Simulation of Components of a Thermal Power Plant Modelica Association Modelica 2006, September 4 th 5 Simulation of Components of a Thermal Power Plant RenØ Schimon Dragan Simic

The Modelica Association Modelica 2006, September 4th – 5th

Simulation of Components of a Thermal Power Plant

René Schimon Dragan Simic Anton Haumer Christian Kral Markus PlainerArsenal Research

Gie�nggasse 2, 1210 Vienna, Austriaphone +43-50550-6347, fax +43-50550-6595, e-mail: [email protected]

Abstract

In this paper different models for simulating compo-nents of thermal power plants and other thermal orthermodynamic processes are presented. The differentsimulation results were performed withDymola whichis based on Modelica. The models were realized withtime domain differential equations and algebraic equa-tions. For all components the �uid was modeled byusing the Modelica.Media library which is part of theModelica standard library.The heat transfer for the heat exchanger componentwas modeld by calculating the heat transfer coef�cientin dependency on the �ow velocity of the medium inthe pipes.

1 Introduction

Arsenal Research currently works on the develope-ment of a simulation library for thermal and thermody-namic processes. Elementary problems like heat trans-fer and �uid dynamics will be processed. To a largeextent the Modelica_Fluid library already covers a lotof important models, which are used to develop partsof thermal power plants. The new library will com-plete the Modelica_Fluid library. Some of the pre-sented models are based on components of the Mod-elica.Fluid library. For some special technical prob-lems theModelica_Fluid library was modi�ed and ex-tended.

2 Extended models to be developed

Arsenal Research is working on speci�c problems re-lated with heat transfer and �uid dynamics. The de-velopment of the following components is currentlyinitiated:

� Centrifugal pump

� An ideal pump based on physical parame-ters

� A pump with losses based on physical para-meter

� Simple pipe comprising pressure losses

� Heat exchanger including pressure losses, ther-mal convection, thermal conduction

� Turbine modeled with a characteristic curve

3 Components

3.1 Fluid �ow machines

In a thermodynamic processes or thermal power plant�uids and different gases have to be transportedthrough pipes. Pipes cause pressure losses. To gen-erate a constant mass �ow, pumps are needed. Yet, insome cases stationary density differences give rise toa constant mass �ow without having a pump, like in anatural circulation boiler. For assistance or to start a�uid �ow, pumps are the most important componentsin thermal processes. Pumps are �uid �ow machines.Mechanical shaft energy is transformed into kineticand potential �ow energy. The impeller which is di-rectly attached on the shaft, accelerates the �uid el-ements. Because of the diffuser effect in the shovelchannels of the impeller wheel, the operating �uidleaves the impeller with increased pressure. Pumpsrepresent a link between pressure increase and �owvelocity or the mass �ow. This context leads to thecharacteristic of a pump. Each pump typ has its typ-ical characteristic in dependency on its geometry androtation speed.

3.1.1 Ideal centrifugal �uid �ow machines

An ideal pump is a �uid �ow machines with an in�-nite number of shovels. The converted energy in the

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Figure 1: Characteristic of an ideal water pump

impeller wheel of the water pump is the kinetic andpotential energy of the operating �uid. Therefore themain equation of the water pump represents the pro-portion between mechanical energy of the input shaftwith respect to the impeller wheel of the water pumpand the speci�c energy of the operating �uid [1].

�m �w= 2 �p �b2 �r � tan(b2) � (r22 �w2�Y¥) (1)

In this equation r2 is the outer radius of the impellerwheel of the water pump, b2 is the outer width of theimpeller wheel, r is the density of the operating �uidand b2 is the outlet angel of the shovel of the impellerwheel. Furthrmore, �m represents the mass �ow of theoperating �uid in the water pump andY¥ represents thespeci�c energy of the impeller wheel for an in�nitenumber of impeller shovels. The ideal pump modelwas implemented Modelica using Dymola as simula-tion tool. Figure 1 shows the linear characteristic ofthe ideal water pump. Pumps as a special �uid �owmachines is detailed processed in [2].

3.1.2 Centrifugal Pump

In realistic pumps, friction, �uid impacts and other�uid dynamic effects cause losses in the water pump.These losses can be split into:

� Decrease of the speci�c energy

� Hydraulic losses in shovel channels

� Impact losses

� Friction losses of the impeller wheel

Figure 2: Characteristic of the cetrifugal water pumpwith losses

A perviously developed model of an ideal pump [3]was used to design a water pump with losses. Thenew model now uses the Modelica.Media library tomodel the �uid. Figure 2 shows the characteristic ofthis model.

3.2 Initialization

In real thermal power plants, some components, likethe turbine, have to be brought up to operational con-ditions by a well de�ned starting procedure. Reasonsfor this starting procedure can be load limits of certaincomponents, cavitation of operating �uids or restric-tion due to the process.

In computer simulations, certain start values de�ne theinitial state of the simulation. Therefore, a simulationusually can be started from any state. From the par-ticular starting point, the system should then reach asteady state condition. The initialization of a complexmodel becomes more dif�cult when using the Model-ica.Media library.

The Modelica.Media library has certain operationallimits. Outside these limits an error occurs. For ex-ample, the start-up procedure of a real pump is verycomplex. At the suction side of the pump the pressuredecreases during the start-up procedure. Without con-trolling the process of starting up a simulation, like ina real system, an error may occur. This, however, maylead to a complex controlling due to the huge numberof physical quantities to be controlled.

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R. Schimon, D. Simic, A. Haumer, C. Kral, M. Plainer


3.3 Pipe as an important part of Heat Ex-

changers

The pipe is one of the most elementary components.A lot of thermal power plant components are based onsimple pipe models. One of these important compo-nents is the heat exchanger.In a real pipe, the pressure drop of a �uid �owingthrough the pipe, decreases due to the wall roughnessof the surfaces. The pressure drop also depends on the�ow velocity and on the roughness of the inner sur-face of the pipe. The cross-section of the pipe alsoin�uences the pressure losses. For circular pipes thepressure drop can be calculated according to:

Dp= l � LD� r � v22

(2)

The pressure drop Dp is a function of a coef�cient offriction, l, the length of the pipe, L, the characteristiclength, D, the density, r, and the velocity, v. The co-ef�cient of friction, l, depends on the Reynolds (Re)number. The Re number is de�ned by (3). The Renumber de�nes the type of �ow. The �ow can be tur-bulent, laminar or in the transient area.

Re=v �D

n(3)

The pressure drop substantially depends on the �owtype. For the laminar area applies:

l=64Re

(4)

For the turbulent area basically applies:

1pl=�2 � log( 2:51

Re �p

l+

k3:71 �D) (5)

In this equation k is the roughness of the inner pipesurface. Figure 3 represents l versus the Re numberfor different �ow types.The Modelica_Fluid library contains a lot of differentpipe models with different levels of abstractions. Arse-nal Research develops extended models based on thecomponents of the Modelica_Fluid library. Simulta-neously, Arsenal Research developed simpli�ed mod-els for easy handling and modeling of test cases, incor-porating less parameters than the comprehensive mod-els. Modelica_Fluid and the extended and the simpli-�ed models are using the same basic equations, withrespect to e.g. friction models, Reynolds equation, etc.

Figure 3: Coef�cient of friction versus different �owtypes

Figure 4 shows the pressure drop versus Re number.The discontinuity indicates the transition from lami-nar (at low Re numbers) to turbulent �uid �ow (at highRe numbers).

Figure 4: Prssuredrop in pipes versus �ow velocity

3.4 Heat Exchanger

Heat Exchangers are very important for nearly everythermal process. In heat exchangers usually two in-teracting �uid circuits are involved. The temperaturesof both �uids are approaching. Yet a certain tempera-ture difference is required to maintain the energy �owfrom the higher temperature �uid to the lower temper-ature �uid. Figure 7 shows a scheme of a pipe heatexchanger.

3.4.1 Heat propagation in Fluids

For modeling a heat exchanger it is necessary to un-derstand how heat propagation in �uids works. Heat

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propagation is described with partial differential equa-tions in one dimension [4] . In standing �uids heat istransported by diffusion. The diffusivity a depends onthe operating �uid. The thermal conduction equationfor one dimension is shown in (6). In this equation qis an additional heat source, T is the temperature andx is the location. The diffusivity a is a �uid property,which is a function of the heat conduction l, the den-sity r and the speci�c heat capacity c, according to (7)

¶T¶t= a � ¶2T

¶x2+q (6)

a=lc �r (7)

In �owing �uids the heat is also transported with the�owing medium, which depends on the �uid velocity.This leads to a remodeling of the heat propagation (6).Properties in a hydrodynamic �ow depend on time andlocation. The temperature is the important propertyin this case. So the temperature depends on the timeand the place in the pipe. The total differential of thetemperature with respect to the time and the place hasto be calculated according to (8). To substitute thiscontext into (6) it is necessary to have an expression[5] for:

¶T¶t

So function (8) has to be divided by dt.

dT =¶T¶t�dt+ ¶T

¶x�dx (8)

dTdt=

¶T¶t+ v � ¶T

¶x(9)

After summarizing equation (9) and (6) we receive anequation for the heat transport in axial direction:

¶T¶t+ v � ¶T

¶x�a � ¶2T

¶x2= q (10)

3.4.2 Heat Transfer caused by Convection

To design a heat exchanger model, different physicaleffects have to be considered. It is necessary to knowthe quantity of heat �ow which is transported from a

Figure 5: Nu number versus increasing �ow velocity

�uid in the pipe to the outside surface. The heat trans-fer between the �uid and the pipe wall has to be mod-eled. This heat transfer happens by means of convec-tion. The heat transfer coef�cient describes the heattransfer between �uid and pipe wall, and is de�ned bythe Nusselt (Nu) number according to (11). The Nunumber is, however, a function of the Re number andof the medium properties. The Re number describesthe type of �ow (laminar, turbulent) and therefore, alsothe Nu Number depends on the type of �ow.

Nu=a �L

l(11)

To determine out the quantity of heat, �owing betweenthe �uid and the pipe wall, the Nusselt-Number has tobe calculated. To transfer high quantities of heat �owhigh Re numbers are necessary. Figure 5 shows the Nunumber versus the Re number.The heat transfer coef�cient a increases with increas-ing Re number. A salient turbulent �ow is important tohave a high quantity of heat transfer. In turbulent areasthe heat transfer increases linear with the Re number[6].

3.4.3 Heat Transfer caused by Diffusion

As in shown in (6), the diffusivity is responsible for theheat propagation in �uids. The Peclet (Pe) number isthe proportion between convective heat transport andheat transport through conduction:

Pe=d � va= Re �Pr (12)

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The Peclet-Number determines whether the diffusionis substantial or can be neglected.

3.4.4 Model of a Pipe

To design a detailed model of a heat exchanger, themodel should consider all the above described physi-cal behaviors. Different types of heat exchangers leadto different results. Every different types of heat ex-changes needs different equations to describe the phys-ical coherence.

� Parallel �ow heat exchangers

� Counter �ow heat exchangers

� Cross �ow heat exchangers

� Plate heat exchangers

Each type of heat exchanger has a different ef�ciencybecause of their different heat transfer behavior. InModelica continuos heat transfer is modeled by heattransfer between n in�nite small pipes. Where n isthe number of elements. To get a model of a heat ex-changer, an in�nite small pipe segment could be themain model. A simply unlagged pipe always has aheat transfer with the environment. Figure 6 showsa model of an in�nite small pipe segment. The com-ponent pipe, models the pressure drop in this in�-nite small segment. The pressure drop is caused bythe friction between the �uid and the inner wall ofthe pipe. The additional connector is a real vector ofthe size 5. This connector transmits the pressure p,speci�c enthalpy h, mass�ow m_�ow, segment lengthL and the characteristic length d to the componentheat transfer. The characteristic length is fora circular cross-section the diameter. The componentheat transfer needs the parameter to calculatethe Nu number, which de�nes the heat transfer coef-�cient a for an in�nite small area. To get the wholeheat transfer through a pipe surface, a has to be mul-tiplied with the pipe surface A according to (14). Themodel heat transfer transmits Gx to the compo-nent convection. Now the energy �ow Qx between�uid and the pipe wall in radial direction caused byconvection can be calculated by:

Qx = Gx �DT (13)

Gx = a �A (14)

Figure 6: Model of an in�nite small pipe segment

The component thermal conduction simulatesthe heat conduction through the wall of the pipe. Thered line which is drawn in in the component pipein Figure 6, indicates the heat transfer in axial di-rection caused by diffusion. The in�uence on heatpropagation caused by diffusion is negligible small.High Pe numbers show that for usual technical appli-cations the diffusion can be neglected. To minimizethe CPU-Time, diffusion was not implemented in theheat exchanger model. At the outer port of thermalconductance an additional heat source could besimulated, considering e.g. solar radiation or a cool-ing environment.

3.4.5 Model of a Heat Exchanger

In a heat exchanger, a second �uid constitutes an ad-ditional heat source. Figure 7 shows the scheme ofa parallel heat exchanger. The second fluid A, cir-cum�ows the pipe which contains the fluid B. Heat�ow interchanges between both �uids. The heat �owsfrom the �uid with higher temperature to the �uid withlower temperature. In a parallel heat exchanger the�uids �ow in the same direction. At the inlet the tem-perature gradient is on its highest level and decreasestowards the �ow outlet. The temperatures of both �u-ids are approaching. Figure 7 shows that heat �owis transported from the hot fluid A to the secondfluid B. The pipe has a mass which also has to beheated up, and therefore, the heat capacity of the pipehas to be considered. The ef�ciency of a heat ex-changer is at its maximum, if the heat �ow betweenboth �uids is as high as possible. For this reason it isimportant that the pipe is a good heat conductor. The

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Figure 7: Scheme of a parallel tube heat exchanger

wall of the pipe conducts heat also in axial direction.This has to be respected in the heat exchanger model,because for some types of heat exchangers, this effectis very important. Figure 7 shows a scheme of a paral-lel pipe heat exchanger and Figure 8 shows the imple-mentation in a Modelica model.Figure 8 shows the model of an in�nite small elementof a �nitely long parallel tube bundle heat exchanger.The model volume is directly taken out of theModel-ica_Fluid library. It was equipped with an additionalconnector. This connector transmits some geometri-cal parameter of the pipe to the volume, so that thevolume of the pipe segment can be calculated. The ad-ditional components, conduction and capacity,model the pipe with heat conduction in axial and ra-dial direction. For a parallel heat exchanger thesecomponents do not have a signi�cant effect. The sec-ond heat transfer component simulates the heat�ow, which is transmitted form the outer �uid to thepipe. In the heat exchanger model the number of ele-ments and the length of the whole pipe bundle has tobe speci�ed.The model of one segment is connected n times oneafter another to model a whole heat exchanger. Figure9 shows the temperature versus the length of the heatexchanger. This is an result taken out of a simulationwith only 10 element. The model contains over 2000algebraic and differential equation.

4 Conclusion

Simulations of components of thermal power plants orof other thermal processes are very complex. Espe-cially the consideration of the complex media of the

Figure 8: Model of a segment of a parallel heat ex-changer

Figure 9: Temperature distribution inside the heat ex-changer

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Modelica.Media library leads to very detailed modelsand precise results. Nevertheless, the Modelica.Medialibrary allows for a high precision of results. For someapplications, however, it makes sense to model somecomponents with a more simpli�ed level of abstrac-tion. Therefore it is necessary to carefully decide onthe detail of abstraction for each model.

Abbreviations

CPU central processing unit

References

[1] J. F. Gülich, Kreiselpumpen. Heidelberger Platz 3,14197 Berlin: Springer Verlag Berlin HeidelbergNew York 2004, 2004.

[2] D. Simic, C. Kral, and H. Lacher, �Optimizationof a cooling circuit with a parameterized waterpump model,� 5th International Modelica Confer-ence 2006, 2006.

[3] D. Simic, C. Kral, and F. Pirker, �Simulation of thecooling circuit with an electrically operated waterpump,� IEEE Vehicle Power and Propulsion Con-ference, VPPC, 2005.

[4] H. Baehr and K. Stephan, Waerme- und Stoffue-bertragung, vol. 5. Au�age. Springer, 2006.

[5] G. Merker and C. Eiglmeier, Fluid- und Wärme-transport � Wärmeübertragung. Stuttgart,Leipzig: B.G. Teubner, 1999.

[6] H. O. jr., Prandtl - Führer durch die Stroemu-ngslehre Grundlagen und Phaenomene, vol. 11.Au�age. Vieweg, 2002.

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Simulation of Components of a Thermal Power Plant Modelica Association Modelica 2006, September 4 th 5 Simulation of Components of a Thermal Power Plant RenØ Schimon Dragan Simic