A Novel Adiabatic Pipe Flow Equation for Ideal Gases

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Jung Seob Kim ◽  
Navneet Radheshyam Singh
Keyword(s):  
Pressure Drop ◽  
Mass Flux ◽  
Pipe Flow ◽  
Flow Equation ◽  
Average Density ◽  
Pressure Relief ◽  
Pipe Length ◽  
Adiabatic Flow ◽  
Relief System ◽  
Common Application

Compressible flow involves variation in the density with changes in pressure and temperature along the pipe length. This article revisits the conventional adiabatic pipe flow equation and finds a fundamental drawback in this equation. The corrected adiabatic pipe flow equation has fixed the fundamental error in the conventional adiabatic pipe flow equation where the average density estimation for the conventional adiabatic equation is lower than the lower bound of the average density based on isothermal temperature. However, both the conventional adiabatic equation and the corrected adiabatic equation result in an over prediction of mass flux due to a deficiency in the average density definition. The over prediction of mass flux is not significant if the pressure drop is less than 40%; however, the pressure drop is usually greater than 40% of the inlet pressure for most pressure relief system applications. The authors offer a novel adiabatic pipe flow equation based on insights presented in this work. The novel adiabatic pipe flow equation is the most suitable solution for the pressure relief system applications as well as any other common application since it better represents the nature of adiabatic flow in a pipe. The experimental data previously published is compared with the predictions to validate the new adiabatic pipe flow model.

Design of Discharge Piping for Pressure Relief Systems

1981 ◽  
Vol 103 (3) ◽  
pp. 190-195
Author(s):  
R. H. Ross
Keyword(s):  
Mach Number ◽  
Simple Technique ◽  
Careful Analysis ◽  
Back Pressure ◽  
Piping System ◽  
Flow Function ◽  
Pressure Relief ◽  
Adiabatic Flow ◽  
Pressure Relief Valves ◽  
Relief System

The ASME Boiler and Pressure Vessel Code and publications by many manufacturers caution the design engineer to consider back pressure in discharge piping when sizing and selecting pressure relief valves. Only general guidelines are given, however, because of widely varying installation requirements. This paper addresses manifolded discharge piping system design. The method of analysis provides a simple technique for determining pressure within a discharge piping system. The method is based on adiabatic flow and uses local Mach number to relate expansion of the gas in the pipes to a mass flow function. The paper illustrates that relief valves discharging into lines and headers should not be sized or selected without careful analysis of the entire relief system.

Modeling Horizontal Well Oil Production Using Modified Brinkman’s Model

2005 ◽  
Author(s):  
Hadi Belhaj ◽  
Shabbir Mustafiz ◽  
Fuxi Ma ◽  
M. Satish ◽  
M. R. Islam
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Pipe Flow ◽  
Horizontal Well ◽  
Oil Production ◽  
Seepage Flow ◽  
Flow Equation ◽  
Darcy Model ◽  
Lower Viscosity ◽  
The Difference

Horizontal well oil production has been numerically studied by using the Modified Brinkman’s Model. This model has been used along with the Darcy-Weisbach pipe flow equation in modeling of coupled porous medium/pipe flow. The results include seepage flow rate along the horizontal well, velocity distribution, pressure drop, and production pressure drop between the two ends of the horizontal well. They have been compared with those from Darcy model. It is found that when the fluid’s viscosity is low, there is a big difference between the results from the two models. However, when the fluid’s viscosity is high, the difference tends to vanish. In addition, two striking findings have been observed: (a) the curves for the distribution of the seepage flow rate along the pipeline are more flat than that from Darcy model. However, a higher viscosity makes the curve more uneven. This reverses the trend from Darcy model. (b) The velocity in the pipe is more uniform by MBM than that by Darcy model. The curves of V ~x become more uniform in the pipe when the fluid has a lower viscosity. This again reveres the trend from the Darcy model.

Geotextile encased columns (GEC) used as pressure-relief system. Instrumented bridge abutment case study on soft soil

2017 ◽  
Vol 45 (3) ◽  
pp. 227-236 ◽  
Author(s):  
F. Schnaid ◽  
D. Winter ◽  
A.E.F. Silva ◽  
D. Alexiew ◽  
V. Küster
Keyword(s):  
Soft Soil ◽  
Pressure Relief ◽  
Bridge Abutment ◽  
Relief System

Thermographic survey of the integrity of a process plant pressure relief system

1985 ◽  
Vol 4 (3) ◽  
pp. 161-163 ◽  
Author(s):  
Brenton G. Jones ◽  
Raymond C. Duckett
Keyword(s):  
Pressure Relief ◽  
Process Plant ◽  
Relief System

Experimental Study of Heat Transfer to Supercritical Pressure Water Flowing in a 2×2 Rod Bundle

2014 ◽  
Author(s):  
Han Wang ◽  
Qincheng Bi ◽  
Linchuan Wang ◽  
Haicai Lv ◽  
Laurence K. H. Leung
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
Pressure Drop ◽  
Wall Temperature ◽  
Mass Flux ◽  
Heat Fluxes ◽  
Outer Diameter ◽  
Square Channel ◽  
Rod Bundle

An experiment has recently been performed at Xi’an Jiaotong University to study the wall temperature and pressure drop at supercritical pressures with upward flow of water inside a 2×2 rod bundle. A fuel-assembly simulator with four heated rods was installed inside a square channel with rounded corner. The outer diameter of each heated rod is 8 mm with an effective heated length of 600 mm. Experimental parameters covered the pressure of 23–28 MPa, mass flux of 350–1000 kg/m2s and heat flux on the rod surface of 200–1000 kW/m2. According to the experimental data, it was found that the circumferential wall temperature distribution of a heated rod is not uniform. The temperature difference between the maximum and the minimum varies with heat flux and/or mass flux. Heat transfer characteristics of supercritical water in bundle were discussed with respect to various heat fluxes. The effect of heat flux on heat transfer in rod bundles is similar with that in tubes or annuli. In addition, flow resistance reflected in the form of pressure loss has also been studied. Experimental results showed that the total pressure drop increases with bulk enthalpy and mass flux. Four heat transfer correlations developed for supercritical pressures water were compared with the present test data. Predictions of Jackson correlation agrees closely with the experimental data.

Experimental Studies of Adiabatic Flow Boiling in Fractal-Like Branching Micro-Channels

2008 ◽  
Author(s):  
Brian J. Daniels ◽  
James A. Liburdy ◽  
Deborah V. Pence
Keyword(s):  
Pressure Drop ◽  
Void Fraction ◽  
Flow Boiling ◽  
Experimental Studies ◽  
Channel Length ◽  
Channel Height ◽  
Channel Network ◽  
Adiabatic Flow ◽  
Numerical Predictions ◽  
Micro Channels

Experimental results of adiabatic boiling of water flowing through a fractal-like branching microchannel network are presented and compared to numerical simulations for identical flow conditions. The fractal-like branching channel network had channel length and width ratios between adjacent branching levels of 0.7071, a total flow length of 18 mm, a channel height of 150 μm and a terminal channel width of 100 μm. The channels were DRIE etched into a silicon disk and pyrex was anodically bonded to the silicon to form the channel top and allowed visualization of the flow within the channels. The water flowed from the center of the disk where the inlet was laser cut through the silicon to the periphery of the disc. The flow rates ranged from 100 to 225 g/min and the inlet subcooling levels varied from 0.5 to 6 °C. Pressure drop across the channel as well as void fraction in each branching level were measured for each of the test conditions. The measured pressure drop ranged from 20 to 90 kPa, and the measured void fraction ranged from 0.3 to 0.9. The pressure drop results agree well with the numerical predictions. The measured void fraction results followed the same trends as the numerical results.

Fanno Design of Blow-Off Lines in Heavy Duty Gas Turbine

2013 ◽  
Author(s):  
Marco Cioffi ◽  
Enrico Puppo ◽  
Andrea Silingardi
Keyword(s):  
Gas Turbines ◽  
Gas Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Design Procedure ◽  
Flow Equation ◽  
Heavy Duty ◽  
Cross Sectional ◽  
Pipe Length ◽  
Choked Flow

In typical heavy duty gas turbines the multistage axial compressor is provided with anti-surge pipelines equipped with on-off valves (blow-off lines), to avoid dangerous flow instabilities during start-ups and shut-downs. Blow-off lines show some very peculiar phenomena and somewhat challenging fluid dynamics, which require a deeper regard. In this paper the blow-off lines in axial gas turbines are analyzed by adopting an adiabatic quasi-unidimensional model of the gas flow through a pipe with a constant cross-sectional area and involving geometrical singularities (Fanno flow). The determination of the Fanno limit, on the basis of the flow equation and the second principle of thermodynamics, shows the existence of a critical pipe length which is a function of the pipe parameters and the initial conditions: for a length greater than this maximum one, the model requires a mass-flow reduction. In addition, in the presence of a regulating valve, so-called multi-choked flow can arise. The semi-analytical model has been implemented and the results have been compared with a three-dimensional CFD analysis and cross-checked with available field data, showing a good agreement. The Fanno model has been applied for the analysis of some of the actual machines in the Ansaldo Energia fleet under different working conditions. The Fanno tool will be part of the design procedure of new machines. In addition it will define related experimental activities.

scholarly journals Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit

2019 ◽  
Vol 874 ◽  
pp. 699-719 ◽  
Author(s):  
Jose M. Lopez ◽  
George H. Choueiri ◽  
Björn Hof
Keyword(s):  
Drag Reduction ◽  
Turbulent Flows ◽  
Pipe Flow ◽  
Domain Size ◽  
Reynolds Numbers ◽  
Weissenberg Number ◽  
Pipe Length ◽  
Low Reynolds Numbers ◽  
Maximum Drag Reduction ◽  
Low Reynolds

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations at low Reynolds numbers ($Re$) using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at $Re$ near transition we find that, indeed, with increasing Weissenberg number ($Wi$), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in $Wi$, the flow fully relaminarizes, in agreement with recent experiments. At even larger $Wi$, a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results at these low$Re$ from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

scholarly journals Effect of Metal Foam Insert Configurations on Flow Boiling Heat Transfer and Pressure Drop in a Rectangular Channel

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4617
Author(s):  
Sanghyun Nam ◽  
Dae Yeon Kim ◽  
Youngwoo Kim ◽  
Kyung Chun Kim
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Mass Flux ◽  
Test Section ◽  
Boiling Heat Transfer ◽  
Metal Foam ◽  
Flow Boiling ◽  
Rectangular Channel ◽  
Saturation Pressure ◽  
Two Phase

Heat transfer under flow boiling is better in a rectangular channel filled with open-cell metal foam than in an empty channel, but the high pressure drop is a drawback of the empty channel method. In this study, various types of metal foam insert configurations were tested to reduce the pressure drop while maintaining high heat transfer. Specifically, we measured the boiling heat transfer and pressure drop of a two-phase vertical upward flow of R245fa inside a channel. To measure the pressure and temperature differences of the metal foam, differential pressure transducers and T-type thermocouples were used at both ends of the test section. While the saturation pressure was kept constant at 5.9 bar, the steam quality at the inlet of the test section was changed from 0.05 to 0.99. The channel height, moreover, was 3 mm, and the mass flux ranged from 133 to 300 kg/m2s. The two-phase flow characteristics were observed through a high-speed visualization experiment. Heat transfer tended to increase with the mean vapor quality, and, as expected, the fully filled metal foam channel offered the highest thermal performance. The streamwise insert pattern model had the lowest heat transfer at a low mass flux. However, at a higher mass flux, the three different insert models presented almost the same heat transfer coefficients. We found that the streamwise pattern model had a very low pressure drop compared to that of the spanwise pattern models. The goodness factors of the flow area and the core volume of the streamwise patterned model were higher than those of the full-filled metal foam channel.

scholarly journals CO2 Pipeline Design: A Review

2018 ◽  
Author(s):  
Suoton P. Peletiri ◽  
Nejat Rahmanian ◽  
Iqbal M. Mujtaba
Keyword(s):  
Pressure Drop ◽  
Flow Equation ◽  
Aspen Hysys ◽  
Resultant Velocity ◽  
Velocity Flow ◽  
Effect Of Impurities ◽  
Paris Climate Agreement ◽  
Second Category ◽  
Pipeline Design ◽  
Better Than

There is need to accurately design pipelines to transport the expected increase of CO2 captured from industrial processes after the signing of the Paris Climate Agreement in 2016. This paper reviews several aspects of CO2 pipeline design with emphasis on pressure drop and models for the calculation of pipeline diameter. Two categories of pipeline equations were identified. The first category is independent of pipeline length and has two different equations. This category is used to specify adequate pipeline diameter for the volume of fluid transported. The optimum economic pipe diameter equation (Eq. 17) with nearly uniform resultant velocity values at different flow rates performed better than the standard velocity flow equation (Eq. 20). The second category has four different equations and is used to calculate pipeline pressure drop or pipeline distance for the installation of booster stations after specifying minimum and maximum pipeline pressures. The hydraulic equation is preferred because it gave better resultant velocity values and the closest diameter value obtained using Aspen HYSYS (V.10) simulation. The effect of impurities on the pressure behaviour and optimal pipeline diameter and pressure loss due to acceleration were ignored in the development of the models. Further work is ongoing to incorporate these effects into the models.

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