Heterogeneity's impact on the sloshing motion in excited tanks

A. Belahsen; H. Essaouini; A. Hamydy

doi:10.1556/1848.2023.00637

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International Review of Applied Sciences and Engineering

Volume/Issue:: Volume 15: Issue 2

Heterogeneity's impact on the sloshing motion in excited tanks

Authors:

A. Belahsen

A. Belahsen Department Physique, FS Tetouan, Abdelmalek Essaâdi University, Morocco

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abdelhadi.gee@gmail.com https://orcid.org/0000-0002-2495-0540

H. Essaouini

H. Essaouini Department Physique, FS Tetouan, Abdelmalek Essaâdi University, Morocco

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hilal_essaouini@yahoo.fr

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A. Hamydy

A. Hamydy Regional Center for Education and Training Professions, Tetouan, Morocco

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a.hamydy@yahoo.fr

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Pages:: 139–146

Online Publication Date:: 11 Jan 2024

Publication Date:: 10 Jun 2024

Article Category:: Research Article

DOI:: https://doi.org/10.1556/1848.2023.00637

Keywords:: CFD; rectangular tank; sloshing; heterogeneous liquid; Fourier

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Abstract

This paper aims to investigate the effect of liquid heterogeneity on sloshing in a two-dimensional rectangular tank. The container is excited horizontally, and the density of the liquid at equilibrium can almost be considered a linear dependence of the depth. The linearized equations representing the sloshing phenomenon are solved numerically using ANSYS 2020 R2 software and analytically using the separation method of variables in conjunction with the Fourier analysis. On the other hand, a comparison study has been carried out between the obtained results and other works related to the same phenomenon. Overall, the results exhibit considerable effects of variation in the Heterogeneity Coefficient β on the free surface's motion and the pressure distribution within the liquid. Furthermore, the free surface of liquid heterogeneity is also affected by the variation of Excitation Frequency Ω and the Filling Rate h of the liquid in the tank.

Abstract

1 Introduction

In recent years, there has been an increasing recognition of the importance of incorporating advanced methodologies to tackle emerging environmental issues such as liquid transportation, especially water [1, 2]. Liquid storage and transporting tanks are structures whose utilizations are increasingly widespread in engineering applications, such as oil transportation, water supply, and the nuclear industry. However, accidents can cause major issues because most liquids transported are chemical substances or human necessities (water). As a result, massive human, economic, and environmental losses may occur. Alternatively, when these containers are exposed to outside excitations, the liquid stored within them naturally oscillates inside, giving rise to free surface movements known as "sloshing". The onset of these oscillations is influenced by many factors, including dimension, geometry, filling rate, and liquid character. As a result, this phenomenon must be minimized as much as possible to avoid damage to the vehicle's stability and safety.

This study introduces a novel ANSYS methodology that aims to contribute to this evolving field of environmental management. By leveraging the capabilities of the ANSYS software, we have developed a simulation framework that allows for the analysis of dynamic scenarios.

In recent decades many studies have been carried out using various methods and technologies to figure out the dynamic behavior of the sloshing effect. For example, Raouf [3] developed the fundamental principles of liquid sloshing to guide the reader through basic theory to advanced analytical and experimental results. The rationale behind our methodology stems from the recognition that traditional modeling approaches often struggle to capture the intricacies of the dynamic behavior of sloshing, which emphasizes the need for advanced simulation tools to address these complex environmental challenges.

Forbes [4] used novel techniques to solve nonlinear equations of motion in the case of a horizontally excited rectangular tank. Besides, he adopted the same methods employed by Agawane et al. [5]. On the other hand, Chen & Xue [6] used Open FOAM and Experimental Validation, in which they carried out a series of numerical simulations to confirm the relationship between frequency, filling level, and other parameters. A while ago, Essaouini et al. [7–9] studied the sloshing of a heterogeneous ideal liquid in a rectangular tank subjected to horizontal dynamic excitation. The results obtained demonstrated that heterogeneity had a significant effect on the size of the liquid's free surface elevation in the stable zone. Bahaoui et al. [10] investigated the impact of variable-density liquid on the sloshing phenomenon in a partially filled 2D rectangular tank years later. Recently, Sulisetyono et al. [11] investigated in sloshing simulation of the tank of LNG ship's motion in the sea with different filling levels of liquid, detailed experimental studies on density-stratified liquids were investigated by Luo et al. [12], and the natural frequencies and modes of liquid sloshing in a rectangular 3D tank with slotted baffles in the middle were investigated by Jamshidi et al. [13].

In this paper, we look at how liquid heterogeneity affects the nature of the response to a horizontal sinusoidal dynamic excitation. First, we consider a liquid with low heterogeneity where the assumed tank has rectangular and rigid walls. The effect of the heterogeneity coefficient on the evolution of the free surface and the pressure distribution is studied. By incorporating the proposed ANSYS methodology, we seek to offer a robust and versatile approach for analyzing and managing transportation and liquid storage systems in dynamic scenarios. Our methodology considers key factors such as spatial heterogeneity, temporal dynamics, and the interactions between various components of this system.

This paper is organized as follows. First section is introduction, the second section covers the equations that control the sloshing of nearly heterogeneous liquids. A numerical investigation is presented in the third section, and the fourth section provides the results and discussions. The main results are established at the end.

2 Numerical model

The numerical simulations of sloshing in a rectangular tank half-filled with heterogenous liquid are shown in Fig. 1. Simulations were conducted in a two-dimensional (2D) domain using the ANSYS Fluent R2 2020 simulation software, as laminar phenomena inherently exhibit unsteady and two-dimensional characteristics. A no-slip boundary condition was imposed to account for interactions at the walls, neglecting the effects of wall adhesion. The governing equations were discretized using finite volume formulation. A first-order Ruler implicit scheme was used to discretize the unsteady term. The scheme (SIMPLE) algorithm was employed for the coupling of pressure and velocity. The pressure term was handled using the pressure staggering option (PRESTO) scheme. The volume fraction was discretized using a compressive scheme. The volume of fluid (VOF) method is used to capture the interface between two immiscible fluids.

Fig. 1.

Configuration of immobile container ‘Own source’

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

It is well known that factors like grid spacing and time step size directly affect the accuracy and stability of the computation, and efficiency of computational fluid dynamics (CFD) simulations. Consequently, to ensure high-quality solutions, comprehensive investigations were conducted into the dependence of the results on grid and time step. The methodology employed in these investigations follows the theoretical framework introduced by Liu [14]. Computations were performed up to a simulation time of t = 10 s. To assess the grid dependence of the solutions, three groups of structured grids were generated: fine (235 × 150), medium (150 × 100), and coarse (75 × 50). The fine mesh system consisted of 235 × 150 non-uniform grids. The first cell size adjacent to the tank wall and free surface was 0.001 m. Grid spacing was decreased to create the medium and coarse grids. Furthermore, three distinct time steps were employed: fine (0.0015 s), medium (0.002 s), and coarse (0.01 s). The parameter chosen for these tests is the average value of the pressure peaks. After conducting tests on the independent mesh and time step, it was determined that the fine grid and time step should be used for all cases results.

In Tables 1 and 2, we present the results related to grid and time step dependencies, respectively. Grid dependence, measured as the relative difference denoted as $ε$ , between the medium and baseline grids, is remarkably low, accounting for less than 0.11%. To clarify, this relative difference $ε$ is defined as $ε = (f_{α} - f_{β}) / f_{β}$ , where the subscripts ‘coarser' and ‘finer' refer to the grids (or time steps) of varying resolution, and $f$ represent the numerical solution.

Table 1.

Summary of the analysis of results with respect to grid dependence ‘Own source’

Grid	Explanation	Density	Average pressure peak values Pa	Relative deference
1	base line	235 × 150	10,370	0.12%
2	medium	150 × 100	10,358	1.77%
3	coarse	75 × 50	10,175

Table 2.

Summary of the analysis of results with respect to time step dependence ‘Own source’

Time step	Explanation	Dimension	Average pressure peak values Pa	Relative deference
1	base line	0.0015	10,404	0.14%
2	medium	0.002	10,419	0.6%
3	large	0.01	10,358

Notably, the results obtained from the coarser grid exhibit a marginal discrepancy of 0.6% compared to the corresponding results from the medium grid. Similarly, the time step's dependence shows a relative difference of less than 0.14%. These findings collectively suggest that, within the considered range, the solutions remain remarkably stable and are minimally affected by variations in grid spacing and time step size.

In our analysis, we introduce refinement ratios denoted as r12 = n2/n1 and r23 = n3/n2, where ‘n' represents the grid spacing or time step size. The subscripts 1, 2, and 3 correspond to the base-line, medium, and large grids or time steps, respectively. To elaborate further, in this study, we performed grid and time step refinements with r12 = 1.56 and r23 = 2 for one set, and r12 = 1.33 and r23 = 5 for another set.

Consequently, we can define the algorithmic order of convergence as ‘p,' which is calculated using the formula: $p = \ln [(f_{3} - f_{2}) / (f_{2} - f_{1})] / \ln (r)$ , where $f$ represents the results obtained from the different grid or time step levels, and ‘r' is the refinement ratio. This calculation helps us assess the rate at which the solution converges as we refine the grid or time step.

The gravitational attraction vector oscillates both backward and forward, causing the fluid surface to move freely. Moreover, the liquid is classified as an incompressible Newtonian fluid. As a result, the continuity equation and momentum equation are considered and given in Eq (4). This expression defines the equation of motion in the moving frame by incorporating the local force acting per unit of fluid mass. According to that, Eq. (4) is written in the x₁ and x₂ directions.

3 Equation of motion

In this part, we introduce the validation of the configuration drawn in Fig. 1. In addition, the demonstration of the linear 2D sloshing cases is also presented. To assess the elevation of the free surface of sloshing in a rectangular liquid-filled tank under sinusoidal horizontal excitation, the linear theory is usually used.

A rectangular tank exposed to horizontal sinusoidal excitation is defined in Fig. 2. We assume an excitation amplitude and a small fluid response for two-dimensional fluid motion. The tank containing a non-viscous and irrotational liquid is characterized by periodic displacement noted as:

X (t) = X_{0} \sin Ω t

(1)

Where X₀ is the excitation amplitude, t is the time and

Ω

the force motion's excitation frequency.

Fig. 2.

Surface elevation under horizontal sinusoidal excitation ‘Own source’

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

We consider an incompressible ideal liquid with a free surface and weakly homogeneous with the density at equilibrium to take the form of:

ρ_{0} (x_{2}) = ρ (1 - β x_{2})

(2)

The flow is assumed to be irrotational in a rectangular tank with length L = π and height h of the liquid in the tank. Therefore, the acceleration of the horizontal sinusoidal excitation of the tank (see Fig. 2) is defined as:

\ddot{X} (t) = - X_{0} Ω^{2} \sin Ω t

(3)

The problem is two-dimensional, and then the coordinates used are Cartesian

x_{1}

and

x_{2}

. According to a linear theory, we can assume that the amplitude of excitation and the fluid response are small. Where

\vec{u} (x_{1}, x_{2}, t)

denotes the displacement of the fluid particle relative to the container (tank), ρ represents the fluid's approximate density, P is the pressure, and β is the quasi-homogeneity coefficient of the liquid. The following are the governing equations for the motion of the liquid in the tank with the excitation effect:

\begin{array}{l} ρ \ddot{\vec{u}} = - ρ g {\vec{x}}_{2} - \vec{grad} P - ρ β g u_{2} {\vec{x}}_{2} - ρ \ddot{X} {\vec{x}}_{1} \\ div \vec{u} = 0 \end{array}} in Ω

(4)

and for kinematics considerations

\begin{array}{l} u_{1} = 0 for x_{1} = 0, x_{1} = π \\ u_{2} = 0 for x_{2} = - h \end{array}}

(5)

\int_{0}^{π} u_{1} (x_{1}, 0, t) d x_{1} = 0 (Constant volume)

(6)

If the pressure below the free surface (free line) is zero, the equilibrium pressure is $- ρ g x_{2}$ .

Let us introduce the dynamic pressure P by:

P = - ρ g x_{2} + p

(7)

The dynamic condition on the free surface

Γ_{t}

P_{Γ_{t}} = 0

, is written as:

P_{|_{Γ}} = ρ g u_{2_{| Γ}}

(8)

4 Solution of the problem

The solution details can be found in the previous authors work [15]. We use the method of separation of variables and Fourier analysis to solve the problem, and we get the following analytical expressions:

The elevation of the free surface η takes the form of:

η (x_{1}, t) = [A_{0} + B_{0} \sum_{n = 1}^{N} C_{n} \frac{\cos ((2 n + 1) x_{1} \times \cosh (2 n + 1) α}{\cosh ((2 n + 1) α h) - \frac{g (2 n + 1) \times \sinh (2 n + 1) α h}{π^{2} h}}] \sin (Ω t)

(9)

Pressure distribution:

We consider the case:

Ω^{2} > β g

Then we have : α = i ξ; ξ = \sqrt{1 - \frac{β g}{Ω^{2}}} real

(10)

and : 0 < ξ < 1; Ω^{2} - β g = Ω^{2} ξ^{2}

(11)

We recall that : \cos i z = \cosh z; \sin (z) = - i s i n h z

Thus, we have : U_{1} = - \frac{4 X_{0}}{π} \sum_{n = 0}^{\infty} \frac{1}{2 n + 1} \frac{\sin (2 n + 1) x_{1} \cosh (2 n + 1) ξ (x_{2} + h)}{\cosh (2 n + 1) ξ h - \frac{g (2 n + 1)}{Ω^{2}} \sinh (2 n + 1) ξ h}

(12)

U_{2} = \frac{4 X_{0}}{π ξ} \sum_{n = 0}^{\infty} \frac{1}{2 n + 1} \frac{\cos (2 n + 1) x_{1} \sinh (2 n + 1) (x_{2} + h)}{\cosh (2 n + 1) ξ h - \frac{g (2 n + 1)}{Ω^{2}} \sinh (2 n + 1) ξ h}

(13)

Based on the two previous equations (12) and (13), we get the expression of the pressure:

P

P (x_{1}, t) = [[ρ {Ω_{0}}^{2} X_{0} (x_{1} - \frac{π}{2}) + \frac{4 ρ {Ω_{0}}^{2} X_{0}}{π}] \sum_{n = 1}^{\infty} C_{n} \frac{\cos [(2 n + 1) x_{1}] \cos [(2 n + 1) α (x_{2} + h]}{\cos [(2 n + 1) α h] - \frac{α g (2 n + 1)}{{Ω_{0}}^{2} - β g} \sin [(2 n + 1) α h]}]

(14)

The dynamic pressure is given by:

p = P \sin Ω t

(15)

And {\begin{cases} u_{1} = U_{1} \sin Ω t \\ u_{2} = U_{2} \sin Ω t \end{cases}

(16)

With

c_{n} = \frac{1}{{(2 n + 1)}^{2}}, A_{0} a n d B_{0}

are parameters that depend on

Ω, X_{0}

and

x_{1}

Therefore: $a = {(β g Ω^{- 2} - 1)}^{1 / 2}$

5 Numerical study

The general motion of fluids can be studied well and efficiently by numerical simulation. In this study, simulations of a heterogeneous liquid stored in a partially filled two-dimensional rectangular tank with length L and still, liquid depth h were performed using the ANSYS 2020 R2 software. A Cartesian system of coordinates $(O x_{1} x_{2})$ is attached to the tank, as shown in Fig. 1.

Under horizontal sinusoidal stimulation, the motion of irrotational and incompressible heterogeneous fluids is considered. In simulations, the parameter follows the liquid's degree of heterogeneity β, as shown by: $ρ_{0} (x_{2}) = ρ (1 - β x_{2})$ where $ρ = 1000 K g / m^{3}$ . In addition, the parameter $Ω$ _] controls the liquid's horizontal excitation frequency: $\ddot{X} (t) = - X_{0} Ω^{2} \sin Ω t$ . The impact of these two variables on the free surface of a heterogeneous liquid was parametrically investigated.

5.1 Validation of a model

By comparing simulation results with those of a 2D numerical model taken into account by Lui & Lin [16], the numerical model is validated. The tank's chosen measurements were length L = 1 m and liquid depth h = 0.5 m. In the presence of a sinusoidal acceleration where the displacement amplitude, the tank was aroused horizontally X₀ = 0.01 m and Ω = 2.657 rad s⁻¹.

The current computational model and that of Liu&Lin determine the free surface elevation of the liquid. [16] are compared in Fig. 3. The outcomes exhibit the same pattern, with nearly no errors found, which makes it possible to evaluate the accuracy of the numerical modeling using ANSYS.

Fig. 3.

A comparison of the free surface profiles generated by the numerical model built using ANSYS (line red) and that in [16] (line black)

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

6 Results and discussion

This section proposes an analysis of the physical behavior of a heterogeneous fluid kept in a rectangular tank that is only partially filled.

The capacity dimensions of the tank are fixed with L = 3.14 m and h = 1 m.

We distinguish two cases below:

$Ω^{2} > β g$ (stable zone)
$Ω^{2} < β g$ (unstable zone): this case has been left out of the discussion, as it corresponds to a resonance phenomenon.

6.1 Evolution of free surface based on the heterogeneity coefficient β

In Fig. 4, the heterogeneity coefficient is an important factor in explaining the oscillation of the ideal liquid's free surface from the inside of a two-dimensional rectangular tank exposed to horizontal sinusoidal excitation with an excitation frequency equal to $Ω = 3 r a d / s$ and a gravity intensity of g = 9.81 m s⁻². It appears that if the liquid is less homogeneous, the elevation of the free surface is more remarkable.

Fig. 4.

Time histories of the free surface elevation of the tank for the sloshing ‘Own source’

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

6.2 Evolution of free surface based on the excitation frequency Ω

At this point, we change the value of the excitation frequency and the extent of its effect on the free surface motion of a heterogeneous liquid (β = 0.1). The liquid partially filled the rectangular tank has h = 1 m where the excitation amplitude is estimated at X₀ = 0.05 m.

The objective is to observe the impact of a change in the excitation frequency on the free surface motion of the heterogeneous fluid and to compare the results to a homogeneous fluid with the same other parameters.

Through Fig. 5, we can conclude that the free surface motion increases as the value of the excitation frequency increases. This behavior is much more significant in the case of a heterogeneous liquid. But when the excitation frequency increases, the height of the free surface tends to decrease. This is because higher frequencies lead to shorter oscillation periods, limiting the time available for the fluid to reach its maximum displacement. Conversely, decreasing the excitation frequency allows for longer oscillation periods, resulting in a higher amplitude of the free surface. This is seen between excitation frequencies $Ω = 2.5 r a d / s$ and $Ω = 3 r a d / s$ .

Fig. 5.

Comparison of time histories of the tank's free surface elevation for liquid sloshing under horizontal excitation (g = 9.81 m s⁻² and h = 1) ‘Own source’

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

6.3 Evolution of free surface based on the filling rate h

In the graph below, we study the effect of the depth of a heterogeneous liquid (β = 0.1) in a 2D rectangular tank subjected to a horizontal sinusoidal excitation with an excitation frequency of 3 rad s⁻¹ and an excitation amplitude of X₀ = 0.05 m on the motion of the free surface.

As shown in the previous results, we notice in Fig. 6 that the effect of the heterogeneous liquid's height h in a 2D rectangular tank on the instability of the free surface motion is prominent. Therefore, if the depth of the liquid is high, the free surface motion becomes greater.

Fig. 6.

Comparison of time histories of the elevation of the free surface of the tank for liquid sloshing under horizontal excitation ( $Ω = 3 r a d / s$ g = 9.81 m s⁻²) ‘Own source’

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

6.4 Pressure distribution at the ends of the tank

Concerning the pressure of a heterogeneous fluid, we must mention that the pressure is affected by the change in the density of the fluid, which itself changes according to the value of the heterogeneous factor with the same equation (2).

Where the value of the $x_{2} = - h$ , the pressure of the heterogeneous liquid at the surface of the free liquid equals the pressure of the homogeneous liquid.

Therefore, the density of the heterogeneous liquid at the free surface is the same as the value of the homogeneous liquid.

In this section, we compare the pressure obtained at the bottom of the tank for both sides of a homogeneous liquid and a heterogeneous liquid using the Ansys 2020 R2 software.

The results in Fig. 7 show the pressure variation in the bottom of the tank in the left and right sides for x₁ = 0 and x₁ = π, respectively. The results show that if the value of the heterogeneity coefficient increases for a liquid inside a tank exposed to a horizontal sinusoidal excitation, the pressure at the bottom of the tank also increases. In other words, if the liquid is less homogeneous in a state of continuous motion, its effects on the tank's structure would be more substantial.

Fig. 7.

Comparison time histories of the pressure at the tank end for x₁ = 0 and x₁ = π based on the heterogeneity coefficient (h = 1 m $Ω$ = 3 rad s⁻¹ g = 9.81 m s⁻²) ‘Own source’

Citation: International Review of Applied Sciences and Engineering 15, 2; 10.1556/1848.2023.00637

7 Conclusion

In this work, the motion of the free surface of a partially filled rectangular container, is impacted by the heterogeneity coefficient since it is considered one of the significant factors in the instability of the free surface in the stable zone $Ω^{2} > β g$ , a horizontal sinusoidal dynamic excitation is applied to the container. In addition, we observed that every increase in the excitation frequency (Ω) altitude and the liquid level (h) inside the tank impacted the motion of a heterogeneous liquid's free surface. With an increase in the heterogeneity coefficient β, the pressure exhibits a noticeable increase.

All numerical studies show that the homogeneous liquid is less responsive to external and internal factors on the liquid inside the tank than the heterogeneous liquid, requiring solutions to reduce tank structure damage.

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International Review of Applied Sciences and Engineering

Print ISSN:: 2062-0810

Online ISSN:: 2063-4269

Editorial Board

Mohammad Nazir AHMAD, Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia

Murat BAKIROV, Center for Materials and Lifetime Management Ltd., Moscow, Russia

Nicolae BALC, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Umberto BERARDI, Toronto Metropolitan University, Toronto, Canada

Ildikó BODNÁR, University of Debrecen, Debrecen, Hungary

Sándor BODZÁS, University of Debrecen, Debrecen, Hungary

Fatih Mehmet BOTSALI, Selçuk University, Konya, Turkey

Samuel BRUNNER, Empa Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland

István BUDAI, University of Debrecen, Debrecen, Hungary

Constantin BUNGAU, University of Oradea, Oradea, Romania

Shanshan CAI, Huazhong University of Science and Technology, Wuhan, China

Michele De CARLI, University of Padua, Padua, Italy

Robert CERNY, Czech Technical University in Prague, Prague, Czech Republic

Erdem CUCE, Recep Tayyip Erdogan University, Rize, Turkey

György CSOMÓS, University of Debrecen, Debrecen, Hungary

Tamás CSOKNYAI, Budapest University of Technology and Economics, Budapest, Hungary

Anna FORMICA, IASI National Research Council, Rome, Italy

Alexandru GACSADI, University of Oradea, Oradea, Romania

Eugen Ioan GERGELY, University of Oradea, Oradea, Romania

Janez GRUM, University of Ljubljana, Ljubljana, Slovenia

Géza HUSI, University of Debrecen, Debrecen, Hungary

Ghaleb A. HUSSEINI, American University of Sharjah, Sharjah, United Arab Emirates

Nikolay IVANOV, Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

Antal JÁRAI, Eötvös Loránd University, Budapest, Hungary

Gudni JÓHANNESSON, The National Energy Authority of Iceland, Reykjavik, Iceland

László KAJTÁR, Budapest University of Technology and Economics, Budapest, Hungary

Ferenc KALMÁR, University of Debrecen, Debrecen, Hungary

Tünde KALMÁR, University of Debrecen, Debrecen, Hungary

Milos KALOUSEK, Brno University of Technology, Brno, Czech Republik

Jan KOCI, Czech Technical University in Prague, Prague, Czech Republic

Vaclav KOCI, Czech Technical University in Prague, Prague, Czech Republic

Imre KOCSIS, University of Debrecen, Debrecen, Hungary

Imre KOVÁCS, University of Debrecen, Debrecen, Hungary

Angela Daniela LA ROSA, Norwegian University of Science and Technology, Trondheim, Norway

Éva LOVRA, Univeqrsity of Debrecen, Debrecen, Hungary

Elena LUCCHI, Eurac Research, Institute for Renewable Energy, Bolzano, Italy

Tamás MANKOVITS, University of Debrecen, Debrecen, Hungary

Igor MEDVED, Slovak Technical University in Bratislava, Bratislava, Slovakia

Ligia MOGA, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Marco MOLINARI, Royal Institute of Technology, Stockholm, Sweden

Henrieta MORAVCIKOVA, Slovak Academy of Sciences, Bratislava, Slovakia

Phalguni MUKHOPHADYAYA, University of Victoria, Victoria, Canada

Balázs NAGY, Budapest University of Technology and Economics, Budapest, Hungary

Husam S. NAJM, Rutgers University, New Brunswick, USA

Jozsef NYERS, Subotica Tech College of Applied Sciences, Subotica, Serbia

Bjarne W. OLESEN, Technical University of Denmark, Lyngby, Denmark

Stefan ONIGA, North University of Baia Mare, Baia Mare, Romania

Joaquim Norberto PIRES, Universidade de Coimbra, Coimbra, Portugal

László POKORÁDI, Óbuda University, Budapest, Hungary

Roman RABENSEIFER, Slovak University of Technology in Bratislava, Bratislava, Slovak Republik

Mohammad H. A. SALAH, Hashemite University, Zarqua, Jordan

Dietrich SCHMIDT, Fraunhofer Institute for Wind Energy and Energy System Technology IWES, Kassel, Germany

Lorand SZABÓ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Csaba SZÁSZ, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Ioan SZÁVA, Transylvania University of Brasov, Brasov, Romania

Péter SZEMES, University of Debrecen, Debrecen, Hungary

Edit SZŰCS, University of Debrecen, Debrecen, Hungary

Radu TARCA, University of Oradea, Oradea, Romania

Zsolt TIBA, University of Debrecen, Debrecen, Hungary

László TÓTH, University of Debrecen, Debrecen, Hungary

László TÖRÖK, University of Debrecen, Debrecen, Hungary

Anton TRNIK, Constantine the Philosopher University in Nitra, Nitra, Slovakia

Ibrahim UZMAY, Erciyes University, Kayseri, Turkey

Andrea VALLATI, Sapienza University, Rome, Italy

Tibor VESSELÉNYI, University of Oradea, Oradea, Romania

Nalinaksh S. VYAS, Indian Institute of Technology, Kanpur, India

Deborah WHITE, The University of Adelaide, Adelaide, Australia

International Review of Applied Sciences and Engineering
Address of the institute: Faculty of Engineering, University of Debrecen
H-4028 Debrecen, Ótemető u. 2-4. Hungary
Email: irase@eng.unideb.hu

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2024
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2023
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Scopus CIte Score Rank	Architecture (Q1) General Engineering (Q2) Materials Science (miscellaneous) (Q3) Environmental Engineering (Q3) Management Science and Operations Research (Q3) Information Systems (Q3)
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International Review of Applied Sciences and Engineering
Publication Model	Gold Open Access Online only
Submission Fee	none
Article Processing Charge	1100 EUR/article
Regional discounts on country of the funding agency	World Bank Lower-middle-income economies: 50% World Bank Low-income economies: 100%
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Subscription Information	Gold Open Access

International Review of Applied Sciences and Engineering
Language	English
Size	A4
Year of Foundation	2010
Volumes per Year	1
Issues per Year	3
Founder	Debreceni Egyetem
Founder's Address	H-4032 Debrecen, Hungary Egyetem tér 1
Publisher	Akadémiai Kiadó
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	2062-0810 (Print)
ISSN	2063-4269 (Online)

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Abstract

Abstract

1 Introduction

2 Numerical model

3 Equation of motion

4 Solution of the problem

5 Numerical study

5.1 Validation of a model

6 Results and discussion

6.1 Evolution of free surface based on the heterogeneity coefficient β

6.2 Evolution of free surface based on the excitation frequency Ω

6.3 Evolution of free surface based on the filling rate h

6.4 Pressure distribution at the ends of the tank

7 Conclusion

References

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