Dynamic Numerical Microchannel Evaporator Model to Investigate Parallel Channel Instabilities

2016 ◽  
Vol 138 (1) ◽  
Author(s):  
Tom Saenen ◽  
John R. Thome
Keyword(s):  
Three Dimensional ◽  
Solid Substrate ◽  
Parallel Channel ◽  
Two Phase ◽  
Pressure Losses ◽  
Stabilizing Effect ◽  
Substrate Properties ◽  
Numerical Solver ◽  
The Stability ◽  
The One

A fully dynamic model of a microchannel evaporator is presented. The aim of the model is to study the highly dynamic parallel channel instabilities that occur in these evaporators in more detail. The numerical solver for the model is custom-built and the majority of the paper is focused on detailing the various aspects of this solver. The one-dimensional homogeneous two-phase flow conservation equations are solved to simulate the flow. The full three-dimensional (3D) conduction domain of the evaporator is also dynamically resolved. This allows for the correct simulation of the complex hydraulic and thermal interactions between the microchannels that give rise to the parallel channel instabilities. The model uses state-of-the-art correlations to calculate the frictional pressure losses and heat transfer in the microchannels. In addition, a model for inlet restrictions is also included to simulate the stabilizing effect of these components. In the final part of the paper, validation results of the model are presented, in which the stability results of the model are compared with the existing experimental data from the literature. Next, a parametric study is performed focusing on the stabilizing effects of the solid substrate properties. It is found that increasing the thermal conductivity and thickness of the solid substrate has a strong stabilizing effect, while increasing the number of microchannels has a small destabilizing effect. Finally, representative dynamic results are also given to demonstrate some of the unique capabilities of the model.

Novel Dynamic Numerical Microchannel Evaporator Model to Investigate Parallel Channel Instabilities

2015 ◽  
Author(s):  
Tom Saenen ◽  
John R. Thome
Keyword(s):  
Three Dimensional ◽  
Parallel Channel ◽  
Two Phase ◽  
One Dimensional ◽  
Pressure Losses ◽  
Initial Validation ◽  
Numerical Solver ◽  
The One ◽  
Flow Conservation ◽  
Stability Results

A novel fully dynamic model of a microchannel evaporator is presented. The aim of the model is to study the highly dynamic parallel channel instabilities that occur in these evaporators in more detail. The numerical solver for the model is custom-built and the majority of the paper is focused on detailing the various aspects of this solver. The one-dimensional homogeneous two-phase flow conservation equations are solved to simulate the flow. The full three-dimensional conduction domain of the evaporator is also dynamically resolved. This allows for the correct simulation of the complex hydraulic and thermal interactions between the microchannels that give rise to the parallel channel instabilities. The model uses state-of-the-art correlations to calculate the frictional pressure losses and heat transfer in the microchannels. In addition, a model for inlet restrictions is also included to simulate the stabilizing effect of these components. In the final part of the paper, initial validation results of the model are presented, in which stability results of the model are compared to existing experimental data from literature. Finally, some representative dynamic results are also given to demonstrate some of the unique capabilities of the model.

Experimental and Numerical Investigation of Air-Particle Two-Phase Flow in Centrifugal Separator

2000 ◽  
Author(s):  
H. J. Kang ◽  
B. Zheng ◽  
C. X. Lin ◽  
M. A. Ebadian
Keyword(s):  
Velocity Distribution ◽  
Separation Efficiency ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Tangential Direction ◽  
Cylinder Surface ◽  
Centrifugal Separator ◽  
Two Phase ◽  
Dust Collection ◽  
Numerical Solver

Abstract The velocity distributions inside a centrifugal separator with outside and inside diameters of 152.4 mm (6″) and 76.2 mm (3″), respectively, have been investigated experimentally and numerically to obtain optimum separation efficiency. Two 12.7 mm (1/2-inch) holes were drilled on the external surface of the separator to measure the velocity distribution in the separator. Two direction velocities (tangential direction along the cylinder surface and axial along the vertical direction) were measured to compare with the numerical simulation results. A 6060P Pitot probe was employed to obtain the velocity distribution. The dust samples (a mixture of steel particle and dust) from the dust collection box were analyzed using a Phillips XL30 Scanning Electron Microscope. FLUENT code is used as the numerical solver for this fully three-dimensional problem. The fluid flow in the separator is assumed to be steady and incompressible turbulent flow. The standard k–ε model was employed in this study. Non-uniform, unstructured grids are chosen to discretize the entire computation domain. Almost 100,000 cells are used to discretize the whole separator. The constant velocity profile is imposed on the inlet plane. The pressure boundary condition is adopted at outlet plane. Comparing the velocity distribution and separation efficiency from the experiment and the numerical modeling shows that the experimental results and the estimated data agree fairly well and with a deviation within ±10%.

Multi-Dimensional Two-Phase Flow Modeling Applied to Interior Ballistics

2011 ◽  
Vol 78 (5) ◽  
Author(s):  
Julien Nussbaum ◽  
Philippe Helluy ◽  
Jean-Marc Herard ◽  
Barbara Baschung
Keyword(s):  
Three Dimensional ◽  
Hyperbolic Model ◽  
Finite Volume Scheme ◽  
Step Method ◽  
Fractional Step Method ◽  
Two Phase ◽  
Decomposition Reactions ◽  
Solid Decomposition ◽  
The One ◽  
Complex Phenomena

Complex phenomena occur in a combustion chamber during a ballistic cycle. From the ignition of the black powder in the primer to the exit of the projectile through the muzzle, two-phase gas-powder mix undertakes various transfers in different forms. A detailed comprehension of these effects is fundamental to predict the behavior of the whole system, considering performances and safety. Although the ignition of the powder bed is three-dimensional due to the primer’s geometry, simulations generally only deal with one- or two-dimensional problem. In this study, we propose a method to simulate the two-phase flows in 1, 2 or 3 dimensions with the same system of partial differential equations. A one-pressure, conditionally hyperbolic model [1] was used and solved by a nonconservative finite volume scheme associated to a fractional step method, where each step is hyperbolic. We extend our study to a two-pressure, unconditionally hyperbolic model [2] in which a relaxation technique was applied in order to recover the one-pressure model by using the granular stress. The second goal of this study is also to propose an improved ignition model of the powder grains, by taking into account simplified chemical kinetics for decomposition reactions in the two phases. Here we consider a 0th-order solid decomposition and an unimolecular, 2nd-order gas reaction. Validation of the algorithm on several test cases is presented.

On the stability of nonlinear waves coexisting with plasma beams

1975 ◽  
Vol 13 (1) ◽  
pp. 173-187 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Nonlinear Wave ◽  
Growth Rates ◽  
Three Dimensional ◽  
Stationary Waves ◽  
One Dimensional ◽  
Long Wavelength ◽  
Long Wave ◽  
Set Up ◽  
The Stability ◽  
The One

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.

scholarly journals Study on Two Types of Stall Patterns in a Centrifugal Compressor with a Wide Vaneless Diffuser

Processes ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1251
Author(s):  
Qian Zhang ◽  
Liang Zhang ◽  
Qiuhong Huo ◽  
Lei Zhang
Keyword(s):  
Flow Rate ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Propagation Speed ◽  
Radius Ratio ◽  
Vaneless Diffuser ◽  
Vaneless Diffusers ◽  
Stall Cells ◽  
The Stability ◽  
The One

Two types of stall patterns in the centrifugal compressor with a wide vaneless diffuser were numerically studied in this paper. We carried out kinds of three-dimensional numerical simulations of the instability process in wide vaneless diffusers with different radius ratios. The results show that there are two kinds of stall patterns in wide vaneless diffusers with different radius ratios. For a short diffuser with a radius ratio of 1.5, the speed of the propagation of stalled cells is relatively high, and the propagation speed and frequency of stall cells do not change with the decrease in the flow rate. For a long diffuser with a radius ratio of 1.8, the propagation velocity of stall cells is smaller to the one in the short diffuser, and increases with the decrease in flow rate. For wide vaneless diffusers with different radius ratios, the main factor causing stall is the outlet reflux. Reducing the radius ratio of the wide vaneless diffuser has an important influence on the stability of the centrifugal compressor.

scholarly journals On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls

1933 ◽  
Vol 142 (847) ◽  
pp. 621-628 ◽  
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Finite Size ◽  
Critical Value ◽  
The Stability ◽  
The One ◽  
Von Mises ◽  
Shearing Motion ◽  
Determining Factor ◽  
Good Agreement

The turbulence problem is still unsolved, through a number of valuable papers have been published on it comparatively recently. But, since Hopf and von Mises proved that uniform shearing motion between two parallel planes was stable for infinitesimal disturbances but unstable for disturbances of a finite size has become more and more widely held. Von mises suggested that the reoughness of the walls might be the determining factor, but the experiments of Schiller have shown that the degree of roughness of the walls is of negligible influence on the critical value of Reynold's number. He concluded that the breakdown of laminar flow depended primarily on the size of the initial disturbance, in agreement eith Osborne Reynold's view. Important papers have been published by Noether and Tollmien, whose conclusions are in contradiction to one another. On the one hand, Noether, by a formal investigation of the asymptotic solutions of the equation governing the two-dimensional disturbances of flow between parallel walls, claims to have proved that all velocity profiles are stable for all values of Reynolds' number. On the other hand, Tollmien has determined a critical value of Reynolds' number for the flow past a flat plate placed edgeways to the stream. This value is in good agreement with the experimental results. There are, however, certain points in his analysis which are not clear and it would be useful to know if the method gave results in agreement with those derived more strictly.

Linear Stability Analysis of LPT Rotor Packets: Part II — Three-Dimensional Results and Mistuning Effects

2004 ◽  
Author(s):  
Roque Corral ◽  
Juan Manuel Gallardo ◽  
Carlos Vasco
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Stability Limit ◽  
Mode Shapes ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Frequency ◽  
Stability Maps ◽  
The Stability ◽  
The One

Part II of this paper compares the aerodynamic damping of a modern Low Pressure Turbine (LPT) interlock bladed-disc to the one obtained when the blades are welded in pairs through the lateral face of the shroud. The damping is computed using the linearized Reynolds averaged Navier-Stokes equations on a moving grid. It is concluded that the increase in stability of the welded-pair with respect the cantilever configuration due to the modification of the mode-shapes, is smaller than the one due to the overall raise of the reduced frequencies of a bladed-disc with an interlock design. The modification of the flutter boundaries due to mistuning effects is taken into account using the reduced order model known as the Fundamental Mistuning Model (FMM). It is shown that the modification on the stability limit of a interlock bladed-disc is negligible, while for a welded-pair configuration an increase of 0.15% on the critical damping may be expected. Two realistic welded-pair bladed-discs are analysed in this work. It is shown that both are aerodynamically unstable, which is in agreement with the experimental observations. Critical reduced frequency stability maps accounting for mistuning effects are derived for both, freestanding and welded in pairs airfoils. The airfoils are assumed to be identical and mechanically uncoupled. The stabilizing effect of mistuning is also retained in these maps.

scholarly journals Analysis of a two-phase model describing the growth of solid tumors

2012 ◽  
Vol 24 (1) ◽  
pp. 25-48 ◽  
Author(s):  
JOACHIM ESCHER ◽  
ANCA-VOICHITA MATIOC
Keyword(s):  
Solid Tumors ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Phase Model ◽  
Biophysical Parameters ◽  
Two Phase ◽  
The Stability ◽  
Cell To Cell Adhesion ◽  
Steady State Solutions ◽  
Well Posed

In this paper we consider a two-phase model describing the growth of avascular solid tumors when taking into account the effects of cell-to-cell adhesion and taxis due to nutrient. The tumor is surrounded by healthy tissue which is the source of nutrient for tumor cells. In a three-dimensional context, we prove that the mathematical formulation corresponds to a well-posed problem, and find radially symmetric steady-state solutions of the problem. They appear in the regime where the rate of cell apoptosis to cell proliferation is less than the far field nutrient concentration. Furthermore, we study the stability properties of those radially symmetric equilibria and find, depending on the biophysical parameters involved in the problem, both stable and unstable regimes for tumor growth.

scholarly journals Dynamics of three dimensional maps

2011 ◽  
Vol 24 (1) ◽  
pp. 105-117
Author(s):  
Asma Djerrai ◽  
Ilhem Djellit
Keyword(s):  
Invariant Manifolds ◽  
Three Dimensional ◽  
One Dimensional ◽  
Research Fields ◽  
Numerical Exploration ◽  
Wide Range ◽  
Planar Maps ◽  
The Stability ◽  
The One ◽  
One Dimensional Maps

Smooth 3D maps have been a focus of study in a wide range of research fields. Their Properties are investigated qualitatively and numerically. These maps show qualitatively interesting types of bifurcations than those exhibited by generic smooth planar maps. We present a theoretical framework for analyzing three-dimensional smooth coupling maps by finding the stability criteria for periodic orbits and characterizing the system behaviors with the tools of nonlinear dynamics relative to bifurcation in the parameter plane, invariant manifolds, critical manifolds, chaotic attractors. We also show by numerical simulation bifurcations that can occur in such maps. By an analytical and numerical exploration we give some properties and characteristics, since this class of three-dimensional dynamics is associated with the properties of one-dimensional maps. There is an interesting passage from the one-dimensional endomorphisms to the three-dimensional endomorphisms.

Transonic and Supersonic Inviscid Flow Equations in 3-D Eccentric Nozzles

2002 ◽  
Author(s):  
Ali Reza Mazaheri ◽  
Homayoon Emdad ◽  
Goodarz Ahmadi
Keyword(s):  
Three Dimensional ◽  
Flow Simulation ◽  
Inviscid Flow ◽  
Analytic Solutions ◽  
Inviscid Flows ◽  
Flow Equations ◽  
The Stability ◽  
The One ◽  
Volume Method ◽  
Steady And Unsteady Flows

Three dimensional unsteady inviscid flows in convergent-divergent nozzles is of importance in understanding the stability of rockets and jet propulsion. A computer program for evaluating unsteady inviscid flow conditions in three-dimensional eccentric as well as concentric nozzles is developed. The program uses the cell-centered finite-volume method based on Roe’s approximate Riemann solver scheme. The flow simulation results in concentric circular nozzles are compared with the one-dimensional analytic solutions and the accuracy of the computation model is verified. The results for steady and unsteady flows through eccentric and concentric convergent-divergent nozzles are then presented. A range of exit to throat areas, pressure ratios, and inlet Mach number are considered.

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