Component 166: Phase-change material storage

Specifications

Line Connections
1	Main fluid inlet
2	Main fluid outlet
3	Heat transfer from main fluid (outlet)
4	PCM-fluid definition (inlet)

General User Input Values Physics Used Characteristic Lines Results Displays Example

General

The component 166 models a PCM storage (here PCM stays for phase change material) including a heat exchanging part for charging / discharging the storage.. To properly understand the description it is highly important to clearly distinguish between the PCM-Fluid (the medium which changes its aggregate state and in which the latent heat is basically stored) and the Fluid (the working medium which flows through the heat exchanger charging / discharging the storage). Contrary to the working medium fluid the PCM-Fluid remains encapsulated within the storage. The working medium fluid flows through the component entering at PIN 1 and leaving at PIN 2. In this way the component 166 is connected to the modelled cycle.

The PCM-Fluid is defined at PIN 4. This can be done either by component 1 or component 33. See chapter PCM-Fluide for details. For modelling an ice storage one can use LibICE as PCM-Fluid on stream type two-phase-fluid.

The spatial alignment of Fluid-channel and the PCM-Fluid vessel can be realized in 2 different configurations:

PCM inside, flow outside - shown in Figure 1b), FCONF = 1 - i.e. the PCM-Fluid vessel wall separates the PCM-Fluid from working medium fluid. E.g. PCM can be inside a tube / cylinder or can be encapsulated in balls which outer area is in contact with a working medium fluid.
PCM outside, flow inside - shown in Figure 1a), FCONF = 2 - in this case the fluid channel wall separates the PCM-Fluid from working medium fluid. E.g. a fluid flow in a tube which is enclosed by a PCM-Fluid.

Figure 1: Spatial alignment. a) PCM outside, flow inside b) PCM outside, flow inside

It is essential to set the consistent geometric parameter values for the fluid channel and the PCM-Fluid vessel according to the spatial alignment. For FCONF=1 the diameter / side length of the fluid channel must be greater than the diameter / side length of the PCM-Fluid vessel. For FCONF=2 the diameter / side length of the PCM-Fluid vessel must be greater than the diameter / side length of the fluid channel.

Furthermore the following geometric types are available:

The fluid channel may be a tube (FGTYPFL=0) or a square channel (FGTYPFL=1)
The PCM-Fluid vessel may have 3 different shapes: cylinder (FGTYPPCM=0), square channel (FGTYPPCM=1), ball (FGTYPPCM=2)

For different combinations of the input values FCONF, FGTYPFL, FGTYPPCM there are different alignments conceivable. Not all those alignments make sense and not all of them are implemented. For FGTYPPCM=2 (PCM-Fluid in balls) only FCONF=1 (PCM inside) is available. Further arrangements are shown in Figure 2. The combination of a square channel inside and a cylinder outside is not implemented.

Figure 2. Schematic drawing of the implemented and not implemented (stricken in red) combination of the PCM-Fluid vessel and fluid channel geometry

User Input Values

FINST	Flag: Determination of transient calculation modes = 0: transient solution according to time series table = 1: Always steady state solution
FINIT	Flag: Initializing state =0: Global, which is controlled via global variable "Transient mode" under Model Options "Extras" ->"Model Options" -> "Simulation" -> "Transient" -> Combo Box "Transient mode" (See -> Used Physics / equations -> Global Initialization of Transient Components ) =1: First run -> Initializing while calculating steady state values =2: Continuation run -> Values from previous time step are input for the present ones
FMODE	Flag: Calculation mode (design / off-design) =0: Global = 1: Local off-design
FCONF	Geometry configuration details =1: PCM inside, flow outside =2: PCM ouside, flow inside
LSTO	Flow length of storage at FINIT=1
FGTYPPCM	PCM vessel wall geometry type =0: tube =1: square channel =2: ball
FSTOPCM	Definition of PCM vessel wall geometry. Required for computing the wall mass and the heat exchanging area: =0: Specify the length LSTO, the heat exchanging area AWPCM and the wall mass MWPCM =1: Specify the length LSTO, the inner diameter / channel side length DIAIPCM and the wall thickness THWPCM
DIAIPCM	Inner diameter / channel side length of the PCM vessel wall
THWPCM	Wall thickness of the PCM vessel
AWPCM	Heat exchanging area between PCM-Fluid and PCM vessel wall
MWPCM	PCM vessel wall mass (not equal to the PCM-Fluid mass!)
FPCMBALL	Definition of the PCM ball geometry: =0: using THWPCM, DIAIPCM for single balls and PHI =1: using THWPCM, AWPCM for single balls and PHI =2: using THWPCM, DIAIPCM for single balls and NBALLS =3: using THWPCM, AWPCM for single balls and NBALLS
NBALLS	Number of PCM balls
FGTYPFL	Fluid channel geometry type =0: tube =1: square channel
FSTOFL	Definition of Fluid channel wall geometry. Required for computing the wall mass and the heat exchanging area: =0: Specify the length LSTO, the heat exchanging area AWFL and the wall mass MWFL =1: Specify the length LSTO, the inner diameter / channel side length DIAIFL and the wall thickness THWFL
DIAIFL	Inner diameter / channel side length of the fluid channel
THWFL	Wall thickness of the fluid channel
AWFL	Heat exchanging area between fluid and fluid channel wall
MWFL	Fluid channel wall mass
FSPECM	Flag: Handling of fluid mass = 1: Fluid mass neglectible = 2: Fluid mass considered, outlet equal inlet mass flow = 3: Fluid mass considered, outlet different from inlet mass flow
FDATPCMV	Specification of thePCM vessel wall material properties =1: constant according to RHOPCMV, LAMPCMV, CPPCMV =-1: according to FMPCMV =-2: according to kernel expressions ERHOPCMV, ECPPCMV, ELAMPCMV
FMPCMV	Specification of PCM vessel wall material : Material Properties of Steel
RHOPCMV	PCM vessel wall material density
LAMPCMV	PCM vessel wall heat conductivity
CPCMV	PCM vessel wall heat capacity
ERHOPCMV	Kernel expression PCM vessel wall material density
ELAMPCMV	Kernel expression PCM vessel wall heat conductivity
ECPCMV	Kernel expression PCM vessel wall heat capacity
FDATFLV	Specification of the fluid channel wall material properties =1: constant according to RHOFLV, LAMFLV, CPFLV =-1: according to FMFLV =-2: according to kernel expressions ERHOFLV, ECPFLV, ELAMFLV
FMFLV	Specification of fluid channel wall material : Material Properties of Steel
RHOFLV	Fluid channel wall material density
LAMFLV	Fluid channel wall material heat conductivity
CFLV	Fluid channel wall material heat capacity
ERHOFLV	Kernel expression fluid channel wall material density
ELAMFLV	Kernel expression fluid channel wall material heat conductivity
ECFLV	Kernel expression fluid channel wall material heat capacity
THISO	Thickness of insulation
LAMISO	Heat conductivity of insulation
FTSTEPS	Controling the sub-time step =0: Scaling the sub-time step according to diffusion numberl and TLSF =1: By specification value TISPEP
TLSF	Sub-time step scaling factor based on theoretical limit
ISUBMAX	Maximum number of time sub steps for initialization
IERRMAX	Maximum allowed error for initializing step
TISTEP	Sub-time step
NFLOW	Number of points in x-direction (flow direction)
NRAD	Number of points in y-direction (direction normal to flow)
TMIN	Lower limit for storage temperature (relevant for walls as well as PCM-Fluid)
TMAX	Upper limit for storage temperature (relevant for walls as well as PCM-Fluid)
FSTAMB	Flag: Definition of ambient temperature =0: Definition specification value (TAMB) =1: Defined from superior model
TAMB	Ambient temperature
ISUN	Index for solar parameters (e.g. component 117)
FALPHI	Determination of the inner alpha number to internal storage =0: according to ALPHI and part load exponent EX12 =1: according to EALPHI
ALPHI	Inner heat transfer coefficient
EX12	Mass flow exponent for inner heat transfer coefficient RALPHI = ALPHI(M1/M1N*EX12)
EALPHI	Kernel expression for Inner heat transfer coefficient
FALPHO	Determination of alpha outside =0: From constant value ALPHO =1: From function EALPHO
ALPHO	Outer heat transfer coefficient (to ambient) when FALPHO=0
EALPHO	Kernel expression for alpha outside
AOUTP	The part of the outer surface being in contact to ambient
CLMPCM	Correction factor to heat conductivity of PCM-Fluid (to account for convection while PCM melting process)
FVOL	Flag: Part-load pressure drop =0: Only depending on mass flow =1: Mass flow and density dependent =2: Constant (equal nominal value)
DP12N	Pressure drop (nominal, fluid flow)
PPCM	Pressure in PCM-Fluid
FSTART	Initialization of the temperature field (FINIT=1) =1: temperature of storage (shell and internal storage) equal TSTART =2: temperature profile computed from steady state solution
TSTART	Initial value of temperature (FINIT=1)
FDIR	Fluid flow direction =0: Normal =1: Reverted, direction of flow is going to be changed by reflecting the numerical grid without changing the connectors. (Caution: Reverting is always carried out, when FDIR=1!)
TIMETOT0	Total time at start of calculation (Sum of previous time steps)
PHI	Void volume fraction - volume fraction of fluid channel not occupied by PCM balls
M1N	Fluid mass flow (nominal)
V1N	Specific volume at inlet (nominal)

The parameters marked in blue are reference quantities for the off-design mode. The actual off-design values refer to these quantities in the equations used.

Generally, all inputs that are visible are required. But, often default values are provided.

For more information on colour of the input fields and their descriptions see Edit Component\Specification values

For more information on design vs. off-design and nominal values see General\Accept Nominal values

Results

T2BEG	Averaged caloric temperature of the storage in the beginning of the time step
T2END	Averaged caloric temperature of the storage at the end of the time step
QSTO	Energy stored during time step (storage and fluid)
QAV	Average stored energy flow in time step (QSTO/TIMEINT)
QAVI	Average energy flow from fluid to storage
QAVO	Average energy flow from storage to environment
RALPHI	Used inner heat transfer coefficient fluid to storage
RALPHO	Used outer heat transfer coefficient (to ambient)
RASTO	Computed heat exchanging area fluid to storage
RWDFL	Computed fluid layer thickness
RTHFL	Computed thickness of fluid channel wall
RWDPCM	Computed PCM layer thickness
RTHPCM	Computed thickness of PCM vessel wall
RMSTO	Overall storage mass
RMPCM	Mass of PCM-Fluid
RVFLUID	Fluid volume
MFLUID	Fluid mass
RTAMB	Ambient temperature
DIFNUMB	Diffusion numberl (relevant for numeric stability and accuracy, has the same meaning as the input value of TLSF)
TIMEINT	Total integration time (current time step)
TIMETOT	Total time at end of calculation (time-series)
TIMESUB	Sub-time step length
ISUB	Number of sub-time steps in the current time step
TISUBREC	Recommended sub-time step length, derived presuming DIFNUMB=TLSF
PREC	Precision indicator: normalized difference between the heat transferred to fluid, the heat stored in the storage (PCM-Fluid + walls) and the heat flow to the environment
PRECPCM	Precision indicator for the calculation in PCM-Fluid

Physics used / Equations

The implementation of component 166 is based on 2D-Grid with Crank-Nicolson-Algorithm similar to component 119. Contrary to component 119 the storage of component 166 consists of multiple layers. Those layers include the fluid channel wall, PCM-Fluid itself and the wall of the PCM vessel. The PCM-Fluid layer has the highest thermal resistance and the highest thermal storage capacity. The PCM-Fluid layer is resolved in the direction normal to the flow by NRAD elements. The fluid channel wall and the PCM vessel wall are resolved each by just one element in the flow normal direction.

The PCM-Fluid, as soon as it becomes liquid, is able to recirculate which, in turn, causes free convection heat flow additionally to the heat conduction. The acceleration of the heat transfer due to convection can be taken into account in the simulation by means of the correction factor CLMPCM. The numeric solution of the heat equation on 2D-grid does not explicitly account for a flow of PCM-Fluid between the grid elements.

The time step length (defined by intervals in time-series) and the sub-time steps (defined in component 166 via FTSTEPS, TISTEP, TLSF) are important for the accuracy and stability of computation. The accuracy regarding the overall energy balance between the fluid and the storage is indicated by the result value PREC. The result value PRECPCM the accuracy of calculation in PCM-Fluid. An additional aid in setting the sub-time step length is provided by the diffusion number (result value DIFNUMB). It is recommended to set the sub-time step width so that the diffusion number does not exceed the value of 10. One can make use of the input value FTSTEPS and set it to 0 while setting the value of TLSF to 10 (standard value of TLSF).

All established PCMs (including ice) change their density / specific volume at phase transition (solid-liquid or liquid-solid) by approximately 9-11%. Due to this fact the volume occupied by the PCM layer in the storage changes as well. The volume change results in the changing of the heat exchanging area between fluid and storage. The PCM-Fluid mass is defined in the initial step of the time-series by the specification of geometry (definition of PCM vessel) and the initial temperature. The temperature value defines the PCM aggregate state and consequently the PCM density. From the known PCM-Fluid density and the PCM vessel volume the PCM mass is computed. This mass does not change in the following time steps.

Characteristic Lines and Matrices

All characteristic lines form a circular buffer. The user doesn´t have to take care of them.

CMFL: Mass of fluid in differential element of storage dV (not used in every case)
CUFL: Internal energy of the fluid in differential element of storage dV (not used in every case)
CDFL: Partial/heat flow between elements of fluid and wall
CHFL: Enthalpy of the fluids in differential element of storage dV
CTFL: Temperature of the fluid in differential element of storage dV
CMPCM: Mass of PCM-fluid in differential element of storage dV
CSTAT: Thermodynamical state of the fluid at the lines

Corresponding to this there are also result curves.

RAMFL: Mass of fluid in differential element of storage dV (not used in every case)
RAUFL: Internal energy of the fluid in differential element of storage dV (not used in every case)
RADFL: Partial/heat flow between elements of fluid and wall
RAHFL: Enthalpy of the fluids in differential element of storage dV
RATFL: Temperature of the fluid in differential element of storage dV
RAMPCM: Mass of PCM-fluid in differential element of storage dV
RASTAT: Thermodynamical state of the fluid at the lines

Specification matrices MXTSTOPCM, MXLAMSTOPCM, MXCPSTOPCM, MXRHOSTOPCM and result matrices RXTSTOPCM, RXLAMSTOPCM, RXCPSTOPCM, RXRHOSTOPCM

The matrix MXTSTOPCM is linked to the output field RXTSTOPCM in the same way as the characteristic curves and result curves mentioned above.

The distribution of the values in the storage and the fluids is stored in both matrices (default matrix MXTSTOPCM for time step t-1 and result matrix RXTSTOPCM for time step t).

For the structure of the matrices, see matrices of component 160.

Displays

Display option 1

Example

Click here>> Component 166 Demo << to load an example.

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