation predicted CHF better than the other ones with average error of −1.03% and root mean square error of 11.91%.

Experimental Investigation of Critical Heat Flux in Microchannels for Flow-Field Probes

2009 ◽  
Author(s):  
Ali Kos¸ar ◽  
Yoav Peles ◽  
Arthur E. Bergles ◽  
Gregory S. Cole
Keyword(s):  
Heat Flux ◽  
Experimental Investigation ◽  
Critical Heat Flux ◽  
Mass Velocity ◽  
Thermal Condition ◽  
Average Error ◽  
New Correlation ◽  
Hydraulic Conditions ◽  
Data Points ◽  
Heated Length

Critical heat flux (CHF) of water in circular stainless steel microchannels with inner diameters ranging from ∼127μm to ∼254 μm was investigated. Forty-five CHF data points were acquired over mass velocities ranging from 1,200 kg/m2s to 53,000 kg/m2s, heated lengths from 2 cm to 8 cm, and exit qualities from −0.2 to 0.15. Most of the exit qualities fell below 0.1. It was found that CHF conditions were more dependent on mass velocity and heated length than on exit thermal condition. The results were also compared to six CHF correlations, with a mean average error ranging from 22% to 261.8%. A new correlation was proposed to better predict the critical heat flux data under the thermal-hydraulic conditions studied in this investigation. In developing the correlation, 319 data points were added from two previous studies.

Critical Heat Flux in Tubes With Cosine Axial Heat Flux

2005 ◽  
Author(s):  
W. Jaewoo Shim ◽  
Joo-Yong Park ◽  
Ji-Su Lee ◽  
Dong Kook Kim
Keyword(s):  
Heat Flux ◽  
Critical Heat Flux ◽  
Mass Flux ◽  
Flux Distribution ◽  
Average Error ◽  
Uniform Heat Flux ◽  
Heat Flux Distribution ◽  
Uniform Heat ◽  
System Pressure ◽  
Data Points

In this study a method to predict CHF (Critical Heat Flux) in vertical round tubes with cosine heat flux distribution was examined. For this purpose a uniform correlation, based on local condition hypothesis, was developed from 9,366 CHF data points of uniform heat flux heaters. The CHF data points used were collected from 13 different sources had the following parameter ranges: 1.01 ≤ P (pressure) ≤ 206.79 bar, 9.92 ≤ G (mass flux) ≤ 18,619.39 kg/m2s, 0.00102 ≤ D (diameter) ≤ 0.04468 m, 0.0254 ≤ L (length) ≤ 4.966 m, 0.11 ≤ qc (CHF) ≤ 21.42 MW/m2, and −0.87 ≤ X (exit qualities) ≤ 1.58. The result of this work showed that the uniform CHF correlation could be used to predict CHF accurately in a non-uniform heat flux heater for wide flow conditions. Furthermore, the location, where CHF occurs in non-uniform heat flux distribution, can also be determined accurately with the local variables: the system pressure (P), tube diameter (D), mass flux of water (G), and true mass flux of vapor (GXt). The new correlation predicted CHF with cosine heat flux, 297 data points from 5 different published sources, within the root mean square error of 12.42% and average error of 1.06% using the heat balance method.

scholarly journals Viscosity Model for Nanoparticulate Suspensions Based on Surface Interactions

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2752
Author(s):  
Benedikt Finke ◽  
Clara Sangrós Sangrós Giménez ◽  
Arno Kwade ◽  
Carsten Schilde
Keyword(s):  
Mechanistic Model ◽  
Model Development ◽  
Rheological Behaviour ◽  
Hybrid Modelling ◽  
Shear Rates ◽  
Drag Forces ◽  
Boehmite Nanoparticles ◽  
Data Points ◽  
Two Parameters ◽  
Physical Phenomena

In this paper, a widely mechanistic model was developed to depict the rheological behaviour of nanoparticulate suspensions with solids contents up to 20 wt.%, based on the increase in shear stress caused by surface interaction forces among particles. The rheological behaviour is connected to drag forces arising from an altered particle movement with respect to the surrounding fluid. In order to represent this relationship and to model the viscosity, a hybrid modelling approach was followed, in which mechanistic relationships were paired with heuristic expressions. A genetic algorithm was utilized during model development, by enabling the algorithm to choose among several hard-to-assess model options. By the combination of the newly developed model with existing models for the various physical phenomena affecting viscosity, it can be applied to model the viscosity over a broad range of solids contents, shear rates, temperatures and particle sizes. Due to its mechanistic nature, the model even allows an extrapolation beyond the limits of the data points used for calibration, allowing a prediction of the viscosity in this area. Only two parameters are required for this purpose. Experimental data of an epoxy resin filled with boehmite nanoparticles were used for calibration and comparison with modelled values.

scholarly journals Torrefaction of Napier Grass and Oil Palm Petiole Waste Using Drop-type Pyrolysis Reactor

2021 ◽  
Author(s):  
Syazmi Zul Arif Hakimi Saadon ◽  
Noridah Osman ◽  
Moviin Damodaran ◽  
Shan En Liew
Keyword(s):  
Residence Time ◽  
Oil Palm ◽  
Waste Product ◽  
Calorific Value ◽  
Napier Grass ◽  
Effect Of Temperature ◽  
Energy Yield ◽  
Pyrolysis Reactor ◽  
Parameter Ranges ◽  
Two Parameters

Abstract Interest in torrefaction has improved along the recent years and it has been studied extensively as a mean of preparing solid fuels. Biomass to be considered as a renewable source of energy must endeavor improvement continuously and where it is more sustainable going forward in which can come from waste product, wild and cultivated plant. The aim of this study is to investigate the effect of temperature and residence time of wild Napier grass and Oil palm petiole from waste. The torrefied samples were derived by pyrolysis reactor mimicking torrefaction procedure. The temperature parameter ranges between 220 and 300 ℃ while residence time parameter is from 10 minutes to 50 minutes of reaction. It was found that as temperature and time increasing, moisture content and amount of O and H atoms decreases as well as both mass and energy yield, but calorific value and the energy density increase along with both two parameters. Between the two parameters, the temperature variation shows more significant changes to the torrefied samples as compared time. The optimized temperature and time are found to be 260 ℃ and 30 minutes, respectively. Remarkably, the usage of pyrolyzer as torrefaction reaction has proved to be a good option since they share similar characteristics while can also produce product with similar properties reflecting torrefaction process.

scholarly journals An Investigation into Sub-Critical Choke Flow Performance in High Rate Gas Condensate Wells

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3992
Author(s):  
Nasriani ◽  
Khan ◽  
Graham ◽  
Ndlovu ◽  
Nasriani ◽  
...  
Keyword(s):  
Flow Rate ◽  
Parameter Variation ◽  
Gas Condensate ◽  
The Other ◽  
High Rate ◽  
Production Data ◽  
Empirical Correlations ◽  
New Correlation ◽  
Production Wells ◽  
Data Points

There have been some correlations in the literature to predict the gas and liquid flow rate through wellhead chokes under subcritical flow conditions. The majority of these empirical correlations have been developed based on limited production data sets that were collected from a small number of fields. Therefore, these correlations are valid within the parameter variation ranges of those fields. If such correlations are used elsewhere for the prediction of the subcritical choke flow performance of the other fields, significant errors will occur. Additionally, there are only a few empirical correlations for sub-critical choke flow performance in high rate gas condensate wells. These led the authors to develop a new empirical correlation based on a wider production data set from different gas condensate fields in the world; 234 production data points were collected from a large number of production wells in twenty different gas condensate fields with diverse reservoir conditions and different production histories. A non-linear regression analysis method was applied to their production. The new correlation was validated with a new set of data points from some other production wells to confirm the accuracy of the established correlation. The results show that the new correlation had minimal errors and predicted the gas flow rate more accurately than the other three existing models over a wider range of parameter variation ranges.

scholarly journals The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness

1998 ◽  
Vol 44 (147) ◽  
pp. 285-292 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Large Scale ◽  
Flow Instability ◽  
Ice Thickness ◽  
Ice Flow ◽  
Perturbation Amplitude ◽  
Sediment Flow ◽  
Viscous Models ◽  
The Stability ◽  
Parameter Ranges ◽  
Ice Sheet Modelling

AbstractA perturbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This sheet-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-sheet modelling.

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