Application of CFD Methods for the Simulation of the Flow Through a Filter in Dependency of the Operating Time

Filters are playing an important role in process engineering, chemical engineering as well as in many machineries like gas turbines, air conditioners or cars. At present it is possible to calculate the flow through a filter and predict the average pressure loss of the flow for the initial state of the filter medium. In the present paper a pragmatic procedure is introduced, which makes it possible to consider the deposition of dust onto the filter and the influence on the flow implied with it. For the application of the method the commercial CFD-Code FLUENT is used. The reasonability of the concept is shown by regarding the characteristic time scales of the flow and the dust deposition. The method is used to simulate the flow through a filter within a quadratic tube in dependence of the operating time.

Theory to Help the Use of Electromagnetic Flow Meters

Compared with other flow meters, the theory of electromagnetic flow meter is well developed. Until now, we are able to predict the three dimensional characteristics of this kind of flow meters with reasonable accuracy. This has given much help to the designers to improve the flow meters. On the other hand, the theory can offer a tool for the users of this kind of flow meters to judge the application situations, estimate the possible measurement error, etc. This paper introduces the recent work of the author on the theory of the electromagnetic flow meter. The basic physical conceptions and equations are given with a brief history review of the theory research. Several examples are given of using the theory to analyze the meters’ behavior in different application situations. They are: effect of the conducting pipe connections; errors caused by a pipe wall of different electromagnetic properties; gas-liquid flow and errors caused by a relative motion of the probe.

Large Eddy Simulations of a Hydrocyclone

Subgrid-scale modeling, which characterizes Large Eddy Simulation (LES), has been used to predict the behavior of a water-fed hydrocyclone operating without an air core. The governing equations were solved by a fractional step method on a staggered grid. The Smagorinsky subgrid-scale model was employed to account for turbulent effects. Numerical results actually capture the main features of the flow pattern and agree reasonably well with experiments, suggesting that LES represents an interesting alternative to classical turbulence models when applied to the numerical solution of fluid flows within hydrocyclones.

Spray Impact Onto a Rigid Wall: Modelling Strategy

The common approach to the modelling of spray impact is to treat the phenomenon as a simple superposition of single drop impact events [1]. The main input for such model formulation is obtained either from experimental [2,3] or theoretical [4,5,6] studies of the impact of a single drop onto a dry wall, onto a uniform, undisturbed liquid film or into a deep pool [7]. However, in [8] it was shown that this conventional approach is not universal in the description of the spray impact and that in the case of relatively dense sprays, the interaction of crowns (Fig. 1) and the oscillations of the liquid-wall film must be taken into account. For example, these interactions result in the emerging of uprising jets during spray impingement of the diesel spray (see Fig. 2). In the study of spray impact we have chosen the following strategy of the modelling: 1. Description (experimental and theoretical) of single dropimpact. Determining of the parameters influencing the splash. 2. Description of the interaction of two drops on the wall surface. 3. Determining of the parameters of the single drop impacts influencing the dynamics of the film formed on the wall. Characterization of the film: the time averaged thickness, the time averaged velocity and its fluctuations. 4. Description of the influence of the oscillating motion of the film on the outcome from a single drop impact. Single drop impact onto a wetted wall—The motion of a kinematic discontinuity in the liquid film on the wall due to the drop impact, the formation of the uprising jet at this kinematic discontinuity and its elevation are analyzed. The theory [4] for the propagation of the kinematic discontinuity is generalized for the case of arbitrary velocity vectors in the inner and outer liquid films on the wall. Next, the mass, momentum balance and Bernoulli equations at the base of the crown are considered to obtain the velocity and the thickness of the jet on the wall. An analytical solution for the crown shape is obtained in the asymptotic case of such high impact velocities that the surface tension and the viscosity effects can be neglected in comparison to inertial effects. The edge of the crown is described by the motion of a rim, formed due to the surface tension. The theoretical predictions of the height of the crown are compared with experiments. The agreement is rather good in spite of the fact that no adjustable parameters are used (see Fig. 3). Three different cases are considered: normal axisymmetric impact of a single drop, oblique impact of a single drop, and impact and interaction of two drops. Next, two new parameters of single drop impact influencing the dynamics of the film formed due to the polydisperse spray impact are identified. The first one is associated with the relative presence of the crown on the film surface and allowing one to estimate the probability of crown interactions. The second parameter is associated with the axial momentum in the plane of the wall. Time-averaged film motion—The theory of the creation of the film by spray can be subdivided into three main parts: 1. The characterization of the spray, particularly definition of the flux vectors of scalar properties (number flux vector, volume flux vector, etc.) and the momentum flux tensor. 2. Boundary conditions at the time-averaged spray/film boundary. 3. Dynamics of the film motion on the wall. The mass and momentum equations of the film are formulated accounting for the volume flux of the spray, the dynamic pressure, and the time-averaged stress vector at the film “free” surface caused by the inertia of the spray. The inertial terms of the liquid in the film contains of the inertia of the time-averaged motion and the inertia of film oscillations. These oscillations are modelled as an ensemble of the radial flows in the film associated with the single drop impacts. The probability of the crown interactions is also taken into account. Jetting at the film surface due to impingement of a dense spray—Here we consider impact of such dense sprays that the probability of single crown to propagate without interaction with another crown is very small. The non-uniformities in the dynamic pressure in such sprays yields the significant fluctuations in the film velocity leading to the shocks and jetting (as in the case of the diesel spray impact shown in Fig. 2). We describe the statistically averaged distribution of drop impacts around a given drop assuming that all the impacting drops are distributed randomly in space and in time. The statistically averaged dynamic pressure around given drop is not uniform either in the time or in the radial direction. The self-similar solution for the statistically averaged radial velocity in the film and its thickness (Fig. 4) is obtained. The characteristic time of the instant of shock is estimated. The theoretical predictions of the jets diameter agree with the experimental data in the order of the magnitude.

Super-Fine Structure in the Critical Flow-Rate of Critical Flow Venturi Nozzles

It is shown that critical flow Venturi nozzles need time intervals, i.e., more than five hours, to achieve steady state conditions. During these intervals, the discharge coefficient varies gradually to reach a value inherent to the pressure ratio applied. When a nozzle is suddenly put in the critical condition, its discharge coefficient is trapped at a certain value then afterwards approaches gradually to the inherent value. Primary calibrations are considered to have measured the trapped discharge coefficient, whereas nozzles in applications, where a constant pressure ratio is applied for a long time, have a discharge coefficient inherent to the pressure ratio; inherent and trapped coefficients can differ by 0.03–0.04%.

Experimental and Numerical Study of the Coanda Effect Used to Reduce Self-Sustained Tones

We present in this paper an experimental and numerical study about the Coanda effect which causes the sudden reattachment of a jet to an inclined plane. This phenomenon induces a large hysteresis loop, which can be used to reduce the noise produced by an airflow crossing two diaphragms in tandem inside a duct. The angle of the inclined wall with horizontal plane and the flow velocity are the two main parameters studied here. With the aim of doing optimal control, we propose to construct for this flow configuration a low-dimensional dynamical system with a basis issued from a Proper Orthogonal Decomposition.

LES of a Three Dimensional Shock-Wave/Boundary Layer Interaction in a Channel Flow

This study deals with the Large Eddy Simulation of a 3D unsteady shock wave/boundary layer interaction, in sight of turbomachinery applications. The simulation of a compressible flow through a 3D channel (ONERA) has been performed in LES, with a third order WENO scheme (Jiang, Shu, 1996) and the mixed scale model (Tenaud, Ta Phuoc, 1996). The flow has already been studied experimentally at ONERA (Cahen, 1995), and numerically with RANS modeling (Gerolymos, Vallet, 1997). The unsteady results obtained by LES within and downstream of the 3D interaction are presented and analyzed. The mean velocity profiles in the interaction zone, are then compared to both experiments and statistical numerical results.

Large Eddy Simulation of the Wake Behind a Turning Ship

This study examines the dynamics of turbulent flow in the wake of a turning ship using the large eddy simulation (LES) technique. LES is applied in conjunction with a random flow generation (RFG) technique originally developed at West Virginia University to provide unsteady inflow boundary conditions. As the ship is turning, the effects of the Coriolis and centrifugal forces on vortical structures are included. The effects of the Coriolis force on the flow-field are assessed and a grid sensitivity study is performed. The predicted turbulence structures are analyzed and compared with the wake of a non-turning ship.

Accuracy of the Operator Splitting Technique for Two-Phase Flow With Stiff Source Terms

Code for analysis of the water hammer in thermal-hydraulic systems is being developed within the WAHALoads project founded by the European Commission [1]. Code will be specialized for the simulations of the two-phase water hammer phenomena with the two-fluid model of two-phase flow. The proposed numerical scheme is a two-step second-order accurate scheme with operator splitting; i.e. convection and sources are treated separately. Operator splitting technique is a very simple and “easy-to-use” tool, however, when the source terms are stiff, operator splitting method becomes a source of a specific non-accuracy, which behaves as a numerical diffusion. This type of error is analyzed in the present paper.

Parametric Study of the Discharge Coefficient on Critical Sonic Nozzles ISO-9300 With Turbulent Boundary Layer

A parametric study on determining discharge coefficient in ISO 9300 [1] toroidal sonic nozzles have been developed. The focus of this paper is to obtain the an analytical model for the calculus of this discharge coefficient on turbulent boundary layer conditions for gases at Pr = 0.7. The problem is divided in two sections: one in which the viscous stresses are taking in to account at boundary layer zone, based on turbulent boundary layer theory and taking as starting point the work carried out by Stratford [2]. Then, curvature of flow field is studied at the nucleus of the nozzle, obtaining discharge coefficient values using numerical simulation for a two-dimensional flow. The results have a good agreement with correlations of ISO-9300 [1], experimental and numerical data of Wu-Yan [3] and the analytical model from Stratford [2].