Savvy Separators: Introduction to Computational Fluid Dynamics (CFD) for Separator Design
Alex Read
Director, Industry Sector Management
Siemens PLM Software

If you work in the field of process and separation, chances are you have come across computational fluid dynamics (CFD). CFD produces a wide range of emotions ranging from abject fear, often involving flashbacks to along forgotten university class and a dizzying array of partial-differential equations, to curiosity and even enthusiasm. The purpose of this article is to allay those fears, answer some questions and help you become an educated consumer of CFD.

CFD for separators

Many would start by asking the "so what" question: Why and when should CFD be cared about? This question will be answered, followed by a brief introduction to CFD including the major multiphase models, answering some frequently asked questions (FAQs) and ending with a short case study example of CFD and automated design exploration being applied to a cyclone separator , all of which will be achieved without recourse to a single equation!

So why should CFD be part of the separator design?

In today's "lower for longer" market, cost reduction is front and centre for all. CFD helps in all the phases of a project: from reducing the initial project costs (CAPEX) and operating costs (OPEX) to helping manage project extensions, such as tying in additional wells to an existing facility.

A subsea separator's job is to separate gases and liquid prior to pumping. Ensuring the separator meets its process requirements is important. The pump or compressor downstream will not perform as desired if there is carry-over or under (liquid in the gas stream and gas in the liquid stream). Should this occur, operations will have a very expensive problem to resolve.

In addition to meeting the minimum process requirements, there are other design considerations. There may be a need to reduce its weight to ease installation, understand how changes in upstream piping impact performance to provide a standardized design able to connect with many Subsea Processing Systems (SPS) configurations, minimize its size to reduce the amount of real estate used, minimize the pressure drop and the use and cost of internals.

Hand calculations, such as Stokes law, can be used to estimate the required residence time, but this involves assumptions about the flow (for example , no short-circuiting or even distribution across the flow area). Physical tests can be run, however these present their own challenges: cost and time, difficulty visualizing the complex multiphase flow, testing with process fluids and high pressures and temperatures introducing significant additional cost and safety concerns.

Using CFD, the flow patterns in upstream piping, inlet devices and within the separator can be predicted to ensure adequate residence time. Each separation mechanism can be studied such as estimating the tendency for liquid droplet re-entrainment due to high gas velocities and improving the performance of internals by increasing the uniformity of the flow to the demisters.

CFD achieves this with relative ease and speed, using actual process fluids, temperatures and pressures. After simulating the initial design, we can run "what-if" design studies to see how the design can be improved. In short, successful use of CFD results in discovering better designs, faster and at a lower cost.

This is predicated on the assumption that the CFD study was conducted correctly, and therefore the results can be trusted. Many of the uncertainties of CFD can be systematically tested for (such as a mesh refinement study), or can be interrogated by an engineer who understands the relevant physics at hand (and not CFD). A common concern is that results must be "tuned" to be accurate. This is not necessarily the case as accuracy can be obtained through systematic testing, quantification and minimization of uncer tainty and error, and by ensuring the problem is adequately posed and modelling assumptions are appropriate for the problem at hand.

The first step in interrogating a CFD solution is to use good engineering judgment. Does the flow field make sense, and if not, why? How does it compare with hand calculations, prior designs that have validation data and simpler analysis methods? In the early stages, CFD mistakes are often typos, so if it looks like the code solved a different problem to the one being investigated, there's a good chance it did!

Next, it takes a deeper explanation to understand the major steps in the simulation process and the potential impact of these on the results.

CFD attempts to solve the Navier-Stokes equations which describe the behavior of fluids. Unfor tunately, solving the Navier-Stokes equations is computationally intractable, so for all practical problems, the Reynolds Averaged Navier-Stokes (RANS) form is used. These suffer from the "closure problem" as they have more unknowns due to averaging which are resolved through the use of turbulence models. Models are also used to incorporate more advanced physics, such as multiphase flow dynamics.

Setting up a CFD study involves four steps:
1. Defining the domain of interest, geometry, flow entry and exit and boundary conditions (for example, velocity at the inlet)
2. Discretizing or meshing the domain: Rather than solving for the fluid behavior (velocity, pressure etc.) at every point in space, we segment the volume using a mesh, then solve the equations only at the center of each cell in the mesh - think of a separator filled with Lego bricks. CFD will tell you what the velocity, pressure, temperature and so on, is at the center of each brick. For completeness, in time-varying problems, time is discretized by solving for time increments, such as every 0.1 seconds.
3. Selecting the physics to simulate, whether the flow is single phase or multiphase, thermal or isothermal.
4. The CFD program then iteratively solves the equations to convergence.
These steps also represent the four areas of uncer tainty and where attention should be focused.

If a 3D CAD model or drawings of the geometry exist and are available, defining the domain typically is not an issue. Defining the flow conditions at the inlet and outlet is more challenging. In separator simulations it is typical to prescribe a droplet size distribution at the inlet, which requires knowing or estimating this. Typically, boundary condition information is available from other analysis methods - for example, from a 1D model of the system, from CFD by extending the domain of interest upstream to some point where there is less uncer tainty or by hand calculations, for example, to estimate minimum droplet sizes. The engineer who performed the CFD study should be able to explain what conditions were used, what these mean physically and why they are appropriate.


Figure 1 : Different cell types: tetrahedral (blue), hexahedral (green), polyhedral (red)

Next, the domain (geometry) needs to be discretized or meshed. This is an important and potentially time-consuming part of the analysis. A good mesh begets good CFD.

The mesh (number, size, and type of cells used) can influence the answer. As an example, if a CFD simulation is trying to simulate a vortex using one cell, the solver only has one point at which it calculates the velocity and pressure to represent the vortex. As the number of cells is increased, decreasing the size of each cell, the resolution and therefore accuracy of the representation of the vortex improves. A similar approach is used to ensure or minimize the influence of the mesh over the solution, the mesh is progressively refined (reducing cell size) until quantities of interest, such as pressure drop, stop changing. A short note on a well-established method for grid convergence studies can be found at1.

There are also different cell types: hexahedral (six sides), polyhedral (many sided, but typically soccer ball shaped with 12-14 sides) or tetrahedral (four sides).

Historically, tetrahedral meshes were often used, since building hexahedral meshes was difficult and time consuming, par ticularly for complex geometries. This is undesirable as tetrahedral cells have poor numerical properties; they artificially make the fluid behave as if it is more viscous. As a consequence, many more tetrahedral cells are required to attain the same level of accuracy as when using hexahedral or polyhedral meshes.

For tunately, meshing packages have improved significantly in the last decade, so it is now possible to build polyhedral or hexahedral meshes, even on complex geometries, without significant overhead.

After building the mesh, the engineer must select the physics to consider. One benefit of CFD is the ability to simplify problems to consider only the physics of interest, making it easier to interrogate and understand results and trends. This is also a double-edged sword as over simplifying can miss impor tant effects. As with boundary condition selection, the engineer performing the analysis should be able to explain the models used, their physical meaning and appropriateness for the problem at hand.

In the separator world multiphase modeling is key. There are three main multiphase models used in CFD:
  • Free-surface or Volume Of Fluid (VOF)
  • Eulerian-Lagrangian Multiphase often shor tened to Lagrangian Multiphase or LMP
  • Eulerian Multiphase (EMP)
In the VOF approach, the interface between the phases is resolved with the mesh. As in Figure 2, if droplets of water fall under gravity through air, CFD can capture the motion of the droplet using the VOF model if there is adequate mesh resolution to capture the shape and motion of the droplet in the mesh.

Consequently, this model is well suited for flows with a well-defined interface between the phases, such as stratified flow, where the mesh can be refined locally to capture the interface. A common application of VOF is to model the sea and its behavior around ships - there is a clear interface between the sea and the air.

VOF can be used to model flows other than stratified but the mesh needs to be refined to capture the multiphase effects at the interface between the phases, such as entrainment of fine droplets into the gas phase. However, this increases the computational cost of the analysis. In the separation world, VOF is often used to evaluate the bulk flow properties of the vessel.


Figure 2 : Droplets modelled using VOF

When the flow is dispersed, either Lagrangian Multiphase (LMP) or Eulerian Multiphase (EMP) is typically used.

In LMP, the continuous flow field is solved using the RANS CFD approach. In the example of droplets falling through air, the air is the continuous phase and the droplets are the dispersed phase. The continuous phase is solved in an Eulerian framework with a fixed mesh and the flow motion relative to the mesh. The full name for LMP is Eulerian-Lagrangian multiphase, but the Eulerian is dropped for expediency.

For the dispersed phase, the trajectory of each particle or droplet is solved for using Newton's second law of motion. The calculation of the droplet or particle motion is performed from the reference frame of the moving droplet, rather than the fixed mesh, which is known as a Lagrangian method. In order to reduce the computational cost and make it applicable to scenarios with a large number of droplets, each droplet represents an ensemble of droplets. Inputs to the motion calculation include submodels for the drag force and dispersion of droplets or par ticles due to turbulence. Additional sub-models can be introduced to include breakup and coalescence of droplets. The interaction between the phases can be either one- or two -way. One-way is where the motion of the droplets is influenced by the continuous phase but the continuous phase does not "see" the droplets; two -way is where both phases influence each other. The one-way coupling is often applied.

This method is an efficient and accurate way to model droplet or particle flow but is less applicable when the volume fraction of droplets or particles is high. Opinions on the volume fraction cut-off vary but are usually in the 5-10 percent range, at which point the model accuracy and stability deteriorate. For particle flows, more advanced models can be used to address this, such as Discrete Element Method (DEM) or Multiphase Particle-in-cell (MP-PIC). In the separator world, LMP is often used to study the motion of droplets in the gas stream.

For Eulerian multiphase, the full RANS equations are solved for each phase. Using the concept of "interpenetrating continua," the continuous and dispersed phases interact through source terms for drag, lift, virtual mass and turbulent dispersion. This makes it an immensely flexible model, able to simultaneously handle any number of phases and any range of volume fractions. Sub-models can be included to account for additional physics such as breakup and coalescence of droplets or bubbles, or heat and mass transfer.

The disadvantages of EMP are that each set of RANS equations comes at a cost (studying many par ticle sizes or phases becomes computationally expensive) and the user needs to understand, and choose, appropriate sub-models and settings. The downside of EMP's flexibility is that it can be applied to a wide range of multiphase flows, which results in multiple sub-models to be understood and applied.

For analysis of separators, EMP can be used to model the full vessel, but is particularly effective in mixing regions where volume fractions exceed the limitations of LMP and in tracking small droplets or bubbles with VOF is computationally expensive.

Having built the mesh, specified boundary conditions and chosen appropriate modelling assumptions, the solver uses iterative techniques to successively improve the solution until "convergence" is attained. Mathematically, convergence describes the limiting behaviour, particularly of a series towards its limit. In CFD, the series is the flow field (values for velocity , pressures etc.). The flow field reaches its limit when the values for velocity, pressure and so on, stop changing from iteration to iteration.

Convergence is often judged by monitoring residuals. Residuals measure the amount by which the discretized equations are not satisfied. A typical rule of thumb is that residual values should have dropped by three orders of magnitude.

If the residual values do not drop and the flow field continues to change, this may indicate that the steady-state assumption does not work due to inherent unstable phenomena like turbulence. Alternatively, it may indicate problems such as poor quality cells in the mesh or an ill-posed problem such as the location or values of boundary conditions.

Case study: Design space exploration of a gas-solid cyclone separator to improve separation efficiency

Having described the steps in setting up a CFD study and building confidence in the result, the following is an example of how CFD should be used to understand and improve the design and per formance of a gas-solid cyclone separator.

The CFD simulations were run using STAR-CCM+®, a Siemens PLM software. Figure 3 shows the geometr y of the separator, streamlines through the device with an iso-surface showing areas of low pressure, volume rendering of pressure contours and a comparison between CFD using multiple methods and experimental data for mean axial velocity at two locations in the cyclone. The purpose of these simulations was model verification, which is why multiple methods were used for the same case.

The baseline geometry for the design study is from an European Research Community On Flow, Turbulence and Combustion (ERCOFTAC) paper where the geometry and experimental data - Laser Doppler Velocimetry(LDV) - of the mean velocity profiles across the cyclone are available. Having validated the base model, CFD allows us to explore design alternatives quickly and easily. It can also be used in conjunction with tools that will automate the simulation process and efficiently explore the design space. In this case, the HEEDS multidisciplinary design exploration software from Siemens PLM, in conjunction with STAR-CCM+, was used.

For the design space exploration study, a constant gas velocity of 25 m/s was applied at the inlet. Sand particles with a diameter of 1.2 μm were introduced at the inlet, such that they accounted for one percent of the volume fraction of the flow. LMP with a one-way coupling to the continuous phase was used, along with the Reynolds Stress Turbulence model (RSM).


Figure 3 : Geometry and flow visualization for baseline design

The automation and design space exploration tool HEEDS uses algorithms to predict the next exploration point in the design space. HEEDS requires the engineer to provide:
  • Design objective(s): There can be more than one and these can be competing. In this case, the objective is to maximize the separation efficiency of the cyclone.
  • Constraints to be applied: In this case, the pressure drop across the separator cannot exceed a cer tain value or else the design will be deemed infeasible.
  • Different load cases to be evaluated, for example if the separation performance is different at different particle loadings.
  • Design variables: Their extents and sensible increments are to be defined. In this case, we vary the radius of the cyclone, the length of the constriction and parallel wall sections.

Figure 4 : Baseline cyclone geometry

Many different approaches have been developed to help explore the design space efficiently. These are often referred to as optimization algorithms and include among others Design of Experiments (DOE), genetic algorithm, downhill simplex and particle swarm. Optimization is often a misnomer since for most industrial applications no single optimal solution or design exists. However, these techniques can be highly effective in identifying better designs.



Figure 5 : Geometry of improved design, velocity magnitude along a plane section through the center of the cyclone and design study history showing the progressive improvement in separation efficiency

An impediment to the application of these methods is their multitude: Users must understand which method to use for any given scenario. HEEDS uses a hybrid and adaptive algorithm called SHERPA, which will switch between different exploration methods (DOE, genetic algorithm and so on) depending on the information it has about the analysis such as the number of variables and time and resources available. The benefit of using these methods is that they find better designs in less iteration than an engineer on their own or other optimization methods.

The correlation plot shows the relationship and degree of correlation between two variables, such as the radius of the cyclone and the cyclone separation efficiency. The numbers on the top right-hand side show the correlation between the two variables represented in the square (1.0 indicates perfect correlation).


Figure 6 : Correlation plot

The correlation plot helps the engineer to interrogate large amounts of data (100-plus designs), and to understand quickly what influences the design. In this case, the cyclone radius has a significant impact on its efficiency and pressure drop (correlation of 0.74 and 0.71 respectively).

Summary

To the non-specialist engineer, CFD can be initially daunting, particularly in more advanced areas such as multiphase flow and separation. While detailed knowledge of sub-models will remain with the specialist, non-specialist engineers can critique CFD results by evaluating whether the physical meaning of the results be explained and asking about the modeling decisions taken and their anticipated influence on the results and quantities of interest. By introducing the main multiphase models used, this article aims to help in this process.

CFD compliments other analysis methods (analytical or experimental). Its successful application can have a significant, positive financial impact on projects: by reducing the cost of design, improving and validating equipment performance and mitigating problems before they occur. Linking CFD with automated design space exploration tools can further the understanding and improvement of separator designs.