**3.1 An approach applied to generating formalized descriptions of virtual simulators**

Formalized descriptions of individual system virtual simulators based on the detailed level as the aggregate are applied (Kurmazenko E.A. at al., 1997; Kurmazenko E.A. at al., 2008). In this case an individual system is presented as an aggregate which implies generation of a closed mathematical description including (Figure 3 a):


When applying the simulation models the alphabet of in parameters, out parameters and controlling parameters shall be correspond to controllable parameters of the system being simulated. The alphabet of perturbation actions is governed by time-varying controllable parameter values of the environment with a specific system in operation and crew present in the PMM atmosphere. The inner perturbation actions are mainly governed by controllable parameter values of the system being simulated. In order to formulate the alphabet of inner states an approach based on a functional description of this description is applied.

Fig. 3. The system presented as the aggregate: a = design aggregate schematic; b = the OGS presentation as aggregate.

As an example generation of a formalized description of the inner state alphabet for the OGS VS is presented on Figure 3 b. In order to formulate the alphabet of inner states the following basic assumptions are made:


With consideration for the given assumptions the formalized description of the inner state alphabet may be presented as:

$$I\_{el}^{\mathbf{r}} = I \frac{R\_{col}^{\mathbf{r}}}{R\_{col}^{\mathbf{r}} + R\_{el}^{\mathbf{r}}} ; \tag{6}$$

$$\mathbf{U}^{\mathsf{T}} = \mathbf{e}\_{a}^{0} + \mathbf{e}\_{c}^{0} + \mathbf{a}\_{a} + \mathbf{a}\_{c} + \text{0.001} (\mathbf{b}\_{a} + \mathbf{b}\_{c}) \frac{I\_{el}^{\mathsf{T}}}{S\_{el}} + I\_{el}^{\mathsf{T}} \mathbf{R}\_{el}^{\mathsf{T}};\tag{7}$$

$$\mathbf{I}\_{\alpha l} = \mathbf{I} - \mathbf{I}\_{\text{el}} \; ; \tag{8}$$

$$\mathbf{G}\_{O\_2\{H\_2\}}^{\mathsf{T}} = \frac{n}{2F} \left[ 2\,\mathrm{A}\_{O\_2\{H\_2\}} I\_{el}^{\mathsf{T}} + \left( A\_{O\_2} + A\_{H\_2} \right) I\_{col}^{\mathsf{T}} \right];\tag{9}$$

$$\left(G\_{H\_{2}\to O\_{2}\left(O\_{2}\to H\_{2}\right)}^{\pi}\right) = \frac{nA\_{O\_{2}}\left(A\_{H\_{2}}\right)}{2F},\tag{10}$$

parameter values of the environment with a specific system in operation and crew present in the PMM atmosphere. The inner perturbation actions are mainly governed by controllable parameter values of the system being simulated. In order to formulate the alphabet of inner states an approach based on a functional description of this description is applied.

Fig. 3. The system presented as the aggregate: a = design aggregate schematic; b = the OGS

As an example generation of a formalized description of the inner state alphabet for the OGS VS is presented on Figure 3 b. In order to formulate the alphabet of inner states the

• A formalized description shall take into consideration only values of controllable parameters of inflow and outflow which govern the regulatory and behavior of system

• thermal/physical properties of electrolyte–produced gas mixtures and coolant over the

• owing to a short time of transient process for a current the mass flows of oxygen, hydrogen in oxygen, hydrogen, oxygen in hydrogen and water vapor are described by

• the main sources of oxygen in hydrogen and hydrogen in oxygen are electrolyzer water

With consideration for the given assumptions the formalized description of the inner state

*<sup>τ</sup> <sup>τ</sup> col*

*<sup>I</sup> U eeaa bb 0,001 I R*

( ) ( ) ( ) *<sup>2</sup> <sup>2</sup> 2 2 2 2*

*<sup>G</sup> 2A I A AI 2F*

*<sup>G</sup> 2F*

*2 2 2 2*

*H O O H*

*n*

τ

*O O H H el O H col*

<sup>⎡</sup> <sup>⎤</sup> = ++ <sup>⎢</sup> <sup>⎥</sup> <sup>⎣</sup> <sup>⎦</sup>

( ) *<sup>2</sup>* ( ) *<sup>2</sup>*

*l*

*<sup>I</sup> <sup>I</sup> el R R* <sup>=</sup> <sup>+</sup> ; (6)

*col el I I* = −*I* ; (8)

<sup>→</sup> <sup>→</sup> <sup>=</sup> , (10)

; (9)

*ed*

*S*

*τ τ*

*O H*

*nA A*

=++++ + + ; (7)

*τ τ<sup>e</sup> col R*

( ) *<sup>τ</sup> 0 0 el τ τ ac ac ac el el*

supply headers in which an uncontrollable electrolysis process takes place.

presentation as aggregate.

functioning;

algebraic equations;

alphabet may be presented as:

τ

τ

following basic assumptions are made:

temperature range investigated are assumed constant;

where: *AO2* , *AH2* =chemical equivalents of oxygen and hydrogen, kg/mol, respectively; ,,, *aabb acac* =Tafel's constants for the anode and cathode; , *0 0 e e a c* = theoretical potentials of the anode and cathode, V for and *a a a c* and Vm2/A, for and *b b a c* , respectively; *F*=Faraday constant, Kl/mol; *O2*( ) *H2 <sup>G</sup>*τ =the mass flow-rate of gas being produced in the electrolyzer oxygen (hydrogen) compartment, kg/s; *2 2* ( ) *<sup>H</sup> O2 2 <sup>O</sup> <sup>H</sup> <sup>G</sup>*τ <sup>→</sup> <sup>→</sup> = the mass flow-rate of oxygen (hydrogen) produced in the hydrogen (oxygen) compartment; *I*, *Iel* , *Icol* = the total electrolyzer current, current through the electrolytic cell and current in the header, A; *n*= the quantity of an electrolytic cells; , *<sup>l</sup> τ τ<sup>e</sup> R R col* = the electric resistance of the header and electrolyzer, Ohm; *Sed* =the electrolytic cell surface area, m2; *U*τ = the electrolyzer voltage, V. The average electrolyzer temperature *Тel*, K, as a function of the supply current *Iel* is determined from regressive dependence

$$T\_{el} = f\_1 \left( T\_{cool} \right) \left( -0.3305 + 0.0034 I\_{el}^2 + 2.085 I\_{el}^{0.5} + \frac{21.29}{I\_{el}^{0.5}} \right),\tag{11}$$

obtained as a result of processing of the data of a computer experiments conducted by using the OGS detailed simulation model.

The hydrogen (oxygen) moisture content downstream the separator, kg/kg

$$\boldsymbol{d}\_{Hz(Oz)}^{\mathrm{T}} = \frac{\left[27.6 + 0.23 \left(T\_{sep}^{\mathrm{T}} - 273\right)^{1.5}\right]}{m\_{sep}} \cdot \frac{\mu\_{H\_2O}}{\mu\_{H\_2(Oz)}}\,,\tag{12}$$

where *H2*( ) *O2* μ , *H2O* μ =the molar masses of hydrogen (oxygen) and water, kg/mol. The temperature of the mass flows of hydrogen and oxygen downstream from the separator *Tsep*, K, is determined by regressive dependence as

$$T\_{sep} = f\_2 \left( T\_{cool} \right) \left( -15.387 + 0.249 I\_{el} + \frac{173.184}{I\_{el}^{0.5}} + \frac{319.898}{I\_{el}} \right) \,\tag{13}$$

The temperature functions *f1 (Tcool)* in the relationship (11) and *f2 (Tcool)* in the relationship (13) are determined as

$$\left[f\_{\,1}\left(T\_{col}\right) = \left[1 + 0.82\left(T\_{el} - 273\right) + 0.03\left(T\_{el} - 273\right)^{2}\right]T\_{el}^{-1};\tag{14}$$

$$\int f\_2 \left( T\_{col} \right) = \left[ 1 + 0.9 \left( T\_{el} - 273 \right) \right] T\_{sep}^{-1} \tag{15}$$

where *Tcool*=the coolant temperature, K.

The similar approach to generation of formalized descriptions of system functioning is adopted for other virtual simulators.

### **3.2 Approach used for formation of the PMM atmosphere formalized description**

When generation the formalized PMM atmosphere description the following basic assumptions are made (Kurmazenko E.A. at al., 1998):


Considering the assumptions made the nonlinear equations of mass balances for the basic components (oxygen, carbon dioxide, nitrogen and water vapor) and trace contaminants as well as the non-linear equation of internal energy balance for the PMM atmosphere reference volume may be written as the equations in deviations:

$$M\_{PMMA}(\boldsymbol{\pi}) = \sum\_{i=1}^{i=4} M\_{PMMA}(\boldsymbol{\pi})\;;\tag{16}$$

$$\mathcal{M}\_{PMM\dot{u}}(\pi) = \mathcal{M}\_{PMM\dot{u}}(\pi - \Delta\pi) + \sum\_{j=1}^{j=n} \left(\pm \mathcal{G}\_{i\bar{j}} \Delta\pi\right);\tag{17}$$

$$M\_{\rm TC} \left( \boldsymbol{\pi} \right) = M\_{\rm TC} \left( \boldsymbol{\pi} - \Delta \boldsymbol{\pi} \right) + \sum\_{k=1}^{k=s} \left( \pm G\_{\rm TCk} \Delta \boldsymbol{\pi} \right) \tag{18}$$

$$\mathcal{U}I(\boldsymbol{\pi}) = \mathcal{U}\left(\boldsymbol{\pi} - \Delta\boldsymbol{\pi}\right) \pm \sum\_{l=1}^{l=p} c\_{p\_i} G\_{il} \Delta\boldsymbol{\pi} \pm \sum\_{m=1}^{m=t} q\_m \Delta\boldsymbol{\pi} \tag{19}$$

In the equations (16)÷(19) the following notation is adopted: *MPMMa*,*MPMMi,MTC*,*U*=the value of atmosphere total mass, *i*-basic component mass, *k-*trace contaminant mass, kg, and atmosphere internal energy, J, respectively; *Gij*, *GTCk*=*i-* basic component mass flow-rate and *k=*trace contaminant mass flow-rate entering and leaving the reference volume, kg/s; *qm*=heat flows due to heat conduction entering and leaving the volume under consideration, W; *<sup>i</sup> cp* = the *i-* basic component specific heat capacity, J/kg °C; , , τ ττ τ − *Δ Δ* = previous time, current time and integration step in time, respectively, s.

The current values of mass flow-rates of the atmosphere basic components and trace contaminants upstream and downstream the reference volume as well as heat flows entering and leaving together with mass flows of atmosphere components and heat conduction are determined at each integration step by the current values of the ingoing and outgoing flows with the system performance virtual simulator values.

### **3.3 Approach used for formation of the 'crew' unit formalized description**

When generating a formalized description of the 'crew' unit the following assumptions are made:

• a single crewmember is considered as the structure of interrelated functioning systems in which incoming mass and energy flows are converted into outgoing mass and heat flows, and activity;


• man-made atmosphere is considered as a mixture of ideal gases the heat capacity of which is governed by its chemical composition and temperature−independent; • trace contaminants due to their low content do not affect the generation of total pressure in the PMM and thermal/physical properties of man-made gaseous

Considering the assumptions made the nonlinear equations of mass balances for the basic components (oxygen, carbon dioxide, nitrogen and water vapor) and trace contaminants as well as the non-linear equation of internal energy balance for the PMM atmosphere

=

=

*PMMi PMMi ij*

*TC TC TCk*

In the equations (16)÷(19) the following notation is adopted: *MPMMa*,*MPMMi,MTC*,*U*=the value of atmosphere total mass, *i*-basic component mass, *k-*trace contaminant mass, kg, and atmosphere internal energy, J, respectively; *Gij*, *GTCk*=*i-* basic component mass flow-rate and *k=*trace contaminant mass flow-rate entering and leaving the reference volume, kg/s; *qm*=heat flows due to heat conduction entering and leaving the volume under consideration,

The current values of mass flow-rates of the atmosphere basic components and trace contaminants upstream and downstream the reference volume as well as heat flows entering and leaving together with mass flows of atmosphere components and heat conduction are determined at each integration step by the current values of the ingoing and

When generating a formalized description of the 'crew' unit the following assumptions are

• a single crewmember is considered as the structure of interrelated functioning systems in which incoming mass and energy flows are converted into outgoing mass and heat

*MM G*

 ττ

 ττ

() ( ) ( )

*MM G*

*M M* τ

() () *i 4 PMMa PMMi i 1*

() ( ) ( )

 τ

1

*j*

1

1 1 *<sup>i</sup> l p m t p il m l m*

= =

 τ

=

 *Δ c G q* = =

*k*

*k s*

=

=

*j n*

=

<sup>=</sup> ∑ ; (16)

 τ

= −Δ + ± Δ ∑ ; (17)

 τ

= − ± Δ± Δ ∑ ∑ (19)

= −Δ + ± Δ ∑ (18)

 τ

τ ττ τ− *Δ Δ* = previous time,

**3.2 Approach used for formation of the PMM atmosphere formalized description**  When generation the formalized PMM atmosphere description the following basic

• the PMM atmosphere is considered as an open thermodynamic system;

assumptions are made (Kurmazenko E.A. at al., 1998):

reference volume may be written as the equations in deviations:

τ

τ

*U U* τ

current time and integration step in time, respectively, s.

() ( )

W; *<sup>i</sup> cp* = the *i-* basic component specific heat capacity, J/kg °C; , ,

outgoing flows with the system performance virtual simulator values.

**3.3 Approach used for formation of the 'crew' unit formalized description** 

 ττ

atmosphere.

made:

flows, and activity;


The initial data used for generating a formalized description of the 'crew' unit also include an activity/rest cycloramas for every crewmember.

Oxygen consumption *GO2* , g/h, is a function of energy expenditure *N*

*O2 <sup>0</sup> G* = *a N* , (20)

in which coefficient *a0* varies in the range from 0.28 to 0.31, g/kcal.

Fig. 4. Enlarged flowchart of human body main functional systems, where: SIG , ( ) *gO2* SIG ,SIG ,SIG ,SIG ,SIG ( ) ( ) ( ) () () *V V bl air W T T 0 c* =signal functions of the Central Nervous System controlled by the oxygen consumption, blood flow, breath volume, water consumption and Thermal Regulation System in dependence from values of ambient temperature and human's body core temperature, respectively; ( )*hb bl i w <sup>i</sup> gw 0 c VM G , ,, , ,, A TT* =the controllable parameters for signal functions.

Carbon dioxide released *GCO2* is a function of energy expenditure *N* is determined as

*<sup>2</sup> G a CO* = *0KrN* , (21)

with the value of the respiratory coefficient *Kr* is determined from empirical dependence

$$K\_{I} = -0.801 + 0.142 \exp\left(\frac{-96.432}{A}\right). \tag{22}$$

The moisture losses as a result of perspiration and respiration *J*, g/h, are also of energy expenditure *N* is determined as

$$J = 91.7 - 0.19N \,\text{.}\tag{23}$$

The quantity of urine donated *U,* g/h, is a function of energy expenditure *N*

$$
\mathcal{U} = 0.19 \text{N} \,\text{.}\tag{24}
$$

Trace contaminant realized *TCi* to be considered as a first order approximation are proportional energy expenditure *N*

$$T\mathbf{C}\_{i} = A\_{i}N\mathbf{.} \tag{25}$$

In calculation of trace contaminants realized the data presented in work (Savina, V.P., & Kuznetsova, T.I., 1980) are used. The data processed for the mixed ration (50 %-natural food products and 50 % sublimated food products) as a function of the ambient temperature are given in Table 1.


Table 1. Initial data for simulation of trace contaminant secretion.
