Simulation and verification of a plate heat exchanger with a built-in tap water accumulator

Transcription

1 Simulation and verification of a plate eat excanger wit a built-in tap water accumulator Anders Eriksson Abstract In order to test and verify a compact brazed eat excanger (CBE wit a built-in accumulation part a simulator as been developed. Te simulator can be used to study te dynamics of te unit giving te user information about te accumulation capabilities. Tis tesis was developed in cooperation wit SWEP International AB in Landskrona Sweden. Te simulator was developed for SSPA s Simnon software using te finite volume metod. Te simulator allows te user to study te impact of different accumulation volumes flow rates temperatures and oter parameters. Introduction In many omes were district eating is not available a common way to provide ot tap water as well as eating is by using a wall-ung gas fired boiler. Te gas burner eats water in a primary circuit wit te elp of a primary eat excanger. Te eated water in te primary circuit is used as eating medium in te radiators or wen tere is a demand to eat sanitary wit te elp of a secondary eat excanger. Wen te primary circuit is cold for example during te summer wen no water is used to eat te radiators tere will be a delay before te primary circuit becomes ot enoug to eat sanitary water in te secondary eat excanger. A common way to solve te problems wit delays and fluctuation is by using an accumulator for sanitary ot water. However an accumulator for ot water requires extra space and increases te price of te system. By using a secondary eat excanger wit a built-in accumulation part tese problems can be overcome since suc a unit can be built into te boiler and be produced as one single unit. Te aim of tis master tesis is to develop a simulator for a prototype compact brazed plate eat excanger wit a built in accumulation part and to verify te simulated results experimentally. Te simulator is developed for SSPA s Simnon software. Pysical model A compact brazed plate eat excanger consists of several corrugated steel plates tat are brazed togeter wit a brazing material in tis case copper. In every plate oles ave been made to form ports troug wic te media can flow. Te plates are designed in suc way tat if every plate is rotated 180 degrees in respect to its neigbor cannels are formed between te plates. Te design allows te media to enter every second cannel via a port on one side and te remaining cannels to be accessed via a port on anoter side. Tis creates two so-called circuits for example one cold and one ot circuit. A common configuration results in all ot cannels being surrounded by two cold cannels except te ones on te front and back of te CBE were one side of te ot cannel excanges eat wit te surroundings and te oter one wit a cold cannel. Since te cold circuit as no cannels excanging eat wit te surroundings in tis configuration tis circuit is called te inner circuit. To simplify te modeling all cannels in te eat excanger and accumulator were assumed to be equivalent and part of an inner circuit. Tis approac allowed eac circuit to be represented by only one of its cannels since tey are all equivalent. If all cannels in a circuit are equivalent te flow as to be equally divided between its cannels. Tis assumption as been

2 proven to be valid by comparing experimental results wit results acquired in SWEP s SSP software were tis assumption is also used. Matematical model Te numerical metod used in tis tesis is te finite volume metod (encefort referred to as FVM [1]. Te FVM was cosen because it results in a model tat is relatively easy to derive from a pysical model and terefore easy to understand gave a good accuracy and a ig simulator performance. Te metod used to derive te FVM is called te control volume approac were a continuity equation is solved for a volume of known size also referred to as an element. Te accumulation terms represents te time-dependent parts of te ODE systems used to calculate te temperatures. Fig 1. Flow distribution inside te CBE prototypes Water eated in te eat excanger part enters te accumulator and is divided between te direct and te bypass circuits. Te ratio between te flows in tese two circuits is called te bypass ratio and is calculated as: mbyp BR = & (1 m& dir Te streams from te direct and bypass circuits are ten combined into one single stream ready to be used as ot tap water. Anoter factor tat affects te performance of te accumulator is te metal of wic te plates are made since tey can accumulate relatively large quantities of eat due to teir mass. Because of tis te eat transfer calculations are based on local eat transfer coefficients on eac side of a plate rater tan te more common overall eat transfer coefficient. Heat is transferred to te wall from a ot cannel and ten transferred to te cold side. Inside te wall te eat can accumulate or be conducted in te lengt direction. Fig 3. A control volume Accumulation = In Out + Production ( Te elements are so small tat te properties inside tem can be assumed to be constant trougout tem. It is also assumed tat no internal eat source or sink exists and tat te pysical properties only vary in te z-direction (te lengt direction. Te latter assumption can be motivated by te plug flow profile associated wit turbulent flow in te cannels. Tese assumptions also apply to te modeling of te walls; te metal is so tin tat te temperature can be assumed to be te same on bot sides of a plate. Te partial differential equation (PDE describing ow te temperature canges over time in a cannel element is given by α = vz + ( T T w (3 t z y ρ Fig. Overview of te eat transfer model An overview of te eat transfer model used in te simulator is found in te figure above. Note tat tis figure sows an example taken from te eat excanger part; in te accumulator part te flow is co-current. Discretization If te plates and cannels are divided into a defined number of sections along te lengt eac section can be approximated as a control volume. Tis metod is called discretization and a discretization grid is used for dividing te domain (te plates and cannels in tis case into elements of known size. Te time dependent continuity equation is ten solved in every grid point resulting in a system of ordinary differential equations.

3 If te number of internal grid points i.e. grid points tat are located inside te domain and not on any of te edges is NGP te total number of grid points used becomes NGP + 1. Te distance between te grid points is calculated via equation 4. Tis distance replaces z in fig 3 and is used to approximate te space derivatives in a discretized domain. L = NGP + 1 (4 For te ot circuit in te eat excanger te ODE system becomes: i Ti Ti 1 = vzi... t αi... ( Ti Twi pd ρ i i (5 Te equation systems for te oter circuits are derived in a similar fasion. Wall temperatures are also calculated via ODE systems; ere te conduction results in a second derivative: λ T = +... w w w t ρ Cp z w w α ( T T i + 1/ i + 1/ w t ρ α... m w w ( T T ci + 1/ w ci + 1/ t ρ m w w (6 Second derivatives are approximated wit a second order approximation given in eq. 7. T T T + T = z w w 1 w w +1 (7 Boundary conditions At te edges of te domains boundary conditions ave to be defined in order to make te ODE systems complete. Since no eat transfer as taken place before te water enters a cannel tis temperature is assumed to be known often called a Diriclet type boundary condition. Heat losses are neglected; terefore te wall temperature space derivative is zero at bot edges of a plate. Tis is also known as a omogenous Neumann boundary condition. Te simulator Te simulator was developed in MatWork s MATLAB software and ten translated to Simnon. Te reason for using MATLAB instead of Simnon for te development was te ability to andle vectors and te better plotting abilities of MATLAB. Tis facilitated studies of ow te number of grid points affected te accuracy and performance. It was also easier to import data files from te experiments to MATLAB. Experimental testing and verification Since te developed simulator is based on many assumptions and simplifications and terefore could produce incorrect results it was necessary to test and verify te model wit experiments. Te results from te experiments were compared wit te simulated results and some of te deviations were corrected by making canges to te model and its parameters. All experiments were carried out in SWEP s laboratory in Landskrona. Experimental equipment Two prototypes of CBEs wit built-in accumulation parts of 1. dm3 and.44 dm3 accumulation capacity were tested. Te prototypes were based on te standard type CBE model B10. Bot ad eat excanger parts consisting of 1 plates and accumulator parts of and 40 plates respectively. Te CBEs were connected to a wall mounted Vaillant ecotec plus 831 combination boiler wit a 31 kw eat output capacity. Temperatures were measured at seven different points using type K termocouples and te results were logged to a computer using WinView CP data acquisition software. Experimental corrections and model canges Wen comparing te simulated results wit te test results it was noticed tat te simulated dynamics were too fast. A typical example of tis is sown in te figure below. Te test results do not fluctuate to te same extent as te simulated and are delayed in time. Te time delay indicates tat te volume in te test system is iger tan te simulated if plug flow is assumed.

4 Sanitary ot water temperature Tested model was canged by placing two imaginary stirred tanks at te outlets of te accumulator and one tank were te two streams are combined. By doing tis te delays caused by te pipes oses connected to te CBE as well as delays in te ports are taken into account by te simulator. Wit tese canges made to te simulator te results were nearly identical to te experimental ones Sanitary ot water temperature Fig 4: results before experimental corrections One of te reasons for tis is tat te actual volume of a circuit was larger tan te simulated one since only te part between te midpoints of te top- and bottom ports of a plate was used in te eat transfer calculations. Tis area is were most of te eat transfer takes place and is used for static simulations in SWEP s SSP software. However in a dynamic simulation tis extra volume affects te time constant of te system. Terefore corrections of te pysical dimensions of te plates were made so tat te entire volume was taken into account. 1/3 Vspec CorrFactVol = 1.04 Vsim V = w pd L =... c corr corr corr corr... = w pd L CorrFactVol 3 (8 (9 Te mass of a plate also differed from te specified one due to te same reasons as for te volume. Using te corrected flow widt and lengt a correction factor for te mass was introduced and multiplied wit te density Tested Fig 5: Results after te introduction of stirred tanks Simulator applications Parameter studies Te performance of te unit is influenced by many parameters suc as te number of plates te bypass ratio and te caracteristics of te primary circuit. Te simulator was used to evaluate te performance wen varying two of tese parameters: te bypass ratio and te number of plates Wen increasing te number of plates in te accumulator te volume increases and more eat energy can tus be stored tis as a great influence on te accumulator performance. m CorrFactMass = m plate spec plate sim = 1.35 w L t ρ ρ corr corr m m mcorr ρm CorrFactMass (10 = (11 Temperature [C] Influence on performance of te accumulator size Te introduction of correction factors improved te results but te results were stilled displaced in time. Tey also fluctuated more tan te experimental results. In order to displace te simulated results in time and to even out te fluctuations even more te 5 No accumulation 40 plates accumulation 80 plates accumulation 160 plates accumulation Reference temp Fig 6: Influence on performance of te number of plates Te bypass ratio determines ow slow te water from te eat excanger part flows troug te

5 bypass circuit compared wit te direct circuit. Te eat stored in te bypass circuit was found to affect te size of te temperature dip by eating cold water from te eat excanger part. Temperature [C] Influence on performance of te bypass ratio BR = 0.01 BR = 0.06 BR = 0.13 BR = 1 Reference temp Fig 7: Influence on performance of te bypass ratio Design One of te main uses of te simulator can be as a tool wen designing new boiler systems. Te needs of te end user and te properties of te boiler will affect te optimal design of te eat excanger-accumulator unit. One example of ow te boiler design can affect te design of te eat excanger-accumulator unit is te primary circuit s influence on te optimal bypass ratio. Te simulator is terefore best used in a feedback process wit te manufacturers of te boilers since many of te design variables are dependent of eac oter. A fully integrated boiler/eat excanger design process would probably yield even better results. Conclusions Te finite volume metod was sown to be a relatively easy metod for developing a simulator for te dynamics of tis eat excanger-accumulator unit. Te simulated results were almost identical to te experimental ones in many cases and te calculations were completed in te matter of a few seconds. However te simulator was adapted to yield accurate results for te experimental setup tat was used and te accuracy may terefore be lower if anoter setup is used. Te simulator may not provide results of te same accuracy wen used for oter applications tan as a part of a gas-fired boiler since only limited intervals of temperatures and flows can be tested wit suc a system. Nomenclature m& Mass flow [kg/s] BR Bypass ratio T Temperature [ C] t Time [s] v Velocity [m/s] α Local eat transfer coeff. [W/m C] ρ Density [kg/m 3 ] Cp Specific eat capacity [J/kgC] NGP Number of grid points L Lengt (flow lengt [m] Distance betw. grid points [m] pd Pressing dept [m] λ Heat conductivity [W/mC] t m Plate tickness [m] V Volume [m 3 ] w Flow widt [m] Subscripts and indices byp dir z w i spec sim corr c Bypass Direct z-direction Wall Cannel grid point index Wall grid point index Hot Specified Corrected Cannel References [1] Nilsson Bernt: Process Simulation Using MATLAB Department of Cemical Engineering Lund University 0.