Spatial model reduction for transport phenomena in environmental and agricultural engineering

Tijdens het ontwerpen van landbouwkundige en industriële installaties is het belangrijk om het energieverbruik van tevoren in te schatten. Simpele berekeningen volstaan om het energieverbruik globaal te schatten, maar vaak kan het energieverbruik significant worden verminderd door de vorm van het systeem slim te kiezen. De invloed van deze verbeteringen kan niet met simpele berekeningen worden voorspeld. Deze promotie gaat over een nieuwe methode om de invloed van de geometrie te analyseren. De methode is gebaseerd op toepassing van complexe functietheorie op stromingsproblemen; de zognaamde potentiaaltheorie. Als voorbeelden worden een warmtewisselaar en een omgekeerde elektrodialyse installatie onderzocht. Als de methode verder wordt uitontwikkeld, dan kan dit in de toekomst leiden tot besparingen van tijd en geld tijdens de ontwerpfase van technische installaties

A simple model for obstructed two-dimensional turbulent channel flow

We have investigated obstructed two-dimensional turbulent channel flow. The objective is to provide a simple building block for design models and to gain physical insight in this type of flow. We have designed a simple model with some unknown parameters to be calibrated against a CFD model. The model divides the domain between an area of main flow and recirculation areas. The model approximates these areas by polygonal shapes. The locations of the vertices of these polygons are the parameters in the model. This way, we can evaluate the simple model using the Schwarz-Christoffel integral. As a consequence, the model can be evaluated much more quickly than CFD models. The main flow is modeled to be irrotational. The recirculation area behind the obstacle is modeled as a stretched monopolar vortex and this requires 4 extra parameters. The other areas of separated flow are simply modeled to be stationary. By calibrating the simple model we have demonstrated that this physical description works reasonably well. Using only 9 parameters, the simple model reaches an error of 22\% of the inflow velocity

Understanding heat transfer in 2D channel flows including recirculation

Inviscid, irrotational two-dimensional flows can be modelled using the Schwarz¿Christoffel integral. Although bounded flows including boundary layer separation and recirculation are not irrotational, a model is presented that uses the Schwarz¿Christoffel integral to model these flows. The model separates the flow domain in the main flow area, where irrotational flow is assumed, and recirculation areas, which are modelled as monopolar vortices. The model has unknown parameters, which are geometric characteristics of the velocity field. The method is demonstrated on a channel with alternating baffles. Many variations of this system were modelled using CFD modelling, and the flow was a typical combination of main flow and recirculation. The CFD results were used as reference to calibrate the parameters of the Schwarz¿Christoffel model. Many parameters appeared to be constant, and calibrating only three variable parameters yielded about 22% error for most velocity fields. After this, heat transfer was added to the CFD models, and the heat flux was analysed using the three variable parameters representing the velocity field. This way, a new model is found for the heat flux from a wall bounding a vortex, which has an error of 7%. Finally, we have calibrated the parameters using a limited number of given velocity vectors, demonstrating that the parameters can be calibrated against a real set of measurements

Modelling of natural-convection driven heat exchangers

Abstract: A lumped model is developed for shell-and-tube heat exchangers driven by natural convection, which is based on a one-dimensional approximation. The heat flux is driven by the logarithmic mean temperature difference. The volumetric air flow rate is driven by the buoyant force. Based on the Boussinesq aproximation, this force is characterised by an analytic expression of the inflow and outflow temperatures. The lumped model is finished by relating the buoyant force to the friction force via the drag coefficient. The model was calibrated and validated based on Computational Fluid Dynamics calculations and physical measurements

Extending potential flow modelling of flat-sheet geometries as applied in membrane-based systems

Abstract The efficiency of chemical reactors can be analysed using the residence time distribution. This research focusses on flat-sheet geometries applied in membrane-based systems. The residence time distribution depends mainly on the 2D velocity field, parallel to the membrane. The velocity average over the transversal direction is calculated using potential flow theory. A combination of real and virtual sources and sinks are used to model the internal inlets and outlets. Furthermore, a novel method is presented to calculate the residence time distribution. By ignoring diffusion and dispersion, every streamline is modelled to have a fixed residence time, which can be calculated with a simple quadrature based on a coordinate transformation. The model predicts the impact of the two-dimensional geometry on the residence time distribution, but it is demonstrated that large zones of nearly stagnant flow have only a limited impact on the residence time distribution. The new model can predict the travelling time from the inlet to each interior location, providing a better tool to analyse spatially distributed chemical reactions. The models agreed highly with pressure measurements (R2 = 0.94¿0.98) and they agreed well with tracer experiments for the residence time (R2 = 0.73¿0.99)