Wind turbines (not to be confused with windmills) were first used to generate electrical power in the 19^{th} century. Scottish innovator James Blyth is largely credited with this invention. Supposedly, Blyth used a wind turbine to generate electricity for his cottage. He later improved the design to provide power to a nearby asylum.

*Different types of VAWTs compared to the operation of a HAWT.*

The use of wind-generated electrical power is continuously increasing. To help with the growing demand, engineers must ensure that wind turbine designs are highly efficient. This is a particular challenge for VAWTs, which struggle with peak efficiencies and starting torque, among other issues. On the other hand, VAWTs have several benefits. For instance, they are easier to install and maintain than HAWTs and don’t need to point windward. VAWTs can also be used in urban areas and in smaller scales and are a low risk for humans and wildlife.

To overcome the shortcomings of VAWTs while harnessing their advantages, we can use pitch control systems. These systems improve the starting torque and efficiency and provide a broader operating range than traditional fixed-pitch VAWTs.

Let’s explore simulation research* from a team at Sam Houston State University and Southeastern Louisiana University that examines how airfoil pitch control affects the efficiency of a VAWT.

The researchers investigated a dynamic control system that contains both pitch and camber controls. This system is comprised of three blades (or airfoils) with flaps at the trailing edge. At the center of the system is a vertical-axis hub that is attached to blade-supporting arms. Each airfoil is connected to one of these support arms and freely pivots with respect to the arm. The independent pivoting enables the airfoils to have adjustable wind attack angles.

With an airfoil pitch control system, the angle between the support arms and airfoils can be altered for any given support arm position. This changes the attack angles between the wind and airfoils, redistributing the air pressure on the airfoil surfaces.

*Top view of a VAWT system with both pitch and camber controls. Image by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston presentation.*

From this system, the researchers modeled a 2D NACA 0012 airfoil within a rectangular area that represents one section of a wind tunnel. To simulate rotation, the rectangular box is moved while the airfoil is fixed in the horizontal direction.

*Left: A NACA 0012 airfoil inside a rectangular wind tunnel. Right: The rectangular box is rotated to simulate an airfoil rotated 30°. The mesh seen here is used for illustration purposes. Images by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston paper.*

The researchers used this model to analyze velocity and pressure at different airfoil pivot angles (wind angles of attack), support arm angles, and wind speeds. Through this, they can determine an optimal pivot angle for any given support arm position, maximizing torque and energy production and achieving a higher efficiency than VAWTs with fixed airfoils.

It’s important to note that this analysis does not include the centrifugal and Coriolis forces found in a VAWT system. As such, this study may be a good start, but the team needs to account for the influence of inertial forces for accurate and proper optimization.

The research team studied their model’s velocity profile at a 30° angle of attack when exposed to a wind speed of 20 m/s. They found the maximum air flow speed (35.6 m/s) near the leading edge of the airfoil and the minimum air flow speed (0.02 m/s) at the leading edge on the bottom side of the airfoil. This air flow behavior is mirrored when studying different airfoil rotation angles.

*Left: The velocity field at a 30° angle of attack. Right: The velocity on the top and bottom airfoil surfaces. Images by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston presentation.*

When looking at the pressure field of the airfoil surface at the same 30° angle of attack, the team noted that the peak pressure occurs in areas with the lowest flow speeds (close to the leading edge at the top of the airfoil) and vice versa. At the bottom of the airfoil, velocity and pressure remain almost constant except for the change near the leading edge.

*Left: The pressure field at a 30° angle of attack. Right: The pressure on the top and bottom airfoil surfaces. Images by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston presentation.*

Moving on, let’s examine the results for torque. Here, the researchers calculated torque in relation to the VAWT’s rotation center from the pressure field on the airfoil surface. As we can see in the following plot, torque increases with the angle of attack until it reaches its peak value at a 90° angle of attack. After this, torque drops and eventually returns to near-initial values as the angle of attack continues to grow.

*The torque with a support arm angle of 30° and wind speed of 20 m/s. Image by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston presentation.*

Next, let’s see how torque values are affected by other support arm angles. The following results indicate that torque peaks at a 90° angle of attack for all support arm angles. As such, designing a control mechanism that keeps NACA 0012 airfoils at a constant 90° angle of attack will maximize device efficiency and energy production.

*Comparisons of the torque distribution and attack angles for various support arm angles. The different curves represent support arm angles ranging from 0° to 90° (left) and 90° to 180° (right) at 10° increments. Images by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston paper.*

In regards to laminar and turbulent wind speeds, when the support arm is constantly at 30°, there is an insignificant gain in torque due to the increased wind speed. Further, wind speed does not affect the torque distribution pattern.

*Comparison of the effects of different wind speeds. Image by J. Ma, C. Koutsougeras, and H. Luo and taken from their COMSOL Conference 2016 Boston presentation.*

Using the knowledge gained from these studies, the researchers found that there is an optimal airfoil pivot angle that yields maximum torque at a given VAWT rotation angle. This information provides guidance for designing airfoil pitch control systems. For their next step, the team can increase the accuracy of their optimization by including centrifugal and Coriolis forces. Like we mentioned before, this is an important step in improving the study.

The researchers also hope to improve their studies by accounting for other factors, including multiple airfoils and support arms as well as the effect of wake from wind passing through one airfoil to another. In future studies, they are considering using a 2D and 3D multiblade model, studying a nonsymmetric airfoil, and more.

- Read the full paper: “Efficiency of a Vertical Axis Wind Turbine (VAWT) with Airfoil Pitch Control“
- Browse the COMSOL Blog for more research on wind turbines:

**The research shown here was presented at last year’s COMSOL Conference in Boston. If you are interested in presenting your own work at this year’s conference, please submit your final abstract by June 30.*

Get more details and submit an abstract:

]]>

Building physics engineers aim to improve the energy performance and sustainability of building envelopes. Although their practices are based on past experience, new materials and building techniques are constantly being developed that offer a wide set of options in building design and thermal management. Let’s see how to model heat and moisture transport in building materials to help reduce energy costs and preserve buildings.

*Building envelopes can be analyzed by modeling heat and moisture transport.*

Controlling moisture is necessary to optimize the thermal performance of building envelopes and reduce energy costs. The thermal properties of insulation or isolation materials usually depend on both temperature and moisture content. Therefore, a coupled heat and moisture model helps us fully analyze the thermal performance of a building component. One example is the dependence of a lime silica brick’s thermal conductivity on relative humidity.

*The moisture dependence of thermal conductivity for lime silica brick.*

The figure above shows that lime silica brick becomes two times less thermally isolating for high relative humidity values.

In addition, we must consider moisture control in the building design process to choose building components that can reduce the risk of condensation. The coupled modeling of heat and moisture transport enables us to analyze different moisture variations and phenomena in building components, such as:

- Drying of moisture resulting from the initial construction
- Condensation due to the migration of moisture from outside to inside during warmer periods
- Moisture accumulation by interstitial condensation due to vapor diffusion during colder periods

Let’s consider a wood-frame wall between a warm indoor environment and a cold outdoor environment. Vapor diffuses through the wall from the high-moisture environment inside to the low-moisture environment outside. This creates high relative humidity values associated with high temperature values close to the exterior panel, with the risk of condensation as a direct consequence.

*The relative humidity distribution in a wood-frame wall.*

Condensation leads to mold growth, which directly affects human health and building sustainability. The rate of mold growth is key data for the preservation of historical buildings, for example. To prevent the risk of interstitial condensation, it is common practice to add a vapor barrier between the interior gypsum panel and the cellulose isolation board. This reduces the moisture values where they are at a maximum. The figure below shows the relative humidity distribution across the wood-frame wall through a wood stud (red lines) and a cellulose board (blue lines), with and without the vapor barrier (dashed lines and solid lines, respectively).

*Effect of a vapor barrier on relative humidity distribution across the wood-frame wall in a wood stud and cellulose board.*

For this model, we consider the building materials to be specific unsaturated porous media in which the moisture exists in both liquid and vapor phases and only some transport processes are relevant. The norm EN 15026 standard addresses the transport moisture phenomena that is taken into account in building materials, following the theory expressed in Ref. 1.

The transport equation established as a standard by the norm accounts for liquid transport by capillary forces, vapor diffusion due to a vapor pressure gradient, and moisture storage.

\xi\frac{\partial \phi}{\partial t} + \nabla \cdot \left(- \xi D_\textrm{w} \nabla\phi -\delta_\textrm{p}\nabla\left(\phi p_\textrm{sat}\right)\right) = G

We model the latent heat effect due to vapor condensation by adding the following flux in the heat transfer equation:

\mathbf{q}= -L_\textrm{V}\delta_\textrm{p}\nabla\left(\phi p_\textrm{sat}\right)

In addition, the moisture dependence of the thermal properties is assessed.

Find details about the moisture transport equation in building materials in the

Heat Transfer Module User’s Guide.

When using the Heat Transfer Module, the *Heat and Moisture Transport* interface adds a:

*Heat and Moisture*coupling node*Heat Transfer in Building Materials*interface*Moisture Transport in Building Materials*interface*Building Material*feature for heat transfer*Building Material*feature for moisture transport*Thin Moisture Barrier*feature for modeling the vapor barrier

Finally, the latent heat source due to evaporation is added to the heat transfer equation by the *Building Material* feature of the *Heat Transfer* interface.

*The model tree and subsequent subnodes when choosing the* Heat Transfer in Building Materials *interface, along with the Settings window of the* Building Material *feature.*

Modeling heat and moisture transport in an unsaturated porous medium is important for analyzing polymer materials for the pharmaceutical industry, protective layers on electrical cables, and food-drying processes, to name a few examples.

For these applications, phenomenological models, such as the one presented above for building materials, may not be available. However, by considering the conservation of heat and moisture in each phase (solid, liquid, and gas), and volume averaging over the different phases, we can derive a mechanistic model.

To compute the moisture distribution, we solve a two-phase flow problem in the porous medium. Two equations of transport are solved: one for the vapor and one for the liquid water. The coupling between the vapor and liquid water operates through the definition of saturation variables, *S*_{vapor} + *S*_{liquid} = 1. The changing water saturation is taken into consideration for the definition of the effective vapor diffusivity and liquid permeability.

For quick processes, with a time scale comparable to the time it takes to reach equilibrium between the liquid and gas phases inside the pores of the medium, a nonequilibrium formulation can be defined through the following evaporation flux:

g_\textrm{evap} =M_\textrm{v}K(a_\textrm{w}c_\textrm{sat}-c_\textrm{v})

In this definition, the equilibrium vapor concentration, defined as the product of the saturation concentration *c*_{sat} and the water activity *a*_{w}, is used to account for the porous medium structure. Indeed, due to capillary forces, equilibrium is reached for concentrations that are lower than in a free medium.

By letting the evaporation rate *K* go to infinity, an equilibrium formulation is obtained with the vapor concentration equal to the equilibrium concentration.

Let’s consider a food-drying process. A piece of potato, initially saturated with liquid water, is placed in an airflow to be dried. Inside the potato, the vapor is transported by binary diffusion in air. We use a Brinkman formulation to model the flow induced by the moist air pressure gradient in the pores. As the liquid phase velocity is small compared to the moist air velocity, Darcy’s law is used for the liquid water flow due to the pressure gradient. The capillary flow, due to the difference between the relative attraction of the water molecules for each other and the potato, is also considered in the liquid water transport.

The vapor and liquid water distributions over time for this model are shown in the following two animations. Note that water can leave the potato as vapor only.

*The liquid water concentration over time.*

The vapor is transported away by the airflow, as shown in this animation:

*The water vapor concentration over time.*

The evaporation causes a reduction of the temperature in the potato. The temperature distribution over time is shown below.

*Temperature distribution over time.*

You can implement the equations in the *Heat Transfer in Porous Media* interface within the Heat Transfer Module and the *Transport of Diluted Species* interface within the Chemical Reaction Engineering Module. This process requires some steps in order to couple the multiphase flow in a porous medium together with the evaporation process.

Read the article “Engineering Perfect Puffed Snacks” on pages 7–9 of

COMSOL News2017 to see how Cornell University researchers used COMSOL Multiphysics to model rice puffing. In this numerically challenging process, the rapid evaporation of liquid water results in a large gas pressure buildup and phase transformation in the grain.

In this blog post, we discussed COMSOL® software features for modeling heat and moisture transport in porous media. COMSOL Multiphysics (along with the Chemical Reaction Engineering Module and Heat Transfer Module) provides you with tools to define the corresponding phenomenological and mechanistic models for a large range of applications. Depending on the dominant transport processes, you can use predefined interfaces or define your own model.

Künzel, H. 1995. *Simultaneous Heat and Moisture Transport in Building Components. One and two-dimensional calculation using simple parameters.* PhD Thesis. Fraunhofer Institute of Building Physics.

- Check out the tutorial models featured in this blog post:

Solar-grade silicon is one of three grades of high-purity silicon. Each grade has different applications and specific purity percentage requirements:

- Metallurgical-grade silicon is 98% pure
- Solar-grade silicon is 99.9999% pure (6N or “six nines”)
- Electronic-grade silicon is 99.9999999% pure (9N)

*The structure of monocrystalline silicon. Solar-grade silicon is almost pure silicon.*

Traditionally, solar-grade silicon is produced using high temperatures (2000°C) to reduce silicon quartz and carbon, resulting in silicon with a 98.5% purity. This isn’t quite pure enough to be considered solar grade, so the silicon must be refined further through a gas phase. With multiple steps and different processes, this method isn’t efficient. It is also energy intensive, expensive, and requires experienced operators.

The method that JPM analyzed starts with raw materials that are highly pure. The silicon is placed into a contaminant-free microwave oven that performs both the heating and gas phase stages of the traditional production process. Since there’s no consecutive refinement processes, this approach is more efficient and cost effective.

*The setup for the microwave furnace. Image by N. Rezaii and J.P. Mai and taken from their COMSOL Conference 2016 Munich paper.*

The microwave furnace consists of five parts:

- Magnetron core, which generates electromagnetic microwaves
- Waveguide, which transmits the microwaves into the resonator
- Resonator (also called the reaction chamber), which includes a crucible to hold the silicon sample
- Tuner, which improves the absorption of the microwaves
- Circulator, which keeps the magnetron from overheating by using a water bath to dissipate the reflective microwave energy

One advantage of an optimized microwave furnace design is that there is reduced heat loss. This is partially due to the selective heating, which heats materials on a volumetric heat input, leading to a temperature drop from the inside out. In addition, there’s less diffusion of the silicon’s impurities because the furnace has a faster warming time and shorter residence time.

To optimize the microwave furnace for solar-grade silicon production, JPM Silicon GmbH studied its internal processes with the COMSOL Multiphysics® software.

The research team set up their model to include the electromagnetic, chemical, and physical phenomena occurring within the microwave furnace. Since some materials have electromagnetic properties that are strongly temperature dependent, the model couples the electromagnetic field distribution and temperature field.

You can learn more about the model setup by reading the full conference paper “Multiphysics Modelling of a Microwave Furnace for Efficient Solar Silicon Production“.

It’s important to use chemically stable structural materials and an inert gas in the microwave furnace to avoid unwanted reactions. Also, the insulation materials must be effective in minimizing heat losses.

The research team used the RF Module to simulate the electromagnetic intensity and distribution in the resonator and silicon sample. They used Maxwell’s equations to determine the propagation of the microwave radiation.

The electric field is higher at the height of the waveguide ports than at any other part of the reaction chamber. The field enhancement in the crucible’s core indicates that this is the optimal location for the crucible to be heated, as shown in the results below.

*The distribution of the electric field in the resonator and waveguide. Image by N. Rezaii and J.P. Mai and taken from their COMSOL Conference 2016 Munich paper.*

The researchers also wanted to see how varying the height of the insulation plate affects the operation of the furnace. They tested three different heights for the plate (which the crucible sits on top of) and reexamined the electric field. The different insulation plate heights include:

- 30 mm
- 40 mm
- 50 mm

*The distribution of the electric field when the height of the insulation plate is 30 mm (left), 40 mm (middle), and 50 mm (right). Images by N. Rezaii and J.P. Mai and taken from their COMSOL Conference 2016 Munich paper.*

The simulation results show that the 40-mm insulation plate performs best. The electric field is focused at the center of the crucible, thus on the silicon sample.

The CFD Module solves for the Navier-Stokes equations, allowing the researchers to find the gas flow velocity distribution. The gas flows from the inlet over the surface of the silicon sample, rather than having a homogeneous velocity. The wall then deflects the flow toward the outlet. The simulation shows that only a slight gas flow exists near the waveguide ports as well as near the top and bottom walls.

*The distribution of gas velocity in the resonator. Image by N. Rezaii and J.P. Mai and taken from their COMSOL Conference 2016 Munich poster.*

To analyze how well the electromagnetic waves heat the silicon sample, the research team examined the heat distribution in the resonator. Their model includes forced heat equations to calculate conduction, convection, and radiation from solids and liquids (Planck’s radiation law) as well as gases (Stefan-Boltzmann law). The dissipated heat, solved with the RF Module, is used as a volumetric heat source. The gas velocity profile, calculated with the CFD Module, helps find the convective thermal losses.

As expected from the electromagnetics study, the hottest point in the resonator is at the crucible’s core. Further, the surrounding insulation layers don’t heat up as much, thanks to their lower thermal conductivity.

*The distribution of heat in the resonator. Image by N. Rezaii and J.P. Mai and taken from their COMSOL Conference 2016 Munich poster.*

By gaining insight into the internal processes of a microwave furnace, researchers from JPM Silicon GmbH were able to optimize their design and pave the way for efficient solar-grade silicon production.

- Explore other examples of solar simulation applications in these blog posts:

In the 1960s, G. Segré and A. Silberberg observed a surprising effect: When carried through a laminar pipe flow, neutrally buoyant particles congregate in a ring-like structure with a radius of about 0.6 times the pipe radius. This correlates to a distance from the parallel walls of around 0.2 times the width of the flow channel. The reason for this behavior, as they would discover decades later, could be traced back to the forces that act on particles in an inertial flow.

Today, we use the term inertial focusing to describe the migration of particles to a position of equilibrium. This technique is widely used in clinical and point-of-care diagnostics as a way to concentrate and isolate particles of different sizes for further analysis and testing.

*Many types of medical diagnostics use inertial focusing for testing and analysis. Image in the public domain, via Wikimedia Commons.*

In order for inertial focusing to be effective in these and other applications, accurately analyzing the migration patterns of the particles is a key step. A new benchmark example from the latest version of COMSOL Multiphysics — version 5.3 — highlights why the COMSOL® software is the right tool for obtaining reliable results.

For this example, we consider the particle trajectories in a 2D Poiseuille flow. To account for relevant forces, we use derived expressions from a similar migration of particles in a 2D parabolic flow inside of two parallel walls (see Ref. 2 in the model documentation). Built-in corrections for both the lift and drag forces allow us to account for the presence of these walls in the simulation analysis.

Note: Lift and drag forces make up the total force acting on neutrally buoyant particles inside a creeping flow. By definition, the gravitational and buoyant forces cancel out one another.

We assume that the lift force acts only perpendicular to the direction of the fluid velocity. It is also assumed that the spherical particles are small in comparison to the width of the channel and that they are rotationally rigid.

To compute the velocity field, we use the *Laminar Flow* physics interface. This is then coupled to the *Particle Tracing for Fluid Flow* interface via the *Drag Force* node. Thanks to the *Laminar Inflow* boundary condition, we can automatically compute the complete velocity profile at the inlet boundary. For the laminar flow of a Newtonian fluid inside two parallel walls, it is known that the profile will be parabolic. This means that we could have directly entered the analytic expressions for fluid velocity. However, we opt to use the *Laminar Flow* physics interface in this case, as it demonstrates the workflow that is most appropriate for a general geometry.

Now let’s move on to the results. First, we can look at the fluid velocity magnitude in the channel. As expected, the velocity profile is parabolic. Note that the aspect ratio of the geometry is 1000:1, so the channel is very long compared to its height. The plot uses an automatic view scale to make the results easier to visualize.

*The parabolic fluid velocity profile within a channel that is bound by two parallel walls.*

We can then shift our attention to the trajectories of the neutrally buoyant particles. Note that in the plot below, the color expression represents the *y*-component of the particle velocity in mm/s. The results indicate that all of the particles are close to equilibrium positions at distances of about 0.3 D on either side of the center of the channel. (D represents the width of the channel). It does, however, take longer for particles released near the center of the channel to reach these positions. Their initial force is weaker as they are released in the area where the velocity gradient is smallest. From the plots, we can see that the particles converge at heights that are 0.2 and 0.8 times the width of the channel. These findings show good agreement with experimental observations.

*The trajectory of particles inside the channel.*

The last two plots show the average and standard deviation of the normalized distance between the particles and the center of the channel. These results verify that the equilibrium distance from the center of the channel is in fact around 0.3 D.

*The average (left) and standard deviation (right) of the normalized distance between the particles and center of the channel.*

In order to effectively use inertial focusing for medical and other applications, you need to first understand the behavior of particles as they migrate through a channel to positions of equilibrium. With COMSOL Multiphysics® version 5.3, you can perform these studies and generate reliable results. This accurate description of inertial focusing serves as a foundation for analyzing and optimizing designs that rely on this technique.

Now it’s your turn! Give our new benchmark model a try:

Interested in learning about further updates in version 5.3 of COMSOL Multiphysics? You can get the full scoop in our 5.3 Release Highlights.

]]>

Artificial ground freezing is a construction technology that involves running an artificial refrigerant through pipes buried underground. As the refrigerant circulates through the pipe network, heat is removed from the ground and ice begins to form around the pipes. This in turn causes the soil to freeze. In other words, the process converts soil moisture into ice. Once the soil is frozen, it is both stronger (sometimes as hard as concrete) and has a greater resistance to water. This allows the soil to provide effective support to the relative infrastructures, particularly those that are larger and more complex.

*Once frozen, soil becomes stronger and more resistant to water.*

For the AGF method to be effective, we need to know the temperature distribution inside the system. Of the physical processes that occur in AGF, the most prominent is the phenomenon of transient heat conduction with phase change. Further, it is also important to consider the relationship between this phase change and the groundwater flow — particularly when there is a higher flow velocity. These elements can impact the development of the freezing wall and thus the strength and reliability of the AGF method.

To study the AGF method, a team of researchers from Hohai University turned to the COMSOL Multiphysics® software. Their case study involves using the method to strengthen soil at a metro tunnel entrance in Guangzhou, China.

For this specific example, the refrigerant that circulates throughout the pipe system is -30ºC brine. The subsurface temperature is reduced until the pore water is frozen and the freezing wall forms. The formation within the frozen area is made up of muddy sand, and the direction of the groundwater flow is primarily horizontal and normal in relation to the axial direction of the tunnel.

To simplify modeling heat transport in a saturated aquifer, the researchers used a 2D model based on a coupling of temperature and flow fields. The model, shown below, is 20 m in both length and height. Note that five monitoring points are included. These points are used to verify the accuracy of the model by comparing the calculated temperature results with *in situ* measurements.

*The AGF model’s geometry, with the monitoring points highlighted (left), and the model grid’s mesh (right). Images by Rui Hu and Quan Liu and taken from their COMSOL Conference 2016 Munich paper.*

In this analysis, the following assumptions are made:

- The ice is incapable of moving and the medium cannot deform
- The aquifer is fully saturated, with a total porosity that remains constant
- The freezing point depression caused by solute concentrations is negligible

According to previous temperature monitoring data from the frozen area, there is an initial ground temperature of 15°C. The figure below shows the initial temperatures in various holes of thermal observation.

*The initial temperatures in different holes for thermal observation. Image by Rui Hu and Quan Liu and taken from their COMSOL Conference 2016 Munich paper.*

The cooling source of the freezing system is the lateral wall of the freezing pipe. Changes in the temperature of the lateral wall have the greatest impact on the temperature distribution within the system. It is possible to use the values from the temperature monitoring of the main pipe as approximations for the estimated temperature of the lateral wall. The plot below shows the fitting function and curve for the lateral wall temperature of the main pipe after a monitoring period of 40 days.

*The fitting function and curve for the lateral wall temperature. Image by Rui Hu and Quan Liu and taken from their COMSOL Conference 2016 Munich paper.*

With regards to groundwater flow, a flow velocity of 0.2 m/d is obtained via field tests. Between upstream and downstream, the head difference is calculated as 0.8 m.

Now onto the results. Let’s consider the temperature distribution and permeability coefficient for a range of times. In terms of temperature, when the freezing time increases, the cold temperature from the freezing pipes is primarily led downstream — with less of an influence upstream. The permeability coefficient results, which illustrate the formation of the freezing wall, indicate that the top and bottom walls form at a faster rate than those walls at upstream and downstream. Note that the freezing wall is entirely closed after 35 days.

*The temperature distribution (left) and permeability coefficient results (right) at various points in time. Images by Rui Hu and Quan Liu and taken from their COMSOL Conference 2016 Munich paper.*

When comparing the closure of the freezing wall and flow velocity, the closing time increases nonlinearly as the flow velocity increases. The time of closure dramatically increases when the velocity is greater than 1.5 m/d. As for the average wall thickness in all directions and relative flow velocity, the influence of the flow velocity on the thickness of the upstream wall is most prominent.

The successful validation of this model offers guidance for the metro tunnel project in Guangzhou, China. With plans to further develop this model, the researchers hope to use it as a resource for improving applications of the AGF method.

- Read the full COMSOL Conference paper: “Simulation of Heat Transfer during Artificial Ground Freezing Combined with Groundwater Flow“
- Browse some additional examples of modeling subsurface flow:

The transport of momentum normal to the boundary in turbulent boundary layers is strongly damped by the presence of the solid wall. Also, the normal component of the turbulence intensity is more strongly suppressed by the proximity to the solid wall than the in-plane components. This means that mass and heat transfer in the normal direction to the wall are also partly blocked. Traditionally, this blocking effect has been dealt with by introducing damping functions for the normal component of the turbulent viscosity in wall-resolved turbulence models.

Using direct numerical simulations, Durbin confirmed that the near-wall damping of the eddy viscosity is caused by the suppression of the turbulence intensity’s normal component according to the following relation:

(1)

\nu _t = {C_\mu }\overline {{v^2}} T\

where *C _{μ}* denotes a model constant, is the variance of the normal component of the turbulent velocity, and

The effect of the wall on the damping of the turbulence intensity is depicted in the figure below. The distance from the surface of a bubble or platelet-shaped object from their centers represents an average of the turbulence intensity at the centerpoint of the bubble or platelet shape.

Close to the walls, the fluctuations of the velocity are much larger in the *x* direction and *y* direction in comparison with the *z* direction. The velocity fluctuations are anisotropic and the surface takes the shape of a platelet. Further away from the wall, the fluctuations are of the same magnitude in all three dimensions: *x*, *y*, and *z*. The velocity fluctuations are isotropic and the surface takes the shape of a spherical bubble. The relative size of the bubbles and platelet shapes represents the relative size of the fluctuating eddies in the different directions.

*A representation of the average velocity fluctuations as imaginary bubbles or platelet shapes. The distance from the surface to the center of the bubbles or platelets represents the average magnitude of the turbulence intensity.*

The v2-f turbulence model describes the anisotropy of the turbulence intensity in the turbulent boundary layer using two new equations, in addition to the two equations for turbulence kinetic energy and dissipation rate. The implementation used in the CFD Module, an add-on product to COMSOL Multiphysics, is based upon the formulation by F. Billard, J. Uribe, and D. Laurence from their 2008 paper.

To accurately describe the transport of turbulence energy and the redistribution of the turbulence energy in different directions, the v2-f model introduces two new equations. The first equation describes the transport of turbulence normal to the wall using a variable that is equal to (usually denoted *φ* or ς in scientific literature). In this equation, denotes the variance of the normal component of the turbulent velocity and *k* denotes the turbulence kinetic energy.

The second equation is an elliptic partial differential equation for the blending coefficient (usually denoted *α* in scientific literature). The elliptic blending equation accounts for nonlocal effects such as the wall-induced damping of the redistribution of turbulence kinetic energy between the normal and parallel directions. Due to the name of the independent variables, this model is often referred to as the *φ-α* version of the v2-f turbulence model. The model is equally as robust as standard isotropic turbulence models and as accurate as the original, less robust formulation of the v2-f model.

The implementation in the CFD Module has been verified using a few benchmark cases, including the periodic hill benchmark. In this model, a flow is forced over two parallel hills where the velocity field is periodic on the two vertical inlet and outlet boundaries (shown in the figure below). This means that while there is a pressure drop from the inlet to the outlet boundary, their velocity fields are identical.

In the figure below, the flow is from left to right. We can see that there is a detachment of the flow with a formation of a recirculation zone behind the hills in the direction of the flow. The size of the recirculation zone and the distance from the inlet to the reattachment of the flow is inherently difficult to predict using RANS turbulence models. The results obtained with the implementation of the CFD Module are in excellent agreement with the results reported in scientific literature.

*Flow over two hills where the velocity profiles at the vertical boundaries above the two hilltops are identical for the inlet and outlet boundaries. The flow is from left to right.*

Another interesting problem is the flow in a hydrocyclone with two tangential inlets. The two outlets are at the top and bottom. The stream from the bottom usually contains the undesired particles, thus it is called the *reject stream*. The outlet stream at the top is referred to as the *accept stream*. The difficulty is to capture the semifree vortex, which is unattainable for standard two-equation models.

For more information about hydrocyclone simulations, see this research paper.

*Left: Velocity field (streamlines) and pressure field (cross-section plot) in a hydrocyclone. Right: Isosurface of the absolute value of the vorticity in the cyclone and pressure cross section. The simulation captures the free vortex in the center of the cyclone.*

The figure below shows the azimuthal component of the velocity just below the top outlet. The profile with a maximum at a radial position just outside of the outlet pipe is in good agreement with the results reported in scientific literature. In addition, the decrease of the azimuthal velocity away from the maximum outward along the radius is in good agreement with the literature.

*Azimuthal component of the velocity as a function of the radius in the cyclone just below its horizontal top outlet.*

To summarize, the new v2-f turbulence model widens the applicability of the CFD Module to include cases that require anisotropic turbulence modeling. This model gives an accuracy that is not possible to obtain with two-equation models, yet it is as robust as standard two-equation models.

- Try it yourself: Get the hydrocyclone tutorial model
- Find out more about the updates to the CFD Module on the Release Highlights page

Let’s start by considering a model of the electrical heating of a busbar, shown below. You may recognize this as an introductory example to COMSOL Multiphysics, but if you haven’t already modeled it, we encourage you to review this model by going through the *Introduction to COMSOL Multiphysics* PDF booklet.

*Electric currents (arrow plot) flowing through a metal busbar lead to resistive heating that raises the temperature (color surface plot).*

In this example, we model electric current flowing through a busbar. This leads to resistive heating, which in turn causes the temperature of the busbar to rise. We assume that there is only heat transfer to the surrounding air, neglecting any conductive heat transfer through the bolts and radiative heat transfer. The example also initially assumes that there isn’t any fan forcing air over the busbar. Thus, the transfer of heat to the air is via natural, or free, convection.

As the part heats the surrounding air, the air gets hotter. As the air gets hotter, its density decreases, causing the hot air to rise relative to the cooler surrounding air. These free convective air currents increase the rate of heat transfer from the part to the surrounding air. The air currents depend on the temperature variations as well as the geometry of the part and its surroundings. Convection can, of course, also happen in any other gas or liquid, such as water or transformer oil, but we will center this discussion primarily around convection in air.

We can classify the surrounding airspace into one of two categories: *Internal* or *External*. Internal means that there is a finite-sized cavity (such as an electrical junction box) around the part within which the air is reasonably well contained, although it might have known air inlets and outlets to an external space. We then assume that the thermal boundary conditions on the outside of the cavity and at the inlets and outlets are known. On the other hand, External implies that the object is surrounded by what is essentially an infinitely large volume of air. We then assume that the air temperature far away from the object is a constant, known value.

*The settings for a constant heat transfer coefficient.*

The introductory busbar example assumes free convective heat transfer to an external airspace. This is modeled using the following boundary condition for the heat flux:

q=h \left(T_{ext}-T \right)

where the external air temperature is *T _{ext}* = 25°C and is the heat transfer coefficient.

This single-valued heat transfer coefficient represents an approximate and average of all of the local variations in air currents. Even for this simple system, any value between could be an appropriate heat transfer coefficient, and it’s worth trying out the bounding cases and comparing results.

If we instead know that there is a fan blowing air over this structure, then due to the faster air currents, we use a heat transfer coefficient of to represent the enhanced heat transfer.

If the surrounding fluid is a liquid such as water, then the range of free and forced heat transfer coefficients are much wider. For free convection in a liquid, is the typical range. For forced convection, the range is even wider: .

Clearly, entering a single-valued heat transfer coefficient for free or forced convection is an oversimplification, so why do we do it? First, it is simple to implement and easy to compare the best and worst cases. Also, this boundary condition can be applied with the core COMSOL Multiphysics package. However, there are some more sophisticated approaches available within the Heat Transfer Module and CFD Module, so let’s look at those next.

A *convective correlation* is an empirical relationship that has been developed for common geometries. When using the Heat Transfer Module or CFD Module, these correlations are available within the Heat Flux boundary condition, shown in the screenshot below.

*The Heat Flux boundary condition with the external natural convection correlation for a vertical wall.*

Using these correlations requires that you enter the part’s characteristic dimensions. For example, with our busbar model, we use the *External natural convection, Vertical wall* correlation and choose a wall height of 10 cm to model the free convective heat flux off of the busbar’s vertical faces. We also need to specify the external air temperature and pressure. These values can be loaded from the ASHRAE database, a process we describe in a previous blog post.

The table below shows schematics for all of the available correlations. They take the information about the surface geometry and use a Nusselt number correlation to compute a heat transfer coefficient. For the horizontally aligned faces of the busbar, for example, we use the *Horizontal plate, Upside* and *Horizontal plate, Downside* correlations.

When using the Forced Convection correlations, you must also enter the air velocity. These convective correlations have the advantage of being a more accurate representation of reality, since they are based on well-established experimental data. These correlations lead to a nonlinear boundary condition, but this usually results in only slightly longer computation times than when using a constant heat transfer coefficient. The disadvantage is that they are only appropriate to use when there is an empirical relationship that is reasonable for the part geometry.

Free Convection | Forced Convection | |
---|---|---|

External | ||

Internal |

*The available* Convective Correlation *boundary conditions.*

Note that all of the above convective correlations, even those classified as Internal, assume the presence of an infinite external reservoir of fluid; e.g., the ambient airspace. The heat carried away from the surfaces goes into this ambient airspace without changing its temperature, and the ambient air coming in is at a known temperature. If, however, we are dealing with convection in a completely enclosed container, then none of these correlations are appropriate and we must move to a different modeling approach.

Let’s consider a rectangular air-filled cavity. If this cavity is heated on one of the vertical sides and cooled on the other, then there will be a regular circulation of the air. Similarly, there will be air circulation if the cavity is heated from below and cooled from above. These cases are shown in the images below, which were generated by solving for both the temperature distribution and the air flow.

*Free convective currents in vertically and horizontally aligned rectangular cavities.*

Solving for the free convective currents is fairly involved. See, for example, this blog post on modeling natural convection. Therefore, we might like to find a simpler alternative. Within the Heat Transfer Module, there is the option to use the *Equivalent conductivity for convection* feature. When using this feature, the effective thermal conductivity of the air is increased based upon correlations for the horizontal and vertical rectangular cavity cases, as shown in the screenshot below.

*The Equivalent conductivity for convection feature and settings.*

The air domain is still explicitly modeled using the *Fluid* domain feature within the *Heat Transfer* interface, but the air flow fields are not computed and the velocity term is simply neglected. The thermal conductivity is increased by an empirical correlation factor that depends on the cavity dimensions and the temperature variation across the cavity. The dimensions of the cavity must be entered, but the software can automatically determine and update the temperature difference across the cavity.

*Temperature distribution in vertically and horizontally aligned cavities using the Equivalent conductivity for convection feature. The free convective air currents are not computed. Instead, the thermal conductivity of the air is increased.*

This approach for approximating free convection in a completely closed cavity requires us to mesh the air domain and solve for the temperature field in the air, but this usually adds only a small computational cost. The disadvantage of this approach is that it is not very applicable for nonrectangular geometries.

Next, let’s consider a completely sealed enclosure, but with a fan or blower inside that actively mixes the air. We can reasonably assume that well-mixed air is at a constant temperature throughout the cavity. In this case, it is appropriate to use the *Isothermal Domain* feature, which is available with the Heat Transfer Module when the *Isothermal domain* option is selected in the Settings window.

*The settings associated with using the Isothermal Domain interface.*

A well-mixed air domain can be explicitly modeled using the Isothermal Domain feature. In the model, the temperature of the entire domain is a constant value. The temperature of the air is computed based upon the balance of heat entering and leaving the domain via the boundaries. The Isothermal Domain boundaries can be set as one of the following options:

*Thermally Insulated*: no heat transfer across the boundary*Continuity*: continuity of temperature across the boundary*Ventilation*: a known mass flow of fluid, of known temperature, into or out of the isothermal domain*Convective Heat Flux*: a user-specified heat transfer coefficient, as described earlier*Thermal Contact*: a specific thermal resistance

Of all of these boundary condition options, the *Convective Heat Flux* is the most appropriate for well-mixed air in an enclosed cavity.

*Representative results when using an Isothermal Domain feature. The well-mixed air domain is a constant temperature and there is heat transfer to the surrounding solid domains via a specified heat transfer coefficient.*

The most computationally expensive approach, but also the most general, is to explicitly model the airflow. We can model both forced and free convection as well as simulate an internal or external flow. This type of modeling can be done with either the Heat Transfer Module or CFD Module.

*An example of computing air flow and temperature within an enclosure.*

If you finished the *Introduction to COMSOL Multiphysics* booklet, you have already solved one example of an internal forced convection model. You can learn more about explicitly modeling airflow in the resources mentioned at the end of this post.

We will finish up this topic by addressing the question: When can free convection in air be ignored and how can we model these cases? When a cavity’s dimensions are very small, such as a thin gap between parts or a very thin tube, we run into the possibility that the viscous damping will exceed any buoyancy forces. This balance of viscous to buoyancy forces is characterized by the nondimensional Rayleigh number. The onset of free convection can be quite varied depending on boundary conditions and geometry. A good rule of thumb is that for dimensions less than 1mm, there will likely not be any free convection, but once the dimensions of the cavity get larger than 1cm, there likely will be free convective currents.

So how can we model heat transfer through these small gaps? If there is no air flow, then these air-filled regions can simply be modeled as either a solid or a fluid with no convective term. This is demonstrated in the Window and Glazing Thermal Performances tutorial. It is also appropriate to model the air as a solid within any microscale enclosed structure.

If these thin gaps are very small compared to the other dimensions of the system being analyzed, you can further simplify the gaps by modeling them via the Thin Layer boundary condition with a *Thermally thick approximation* layer type. This boundary condition introduces a jump in temperature across interior boundaries based on the specified thickness and thermal conductivity.

*The Thin Layer boundary condition can model a thin air gap between parts.*

We can use the previous two approaches within the core COMSOL Multiphysics package. In the Heat Transfer Module, there are additional options for the Thin Layer condition to consider more general and multilayer boundaries, which can be composed of several layers of materials.

Before closing out this discussion, we should also quickly address the question of radiative heat transfer. Although we haven’t discussed radiation here, an engineer must always take it into consideration. Surfaces exposed to ambient conditions will radiate heat to the surroundings and be heated by the sun. The magnitude of radiative heating from the sun is significant — about 1000 watts per square meter — and should not be neglected. For details on modeling radiative heat transfer to ambient conditions, read this previous blog post.

There will also be radiative heat transfer between interior surfaces. Radiative heat flux between surfaces is a function of the difference of temperature to the fourth power. Keep in mind that radiative heat transfer between two surfaces at 20°C and 50°C will be 200 watts per square meter at most, but rises to 1000 watts per square meter for surfaces at 20°C and 125°C. To correctly compute the radiative heat transfer between surfaces, it is also important to compute the view factors with the Heat Transfer Module.

Today we looked at several approaches for modeling convection, starting from the simplest approach of using a constant convective heat transfer coefficient. We then discussed using an Empirical Convective Correlation boundary condition before going over how to use an effective thermal conductivity within a domain and an isothermal domain feature, approaches with higher accuracy and only a slightly greater computational cost. The most computationally intensive approach — explicitly computing the flow field — is, of course, the most general. We also touched on when it is appropriate to neglect free convection entirely and how to model such situations. You should now have a greater understanding of the available options and trade-offs for modeling free and forced convection. Happy modeling!

- Learn about explicitly modeling air flow and heat transfer on the COMSOL Blog
- Get an introduction to simulating heat transfer in an archived webinar

Cerebral or intracranial aneurysms occur when arterial vessels fill with blood and expand out in a balloon-like bulge, thinning the vessel wall. If the bulge ruptures, this could cause hemorrhaging. Doctors can treat these bulges (or aneurysm sacs) in multiple ways, such as with surgical treatments or through endovascular methods.

*Different types of aneurysms in blood vessels. Images by G. Mach, C. Sherif, U. Windberger, R. Plasenzotti, and A. Gruber and taken from their COMSOL Conference 2016 Munich presentation.*

Today, let’s focus on endovascular methods (for example, using a flow-diverting stent), which slow the blood flow into an aneurysm sac. This starts the clotting process and eventual cicatrization of the diseased area, helping to protect the vessel walls and reduce the risk of a hemorrhage.

*A typical stent. Image by Lenore Edman — Own work. Licensed under CC BY 2.0, via Flickr Creative Commons.*

Normally, when researchers study these methods with numerical simulation, they model the blood flow in the intracranial aneurysms and cerebral arteries by assuming that blood is a Newtonian fluid with a constant viscosity. This is based on the assumption that the blood flow has a very high velocity and shear rate, meaning that its shear-thinning behavior can be ignored.

This assumption might not be true when applied to flow-diverting stents, which slow the blood flow and decrease the shear rate inside the aneurysm sac, making the blood behave in a less Newtonian way.

This brings up an important question: Due to the differences in blood flow around a flow-diverting stent, is modeling it as a Newtonian fluid accurate? To answer this, the Cerebrovascular Research Group Vienna, with members from the Vienna University of Technology, Hospital Rudolfstiftung, and Medical University of Vienna, analyzed blood flow in an aneurysm sac and blood vessel using the CFD Module with COMSOL Multiphysics.

As a first step, the team measured human blood viscosity at different shear rates and used this data to generate model parameters. They also made note that the blood viscosity is dependent on multiple factors, including the shear rate, hematocrit (HCT), and temperature.

Next, the team created a model of an intracranial sidewall aneurysm, which is depicted as a round bulge on the side of a cerebral parent blood vessel. This aneurysm is treated by a complex flow-diverting stent, which is located near the aneurysm in the parent vessel and subtracted from the blood-filled vessel domain.

*Left: The model geometry, including the parent vessel, cerebral aneurysm, and flow-diverting stent. This image shows the aneurysm neck plane and the stent-induced vessel wall expansion. Right: The mesh used for the model. Images by G. Mach et al. and taken from their COMSOL Conference 2016 Munich presentation.*

Taking a closer look at the stent, we see that it has a permeability of 55%, similar to industrial samples, and is made of 16 wires that are knitted into a mesh. This is less complicated than real stents, which contain more wires and have smaller cross sections.

*The flow-diverting stent’s waving pattern, with one wire highlighted to show the pattern. Image by G. Mach et al. and taken from their COMSOL Conference 2016 Munich paper.*

Using their model and blood viscosity parameters as a basis, the team studied blood flow in the stented structure via CFD simulations. They were able to see how the velocity profile of the modeled fluid changes with two different models:

- A Newtonian model that has a constant dynamic viscosity
- A Carreau-Yasuda model, one of the most common non-Newtonian models for human blood viscosity

*Comparison of the blood viscosity values for measured data with the different models. Image by G. Mach et al. and taken from their COMSOL Conference 2016 Munich paper.*

When looking at the values for viscosity, we see that, unlike the constant viscosity in the Newtonian model, the dynamic viscosity of the non-Newtonian Carreau-Yasuda model ranges from 3.57 MPa·s to 7.1 MPa·s.

*Viscosity profiles for the Newtonian model (left) and Carreau-Yasuda model (right). Images by G. Mach et al. and taken from their COMSOL Conference 2016 Munich presentation.*

Between the two models, the Carreau-Yasuda model has a slightly larger range of shear rates as well as higher values for the total flow rate into the aneurysm sac and average velocity within it. As a note, all of these comparisons are made when the *systole*, the highest velocity profile value, appears at the inlet plane.

*Blood flow velocity profiles for the Newtonian model (left) and Carreau-Yasuda model (right). Images by G. Mach et al. and taken from their COMSOL Conference 2016 Munich paper.*

These numerical results indicate that the Newtonian model overestimates the flow-diverting stent’s effect by around 4–6%. Although the flow profiles don’t show these differences, they are indicated by the characteristic numbers. Therefore, it appears that the Newtonian model is not accurate enough to analyze blood flow past endovascular devices.

*The difference in velocity profiles when the Newtonian model is removed from the Carreau-Yasuda model. Image by G. Mach et al. and taken from their COMSOL Conference 2016 Munich paper.*

The research discussed today provides a solid foundation for testing the accuracy of Newtonian and non-Newtonian blood flow models. The team plans to continue improving the accuracy of their models by making more blood measurements at lower shear rates and gathering 3D images of actual flow-diverting stents *in vivo*. By using the new data and tomographic images, they hope to enhance their model’s accuracy.

- Read the full COMSOL Conference paper: “A Non-Newtonian Model for Blood Flow behind a Flow Diverting Stent“
- Check out other medical-related uses of COMSOL Multiphysics:

Have you ever walked down a city street and felt dwarfed by the tall buildings around you, as if you were walking through an artificial ravine or canyon? Well, this type of environment has a name: an urban (or street) canyon. An urban canyon occurs when a street is surrounded by tall buildings on both sides, creating an environment similar to that of a canyon.

*The entrance to an urban canyon. Image by Kanwar Sandhu — Own work. Licensed under CC BY-SA 2.0, via Flickr Creative Commons.
*

In many of the highly populated areas that these canyons exist, air pollution is a large problem. According to the World Health Organization (WHO), more than 80% of the people living in urban areas that monitor air pollution are subjected to air quality levels exceeding WHO limits. Such poor air quality can lead to a variety of health issues for city dwellers. To combat this issue, there is a need for urban planning and design strategies that focus on reducing air pollution and restoring air quality. One possible method is adding vegetation and greenery to urban canyons.

*Trees along a city street. Image by La Citta Vita — Own work. Licensed under CC BY-SA 2.0, via Flickr Creative Commons.*

Vegetation improves air quality by absorbing and retaining fine dust particles and gaseous pollutants, affecting pollutant deposition and dispersion. Adding greenery to urban canyons has other benefits, such as improving building energy performance, reducing the heat island effect of cities, and managing stormwater runoff. In addition, such greenery can be aesthetically pleasing.

While recent studies have investigated using greenery in this manner, more information about its effectiveness and use is needed before we can give this technique the green light. For instance, vegetation’s size, shape, and the characteristics of individual plants (like leaf size and porosity) can all factor into its effectiveness.

Based on this need, researchers from the University of Genova and the University of Bologna performed a simulation study to see how greenery affects pollution reduction in a straight urban canyon. They also compared the effects of different types of greenery and wind velocity. Let’s take a look at their work.

The research team’s CFD model depicts a straight road — 20 m wide and 100 m long — that is surrounded on either side by a continuous line of buildings. These buildings, shown in light gray in the image below, are all 20 m tall. In their analysis, the team only needed to account for half of the geometry due to its symmetry.

Air flows into the model from an inlet section (labeled 1) and moves along the road’s main axis before exiting from the outlet section (labeled 2). To help focus on the reduction in pollution caused by the greenery, the incoming air is pollution free.

*The geometry of the urban canyon model. Image by S. Lazzari, K. Perini, E. Rossi di Schio, and E. Roccotiello and taken from their COMSOL Conference 2016 Munich paper.*

To further simplify their model, the researchers didn’t account for the disruptions that cars create in the fluid flow within an urban canyon. However, this does not mean that cars were ignored completely. As passenger vehicles are the main source of road pollution, the team’s study focuses on one major car pollutant: CO_{2}. This pollutant is uniformly generated within the volume, V_{c} (depicted in red above), and transported via convection and diffusion. The volume, located in the middle of the road, has a width of 5 m and height of 0.5 m.

The plants are modeled as a Darcian porous medium that is saturated by air and able to absorb pollutants (diluted species). By changing the values of porosity and permeability as well as the reduction reaction, the team can tailor their model to a desired plant species. This flexibility enables them to easily study different plant species and shapes of greenery. In this study, for instance, they analyzed two different greenery shapes:

- Continuous green façade that is 0.3 m thick
- Continuous hedge that is 1.5 m tall and 1 m wide

In addition to these two geometries, a third geometry of a “clear” canyon — with pollution but without plants — is used for comparison.

*Qualitative cross sections showing the geometries of a continuous green façade (left) and hedge (right). Images by S. Lazzari, K. Perini, E. Rossi di Schio, and E. Roccotiello and taken from their COMSOL Conference 2016 Munich paper.*

Using this model, the team compared pollutant concentrations in the clear canyon, green façade, and green hedge for inlet velocities of 0.5 m/s and 3 m/s. The results are shown in the following tables.

Plane 0.3 m from Ground | Plane 1 m from Ground | Canyon Outlet | Canyon Overall Volume | |
---|---|---|---|---|

Clear Canyon | 207.65 | 5.379 | 14.568 | 7.107 |

Green Façade | 184.86 | 0.256 | 14.472 | 6.435 |

Green Hedge | 189.87 | 0.272 | 15.765 | 6.868 |

*The pollutant concentrations of the three geometries in mol/m ^{3} for an inlet velocity of 0.5 m/s.*

Plane 0.3 m from Ground | Plane 1 m from Ground | Canyon Outlet | Canyon Overall Volume | |
---|---|---|---|---|

Clear Canyon | 34.127 | 0.791 | 2.537 | 1.244 |

Green Façade | 27.471 | 0.00489 | 1.666 | 0.832 |

Green Hedge | 26.862 | 0.00448 | 1.860 | 0.931 |

*The pollutant concentrations of the three geometries in mol/m ^{3} for an inlet velocity of 3 m/s.*

The initial results indicate that greenery has a positive effect on reducing the overall pollution in an urban canyon and that (obviously) a faster wind speed also reduces the overall pollution volume. As for the two different plant types, the team found that the green façade is better at reducing pollution than the green hedge.

*The mesh for the green hedge scenario (left) and the air velocity distribution for the green hedge scenario with a wind velocity of 3 m/s (right). Images by S. Lazzari, K. Perini, E. Rossi di Schio, and E. Roccotiello and taken from their COMSOL Conference 2016 Munich paper.*

For these researchers, this analysis is the first of multiple studies of using greenery to enhance air quality in dense urban areas. In the future, the team intends to run more numerical and experimental investigations, including studying the trap effects of plants in an innovative chamber. With this experimental data, they hope to further improve their model.

- Read the full COMSOL Conference paper: “Simplified CFD Modeling of Air Pollution Reduction by Means of Greenery in Urban Canyons“
- Check out other blog posts related to CFD modeling:

Stretching across 6300 km, the Yangtze River is the world’s third longest river and the longest river in Asia. Throughout history, humans have relied on this river for irrigation, transportation, and many other purposes. Today, the Yangtze River is one of the busiest waterways in the world, with multiple major cities settled on its banks.

*The Yangtze River. Image by Perfect Zero — Own work. Licensed under CC BY 2.0, via Flickr Creative Commons.*

To protect these cities and their inhabitants from issues like flooding, we can build embankments and use bank protection structures to maintain their safety. Bank protection structures commonly use steel sheet piles to support embankments. These structures have applications in waterway engineering, wharf construction, and cofferdam excavation.

*A (partially disrupted) steel sheet piling. Image by Evelyn Simak — Own work. Licensed under CC BY-SA 2.0, via Wikimedia Commons.*

Problems can arise when these structures deform and eventually collapse due to issues like fluctuating river levels. To avoid this and maintain the safety of bank protection structures, engineers can use multiphysics modeling to predict the deformation and its causes.

With this in mind, a research team from the School of Earth Science and Engineering at Hohai University used the COMSOL Multiphysics® software to analyze the deformation of a bank protection structure in the Nanjing section of the Yangtze riverbank.

A bank protection structure’s deformation is affected by soil pressure from excavating riverways as well as changes in the hydrostatic (or water) pressure due to the seasonal fluctuations of the river’s water level. These fluctuations can in turn cause changes in the soil seepage field and groundwater level, affecting the soil’s mechanical properties.

*Left: The bank protection structure and surrounding environment. Right: The grid of the resulting model. Images by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich paper.*

To account for these variables when predicting deformation, the researchers created a 2D water-soil model based on the Deep Excavation model in the Application Gallery and coupled it to Darcy’s law. The model analyzes a section vertical to the bank protection structure’s steel sheet piles, shown in the left image above. The soil around the piles has three layers, based on the soil’s physical-mechanical properties. The researchers also used an ideal elastoplastic model and a Drucker-Prager yield criterion.

*The bank protection structure. Image by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich poster.*

The researchers’ model uses data gathered from monitoring the water level of the Yangtze River over 120 days as well as from four displacement monitoring points. The river’s water level fluctuations in the simulation are based on this measured data.

*Left: The monitoring data for water level fluctuations in the Yangtze River. Right: The horizontal displacement of four monitoring points. Images by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich paper.*

Overall, the researchers’ simulation has three steps:

- Calculating the embankment’s groundwater seepage field by accounting for water level fluctuation or change in river level.
- Using a strength reduction method to adjust the soil shear strength parameters by the groundwater table.
- Determining deformation with the modified deep excavation model.

Let’s take a look at the results from this simulation.

The results show that while deformation is stable during early excavation, afterwards it is affected mostly by water level fluctuation. For example, let’s look at a few plots showing how a bank protection structure is affected by a water level of -6 m.

At this level, a water head difference on the side of the pile results in a groundwater discharge and change in groundwater level. As seen below, the total pressure varies under the water level and there is a relatively large structural displacement in the excavation’s middle part under the hydrostatic and soil pressure. The maximum observed displacement is 60 mm.

*Left: The total pressure and seepage fields, with the white line representing the groundwater level. Right: The steel sheet pile’s displacement. Images by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich paper.*

As shown below, the plastic deformation is mostly located in the soil’s first layer below the water level depth.

*The structure’s plastic deformation when the river’s water level is at -6 m. Image by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich paper.*

When using the monitoring data to find the model’s horizontal deformation, the researchers found that the structure’s main deformation is displacement and that there is a good consistency in the variation of horizontal displacements and water level fluctuations. This displacement is relatively small because of the resistance of the struts on top of the pile.

As a final point of interest, the team explored how extreme water level instances affect deformations. To achieve this, they used water-level monitoring data to find the Yangtze River’s highest (-0.3 m) and lowest (-8.4 m) water levels in the past 10 years.

The extremely high water level case has a small plastic area and its plastic deformation is confined to the soil’s first level, while the extremely low water level case has a larger plastic area that stretches into the third soil layer.

*The plastic zone distribution in the extremely high water level case (left) and extremely low water level case (right). Images by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich paper.*

The maximum horizontal displacement is 25.1 mm for the high water level case and 65 mm for the low water level case. This latter value exceeds the project’s warning value of 56 mm. Further, the maximum shear stress for the low water level case is 18.5 MPa. This is lower than the steel sheet pile’s yield limit of 335 MPa. As a result, there is a chance of excessive structural deformation and a higher risk of the structure collapsing when the water level is extremely low. This must be addressed when designing bank protection structures.

*The steel sheet pile’s horizontal displacement (left) and generalized shear stress (right) for both the extremely high and low water level cases. Images by R. Hu and Y. Xing and taken from their COMSOL Conference 2016 Munich paper.*

With their multiphysics model, the researchers successfully confirmed that fluctuating river levels affect the lateral displacement of the steel sheet piles in a bank protection structure and that the plastic zone distribution is related to groundwater level depth.

Moving forward, the team wants to validate and improve their model by comparing their results with long-term *in situ* development measurements. Through this, they hope to offer helpful suggestions to those designing bank protection structures.

- Read the researchers’ full paper: “Numerical Simulation of Bank Protection Structure Deformation due to River Level Fluctuations“
- Browse these blog posts on geomechanics and subsurface flow:

One way to simplify the designs of key process equipment, such as rotating packed bed reactors and centrifugal disc atomizers, is to replace conventional centrifugal pumps with a less complicated alternative: rotating cone micropumps.

*A conventional centrifugal pump (left) and rotating cone micropump (right). Images by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston presentation.*

Before they can be used as replacements, rotating cone micropumps need further analysis. In particular, research on the velocity profiles over the rotating conical surfaces is quite important in process manufacturing industries. Such studies show that fluid velocity distributions greatly affect the efficiency of process equipment.

To fill this research gap, a team from Texas A&M University used COMSOL Multiphysics CFD simulations to accurately investigate the pump performance of a rotating cone micropump — a more efficient approach than trial-and-error empirical studies.

The researchers used COMSOL Multiphysics to develop a realistic fluid dynamics model of a rotating cone micropump, which analyzes both laminar and turbulent flow regimes using the 3D transient Navier-Stokes equations.

The researchers looked at how the flow and pressure fields are affected by changing the micropump’s geometrical and operational parameters, including:

- Cone height and semiangle
- Ratio of outer to inner radius
- Angular rotational speed

As seen in the following schematic, the model geometry is comprised of a vertical and rotating inner cone, rotating inner solid cone, and stationary outer cone. The fluid in this model is water.

*Rotating cone micropump geometry. Here,* H *is the height of the cone,* α *is the cone semiangle, and* R_{0} *is the upper radius. Image by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston presentation.*

The research team used an unstructured mesh with tetrahedral elements and tested different element sizes to see how the number of elements (mesh resolution) affects the computation results. The results show that the computed pressure head varies to a very small extent with the number of elements (48,000; 92,000; and 124,000), indicating that the results are within the required accuracy for the lowest number of elements (48,000).

*Tetrahedral mesh with 48,000 elements. Image by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston presentation.*

To expand the reach of this study, the researchers created a dedicated user interface for running the model (an app) using the Application Builder in COMSOL Multiphysics. For more information about the researchers’ model and simulations, check out the full paper.

Let’s go over a few of the research team’s results now, beginning with the fluid velocity and pressure profiles for rotating cone micropumps with two different cone semiangles. The plots below show that the velocity magnitude remains below 0.1, which for this system corresponds to a Reynolds number of around 1.5. Within this range of Reynolds numbers, viscous forces are the main driver of flow for micropumps. As for the velocity patterns, these switch from the axial direction at the inlet to the angular direction at the angled region. Upon leaving the cone’s angled region, the velocity transitions into a combination of angular and axial behavior.

*Velocity profiles for a rotating cone micropump with a semiangle of 12° (left) and 45° (right). Both cones give a volumetric flow rate of 1 ml/s. Images by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston paper.*

Moving on to the corresponding fluid pressure profiles, these indicate that the micropump’s hydraulic head is a weak function of both the cone semiangle and rotating cone’s height. While the micropump head is greatly affected by the frequency of rotation, the hydrodynamic head remains below 135 Pa, even at the maximum rotational speed of 12,000 RPM.

*Fluid pressure profiles for a rotating cone micropump with a semiangle of 12° (left) and 45° (right). Both cones have a volumetric flow rate of 1 ml/s. Images by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston paper.*

The researchers also predicted the head curve for various angular rotational speeds by repeatedly running the model for each volumetric flow rate and angular speed pair as well as calculating outlet pressure. The outlet pressure shows a near linear decrease with an increasing volumetric flow rate. The micropump head is also almost proportional to the square of the rotational speed.

*Comparison of the micropump head with different RPM values. Image by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston paper.*

Other factors, including the fluid’s viscosity and density, can also affect the pressure head that the rotating cone micropump produces. To demonstrate, two head curves for liquids with different viscosities and densities and the same operating conditions are compared below. Water, the more viscous and dense fluid, generates a larger pressure difference throughout the range of flow rates than the other fluid, diethyl ether. For conventional centrifugal pumps, the opposite is true. However, the pressure head behavior trends for water and diethyl ether are similar and agree with those for centrifugal pumps.

*Comparison of pressure head curves for water and diethyl ether at 12,000 RPM. Image by A. Uchagawkar, M. Vasilev, and P. Mills and taken from their COMSOL Conference 2015 Boston paper.*

Overall, rotating cone micropumps can create comparatively large throughputs, but the pressure heads that they create don’t compare to those of conventional centrifugal pumps. Therefore, this rotating cone micropump design is best suited for applications requiring small pressure heads like microprocess systems. In these cases, rotating cone micropumps are a good choice due to their simplicity and performance.

Moving forward, the team notes that they can optimize their rotating cone micropump design. By using CFD simulations, they can evaluate the effects of adding modifications to the cone head surface, such as spiral fins. These results can then be compared with empirical data.

- Get more details about the research: “Hydrodynamic Modeling of a Rotating Cone Pump Using COMSOL Multiphysics® Software“
- Watch an 18-minute archived webinar on CFD simulation
- Browse additional CFD blog posts: