The Application of the Integral Momentum Balance on the Pressure Drop of a Sudden Contraction

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Andreas Malcherek ◽  
Sebastian Müller
Keyword(s):  
Pressure Drop ◽  
Control Volume ◽  
Pressure Coefficient ◽  
Momentum Balance ◽  
Simple Analytical Expression ◽  
Pressure Drops ◽  
Pressure Distributions ◽  
Contraction Ratio ◽  
Sudden Contraction ◽  
New Formulation

Abstract A new approach based on the momentum balance to calculate the pressure drop in turbulent flow through sharp-edged axisymmetric sudden contractions is presented. The momentum balance needs the velocity as well as the pressure distributions on the boundaries of the control volume. These distributions are obtained by a series of numerical simulations with different settings for the discharge, as well as the contraction ratio. The numerical model itself is validated by the comparison of the simulated and measured pressure drops in a laboratory experiment at different positions. To get easily applicable hydraulic formulations for the pressure drop depending on the discharge and the contraction ratio, the missing momentum and pressure coefficients are determined from the simulated velocity and pressure distributions. Only the pressure coefficient shows a dependency on the contraction ratio. After fitting the dependency by a simple analytical expression, a new formulation for the hydraulics of a sharp-edged sudden contraction based solely on momentum balance was obtained. The comparison with own experimental results as well as the classical parameterization of Idelchik show in both cases very good agreement.

Experimental and Computational Analyses of Pressure Differentials in Flexible Ducts With Different Bent Angles

2007 ◽  
Author(s):  
Ray R. Taghavi ◽  
Wonjin Jin ◽  
Mario A. Medina
Keyword(s):  
Pressure Drop ◽  
Static Pressure ◽  
Complex Geometry ◽  
Analysis Data ◽  
Secondary Flows ◽  
Low Flow ◽  
Pressure Drops ◽  
Pressure Distributions ◽  
Geometrical Effects ◽  
Cfd Analyses

A set of experimental analyses was conducted to determine static pressure drops inside non-metallic flexible, spiral wire helix core ducts, with different bent angles. In addition, Computational Fluid Dynamics (CFD) solutions were performed and verified by comparing them to the experimental data. The CFD computations were carried out to produce more systematic pressure drop information through these complex-geometry ducts. The experimental setup was constructed according to ASHRAE Standard 120-1999. Five different bent angles (0, 30, 45, 60, and 90 degrees) were tested at relatively low flow rates (11 to 89 CFM). Also, two different bent radii and duct lengths were tested to study flexible duct geometrical effects on static pressure drops. FLUENT 6.2, using RANS based two equations - RNG k-ε model, was used for the CFD analyses. The experimental and CFD results showed that larger bent angles produced larger static pressure drops in the flexible ducts. CFD analysis data were found to be in relatively good agreement with the experimental results for all bent angle cases. However, the deviations became slightly larger at higher velocity regimes and at the longer test sections. Overall, static pressure drop for longer length cases were approximately 0.01in.H2O higher when compared to shorter cases because of the increase in resistance to the flow. Also, the CFD simulations captured more pronounced static pressure drops that were produced along the sharper turns. The stronger secondary flows, which resulted from higher and lower static pressure distributions in the outer and inner surfaces, respectively, contributed to these higher pressure drops.

A Unified Theory for the Pressure Change of Sudden Expansions and Contractions Based on the Momentum Balance

2021 ◽  
Author(s):  
Sebastian Müller ◽  
Andreas Malcherek
Keyword(s):  
Control Volume ◽  
Pressure Change ◽  
Sudden Expansion ◽  
Momentum Balance ◽  
Unified Approach ◽  
Pressure Distributions ◽  
Analytical Functions ◽  
Specific Geometry ◽  
Control Volumes ◽  
Pressure Changes

Abstract In this paper a unified approach based on the momentum balance is presented, capable of predicting the pressure change of sudden contractions and sudden expansions. The use of empirically determined correction coefficients is not necessary. Therefore, the momentum balance is derived similarly for both applications but with different control volumes. The control volume takes into account the specific geometry of the hydraulic structure. With a properly chosen control volume, the unified approach requires coefficients that account for the velocity as well as pressure distributions on the boundaries of the control volume. These coefficients can be obtained by parameterizing the results of numerical simulations by simple analytical functions. The numerical model itself is validated by checking the simulated pressure change against calculated or measured pressure changes. It is found that the formulation of the momentum balance for the sudden expansion is more complex compared with the sudden contraction. The prediction of the pressure change of flows through sudden expansions can be improved by applying the momentum balance non-idealized. Most of the correction coefficients originate from an inappropriate application of Bernoulli’s energy conservation principle. Consequently, this leads to a gap between theory and experimental results. The proposed unified approach solely contains physical coefficients that are used to substitute integrals by averaged expressions.

Mountain-Top Vortices as Causes of Large Errors in Altimeter Heights

1949 ◽  
Vol 30 (2) ◽  
pp. 39-44 ◽  
Author(s):  
F. A. Brooks
Keyword(s):  
Pressure Drop ◽  
Ground Surface ◽  
Maximum Error ◽  
Maximum Pressure ◽  
Strong Wind ◽  
High Mountains ◽  
Pressure Drops ◽  
Pressure Distributions ◽  
Maximum Pressure Drop ◽  
Vortex Axis

There have been uncontradicted reports of large altimeter errors in the vicinity of high mountains. A brief survey of pressure distributions over an airfoil with flaps shows a maximum pressure drop below static pressure of twice the velocity head. Applying this ratio to a 14,000-foot mountain in a 100-mph wind a maximum error of 700 feet is indicated. This is important, but not enough to explain the occasional reports of 2 to 3,000-foot errors. Pressure drops of this magnitude exist in tropical cyclones, and even greater depression is known in tornadoes. The pressure drop at the ground surface is seen to have an axial connection with the natural low pressure aloft. The strength of the vortex is shown to depend on the outside tangential input by the wind where the whirl velocity can be very moderate, and the superspeed spin inside a vortex is shown to be dependent on radial inflow of air which is discharged along the vortex axis. Procedures are suggested for locating mountain tornadoes and thorough investigation urged so that the great hazards of mountain vortices in a strong wind will become generally known.

Comparison between Pressure Drop Profile of a Horizontal Well as a Water Injector and as an Oil Producer in a Five-Spot Waterflood Pattern

2007 ◽  
Vol 18-19 ◽  
pp. 265-270
Author(s):  
E. Steve Adewole ◽  
O.A. Olafuyi
Keyword(s):  
Pressure Drop ◽  
Horizontal Well ◽  
Mobility Ratio ◽  
Pressure Drops ◽  
Pressure Distributions ◽  
Dimensionless Pressure ◽  
Water Breakthrough

This paper compares the pressure drop profiles of both horizontal well producer and injector in a 5spot waterflood pattern. Dimensionless pressure distributions for each pattern were utilised. All computations were limited to conditions of unit mobility ratio; i.e., before water breakthrough condition. Results show that a normal 5-spot flood pattern, with a horizontal well producer, offers higher pressure drops, but early water breakthrough tendencies, than as an injector for the same reservoir and wellbore conditions. An inverted pattern, under the same conditions, produces clean oil for a longer time, before water breakthrough possibilities.

Experimental and Analytical Study of the Pressure Drop Across a Double-Outlet Vortex Chamber

2006 ◽  
Vol 129 (1) ◽  
pp. 100-105 ◽  
Author(s):  
Ali M. Jawarneh ◽  
P. Sakaris ◽  
Georgios H. Vatistas
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Analytical Study ◽  
Pressure Coefficient ◽  
Vortex Chamber ◽  
Core Size ◽  
Chamber Length ◽  
The Core ◽  
Swirl Velocity ◽  
New Formulation

This paper presents experimental and analytical results concerning the pressure drop and the core size in vortex chambers. The new formulation is based on the conservation of mass and energy integral equations and takes into account the presence of two outlet ports. The diminishing vortex strength is introduced through the vortex decay factor. The influence of vortex chamber geometry, such as diameter ratio, aspect ratio, and Reynolds number, on the flow field have been examined and compared with the present experimental data. It is shown that the presence of the swirl velocity component makes the pressure drop across a vortex chamber significantly different than the familiar unidirectional pipe flow. When the chamber length is increased, the vortex diminishes under the action of friction, producing a weaker centrifugal force which leads to a further pressure drop. It is revealed that by increasing the Reynolds number, the cores expand resulting into a larger pressure coefficient. For a double-outlet chamber where the flow is divided into two streams, the last parameter is found to be less than that of a single-outlet.

Experimental and Analytical Studies on Frictional Pressure Drops of Gas-Liquid Two-Phase Flow in Mini-Micro Pipes and at Vena Contract and Expansion

2007 ◽  
Author(s):  
Hiroyasu Ohtake ◽  
Hideyasu Ohtaki ◽  
Masato Hagiwara ◽  
Yasuo Koizumi
Keyword(s):  
Pressure Drop ◽  
Two Phase Flow ◽  
Liquid Velocity ◽  
Experimental Results ◽  
Phase Flow ◽  
Two Phase ◽  
Pressure Drops ◽  
Frictional Pressure Drop ◽  
Sudden Contraction ◽  
Sudden Enlargement

The frictional pressure drops of gas-liquid two-phase flow in mini-micro pipes and at vena contract and expansion were investigated experimentally and analytically. Pressure drops of straight pipe, sudden enlargement and sudden contraction of gas-liquid two-phase flow in mini-pipes were measured. Test liquid was water at room temperature; test gas was argon. The diameter of the test mini-pipe was 0.5, 0.25 and 0.12 mm, respectively; the length was 500, 250 and 50 mm, respectively. The cross-sectional ratio of the contraction was about 1000; the ratio of the enlargement was about 0.001. The pressure drop data and the flow pattern were collected over 3.0 < UG < 130 m/s for the superficial gas velocity and 0.02 < UL < 6.0 m/s for the superficial liquid velocity. The two-phase friction multiplier data for D > 0.5 mm showed to be in good agreement with the conventional correlations. On the other hand, the two-phase friction multiplier data for D < 0.25 mm differed from the calculated values by the conventional correlations. Then, thickness of liquid film around a gas plug and size of gas core were estimated and the effect of frictional pressure drop on channel size was discussed through Knudsen Number of gas and instability on liquid-gas interface. Namely, the effect of mini-pipe was rarefaction effects, Kn<0.1. New correlation of frictional pressure drop of gas-liquid two-phase flow is proposed for mini pipes. The coefficients of sudden enlargement and sudden contraction in mini-pipes for the gas-water two-phase flow were modified from the present experimental results. The experimental results were also examined through numerical simulation by a commercial code.

Flow and Heat Transfer of Nanofluids With Temperature Dependent Properties

2010 ◽  
Author(s):  
Ehsan Ebrahimnia Bajestan ◽  
Hamid Niazmand ◽  
Metin Renksizbulut
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Prandtl Number ◽  
Thermophysical Properties ◽  
Particle Concentration ◽  
Control Volume ◽  
Straight Pipe ◽  
Pressure Drops ◽  
Curved Pipe ◽  
Curvature Effects

Numerical simulations of laminar convective heat transfer with nanofluids in two different geometries involving a straight pipe and a 90° curved pipe are presented. The Navier-Stokes and energy equations for an incompressible Newtonian fluid are solved in a body fitted coordinate system using a control-volume method. In the present work, the nanofluid is a mixture of water and alumina particles, and its thermophysical properties are considered as a function of temperature as well as particle concentration. The accuracy of the models employed for estimating the effective thermophysical properties of this nanofluid are first evaluated using available experimental data for heat transfer in a straight pipe. The same models are then employed for the simulation of flows in a curved pipe. Present results indicate that both the nanoparticle and curvature effects enhance the heat transfer performance but at the expense of increased pressure drop. However, in the present case, the nanoparticle contribution to the pressure drop is dominant, which increases by up to two orders of magnitude at higher nanoparticle concentrations. The ratio of the nanofluid Prandtl number to the based fluid Prandtl number is established as a criterion for the choice of a nanofluid. This ratio must be less than 1 to achieve higher heat transfer rates with relatively low pressure drops as the particle concentration is increased.

scholarly journals A New Formulation of Maxwell’s Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 868
Author(s):  
Simona Fialová ◽  
František Pochylý
Keyword(s):  
Numerical Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Control Volume ◽  
Control Volume Method ◽  
Integral Forms ◽  
New Formulation ◽  
Electrical Induction ◽  
Volume Method ◽  
Integral Identities

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

Airfoil Design in Subcritical and Supercritical Flows

1979 ◽  
Vol 46 (4) ◽  
pp. 761-766 ◽  
Author(s):  
W. C. Chin ◽  
D. P. Rizzetta
Keyword(s):  
Reasonable Agreement ◽  
Relaxation Method ◽  
Supercritical Pressure ◽  
Small Disturbance ◽  
Trailing Edge ◽  
Difference Analysis ◽  
Pressure Distributions ◽  
Basic Ideas ◽  
New Formulation ◽  
Supercritical Flows

The “inverse” or “design” problem in aerodynamics, which solves for the airfoil shape that induces a prescribed chordwise surface pressure subject to additional requirements on trailing edge closure, is considered in the transonic small-disturbance limit. A new formulation for the stream function ψ is suggested which uses well-set Neumann conditions on the chordwise slit, with the degree of closure dictated by a specified jump in ψ across the downstream slit emanating from the trailing edge. The boundary-value problem is solved by a type-dependent relaxation method that automatically generates closed airfoils on convergence. Computed airfoil shapes using subcritical and supercritical pressure distributions obtained from existing finite-difference analysis codes, in the latter case, with and without shockwaves, give results in reasonable agreement with the original specified shapes, and validate the basic ideas.

Experimental Study of Evaporation Heat Transfer Characteristics and Pressure Drops of R410A and R134a in a Multiport Mini-Channel

2009 ◽  
Author(s):  
Jatuporn Kaew-On ◽  
Somchai Wongwises
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Transfer Coefficients ◽  
Pressure Drops ◽  
Heat Transfer Coefficients ◽  
Evaporation Heat ◽  
Evaporation Heat Transfer ◽  
R 134A

The evaporation heat transfer coefficients and pressure drops of R-410A and R-134a flowing through a horizontal-aluminium rectangular multiport mini-channel having a hydraulic diameter of 3.48 mm are experimentally investigated. The test runs are done at refrigerant mass fluxes ranging between 200 and 400 kg/m2s. The heat fluxes are between 5 and 14.25 kW/m2, and refrigerant saturation temperatures are between 10 and 30 °C. The effects of the refrigerant vapour quality, mass flux, saturation temperature and imposed heat flux on the measured heat transfer coefficient and pressure drop are investigated. The experimental data show that in the same conditions, the heat transfer coefficients of R-410A are about 20–50% higher than those of R-134a, whereas the pressure drops of R-410A are around 50–100% lower than those of R-134a. The new correlations for the evaporation heat transfer coefficient and pressure drop of R-410A and R-134a in a multiport mini-channel are proposed for practical applications.

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