Model Development for Fluid Flow Applications

**Principal Investigator:**

Philipp Gerstner

**Affiliation:**

Engineering Mathematics and Computing Lab (EMCL), Ruprecht-Karls-Universität Heidelberg (Germany)

**Local Project ID:**

hka14

**HPC Platform used:**

JUQUEEN (JSC)

**Date published:**

*The dynamic behaviour of fluid motion is driven by processes on a wide range of spatial and temporal scales. In a project run by Heidelberg University scientists, parts of model systems that describe fluid dynamics and temperature evolution were investigated. The models are formulated in terms of velocity, temperature, pressure, and density. The researchers employ a hierarchy of different physical models with an increasing degree of complexity. Additionally, uncertain input parameters are taken into account.*

**Part 1: Thermal electro hydrodynamics**

In general, heat exchanging systems are based on the principle of natural convection, which arises due to density variations of fluids with non-homogenous temperature distribution. In natural convection, the fluid serves as heat carrier between a warm object and a cooling system. In such a configuration, warm fluid close to the object rises, while cold fluid close to the cooling system descends. Thus, a circular-shaped fluid structure develops that enhances heat transfer by convection. However, when considering heat exchanging systems in environments without gravitation, such as satellites and spacecraft, the force behind these mechanisms is not present anymore. One option to overcome this issue requires the use of dielectric fluids combined with an applied electric voltage between object and cooling system. The resulting dielectrophoretic force gives rise to emergence of a certain number of vortices being formed by the fluid. Due to these vortices, a convective heat transfer is established. The scenario can be modelled by means of the Boussinesq equations for natural convection, augmented by additional terms involving an electric potential. This set of equations is solved by means of the Finite Element Method (FEM) which is implemented in the software package HiF low 3. Figure 1 illustrates the stationary final state of the simulation for a silicone oil being contained in a vertical cylinder annulus.

**Part 2: Method comparison for meteorological applications**

The formation of clouds and precipitation processes occupy a central role in current research about climate change. Compared to the temporal and spatial scales of global climatic phenomena, such as the several-thousand-kilometre gulfstream being modelled for months of time, these processes often occur on small scales—a few hundred meters in space and only several minutes or hours in time.

Among these processes shower or weak tornadoes are typical examples. Severe storms, such as tropical cyclones, are another category of weather phenomena where local weather forecasts with high precision in space and time are needed.. Based on precise and fast numerical forecasts, emergency management has the chance to evacuate precisely affected regions in time to save human lives.

In order to fulfil the demands of a computer-aided forecast, extremely fine scales with respect to both space and time are needed. The cells in the discrete spatial grid have to be small enough such that single clouds are covered by at least one whole cell. The increase in spatial resolution leads to a proportional rise in the demands of compute power.

In current models for numerical weather and climate prediction, simulation of fluid dynamics based on compressible Navier-Stokes equations serves as a main source for restrictions on the resolution over time. These equations are valid for all Mach numbers and consider all sources of compressibility, meaning, changes in density due to both temperature and pressure variations. Therefore, these equations do not only resolve the velocity field of interest, but also the sound of wind, which is caused by density variations on very small temporal and spatial scales. For many relevant atmospheric fluid flows, only the velocity field at Mach numbers much smaller than one is actually of interest, not the above mentioned acoustic modes of the fluid flow. A scale analysis for flows at Mach numbers smaller than one shows that density variations are mainly due to temperature differences and that the contribution of the pressure onto these variations is negligible.

This way, it is possible to filter out acoustic effects from the model, thus allowing the use of much lower temporal resolutions when conducting numerical simulations. This simplification is known as Low-Mach number approximation and results in a more efficient simulation of meteorological phenomena compared to the full model given by the compressible Navier-Stokes equations.

**Part 3: Uncertainty quantification for a blood pump device**

There are 40 million people who are affected by the heart failure worldwide. That number is constantly growing due to unhealthy diet habits and an aging population . Heart failure and heart disease place a lot of pressure on the patients and their families, but also on the social health system. Heart failure happens when the pumping or the relaxing action of the heart is insufficient, leading to a weakening of the cardiovascular system. Here, the blood pump comes into play, because it can provide additional oxygen and other nutrients to the cells.

Despite the fact that heart transplants are the best option for heart failure patients, the lack of donor hearts is considerably large. Hence the ventricular assist device (VAD) is currently one of available alternatives for the heart disease patients. The number of blood pump implants has increased significantly over the last few years, and has already surpassed the number of patients that have received heart transplants. However, the mortality of VAD implants is still notable—around 25% after the first year implantation. Therefore, there are still aspects with respect to performance of the blood pump to be improved.

In our work, we provide an efficient approach to model the blood pump, and on top of that, we quantify the uncertainties caused from the input parameters in our numerical model. In this study, three uncertain sources are considered: inflow boundary condition, dynamic viscosity and rotor’s speed. Our numerical results provide more information in terms of quantifying uncertainties, which are useful for further improving the blood pump device.

**Research Team:**

Martin Baumann, Simon Gawlok, Philipp Gerstner, Vincent Heuveline, Nils Schween, Chen Song

Engineering Mathematics and Computing Lab (EMCL), Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany

**Scientific Contact:**

Philipp Gerstner

Engineering Mathematics and Computing Lab (EMCL)

Interdisciplinary Center for Scientific Computing (IWR)

Heidelberg University, Germany

Im Neuenheimer Feld 205, D-69120 Heidelberg (Germany)

email: philipp.gerstner[at]uni-heidelberg.de