# Heat and fluid-dynamic calculations & simulations

Huygens Engineers performs the necessary calculations and simulations during the process of development and engineering. The share of calculation and simulation varies widely among projects. In some projects the share is 100%. We aim to keep analytical insight as the main driver for design, with subsequent confirmation through FEA.

Huygens Engineers delivers calculation and simulation services in the fields of mechanics, heat, fluid flow and electromagnetics. For heat and fluid-dynamics, we have capabilities on the following subjects:

- Flow modeling and flow calculations
- Optimizing cooling and heating
- Acoustic numerical simulations

## Flow modeling and flow calculations

One application-field of flow analysis is the analytical modeling and prediction of the flow field around lifting surfaces such as wings and propellers. Their geometry influences the flow. The reduction of drag and increase of the propulsion and lift will lead to a greater efficiency. Flow simulations are mainly done in ANSYS Fluent, on a 36-core calculation cluster.

Prediction of thrust and drag in oscillating foils lies at the basis of Huygens Engineers. The founders started their cooperation on a large, highly disciplined and AP Moller-Maersk funded project to investigate the technical and economic feasibility of flapping foil propulsors for container ships. The program comprised of several phases, including an analytical prediction of thrust and efficiency, and culminated on the scientific side in a successful systematic measurement program performed at MARIN. The results of the measurement program have been presented at the ONR conference in Gothenburg and have been published under the name “A Systematic Experimental Study on Powering Performance of Flapping Foil Propulsors”. CFD modelling of the performance of the flapping foils was done after the measurement program. The illustration shows a CFD simulation of a flapping foil, while the video demonstrates the flapping propulsor in practice.

Another application of flow simulation is the steady-state modeling of laminar and turbulent flows. Flow simulations are used to predict specific system characteristics such as the pressure drop and heat flow in a heat exchanger or the temperature of a cooling fin, which would be hard to estimate analytically. A few objects of steady state flow simulation are displayed in the figure below. Taking the case of the flow over a ribbed profile as an example, the goal was to gather gradient information of the flow around/in the cavities, which determines the convection characteristics of the flow.

In the previous examples of flow simulations, the steady-state solutions were sufficient to analyze the situation. However, sometimes these will not suffice, and modeling of unsteady flows is needed. The** **video shows an unsteady convection around a heating element, as simulated in ANSYS Fluent. Since the heating element is constantly raising the temperature of the environment/the surrounding gases, no steady-state solution can be used to describe the process.

Simulations with moving geometries require a high-quality mesh. Making such a mesh for the complete geometry is challenging, especially in the case of large displacements. A common approach for situations like these is the use of overset meshes, where individual components are meshed separately and can overlap (almost) arbitrarily. An example of the mesh, flow and pressure fields of a 2-lobe-pump can be found in the figure and video, where every component grid is given a different color. The mesh consists of field cells were the governing equations (transport equations of mass, momentum and energy) are solved, fringe cells which are solved by interpolation from the field cells from the other respective mesh, and dead cells which are irrelevant for the solution.

In some situations, the geometry is restricted by certain building requirements. This is, for example, the case if a transition piece for a circular to a square form needs to be designed for maximum flow uniformity. The figure shows a close-up of the mesh and the velocity contours of the geometry of an air duct.

## Optimizing cooling and heating

Thermal behavior of a system can sometimes have a major influence of the operating life of a mechanism. The analysis is often very complex, due to flow around the structure, as well the effect of moving parts. 3D calculations on the thermal behavior of such a system can therefore become very complicated and time-consuming, while the accuracy of these type of calculations is sometimes doubtful. In situations like this, it can be time-effective to perform analytical 1D or 2D calculations in Mathcad or Python, converting complex convection, conduction or radiation problems to well-known empirical relations. The figure provides an example of such an approach. Heat exchange and heat build-up in the marine propulsor resulted in insight as to appropriate oil viscosity and appropriate cooling methods.

Besides performing analytical calculations, Huygens Engineers also simulates stationary and transient temperature profiles in solids. As heat is transported through (poor) conduction within solids, applications like plastic molding require active cooling and heating, which needs to be predicted accurately to ensure the product quality.

The conductivity can vary largely within one model and is not necessarily constant for the entire temperature range. For example, in case of plastic molding, a steel mold will conduct heat much faster than the plastic product. For organic materials, like meat, varying thermal properties are also very common, as freezing and boiling effects of the water and fat content will influence the specific heat and conductivity. An example of transient cooling in a low conductivity meat product and a video of transient cooling in a high conductivity mold can be viewed in the figure below.

In convection-oriented cases, Huygens Engineers determines convection coefficients through detailed simulation, validation and measurement of elements in a flow.

A specific phenomenon with regard to cooling and heating is that of a thermal shock and related material stress. A sensor utilized in a cyclical temperature environment did not reach the desired service-life targets when subjected to cycles where temperature rapidly increased from -30 °C to 60 °C. Simulation in ANSYS transient thermal showed that two effects caused mechanical stress to exceed acceptable values during this cycle. The first effect is a difference in thermal expansion due to the slow propagation of temperature, which in turn is caused by the low thermal conductivity of stainless steel. The second effect is a large difference in thermal expansion coefficients (almost by a factor 2) between austenitic stainless steel, used in the casing, and precipitation of hardening stainless steel, used in the element containing the strain gauges. The video shows a visualization of this thermal shock as described.

Sometimes programming is the way to go. Huygens Engineers has experience in transient simulation of cyclical two-dimensional cooling of drum motors in interaction with the belt that it drives. Drum-motors in belting applications cool through cyclical contact of parts of the drum with the belt during rotation and subsequent transient thermal conduction. This cyclical process results in a long-term cyclical thermal equilibrium of the belt and the drum-motor, as each go through their periodic motion. The polymer of the belt conducts heat poorly, and belts may or may not be subjected to temperatures at which mechanical strength drops below specification. Huygens Engineers developed a 2D finite-difference Python-simulation for hot product environments for application engineering. The figure below shows a simulation of finite difference implementation, thermal performance prediction and a discretized numerical model in Python.

Besides conduction and convection, radiation may play a role in heat transport. Shown in the figure is an ANSYS simulation of radiative heat transfer from Infrared (IR) heaters to a plastic part. This approach is used by one of our customers to realize controlled local heating in the geometry. By performing IR absorption measurements on the material, Huygens Engineers was able to calculate the heat absorption of the plastic material. The figure shows a transient simulation of radiative heating of plastic.

## Acoustic numerical simulations

Acoustic numerical simulations can be used to design quieter equipment, give insight into noise problems and/or assess proposed solutions. The figure shows the numerical sound analysis of a machine in the food-industry that displayed unwanted noise. Huygens Engineers could easily show that a standing wave was the cause, which could readily be eliminated.

Thanking you for your interest, we welcome you to ask us any question, and invite you to consider whether we could mean something for you.