=Paper=
{{Paper
|id=Vol-2608/paper41
|storemode=property
|title=Information technology in the modeling of dry gas seal for centrifugal compressors
|pdfUrl=https://ceur-ws.org/Vol-2608/paper41.pdf
|volume=Vol-2608
|authors=Lyudmyla Rozova,Gennadii Martynenko
|dblpUrl=https://dblp.org/rec/conf/cmis/RozovaM20
}}
==Information technology in the modeling of dry gas seal for centrifugal compressors==
https://ceur-ws.org/Vol-2608/paper41.pdf
Information Technology in the Modeling of Dry Gas Seal
for Centrifugal Compressors
Lyudmyla Rozova 1[0000-0002-0781-7473] and Gennadii Martynenko 2[0000-0001-5309-3608]
National Technical University “Kharkiv Polytechnic Institute”, Department of Dynamics and
Strength of Machines, NTU “KhPI”, 2, Kyrpychova str., 61002, Kharkiv, Ukraine
1
luda.rozova@gmail.com, 2 gmartynenko@ukr.net
Abstract. The developed specialized software package for computer modeling
of dry gas seals for the rotors of centrifugal compressors is presented. This
software package implements the mathematical model that describes improved
methodology for seals modeling and solving under steady-state compressor op-
erating conditions. It allows to make a model of working gap between the seal
rings, which changes under the influence of gas pressure and temperature. This
improved computer modeling can provide the reliable operation of dry gas
seals. The developed software package has been tested on real constructions of
dry gas seals with different types of groves. The results of test solutions were
compared with available in literature and experimental studies.
Keywords: Computer Simulation, Engineering Software, Compressor Gas
Seals
1 Introduction
The issues of computer modeling and information technology are very relevant in the
study of engineering objects. Increasingly, they are the basis of a computer experi-
ment, which in most cases can be used to replace the implementation of expensive
real experimental studies during finishing work and in the process of servicing work-
ing structures. Computer technology capabilities allow for rather accurate modeling
and numerical research of engineering structures, using existing technical software
systems for general engineering solutions. Particular difficulty in this case is the need
to solve problems from different areas of physics within the solution of general tech-
nical problem [1].
Another way is to create specialized software products using different program-
ming languages and environments. This allows to use more accurate mathematical
models for analysis, taking into account processes and phenomena of different physi-
cal nature. The use of such information technology for modeling improves quality of
design work when creating prototypes and industrial designs [2].
The need to create a specialized software package also arose for the modeling of
dry gas seals for the rotors of centrifugal compressors, designed to maintain gas pres-
sure in main gas pipelines [3]. Such compressor are shown in Figure 1.
Copyright © 2020 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
This type of seals is shown in Figure 2. It has been widely applied in view of a
number of advantages. The main ones are: the possibility of operation at high rotation
speeds for compressor rotor; the absence of an expensive oil supply system; minimal
gas leakage during operation [4, 5].
Fig. 1. Centrifugal compressor
Fig. 2. Dry gas seals
Dry gas seals can work stably and reliably with various gases and under various
operation conditions only in the case of it very accurate modeling and solving. An
improved methodology of gas seals analysis under steady-state operation conditions
should include solving of gasdynamics, heat transfer and thermoelasticity prob-
lems [5].
The seals system is one of the most critical centrifugal compressor systems. That is
why the presence of improved methodology for gas seals modeling and software
product that implements this methodology makes a huge contribution to the reliable
operation of the system as a whole.
This paper is devoted to the issues of using information technology for computer
modeling of processes that take place during the operation of dry gas seals and the
creation of specialized software package for modeling and solving.
2 Formal problem statement
The aim of this work is to present the developed specialized software package for
computer modeling and solving of dry gas seals for the rotors of centrifugal compres-
sors. This software package implements the mathematical model that describes im-
proved methodology for seals modeling under steady-state compressor operating con-
ditions.
3 Literature review
An analysis of the existing researches, dedicated to the modeling of gas face seals, has
shown the relevance of this problem. Despite the large number of publications on this
topic, many issues of modeling and solving remain open.
The main operation condition of dry gas seals is the existence of the necessary gap
between the seal rings with a thickness of 3-4 μm (micrometer) in steady state opera-
tions, supported by the gas pressure (Fig. 2). The necessary gas pressure between the
rings in working condition is created and maintained due to the special type of micro-
grooves on the rotating seal ring, with a depth of 6-7 μm.
The type of grooves is selected, taking into account the operation features of seals.
More often spiral grooves are used. Considering such small gaps between the sealing
rings and the shallow depth of the grooves, much attention is paid to computer model-
ing and solving of gas seals.
Nowadays, the existing universal engineering software packages based on the fi-
nite element method are widely used for modeling and solving of dry gas seals. So, in
studies [6, 7, 8, 9, 10], well-known general technical software packages are used to
analyze the gas pressure between the rings. These works are devoted to the selection
of the optimal type of microgrooves for direct and reverse seal operation, by calculat-
ing the gas pressure in the gas layer between the rings. The influence of the surface
treatment of the rings on the working pressure of the gas in the gap is studied [11].
Existing software packages are also used for modeling and visualization of calcula-
tion results.
However, it is necessary to take into account the temperature distribution in the
seal rings and the appearance of temperature strains in rings.
Taking into account these strains is necessary in view of small gap between the
rings. Temperature strains can lead to redistribution of gas pressure between the seals
rings and incorrect seals operation. The literature review on solving of heat-transfer
and thermoelasticity tasks for dry gas seals showed the existence of a few number of
papers devoted to this problem [12, 13, 14].
So, in studies [12, 14], the temperature distribution in the rings is taken into ac-
count. The appearance of temperature strains is taken into account in [13]. These
problems are solved by using of general technical software packages. Either an alter-
native to this are developed programs, which are based on simplified engineering
solution methods. The above tasks are solved separately, because of their rather diffi-
cult simultaneous analysis.
Existing software packages allow to create accurate model research object, visual-
ize the results of the solution. However, the existing general technical software sys-
tems are designed to solve a wide class of problems and they, of course, cannot fully
take into account the aspects of a highly specialized task in solving a specific problem
for a particular object. The presence of a specialized program allows more accurately
and adequately simulate processes, and take into account the relationship between
phenomena of different physical nature.
Therefore, the creation of specialized software package for computer modeling and
solving of dry gas seals is a relevant problem today.
4 Specialized software package GasDin
In this paper, the developed specialized software package GasDin is presented that
implements an improved methodology of modeling of dry gas seals for the rotors of
centrifugal compressors. This methodology is based on iterative solution of related
gasdynamic, heat transfer and thermoelasticity tasks.
4.1 Theoretical basis
The two-dimensional distribution of gas pressure in the gap between the seal rings is
described by the nonlinear gas lubrication equation. After some conversions, taking
into account the temperature changes, this equation has the form [15]:
1 3p 1 3 p
h 12 h pz h 12h p x 0 , (1)
x Tav x z Tav z
where – dynamic coefficient of viscosity for gas; Тav=Тav(x,z) – an average integral
function of changing the gas temperature over the gap thickness (along the y coordi-
nate); h – the thickness of the gas layer; р=P2 – is the square of the gas pressure; –
the angular velocity of rotating ring.
The temperature distribution in the gas film between the rings is described by the
heat equation, taking into account the heat generation in the gas layer due to viscosity
and convective heat transfer [15]:
T T T v x v z PC v T
2 2
T
kT kT kT
v x v z 0 , (2)
x x y y z z y y RT x z
where kT – thermal conductivity of the gas film; T=T(x,y,z) – gas temperature; vx and
vz – gas velocity components along the gap; Сv – specific gas heat intensity ratio at a
constant volume; R – universal gas constant.
The boundary conditions for equations (1), (2) are the set values of temperature
and pressure at the inlet and outlet of the seal.
The temperature distribution in working rings is:
(kT1, 2 T ) 0 , (3)
where kT1 and kT2 – thermal conductivities of rotating and axially movable seal rings.
4.2 Computer modeling methodology
An algorithm based on the use of the Bubnov-Galerkin method in combination with
the finite element method has been developed to solve the gasdynamic task for dry
gas seals. The finite element method in variational formulation is used for solving the
heat transfer and thermoelasticity tasks. Because of non-linearity of formulated tasks,
an iterative algorithm of their simultaneous solution has been developed.
The conversion of cumbersome analytical expressions for resolving system of non-
linear equations, which formed the basis of the GasDin software package, were made
using package of computer mathematics. These expressions were automatically trans-
lated into the codes of C++ programming language. Thus, it was possible to avoid
numerous mistakes. Analytical expressions were also used in testing to compare the
results of calculations.
This software package has been developed by use of C++ programming language.
The main window of the developed software package is shown in Figure 3.
Fig. 3. The main window of the software package GasDin
The main requirement for the service part of the software package was the creation
of an on-screen menu with corresponding “buttons”, allowing to manage standard set
of work with files and program modules, various forms of data input and output, visu-
alization of results of calculations.
4.3 Structure and implementation of the software package GasDin based on
the use of integrated technologies
Block scheme of software package GasDin is presented on Figure 4.
Fig. 4. Block scheme of software package GasDin
It should be noted that the solution of heat transfer and thermoelasticity tasks, the
visualization of the obtained pressure fields and gas velocities in the gap is carried out
using universal finite element software package. Data exchange between the software
packages during iterative process is carried out by specially designed programs.
The developed software package allows solving for databases located in any direc-
tory. The initial data for the gasdynamic solution are: the gas pressure at the inlet and
outlet of the seal P2 and P0, the external and internal radius of the flow region r2 and
r0, the working gap , the depth of the grooves, the specific gas heat intensity ratio at
a constant volume Сv, universal gas constant R, gas temperature at the inlet and outlet
of the seal T2 and T0, the angular velocity of rotation ω, the accuracy of the gasdy-
namic calculation .
The software package GasDin allows to perform two types of gasdynamic solu-
tions: at a constant temperature of the gas layer, and taking into account heat genera-
tion and temperature changes in the gas layer. The non-linear differential equation of
gas lubrication is solved (1). The system of nonlinear algebraic equations for un-
known pressure and temperature at the nodes of the finite element grid is solved by
the method of simple iterations, where the linearized system is solved at each iteration
using the Gauss method. The end of the iterative process is determined by the user-
specified accuracy of solution. Setting of gas temperature field at each iteration is
carried out by specially created programs for automatic transfer of the temperature
distribution to the software package GasDin, obtained by solving the heat transfer task
for gas film and working rings.
The results obtained by gasdynamic calculation are recorded to special files. They
contain the values of the pressure in the nodes, the coordinates of the nodes. The val-
ue of gas leakage through the seal, resulting gasdynamic force, are also calculated.
The developed software package also allows for the initial selection of the working
gap between the seals by aligning the gasdynamic and gasostatic resulting forces. The
gasostatic force is calculated during the preparation of the initial data after thorough
study of the working drawings, the method of sealing of non-rotating ring and setting
the boundary conditions.
After gas-dynamic solution, the software package calculates the intensity of heat
sources in the gas layer and exports them into the database to solve the heat transfer
problem. Further, the temperature fields of rings and pressures in the gas layer are
exported into the corresponding databases for solving the thermoelasticity problem in
three-dimensional and axisymmetric simulations, taking into account the possible
mismatch of grids. Recalculation of the working gap, taking into account the obtained
strains of seal rings, is also performed automatically.
4.4 Testing and practical use of software package GasDin
Testing of the created software package GasDin was carried out by solving test tasks
for special cases which have an analytical solution, such as the distribution of gas
pressure in the gap without grooves. Also, test solutions were compared with solu-
tions in literature and experimental studies [15].
To determine the gas pressure in the gap between the rings, the region of the gas
layer is considered, taking into account the cyclic periodicity conditions, containing a
groove and a land. The results of the gasdynamic solution were checked in two stages.
It is known, that for gas layer with constant thickness and temperature, the gas lubri-
cation equation (1) has an analytical solution.
1 Р02 1 Р02
P2 ln r 1; Р 1 ln r . (4)
ln r0 ln r0
The solving results agreed with the results of the analytical solution up to the accu-
rate to five decimal places and are shown in Figure 5. The exact solution values are
marked with squares. For solutions, the following initial data were used: r0=53.6 mm;
r1=68 mm; r2=80 mm; P0=1 atm; P2=53 atm; the thickness of the gas layer outside the
groove h1=3 μm; in the groove h2=11 μm.
Fig. 5. Pressure distribution in the gas layer without grooves
Testing of the iterative solution algorithm and the created software package was al-
so carried out for the real designs of dry gas seals used at the Joint Stock Company
“Sumy Machine-Building Science-and-Production Association”, Sumy, Ukraine. To
determine gas pressure in the gap between the rings, the region of gas layer is consid-
ered taking into account the cyclic periodicity conditions. Solution model contains a
groove and a land. Geometric and operating parameters of the seal with spiral
grooves: r0=101 mm; r1=112.1 mm; r2=125 mm; P0=1.3 atm; P2=60.8 atm; the thick-
ness of the gas layer outside the groove h1=3 μm; in the groove h2=10 μm.
Figure 6a shows the distribution of gas pressure in the gap, taking into account
temperature changes; Figure 6b the distribution of gas velocities in the gap.
a) b)
Fig. 6. For seals with spiral grooves: a) gas pressure distribution in the gap, taking into account
temperature changes; b) the distribution of gas velocities in the gap
The developed solution algorithm and software package allows to find the gas
pressure distribution for any type of grooves. Figure 7 shows the gas pressure distri-
bution for seals with T-grooves under direct (Fig. 7a) and reverse (Fig. 7b) operation
modes. The results of the gas pressure distribution in gap are in a good agreement
with available in literature for seals with spiral grooves and T-grooves [6, 7, 8].
a) b)
Fig. 7. Gas pressure distribution for seals with T-grooves: a) direct operation mode; b) reverse
operation mode
An axisymmetric model of seal rings and gas layer is used for heat transfer solu-
tion. To determine the strain state of seal working rings, three-dimensional ring mod-
els are used taking into account the conditions of cyclic symmetry shown in Figure 8.
a) b)
Fig. 8. The working rings models with spiral grooves: a) axially movable ring; b) rotating ring
It should be noted, that the Joint Stock Company “Sumy Machine-Building Sci-
ence-and-Production Association” has created an experimental stand for dry gas seals.
It determines the inlet and outlet pressure in seals, determines the gas velocities and
temperature around seal rings, which can be used as the initial data for solutions. The
gas temperature at the inlet and outlet of seals and the flow characteristics of seals are
also determined.
As mentioned above, the heat transfer modeling for seal rings is done in axisym-
metric setting. The resultant temperature distribution is shown in Figure 9.
Experiments for studied seals showed that gas in the gap heats up on average to 40-
50°C, in the absence of contact of surfaces. As a result of computer modeling studies,
the gas at the outlet is heated up to 46°C (319 K) for these seals. That is in a good
agreement with experimental data.
The developed software package allows to determine the gas leakage through the
seal, according to the integral expression for the gas leakage:
2
1 P
Qr 12 RT h P r d
3
(5)
0
The gas leakage obtained as a result of computer modeling of studied gas seals us-
ing developed software package GasDin is 1.03×10-3 kg/s. The changes of working
gap caused by straining of seal rings are taken into account.
Fig. 9. Temperature distribution in gas seals
The calculated gas leakage differs from the experimental value for this seal design
by 9%. It can be considered a good result.
The test modeling and solving confirm the reliability of results obtained using the
developed software package GasDin.
5 Conclusion
Information technologies are widely used for computer modeling of various engineer-
ing facilities. Their use allows to improve the accuracy of designed facilities, reduce
the service costs. Presented in this paper specialized software package allows to carry
out computer modeling and solving of gas seals of centrifugal compressors.
The advantage of the developed software package GasDin is the ability to find the
distribution of gas pressure in the gap between the seal rings at a constant temperature
and taking into account of temperature changes. It is an advantage over existing gen-
eral engineering software packages. Seeing that, the distribution of gas pressure in the
gap is described by a non-linear equation related to particular part of gasdynamic, the
theory of gas lubricant.
Also, the software package GasDin implements an iterative algorithm for modeling
and solving of gas seals. It allows to make a model of working gap between the seal
rings, which changes under the influence of gas pressure and temperature. This im-
proved computer modeling can provide the reliable operation of dry gas seals.
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