HUNGARIAN JOURNAL OF 
INDUSTRY AND CHEMISTRY 

Vol. 51(1) pp. 35–42 (2023) 

hjic.mk.uni-pannon.hu 
DOI: 10.33927/hjic-2023-06 

DEVELOPMENT OF A DIGITAL TWIN FOR GAS MIXING IN A 
GENERATOR 

OLGA SHYPUL 1*, VADYM GARIN1, DENYS TKACHENKO1, SERGIY PLANKOVSKYY2 AND OLEG 
TRYFONOV1 

1 National Aerospace University “Kharkiv Aviation Institute”, 17 Chkalova Street, Kharkiv, 61070, 
UKRAINE 

2 O. M. Beketov National University of Urban Economy in Kharkiv, 17 Marshala Bazhanova Street, 
Kharkiv, 61002, UKRAINE 

The subject of this research is the development of a digital twin for the process of mixing the components of a 
gas mixture in the mixer of a mixture generator. The problem is motivated by the concept of digitalizing modern 
production and is considered in relation to the technology in question for generating a gas mixture of a given 
composition and homogeneity. A gas-dynamic model of an unsteady flow has been constructed and a numerical 
study carried out using the Ansys Fluent software. The Reduced Order Model was developed and used in the 
Ansys Twin Builder platform to build the digital twin.  

Keywords: digital twin, reduced order model, numerical simulati on, gas mixer 

1. Introduction 

The incentive for developing digital twins (DT) in the 

process of generating gas mixtures is the digitalization of 

modern technologies. A DT is a virtual copy of a real 

system characterized by continuous and automatic 

synchronization as well as feedback between the real and 

digital domains.  

Many authors have diversified the typical 

development process of DTs [1]-[8]. All of the 

aforementioned referenced studies added their own 

values to define their DT. In almost all of these works, 

given the large number and variety of systems for which 

DTs can be created, the authors paid special attention to 

structuring the process of creating a DT. Therefore, the 

authors of [1] presented a five-dimensional model of a 

DT in which all stages for creating, implementing and 

monitoring the operation of equipment as well as 

recording data are accounted for. A more simplified 

scheme for creating a DT is provided by the authors of 

[2]-[4] in which the importance of individual aspects of 

the DT are emphasized. In [2], the authors insist on the 

importance of the digital component in the creation and 

implementation of a DT, which depends on the speed of 

process control and data exchange between elements of 

the system. In [3], the importance of communication as 

well as information exchange between a DT and a real 

system, in addition to monitoring the operation of a 

system in real time, is considered. A more unusual 

 

Received: 8 Apr 2023; Revised: 17 Apr 2023; 
Accepted: 19 Apr 2023  
*Correspondence: o.shipul@khai.edu 

concept was proposed in [4], in which the evolution of 

the state of the object when creating a DT is considered. 

Furthermore, the peculiarities and relevance of creating 

duplicates of multiphysics models, which should process 

large arrays of heterogeneous data, are addressed in [4]. 

Currently, many studies provide a comprehensive 

theoretical justification for the concept of creating a DT 

as well as the importance of the stages necessary to create 

and implement a DT of a real system or process amongst 

other research objectives. Such works are analysed in a 

review article [5], moreover, a group of practically 

oriented studies [6]-[9] is provided. In [6], the authors 

proved the importance of creating a DT when designing 

a large complex system. They came to the conclusion that 

a preliminary analysis of the system in a digital format 

will help to avoid many expensive problems when 

constructing and adjusting real equipment. In light of 

this, a new wind turbine controller was created in [7] in 

which the Functional Mock-up Interface (FMI) was used 

to combine the CFX and Maxwell 3D models as well as 

the capabilities of the Ansys Twin Builder platform 

applied to create a DT. Lastly, an exemplary example of 

combining a real braking device with its DT into one 

system is given in which data exchange took place in real 

time [8]. Within the framework of this work, a DT to 

form a fuel mixture in the system in which it is generated 

is developed, which should automatically provide the 

required composition of components in the mixture and 

the degree of its homogeneity. 

https://doi.org/10.33927/hjic-2023-06
mailto:o.shipul@khai.edu


 SHYPUL, GARIN, TKACHENKO, PLANKOVSKYY AND TRYFONOV 

Hungarian Journal of Industry and Chemistry 

36 

2. Problem statement 

International standards [9]-[12] have been developed on 

the basis of state-of-the-art research into the 

digitalization of production, which regulate the 

construction of automation systems, integration of 

technical processes or operation of industrial equipment 

using digital technologies. These standards define two 

types of twins, namely digital and physical ones. 

A DT consists of three parts: 

1. A data collection and device management 
facility in which signatures are also combined. 

The collected data is pre-processed by the data 

collection facility. 

2. The core, which is responsible for its general 
operation and management as well as consists 

of computing environments. 

3. The user object, with the help of which various 
human-system interactions take place, can be 

provided both in the cloud and in the local 

network. 

A physical twin consists of an experimental setup, 

sensors that facilitate data collection and a device control 

system to regulate executive functions. In the case of 

extremely complex non-stationary workflows or when it 

is not possible to install sensors, numerical modelling can 

provide an alternative source of data acquisition. 

To ensure the specific heat consumption remains 

stable during cyclic thermal processing, simultaneous 

control of the mass of the fuel mixture and the pressure 

applied on the charge in the combustion chamber is 

necessary to form the mixture, fill the chamber and make 

subsequent corrections. In accordance with the specified 

requirements, a system for forming the fuel mixture in 

the thermal pulsation system was developed, which is 

described in detail in [13]. 

The object of this study is to develop a mixer for 

mixing gaseous components, which is part of the fuel 

generator of an automated thermal pulse processing unit, 

described in detail in [14]. Mixing is frequently one of 

the most important processes in various industries. All 

starting materials and products, for example, in the 

chemical industry, must be homogeneous. In a paper 

where mixing in reservoirs was studied, a relationship 

was established between the flow structure in a tank and 

its geometry [15]. The aforementioned study considered 

a DT of the process of mixture formation in a mixing 

chamber by determining the composition of components 

and degree of homogeneity of the gas mixture obtained. 

The physical twin of our research objective is a two-

component mixer (Figure 1), which partly consists of a 

steel body (1), lid (2) and technological plugs (corks) (3). 

The components of the gas mixture enter through special 

jets (nozzles) (4) which are further mixed by counter 

currents in the chamber (5). Differences in the cross-

sectional areas of the through hole in the jets through 

which the fuel and oxidizer enter control the 

stoichiometric ratio of the components of the mixture 

being a supercritical flow at a constant pressure [16]. 

An aPriori physical twin consists of an experimental 

setup, components that collect data (sensors) and a device 

control system (executive function). The latest approach 

to the creation of DTs suggests the possibility of 

representing a physical twin by mathematically 

modelling it, which is necessary due to the complexity 

and sometimes even the impossibility of installing 

sensors as well as measuring the control parameters of 

processes in real time. For example, this applies to 

hermetic objects of a small or limited volume and fast-

acting processes that occur in them. The mixer in 

question required to mix the components of a gas mixture 

also falls into this category, that is, where the control 

parameters are the total mass of the components and the 

degree of homogeneity of the mixture. By studying the 

simulation of this process, special and extremely 

expensive equipment is not required to experimentally 

determine these parameters in the mixer.  

3. Modelling of gas mixing in a mixer 

The calculation area is the internal cavity of the gas mixer 

(Figure 2a). The calculation grid (Figure 2b), consisting 

of 152042 polyhedral elements, was built in the Ansys 

Fluent Meshing module to make further calculations in 

the Ansys Fluent system [17]. In order to model the wall 

flow of gases accurately, 5 prismatic layers with a growth 

factor of elements equal to 1.2 were built. 

To solve the defining equations of the model, the 

Finite Volume Method (FVM) was used, according to 

which the values of physical variables were calculated 

only at the center of the elements, while the mass flows, 

momentum and energy were calculated at the edges of 

these elements. 

3.1. Boundary and initial conditions  

Mixing of the methane-oxygen mixture in the expected 

stoichiometric ratio according to the reaction 
 

 

СН4+2О2 → СО2+2Н2О  

 

Figure 1. Mixer model 

1 – body; 2 – lid; 3 – corks; 4 – nozzles; 

5 – chamber; 6 – fittings; 7 – sensors 



DEVELOPMENT OF A DIGITAL TWIN FOR GAS MIXING IN A GENERATOR 

51(1) pp. 35–42 (2023) 

37 

was investigated. The directions of the supersonic flow 

of the gaseous components were normal at the inlets. The 

calculations were made while the system was stationary. 

At the tip of the jet, the speed of the gas flow was equal 

to the speed of sound. The computational model 

consisted of two domains with a common interface. 

While a force was applied, the average molar 

concentrations of oxygen and methane at the outlet of the 

mixer were monitored. 

The pressures of methane and oxygen gas at the 

inlet to the mixer were set at 4.340 and 4.104 atm, 

respectively. The initial temperature of both gases at the 

inlets was 20 °C. 

A single-phase multicomponent flow model was 

used to describe the mixing. The equations used to 

calculate the composition of the mixture were as follows 

[18]: 

 

 
𝜕𝜌

𝜕𝑡
+ 𝑑𝑖𝑣(𝜌�⃗� ) = 0 (1) 

 

 

 𝜌
𝑑�⃗⃗� 

𝑑𝑡
= 𝑑𝑖𝑣𝑃 + 𝑓  (2) 

 

 

𝜌
𝑑𝑒

𝑑𝑡
= 𝑑𝑖𝑣(𝜆𝑔𝑟𝑎𝑑𝑇) + 𝑃 · 𝑔𝑟𝑎𝑑�⃗�  (3) 

 

 

where ρ denotes the density of the mixture; �⃗�  represents 

the velocity vector; P stands for the stress tensor; T refers 

to the gas temperature; λ is the thermal conductivity 

coefficient of the gas; and e denotes the internal energy 

of the gas. 

To ensure that the fuel mixture is stratified from 

components of different densities, the effect of volume 

forces, namely gravity, was taken into account (𝑓 ). When 

calculating the density and gas constant of the mixture, 

standard mixing rules were used:  

 

 

 
1

𝜌
= ∑

𝑐𝑖

𝜌𝑖

𝑁
𝑖=1  ,    𝑅 = ∑ 𝑐𝑖

𝑁
𝑖=1 𝑅 (4) 

 

 

where (ρi) denotes the density of the components i of the 

mixture; R is the universal gas constant, ci, represents the 

molar concentration of the components i. 

To determine the degree of homogeneity of the 

mixture (ϑ), the following expression was used: 

 

 𝜗 =
𝜎𝐶𝑓

[𝐶𝑓]
 (5) 

 

where [Cf] denotes a given value of the molar 

concentration of the fuel, which corresponds to the 

stoichiometric ratio and σCf stands for the best estimate 

of the root-mean-square deviation of the molar 

concentration of the fuel as defined as:

 

 𝜎𝐶𝑓 = √
∫ (𝐶𝑓−𝑀𝐶𝑓)

2
 𝑑𝑠

𝑠

𝑆𝑜𝑢𝑡𝑙𝑒𝑡
 (6) 

 

 

where Soutlet denotes an area of an outlet from the mixer; 

Cf stands for the molar concentration of the fuel, MCf 

denotes the following mathematical expression of the 

molar concentration of the fuel: 

 

 𝑀𝐶𝑓 =
∫ 𝐶𝑓  𝑑𝑠𝑠

𝑆𝑜𝑢𝑡𝑙𝑒𝑡
 (7) 

 

The mixture was considered to meet the 

requirements in accordance with the conditions below: 

 

 

 [𝐶𝑓] − 𝛿 · [𝐶𝑓] ≤ 𝑀𝐶𝑓 −  𝜎𝐶𝑓  ∪ (8) 

 ∪  𝑀𝐶𝑓 + 𝜎𝐶𝑓 ≤ [𝐶𝑓] + 𝛿 · [𝐶𝑓]  

 

 

where δ denotes the given permissible deviation in the 

mass concentration of the fuel. 

An automatic time step was used for the calculation. 

The pressure-velocity coupling scheme was selected as 

the Pressure-Implicit with Splitting of Operator (PISO). 

For the discretization of parameters, Second Order 

Upwind Scheme was used.  

 
a 

 

 
b 

Figure 2. Cross-section of the calculated model of the mixer 

(a) and finite element grid (b) 



 SHYPUL, GARIN, TKACHENKO, PLANKOVSKYY AND TRYFONOV 

Hungarian Journal of Industry and Chemistry 

38 

3.2. The obtained results  

The velocity fields of gas flows, the mass flow of the 

components of the gas mixture through the mixer as well 

as the pressure and temperature fields were obtained by 

applying Computational Fluid Dynamics (CFD) 

modelling. The temperature and pressure distribution 

across the cross-section of the mixer and in the nozzles is 

presented in Figures 3 and 4. 

After travelling through the jet, a significant local 

decrease in temperature and pressure was observed due 

to the acceleration of the gas flow and the supercritical 

flow regime (Figure 5). 

Undoubtedly, such heterogeneous flow conditions 

affect how accurately the components of the fuel mixture 

are dosed and must be taken into account when 

performing calculations. The distribution of the molar 

concentration of methane across the cross-sections of the 

mixer and at its outlet is shown in Figure 6. 

CFD simulation results show that the mixer ensured 

that the fuel mixture was highly homogenous. According 

to the normalized estimate of the root-mean-square 

deviation of the molar concentration of methane, the 

deviation of the methane content from the stoichiometric 

value did not exceed 3 %. 

4. Development of a DT of the mixer 
connected to the system generating the 
fuel mixture 

The concept of a DT using Ansys Twin Builder 

numerical modelling technologies was proposed by 

ANSYS, Inc. [19]. The results of simulations using DTs 

can be calibrated based on the operating parameters of 

the physical process. The direct connection between the 

finite element method in its usual sense and the control 

scheme slows down the calculation speed when 

predicting the output parameters. Therefore, when 

developing a DT, Reduced Order Models (ROM) were 

used. Creating a ROM is possible by studying the physics 

of the process and extracting its global behaviour from 

the offline simulation. This can be obtained directly on 

the basis of the preliminary results from finite-element 

modelling by only taking into account the main features 

of the system and process. Since the calculation of the 

result in a separate object subjected to digital Reduced 

Order Modelling requires only simple algebraic 

operations, e.g. the addition of vectors and evaluation of 

response surfaces, the calculation process only requires 

technical resources for a short period of time and the 

result can be obtained in almost real time. 

  

 

 
 

a 

 

 
 

b 

Figure 4. Pressure fields in the central section of the mixer (a) 

and its nozzles (b) 

 

 
a 

 

 
b 

Figure 3. Temperature fields in the central section (a) of the 

mixer and its nozzles (b) 



DEVELOPMENT OF A DIGITAL TWIN FOR GAS MIXING IN A GENERATOR 

51(1) pp. 35–42 (2023) 

39 

With parametric ROM, the model can be evaluated and 

variations in the results quickly investigated depending 

on the values of the input parameters, thereby 

emphasizing the importance of suitable ROMs when 

simulating the operation of a complex multifunctional 

system. 

Of course, the results of a DT will be as reliable as 

the input data used to describe the object or process being 

modelled as comprehensively as possible. Typically, an 

enormous number of data points were recorded from the 

full-scale model. Several of the most likely characteristic 

modes were selected from the set of all the generated 

data, from which a simplified numerical calculation was 

subsequently made. Therefore, it is possible to 

thoroughly understand how the equipment is operated in 

different modes. To implement this approach in Ansys 

Twin Builder, a special hierarchy of input data was drawn 

up. Having such a hierarchy of data files is undoubtedly 

advantageous because from this it is possible to 

immediately match the data coming from analog sensors 

with a DT, that is, a calculation program. 

The DT of the mixer in the current study was 

created using the Ansys Fluent and Ansys Twin Builder 

programs. 

In the first stage, a complex model of the gas-

dynamic process of mixture formation of different 

component compositions was carried out in Ansys Fluent 

in order to determine the parameters that were later 

transferred to the ROM block of the model necessary for 

creating a DT in Ansys Twin Builder. The ROM of the 

model was transferred in Functional Mock-up Unit 

(FMU) format. A series of calculations was carried out to 

prepare the personnel unit required for the construction 

of the DT using the ROM model according to the 

established range of varied parameters. 

To create a digital counterpart to this process, the 

pressures of the fuel and oxidizer at the inlets were 

selected as the initial parameters. As control (output) 

parameters, the molar concentration of the components 

of the gas mixture and its quality were selected. The 

parameter describing the quality of the gas mixture 

showed the non-compliance rate along with the 

stoichiometric value of the gas component in the 

following form: 

 

^2

sqrt(areaAve((areaAve(CH4IdealGas.MolarFraction) @ Outlet

H4IdealGas.MolarFraction) @ Outlet) /

/(areaAve(CH4IdealGas.MolarFraction) @ Outlet).

C

−

−  

 

According to the algorithm of the parametric 

calculation, the number of variations (the design points 

that were used to build the so-called learning points or 

snapshots of the ROM) required was determined. In the 

case under consideration, 16 of them were found. The 

scatter plot of variations in the initial data lies within 

10 % of the deviations and is determined randomly. 

Therefore, in the framework of solving a parametric 

problem, after a series of gas-dynamic calculations on the 

 
a 

 

 
b 

Figure 5. Velocity field throughout the volume of the mixer 

(a) and in the jets (b) 

 
a 

 

 
b 

Figure 6. Molar concentration of the fuel injected into the 

mixing chamber (a) and at the outlet from the mixer (b) 



 SHYPUL, GARIN, TKACHENKO, PLANKOVSKYY AND TRYFONOV 

Hungarian Journal of Industry and Chemistry 

40 

full Fluent model of the mixing process were made, basic 

data were obtained for the ROM of the DT (Figure 7), 

which clearly show the variations in the values of the 

inlet pressure parameters of the components of the 

mixture and the corresponding values at the outlet, that 

is, the parameter defining the quality of the gas mixtures. 

To view the goodness of fit for the output 

parameters in a ROM, the absolute error (L-Infinity 

Norm Error) was calculated for each snapshot (Figure 8) 

according to the following expression: 

 

 𝑌𝑖 = 𝑚𝑎𝑥𝑗=1…𝑁|𝑌𝑖,𝑗 − 𝑌𝑖,𝑗⃗⃗⃗⃗  ⃗| (9) 

 

where Yi denotes the i-th snapshot; Yi,j refers to the j-th 

entity of the i-th snapshot; and 𝑌𝑖,𝑗⃗⃗⃗⃗  ⃗ represents the ROM 

approximation of the j-th entity of the i-th snapshot. 

A simplified mixer model can be considered to be a 

complete DT. Meanwhile, considering the mixer as a 

separate structural component of some hydraulic system, 

the resulting FMU model of the mixer will act as a 

structural unit of a higher-order circuit, e.g. "cylinder - 

mixer - working tank". In terms of all these calculations, 

the resulting model should be loaded into the Ansys Twin 

Builder platform as a separate component. 

When adding a model of an FMU mixer, attention 

must be paid to the model-carrying input and output 

parameters created when the ROM was built. 

Therefore, when adding a mixer to the scheme of 

the digital double, all the parameters of the model of 

interest were noted before it was imported. The initial 

parameters here were the values of the Fluel_in_Press 

and Fluel_in_Oxi pressures specified in the Ansys Fluent 

parametric study at the outlets of the two cylinders of 

gases that were being mixed. Since the mass content of 

each component of the mixture at the outlet of the mixer 

was determined as initial and control parameters, the DT 

was successfully added to the DT project. 

In Ansys Twin Builder, data can be assigned in 

many ways to describe how the equipment is operated or 

its individual link. The input parameters for this ROM of 

the mixer can be loaded from an external medium in 

tabular format, the data of "frames" - pre-saved 

measurements from analog devices (sensors) at a certain 

time interval - used or a continuous streaming of data 

recorded from when the equipment was used with the 

help of additional macros. When using this mixer as part 

of a DT of a higher order, the input parameters for the 

mixer were determined by the output parameters of the 

previously stationary element, e.g. the gas pressure at the 

outlet of each of the cylinders. In this work, given that 

the mixer itself was calibrated and verified, it is sufficient 

to use the standard "2D Lookup Table" scheme to 

determine the pressure of the two oxidizers at each inlet 

of the mixer. With the help of "2D Lookup Table" 

schemes, since the pressures at the inlets to the mixer are 

represented as tabular functions over time, it is important 

P
re

ss
u

re
 (

P
a)

 ,
 ×

1
0

5
 

Points Name

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

2.7

2.5

3.1

2.9

3.5

3.3

3.9

3.7

99.65

99.7

99.50

99.55

99.40

99.45

99.25

99.35

99.6

99.30

M
ix

in
g

 Q
u

a
li

ty
 (

%
) 

Mixing QualityPressure CH4Pressure O2  

Figure 7. Design points vs. parameters 

 

 

1

0

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Points Name

L
-I

n
fi

n
it

y
 N

o
rm

 E
rr

o
r 

, 
×

1
0

-6
 

 

Figure 8. L-Infinity Norm Error for the points taken into 

account in the construction of the response surface 



DEVELOPMENT OF A DIGITAL TWIN FOR GAS MIXING IN A GENERATOR 

51(1) pp. 35–42 (2023) 

41 

to match the time ranges of the input parameters with the 

time settings of the entire solution defined for the project 

(Figure 9).  

The calculation is performed by applying standard 

solver settings using the Adaptive Step Trapezoid Rule 

method to integrate time. Temporary settings cover all 

the calculation frames.  

After preparing and adjusting the model of the DT 

of the two-component mixer, a calculation was made, the 

result of which was presented in the form of two-

dimensional dependence graphs (Figure 10) showing 

changes in the mass fractions of the components of the 

mixture against the number of snapshots (time). The 

horizontal axis indicates the number of the calculated 

snapshot and the vertical axis indicates the mass fraction 

of the component of the gas mixture.  

Given that the mass fraction of the components of 

the gas mixture controlled at each calculation point was 

one, the law of conservation of mass was not violated. 

The graphs obtained from the built DT with regard to the 

process of generating the fuel mixture provide visual 

representations of the percent composition of the mass 

fractions of each gas mixture depending on the pressure 

at the outlet of each cylinder. Furthermore, how the 

composition of the mixture changes when the pressure of 

each component of the fuel mixture at the inlet to the 

mixer deviated from its optimal value was determined. 

5. Conclusion  

The construction of a DT of the system generating the 

fuel mixture based on the results of a numerical 

simulation was considered. A combined approach was 

used to build a DT. An element of the generation system 

with a complex flow pattern was modelled by a 

numerical experiment, the results of which were used to 

build its ROM. This model was used as the structural unit 

of the higher-order contour. 

The graphs obtained from the built DT of the 

process used to generate the fuel mixture provide a visual 

representation of the percent composition of mass 

fractions of each gas mixture depending on the pressure 

at the outlet of the cylinders. Furthermore, how the 

composition of the mixture changed when the pressure of 

each component of the fuel mixture at the inlet to the 

mixer deviated from the optimal value could be 

determined. 

Acknowledgements 

The authors would like to express their gratitude to 

CADFEM UA LLC, an official partner of ANSYS, Inc. 

in Ukraine, for helping license the software.  

 
 

Figure 9. The scheme of the DT of the mixer 

 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Times [s] – Design Points

M
a
ss

 F
ra

c
ti

o
n

 C
H

4

0.155

0.150

0.160

0.165

0.170

0.175

0.180

0.185

0.190

0.195

 
a 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Times [s] – Design Points

M
a
ss

 F
ra

c
ti

o
n

 O
2

0.810

0.805

0.815

0.820

0.825

0.830

0.835

0.840

0.845

0.850

 
b 

Figure 10. Mass fractions in the form of particles of the components of the gas mixture (а – CH4; b – O2) 



 SHYPUL, GARIN, TKACHENKO, PLANKOVSKYY AND TRYFONOV 

Hungarian Journal of Industry and Chemistry 

42 

REFERENCES 

[1] Qi, Q.; Tao, F.; Hu, T; Answer, N.; Liu, A.; Wei, Y.; 
Wang, L.; Nee, A.Y.C.: Enabling technologies and 

tools for digital twin, J. Manuf. Syst., 2021, 58(B), 

3–21, DOI: 10.1016/j.jmsy.2019.10.001 

[2] Cimino, C.; Negri, E.; Fumagalli, L.: Review of 
digital twin applications in manufacturing, Comput. 

Ind., 2019, 113, 103130, DOI: 
10.1016/j.compind.2019.103130 

[3] Sinner, P.; Daume, S.; Herwig, C.; Kager, J.: Usage 
of digital twins along a typical process development 

cycle, Adv. Biochem. Eng. Biotechnol., 2021, 176, 

71–96, DOI: 10.1007/10_2020_149 

[4] Brovkova, M.; Molodtsov, V.; Bushuev, V.: 
Implementation specifics and application potential 

of digital twins of technological systems, Int. J. Adv. 

Manuf. Technol., 2021, 117(7-8), 2279–2286, DOI: 
10.1007/s00170-021-07141-z 

[5] Kritzinger, W.; Karner, M.; Traar, G.; Henjes, J.; 
Sihn, W.: Digital Twin in manufacturing: A 

categorical literature review and classification, 

IFAC-PapersOnLine, 2018, 51(11), 1016–1022, 
DOI: 10.1016/J.IFACOL.2018.08.474 

[6] Sӧderberg, R.; Wӓrmefjord, K.; Carlson, J.S., 
Lindkvist, L.: Toward a Digital Twin for real-time 

geometry assurance in individualized production, 

CIRP Ann. Manuf. Technol., 2017, 66(1), 137–140, 
DOI: 10.1016/j.cirp.2017.04.038 

[7] Robles, J.; Baca, G.; Chong, J.; Gonzales, S.: 
Nonsingular terminal sliding mode control for a 

variable speed wind turbine system using Face 

Mock-Up Interface co-simulation, 11th Int. 

Conf. Power Energy Electr. Eng. (CPEEE), Shiga, 

Japan, 2021, 158–164, DOI: 
10.1109/CPEEE51686.2021.9383360 

[8] Nauri, I.M.; Ihwanudin, M.; Sumarli; Mindarta, 
E.K.; Harly, M.; Putra A.B.; Awanggapati, 

B.;Ismail, H.: Development of integrated hardware-

in-the-loop (hil) test bench anti-lock brake system 

(abs) instrument, J. Phys. Conf. Ser., 2020, 1700(1), 

012097, DOI: 10.1088/1742-6596/1700/1/012097 

[9] ISO/FDIS 23247-2:2021(E) Automation systems 
and integration — Digital twin framework for 

manufacturing — Part 1: Overview and general 

principles, 2020 

[10] ISO/FDIS 23247-2:2021(E) Automation systems 
and integration — Digital twin framework for 

manufacturing — Part 2: Reference architecture, 

2021 

[11] ISO 23247-3:2021(E) Automation systems and 
integration — Digital twin framework for 

manufacturing — Part 3: Digital representation of 

manufacturing elements, 2021 

[12] ISO/FDIS 23247-4:2021(E) Automation systems 
and integration — Digital twin framework for 

manufacturing — Part 4: Information exchange, 

2021 

[13] Plankovskyy, S.; Popov, V.; Shypul, O.; Tsegelnyk, 
Y.; Tryfonov, O.; Brega, D.: Chapter 15 - Advanced 

thermal energy method for finishing precision parts, 

in: Advanced Machining and Finishing, Gupta, K.; 

Pramanik, A. (Eds.), (Elsevier, Amsterdam, 

Netherlands), 2021, pp. 527–575, DOI: 10.1016/B978-
0-12-817452-4.00014-2 

[14] Shypul, O.; Garin, V.; Tkachenko, D.; Zaklinskyy, 
S.; Tryfonov, O.; Plankovskyy, S.: Development of 

a digital twin of reservoir filling by gas mixture 

component, in: Advances in intelligent systems and 

computing, Shkarlet, S.; Morozov, A.; Palagin, A. 

(Eds.), (Springer: Cham), 2022. (In press) 

[15] Tarcsay, B.L.; Egedy, A.; Bobek, J.; Rippel-Pethő, 
D.: Investigation of mixing in tanks of a special 

geometry, Hung. J. Ind. Chem., 2019, 47(2), 63–70, 
DOI: 10.33927/hjic-2019-21 

[16] Plankovskyy, S.I.; Shypul, O.V.; Zaklinskyy, S.A.; 
Tryfonov, O.V.: Dynamic method of gas mixtures 

creation for plasma technologies, Probl. At. 

Sci. Technol., 2018, 117(5), 121–125, 

https://vant.kipt.kharkov.ua/ARTICLE/VANT_201

8_5/article_2018_5_121.pdf 

[17] ANSYS CFX Reference Guide, 
https://ansyshelp.ansys.com/account/secured?retur

nurl=/Views/Secured/prod_page.html?pn=CFX&pi

d=CFX&lang=en, (accessed 12.10.2021) 

[18] Menter, F.R.: Two-equаtion eddy-viscosity 
turbulence models for engineering applications, 

АIАА Journаl, 1994, 32(8), 1598–1605, DOI: 
10.2514/3.12149 

[19] 32nd ANSYS Twin Builder Reference Guide, 
https://ansyshelp.ansys.com/account/secured?retur

nurl=/Views/Secured/prod_page.html?pn=Twin%2

0Builder&pid=TwinBuilder&lang=en, (accessed 

14.02.2022) 

 

 

 

https://doi.org/10.1016/j.jmsy.2019.10.001
https://doi.org/10.1016/j.compind.2019.103130
https://doi.org/10.1016/j.compind.2019.103130
https://doi.org/10.1007/10_2020_149
https://doi.org/10.1007/s00170-021-07141-z
https://doi.org/10.1007/s00170-021-07141-z
https://doi.org/10.1016/J.IFACOL.2018.08.474
https://doi.org/10.1016/j.cirp.2017.04.038
https://doi.org/10.1109/CPEEE51686.2021.9383360
https://doi.org/10.1109/CPEEE51686.2021.9383360
https://doi.org/10.1088/1742-6596/1700/1/012097
https://doi.org/10.1016/B978-0-12-817452-4.00014-2
https://doi.org/10.1016/B978-0-12-817452-4.00014-2
https://doi.org/10.33927/hjic-2019-21
https://vant.kipt.kharkov.ua/ARTICLE/VANT_2018_5/article_2018_5_121.pdf
https://vant.kipt.kharkov.ua/ARTICLE/VANT_2018_5/article_2018_5_121.pdf
https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/prod_page.html?pn=CFX&pid=CFX&lang=en
https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/prod_page.html?pn=CFX&pid=CFX&lang=en
https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/prod_page.html?pn=CFX&pid=CFX&lang=en
https://doi.org/10.2514/3.12149
https://doi.org/10.2514/3.12149
https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/prod_page.html?pn=Twin%20Builder&pid=TwinBuilder&lang=en
https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/prod_page.html?pn=Twin%20Builder&pid=TwinBuilder&lang=en
https://ansyshelp.ansys.com/account/secured?returnurl=/Views/Secured/prod_page.html?pn=Twin%20Builder&pid=TwinBuilder&lang=en