A Hybrid Model to Predict the Onset of Gas Entrainment With Surface Tension Effects

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
W. Saleh ◽  
R. C. Bowden ◽  
I. G. Hassan ◽  
L. Kadem
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Liquid Region ◽  
Two Dimensional ◽  
Poor Agreement ◽  
Critical Height ◽  
Gas Entrainment ◽  
Good Agreement

The onset of gas entrainment in a single downward discharge, from a stratified gas-liquid region, was modeled. The discharge was modeled as a point-sink and Kelvin–Laplace’s equation was used to incorporate surface tension effects. Consequently, a criterion to characterize the dip radius of curvature, at the onset of gas entrainment, was required. The dip geometry was experimentally investigated and a correlation was developed relating the dip radius of curvature to the discharge Froude number. The correlation was used in conjunction with the theoretical model. It was found that the predicted critical height demonstrated good agreement with experimental data with the three-dimensional point-sink approach, while poor agreement using the two-dimensional finite-branch approach was found. The inclusion of surface tension improved the model’s capability to predict the critical height, particularly at discharge Froude numbers below 1.

Modeling the Onset of Gas Entrainment in a Single Downward Discharge From a Stratified Gas-Liquid Region With Liquid Crossflow

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
R. C. Bowden ◽  
I. G. Hassan
Keyword(s):  
Experimental Data ◽  
Froude Number ◽  
Liquid Region ◽  
Flow Conditions ◽  
Critical Height ◽  
High Discharge ◽  
Gas Entrainment ◽  
Model Predictions ◽  
Pipe Inlet ◽  
Made In

The critical height at the onset of gas entrainment, in a single downward oriented discharge from a stratified gas-liquid region with liquid crossflow, was modeled. The assumptions made in the development of the model reduced the problem to that of a potential flow. The discharge was modeled as a point-sink while the crossflow was said to be uniform at the main pipe inlet. The potential function was determined from a superposition of known solutions for a point-sink and uniform flow. The resulting system of three equations demonstrated that the flow field was dominated by the discharge and crossflow Froude numbers. The system was solved numerically and provided a relationship between the geometry, flow conditions, dip location, and critical height. The model predicted that the critical height increased with the discharge Froude number and decreased with the crossflow Froude number. With no imposed crossflow, the model prediction demonstrated agreement with transient and quasisteady experimental data to within ±30%. Existing experimental correlations showed inconsistent crossflow effects on the critical height and disagreed with the model predictions at high discharge Froude numbers.

Design Methods of Volute Casings for Turbocharger Turbine Applications

1996 ◽  
Vol 210 (2) ◽  
pp. 149-156 ◽  
Author(s):  
H Chen
Keyword(s):  
Experimental Data ◽  
Potential Flow ◽  
Design Method ◽  
Three Dimensional ◽  
Design Methods ◽  
Two Dimensional ◽  
Aerodynamic Design ◽  
3D Design ◽  
Flow Equations ◽  
Good Agreement

This paper discusses aerodynamic design methods of volute casings used in turbocharger turbines. A quasi-three-dimensional (Q-3D) design method is proposed in which a group of extended two-dimensional potential flow equations and the streamline equation are numerically solved to obtain the geometry of spiral volutes. A tongue loss model, based on the turbulence wake theory, is also presented, and good agreement with experimental data is shown.

The Numerical Simulation Research of Gas Entrainment Based on Three-Dimensional Model

2017 ◽  
Author(s):  
Yilin Zhang ◽  
Shanfang Huang
Keyword(s):  
Experimental Data ◽  
Mass Flow Rate ◽  
Cross Section ◽  
Flow Rate ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gas Entrainment ◽  
Simulation Results

Two kinds of three-dimensional model are built to simulate the gas entrainment process through a small break in the horizontal coolant pipe at the bottom of the stratified flow. The results were compared with the two-dimensional simulation results and the experimental data. In terms of the two-phase distribution, the simulation results agree well with the experimental data and show much superiority compared with the two-dimensional model. The results verify the reliability of model building, condition setting and calculating method qualitatively and quantitatively. In general, after gas entrainment, the average velocity over cross section increases obviously, but the mass flow rate decreases contrarily. This is because that void fraction meanwhile reduces the fluid density. In addition, it is found that the larger the void fraction of vapor is, the higher the average discharge velocity of the fracture cross-section fluid is. Besides, with the larger internal and external pressure difference, the gas volume fraction and the flow velocity in the break increase, resulting in the mass flow rate increasing along with them. However, since the critical height increases as well, the total loss amount of liquid in the stable effluent stage decreases, and the time before entrainment becomes shorter.

scholarly journals MODELING OF ELASTIC-PLASTIC DEFORMATION OF ELEMENTS OF SPATIAL STRUCTURES DURING PULSE INTERACTION WITH FLUID BASED ON THE GODUNOV'S METHOD OF INCREASED ACCURACY

2019 ◽  
Vol 81 (4) ◽  
pp. 488-499
Author(s):  
Wang Cheng ◽  
Yang Tonghui ◽  
Li Wan ◽  
Tao Li ◽  
M.H. Abuziarov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Shock Waves ◽  
Elastoplastic Deformation ◽  
Three Dimensional ◽  
Numerical Results ◽  
Two Dimensional ◽  
Wave Processes ◽  
Detonation Products ◽  
Comparison Of The Results ◽  
Good Agreement

The spatial problem of internal explosive loading of an elastoplastic cylindrical container filled with water in Eulerian - Lagrangian variables using multigrid algorithms is considered. A defining system of three-dimensional equations of the dynamics of gas, fluid, and elastoplastic medium is presented. For numerical modeling, a modification of S.K. Godunov scheme of the increased accuracy for both detonation products and liquids, and elastoplastic container is used. At the moving contact boundaries “detonation products - liquid”, “liquid - deformable body”, the exact solution of the Riemann's problem is used. A time dependent model is used to describe the propagation of steady-state detonation wave through an explosive from an initiation region. In both cases, the initiation of detonation occurs at the center of the charge. Two problems have been solved: the first task for the aisymmetric position of the charge, the second for the charge shifted relative to the axis of symmetry. In the first task, the processes are two-dimensional axisymmetric in nature, in the second task, the processes are essentially three-dimensional. A comparison is made of the results of calculations of the first problem using a three-dimensional method with a solution using a previously developed two-dimensional axisymmetric method and experimental data. Good agreement is observed between the numerical results for the maximum velocities and circumferential strains obtained by various methods and experimental data. There is good agreement between the numerical results obtained by various methods and the known experimental data. Comparison of the results of solving the first and second problems shows a significant effect of the position of the charge on the wave processes in the liquid, the processes of loading the container and its elastoplastic deformation. The dynamic behavior of a gas bubble with detonation products is analyzed. A significant deviation of the bubble shape from the spherical one, caused by the action of shock waves reflected from the structure, is shown. Comparison of the results of solving the first and second problems showed a significant effect of the charge position on wave processes in a liquid, the processes of loading a container and its elastoplastic deformation. In particular, in the second problem, shock waves of higher amplitude are observed in the liquid when reflected from the walls of the container.

scholarly journals MODELING OF ELASTIC-PLASTIC DEFORMATION OF ELEMENTS OF SPATIAL STRUCTURES DURING PULSE INTERACTION WITH FLUID BASED ON THE GODUNOV'S METHOD OF INCREASED ACCURACY

2019 ◽  
Vol 81 (4) ◽  
pp. 489-500
Author(s):  
Cheng Wang ◽  
Tonghui Yang ◽  
Wan Li ◽  
Li Tao ◽  
M.H. Abuziarov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Shock Waves ◽  
Elastoplastic Deformation ◽  
Three Dimensional ◽  
Numerical Results ◽  
Two Dimensional ◽  
Wave Processes ◽  
Detonation Products ◽  
Comparison Of The Results ◽  
Good Agreement

The spatial problem of internal explosive loading of an elastoplastic cylindrical container filled with water in Eulerian - Lagrangian variables using multigrid algorithms is considered. A defining system of three-dimensional equations of the dynamics of gas, fluid, and elastoplastic medium is presented. For numerical modeling, a modification of S.K. Godunov scheme of the increased accuracy for both detonation products and liquids, and elastoplastic container is used. At the moving contact boundaries “detonation products - liquid”, “liquid - deformable body”, the exact solution of the Riemann's problem is used. A time dependent model is used to describe the propagation of steady-state detonation wave through an explosive from an initiation region. In both cases, the initiation of detonation occurs at the center of the charge. Two problems have been solved: the first task for the aisymmetric position of the charge, the second for the charge shifted relative to the axis of symmetry. In the first task, the processes are two-dimensional axisymmetric in nature, in the second task, the processes are essentially three-dimensional. A comparison is made of the results of calculations of the first problem using a three-dimensional method with a solution using a previously developed two-dimensional axisymmetric method and experimental data. Good agreement is observed between the numerical results for the maximum velocities and circumferential strains obtained by various methods and experimental data. There is good agreement between the numerical results obtained by various methods and the known experimental data. Comparison of the results of solving the first and second problems shows a significant effect of the position of the charge on the wave processes in the liquid, the processes of loading the container and its elastoplastic deformation. The dynamic behavior of a gas bubble with detonation products is analyzed. A significant deviation of the bubble shape from the spherical one, caused by the action of shock waves reflected from the structure, is shown. Comparison of the results of solving the first and second problems showed a significant effect of the charge position on wave processes in a liquid, the processes of loading a container and its elastoplastic deformation. In particular, in the second problem, shock waves of higher amplitude are observed in the liquid when reflected from the walls of the container.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

APPLICATION OF A NEW HAMILTONIAN OF INTERACTION TO THREE-DIMENSIONAL STRUCTURES

2004 ◽  
Vol 18 (09) ◽  
pp. 1351-1368
Author(s):  
ANDREI DOLOCAN ◽  
VOICU OCTAVIAN DOLOCAN ◽  
VOICU DOLOCAN
Keyword(s):  
Experimental Data ◽  
Cohesive Energy ◽  
Noble Gases ◽  
Three Dimensional ◽  
The Other ◽  
Ionic Crystals ◽  
Coupling Constant ◽  
Good Agreement

Using a new Hamiltonian of interaction we have calculated the cohesive energy in three-dimensional structures. We have found the news dependences of this energy on the distance between the atoms. The obtained results are in a good agreement with experimental data in ionic, covalent and noble gases crystals. The coupling constant γ between the interacting field and the atoms is somewhat smaller than unity in ionic crystals and is some larger than unity in covalent and noble gases crystals. The formulae found by us are general and may be applied, also, to the other types of interactions, for example, gravitational interactions.

Compressor Performance 2D Modelling at Reverse Flow Conditions

2010 ◽  
Author(s):  
L. Gallar ◽  
I. Tzagarakis ◽  
V. Pachidis ◽  
R. Singh
Keyword(s):  
Experimental Data ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Engine Performance ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Compressor Surge ◽  
Compressor Performance ◽  
Shaft Failure

After a shaft failure the compression system of a gas turbine is likely to surge due to the heavy vibrations induced on the engine after the breakage. Unlike at any other conditions of operation, compressor surge during a shaft over-speed event is regarded as desirable as it limits the air flow across the engine and hence the power available to accelerate the free turbine. It is for this reason that the proper prediction of the engine performance during a shaft over-speed event claims for an accurate modelling of the compressor operation at reverse flow conditions. The present study investigates the ability of the existent two dimensional algorithms to simulate the compressor performance in backflow conditions. Results for a three stage axial compressor at reverse flow were produced and compared against stage by stage experimental data published by Gamache. The research shows that due to the strong radial fluxes present over the blades, two dimensional approaches are inadequate to provide satisfactory results. Three dimensional effects and inaccuracies are accounted for by the introduction of a correction parameter that is a measure of the pressure loss across the blades. Such parameter is tailored for rotors and stators and enables the satisfactory agreement between calculations and experiments in a stage by stage basis. The paper concludes with the comparison of the numerical results with the experimental data supplied by Day on a four stage axial compressor.

A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Computational Analysis ◽  
Three Dimensional ◽  
Technical Note ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Displacement Method ◽  
Stress Concentrations ◽  
The Past ◽  
The Matrix ◽  
Triangular Elements

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

A New Approach to Thin Aerofoil Theory

1951 ◽  
Vol 3 (3) ◽  
pp. 193-210 ◽  
Author(s):  
M.J. Lighthill
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Approximate Solutions ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
General Technique ◽  
New Approach ◽  
Flow Problems ◽  
Physical Problems ◽  
First Approximation

SummaryThe general technique for rendering approximate solutions to physical problems uniformly valid is here applied to the simplest form of the problem of correcting the theory of thin wings near a rounded leading edge. The flow investigated is two-dimensional, irrotational and incompressible, and therefore the results do not materially add to our already extensive knowledge of this subject, but the method, which is here satisfactorily checked against this knowledge, shows promise of extension to three-dimensional, and compressible, flow problems.The conclusion, in the problem studied here, is that the velocity field obtained by a straightforward expansion in powers of the disturbances, up to and including either the first or the second power, with coefficients functions of co-ordinates such that the leading edge is at the origin and the aerofoil chord is one of the axes, may be rendered a valid first approximation near the leading edge, as well as a valid first or second approximation away from it, if the whole field is shifted downstream parallel to the chord for a distance of half the leading edge radius of curvature ρL. It follows that the fluid speed on the aerofoil surface, as given on such a straightforward second approximation as a function of distance x along the chord, similarly is rendered uniformly valid (see equation (52)) if the part singular like x-1 is subtracted and the remainder is multiplied by .

Sign in / Sign up

Export Citation Format

Share Document