Energetic Macroscopic Representation (EMR) : New Approach For Multiphysics Energetic Flows Modelling
Energetic Macroscopic Representation (EMR) : New Approach For Multiphysics Energetic Flows Modelling
Energetic Macroscopic Representation (EMR) : New Approach For Multiphysics Energetic Flows Modelling
Abstract: Developed in 2000 to analyse and control electromechanical systems, Energetic Macroscopic
Representation (EMR) has been extended over the years to cover other energetic domains by using
kinetic and potential variables based on action-reaction principle; so that the product of these variables is
homogeneous to the power unit. The necessity of more than two variables for some multiphysics energetic
flows modelling has led to specific EMR with three and four ports, going away from the basic principle,
particularly in thermo-pneumatic and thermo-fluidic domains. The contribution of this paper is to
propose a new approach of EMR modelling for the multi-variable energetic flows to comply with the
basic action-reaction principle whose two variables product is homogeneous to the power unit.
Keywords: EMR formalism, multiports EMR, multiphysics modelling, graphical modeling tool.
TO MULTIPHYSICS SYSTEMS MODELLING Fig. 1 . EMR basic pictograms extended to other domains
2. 1 Initial aim of the EMR formalism In order to extend the EMR application domain , Fig. 2 points
out an example of an energetic conversion from electrical
Based on action-reaction principle like Bond-Graph (BG), domain (current and voltage as action-reaction variables) to
EMR is endowed with physical causality principle contrary to electrochemical domain (molar flow and free enthalpy as
BG (Bouscayrol et al. 2005a). Furthermore, beyond these action-reaction variables) (Hissel et al. (2008)). It can be seen
strengths for being able to describe electro-mechanical another example onto Fig. 3 referring to energy conversion
systems according to both action-reaction and causal from electrical domain to thermal domain in which action-
principles, EMR further feature is control ability namely reaction variables are highlighted by current and overvoltage
Maximum Control Structure (MCS) which is deduced from for the electrical domain and for the thermal domain: entropy
the EMR of the modelled system by applying inversion rules. flow and temperature.
In fact, a complex system of several energy sources and Electrical domain Electrochemical
domain
several energy conversion units can be accurately modelled
I n&
by the EMR tool more synthetically with a clear readability
V ∆G
in the macroscopic point of view compared to other graphical
modelling tools. Moreover, EMR can be easily grasped by Fig. 2: Multi-domain conversion: energetic flow from
experts who haven’t even got used to this modelling electrical domain to electrochemical domain
formalism allowing communication facility between different
research fields. Electrical domain Thermal domain
PV = n& RT (1) Fig. 5: EMR multiports (four ports) for mono physical
domain conversion
P [Pa] pressure
T [K] Temperature This representation has been chosen for liquid flow, like
3 water in the electrolyser case, because contrary to the
V [m ] volume pneumatic domain allowing perfect gas law, the only
H& = m& c p T (2) modelling equation linking the fluidic and the thermal
domain is as follows (Agbli et al. 2011b):
H& Enthalpy flow
-1 -1
(
H& = m& c p T + P / ρ + ρ v 2 / 2 ) (3)
c p [J kg K ] specific isobar heat capacity -3
ρ [kg m ] the fluid density
That led to four energetic variables ( ( H& ) , ( P ) , (T ) , (m& ) ) -1
v [m s ] the fluid speed
because the describing equations cannot be separated into the
two energetic domains like thermal and pneumatic domains. Contrary to Chrenko et al. (2009) the four variables cannot be
Moreover, considering the independent variables allowing an reduced and the Fig. 5 pictogram has been retained (Agbli et
accurate description, the number of ports can be reduced to al. 2011b).
three EMR variables ( ( P ) , (T ) , (m& ) ) for the gaseous fuel Fig.6 summarises the three ports EMR pictograms needed for
flow modelling (Chrenko et al. 2009) as shown onto Fig. 4. modelling into the thermo-pneumatic domain. Regarding the
• • two pictograms in the last column , the potential coupling
m1 m2
P1 P2
between the multiports EMR and the formal power flow
T1 T2 EMR is pointed out: two ports formal EMR and three ports
EMR.
Fig. 4: Multiports EMR (three ports) for mono physical ES
domain conversion
Energy Source Mono-physical
Multi-physical Mono-physical
This three port approach has been applied to the different conversion conversion coupling
However, in order to come back to the initial power flow Fig. 9: Multivariable (four variables) current EMR; (b)
modelling based on the action-reaction principle, it is Simplified EMR proposed
possible to enunciate the domains linkage by expressing it in
a way that the physical link between domains and the power
flow principle can be together highlighted. Therefore, two of 4.2 New EMR approach describing multivariable
the three energetic variables whose product is homogeneous energetic flow: thermo-pneumatic and thermo-
to the power unit can be chosen. Consequently, the last fluidic domains
unchosen variable must be shown up in order to avoid hiding
the physical domain from which it is related to. Thus, the two The three and the four ports EMR describing the thermo-
action-reaction variables choice is made by considering the pneumatic and the thermo-fluidic domains respectively can
main physical domain carrying the described energetic flow be anew rewritten within the new frame introduced
(“carrier domain”) so that, the underlying physical domain previously. By considering the linear relationship between
(“carried domain”) will be described by the last variable. molar flow and volume flow, the thermo-pneumatic domain
Having thereby, for the multidomain-multivariable energetic three ports EMR modelling the decoupling of the thermal
flow, a carrier domain with its action-reaction variables and domain is done onto the Fig.10a and the related new
the carried domain (or domains) with its (or their) own approach onto Fig.10b.
action-reaction variables. Then, the initial action reaction Given the previous definition regarding this new approach,
principle based on power flow modelling is maintained by the carrier domain in the thermo-pneumatic domain (gas
properly defining and expressing the action-reaction flow) is the pneumatic domain and the carried domain is the
variables. Hence, the global action variable is defined by thermal domain. Hence, the representation complies with the
considering in parenthesis the carrier domain action variable power flow modelling:
and as its subscript the action variable (or variables separated
by a comma) related to the carried domain (or domains). Ppneumatic [W ] = P ⋅ V& (5)
Also, the global reaction variable is defined by considering in
parenthesis the carrier domain reaction variable and as its Pthermal [W ] = T ⋅ ∆ S q (6)
subscript the reaction variable (or variables separated by a
comma) related to the carried domain (or domains). V& Volume flow
∆ S q Entropic flow
5. CONCLUSIONS
Thermo-pneumatic Thermal domain Thermo-pneumatic Thermal domain
domain domain
T T
Developed twelve years ago, EMR has been extended beyond
V& ∆Sq ∆S q its initial physical domains like electrical, mechanical and
P (V& )T
V& (V& )
T
P P
T
electromechanical domain. Because of its relevance to
T P properly describe, in the analysis and control frame, the
Thermo-pneumatic Thermo-pneumatic
domain domain multi-physics energetic tools, EMR modelling fields have
Fig.10: (a)(a)Thermo-pneumatic domain:(bThe
) current three been expanded to other physical domains such as thermal,
EMR ports model; (b) The new approach electrochemical, thermodynamic, fluidic, pneumatic and so
on. Initially based on the modelling of power flow according
By the same way, from the thermo-fluidic domain is to action-reaction principle, multiports EMR has been
generated a thermal domain process. The current considered in order to suitably describe the strongly coupled
representation and the proposed one are given onto the Fig. domain like thermo-pneumatic and thermo-fluidic domains,
11a and the Fig. 11b. The four variables are the volume flow, going away from the initial power flow modelling purpose.
the pressure, the temperature and the enthalpy flow.
This paper proposes a new EMR approach for the modelling
Thermo-fluidic Thermal domain Thermo-fluidic Thermal domain
of the multidomain-multivariable energetic flows in order to
domain domain
T come back to the first EMR principle complying with the
V& T
P ∆S q
& (V& ) T ∆S q power flow modelling based on the action-reaction principle.
T V
P (V& )
H& T ( P ) H& T
E ∆G T GH 2
•
nH2 SH2 •
Patm
•
T •
n O2 S O2
nO2 V O2
•
T GH2O
n H 2O S H 2 O GO 2
I EL • PA
nH 2O
ES
VEL I EL ∆SqηTotal
•
PA V H 2O _ CONS
∆Sq1
η(IEL) T T Tamb ∆S q −conv Thermal losses
∆Sq _ H2O _ outAC ∆S q−conv TH 2O
within the atmospere
T H 2O _ T
A
∆Sq2
∆S q _ O2 T
T
∆Sq _ H 2O _ outA ∆Sq _ H2O _ Mem,H2 T (V& )
O2 T
O2
Produced
Pout
oxygen
(V& )
H2O_in T
H2O _ A
(V& )
H2O_in T
(V& )
H2O_in T
H2O
H2O (P ) (P )
H2O
(P ) (V& )
H2O_ ∆ina H&
Anodic tank
H2O_in H& H2O_in H& H2O H&
H2O
H2O
(P& ) (V& ) •
H2O H2O
(P& )
H2Oa T
H2O
H2O T
H2O
H2O_out HH O
(Pout)T
2
H2O
Anodic thermo-hydraulic circuit model (P& ) (V& ) (V& )
H2O_out H&
H2O _out
Anodic tank
H2Oa T H2O_out H&
H2O H2O H2O
(P )
H2Oc H&
H2O
(V& H2O_MemT) H2O
(V& )
H2O_out HH O
•
2
H2O
(P& ) (Pout)T H2O _out Cathodic tank
(V& )
H2O_∆inc T
(P& )
H2Oc T
H2Oc T
H2O
H2O H2O
(V& ) (V& )
(P )H2Oc H&
H2O
(V& )
H2O_out H&
H2O_out H&
H2O
H2 T
H2
Produced
H2O
Fig. 12: PEM electrolyser EMR model adapted in the thermo-pneumatic and the thermo-fluidic domains Agbli et al. (2011b)