Scipedia

Salvetti, M.

Singh, J.

Capellini, K.

Mariotti, A.

Celi, S.

Effect of the Carotid Geometry on the Onset of Atherosclerotic Plaques

Glazunov, Mikhail

Revell, A.

Schlatter, P.

Rezaeiravesh, Saleh

Comparison between linear and non-linear multifidelity models for turbulent flow problems

Sanmarti, O.

Vera, J.

Torras, S.

Pérez-Segarra, C.

The 9th European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS Congress 2024
3–7 June 2024, Lisboa, Portugal
MATHEMATICAL AND NUMERICAL APPROACH OF
ENCAPSULATED PHASE CHANGE MATERIAL IN
STRUCTURED THERMOCLINE SYSTEMS
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra∗
Heat and Mass Transfer Technological Center (CTTC), Technical University of Catalonia -
BarcelonaTech (UPC), Carrer de Colom 11, 08222 Terrassa (Barcelona), Spain
e-mail: cdavid.perez.segarra@upc.edu
Key words: Unsteady one-dimensional model, Finite volume method, Encapsulated phase
change material, Structured thermocline, Thermal energy storage
Summary. An unsteady one-dimensional computational model has been developed to inves-
tigate the integration of encapsulated phase change materials in a structured thermal energy
storage system. The model has been validated against experimental results available in the lit-
erature. The study examines three different phase change materials (NaNO3, KOH, and H380),
focusing on how the accumulated energy varies with the thickness of the phase change material
layer and the proximity of the melting point to the system’s operating temperatures.
1 INTRODUCTION
The intermittent nature of renewable energies may delay their rapid growth. To overcome
this challenge, novel energy storage methods or enhancements to existing ones are required.
Thermal energy storage has been extensively studied as a potential solution to this issue. These
systems can be used in conjunction with concentrated solar power, where molten salt is used as
a heat transfer fluid. However, molten salt is the most expensive component of these systems.
Therefore, in recent years, alternatives have been studied where only a single tank is needed,
and a solid filler and encapsulated phase change material (EPCM) is used to substitute a part
of the fluid. A promising alternative that has emerged in recent years is the use of structured
solid filler materials made from waste materials such as ceramics or concrete [1].
A promising approach to advance the development of structured thermoclines is to integrate
EPCM into this innovative type of system [2]. The objective of this study is to develop a
mathematical and numerical model that couples the EPCM in both spheres and tubes with
structured thermoclines. The model involves a one-dimensional discretization of the filler ma-
terial structure, with another one-dimensional discretization of spheres or tubes applied in the
EPCM regions. The energy equation is solved using an enthalpy method to account for phase
change. Unlike other one-dimensional EPCM models in the literature [3], an innovative aspect
of this model lies in its capability to account for volume changes of the phase change material
inside the spheres or tubes during the transition from solid to liquid states. This is achieved
by integrating the mass equation, leading to changes in the apparent diameter of the EPCM
domain while maintaining a constant diameter of the spheres or tubes.
This study is innovative in its aspiration to integrate an existing technology (EPCM) into
a novel thermal energy storage system (structured thermocline). After the model is validated
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
against experimental data, it is used to obtain the accumulated energy for three different mate-
rials (NaNO3, KOH, H380) in function of the thickness of the phase change material layer and
the proximity of the melting point to the system’s operating temperatures.
2 METHODOLOGY
2.1 Case geometry
The thermal energy storage (TES) system under study is a structured type that incorporates
encapsulated phase change material in tube format, with an outer diameter of 33.7mm, a thick-
ness of 2mm, and a void fraction between the molten salt and the tubes of 0.47. The geometrical
design includes a solid filler material composed of waste ceramic products. The ceramic matrix
has perforations through which molten salt flows, facilitating thermal energy storage. The TES
system is depicted in Figure 1, showcasing two configurations: one with the EPCM positioned
at the bottom and the other with the EPCM at the top. The structure includes a buffer region
at the top and a sump region at the bottom, which zones are used to extract or inject the fluid
and give some thermal inertia to the system.
Thot
Tcold
Thot
Tcold
EPCM
EPCM
Figure 1: Thermocline structured geometry representation with EPCM positioned at the bottom (left)
and top (right). Figure extracted from [4].
Regarding the two studied cycles, during the charging process, molten salt flows from the
top to the bottom of the tank until the temperature at the bottom reaches a predetermined
cutoff temperature. Conversely, the flow direction reverses during the discharging process, and
molten salt is discharged from the bottom to the top until the top temperature achieves the
cutoff temperature. Table 1 shows the main geometrical and operational parameters used in the
simulations.
2
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
Table 1: Main geometrical and operational parameters considered in this study.
Parameter Acronym Value
Tank diameter Dtank 45 m
Height of the sump region hbot 1 m
Height of the tank bed hbed 11.5 m
Height of the buffer region (at Tcold) htop 0.5 m
Channel diameter d 0.01 m
Distance between channels Ltp 0.02 m
Channels arrangement Arr. 30°C
Hot temperature Thot 385°C
Cold temperature Tcold 290°C
Cutoff temperature difference ∆Tco 15°C
Overall tank mass flow charge ṁcall 1635 kg/s
Overall tank mass flow discharge ṁdall 837 kg/s
2.2 Governing equations
The molten salt and filler material are modelled using a one-dimensional discretization along
the axial direction, divided intoN control volumes (CVs). The equations presented by Schumann
in 1929 [5] are solved for a porous solid in contact with a fluid. These equations are enhanced by
modifying the wetted area to consider the convection with all the tubes instead of the traditional
solid particles. The energy conservation equations for molten salt and solid filler material are
given in Equations (1) and (2). The encapsulated phase change material is modelled with a
radial discretization for each of the N control volumes, using M CVs in the radial direction.
The energy conservation equation includes the latent heat by relating enthalpy and temperature,
as shown in Equation (3). Convective terms are applied as boundary conditions. Special energy
balances are applied for the buffer and sump regions. The governing equations are as follows:
ϵρfcp,f
(
∂Tf
∂t
+ vz,f
∂Tf
∂z
)
= α(Ts − Tf )aw +
∂
∂z
(
λf
∂Tf
∂z
)
− q̇f,lost (1)
(1− ϵ)ρscp,s
(
∂Ts
∂t
)
= α(Tf − Ts)aw +
∂
∂z
(
λs
∂Ts
∂z
)
− q̇s,lost (2)
ρpcm
(
∂hpcm
∂t
)
=
∂
∂r
(
λpcm
∂Tpcm
∂r
)
(3)
In these equations, ρ, λ, and cp are the density, thermal conductivity, and specific heat,
respectively, α is the local heat transfer coefficient, and ϵ the void fraction, which is the molten
salt volume relative to the total volume. aw is the wetted area per unit volume, vz,f the velocity
of the fluid flow, and q̇lost represents the heat losses per unit volume to the ambient. The
subindex f refers to the fluid, and the subindex s refers to the solid. For the case inside the
channels in the structured thermocline, the empirical correlation for Nusselt is obtained following
Taborek et al.’s correlations [6]. In the case of the EPCM, a correlation for tubes in cross-flow
is used, following the work of Zukauskas [7].
3
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
2.3 Thermophysical properties
The properties of the molten salt, specifically Solar Salt, are taken from Zavoico et al. [8].
The solid filler material has a density of 2785 kg/m3, a thermal conductivity of 0.57 W/mK,
and a specific heat capacity of 1148 J/kgK. Finally, Table 2 presents the properties of the PCMs
examined in this study.
Table 2: Thermophysical properties of the used PCM.
Property NaNO3 [9] KOH [10] H380 [11]
Density (kg/m3) 2075 2040 2050
Specific heat (kJ/kgK) 1444 1340 1530
Latent heat (J/kg) 1.75E5 1.34E5 2.25E5
Thermal conductivity (W/mK) 0.5 0.5 0.56
Melting Point (°C) 306 380 382
3 CODE VERIFICATION AND VALIDATION
For the verification of the code and validation of the mathematical formulation, an experi-
mental setup is simulated to compare the computational results with the ones obtained in the
experiments. The experimental setup, presented by Keilany et al. [12], comprises a thermal
energy storage system with several key parameters. The storage tank has a diameter of 1.2 me-
ters and a filler height of 2.53 meters. The system starts at an initial temperature of 312°C, the
maximum temperature achieved during the experiment, indicating the upper limit of the tem-
perature range. The minimum temperature observed in the system is 226°C, marking the lower
limit during the cycle. The experiment simulates a discharge cycle, extracting thermal energy
from the storage material. The heat transfer fluid used in the system is Jarytherm Oil, with a
mass flow rate of 0.555 kg/s. The EPCM used is sodium nitrate (NaNO3), configured as a tube
to provide a specific surface area for heat exchange. The filler material in the tank is Alumina
(Packed Bed distribution), which provides structural support and thermal conductivity.
Figure 2 compares the experimental results and the computational results derived from the
model proposed in this study. The temperature profiles shift from left to right, starting from
a uniform temperature of 312 ºC. The temperature profiles exhibit a very similar pattern,
and a change in the slope of the profile can be observed on the right side of the plot. This
change corresponds to the location of the EPCM changing phase. The results obtained from
this comparison are satisfactory for validating the mathematical formulation. Additionally, a
numerical study was conducted to determine the appropriate number of nodes and time steps,
verifying that the simulation results are independent of these parameters. The structured layer
of the thermocline has been validated against the computational results of Vera et al. [13, 14].
Although the model can consider heat losses to the exterior, such losses have been neglected in
this study.
4
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
Figure 2: Comparison with the experimental results of Keilany et al. [12] for temperature profiles over
time.
4 RESULTS
The previously presented structure is simulated, incorporating the three alternatives for the
EPCM: NaNO3, KOH, and H380. The EPCM is positioned at the lower part for the NaNO3
case and the upper part for the H380 and KOH cases. Results are obtained for the accumulated
energy in each of the three cases, considering the thickness of the phase change material layer
and the proximity of the melting temperature to the system’s operating temperature. All the
presented results are obtained under cyclic periodic conditions.
Figure 3 shows the accumulated energy relative to the EPCM thickness, which is the percent-
age of EPCM relative to the total height of the filler material. In all cases, optimal results are
achieved when utilizing a small EPCM height relative to the total height of the filler material
bed. NaNO3 exhibits poor performance and, in some cases, even negative performance. This
could be attributed to its melting temperature of 306 ◦C. With a cut-off temperature difference
of 15 ◦C and a cold temperature of 290 ◦C, it falls outside the melting/solidification range of
the EPCM.
It can be observed that despite the less favourable physical properties of energy density
and latent heat for KOH, it exhibits superior performance across all heights and lower cutoff
temperature differences. This observation may be attributed to temperature differences of the
hot/cold temperature, the EPCM’s melting temperature, and the cutoff temperature difference.
H380*, which is a fictional EPCM with 380 ◦C as a melting temperature, is simulated, and it can
be seen that it exhibits superior performance for all thicknesses due to its better thermophysical
properties and the same melting temperature as KOH.
5
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
0 10 20 30 40 50
1,100
1,150
1,200
1,250
1,300
1,350
1,400
EPCM thickness (%)
A
cc
u
m
u
la
te
d
en
er
g
y
(M
W
h
) NaNO3
KOH
H380
H380*
Figure 3: Accumulated energy as a function of thickness percentage of EPCM for three materials as
EPCM for a cutoff temperature difference of 15◦C.
In Figure 4, the accumulated energy is evaluated for a fictional EPCM where its melting
temperature is considered as the distance between the hot region for the top EPCMs and the cold
region for the bottom EPCMs. Given a cut-off temperature of 15 ◦C, the EPCM’s effectiveness
diminishes if the temperature difference exceeds this threshold. The top EPCMs (H380 and
KOH) perform well within the 10-15 ◦C range, whereas the bottom EPCM (NaNO3) begins to
decline in effectiveness when the temperature difference surpasses 10 ◦C.
0 5 10 15 20 25
1,100
1,150
1,200
1,250
1,300
1,350
1,400
1,450
1,500
Distance from hot/cold temperature (◦C)
A
cc
u
m
u
la
te
d
en
er
gy
(M
W
h
) NaNO3
KOH
H380
No PCM
Figure 4: Accumulated energy as a function of the distance of the melting temperature from the hot/cold
temperature for three materials as EPCM and without EPCM for a cutoff temperature difference of 15◦C
and a EPCM thickness of 10 %.
6
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
5 CONCLUSIONS
The integration of encapsulated phase change material in a structured thermal energy storage
system is studied. The fluid and filler material are discretised using an unsteady one-dimensional
approach, while the EPCM is discretised one-dimensionally in the radial direction. The model
is well-verified and validated using experimental results from other authors. Optimal results are
achieved when the EPCM constitutes a small part of the height relative to the filler material
bed and a distance between the melting point and the hot/cold regions of 10-15 ◦C.
Despite KOH having thermally unfavourable properties, it exhibits superior performance.
NaNO3 demonstrates poor performance at low cutoff temperature differences due to its high
melting temperature (306 ◦C) with respect to the cold temperature (290◦C), preventing melting
at low cutoff temperatures. H380 possesses favourable thermal properties, but its relatively
high melting temperature (382 ◦C), close to the hot temperature (385 ◦C), limits its latent heat
energy utilisation. H380* has a better behaviour than KOH, confirming the importance of the
distance of the melting temperature from the hot temperature. The top EPCMs (H380 and
KOH) perform well within the 10-15 ºC range (close to the 15 ◦C cutoff temperature), whereas
the bottom EPCM (NaNO3) begins to decline in effectiveness when the temperature difference
surpasses 10 ◦C.
In future work, a more detailed study will be conducted on the EPCM thickness and the
distance of the melting temperature of different materials from the hot/cold temperatures for
various cut-off temperatures and different EPCM thicknesses. This study will be valuable for
determining the optimal material for a specific structured TES, as well as identifying the ideal
operational parameters to maximize the potential of the EPCM.
6 ACKNOWLEDGEMENTS
This work is carried out in the framework of the Newcline project. It is supported under the
umbrella of CSP-ERA.NET 1st Cofund Joint Call and by the following National Agencies: AEI
(Spain), CDTI (Spain), Jülich (Germany), SFOE (Switzerland). CSP-ERA.NET is supported
by the European Commission within the EU Framework Programme for Research and Inno-
vation Horizon 2020 (Cofund ERA-NET Action, Nº 838311). The first author acknowledges
the financial support from the “Departament de Recerca i Universitats de la Generalitat de
Catalunya” and the “Fons Social Europeu” with the predoctoral grant JOAN ORÓ FI AGAUR
(2023 FI 00192).
REFERENCES
[1] L. Boquera, J.R. Castro, A.L. Pisello, L.F. Cabeza, ”Research progress and trends on the
use of concrete as thermal energy storage material through bibliometric analysis,” J. Energy
Storage, vol. 38, p. 102562, 2021. DOI: 10.1016/j.est.2021.102562.
[2] O. Sanmart́ı, J. Vera, S. Torras, C.D. Pérez-Segarra, ”Parametric study for a structured
thermal energy storage system for concentrated solar power plants,” Energy, vol. 305, p.
132271, 2024. DOI: 10.1016/j.energy.2024.132271.
[3] P.A. Galione, C.D. Pérez-Segarra, L. Rodŕıguez, A. Oliva, J. Rigola, ”Multi-layered solid-
PCM thermocline thermal storage concept for CSP plants. Numerical analysis and perspec-
tives,” Appl. Energy, vol. 142, pp. 337–351, 2015. DOI: 10.1016/j.apenergy.2014.12.084.
7
Oriol Sanmart́ı, Jordi Vera, Santiago Torras and Carlos D. Pérez-Segarra
[4] O. Sanmart́ı, J. Vera, S. Torras, C.D. Pérez-Segarra, ”Numerical investigation of phase
change material integration in structured thermocline systems for concentrated solar
power,” Journal of Physics: Conference Series, vol. 2766, no. 1, p. 012216, 2024. DOI:
10.1088/1742-6596/2766/1/012216.
[5] T.E.W. Schumann, ”Heat transfer: A liquid flowing through a porous prism,” J. Frankl.
Inst., vol. 208, pp. 405–416, 1929. DOI: 10.1016/S0016-0032(29)91186-8.
[6] J. Taborek, ”Double-Pipe and Multitube Heat Exchangers with Plain and Longi-
tudinal Finned Tubes,” Heat Transfer Engineering, vol. 18, pp. 34–45, 1997. DOI:
10.1080/01457639708939894.
[7] A. Žukauskas, ”Heat Transfer from Tubes in Crossflow,” in Advances in Heat Transfer, vol.
8, J.P. Hartnett and T.F. Irvine, Eds. Elsevier, pp. 93–160, 1972. DOI: 10.1016/S0065-
2717(08)70118-7.
[8] A.B. Zavoico, Solar Power Tower Design Basis Document, Revision 0, Sandia National Lab.
(SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore,
CA (United States), 2001. DOI: 10.2172/786629.
[9] T. Bauer, D. Laing, R. Tamme, ”Characterization of Sodium Nitrate as Phase Change
Material,” Int. J. Thermophys., vol. 33, pp. 91–104, 2011. DOI: 10.1007/s10765-011-1113-
9.
[10] M.A. Geyer, ”Thermal Storage for Solar Power Plants,” in Solar Power Plants: Fundamen-
tals, Technology, Systems, Economics, C.-J. Winter, R.L. Sizmann, L.L. Vant-Hull, Eds.
Berlin, Heidelberg: Springer, pp. 199–214, 1991. ISBN: 978-3-642-61245-9.
[11] A. Crespo, C. Barreneche, M. Ibarra, W. Platzer, ”Latent thermal energy storage for solar
process heat applications at medium-high temperatures – A review,” Sol. Energy, vol. 192,
pp. 3–34, 2019. DOI: 10.1016/J.SOLENER.2018.06.101.
[12] M.A. Keilany, S. Vannerem, M. Milhé, Q. Falcoz, J.-J. Bézian, G. Flamant, ”Experimental
and numerical study of combining encapsulated phase change material to sensible heat
storage material in one-tank pilot scale thermal energy storage,” J. Energy Storage, vol. 51,
p. 104504, 2022. DOI: 10.1016/j.est.2022.104504.
[13] J. Vera Fernandez, G. Colomer, O. Sanmart́ı, C. Perez, ”Modelization of a molten
salt thermal energy storage for concentrated solar power,” in 8th European Congress on
Computational Methods in Applied Sciences and Engineering, 2022. DOI: 10.23967/ecco-
mas.2022.182.
[14] J. Vera Fernandez, O. Sanmart́ı, S. Torras, C.D. Perez Segarra, ”Parametric Study of
Structured Thermocline Storage Systems,” in EuroSun 2022 - ISES and IEA SHC Inter-
national Conference on Solar Energy for Buildings and Industry, 2022. DOI: 10.18086/eu-
rosun.2022.13.22.
8


Mathematical and Numerical Approach of Encapsulated Phase Change Material in Structured Thermocline Systems

Liguori, F.

Madeo, A.

Marfia, S.

Sacco, E.

A mixed hybrid-stress virtual element for plane elasticity

Al-Shabab, A.

Silva, P.

Tsoutsanis, P.

Skote, M.

Automated Flow Physics Identification and Classification in Multiphysics Multifidelity Simulations

Leonetti, L.

Magisano, D.

Garcea, G.

Large rotation isogeometric shell model for alternating stiff/soft curved laminates  including warping and thickness strain with minimal dofs

The 9th European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS Congress 2024
3–7 June 2024, Lisboa, Portugal
COMPARATIVE STUDY OF ORIFICE SHAPES ON SHOCK
ABSORBER: IMPACT ON ENERGY DISSIPATION AND
CAVITATION
Paulo A. S. F. Silva1, Ahmed A Sheikh Al-Shabab1 and Panagiotis
Tsoutsanis1, Martin Skote1
1 School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43
0AL, UK
Key words: Shock Absorber, CFD, Multiphase Flow, Cavitation, Orifice Design
Summary. Aircraft shock absorbers rely on orifice designs to control fluid flow and optimize
damping performance. This study presents a computational fluid dynamics (CFD) analysis
of circular, rectangular, semicircular, and cutback orifice profiles in oleo-pneumatic shock ab-
sorbers. Using OpenFOAM with the Schnerr-Sauer cavitation model and k-omega SST tur-
bulence model, we investigated the effects of orifice shape and length-to-diameter (L/D) ratio
on pressure drop, velocity distribution, cavitation inception, and discharge coefficients. Results
show that rectangular orifices generate higher damping pressures but promote earlier cavitation,
while semicircular shapes offer balanced performance with controlled cavitation. Circular designs
demonstrate superior discharge coefficients across L/D ratios. This research provides insights
for optimizing shock absorber performance, enhancing vehicle safety and passenger comfort.
1 Introduction
Shock absorbers are critical components in aircraft and automotive suspension systems, re-
sponsible for attenuating vibrations and dissipating kinetic energy during landing or over rough
terrain. The damping performance and dynamic stability of these systems are dictated by com-
plex fluid flows within hydraulic control elements, with orifices playing a pivotal role in creating
pressure drops to develop controllable damping forces. However, excessive pressure reduction
risks the onset of cavitation – the formation of vapor bubbles which can induce noise, component
erosion, and performance loss if left uncontrolled. Previous studies have established correlations
between orifice geometry and cavitation inception. Pearce and Lichtarowicz [1] and Nurick et al.
[2] investigated the influence of geometry on discharge coefficients and cavitation characteristics
in submerged orifices. Recent works by Ge et al. [3, 4, 5] have explored the effects of liquid
properties, temperature, and cavitation number on cavitation dynamics in nozzles, while Apte
et al. [6] and Li et al. [7] evaluated various turbulence models for simulating cavitating flows.
In the context of shock absorbers, early research by Milwitzky and Cook [8] presented basic
models for shock absorber dynamics during landing impact. More recent studies, such as those
by Alonso et al. [9] and Ding et al. [10], have employed computational fluid dynamics (CFD)
to analyze internal flows and calculate discharge coefficients in shock absorber orifices.
Despite these advancements, there remains a lack of comprehensive research exploring the
impact of orifice shape and dimensions on the multiphase flow dynamics and damping perfor-
mance of shock absorbers. This study aims to elucidate the complex interactions between orifice
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
geometry, cavitating flow dynamics, and damping performance of aircraft shock absorbers during
drop-test conditions. The specific objectives are:
• To quantify the influence of orifice shape and length-to-diameter ratio on pressure drop,
velocity distribution, and vapor formation using high-fidelity CFD analysis.
• To compare the discharge coefficients and damping loads of circular, rectangular, semi-
circular, and cutback orifice profiles during critical conditions.
• To provide design guidelines for optimizing orifice geometry based on target shock absorber
performance metrics.
2 Numerical Methods
This study employs the open-source CFD software OpenFOAM to investigate cavitating
flow in shock absorber orifices. The compressible Unsteady Reynolds Averaged Navier-Stokes
(URANS) equations are coupled with the volume of fluid (VOF) method for multiphase flow
modeling. The governing equations for conservation of mixture mass, momentum, and energy
are:
∂ρm
∂t
+∇ · (ρmUm) = 0 (1)
∂(ρmUm)
∂t
+∇ · (ρUmUm) = −∇pm +∇ · [µm(∇Um +∇UmT )] + ρmg + F (2)
∂(ρE)
∂t
+∇ · [Um(ρE + p)] = ∇ · [k∇T ] (3)
where subscript m denotes mixture quantities, ρ is density, Um is velocity, p is pressure, µ is
dynamic viscosity, g is gravitational acceleration, F is surface tension force, E is total energy, k
is thermal conductivity, and T is temperature.
The Schnerr-Sauer cavitation model is employed to capture phase change:
R =
ρvρl
ρm
α(1− α) 3
RB
√
2|p− psat|
3ρl
(4)
where R is the mass transfer rate, α is vapor volume fraction, RB is bubble radius, and psat
is saturation pressure.
Turbulence is modeled using the k-omega Shear Stress Transport (SST) model. The shock
absorber geometry, illustrated in Figure 1, consists of upper and lower cylinders connected by
a central orifice plate. Four orifice designs were tested: semicircle, cutback, rectangular, and
circular, with length-to-diameter (L/D) ratios ranging from 0.5 to 1.28.
Table 1 summarizes the key simulation parameters. The piston motion is specified based on
experimental stroke profiles for drop tests [8]. A polynomial equation of state is used for the oil,
while nitrogen is treated as an ideal gas.
The grid independence was established through a refinement study and assessing the velocity
magnitude at the orifice as can be seen in Figure 2, the final mesh containing 41.2k cells provide
2
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
Figure 1: Geometry schematic of shock absorber
a balance between accuracy and computational efficiency. The PIMPLE algorithm is used for
pressure-velocity coupling with a maximum Courant number of 10.
3
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
Table 1: Parameters for the shock absorber simulation
Parameter Value
Domain length [mm] 505
Upper Chamber radius [mm] 45.27
Lower Chamber radius [mm] 37.31
Orifice radius [mm] 4.05
Orifice position [mm] 193.97
Orifice length [mm] 4.05-12.00
Oil level [mm] 386
Total simulation time [s] 0.15
Saturation pressure [Pa] 2300
Initial pressure [Pa] 299921.941
Initial fluid temperature [K] 300
Oil Density [kg/m3] 867
Gas Density [kg/m3] 1.205
Oil Kinematic Viscosity [m2/s] 1.35 × 10−2
Figure 2: Grid independence study showing convergence of pressure (top) and velocitybottom at the
orifice.
4
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
3 RESULTS AND DISCUSSION
Figure 3 illustrates the pressure drop across various orifice designs and L/D ratios as a func-
tion of stroke displacement. The rectangular orifice consistently produced the highest damping
pressures, followed by the cutback, circular, and semi-circular designs. Increasing L/D ratio
had a marginal effect on pressure drop for sharp-edged orifices (rectangular and cutback) but
decreased it for circular shapes. The rectangular design exhibited the lowest average deviation
(1.67%) across L/D ratios, indicating consistent performance.
Figure 3: Pressure drop by stroke displacement for various orifice shapes and lengths according to
line color Black (L/D = 0.5), Blue (L/D = 0.69), Green (L/D = 0.89), red (L/D = 1.08) and Cyan
(L/D = 1.28)
Orifice velocity magnitudes varied significantly with shape profile, as shown in Figure 4. The
rectangular geometry generated the highest velocities, often exceeding 125 m/s, with increasing
L/D ratio promoting higher velocities. Cutback shapes experienced the lowest peak velocities
due to greater flow separation. Circular designs showed minimal variation (0.41% for circle,
0.18% for semicircle) across L/D ratios, demonstrating robust velocity profiles.
Figure 5 depicts the change in averaged density at the orifice, indicating cavitation on-
set.Sharp density drops for rectangular, circular, and cutback shapes indicate vapor formation
at the orifice. The semi-circular shape maintained constant density, suggesting downstream
5
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
Figure 4: Orifice Velocity by stroke displacement for various orifice shapes and lengths according to
color: Black (L/D = 0.5), Blue (L/D = 0.69), Green (L/D = 0.89), red (L/D = 1.08) and Cyan
(L/D = 1.28)
cavitation development. Increasing orifice length had limited influence on cavitation behavior
at the orifice.
Figure 6 presents a comparative study of oil-gas interaction for various orifice shapes at two
critical time instances. At t=0.025s, the rectangular profile showed strong disturbances from
vapor structures, while the circular shape exhibited minimal upstream cavitation influence. At
t=0.05s, recirculation patterns became apparent, re-energizing the shear layer and highlighting
the complex flow dynamics.
3.1 Discharge Coefficient Comparison
Table 2 compares the averaged discharge coefficients (Cd) across orifice shapes and L/D ra-
tios with theoretical predictions. Circular and semi-circular designs showed superior performance
with Cd values consistently between 0.94-0.96, significantly higher than theoretical predictions.
The rectangular orifice exhibited the lowest Cd values (0.62-0.66), closer to theoretical predic-
tions, possibly due to flow instabilities and sensitivity to entry geometry.
6
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
Figure 5: Density at the orifice probe by stroke displacement for various orifice shapes and lengths
according to color: Black L/D = 0.5, Blue L/D = 0.69, Green L/D = 0.89, red L/D = 1.08 and Cyan
L/D = 1.28
Table 2: Time-averaged discharge coefficients for various orifice shapes across L/D ratios
L/D Rectangular Circle Semi Circle Cutback Theory [11]
0.5 0.66 0.94 0.95 0.85 0.65
0.69 0.64 0.95 0.94 0.94 0.68
0.89 0.62 0.95 0.95 0.98 0.71
1.08 0.62 0.95 0.96 0.93 0.77
1.28 0.62 0.95 0.96 0.94 0.78
4 Conclusions
This study presents a comprehensive CFD analysis of the influence of orifice design on the
internal cavitating flow and energy dissipation in oleo-pneumatic shock absorbers. Key findings
include:
• The rectangular orifice design exhibited the highest damping pressure drop and the steepest
7
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
pressure gradient along the orifice length, making it favorable for energy dissipation.
• The cutback and rectangular geometries demonstrated early cavitation inception, while
the circular shapes resisted initial vapor formation, highlighting the strong influence of
orifice entrance sharpness on cavitation characteristics.
• The semi-circular profile achieved a balance between smooth flow and controlled cavitation,
optimizing the operating range.
• When examining the impact of L/D variation on results, we observed a moderate level of
difference across all designs investigated. Notably, the pressure drop across the rectangular
orifice exhibited the most significant variation, reaching up to 10%.
• The discharge coefficient was significantly affected by orifice shape and L/D ratio, with
the circular and semi-circular designs showing superior performance compared to the rect-
angular design.
REFERENCES
[1] Pearce, I. D., and A. Lichtarowicz. ”Discharge performance of long orifices with cavitating
flow.” Proceedings of Second Fluid Power Symposium, Guildford, UK. 1971.
[2] Nurick, W. H. ”Orifice cavitation and its effect on spray mixing.” (1976): 681-687.
[3] Ge, Mingming, et al. ”Cavitation dynamics and thermodynamic effects at elevated temper-
atures in a small Venturi channel.” International Journal of Heat and Mass Transfer 170
(2021): 120970.
[4] Ge, Mingming, et al. ”Intensity and regimes changing of hydrodynamic cavitation consid-
ering temperature effects.” Journal of Cleaner Production 338 (2022): 130470.
[5] Ge, Mingming, et al. ”Dynamic mode decomposition to classify cavitating flow regimes
induced by thermodynamic effects.” Energy 254 (2022): 124426.
[6] Apte, Dhruv, Mingming Ge, and Olivier Coutier-Delgosha. ”Numerical investigation of
a cavitating nozzle for jetting and rock erosion based on different turbulence models.”
Geoenergy Science and Engineering 231 (2023): 212300.
[7] Li, L., Xu, Y., Ge, M., Wang, Z., Li, S., & Zhang, J. (2023). ”Numerical investigation of
cavitating jet flow field with different turbulence models”. Mathematics, 11(18), 3977.
[8] Milwitzky, Benjamin, and Francis E. Cook. Analysis of landing-gear behavior. No. NACA-
TN-2755. 1952.
[9] Alonso, M., and Á. Comas. ”Modelling a twin tube cavitating shock absorber.” Proceedings
of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 220.8
(2006): 1031-1040.
[10] Ding, Y. W., Wei, X. H., Nie, H., & Li, Y. P. (2018). ”Discharge coefficient calculation
method of landing gear shock absorber and its influence on drop dynamics.” Journal of
vibroengineering, 20(7), 2550-2562.
8
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
[11] Dixon, John C. The shock absorber handbook. John Wiley & Sons, 2007.
9
Paulo A. S. F. Silva, Ahmed A Sheikh Al-Shabab, Panagiotis Tsoutsanis and Martin Skote
Figure 6: Volume fraction of liquid for all designs for L/D=0.5 at t=0.025s and t=0.05s
10


Comparative Study of  Orifice Shapes on Shock Absorber: Impact on Energy Dissipation and Cavitation

Santos, D.

Hopman, J.

Trias, F.

On the Conditions for a Stable Projection Method on Collocated Unstructured Grids

Balcazar-Arciniega, Nestor

Rigola, J.

Oliva, A.

Unstructured conservative level-set method for interfacial transport processes on adaptive and fixed collocated meshes

Scuoppo, R.

Pasta, S.

On the Modeling of Left Atrial Appendage Inversion: a Reverse Growth Analysis

Not a member yet

Effect of the Carotid Geometry on the Onset of Atherosclerotic Plaques

Comparison between linear and non-linear multifidelity models for turbulent flow problems

Mathematical and Numerical Approach of Encapsulated Phase Change Material in Structured Thermocline Systems

A mixed hybrid-stress virtual element for plane elasticity

Automated Flow Physics Identification and Classification in Multiphysics Multifidelity Simulations

Large rotation isogeometric shell model for alternating stiff/soft curved laminates including warping and thickness strain with minimal dofs

Comparative Study of Orifice Shapes on Shock Absorber: Impact on Energy Dissipation and Cavitation

On the Conditions for a Stable Projection Method on Collocated Unstructured Grids

Unstructured conservative level-set method for interfacial transport processes on adaptive and fixed collocated meshes

On the Modeling of Left Atrial Appendage Inversion: a Reverse Growth Analysis

13,125

33,380