Component 165: Thermal regenerator / Bulk material storage

Specifications

Line Connections
1	Main inlet, normal flow direction
2	Main outlet, normal flow direction
3	Main inlet, reverted flow direction
4	Main outlet, reverted flow direction
5	Heat transfer from main fluid (outlet)

General User Input Values Physics Used Characteristic Lines Results Displays Example

General

The component 165 can be used to model a thermal regenerator (e.g. cowper) / a bulk material storage. Thereby there is a difference between the internal storage (suffix "IS" in parameter names e.g. FDATAIS) and the shell (suffix "S" in parameter names e.g. FDATAS). The shell may have cylinder shape or be a square channel. The shell geometry determines the overall storage volume in which the internal storage material is enclosed.

The shell wall and the internal storage mass may consist of different materials and may have heat transfer coefficient values regarding the heat transfer to or from the working fluid medium. One can specify different material properties as well as heat transfer coefficients in the corresponding input fields.

For the alternating flow directions in the storage while charging and discharging phase there are PINs 1, 2 and 3, 4 as well as the flag FDIR provided . The component expects the working medium to either flow from PIN 1 to PIN 2 or from PIN 3 to PIN 4. A simultaneous specification of mass flow values > 0 on all four PINS does not make sense and is not allowed.

For the calculation of the pressure loss in the working medium flow there is an EBSILON standard algorithm with the nominal value DP12N and the Off-Design scaling as well as the formulas according to VDI Heat Atlas L1.6. The last method requires 2 additional parameters

the characteristic diameter of the storage elements - this can be either computed using the value of FV (outer surface to volume ratio) or directly specified as the value of DPC
pressure drop shape factor - this is specified directly as the value of PHIDP (see Table 1 in L 1.6 VDI WA for details)

The heat transfer coefficient to internal storage can be specified directly (parameters ALPHIIS, EALPHIIS, EXALPHIIS). Alternatively, one can use the formulas according to VDI Heat Atlas G9 (FALPHIIS=2). The last technique requires, like the pressure loss calculation, the characteristic diameter of the storage elements and the corresponding shape factor. The shape factor for the calculation of the heat transfer coefficient is defined by means of the parameters FSFALF and SFALF.

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
FALGS	Flag: Determination of transient calculation algorithms for the shell wall = 1: Crank-Nicolson-Algorithm = 4: Combined numerical and analytical solution
FALGIS	Flag: Determination of transient calculation algorithms for the internal storage = 1: Crank-Nicolson-Algorithm = 4: Combined numerical and analytical solution
FGTYP	Shell wall geometry type =0: tube =1: square channel
FSTO	Shell wall geometry definition. Required for computing the mass and the heat exchanging area: =0: Length LSTO, area ASTO and mass MSTO are given =1: Length LSTO, inner diameter / channel side length DIAI and wall thickness THSTO are given
LSTO	Shell wall length in flow direction
DIAI	Shell inner diameter / channel side length
THSTO	Shell wall thickness
ASTO	Heat exchanging area between fluid and shell wall
MSTO	Shell wall mass
PHI	Free cross section fraction (void volume fraction or porosity)
FV	Outer surface to volume ratio of the internal storage
FDPC	Schalter zur Berechnung des charakteristischen (äquivalenten) Durchmessers der Speicherelemente =0: Berechnung mittels FV =1: gemäß DPC
DPC	Characteristic (equivalent) diameter of the storage elements (VDI Heat Atlas L1.6 Table 1)
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
FDATAS	Specification of the shell wall material properties =1: constant according to RHOS, LAMS, CPS =-1: according to FMSHELL =-2: accoring to kernel expressions ERHOS, ECPS, ELAMS
FMSHELL	Specification of shell wall material : Material Properties of Steel
RHOS	Shell wall material density
LAMS	Shell wall material heat conductivity
CPS	Shell wall material heat capacity
ERHOS	Kernel expression shell wall material density
ELAMS	Kernel expression shell wall material heat conductivity
ECPS	Kernel expression shell wall material heat capacity
FDATAIS	Specification of the internal storage material properties (bulk material, storage pattern elements) =1: constant according to RHOIS, LAMIS, CPIS =-1: according to FMINST =-2: according to kernel expressions ERHOIS, ECPIS, ELAMIS
FMINST	Specification of internal storage material : Material Properties of Steel
RHOIS	Internal storage material density
LAMIS	Internal storage material heat conductivity
CPIS	Internal storage material heat capacity
ERHOIS	Kernel expression internal storage material density
ELAMIS	Kernel expression internal storage material heat conductivity
ECPIS	Kernel expression internal storage material heat capacity
THISO	Thickness of shell insulation
LAMISO	Heat conductivity of insulation
FTSTEPS	Flag: Specification of (sub-) time steps =1: By specification value TISPEP =2: 0.2 of the stable theoretical time increment =3: 0.5 of the stable theoretical time increment =4: 1.0 of the stable theoretical time increment =5: 2.0 of the stable theoretical time increment =6: 5.0 of the stable theoretical time increment
ISUBMAX	Maximum number of time sub steps for initialization (FINIT=1 and FALGIS=1)
IERRMAX	Maximum allowed error for initializing step (FINIT=1 and FALGIS=1)
TISTEP	Sub-time step (FALGIS=1 or FALGS=1)
NFLOW	Number of points in x-direction
NYS	Number of points in storage wall normal direction for shell wall (FALGS=1)
NYIS	Number of points in storage wall normal direction for internal storage (FALGIS=1)
TAUADJ	Correction factor for the time constant of the storage wall (FALGIS=4 or FALGS=4)
LAMADJ	Multiplication factor to 1/LAMBDA - the walls heat conductivity resistance (FALGIS=4 or FALGS=4) Setting LAMADJ=0 is equivalent to neglecting the walls heat conductivity resistance: either the wall thickness is infinitely small or lambda value is infinitely high Setting LAMADJ=1 is equivalent to computing the walls heat conductivity with the original value of LAMBDA and wall thickness LAMADJ<1 leads to decreasing the walls heat conductivity resistance LAMADJ>1 leads to increasing the walls heat conductivity resistance
TMIN	Lower limit for storage temperature
TMAX	Upper limit for storage temperature
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)
FALPHIS	Determination of the alpha number to shell wall =0: according to ALPHIS and part load exponent EXALPHIS =1: according to EALPHIS
ALPHIS	Inner heat transfer coefficient to shell wall
EALPHIS	Kernel expression for inner heat transfer coefficient to shell wall
EXALPHIS	Mass flow exponent for internal alpha number to shell wall
FALPHIIS	Determination of the alpha number to internal storage =0: according to ALPHIIS and part load exponent EXALPHIIS =1: according to EALPHIIS =2: using geometry and formulas from VDI Heat Atlas G9
ALPHIIS	Inner heat transfer coefficient to internal storage
EALPHIIS	Kernel expression for Inner heat transfer coefficient to internal storage
EXALPHIIS	Mass flow exponent for Inner heat transfer coefficient to internal storage
FSFALF	Determination of the shape factor for ALPHIIS calculation according to VDI Heat Atlas G9 =0: using value of SFALF =1: using formula for balls =2: using formula for cylinder cuts or cubes =3: using formula for Raschig rings =4: using formula for Bern saddles
SFALF	Shape factor for ALPHIIS calculation according to VDI Heat Atlas G9
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
FDP12	Pressure loss calculation =0 : DP12N =1: according to geometry and VDI Heat Atlas L1.6
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)
PHIDP	Pressure drop shape factor of internal storage (FDP12=1) (VDI Heat Atlas L1.6 Table 1)
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 =3: temperature of storage (shell and internal storage) and fluid equal TSTART
TSTART	Initial value of temperature (FINIT=1)
FDIR	Stream direction =0: normal, fluid flow from PIN 1 to PIN 2 =1: reverted, fluid flow from PIN 3 to PIN 4
DIRLAST	Stream direction in the previous time step
TIMETOT0	Total time at start of calculation (Sum of previous time steps)
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

TAVBEG	Averaged caloric temperature of the storage in the beginning of the time step
TAVEND	Averaged caloric temperature of the storage at the end of the time step
T2BEG	Outlet temperature of fluid in the beginning of time step
T2END	Outlet temperature of fluid in the end of time step
QSTO	Energy stored during time step (internal storage, shell wall 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
RALPHIIS	Used inner heat transfer coefficient fluid to internal storage
RALPHO	Used outer heat transfer coefficient (to ambient)
RASTO	Used overall heat exchanging area of storage (shell + internal storage)
RTHSTO	Equivalent plane thickness (internal storage)
RMSTO	Used overall mass of storage (shell + internal storage)
RVFLUID	Used flow volume of fluid
MFLUID	Mass of fluid in storage (FSPECM>1)
PFLAV	Average pressure in fluid
HFLAV	Average enthalpy in fluid
TFLAV	Average temperature in fluid
RHOFLAV	Average density of fluid (FSPECM>1)
RTAMB	Ambient temperature used in calculation
BIOTIS	Biot number internal storage
TIMEINT	Total integration time (current time step)
TIMETOT	Total time at end of calculation (time-series)
DIRCUR	Stream direction at current time step (0=normal, 1=reverted)
PREC	Precision indicator: normalized difference between the heat transferred to fluid, the heat stored in the storage (internal storage + shell wall) and the heat flow to the environment
RALPHIS	Used inner heat transfer coefficient fluid to shell
BIOTS	Biot number shell

Physics used / Equations

The calculation of the component 165 is based on the simplification of the internal storage geometry. The real storage pattern of a regenerator can be replaced by the equivalent plate geometry. Doing so one has to keep equal the overall mass and the overall heat exchanging surface area of the real storage pattern and of the simplified plate.

The internal storage is specified by two parameters

FV - outer surface to volume ratio
PHI - free cross section fraction (also known as void volume fraction or porosity)

Once f_V, φ and the overall volume (storage pattern and the void volume) are known, the volume of the internal storage and its contact surface area can be computed. The results are used to define the equivalent plate. The equivalent plate represents the internal storage in the calculation of the heat transfer as well as heat charge and discharge.

The overall fluid flow is internally split according to the area ratio into part flows regarding the shell and regarding the internal storage. The sub-system fluid-shell wall and the sub-system fluid-internal storage are treated separetely in the simulation. Finally the mean values of temperature, enthalpy are obtained by average according to the mass fractions.

For the heat conduction calculations there are 2 alternative algorithms available for both the shell wall and the internal storage (control via parameters FALGS, FALGIS). See Component 119 for details.

Characteristic Lines and Matrices

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

CMFL: Mass of fluid1 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)
CHFL: Enthalpy of the fluids in differential element of storage dV
CTFL: Temperature of the fluid in differential element of storage dV
CDATS: Partial/heat flow between elements of fluid and shel wall
CDATIS Partial/heat flow between elements of fluid and internal storage wall
CSTAT: Thermodynamical state of the fluid at the lines
CQHIST: History of the heat flows
CTIHIST: History of the time steps
CMODDATAS: Storage for various transient data shell
CMODDATAIS: Storage for various transient data internal storage

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)
RAHFL: Enthalpy of the fluids in differential element of storage dV
RATFL: Temperature of the fluid in differential element of storage dV
RADATS: Partial/heat flow between elements of fluid and shel wall
RADATIS Partial/heat flow between elements of fluid and internal storage wall
RASTAT: Thermodynamical state of the fluid at the lines
RAQHIST: History of the heat flows
RATIHIST: History of the time steps
RAMODDATAS: Storage for various transient data shell
RAMODDATAIS: Storage for various transient data internal storage

Specification matrices MXTSTOS, MXTSTOIS and result matrices RXTSTOS, RXTSTOIS

The matrix MXTSTOS is linked to the output field RXTSTOS 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 MXTSTOS for time step t-1 and result matrix RXTSTOS for time step t).

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

Displays

Display option 1

Example

Click here>> Component 165 Demo << to load an example.

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