МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ
DOI: https://doi.org/10.15407/itm2025.04.019 Among the various automation units used in pneumatic–hydraulic systems of rocket hardware, check valves are widely employed. They are most commonly used in the filling lines of different tanks and in the pressurization lines of launch vehicle propellant t...
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| author | CHERNIAVSKYI, O. S. DOLGOPOLOV, S. I. SHEVCHENKO, S. A. |
| author_facet | CHERNIAVSKYI, O. S. DOLGOPOLOV, S. I. SHEVCHENKO, S. A. |
| author_institution_txt_mv | [
{
"author": "O. S. CHERNIAVSKYI",
"institution": "Oles Honchar Dnipro National University, 72 Nauky Avenue, Dnipro 49045, Ukraine; e-mail: o.s.cherniavskyi@gmail.com"
},
{
"author": "S. I. DOLGOPOLOV",
"institution": "Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and State Space Agency of Ukraine, 15 Leshko-Popel St., Dnipro 49005, Ukraine; e-mail: dolmrut@gmail.com"
},
{
"author": "S. A. SHEVCHENKO",
"institution": "Institute of Transport Systems and Technologies of the National Academy of Sciences of Ukraine, 5 Pisarzhevsky St., Dnipro 49005 Ukraine; e-mail: sergiishevch@gmail.com"
}
] |
| author_sort | CHERNIAVSKYI, O. S. |
| baseUrl_str | https://journal-itm.dp.ua/ojs/index.php/ITM_j1/oai |
| collection | OJS |
| datestamp_date | 2026-07-13T20:26:18Z |
| description | DOI: https://doi.org/10.15407/itm2025.04.019
Among the various automation units used in pneumatic–hydraulic systems of rocket hardware, check valves are widely employed. They are most commonly used in the filling lines of different tanks and in the pressurization lines of launch vehicle propellant tanks, where they prevent reverse flow and the ingress of vapors into the pressurization system. In liquid rocket engines (LREs), check valves are installed in drainage lines and in inert gas purging circuits. Particular attention is given to the use of check valves in reconfigurable hydraulic systems, in which the flow direction changes during the LRE operation. The goal of this study is to develop a mathematical model of dynamic processes in a check valve, verify it using CFD simulations of the pressure distribution over the valve poppet surface, and apply it to the analysis of transient processes in a reconfigurable hydraulic system. To determine the flow force acting on the valve poppet, this paper proposes an approach in the lumped-parameter approximation based on the flow rate balance of the working fluid in the valve flow passage. The model considers the radial inflow at the valve inlet, which depends on the poppet travel, and the peripheral flow through the narrow clearance between the valve body and the poppet. To implement this approach, it is sufficient to know the valve geometry and the discharge coefficients, which are assumed to be constant. For a reconfigurable propellant feed system containing check valves, a mathematical model of low-frequency dynamic processes was developed, and transient processes during the LRE startup were simulated. During the startup, the propellant feed of the LRE gas generator is automatically switched by the check valves from the start tank supply to the pump supply. Transient processes were simulated for the flow force acting on the check valve poppet determined using CFD simulation and the lumped-parameter approximation. A satisfactory agreement between the results of these two approaches was demonstrated. The possibility of using the proposed lumped-parameter approximation to determine the flow force acting on the check valve poppet was justified, thus enabling the development of mathematical models of dynamic processes in reconfigurable hydraulic systems without resorting to computationally expensive CFD simulations.
REFERENCES
1. Sutton G. P., Biblarz O. Rocket Propulsion Elements. 9th ed. Hoboken: John Wiley & Sons, 2017. 800 pp.
2. Huze D. K., Huang D. H. Design of Liquid Propellant Rocket Engines. NASA SP 125. Washington: NASA, 1971. 472 pp.
3. Cherniavskyi O. S., Chevchenko S. A., Dolgopolov S. I. Mathematical modeling of the dynamic processes during check valve operation in the branched reconfigurable system of a liquid rocket engine. Aerospace Technic and Technology. 2025. No. 4. Special Iss. 2. Pp. 93-101.
4. Pylypenko O., Dolgopolov S., Nikolayev O., Khoriak N., Kvasha Yu., Bashliy I. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. V. 18. No. 6. Pp. 97-112.
5. Koptilyy D., Marchan R., Dolgopolov S., Nikolayev O. Mathematical modeling of transient processes during start-up of main liquid propellant engine under hot test conditions. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1-4 July 2019. 15 pp.
6. Kobielski M. J., Skarka W., Skarka M. Comparison of pressure loss evaluation fidelity in turbulent energy dissipation models of poppet check valves using computational fluid dynamics (CFD) software. Technical Sciences, 2024. V. 27. Pp. 19-31. https://doi.org/10.31648/ts.9732
7. Filo G., Lisowski E., Rajda J. Design and flow analysis of an adjustable check valve by means of CFD method. Energies. 2021. V. 14. No. 8. 2237. https://doi.org/10.3390/en14082237
8. Klas R., Habán V., Rudolf P. Analysis of in line check valve with respect to the pipeline dynamics. EPJ Web of Conferences. 2017. V. 143. 02051. https://doi.org/10.1051/epjconf/201714302051
9. Lang S. A review of check valves in unsteady flow. Proceedings of the 2024 ASME Pressure Vessels & Piping Conference, V003T04A001.
10. Domagała M., Fabis Domagała J. A. Review of the CFD method in the modeling of flow forces. Energies. 2023. V. 16. No. 16. 6059. https://doi.org/10.3390/en16166059
11. Pusztai T., Siménfalvi Z. CFD analysis on a direct spring loaded safety valve to determine flow forces. Pollack Periodica. 2021. V. 16. No. 1. Pp. 109-113. https://doi.org/10.1556/606.2020.00122
12. Zong C., Zheng F., Chen D., Dempster W., Song X. CFD analysis of the flow force exerted on the disc of a direct operated pressure safety valve in energy system. Journal of Pressure Vessel Technology, 2020. V. 142. No. 1. 011702. https://doi.org/10.1115/1.4045131
13. Finesso R., Rundo M. Numerical and experimental investigation on a conical poppet relief valve with flow force compensation. International Journal of Fluid Power. 2017. V. 18. No. Pp. 111-122.https://doi.org/10.1080/14399776.2017.1296740
14. Wu D., Li S., Wu P. CFD simulation of flow pressure characteristics of a pressure control valve for automotive fuel supply system. Energy Conversion and Management. 2015. V. 101. Pp. 410-419.https://doi.org/10.1016/j.enconman.2015.06.025
15. Lisowski E., Rajda J. Analysis of the design of a poppet valve by transitory simulation. Energies. 2019. V. 12. No. 5. 889. https://doi.org/10.3390/en12050889
16. Marchan R. A. Small-scale supersonic combustion chamber with a gas-dynamic ignition system. Combustion Science and Technology. 2011. V. 183. No. 11. Pp. 1236-1265.https://doi.org/10.1080/00102202.2011.589874
17. Marchan R., Oleshchenko A., Vekilov S., Arsenuk M., Bobrov O. 3D printed acoustic igniter of oxygen-kerosene mixtures for aerospace applications. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1-4 July 2019. 14 pp.
18. Raman, G., Srinivasan, K. The powered resonance tube: From Hartmann's discovery to current active flow control applications. Progress in Aerospace Sciences, 2009. V. 45. No. 4 5. Pp. 97-123.https://doi.org/10.1016/j.paerosci.2009.05.001
19. Guillon M. Hydraulic Servo Systems: Analysis and Design. Butterworth, 1969. 462 pp.
20.Habing R. A., Peters M. C. A. M. An experimental method for validating compressor valve vibration theory. Journal of Fluids and Structures. 2006. V. 22. No. 5. Pp. 683-697.https://doi.org/10.1016/j.jfluidstructs.2006.03.003 |
| first_indexed | 2025-12-17T12:05:41Z |
| format | Article |
| fulltext |
19
Авіаційна та ракетно-космічна техніка
Aeronautical and space-rocket engineering
UDK 621.454.2 https://doi.org/10.15407/itm2025.04.019
O. S. CHERNIAVSKYI1, S. I. DOLGOPOLOV2, S. A. SHEVCHENKO3
MODELING OF A CHECK VALVE OPERATION IN THE RECONFIGURABLE
HYDRAULIC FEED SYSTEM OF A LIQUID ROCKET ENGINE
1 Oles Honchar Dnipro National University, 72 Nauky Avenue, Dnipro, 49045 Ukraine; e-mail:
o.s.cherniavskyi@gmail.com
2Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and State Space Agency of
Ukraine, 15 Leshko-Popelya Str., Dnipro, 49005 Ukraine; e-mail: dolmrut@gmail.com
3 Institute of Transport Systems and Technologies of the National Academy of Sciences of Ukraine, 5 Pisarzhev-
sky Str., Dnipro, 49005 Ukraine; e-mail: sergiishevch@gmail.com
Серед різноманіття агрегатів автоматики пневмогідравлічних систем ракетної техніки широке засто-
сування знайшли зворотні клапани. Найчастіше їх використовують у лініях заправлення різних ємностей,
у магістралях наддуву паливних баків ракет-носіїв, де вони запобігають зворотному потоку та проникнен-
ню парів у системи наддуву. У рідинних ракетних двигунах (РРД) зворотні клапани встановлюють у дре-
нажних лініях та в лініях продування інертними газами. Окрему увагу заслуговує використання зворотних
клапанів у гідравлічних системах змінної структури, у яких під час роботи РРД відбувається зміна напря-
мків потоків рідини. Метою роботи є розроблення математичної моделі динамічних процесів у зворотному
клапані, верифікованої за результатами CFD–розрахунків розподілу тиску на поверхні тарілки запірного
органу, та застосування цієї моделі для аналізу перехідних процесів у гідравлічній системі змінної струк-
тури. Для визначення сили дії потоку на тарілку клапана запропоновано підхід у наближенні із зосередже-
ними параметрами, який ґрунтується на балансі витрат робочої рідини у проточній частині клапана. Розг-
лянуто потік у радіальному напрямку на вході клапана, який залежить від ходу тарілки, та потік на пери-
ферії запірного органу, у вузькій щілині між корпусом і тарілкою. Для реалізації цього підходу достатньо
знати геометричні характеристики клапана та значення коефіцієнтів витрати, які приймаються постійни-
ми. Для гідравлічної системи живлення пальним змінної структури, що містить зворотні клапани, розроб-
лено математичну модель низькочастотних динамічних процесів і виконано розрахунки перехідних про-
цесів під час запуску РРД. У процесі запуску двигуна живлення пальним його газогенератора автоматично
перемикається за допомогою зворотних клапанів: живлення від пускового бачка змінюється на живлення
від насоса. Розрахунки перехідних процесів виконано для двох варіантів завдання сили дії потоку на тарі-
лку зворотного клапана: за результатами CFD–аналізу та за наближенням із зосередженими параметрами.
Показано задовільну узгодженість результатів цих розрахунків. Обґрунтовано можливість використання
запропонованого наближення із зосередженими параметрами для визначення сили дії потоку на тарілку
зворотного клапана для побудови математичних моделей динамічних процесів у гідравлічних системах
змінної структури без залучення трудомістких CFD–розрахунків.
Ключові слова: рідинний ракетний двигун, система живлення змінної структури, зворотний кла-
пан, математичне моделювання, CFD-аналіз, сила дії потоку рідини, запуск двигуна.
Among the various automation units used in pneumatic–hydraulic systems of rocket hardware, check
valves are widely employed. They are most commonly used in the filling lines of different tanks and in the pres-
surization lines of launch vehicle propellant tanks, where they prevent reverse flow and the ingress of vapors into
the pressurization system. In liquid rocket engines (LREs), check valves are installed in drainage lines and in inert
gas purging circuits. Particular attention is given to the use of check valves in reconfigurable hydraulic systems,
in which the flow direction changes during the LRE operation. The goal of this study is to develop a mathematical
model of dynamic processes in a check valve, verify it using CFD simulations of the pressure distribution over the
valve poppet surface, and apply it to the analysis of transient processes in a reconfigurable hydraulic system. To
determine the flow force acting on the valve poppet, this paper proposes an approach in the lumped-parameter
approximation based on the flow rate balance of the working fluid in the valve flow passage. The model considers
the radial inflow at the valve inlet, which depends on the poppet travel, and the peripheral flow through the nar-
row clearance between the valve body and the poppet. To implement this approach, it is sufficient to know the
valve geometry and the discharge coefficients, which are assumed to be constant. For a reconfigurable propellant
feed system containing check valves, a mathematical model of low-frequency dynamic processes was developed,
and transient processes during the LRE startup were simulated. During the startup, the propellant feed of the LRE
gas generator is automatically switched by the check valves from the start tank supply to the pump supply. Tran-
sient processes were simulated for the flow force acting on the check valve poppet determined using CFD simula-
tion and the lumped-parameter approximation. A satisfactory agreement between the results of these two ap-
© O. S. Cherniavskyi, S. I. Dolgopolov, S. A. Shevchenko, 2025
Техн. механіка. – 2025. – № 4.
https://doi.org/10.15407/itm2025.04.0
mailto:o.s.cherniavskyi@gmail.com
mailto:dolmrut@gmail.com
mailto:sergiishevch@gmail.com
20
proaches was demonstrated. The possibility of using the proposed lumped-parameter approximation to determine
the flow force acting on the check valve poppet was justified, thus enabling the development of mathematical
models of dynamic processes in reconfigurable hydraulic systems without resorting to computationally expensive
CFD simulations.
Keywords: liquid rocket engine, branched reconfigurable feed system, check valve, mathematical model-
ing, CFD analysis, fluid flow force, engine startup.
Introduction. Among the wide range of automation units in pneumatic–
hydraulic systems of rocket technology, check valves are widely used. They are most
often installed in filling lines of various tanks and in pressurization lines of launch-
vehicle propellant tanks, where they prevent reverse flow and the ingress of vapors
into the pressurization system [1]. In liquid propellant rocket engines (LPREs), check
valves are installed in the lines that deliver liquid and gaseous propellant
components, as well as in drain lines, to ensure reliable isolation between the
oxidizer and fuel circuits. In reusable start LPRE systems of upper stages and
spacecraft, they are placed in inert gas purge lines between engine duty cycles [2].
The use of check valves in variable‑structure hydraulic systems merits special
attention [3]. In such systems the direction of liquid flow changes during LPRE
operation. A representative example is the fuel feed system in staged-combustion
LPRE cycles [4, 5], where ignition of the propellant components is accomplished
using a starting fuel. After engine start and transition to steady operation, the feed
switches over to the main fuel.
Reliable prediction of LPRE start up performance requires validated
mathematical models of the dynamic processes in the engine systems and units. In
staged-combustion LPREs, modeling the flow direction reversal and the dynamics
of check valve operation is of particular importance.
A number of recent papers have addressed check valve operation [6 – 8]. They
consider various aspects: design and improvement of structures, methods to reduce
hydraulic resistance [6], and determination of static and dynamic characteristics [7,
9]. Various approaches have been examined for modeling the dynamics of direct
acting safety valves with a poppet closure member [10 – 13].
To tackle these problems, many researchers employ CFD analysis [6–8, 10–
15]. For example, [6] performed CFD modeling of a poppet type check valve in
ANSYS Fluent to select an adequate turbulence model for accurate prediction of
hydraulic losses. Paper [7] focuses on improving the discharge characteristics of
an adjustable check valve and reducing pressure losses. The dependence of the
valve flow coefficient on the working fluid volumetric flow rate was established.
The authors of [10] highlight two principal CFD approaches for modeling flow
forces in hydraulic valves. The first fixes the position of the moving part (no
motion), used in both steady and unsteady regimes. The second accounts for
motion of the closure member under flow action and is implemented via FSI
modeling (fluid–structure interaction), which tracks fluid–solid interaction. The
first approach is used in [11, 12] to evaluate force distribution over a safety valve
poppet. An example of the FSI approach is [13], where user defined functions
update the poppet position at each time step based on flow and spring forces.
Study [14] describes direct and indirect methods of CFD modeling for a poppet
type safety valve. Boundary conditions were inlet and outlet pressures: in the
direct method the outlet pressure is kept constant, while in the indirect method
both inlet and outlet pressures are varied. The authors of [15] developed a CFD
model of a poppet valve that reproduces its behavior in both steady and transient
regimes. Pressure and flow rate were prescribed for steady runs and fixed pressure
for transients.
Although FSI models reproduce valve dynamics with high fidelity, they are
computationally expensive. In large hydraulic systems where a check valve is only
one of many components their use is constrained. Lumped parameter models are
widely used in such cases. They capture system dynamics with far lower
21
computational cost. A combined approach is the most rational: local hydrodynamic
effects (pressure forces, flow coefficients, etc.) are obtained from CFD, while the
overall system dynamics are computed using a lumped parameter model. This
approach is implemented, for example, in [8], which investigated hydrodynamic
effects leading to undesirable water hammer in pipeline systems. The present work
adopts a similar combined approach.
The objective of this work is to develop a mathematical model of the dynamic
processes in a check valve, verified against CFD results for the pressure
distribution over the poppet surface, and to apply this model to analyze transients
in a variable structure hydraulic system.
Reconfigurable fuel feed hydraulic system. The objects of study are check
valves in the fuel feed hydraulic system of a reusable start LPRE. Ignition of the
propellant components is provided by gas-dynamic igniters [16, 17]. Their operat-
ing principle relies on the Hartmann–Sprenger effect [18]. A fragment of the com-
putational scheme of the variable structure fuel feed system under study is shown
in Fig. 1. The scheme includes feed lines connecting the gas generator, starting
tank, fuel pump, and two check valves. At the initial stage of start, fuel is delivered
to the gas generator from the starting tank. After ignition in the gas generator the
turbopump shaft spins up, the fuel pump builds high pressure, and the check valves
close off the flow from the starting tank and open the pump feed.
The check valves are identical in design and characteristics. Their computa-
tional scheme is given in Fig. 2. To reduce the region of unstable valve behavior
during engine start the radial clearance between the poppet and the body has a
minimal area. This design feature increases the flow force acting on the poppet
from the inlet side even at small clearances between the poppet and the seat. In
addition, the inlet nozzle diameter is smaller than the seat diameter. This must be
accounted for in valve hydrodynamics because the flow turns before entering the
annular clearance between the poppet and the seat.
oggm – oxidizer flow rate to the gas generator; fggm , fbm , fpm – fuel flow rates in the
respective branches; 1p – pressure at the branching node; ggp – gas generator pressure;
Bp – starting tank pressure; Pp – fuel pump discharge pressure
Fig. 1 – Schematic of the gas generator fuel feed system
22
1 – body; 2 – poppet; 3 – spring; 4 – baffle; 5 – seat;
sd – seat diameter; bd – inner body diameter;
pd – poppet diameter; inp , outp – fluid pressures at the valve inlet and outlet
Fig. 2 – Schematic of the check valve
Mathematical model of the dynamics of the reconfigurable feed system.
The low frequency mathematical model of the gas generator feed system under
study (see Fig. 1) comprises: a lumped parameter model of the hydraulic lines, an
equation for the gas generator pressure, and equations of motion for the check
valve closure members. To build the dynamics model of the hydraulic lines, we
used an approach developed for extended, branched pipelines [4, 5]. First, the fre-
quency responses of the different branches of the hydraulic system are obtained by
the impedance method for a distributed parameter system. Next, a lumped parame-
ter model is assembled whose coefficients are chosen so that the frequency re-
sponses of the distributed and lumped models agree within a specified accuracy
over the target frequency band.
Following this approach, the nonlinear lumped parameter model of the dynamics
of the variable structure fuel feed hydraulic system takes the form of equations (1) – (5)
( )fp 2
fp p 1 fp V2 fp= − − +
dm
J p p m
dt
, (1)
( ) 2fb
fb b 1 fb V1 fb= − − +
dm
J p p m
dt
, (2)
1
1 fp fb fgg= + −
dp
C m m m
dt
, (3)
( )fgg 2
fgg 1 gg fgg V3 fgg= − − +
dm
J p p m
dt
, (4)
sggogg
gg
gggggg
gg
fgg
mmm
dt
dp
TR
V
−+=
, (5)
23
gg
gg
1
1gg gg
sgg gg
gggg gg
2
1
+
−
=
+
A p
m
R T
,
here – is the fuel density; oggm – is the oxidizer flow rate supplied to the gas
generator; sggm – is the mass flow rate of combustion products leaving the gas
generator; fp , fb , fgg – are hydraulic resistance coefficients obtained from
hydraulic calculation; fpJ , fbJ , fggJ – are inertial resistance coefficients
determined from the pipeline geometry; V1 , V2 , V3 – are hydraulic resistance
coefficients of the check valves determined by their effective flow areas; ggV is
volume of the combustion chambers in the preburner; ggR is specific gas constants
of the combustion products in the preburner; ggT is temperature of the combustion
products in the preburner; gg is adiabatic indice (ratios of specific heats) of the
combustion products in the preburner; ggA is critical nozzle throat area of the
preburner; 1С is concentrated compliance.
The motion of each check valve poppet is governed by the equation of motion:
2
ms flow sp2
= −
d x
m F F
dt
, (6)
here msm – mass of the moving parts; x – poppet lift; flowF – flow induced force
on the poppet; spF – spring force; dry friction is neglected due to its small
magnitude.
The flow-induced force flow pr imp= +F F F is represented as the sum of a stat-
ic component prF and a momentum (reactive) component impF . Since the momen-
tum component is relatively small compared with the static one, only the static
component is considered in the following analysis; for brevity, it will be referred
to as the flow force.
To evaluate the flow force prF , the pressures at the inlet in p and outlet outp
of the check valve are used. These pressures are computed as functions of the pres-
sure in the adjacent network node and the liquid mass flow rate through the valve:
i,j2
in n i in i,j i,j in i,j= − −
dm
p p m J
dt
, (7)
i,j2
out n j out i,j i,j out i,j= + +
dm
p p m J
dt
, (8)
here n ip and n jp – are the pressures i -th and j -th – at the upstream and
downstream nodes of the hydraulic network, respectively; i,jm – mass flow in the
corresponding pipeline segment; in i,j and out i,j – are hydraulic resistance
coefficients of the upstream and downstream segments; in i,jJ and out i,jJ – are the
corresponding inertial resistance coefficients.
24
Determination of the flow force on the check valve poppet. To determine
the pressure distribution over the poppet surface at different valve openings, we
performed CFD analysis of the working fluid flow. The calculations were carried
out in SOLIDWORKS Flow Simulation using a steady state approach for fixed
poppet positions. The geometric model of the flow passage reproduced the critical
regions: the valve seat, the sealing element, the clearance between the poppet and
the body, and the inlet and outlet ducts.
In the CFD model, the mesh was locally refined in the narrow clearance be-
tween the poppet and the seat and in the zone where the jet forms in the annular
clearance between the poppet and the body. The minimum cell size was 0.005 mm,
and the total number of cells was about 9000000.
The valve walls were stationary with a roughness of 20 μm. The poppet was
modeled as a stationary wall fixed at the specified lift. In all runs, the downstream
pressure behind the poppet 2p was held constant at 0.1 MPa.
The CFD solutions yielded pressure and velocity fields in the computational
domain for a set of poppet lifts and pressure differentials. Using these data, we
obtained the dependence of the flow force prF on the poppet as a function of lift
for different pressure differentials in out = −p p p across the valve. This depend-
ence for 0.10 =p MPa is presented in Fig. 3.
At small lifts the dominant hydraulic resistance is the narrow throttling clear-
ance between the seat edge and the poppet, and the flow force increases almost
linearly with lift. As the valve opens further, the principal throttling element be-
comes the annular clearance between the poppet and the body, which then ac-
counts for the largest portion of the total pressure drop.
1 – CFD; 2 – m in=p p ; 3 – m out=p p ; 4 – in out
m
2
+
=
p p
p ; 5 – mp by equation
(12) 10 0=a and 20 0=a ; 6 – mp by equation (12) 10 20.25=a a and 20 0=a
Fig. 3 – Dependence of the static component of the flow-induced force prF on the
valve poppet lift
s
=
x
x
d
at 0.10 =p MPa
25
An engineering approximation for the static component of the flow force on
the poppet is commonly used [19]:
pr in out eff( )= − F p p A ,
here inp and outp – inlet and outlet pressures of the check valve; effA – effective
area of the poppet.
In rough estimates effA is sometimes taken as a constant equal to the seat area
or the poppet face area, depending on the design. For higher accuracy, however,
effA must be treated as a function of the pressure differential and of the clearance
between the poppet and the seat.
In [20] the flow force is accounted for through a semi empirical lift coefficient
expressed as a function of poppet lift fc , which corrects the difference between the
actual force flowF and the simple pressure difference force acting on the poppet area
flow in out s f( )= − F p p f c .
In [14], the flow-induced force flowF was expressed in the form:
2 2
flow in 1 out 2( / 2) ( / 2)= + + + + F p u p u m ,
where and – coefficients have units of area and represent the effective poppet
area on the inlet and outlet sides, respectively; – coefficient accounts for the flow
velocity in the clearance. These coefficients are obtained from CFD calculations.
To capture the pressure non uniformity more accurately, we apply a split sur-
face approach that accounts separately for the pressures acting on different parts of
the poppet. For the present valve, using the computational scheme in Fig. 2, the
flow force prF can be written in the form:
pr in s m p s out p( )= + − − F p A p A A p A , (9)
where sA – seat area,
2
s s / 4= A d ; pA – poppet face area, 2
p p / 4= A d ; pd –
poppet diameter; mp – pressure in the annular cavity А bounded by the area
( p s−A A ).
If, in (9), one sets m out=p p , the resulting flow-induced force prF becomes
constant, which fails to reflect its variation from the CFD results (see curve 2 in
Fig. 3). A similar outcome occurs for m out=p p or in out
m
2
+
=
p p
p (see curves 3
and 4 in Fig. 3).
To reconcile the force prF computed by equation (9) with the CFD results, the
flow passage of the check valve from inlet to outlet is split into two segments. Ne-
glecting the compliance of cavity A, the momentum equations for these segments
are written as:
( ) 2
in m 10 1 1= + +p p a a m , (10)
( ) 2
m out 20 2 2= + +p p a a m , (11)
26
where 1a , 2a – pressure-loss coefficients determined by the minimum effective
flow areas on the segments
( )
1 2
1 1
1
2
=
a
A
,
( )
2 2
2 2
1
2
=
a
A
;
1A , 1 – are the area and the discharge coefficient of the annular clearance be-
tween the poppet and the seat
1 s= A d x ;
2A , 2 – are the area and the discharge coefficient of the radial clearance be-
tween the body and the poppet
2 2
2 b p( ) / 4= −A d d ,
bd – is the inner body diameter; 10a , 20a – additional pressure-loss coefficients
accounting for turning, local, and friction losses (unlike 1a and 2a ); 1m , 2m –
mass flows in segments 1 and 2.
Assuming 1 2=m m , (10) and (11) yield an expression for the pressure in cavity
А in terms of mp :
( ) ( )
( ) ( )
in 20 out 102 2
2 2 1 1
m
10 202 2
1 1 2 2
1 1
2 2
1 1
2 2
+ + +
=
+ + +
p a p a
A A
p
a a
A A
. (12)
Using mp from equation (12) to compute prF with 10 0=a and 20 0=a pro-
duces the curve in Fig. 3 (curve 5), which reproduces the qualitative increase of
prF with poppet lift observed in the CFD results. Including additional pressure
losses on the first segment 10 0a yields satisfactory quantitative agreement be-
tween the predictions of equations (9) and (12) and the CFD results; this is illus-
trated by curve 6 in Fig. 3 (obtained for representative values of 10 20.25=a a rela-
tive to the segment-loss terms).
Satisfactory agreement for prF was also obtained for other pressure differen-
tials across the check valve (see Fig. 4).
1 – CFD; 2 – mp by equation (12) for 10 20.25=a a and 20 0=a
Fig. 4 – Dependence of the flow force prF on poppet lift
s
=
x
x
d
27
4. Results of transient simulations.For the transient simulations of the LPRE
gas generator feed system, the boundary conditions were: a constant pressure in
the starting tank Bp , the oxidizer flow rate to the gas generator oggm , and the fuel
pump discharge pressure pp . The increases in oxidizer flow rate and in pump dis-
charge pressure were prescribed as linear functions of time, which reflects the
physics of start up: a progressively increasing oxidizer supply and a gradual pres-
sure rise in the pump line as the turbine spins up.
Transient calculations for the variable structure fuel feed system during engine
start were performed using the mathematical model (1) – (8). In this model, the
flow induced force acting on the check valve poppet, prF , was either taken from
CFD analysis or approximated by the lumped parameter method using equations
(9), (12).
At the initial stage of start, fuel is supplied to the gas generator only from the
starting tank and reaches its maximum values. This occurs because there is no
counter pressure in the gas generator. After ignition in the gas generator and tur-
bine spin up, the pressure behind the pump begins to rise. When the pump dis-
charge pressure reaches a certain level, the fuel feed switches to the pump. This
switching is automatic and is performed by check valves 1 and 2.
a
b
a – time window 0–1.2 s; b – time window 0.75–0.83 s; solid lines – flow
force prF from CFD; dashed lines – flow force prF from equations (9), (12)
Fig. 5 – Evolution of check valve 1 parameters during LPRE start up
28
Figures 5 and 6 show the operating characteristics of the check valves during
start up: time histories of the relative fuel mass flows ( fpm , fbm ), the relative inlet
pressures ( in1p , in2p ) and outlet pressures ( out1p , out2p ) of the check valves, and
the relative effective flow areas ( 1A , 2A ) of the valves (normalized by their maxi-
mum values). Relative flow values were defined as the ratio of the current fuel
flow to the maximum fuel flow in the gas generator. The reference pressure level
was the gas generator pressure at the nominal operating point.
Analysis of Figs. 5 and 6 indicates that closing of valve 1 and opening of
valve 2 begin simultaneously at 0.76 s. This is accompanied by a decrease of the
flow through valve 1 and an increase through valve 2. The opening of valve 2 un-
der a steadily rising pump discharge pressure proceeds monotonically, without
poppet oscillations (see Fig.
6). In contrast, the closing
of valve 1 under the action
of backpressure 1p is non
monotonic and is accompa-
nied by oscillations of the
poppet lift (see Fig. 5). This
behavior of valve 1 lift is
caused by the fact that par-
tial throttling and flow re-
duction through the valve
lowers the pressure at 1p .
The drop can be sufficient
to drive the poppet toward
reopening. For valve 1
these conditions occur at
0.776 s, 0.786 s, and 0.800
s. Fast chattering of the
valve 1 poppet produces
local disturbances and tran-
sients not only in the
branch of valve 1 but in the
entire hydraulic system.
The transient simula-
tion results obtained using
CFD based flow forces and
those using the lumped pa-
rameter approximation
agree well overall. A dif-
ference is observed for the
force prF on the poppet of valve 1, which leads to different actuation times. The
largest difference in the onset time of actuation, corresponding to complete closure
of the valve, does not exceed 0.0021 s.
а
b
а – time window 0–1.2 s; b – time window 0.75–0.83 s;
solid lines – flow force prF from CFD; dashed lines –
flow force prF from equations (9), (12)
Fig. 6 – Evolution of check valve 2 parameters during
LPRE start up
29
The proposed lumped parameter method for approximating the flow induced
forces on the poppets of check valves enables the development of mathematical
models of variable structure hydraulic systems and transient analyses with suffi-
cient accuracy without resorting to costly CFD calculation.
Conclusions.
1. An approach is proposed for determining the flow induced force on a check
valve poppet using a lumped parameter approximation based on a balance of the
working fluid flow rates in the valve passage. The model considers a radial inflow
at the valve inlet, which depends on poppet lift, and the peripheral flow in the nar-
row clearance between the body and the poppet. To apply this approach, it is suffi-
cient to know the geometric parameters of the valve and to use discharge coeffi-
cients taken as constants.
2. For a variable structure fuel feed hydraulic system containing check valves,
a low frequency mathematical model of the dynamic processes was developed, and
transient calculations were performed for LPRE start up. During start up, the gas
generator fuel feed automatically switches from the starting tank to the pump via
the action of check valves. Transients were computed for two variants of the flow
force model on the check valve poppet: one based on CFD analysis and one based
on the lumped parameter approximation. The two approaches showed satisfactory
agreement.
3. The feasibility of using the proposed lumped parameter approximation for
the flow induced force on a check valve poppet has been substantiated for con-
structing mathematical models of dynamic processes in variable structure hydrau-
lic systems without the need for labor intensive CFD calculations.
1. Sutton G. P., Biblarz O. Rocket Propulsion Elements. 9-te ed. Hoboken: John Wiley & Sons, 2017. 800 p.
2. Huze, D. K., Huang D. H. Design of Liquid Propellant Rocket Engines. NASA SP-125. Washington: NASA,
1971. 472 p.
3. Cherniavskyi O., Shevchenko S., Dolgopolov S. Mathematical modeling of the dynamic processes during check
valve operation in the branched reconfigurable feed system of a liquid rocket engine. Aerospace engineering
and technology. 2025. No. 4, special issue 2, (206). P. 93–101.
4. Pylypenko O., Dolgopolov S., Nikolayev O., Khoriak N., Kvasha Yu., Bashliy I. Determination of the thrust
spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation.
2022. Vol. 18, № 6. P. 97–112.
5. Koptilyy D., Marchan R., Dolgopolov S., Nikolayev O. Mathematical modeling of transient processes during
start-up of main liquid propellant engine under hot test conditions. Proceedings of the 8th European Confer-
ence on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1–4 July. 2019. 15 p.
6. Kobielski M. J., Skarka W., Skarka M. Comparison of pressure-loss evaluation fidelity in turbulent energy
dissipation models of poppet check valves using computational fluid dynamics (CFD) software. Technical
Sciences. 2024. Vol. 27. Р. 19–31. https://doi.org/10.31648/ts.9732
7. Filo G., Lisowski E., Rajda J. Design and Flow Analysis of an Adjustable Check Valve by Means of CFD
Method. Energies. 2021. Vol, 14. No. 8. P.2237. https://doi.org/10.3390/en14082237
8. Klas R., Habán V., Rudolf P. Analysis of in-line check valve with respect to the pipeline dynamics. EPJ Web of
Conferences. 2017. Vol. 143. P. 02051. https://doi.org/10.1051/epjconf/201714302051
9. Lang S. A review of check valves in unsteady flow. Proceedings of the 2024 ASME Pressure Vessels & Piping
Conference, V003T04A001.
10. Domagała M., Fabis-Domagała J. A Review of the CFD Method in the Modeling of Flow Forces. Energies.
2023. Vol 16, No. 16. P. 6059. https://doi.org/10.3390/en16166059
11. Pusztai T., Siménfalvi Z. CFD analysis on a direct spring-loaded safety valve to determine flow forces. Pollack
Periodica. 2021. Vol.16. No.1. Pp. 109–113. https://doi.org/10.1556/606.2020.00122
12. Zong C., Zheng F., Chen D., Dempster W., Song X. CFD Analysis of the Flow Force Exerted On the Disc of a
Direct-Operated Pressure Safety Valve in Energy System. Journal of Pressure Vessel Technology. 2020.
Vol.142, No.1. P.011702. https://doi.org/10.1115/1.4045131
13. Finesso R., Rundo M. Numerical and experimental investigation on a conical poppet relief valve with flow
force compensation. International Journal of Fluid Power. 2017. Vol. 18, No. 2. Pp. 111–122.
https://doi.org/10.1080/14399776.2017.1296740
https://doi.org/10.31648/ts.9732
https://doi.org/10.3390/en14082237
https://doi.org/10.1051/epjconf/201714302051
https://doi.org/10.3390/en16166059
https://doi.org/10.1556/606.2020.00122
https://doi.org/10.1115/1.4045131
https://doi.org/10.1080/14399776.2017.1296740
30
14. Wu D., L, S., Wu P. CFD simulation of flow-pressure characteristics of a pressure control valve for automotive
fuel supply system. Energy Conversion and Management. 2015. Vol. 101. P. 410–419.
https://doi.org/10.1016/j.enconman.2015.06.025
15. Lisowski E., Rajda J. Analysis of the Design of a Poppet Valve by Transitory Simulation. Energies. 2019.
Vol. 12, No. 5. P. 889. https://doi.org/10.3390/en12050889
16. Marchan R. A. Small-scale supersonic combustion chamber with a gas-dynamic ignition system. Combustion
Science and Technology. 2011. Vol. 183, № 11. P. 1236–1265. https://doi.org/10.1080/00102202.2011.589874
17. Marchan R., Oleshchenko A., Vekilov S., Arsenuk M., Bobrov O. 3D printed acoustic igniter of oxygen-
kerosene mixtures for aerospace applications. Proceedings of the 8th European Conference on Aeronautics and
Space Sciences (EUCASS), Madrid, Spain, 1–4 July. 2019. 14 р.
18. Raman G., Srinivasan K. The powered resonance tube: From Hartmann's discovery to current active flow
control applications. Progress in Aerospace Sciences. 2009. Vol. 45, No. 4-5. P. 97–123.
https://doi.org/10.1016/j.paerosci.2009.05.001
19. Guillon M. Hydraulic servo systems: Analysis and design. Butterworth, 1969. 462 p.
20.Habing R. A., Peters M.C.A.M. An experimental method for validating compressor valve vibration theory. Journal
of Fluids and Structures. 2006. Vol. 22, No. 5. P. 683–697. https://doi.org/10.1016/j.jfluidstructs.2006.03.003
Received on October 22, 2025,
in final form on December 1, 2025
https://doi.org/10.1016/j.enconman.2015.06.025
https://doi.org/10.3390/en12050889
https://doi.org/10.1080/00102202.2011.589874
https://doi.org/10.1016/j.paerosci.2009.05.001
https://doi.org/10.1016/j.jfluidstructs.2006.03.003
|
| id | oai:ojs2.journal-itm.dp.ua:article-151 |
| institution | Technical Mechanics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-14T01:00:50Z |
| publishDate | 2025 |
| publisher | текст 3 |
| record_format | ojs |
| resource_txt_mv | journal-itmdpua/e2/cc2ee718b21df1f9924ce7ffc29aaee2.pdf |
| spelling | oai:ojs2.journal-itm.dp.ua:article-1512026-07-13T20:26:18Z MODELING OF THE CHECK VALVE OPERATION IN THE RECONFIGURABLE HYDRAULIC FEED SYSTEM OF A LIQUID ROCKET ENGINE МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ CHERNIAVSKYI, O. S. DOLGOPOLOV, S. I. SHEVCHENKO, S. A. рідинний ракетний двигун, система живлення змінної структури, зворотний клапан, математичне моделювання, CFD-аналіз, сила дії потоку рідини, запуск двигуна. liquid rocket engine, branched reconfigurable feed system, check valve, mathematical modeling, CFD analysis, fluid flow force, engine startup. DOI: https://doi.org/10.15407/itm2025.04.019 Among the various automation units used in pneumatic–hydraulic systems of rocket hardware, check valves are widely employed. They are most commonly used in the filling lines of different tanks and in the pressurization lines of launch vehicle propellant tanks, where they prevent reverse flow and the ingress of vapors into the pressurization system. In liquid rocket engines (LREs), check valves are installed in drainage lines and in inert gas purging circuits. Particular attention is given to the use of check valves in reconfigurable hydraulic systems, in which the flow direction changes during the LRE operation. The goal of this study is to develop a mathematical model of dynamic processes in a check valve, verify it using CFD simulations of the pressure distribution over the valve poppet surface, and apply it to the analysis of transient processes in a reconfigurable hydraulic system. To determine the flow force acting on the valve poppet, this paper proposes an approach in the lumped-parameter approximation based on the flow rate balance of the working fluid in the valve flow passage. The model considers the radial inflow at the valve inlet, which depends on the poppet travel, and the peripheral flow through the narrow clearance between the valve body and the poppet. To implement this approach, it is sufficient to know the valve geometry and the discharge coefficients, which are assumed to be constant. For a reconfigurable propellant feed system containing check valves, a mathematical model of low-frequency dynamic processes was developed, and transient processes during the LRE startup were simulated. During the startup, the propellant feed of the LRE gas generator is automatically switched by the check valves from the start tank supply to the pump supply. Transient processes were simulated for the flow force acting on the check valve poppet determined using CFD simulation and the lumped-parameter approximation. A satisfactory agreement between the results of these two approaches was demonstrated. The possibility of using the proposed lumped-parameter approximation to determine the flow force acting on the check valve poppet was justified, thus enabling the development of mathematical models of dynamic processes in reconfigurable hydraulic systems without resorting to computationally expensive CFD simulations. REFERENCES 1. Sutton G. P., Biblarz O. Rocket Propulsion Elements. 9th ed. Hoboken: John Wiley & Sons, 2017. 800 pp. 2. Huze D. K., Huang D. H. Design of Liquid Propellant Rocket Engines. NASA SP 125. Washington: NASA, 1971. 472 pp. 3. Cherniavskyi O. S., Chevchenko S. A., Dolgopolov S. I. Mathematical modeling of the dynamic processes during check valve operation in the branched reconfigurable system of a liquid rocket engine. Aerospace Technic and Technology. 2025. No. 4. Special Iss. 2. Pp. 93-101. 4. Pylypenko O., Dolgopolov S., Nikolayev O., Khoriak N., Kvasha Yu., Bashliy I. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. V. 18. No. 6. Pp. 97-112. 5. Koptilyy D., Marchan R., Dolgopolov S., Nikolayev O. Mathematical modeling of transient processes during start-up of main liquid propellant engine under hot test conditions. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1-4 July 2019. 15 pp. 6. Kobielski M. J., Skarka W., Skarka M. Comparison of pressure loss evaluation fidelity in turbulent energy dissipation models of poppet check valves using computational fluid dynamics (CFD) software. Technical Sciences, 2024. V. 27. Pp. 19-31. https://doi.org/10.31648/ts.9732 7. Filo G., Lisowski E., Rajda J. Design and flow analysis of an adjustable check valve by means of CFD method. Energies. 2021. V. 14. No. 8. 2237. https://doi.org/10.3390/en14082237 8. Klas R., Habán V., Rudolf P. Analysis of in line check valve with respect to the pipeline dynamics. EPJ Web of Conferences. 2017. V. 143. 02051. https://doi.org/10.1051/epjconf/201714302051 9. Lang S. A review of check valves in unsteady flow. Proceedings of the 2024 ASME Pressure Vessels & Piping Conference, V003T04A001. 10. Domagała M., Fabis Domagała J. A. Review of the CFD method in the modeling of flow forces. Energies. 2023. V. 16. No. 16. 6059. https://doi.org/10.3390/en16166059 11. Pusztai T., Siménfalvi Z. CFD analysis on a direct spring loaded safety valve to determine flow forces. Pollack Periodica. 2021. V. 16. No. 1. Pp. 109-113. https://doi.org/10.1556/606.2020.00122 12. Zong C., Zheng F., Chen D., Dempster W., Song X. CFD analysis of the flow force exerted on the disc of a direct operated pressure safety valve in energy system. Journal of Pressure Vessel Technology, 2020. V. 142. No. 1. 011702. https://doi.org/10.1115/1.4045131 13. Finesso R., Rundo M. Numerical and experimental investigation on a conical poppet relief valve with flow force compensation. International Journal of Fluid Power. 2017. V. 18. No. Pp. 111-122.https://doi.org/10.1080/14399776.2017.1296740 14. Wu D., Li S., Wu P. CFD simulation of flow pressure characteristics of a pressure control valve for automotive fuel supply system. Energy Conversion and Management. 2015. V. 101. Pp. 410-419.https://doi.org/10.1016/j.enconman.2015.06.025 15. Lisowski E., Rajda J. Analysis of the design of a poppet valve by transitory simulation. Energies. 2019. V. 12. No. 5. 889. https://doi.org/10.3390/en12050889 16. Marchan R. A. Small-scale supersonic combustion chamber with a gas-dynamic ignition system. Combustion Science and Technology. 2011. V. 183. No. 11. Pp. 1236-1265.https://doi.org/10.1080/00102202.2011.589874 17. Marchan R., Oleshchenko A., Vekilov S., Arsenuk M., Bobrov O. 3D printed acoustic igniter of oxygen-kerosene mixtures for aerospace applications. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1-4 July 2019. 14 pp. 18. Raman, G., Srinivasan, K. The powered resonance tube: From Hartmann's discovery to current active flow control applications. Progress in Aerospace Sciences, 2009. V. 45. No. 4 5. Pp. 97-123.https://doi.org/10.1016/j.paerosci.2009.05.001 19. Guillon M. Hydraulic Servo Systems: Analysis and Design. Butterworth, 1969. 462 pp. 20.Habing R. A., Peters M. C. A. M. An experimental method for validating compressor valve vibration theory. Journal of Fluids and Structures. 2006. V. 22. No. 5. Pp. 683-697.https://doi.org/10.1016/j.jfluidstructs.2006.03.003 DOI: https://doi.org/10.15407/itm2025.04.019 Серед різноманіття агрегатів автоматики пневмогідравлічних систем ракетної техніки широке застосування знайшли зворотні клапани. Найчастіше їх використовують у лініях заправлення різних ємностей, у магістралях наддуву паливних баків ракет-носіїв, де вони запобігають зворотному потоку та проникненню парів у системи наддуву. У рідинних ракетних двигунах (РРД) зворотні клапани встановлюють у дренажних лініях та в лініях продування інертними газами. Окрему увагу заслуговує використання зворотних клапанів у гідравлічних системах змінної структури, у яких під час роботи РРД відбувається зміна напрямків потоків рідини. Метою роботи є розроблення математичної моделі динамічних процесів у зворотному клапані, верифікованої за результатами CFD–розрахунків розподілу тиску на поверхні тарілки запірного органу, та застосування цієї моделі для аналізу перехідних процесів у гідравлічній системі змінної структури. Для визначення сили дії потоку на тарілку клапана запропоновано підхід у наближенні із зосередженими параметрами, який ґрунтується на балансі витрат робочої рідини у проточній частині клапана. Розглянуто потік у радіальному напрямку на вході клапана, який залежить від ходу тарілки, та потік на периферії запірного органу, у вузькій щілині між корпусом і тарілкою. Для реалізації цього підходу достатньо знати геометричні характеристики клапана та значення коефіцієнтів витрати, які приймаються постійними. Для гідравлічної системи живлення пальним змінної структури, що містить зворотні клапани, розроблено математичну модель низькочастотних динамічних процесів і виконано розрахунки перехідних процесів під час запуску РРД. У процесі запуску двигуна живлення пальним його газогенератора автоматично перемикається за допомогою зворотних клапанів: живлення від пускового бачка змінюється на живлення від насоса. Розрахунки перехідних процесів виконано для двох варіантів завдання сили дії потоку на тарілку зворотного клапана: за результатами CFD–аналізу та за наближенням із зосередженими параметрами. Показано задовільну узгодженість результатів цих розрахунків. Обґрунтовано можливість використання запропонованого наближення із зосередженими параметрами для визначення сили дії потоку на тарілку зворотного клапана для побудови математичних моделей динамічних процесів у гідравлічних системах змінної структури без залучення трудомістких CFD–розрахунків. ПОСИЛАННЯ 1. Sutton G. P., Biblarz O. Rocket Propulsion Elements. 9‑te ed. Hoboken: John Wiley & Sons, 2017. 800 p. 2. Huze, D. K., Huang D. H. Design of Liquid Propellant Rocket Engines. NASA SP‑125. Washington: NASA, 1971. 472 p. 3. Чернявський О. С., Шевченко С. А., Долгополов С. І. Математичне моделювання динамічних процесів під час роботи зворотного клапана в системі живлення змінної структури в рідинному ракетному двигуні. Авіаційно-космічна техніка і технологія. 2025. № 4 спецвипуск 2 (206) С. 93–101. 4. Pylypenko O., Dolgopolov S., Nikolayev O., Khoriak N., Kvasha Yu., Bashliy I. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. Vol. 18, № 6. P. 97–112. 5. Koptilyy D., Marchan R., Dolgopolov S., Nikolayev O. Mathematical modeling of transient processes during start-up of main liquid propellant engine under hot test conditions. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1–4 July. 2019. 15 p. 6. Kobielski M. J., Skarka W., Skarka M. Comparison of pressure‑loss evaluation fidelity in turbulent energy dissipation models of poppet check valves using computational fluid dynamics (CFD) software. Technical Sciences. 2024. Vol. 27. Р. 19–31. https://doi.org/10.31648/ts.9732 7. Filo G., Lisowski E., Rajda J. Design and Flow Analysis of an Adjustable Check Valve by Means of CFD Method. Energies. 2021. Vol, 14. No. 8. P.2237. https://doi.org/10.3390/en14082237 8. Klas R., Habán V., Rudolf P. Analysis of in‑line check valve with respect to the pipeline dynamics. EPJ Web of Conferences. 2017. Vol. 143. P. 02051. https://doi.org/10.1051/epjconf/201714302051 9. Lang S. A review of check valves in unsteady flow. Proceedings of the 2024 ASME Pressure Vessels & Piping Conference, V003T04A001. 10. Domagała M., Fabis‑Domagała J. A Review of the CFD Method in the Modeling of Flow Forces. Energies. 2023. Vol 16, No. 16. P. 6059. https://doi.org/10.3390/en16166059 11. Pusztai T., Siménfalvi Z. CFD analysis on a direct spring‑loaded safety valve to determine flow forces. Pollack Periodica. 2021. Vol.16. No.1. Pp. 109–113. https://doi.org/10.1556/606.2020.00122 12. Zong C., Zheng F., Chen D., Dempster W., Song X. CFD Analysis of the Flow Force Exerted On the Disc of a Direct‑Operated Pressure Safety Valve in Energy System. Journal of Pressure Vessel Technology. 2020. Vol.142, No.1. P.011702. https://doi.org/10.1115/1.4045131 13. Finesso R., Rundo M. Numerical and experimental investigation on a conical poppet relief valve with flow force compensation. International Journal of Fluid Power. 2017. Vol. 18, No. 2. Pp. 111–122. https://doi.org/10.1080/14399776.2017.1296740 14. Wu D., L, S., Wu P. CFD simulation of flow‑pressure characteristics of a pressure control valve for automotive fuel supply system. Energy Conversion and Management. 2015. Vol. 101. P. 410–419. https://doi.org/10.1016/j.enconman.2015.06.025 15. Lisowski E., Rajda J. Analysis of the Design of a Poppet Valve by Transitory Simulation. Energies. 2019. Vol. 12, No. 5. P. 889. https://doi.org/10.3390/en12050889 16. Marchan R. A. Small-scale supersonic combustion chamber with a gas-dynamic ignition system. Combustion Science and Technology. 2011. Vol. 183, № 11. P. 1236–1265. https://doi.org/10.1080/00102202.2011.589874 17. Marchan R., Oleshchenko A., Vekilov S., Arsenuk M., Bobrov O. 3D printed acoustic igniter of oxygen-kerosene mixtures for aerospace applications. Proceedings of the 8th European Conference on Aeronautics and Space Sciences (EUCASS), Madrid, Spain, 1–4 July. 2019. 14 р. 18. Raman G., Srinivasan K. The powered resonance tube: From Hartmann's discovery to current active flow control applications. Progress in Aerospace Sciences. 2009. Vol. 45, No. 4‑5. P. 97–123. https://doi.org/10.1016/j.paerosci.2009.05.001 19. Guillon M. Hydraulic servo systems: Analysis and design. Butterworth, 1969. 462 p. 20.Habing R. A., Peters M.C.A.M. An experimental method for validating compressor valve vibration theory. Journal of Fluids and Structures. 2006. Vol. 22, No. 5. P. 683–697. https://doi.org/10.1016/j.jfluidstructs.2006.03.003 текст 3 2025-12-11 Article Article application/pdf https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/151 Technical Mechanics; No. 4 (2025): Technical Mechanics; 19-30 Институт технической механики Национальной академии наук Украины и Государственного космического агентства Украины; № 4 (2025): Technical Mechanics; 19-30 ТЕХНІЧНА МЕХАНІКА; № 4 (2025): ТЕХНІЧНА МЕХАНІКА; 19-30 en https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/151/61 Copyright (c) 2025 Technical Mechanics |
| spellingShingle | рідинний ракетний двигун система живлення змінної структури зворотний клапан математичне моделювання CFD-аналіз сила дії потоку рідини запуск двигуна. CHERNIAVSKYI, O. S. DOLGOPOLOV, S. I. SHEVCHENKO, S. A. МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ |
| title | МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ |
| title_alt | MODELING OF THE CHECK VALVE OPERATION IN THE RECONFIGURABLE HYDRAULIC FEED SYSTEM OF A LIQUID ROCKET ENGINE |
| title_full | МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ |
| title_fullStr | МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ |
| title_full_unstemmed | МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ |
| title_short | МОДЕЛЮВАННЯ РОБОТИ ЗВОРОТНОГО КЛАПАНА В ГІДРАВЛІЧНІЙ СИСТЕМІ ЖИВЛЕННЯ РІДИННОГО РАКЕТНОГО ДВИГУНА ЗМІННОЇ СТРУКТУРИ |
| title_sort | моделювання роботи зворотного клапана в гідравлічній системі живлення рідинного ракетного двигуна змінної структури |
| topic | рідинний ракетний двигун система живлення змінної структури зворотний клапан математичне моделювання CFD-аналіз сила дії потоку рідини запуск двигуна. |
| topic_facet | рідинний ракетний двигун система живлення змінної структури зворотний клапан математичне моделювання CFD-аналіз сила дії потоку рідини запуск двигуна. liquid rocket engine branched reconfigurable feed system check valve mathematical modeling CFD analysis fluid flow force engine startup. |
| url | https://journal-itm.dp.ua/ojs/index.php/ITM_j1/article/view/151 |
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