FluidDynamics Library for Coarse-Grid CFD-Simulation inModelica

Dr. Stefan Wischhusen1 Timo Tumforde1 Hans-Herrmann Wurr1

1XRG Simulation GmbH, Germany, {wischhusen, tumforde@xrg-simulation.de}

Abstract

This paper describes the content and the use of the newFluidDynamics Library which can be applied to carry outCFD simulations using Modelica as an open modellinglanguage. Typical applications until now have been inautomotive, aircraft and buildings development. In thispaper a fire dynamics and smoke removal simulation ispresented. These simulations are very important in theprocess of approving a building permission. The Fluid-Dynamics Library helps to identify promising ventilationand control setups and speeds up the simulation processsignificantly.Keywords: CFD, Coarse grid, Computational-Fluid-Dynamics, Navier-Stokes, FluidDynamics Library

1 Introduction

For simulations of air-conditioned spaces differentapproaches can be suitable. In 1D-simulation-toolsoften a single node model is used to model the mass andenergy balance for a complete room or building. Those“Lumped”-models are designed for quick simulationsof longer time intervals and are supplied by manyfree or commercial Modelica libraries on the market(examples: HumanComfort Library, AIX Library,Buildings Library). For a more detailed analysis ofthe inhomogeneous air states and air velocities withinthe compartment the user has to model the air flowbetween the discrete volumes, or else he has to establishNavier-Stokes equations which can describe the airflow in 3D. Those Navier-Stokes-based equations areimplemented in free or commercial CFD software,like OpenFoam, Ansys Fluent, Star CCM+ and soon. For a combined calculation of both modellingapproaches, an interfacing software (Middleware) isrequired, which handles the exchange of variables at themodel boundaries or connections (i.e., inlets and outletsof the air spaces). For this purpose TISC [TIS(2018)]or MpCCI [MPC(2018)] may be used. Although thecoupling works fine in general, it requires up to threesoftware licenses. Even in case of a built-in solution(e.g. Ansys Simplorer) a coupled solution requires more

computational resources and/or the decoupled solutionand data exchange at discrete time points may generatebalance failures.

A Modelica-based coarse grid CFD-solution hasthe following advantages:

1. Save time by faster Modelica simulations

2. Instant simulation success through convergencecontrol of the variable-step solver

3. Reduced license costs with only one simulationsoftware when coupled to Modelica models

4. Reduced elapse time for iterative work and controldesign loops through faster simulations

5. Model customization since the code is open

6. Efficient modeling through symbolic manipulationof the Modelica source code

2 FluidDynamics Library OverviewThe FluidDynamics Library, available in Dymola 2018FD01, consists of the following packages:

• Basics

• Weather

• Zones

• CFD

• Examples

The Basics package supplies all fundamental def-initions which are shared by several models, such asrecords, icons or functions.

The integrated weather model of the Weather Packageis able to read arbitrary weather data tables and providesthe interpolation to the zone model. Moreover, themodel can convert the intensity of radiation to theeffective area according to its spatial orientation. All

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Figure 1. Package overview of the FluidDynamics Library

necessary weather information is bundled and sent to thezone model via a standardized weather connector.

The Zones Package contains models to develop mobileor stationary applications. Mobile applications can bebuilt with models e.g. for aircraft [Michaelsen(2015)]vehicle cabins. All models can individually be built andfitted. The Modelica Code is readable.

The CFD package contains a Modelica-based,three-dimensional grid model. The model is composedof cubic cells. Each cell, which is used to apply thefinite-volume-method, may represent a solid or an aircell. The energy and mass balances are calculatedin energy cells, while the mass and heat flows arecalculated in the so-called flow cell. Here, the influenceof the turbulence, the shear forces acting to the air, thegravity and the buoyancy force is taken into account.By using the Navier-Stokes equations, as found inCFD simulation software, realistic flow conditionscan be calculated. At the edges of the grid standardinterfaces allow an easy connection with models fromother libraries. Thus, e.g. a whole building can berepresented by one-dimensional wall models from theZones package connected to the interior representedby the CFD grid model. On demand one can easilyexchange the grid model with a lumped volume modelfor the air side. Of course, Modelica.Fluid interfacesof the Modelica Standard Library are also available.Moreover, symmetric and periodic boundary conditionscan be defined in order to reduce the computationaleffort for larger rooms. Furthermore, the grid modelcontains all geometric information about the radiationexchange between surfaces. Thus, in advance the viewfactors to determine the thermal radiation between thesurface pairs are calculated by the software, which isrequired to determine for example internal shading.The spacing and relative orientation of the surfaces arerelevant for the exchanged heat radiation.

The Examples package contains models for demonstra-tion of the library capabilities and typical applications.

Figure 2. Building example model from Examples package

2.1 Coarse-grid CFD modelWhen modelling a viscous, heat conducting flow, theNavier-Stokes equations are the basic governing equa-tions. They consist of the continuity equation which rep-resents mass conservation, momentum equation whichis derived from Newton’s Law of Motion and the energyequation which stands for energy conservation. Since theanalytical solution is obtainable in only a limited numberof cases, one is forced to approximate these equationsto obtain workable results. Therefore, using one of thediscretisation methods, Navier-Stokes equations in theirdifferential or integro-differential form are transformedinto a set of algebraic equations. Discretised equationsare numerically solved in a number of discrete points inspace and time. There are multiple numerical approachesto CFD modelling including Finite Volume Method, Fi-nite Element Method and Finite Difference Method. Outof them all, the Finite Volume Method is most widelyused for fluid flow problems since it is conservative bydefault as long as the surface integrals are equal for allcontrol volumes sharing the boundary. In the Modelica-based approach presented here, the Navier-Stokes equa-tions are used to capture conservation of mass, momen-tum, energy and other associated transport phenomenafor Newtonian fluids. The general form of all these equa-tions for a conserved scalar density q in a coordinatesystem at rest (not moving with the fluid) is given by[Versteeg and Malalasekera(1995)]:

∂t(ρ q)︸ ︷︷ ︸

local timedependent

change

+ div(ρ~cq

)︸ ︷︷ ︸convective

term

= div(Γ grad q

)︸ ︷︷ ︸diffusive /conductive

term

+ Sq︸︷︷︸sourceterm

(1)

where ”∂t” is the partial derivative with respect to time,”div” represents the local divergence of a vector fieldand ”grad” the local gradient vector of a scalar field.Moreover ρ denotes the mass density, Γ is a diffusion

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coefficient also known as conductivity in heat transportproblems. The term ~c = (u,v,w) represents the flowvelocity vector, which is the time derivative of theposition vector~r = (x,y,z) in a given coordinate systemwith coordinates (x,y,z).

Each time derivative of each balance equation is apotential state in the jacobian matrix of the systemmodel. Due to this fact the numerical effort for solvingincreases exponentially with the number air volumes inthe grid model. Typically, up to 2.000 volumes can behandled with state-of-the-art work stations. Thus, thefluid dynamics library offers a coarse grid simulation.For a detailed view on the flow field a standard CFDsimulation has to be carried out.

The spatial discretization (i.e., grid generation) ofthe air-conditioned space into cubic volumes is assistedthrough the free edition of the XRG Score Application(Microsoft Excel Addin), which creates the requiredgeometry record (incl. view factors) for simulation.This Score edition is always shipped together withthe FluidDynamics library. Moreover, it provides thepost-processing of temperatures, and velocities in 2dimages (grid plot).

3 Application to Fire Dynamics andSmoke Removal Simulation

One possible application of the FluidDynamics Libraryis the usage for a fire dynamics and smoke removal sim-ulation. In the following an exemplary use-case of a fireincident in an open-plane office is presented.

3.1 Description of the Use case scenario

The use-case scenario deals with a fire incident rep-resented by an inflammation of a large-scale printerwithin a typical open-plan office with a floor space of1000 m2 and workplaces for 64 people. Additionally,a kitchen counter is placed within the office. Anoverview of the office geometry is given in Figure 3.The installed fire-fighting system consists of automaticsmoke detection devices as well as a mechanical smokeexhaust ventilation system.

The heat and smoke release can be described with aquadratic increasing curve until the maximum heatrelease rate is reached [VDI(2009)]. After that the heatand smoke release rate stays at a constant level. Anappropriate value for the maximum heat release rate ofa large-scale printer is 600 kW. The smoke extractionsystem is sized with a volume flow rate of 60000 m3/hand is activated simultaneously with smoke detection.

Figure 3. Overview about the office geometry

This can be assumed to be no later than 120s afterignition according to [VDI(2009)]. Figure 4 shows thetransient development of the heat release rate togetherwith the smoke release flux and the exhaust air volumeflow rate.

Figure 4. Course of heat and smoke release rate

The fire scenario shall be modeled and simulated both inCFD with ANSYS Fluent with a high locale resolutionand with the Coarse Grid model of the FluidDynamicsLibrary.

ANSYS Fluent is one of the most popular tools ofthe Computational Fluid Dynamics. The 3D-model ofthe office which is built in the ANSYS DesignModeleris displayed in Figure 5. The red volume is the sourceof fire. After activation of the smoke exhaust ventilationsystem the smoke is extracted via the 6 extraction pointscolored in orange. The green marked areas representopening surfaces for fresh air entering the room in thecase of fire. The air volume is meshed with the ANSYSMeshing Tool. The mesh consists of 4047834 cells intotal.

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Figure 5. 3-D model of the office for CFD-Simulation withANSYS Fluent

The Dymola/Modelica model of the same scenario usingthe FluidDynamics Library is displayed in Figure 6.It consists of the grid model of the room itself andfurther sub-components representing the main boundaryconditions. A fire model computes the transient heat andsmoke release within the grid. The air inlet model and 6extraction models supply information about the ambientconditions at the opening surfaces and the volume flowrate at the extraction points. The coarse grid has aresolution of 13x8x9 hexagonal cells, so that in total 936cells are used.

Figure 6. System model of the office for coarse grid simulationwith the FluidDynamics Library

For the CFD-simulation with ANSYS Fluent a PCsystem with 8 cores (Intel(R) Core(TM) i7-6950XCPU @3,00 GHz) and 128GB RAM is used in parallelcomputation mode. The coarse grid simulation with theFluidDynamics Library in Dymola is proceeded with aPC with a Intel(R) Core(TM) i5-2500 CPU @ 3,30GHzprocessor and 16 GB RAM in single-core computationmode.

3.2 Comparison of Simulation results

In the following, the results of both the CFD-simulationin ANSYS Fluent and the Coarse-Grid simulationwith the FluidDynamics Library are presented for thedescribed fire incident within the office. Therefore theoptical densities and air temperatures are visualized forboth cases in cut A-A from Figure 3 for the exemplarymoment of 600s after the ignition of the fire. Moreover,the computation time for both cases is analyzed consid-ering the used resources.

Figure 7 shows the local optical densities after600s for cut A-A computed with ANSYS Fluent. Onecan see that the smoke has spread along the ceilinginto the room. Moreover, clear layers of smoke and aircan be noticed. The lowest point of the smoke layer isapproximately 2,20m above the floor. At the extractionpoints holes within the smoke layer can be founddue to the so called plug-holing effect. Plug-holingdescribes the effect when air from beyond the smokelayer is sucked to the extraction points due to highvertical velocities at those positions which leads to thementioned holes within the smoke layer.

Figure 7. Local optical densities in cut A-A (see Figure 3)after 600s (ANSYS Fluent)

The local optical densities in cut A-A at 600s after igni-tion are displayed in Figure 8 for the results computedwith the FluidDynamics Library in Dymola. It can alsobe seen that the smoke has spread along the ceilinginto the room and a distinct smoke layer is existent.Compared to the result which is computed with ANSYSFluent the local plug-holing effects are not visible.Nevertheless, a very similar thickness of the smoke layercan be stated. The lowest point of the smoke layer inthe result created with the FluidDynamics Library isapproximately 2,30m above the floor.

In addition to the local optical densities the computedair temperatures shall be compared for both approaches.Figure 9 shows the local temperature after 600s forcut A-A computed with ANSYS Fluent. It is obvious

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Figure 8. Local optical densities in cut A-A (see Figure 3)after 600s (FluidDynamics Library)

that the highest air temperatures can be found in thesurrounding of the fire. The further away from thefire the lower are the temperatures in the smoke layer.The previously described plug-holing effect at theextraction points can also be seen in this temperatureplot. In the areas in which workers are potentiallypresent, temperatures only slightly above the ambientand starting temperature can be found.

Figure 9. Local temperatures in cut A-A (see Figure 3) after600s (ANSYS Fluent)

The temperature plot in Figure 10 shows the localtemperatures in cut A-A for 600s after ignition, whichare computed with the coarse grid model of the Fluid-Dynamics Library. Generally, a very similar situationcompared to the result of the CFD simulation withANSYS Fluent can be seen. The highest temperaturesin the smoke layer can also be found in the directsurrounding of the fire source. With increasing distancefrom the fire source the smoke layer temperaturesdecrease. In the lower zones in which people can bepotentially present, the temperatures hardly exceed thestarting room temperatures of 20◦C.

Figure 10. Local temperatures in cut A-A (see Figure 3) after600s (FluidDynamics Library)

Considering the generally well matching results ofboth simulations, the computational effort is of specialinterest. As described above the CFD simulation withANSYS Fluent is conducted with a multi-core PC inparallel computation mode while for the coarse gridsimulation in Dymola a PC is used in single-coremode. While the CFD simulation can be started di-rectly after initialization, the coarse grid model needsto be initialized dynamically fading in the physicaleffects step by step. This initialization process needsmost of the computation time but only has to be doneonce, so that a simulation can be repeated with a mod-ified set of input parameters with significantly less effort.

Figure 11 shows the time needed for computationfor the single simulations. Comparing just the pure ef-fort for one single simulation the coarse grid simulationwith the FluidDynamics Library in Dymola took 21.4hwhile 14.75h were needed for the initialization processand 6.65h for the simulation itself. The CFD simulationwith ANSYS Fluent took 29.63h in total. Consideringthe differences in the hardware of 8 cores computingin parallel in the CFD simulation and one core beingused in the coarse grid simulation it can be stated thatthe FluidDynamics approach needs significantly lessresources for computation. This makes the usage ofthe coarse grid model of the FluidDynamics Libraryinteresting for optimization processes, e.g. for finding avolume flow rate which is as small as possible to fulfillcertain safety requirements.

Figure 11. Comparison of computational effort

4 ConclusionsThe comparison of the results of the simulated use caseshows that the coarse grid approach of the FluidDynam-ics Library in Dymola delivers very similar results as thedetailed CFD approach in ANSYS Fluent does. Eventhough local effects like plug-holing at extraction pointsare not captured in the coarse grid results the overalldistribution of optical densities and air temperaturescorrespond very well to the ones computed with ANSYSFluent.

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The significantly less computational effort of thecoarse grid approach in the FluidDynamics Librarymakes it possible to conduct several simulations with theaim of optimization of e.g. necessary volume flow rateseven with medium tier hardware. With this advantagethe FluidDynamic Library can be used to plan, size andoptimize smoke extraction systems in less time and withsignificantly lower costs than with detailed CFD toolsand several iteration loops. In the process of approving abuilding permission this can cause a noticeable speed-upand also a significant reduction of costs due to the factthat the amount of necessary expensive CFD simulationscan be limited to one single loop in the best case.

References[VDI(2009)] Engineering methods for the dimensioning of

systems for the removal of smoke from buildings. VereinDeutscher Ingenieure, 2009.

[MPC(2018)] Mpcci - multiphysics interface, 2018. URLhttps://www.mpcci.de/.

[TIS(2018)] Tisc suite, 2018. URL https://www.tlk-thermo.com/index.php/en/software-products/tisc-suite.

[Michaelsen(2015)] et al. Michaelsen. Dynamic simulation ofan aircraft compartment coupled to a ventilation system.AST 2015, 2015.

[Versteeg and Malalasekera(1995)] H. Versteeg andW. Malalasekera. An introduction to computationalfluid dynamics, The finite volume method. LongmanScientific & Technical, 1995.

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May 17-18, 2018, Tokyo, Japan DOI

10.3384/ecp1814871