Turbulent flows are characterized by instable eddies, which emerge, fall apart, and disappear again, and therefore constantly moving the fluid. Turbulent flows are therefore always unsteady. The turbulent eddies decay into smaller and smaller eddies, until the kinetic energy is dissipated by viscous dissipation. The lengthscale of these smallest eddies, the so-called Kolmogorov length-scale, is often very small, being on the order of micrometers.

The set of equations which is solved in a standard CFD analysis are the continuity equation (mass conservation) and the 3 “Navier-Stokes” equations (momentum conservation in 3 dimensions). We thus have 4 equations for 4 unknown variables – the pressure and the velocity in 3 dimensions. To fully solve these equations numerically, including a correct calculation of turbulence is possible. This approach is called DNS: “Direct Numerical Simulation”. The required computational power is extreme, and a DNS approach is not possible for industrial applications. The required computational power scales as , making it impossible to calculate flows with high Reynolds numbers. DNS is used extensively at universities, however, to study the fundamentals of turbulent flows.

In industrial applications, we are constantly making a trade-off between (1) a correct physical approach, and (2) the available budget and computational resources. In most cases, a “steady-state” solution is calculated, thus time-averaging the flow. Here problems arise: we try to solve an unsteady, turbulent flow using a time-averaged method.

For this steady-state solution, the Navier-Stokes equations are time-averaged, which results in the RaNS equations: the Reynolds-averaged Navier Stokes equations. In the mathematical process of Reynolds-averaging, 6 new variables are created: the so-called Reynolds stresses. Here the fundamental problem of solving turbulent flows becomes clear: we have a “closure problem”: more unknown variables than governing equations. Mathematically we cannot solve the RaNS equations as we don’t have sufficient equations. These equations are modelled with “turbulence models”.

With turbulence models, we simulate the characteristics of turbulent flows. A turbulence model therefore always is a simplification of reality – often useful, never fully correct, not seldom completely wrong. The knowledge and experience of the CFD specialist is crucial to apply the turbulence model and asses to the results.

The many different turbulence models are categorized by the amount of partial differential equations (PDE’s) which are solved. The “zero-equation models” are simple, arithmetic correlations. They are computationally inexpensive, and are rarely used to obtain final results. “One-equation models”, such as the Spalart-Allmeras model, are a bit more expensive, and are used in specific fields.

“Two-equation models” are more often used. They solve 2 PDE’s: one for the turbulent kinetic energy and the energy dissipation , or the specific dissipation . These and models have proven its use throughout the years, and are able to produce useful results. A mix between these models, the SST model has gained popularity, as it tries to combine the strong points of both.

Numerically more expensive are the Reynolds stress models, which directly solve the 6 components of the Reynolds stresses. This model is used to solve more complex flows, such as flows which larges areas of flow separation, swirl or recirculation.

A completely different approach is to perform a “Large Eddy Simulation”. Turbulence is not fully calculated as in DNS, but also not completely averaged and modelled as in RaNS. Larger eddies are calculated in a transient simulation, and the smaller (sub-grid length) eddies are modelled. For specific situations, LES is a useful choice. The computational costs are somewhat in between DNS and RaNS.

The computational power continues to increase. Research on turbulence is more active than ever, and much effort is made to make numerical methods faster and more robust. It had been expected that LES would largely replace RaNS methods, but so far a large “transition” did note take place. Who knows: maybe in the far future DNS is the standard, and our current turbulence models are seen as completely outdated. For the coming decades, RaNS and the various turbulence models will remain the golden standard for many practical applications.

]]>The thin fluid layer close to the wall is referred to as the boundary layer. For increasing Reynolds numbers the boundary layers continues to decrease in thickness. The Reynolds number, defined as Re = (ρ U L)/μ, is the ratio between inertial forces and viscous forces. In a highly turbulent flow with a high Reynolds number, viscous forces hardly play a role.

For the hypothetical case of Re →∞, the boundary layer is infinitely thin, and consequently every wall is seen as “rough” to some extent by the flow.How much the roughness affects the flow depends on the ratio between the boundary layer thickness and the size of the roughness. A turbulent boundary layer can be divided into a number of layers. The layer directly bordering the wall is called the viscous sublayer. The flow behaviour in the viscous sublayer is identical to a laminar (viscous, layered) flow: in both cases, viscous forces are dominant

The size of the wall roughness k_{s}compared to the thickness of the viscous sublayer is key. We can distinguish 3 different regimes for turbulent flows

k_{s} < viscous sublayer thickness | Hydraulically smooth | The roughness is small compared to the viscous sublayer. Consequently, the roughness does not affect the flow. |

k_{s} = 1 – 14 x viscous sublayer thickness | Transitionally rough | Roughness affects the flow. Viscous friction and roughness friction both play a role. |

k_{s} > 14 x viscous sublayer thickness | Fully rough | The roughness is large compared to the viscous sublayer, and completely alters the boundary layer dynamics. Friction caused by roughness is dominant, and the friction becomes independent of the viscosity. |

Earlier we mentioned that the flow behavior of a laminar flow and the viscous sublayer are identical. Consequently, roughness does not affect the flow in a laminar flow.

The friction is made dimensionless using a friction coefficient C_{F}. Together with the Reynolds number and the roughness, C_{F}is related to the pressure drop. In figure 2 we show the well-known Moody diagram[RV1] , in which this relation is made explicit for pipe flow.The roughness does not only affect the friction, but also the velocity profile in the boundary layer. The velocity gradient decreases together with the shear stress on the wall.

For hydraulically smooth flows, the friction coefficient equals C_{F,smooth}: the roughness does not yet affect the flow. For a fully rough flow, C_{F}becomes a constant value; it no longer depends on the Reynolds number. In fully rough flows, energy is dissipated by pressure forces acting on the roughness rather than by viscous skin friction. Consequently, the viscosity (and thus the Reynolds number) becomes irrelevant. In the transitionally rough regime, both effects (viscous skin friction and pressure forces) are of comparable magnitude.

Roughness in itself is difficult to quantify. Let us take figure 2 for instance, in which we show a sawtooth roughness profile. The roughness parameters (such as an averaged height) can be easily calculated. For the fluid friction, however, the direction of the flow matters. A similar behavior is observed for welding seams or turned parts: whether the machined roughness is streamwise or transverse differs.

In many commercial CFD software, the equivalent sandgrain roughness can be used as an input parameter. The roughness must be related to an equivalent sandgrain roughness. How the roughness affects the flowfield and the friction is calculated using available experimental data. Most of these experiments are performed in pipe flow. The classical experiments by Nikuradse in the ’30 of the last century are still heavily used. To which extend the roughness behavior is universal is not yet entirely known. Also for completely different types of flow (e.g. flow over a wing), these pipe flow experiments are used. Active research is ongoing to better understand the universal- and non-universal effects of roughness.

Consequently the field of roughness in CFD advances quickly. It is expected that many studies on numerical methods and roughness will be published in the coming years. By the implementation of this knowledge in new models, the quality of the roughness models will be improved continuously.

]]>Performing a correct CFD analysis is not straightforward, and much expertise and knowledge about the subject is necessary before a good analysis can be made. We usually divide a problem into 3 components:

- The customer’s question
- The geometry
- The boundary conditions

A well-posed question is of prime importance, as we adapt our approach to problem

Therefore, it is important that the customer knows what he wants to know. Is a single pressure drop value needed? Or is extended knowledge about the flowfield necessary? Is an “order of magnitude” of the pressure drop sufficient, or are at least 4 decimal places necessary?

In the process of formulating the question, we also try to understand the flow itself. Does the temperature play a role? Is the flow composed of a single fluid, or a mixture between multiple phases? What about the presence of membranes, filters or porous media? Membrane filters are often modelled as porous media with a replacing resistance coefficient, which is often determined experimentally. The (computational) costs increase with the complexity of a flow. Therefore, we prefer to simplify a flow just to heart of the problem.

A clear question enables us to perform a correct analysis. The results we deliver are adapted to the demands of the customer.

A good mesh quality is crucial for a correct CFD analysis. In a mesh, the flow domain is divided in a large number of tiny volumes. The conservation laws (mass, momentum, energy) are applied to these control volumes. By doing so, the flow field is calculated.

In the figure, a pipe tee is shown. The flow goes through the pipe, so we make a mesh of the flow domain. In the figure we show a typical mesh, in which we always locally refine the mesh close to the walls. Here the velocity gradient is large, and a fine mesh is needed for a correct simulation.

To increase the mesh quality, we often simplify the geometry. A too detailed geometry results in meshing issues, whereas many components hardly affect the flowfield. Typical examples of “troublemakers” are:

- Nuts, bolts, threads, etc
- Thin walls
- Sharp edges
- Thin flow passages

We always process the geometry, in close consultation with the customer, so that a good mesh is made without losing important geometry features.

Often, a customer seeks an ideal design for his problem. In those cases, the geometry is not known a priori, but part of the customer’s question. In the design of the optimal geometry, we of course take the manufacturability into account.

After a mesh is created, we pre-process the CFD simulation and we have to set our boundary conditions. This starts with defining the global properties of our flow domain. The fluid must be known, with the density and viscosity being the most crucial parameters. For more complex flows, such as multiphase flows these parameters must be known for all flow components. A multiphase flow is a mixture between multiple immiscible components, such as a liquid-gas mixture, a fluid with solid particles, or immiscible liquids, such as an oil-water mixture. For problems involving heat transfer, also the thermal material properties must be known. The same holds for compressible fluids, such as high-speed gasses.

Hereafter we set the boundary conditions of the domain.

- Inlet
- Something must be known about the amount of fluid entering the domain. This can be a (mass) flow rate, but also a pressure or a velocity.

- If applicable, a temperature must be given.

- Outlet
- Just as with the inlet, something must be known about the flow leaving the domain. Often this is the (ambient) pressure, but a (mass) flow rate is also possible.

- Wall
- The “no-slip condition” is the condition that the fluid directly at the wall has the same velocity as the wall itself. Usually the walls are non-moving, just as the fluid close to the wall. Walls with a speed also occur, for instance in turbomachinery. Sometimes wall roughness plays a role, affecting the flow field and the friction.

- If heat transfer plays a role, it must be clear if the walls have some temperature or whether the walls are adiabatic (no heat transfer).

We now return to the original question of the costumer. With a well-posed question, a clear geometry and evident boundary conditions, it is possible to perform a concise CFD analysis. With a well-posed question, it is also possible to give a clear answer. CFD specialists are always able to help you to define a problem. With this article, we hope to have been able to assist you in defining your fluid problem.

]]>Fluid dynamics are studied in 3 different ways: analytically, numerically and experimentally. Analytical calculations are useful or “order of magnitude” estimations. We gain insight in the relevant system parameters by doing so, we can calculate the approximate pressure drop, or we can determine whether a flow is laminar or turbulent. Furthermore, a solid understanding of the mathematical description of a flow is pivotal to correctly interpret experiments or simulations. To calculate a flow profile with a sum by hand, however, is only possible for the most simplified class of problems, such as a steady laminar pipe flow. Transient flows, turbulent flows, or flows in more complex geometries cannot be calculated similarly by analytical means.

Traditionally, if analytical calculations were not sufficient, we relied on experimental investigations. Experiments provide an enormous understanding of the dynamics of a flow. We can visualize a flow by adding smoke of dye. And we can quantify a flow with velocity-, temperature- and pressure measurements. Earlier most of these measurements were “intrusive” – a probe was directly put in a flow. Over the last 2 decades, we switched to optical methods, such as Particle Image Velocimetry (PIV), Particle Tracking Velocimetry (PTV) and Laser Doppler Anemometry (LDA). Here, the flow is illuminated with a laser, whose light is reflected by added tracer particles. The velocity is measured by the redshift (LDA), or by making two photos, which are correlated (PIV, PTV).

Experiments have their limitations, however. Experiments are relatively costly, both in equipment as in manpower. Making good experimental setups and performing multiple iterations are very time-consuming.

Only relatively recently, computer simulations became popular for industrial applications. Earlier, numerical simulations were only performed by universities and specialized companies such as Boeing and NASA. In the nineties, user-friendly commercial codes were introduced, which enabled the use of numerical simulations for a larger group of companies.

In numerical simulations, the underlying mathematical flow equations (the Navier-Stokes equations) are calculated numerically and solved at discrete points. This technique is commonly referred to as computational fluid dynamics (CFD). The Navier-Stokes equations are often simplified to the Reynolds-averaged Navier-Stokes equations. By doing so, the turbulence properties are averaged in time. As shown in the figure, a geometry is split up in tiny volumes. The conservation laws of mass, momentum, and energy are applied to these volumes. Resultantly, the entire *mesh* is analyzed and we obtain the numerical solution.

In the translation from a real flow to the numerical solution, we have to simplify the flow. Usually, we simplify the geometry to ease the meshing, and the turbulence properties are modeled in a simplified way. Consequently, some people are skeptical about the benefits of numerical simulations.

However, simulations have a number of significant advantages over experiments. Firstly: numerical simulations are faster and cheaper than experiments. Secondly: iterating is easier. A different geometry, a different fluid, a larger velocity of volume flux: all are parameters which can be varied. In this way, a design process is simplified and faster. Thirdly: in experiments, we mostly measure a single important parameter, such as the pressure drop. In simulations, all flow data is available. We can visualize the flow with velocity vectors, movies, contour plots and streamlines. Therefore, we gain more insight of the flow, and better understand its problematic areas.

Will simulations completely replace experiments? No, probably not. Experiments always result in valuable insight without any simplifications. And in more specific research areas, experimental validations for the numerical simulations are often needed due to the complexity of the flow. In this way, experiments, numerical simulations and analytical methods all give a different way of understanding a flow. In that sense, they are completely complementary and will remain like that for the time being.

]]>DEMCON Bunova becomes part of just a hand full of specialists in the BENELUX that received this award based on their experience in solving complex physical problems with COMSOL Multiphysics.

We see that title as a recognition of the work we do and thank COMSOL for their confidence.

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