scholarly journals Models for water steam condensing flows

2012 ◽  
Vol 33 (1) ◽  
pp. 67-86
Author(s):  
Włodzimierz Wróblewski ◽  
Sławomir Dykas ◽  
Tadeusz Chmielniak
Keyword(s):  
Stokes Equations ◽  
Fluid Model ◽  
Vapour Phase ◽  
Separate Flow ◽  
Navier Stokes ◽  
Governing Equations ◽  
State Equations ◽  
Water Steam ◽  
Condensing Flows ◽  
Two Fluid Model

Models for water steam condensing flows The paper presents a description of selected models dedicated to steam condensing flow modelling. The models are implemented into an in-house computational fluid dynamics code that has been successfully applied to wet steam flow calculation for many years now. All models use the same condensation model that has been validated against the majority of available experimental data. The state equations for vapour and liquid water, the physical model as well as the numerical techniques of solution to flow governing equations have been presented. For the single-fluid model, the Reynolds-averaged Navier-Stokes equations for vapour/liquid mixture are solved, whereas the two-fluid model solves separate flow governing equations for the compressible, viscous and turbulent vapour phase and for the compressible and inviscid liquid phase. All described models have been compared with relation to the flow through the Laval nozzle.

scholarly journals AN UNSTEADY ANALYSIS OF NONLINEAR TWO‐LAYERED 2D MODEL OF PULSATILE FLOW THROUGH STENOSED ARTERIES

2003 ◽  
Vol 8 (3) ◽  
pp. 229-246 ◽  
Author(s):  
P. K. Mandal
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Plasma Layer ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Numerical Illustration ◽  
Navier Stokes Equations ◽  
Effective Measure ◽  
Two Fluid Model

The effects of red cell concentration and peripheral layer viscosity on physiological characteristics of pulsatile flow in presence of mild stenosis are investigated. The flowing blood is represented by a two‐fluid model, consisting of a core region of suspension of all the erythrocytes assumed to be non‐Newtonian (inhomogeneous Newtonian) and a peripheral plasma layer free from cells of any kind as a Newtonian fluid. In the realm of the flow characteristics of blood the viscosity is taken to be a function of hematocrit in a manner that it varies radially only in the central core characterising its non‐Newtonian behaviour while it remains constant in the plasma region. The arterial wall motion and its effect on local fluid mechanics is also incorporated in the present theoretical study. Finite difference scheme has been used to solve the unsteady Navier‐Stokes equations in cylindrical coordinates assuming axial symmetry under laminar conditions, so that the problem effectively becomes two‐dimensional. The nonlinear terms appearing in the Navier‐Stokes equations governing blood flow are accounted for. Finally, the numerical illustration presented at the end of the paper provides an effective measure of the flux, the resistive impedance and the wall shear stress quantitatively in order to validate the applicability of the present model.

scholarly journals Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Ponalagusamy ◽  
Ramakrishna Manchi
Keyword(s):  
Theoretical Study ◽  
Fluid Model ◽  
Porous Wall ◽  
Governing Equations ◽  
Rate Of Increase ◽  
Special Cases ◽  
Stenosed Artery ◽  
Flow Through ◽  
Two Fluid Model ◽  
Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Choice and Limits of a Fluid Model for the Numerical Study in Dynamic Fluid Structure Interaction Problems

2003 ◽  
Author(s):  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Dominique Lemoine ◽  
Bernard Peseux
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Solution ◽  
Fluid Structure ◽  
Design Engineers ◽  
Inviscid Incompressible Fluid ◽  
Basic Fluid

This paper is related to the study of a nuclear propulsion reactor prototype for the French Navy. This prototype is built on ground and is to be dimensioned toward seismic loading. The dynamic analysis takes the coupled fluid structure analysis into account. The basic fluid models used by design engineers are inviscid incompressible or compressible. The fluid can be described in a bidimensional by slice or a three-dimensional approach. A numerical study is carried out on a generic problem for the linear FSI dynamic problem. The results of this study are presented and discussed. As a conclusion, the three-dimensional inviscid incompressible fluid appears to be the best compromise between the description of physical phenomena and the cost of modeling. The geometry of the reactor is such that large displacements of the structure in the fluid can occur. Therefore, the linearity hypothesis might not be longer valid. The case of large amplitude imposed oscillating motion of a cylinder in a confined fluid is numerically studied. A CFD code is used to investigate the fluid behavior solving the NAVIER-STOKES equations. The forces induced on the cylinder by the fluid are computed and compared to the linear solution. The limit of the linear model can then be exhibited.

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

Cavitating Flow Simulation in a Closed Pump Sump by Two-Fluid Model and Its PIV Verification

2003 ◽  
Author(s):  
Yu Xu ◽  
Yulin Wu ◽  
Shuhong Liu ◽  
Yong Li
Keyword(s):  
Fluid Model ◽  
Flow Simulation ◽  
Cavitating Flow ◽  
Governing Equations ◽  
Two Phase ◽  
Averaged Equations ◽  
Flow Through ◽  
Pump Sump ◽  
Two Fluid Model ◽  
Two Fluid

In this paper, the two-fluid model was adopted to analyze the cavitating flow. Based on Boltzmann equation, governing equations for two-phase cavitating flow were obtained by using the microscopic kinetic theory, in which the equation terms for mass and momentum transportations can be obtained directly. Then the RNG k–ε–kg turbulence model, that is RNG k–ε model for the liquid phase and kg model for the cavity phase, was used to close the Reynolds time-averaged equations. According to the governing equations above, the simulation of the two-phase cavitating flow through a closed pump sump has been carried out. The calculated results have been compared with a PIV experiment. Good agreement exhibited.

scholarly journals Investigating the Effect of the Closure in Partially-Averaged Navier–Stokes Equations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Filipe S. Pereira ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Coherent Structures ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Auxiliary Functions ◽  
Modeling Accuracy

The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

Effects of Non-Dimensional Parameters on Formation and Break Up of Cylindrical Droplets

2004 ◽  
Author(s):  
Mohammad Taeibi-Rahni ◽  
Shervin Sharafatmand
Keyword(s):  
Stokes Equations ◽  
Fluid Model ◽  
Time Dependent ◽  
Navier Stokes ◽  
Ohnesorge Number ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Dimensional Parameters ◽  
Break Up ◽  
Eotvos Number

The consistent behavior of non-dimensional parameters on the formation and break up of large cylindrical droplets has been studied by direct numerical simulations (DNS). A one-fluid model with a finite difference method and an advanced front tracking scheme was employed to solve unsteady, incompressible, viscous, immiscible, multi-fluid, two-dimensional Navier-Stokes equations. This time dependent study allows investigation of evolution of the droplets in different cases. For moderate values of Atwood number (AT), increasing Eotvos number (Eo) explicitly increases the deformation rate in both phenomena. Otherwise, raising the Ohnesorge number (Oh) basically amplifies the viscous effects.

Sign in / Sign up

Export Citation Format

Share Document