First things first: We start the time-dependent simulation at time t = 0 with an initial state, where the velocity field is equal to zero in the whole fluid domain. Even the velocity of the lid is equal to zero. Therefore, the Reynolds-Number Re and the kinetic energy are initially zero.

The Reynolds Number is defined as follows: Re = u*h*rho/eta. Therein u is the lid-velocity, h is the height of the cavity, rho is the density and eta is the dynamic viscosity of the fluid. Since the lid-velocity is a function of time, the Reynolds Number is a function of time too. For t in [0,1], the lid velocity is acceleratated from u = 0 to u=100. For t > 1, u is constantly equal to 100 and as a result Re is constantly equal to 10.000= 1e+05.

How to calculate the Volume Vortex Fraction: First, the velocity gradient L := nabla v, which is a rank 2 tensorfield, is calculated in each node of the grid. The cartesian coordinates of L are: L_ij := d_i v_j ( i = 1,2,3 ; j = 1,2,3 ) where d_i is the partial derivative operator in the i-direction and v_j is the j-coordinate of the velocity vector. In the next step we decompose the tensor L into a symmetric part S and an antisymmetric part W: S := 1/2 ( L + L^T ) and W := 1/2 ( L - L^T ) S_ij := 1/2 ( L_ij + L_ji ) and W_ij := 1/2 ( L_ij - L_ji ) In the next step we calculate the quantity Q in each node as follows: Q := 1/2 ( ||W||^2 - ||S||^2 ) where ||.|| is the Frobeniusnorm. To calculate ||S||^2, you simply have to square all elements of S and add them up. Proof that: ||W||^2 = 1/2 | curl v |^2 Next, we normalize the scalar field Q: Qn := 1 if Q > 0 Qn := 0 if Q <= 0 In the last step we integrate the function Qn over the flow domain G: VVF(t) := int_G Qn(x,y,z,t) dV Proof that VVF is the percentage of the Fluid Volume, where Q > 0 holds.

First things first: We start the time-dependent simulation at time t = 0 with an initial state, where the velocity field is equal to zero in the whole fluid domain. Even the velocity of the 4 sidewalls is equal to zero. Therefore, the Reynolds-Number Re and the kinetic energy are initially zero.

The Reynolds Number is defined as follows: Re = u*h*rho/eta. Therein u is the lid-velocity, h is the height of the cavity, rho is the density and eta is the dynamic viscosity of the fluid. Since the lid-velocity is a function of time, the Reynolds Number is a function of time too. All sidewalls have the same velocity magnitude. For t in [0,1], the lid velocity is acceleratated from u = 0 to u = 1. For t > 1, u is constantly equal to 1 and as a result Re is constantly equal to 100.

How to calculate the Volume Vortex Fraction: First, the velocity gradient L := nabla v, which is a rank 2 tensorfield, is calculated in each node of the grid. The cartesian coordinates of L are: L_ij := d_i v_j ( i = 1,2,3 ; j = 1,2,3 ) where d_i is the partial derivative operator in the i-direction and v_j is the j-coordinate of the velocity vector. In the next step we decompose the tensor L into a symmetric part S and an antisymmetric part W: S := 1/2 ( L + L^T ) and W := 1/2 ( L + L^T ) S_ij := 1/2 ( L_ij + L_ji ) and W_ij := 1/2 ( L_ij - L_ji ) In the next step we calculate the quantity Q in each node as follows: Q := 1/2 ( ||W||^2 - ||S||^2 ) where ||.|| is the Frobebniusnorm. To calculate ||S||^2, you simply have to square all elements of S and add them up. Proof that: ||W||^2 = 1/2 | curl v |^2 Next, we normalize the scalar field Q: Qn := 1 if Q > 0 Qn := 0 if Q <= 0 In the last step we integrate the function Qn over the flow domain G: VVF(t) := int_G Qn(x,y,z,t) dV Proof that VVF is the percentage of the Fluid Volume, where Q > 0 holds.

The separator separates an oil-air mixture from a screw compressor, with finely distributed oil droplets, into the two phases oil and air.

The vortex volume fraction VVF is a dimensionless global parameter and a measure of how strongly the flow is dominated by vortices. The VVF can be calculated for laminar as well as for turbulent flows. In the case of a rigidly rotating fluid with constant angular velocity, which is a purely laminar flow, the VVF will be equal to 1 and this means that the vortex covers the entire flow area. In contrast, in a pure shear flow VVF is equal to 0. In the Lid-Driven Cavity, the VVF depends on the Reynoldsnumber. Numerical experiments for 1000 < Re < 10000 show, that VVF increases with Re, what is intuitively expected. For my definition of VVF, see the video "Lid-Driven Cavity: Vortex Volume Fraction", September 08, 2024. Thank you for watching.

But sir what is Re and why with less time it is steady state

In this project, we have used the k-omega SST model.

For this LES-Simulation: Simcenter STAR-CCM+ plm.sw.siemens.com/de-DE/simcenter/fluids-thermal-simulation/star-ccm/

This VOF simulation requires an extremely fine grid and a relatively small time step in order to resolve the flow in detail without adaptive methods. In this case, an unstructured two-dimensional grid with almost 400000 cells (polygonal and prism-layer cells) was used. The average size of the cells in the core was 0.16 % of the characteristic length (diameter of the flow domain). Ten prism layers with a total thickness of 0.08 % in relation to the characteristic length were used on the wall. The size of the time step was 0.2ms. The VOF model was used without the optional sharpening factor. I hope this is helpful.

Thanks a lot taking the time to answer my question. Is is ineed helpful look at the video and also to understand the grid resolution. I've done something similar in 2D with around 500k cells and VOF, in StarCCM+. For me was interesting to see that by using the tria mesh the results seemed more realistic than by using poly mesh. Thanks again and good luck with your projects.

Korrekt! Oben links LES, unten rechts RANS.

Those two parts are mainly created to describe specific areas inside the cyclone separator. By using volumetric controls under ( automated mesh -> custom controls -> volumetric control) the user can specify different mesh settings for different areas. In the tutorial this is used to create a very dense mesh inside the cyclone separator to resolve the swirling motion properly.

@@cedricgrotzner1684 Thanks for your lucid explanation :) Now it makes sense .

Eine stehende Welle als Überlagerung einer links- und einer rechtslaufenden Welle setzt voraus, dass beide Laufrichtungen gleichberechtigt sind. Bei der ebenen Poiseuille-Strömung ist diese links-rechts Symmetrie nicht gegeben, da es im gewählten Bezugssystem, in dem die festen Ränder ruhen, eine mittlere Strömung von links nach rechts gibt. Für das von uns gewählte Modell wäre die Antwort also: Nein.

Die ebene Poiseuille-Strömung (Grundzustand) ist für Reynoldszahlen Re < 49.6 monoton stabil (Energiebetrachtung) und für Re > 5772 linear instabil. Der Übergang zur Turbulenz kann ab Re = 1000 erfolgen (Drazin & Reid, 1981).

The only other explaination is that K-Epsilon models offer a reasonable balance between accuracy, computational expense, and resilience

The settings in tutorials are typically due to educational reasons or due to simplicity. Of course one can use these settings as a starting point, but for better results one has to adjust the cfd-model. For a gear pump I recommend the k-omega-SST turbulence model, which combines the advantages of the k-epsilon and the k-omega model.

Thank you for your comment, I’ll compare the results to one another, maybe the difference is so small that one can use either models

Thank you. In the meantime, try this YT-Video: ANSYS FLUENT TRAINING: Golf ball Aerodynamics, CFD Simulation by ANSYS Fluent (kzbin.info/www/bejne/kIvOZGWthpxgfac)

For Details, please see the STAR-CCM+ Documentation: "Porous Resistance: Orthotropic Media" Tutorial. This tutorial solves the same problem as the "Porous Resistance: Isotropic Media" Tutorial, except that the fluid in the porous region cannot flow in any direction other than the bulk flow (y-) direction. This type of orthotropic porosity is specified by assigning large values to the inertial and viscous resistance components in the cross-flow directions (x- and z- directions in this case). The values of the components in the y-direction are the same as in the "Porous Resistance: Isotropic Media" Tutorial. Space: Three-Dimensional Material: Gas Flow: Segregated Flow Equation of State: Constant Density Time: Steady Viscous Regime: Turbulent, Reynolds-Averaged Navier-Stokes Reynolds-Averaged Turbulence: K-Epsilon Turbulence K-Epsilon Turbulence Models: Standard K-Epsilon K-Epsilon High y+ Wall Treatment: High y+ Wall Treatment The Video shows a modification of the original STAR-CCM+ model.

@@CFD-Bielefeld thanks for your explanation, but I couldn't find the video on your channel, I would be grateful if you could tell me which one?

The current video only shows the result, the full tutorial has not been implemented as a video so far.

Yes, it's a tutorial. For Details please see the "Porous Resistance: Orthotropic Media"-Tutorial from the STAR-CCM+ Documentation: "This tutorial solves the same problem as the Porous Resistance: Isotropic Media, except that the fluid in the porous region cannot flow in any direction other than the bulk flow (y-) direction. This type of orthotropic porosity is specified by assigning large values to the inertial and viscous resistance components in the cross-flow directions (x- and z- directions in this case)."

Wir werden ein zweites Experiment (mit Video) dazu durchführen. Geplant ist die Verwendung von Lebensmittelfarbe, um die Parabel besser sehen zu können. Wir vergleichen ferner die Messung mit der Theorie.