Liquid Fill Level Research Articles

Small-scale BLEVE: Near-field aerial shock overpressure and impulse

This paper presents an investigation into one of the most damaging hazards associated with Boiling Liquid Expanding Vapor Explosion (BLEVE), specifically focusing on the near-field overpressure and impulse effects. Experiments were conducted at a small-scale to study the overpressure and impulse using aluminum tubes with a diameter of 50 mm and a length of 300 mm. The tubes were filled with pure propane liquid and vapor. The controlled variables, in this work included the failure pressure, the liquid fill level, and the weakened length along the tube top. These variables control the strength of the overpressure characterized by the peak overpressure amplitude, duration of this overpressure event, and the resultant impulse. Notably, these experiments at a small scale included experiments with a 100 % liquid fill level. This further confirmed that the vapor space is the main driver of the lead overpressure hazard. High-speed cameras and blast gauges effectively illustrated the progressive formation of the shock wave in both temporal and spatial dimensions. Furthermore, various predictive models available in the literature are discussed in this paper and new correlations were developed to quantify the overpressure duration and impulse. The current analysis aims to predict the potential consequences of overpressure events during a BLEVE.

Correlations to estimate the ground loading from small scale propane BLEVE experiments

This paper presents small-scale propane BLEVE (Boiling Liquid Expanding Vapor Explosion) experiments coupled with an investigation into ground loading dynamics. The experiments utilized cylindrical aluminum pressure vessels, with a diameter of 50 mm and a length of 300 mm. The controlled variables included burst pressure, liquid fill level, and weakened length. Both high and low-speed measurements of internal pressure and ground force were conducted during the experiments. The dependent variables analyzed were peak total ground load, force duration, and impulse. The findings from the study show trends in ground force and impulse with alterations in failure pressure, fill level and weakened length. Specifically, ground force and impulse exhibit an upward trend with increasing failure pressure, fill level and weakened length (cut length). For the first time, comprehensive correlations have been developed, incorporating the controlled variables, as well as theoretical boiling wave speed and vapor speed, to estimate the dependent variables, which represents a significant contribution in the field. However, the study does acknowledge the presence of scatter in the data, which are believed to be associated with the intricacies of the vessel opening process. It should be noted that this correlation has not been validated for larger scales. Once validated on a larger scale, these correlations can be directly applied in the design and practice of civil infrastructure to enhance the structural integrity. Additionally, the research has direct implications for industrial applications, allowing for the quantitative assessment of risks associated with bridge collapse during the transportation of PLGs.

Uncertainty propagation in the simulation of a nuclear power plant operational transient

With the continuous deployment of various intermittent energy sources on the grid there is an increasing opportunity for nuclear reactors to perform power maneuvers which can help alleviate issues related to supply oscillations during some periods of high renewable output. While utility specific codes can model such transients for safety assessments, there is a need to increase confidence in the application of these codes and to quantify the capabilities and accuracies of models in predicting these transients. In this work a power maneuver from 100 % full power to 59 % full power for a large CANDU reactor was studied using the TRACE-PARCS toolset. The work was computationally expensive as it examined both the effects of i) nuclear data library uncertainty which requires re-generation of the few-group cross sections and regeneration of an equilibrium core using 4 years of synthetic fuelling, and ii) initial core burn-up distribution involving the simulation of online fuelling operations over a period of 1400 days.The figures of merit considered in this work include changes in the average liquid zone controller fill level, individual channel powers, and the timing of adjuster bank withdrawals and reinsertions. Amongst the 100 s of simulated transients, the average time between adjuster bank withdrawals to override the Xenon transient and absolute standard deviations in these timings were found to be consistent between different nuclear datasets. The observed standard deviations were small, suggesting that the sensitivity to both nuclear data and initial core configuration is relatively small for both the adjuster withdrawal phase and the reinsertion phase. The contributions to total uncertainty due to both the core initial conditions and the nuclear data uncertainty were determined. During the early phase of the transient (i.e., adjuster withdrawals) nuclear data uncertainty and initial condition uncertainties were found to contribute nearly equally to total uncertainty, with slightly larger contributions due to nuclear data uncertainty. For adjuster bank reinsertions later in the transient it was observed that the contribution to total uncertainty by initial condition uncertainty was on average twice that of nuclear data uncertainties.The transients were compared to an actual power maneuver in a ∼900 MW CANDU reactor. In all cases, the model’s behaviour, while qualitatively correct, systematically over-predicted the time durations between adjuster movements and this difference exceeded the envelope of simulations that account for nuclear data and initial core configuration. Sensitivity studies performed to investigate the discrepancies suggest that additional refinements to the RRS emulator used in this work are required to match the station RRS more closely and that the transient evolution is highly sensitive to the initial excess reactivity in the core, which was observed to be lower in the station than in the TRACE simulations. Based on the simulation results the combined impact of the emulator responses, initial average zone levels, and incrementals modelling have a larger uncertainty than those related to nuclear data and initial core burnup distribution.

Modeling and simulation of cryogenic propellant tank pressurization in normal gravity

The self-pressurization process of cryogenic propellant storage under a normal gravity condition often involves turbulent mixing in the liquid region and complex flow fields in the vapor region caused by heat leak into a cryogenic tank. Over time, the cryogenic tank pressurizes due to a temperature increase in the vapor phase and the heat and mass transfer across the liquid–vapor interface. A nodal simulation approach was employed to study the long term transients of tank self-pressurization. In this paper, mechanistic models and correlations were implemented to simulate the self-pressurization of Multipurpose Hydrogen Test Bed experiments with a commercial nodal code, namely, Systems Improved Numerical Differencing Analyzer with Fluid Integrator (SINDA/FLUINT). A lump number sensitivity study on the prediction of tank pressure and temperature was performed to determine the number of lumps appropriate for a 50% initial liquid fill level. Uniform heat flux boundary conditions were implemented on both phases during the tank self-pressurization with an estimated heat leak provided by NASA. Numerical simulation showed that the predicted pressure profiles of the 50% and 90% fill level cases agreed well with experimental data. In the liquid region, temperatures were primarily uniform and close to saturation due to turbulent natural convection mixing. Findings showed the current model overestimated the temperature profiles in the vapor region when assuming heat conduction transfer.

Effect of Ovality on the Buckling Behavior of Thin-Walled Liquid-Filled Conical Tanks

This study investigates the influence of ovality on the buckling behavior of thin-walled liquid-filled conical tanks through comprehensive numerical simulations. The structural stability of conical tanks is of paramount importance in various engineering applications, such as storage vessels and aerospace structures. However, the presence of ovality, characterized by deviations from perfect circularity, can significantly affect the structural response and integrity of these tanks. To explore the effects of ovality, a finite element analysis (FEA) approach is employed, considering various ovality levels in the tank geometry. A comprehensive parametric study is conducted, varying key parameters such as tank dimensions, material properties, and liquid filling levels. The buckling behavior of the tanks is assessed by examining critical buckling loads and corresponding deformation modes. Results from the numerical simulations reveal that even small levels of ovality can substantially reduce the buckling load capacity of conical tanks. As ovality increases, the onset of buckling occurs at lower applied loads, leading to premature structural failure. The presence of liquid filling further exacerbates the buckling phenomenon, with the liquid sloshing effect amplifying the structural response. The study also investigates the influence of different materials on the buckling behavior of conical tanks subjected to ovality. It is found that the material stiffness and yield strength play a crucial role in determining the critical buckling load and mode shape. Furthermore, the effect of liquid fill level is explored, demonstrating that higher fill levels increase the vulnerability to buckling.

Experimental research on the two-phase explosive boiling mechanism of superheated liquid under different leakage conditions

In this study, a 17 L cube vessel was designed to simulate the explosive boiling of high-pressure liquefied gas after the leakage of the storage tank. The influence of leakage conditions such as crack position, crack diameter, and initial liquid fill level were investigated. Results indicate that when the crack is at the gas phase and gas-liquid interface, the rapid boiling of the liquid is caused by the leakage and significant pressure rebound is occurred. What’s more, cracks located under the gas-liquid phase may also cause a significant rebound in pressure. As the crack diameter increases, the two-phase flow boiling intensity first increases and then decreases, and it reaches the maximum when the diameter is 30 mm. Furthermore, a concept of the critical liquid level difference was proposed, and its influencing factors were studied. Under the experimental conditions in this article, BLEVE will not occur if the height between the liquid level and the crack is above the critical liquid level difference.

Influence of liquid fill level on the blast created by a water BLEVE in a tubular geometry

Influence of liquid fill level on the blast created by a water BLEVE in a tubular geometry

Optimal design of vertical porous baffle in a swaying oscillating rectangular tank using a machine learning model

The sloshing-induced impact loads on the tank wall are significant when the liquid in a tank is excited at and around its natural frequencies, which are highly reliant on the tank's geometry and liquid fill level. Herein, To design the optimal porous baffle for mitigation of liquid sloshing, a machine learning algorithm based on the MLPR model is adopted. First, a sloshing database comprising of different features such as porosity, baffle arrangement, submergence depth of the baffle, motion period, and free-surface elevation at the tank wall is prepared from the sloshing experiments in a swaying rectangular tank with the vertical porous baffle. Then, the detailed feature study is conducted on the database. The MLPR model is trained and validated after preprocessing the data, and the predictions on the free-surface elevation are made for 3520 combinations of feature values using the trained model. A comparison with the available experimental data shows that a well-trained machine learning model can predict well the physical characteristics that occurred in a sloshing tank. A fully submerged single baffle with a porosity of 0.1375 is obtained as the optimal baffle. It reduces significantly the liquid sloshing at resonance, especially the first-mode resonance peak, compared to the no-baffle tank.

Ground loading from BLEVE through small scale experiments: Experiments and results

The ground force generated by a BLEVE is a hazard that has been seldom studied, even though BLEVE has been source of many research works in the past decades. However, emergency responders have been asking questions the risk and consequences of a BLEVE on a bridge and other critical infrastructures for a while, with no answer so far. Moreover, a tank truck accident in Bologna in August 2018 has shown that bridge collapse may result from such scenario.This paper presents the experimental work done with a small scale apparatus reproducing realistic BLEVE failure with a cylindrical tube. Load cells were placed under the base plate holding the tube to measure the local ground force generated by the explosion. Forces from 10 kN to 55 kN were measured for a 50 mm diameter tube with 300 mm length failing at pressures from 10 to 32 Bar. The ground force signals are interpreted together with the imaging and internal pressure signal. The synchronization between violent boiling, repressurization in the vessel and strong ground force is clear through this comparison. Different ground force signals were observed depending on the fill level and weakened length of the tube. The maximum ground force and impulse vary almost linearly with failure pressure and liquid fill level. It is less clear for the influence of weakened/opening length of the tube. More data is required to conclude on this parameter influence.

Two-phase expanding mechanism and pressure response characteristic of boiling liquid expanding vapor explosion under rapid depressurization

The two-phase flow evolution, internal pressure, and thermodynamics responses during a BLEVE (boiling liquid expanding vapor explosion) process with water are assessed. Various initial pressures ranging from 1.7 to 5.7 barg, liquid fills load and different pressure relief ways were tested. Results show that after the pneumatic valve was opened, the rise velocity of the bubble increased first, and then decreased until the rupture or collision of the bubbles. The countercurrent flow reversed to the mainstream was experimentally observed and inhibited the expansion flow to reduce the boiling intensity. Thus, as the initial pressure increased, the average rate of pressure rose first increased, then slightly decreased due to the competitive effects of expansion flow and countercurrent flow. The interactions between the rarefaction wave driven by a sudden opening of a valve and the medium degree of superheat, control the pressure response, and the delay of boiling can be classified into the rarefaction wave control region (dp/dt < 0) and the superheat degree control regime (dp/dt> 0). And the effect of the liquid fill level on the rate of pressure rise was not affected by the countercurrent flow. The boiling explosion after the crack formed was intensified with pressure relief action caused by a separate piece of equipment, due to the enhanced heterogeneous boiling on the inner wall.

Measurement of Conductivity and Liquid Fill in Partially Filled Pipe Using Capacitive-Coupled Noncontact Probe

A noncontact capacitively coupled probe for the measurement of the liquid fill level and conductivity in a partially filled but horizontally kept pipe is presented. Capacitively coupled electrodes are used for conductivity measurements, but the error is high when the tube is partially filled with liquid. In this letter, we propose to use the values of the coupling capacitors formed between the liquid column and conductive electrodes to calculate the fill level and estimate the conductivity of water in the pipe. The resistance of the liquid column is determined using a recently reported autobalancing signal conditioning circuit. The circuit is designed to provide voltage directly proportional to the resistance of the water column. Voltages at the relevant nodes of the circuit are tapped to compute the equivalent coupling capacitance values. The resistance of the liquid column along with fill level determined through coupling capacitance values helps in measuring the conductivity of water flowing through the pipe. A worst-case error of ±0.9% was obtained in measuring the conductivity, and a worst-case error less than 0.52% was observed in the water fill level measurement from a prototype noncontact water conductivity measurement probe for a partially filled pipe that has been developed and tested.

Effect of porous baffle on sloshing pressure distribution in a barge mounted container subjected to regular wave excitation

An experimental study has been carried out to assess the sloshing pressure expected on the side walls of the tank and on top panel. A liquid fill level with an aspect ratio (hs /l, where hs is the static liquid depth and l is the tank length) of 0.488 is considered which corresponds to 75% liquid fill level. In view of suppressing sloshing oscillation and consequent sloshing pressure, the baffle wall configurations such as porous wall at l/2 and porous walls at l/3 and 2l/3 were adopted. Three porosities of 15%, 20.2%, and 25.2% were considered. The sloshing tank is fitted into the freely floating barge of model scale 1:43. The barge is kept inside the wave flume in the beam sea conditions. The effects of wave excitation frequencies and on the sloshing pressure variation have been studied in detail. For comparison purpose, solid wall placed at l/2 (Nasar and Sannasiraj, 2018) is also considered and, the salient results are herein reported.

A Framework for the Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors

Industrialization of bioreactors has been achieved by applying several core concepts of science and engineering. Modeling has deepened the understanding of biological and physical phenomena. In this paper, the state of existing cell culture models is summarized. A framework for development of dynamic and computationally feasible models that capture the interactions of hydrodynamics and cellular activities is proposed. Operating conditions are described by impeller rotation speed, gas sparging flowrate, and liquid fill level. A set of admissible operating states is defined over discretized process parameters. The burden on a dynamic solver is reduced by assuming hydrodynamics at its fully developed state and implementation of compartmental modeling. A change in the conditions of operation is followed by hydrodynamics switching instantaneously to the steady state that would be reached under new conditions. Finally, coupling the model with optimization solvers leads to improvements in operation.

Sloshing of liquid in partially liquid filled toroidal tank with various baffles under lateral excitation

A technique to study effect of various baffles on liquid oscillations in partially filled rigid toroidal tanks is first developed by extending the semi-analytical scaled boundary finite element method (SBFEM), which utilizes the advantages of both the boundary element (BEM) and finite element methods (FEM). As found in the BEM, only the boundary is discretized to reduce the space by one, and no fundamental solution is needed unlike the BEM. The calculated liquid domain is divided into several simple sub-domains so that the liquid velocity potential in each liquid sub-domain becomes the class C1 with continuity boundary conditions. Based on the linear potential theory and weighted residual method, the semi-analytical solutions of the liquid velocity potential corresponding to each sub-domain are obtained by means of SBFEM, where the geometry of each sub-domain is transformed into scaled boundary coordinates, including the radial and circumferential coordinates by using a scaling centre, and the finite-element approximation of the circumferential coordinate yields the analytical equation in the radial coordinate. By discretizing the flow boundaries, the integral equation governed on the boundary is formulated into a general matrix eigenvalue problem. Based on the eigenvalue problem and multimodal method, an efficient methodology is adopted to computer the sloshing masses and sloshing force. Accuracy, simple and fast numerical computations are observed by the convergence study, and excellent agreements have been achieved in the comparison of results obtained by the proposed approach with other methods. Meanwhile, several baffle configurations are considered including the horizontal bottom-mounted and surface-piercing ring baffles as well as their combination form, bottom-mounted and surface-piercing ring baffles as well as their combination, and free surface-touching baffles. The effects of baffled arrangement, the ratio b/a of elliptical cross section, liquid fill level, and baffles' length upon the sloshing frequencies, the associated sloshing mode shapes and sloshing forces are investigated in detail and some conclusions are outlined. The results show that the present method allows for the simulation of complex 3D sloshing phenomena using a relative small number of degrees of freedom while the mesh consists of two-dimensional elements only.

Transient Sloshing in Partially Filled Laterally Excited Horizontal Elliptical Vessels With T-Shaped Baffles

The transient sloshing in laterally excited horizontal elliptical containers with T-shaped baffles is first investigated by using a novel semi-analytical scaled boundary finite-element method (SBFEM). The proposed method combines the advantages of the finite-element and the boundary element methods (BEMs) with unique properties of its own, in which a new coordinate system including the circumferential local coordinate and the radial coordinate has been established. Only the boundary of the computational domain needs to be discretized in the circumferential direction as the same as the BEM and the solution in the radial direction is analytical. Assuming ideal, irrotational flow and small-amplitude free-surface elevation, the formulations (using a new variational principle formulation) and solutions of SBFEM equations for an eigenvalue problem under zero external excitation (free sloshing problem) are derived in detail. Subsequently, based on an appropriate decomposition of the container-fluid motion, and considering the eigenvalues and eigenmodes of the above eigenvalue problem, an efficient methodology is proposed for externally induced sloshing through the calculation of the corresponding sloshing masses and liquid motion. Several numerical examples are presented to demonstrate the simplicity, versatility, and applicability of the SBFEM during the simulation of sloshing problems of complex containers, and excellent agreement with the other methods is observed. Meanwhile, three T-shaped baffle configurations are considered including surface-piercing baffle, bottom-mounted baffle and their combination form, and Y-shaped configuration evolved from that of T-shaped baffle has been taken into consideration as well. The liquid fill level, arrangement and length of those baffles affecting the sloshing masses, and liquid motion are investigated in detail. The results also show that the present method can easily solve the singularity problems analytically by choosing the scaling center at the tip of the baffles and allows for the simulation of complex sloshing phenomena using far less number of degrees-of-freedom.

Liquid sloshing in partly-filled laterally-excited cylindrical tanks equipped with multi baffles

Baffles are used effectively to reduce the sloshing response of liquid in the liquid storage containers. This study is aimed at analysis of transient lateral sloshing in a partially-filled cylindrical tank with multi baffles including floating circular baffle, wall-mounted ring baffle, floating ring baffle and their combination form, and those baffles with inclination using a coupled multimodal method and scaled boundary finite element method (SBFEM). Slosh frequencies and mode shapes are initially estimated using the extending semi-analytical SBFEM by applying the linearized free surface boundary condition using the zoning method, where the liquid domain is firstly divided into several simple sub-domains so that the liquid velocity potential in each sub-domain has continuous boundary conditions of class C1. As a key point, a new type of local co-ordinate system for SBFEM with axisymmetric geometry is presented for each sub-domain. Based on the multimodal method, significant improvement in computational time is achieved by reducing the generalized eigenvalue problem to a standard one involving only the velocity potentials on the two-dimensional half free-surface length. The generalized coordinates of the free-surface oscillations under a lateral excitation are then obtained from superposition of the natural slosh modes. The sloshing mass and lateral slosh force are also formulated in terms of the generalized coordinates and hydrodynamic coefficients. The validity of the model is examined through comparisons with available other solutions, and the results show that the present method has higher accuracy and efficiency with a very small number of degrees of freedom for the simulation of the complex sloshing problem partly-filled laterally-excited cylindrical tanks. It is also shown that consideration of only the first sloshing mass is adequate to represent the dynamic behavior of the liquid container quite accurately. The effects of liquid fill level, baffled arrangement and length of those baffles upon the sloshing masses and sloshing forces are discussed in detail.

A numerical study of the effects of the T-shaped baffles on liquid sloshing in horizontal elliptical tanks

A semi-analytical scaled boundary finite-element method (SBFEM) is firstly extended to study the effects of the T-shaped baffle on liquid sloshing in horizontal elliptical tanks. The proposed method is based on the finite-element technology and gains the advantages of the boundary element method as well. Only the boundary is discretized reducing the spatial discretization by one, no fundamental solution is required and singularity problems can be modeled rigorously. Based on linear potential theory, the formulations (using new variational principle formulation) and the solutions of SBFEM equations for the sloshing problems are derived in details. As a key point, the solution for the inclusion of flow velocity along the baffles, which is called the side-faces of bounded domain in SBFEM, is also expressed in details. The accuracy, simplicity and convergence of the present method are demonstrated via numerical examples, and excellent agreement with the other method is observed. Meanwhile, three T-shaped baffled configurations are considered including surface-piercing baffle, bottom-mounted baffle and their combination form, and Y-shaped baffled configuration evolved from that of T-shaped baffle has been taken into consideration as well. The effects of liquid fill level, baffled arrangement and length of those baffles upon the sloshing frequencies, the associated sloshing mode shapes and sloshing wave height are investigated in details. The results also show that the present method has strong ability to resolve singularity problems analytically by choosing the scaling center at the tip of the baffles and allows for the simulation of complex sloshing phenomena using a very small number of degrees of freedom while the mesh consists of one-dimensional elements only.

Modal Analysis of Transient Liquid Sloshing in Partially-Filled Tanks

To investigate the dynamic characteristics of liquid sloshing in partially-filled tanks, FLUENT simulation for liquid sloshing in cylinder tanks with the 40% liquid fill level and subject to lateral accelerations of 0.1 g-0.4 g were carried out. By the observation of transient sloshing force and the liquid free surface, it was found that the liquid sloshing is a periodic oscillation. Fourier transform was utilized to transform the sloshing forces in the time domain to the signals in the frequency domain. By spectrum analysis, it was found that the first-order oscillation that has the biggest amplitude is the most important one for liquid sloshing. For further command on liquid sloshing, modal shapes for the first sixth modal were acquired by ANSYS. It is drawn that the odd modals have anti-symmetrical shapes and the first-order oscillation makes the biggest contribution on liquid sloshing, the even modals have symmetrical shapes and could not contribute to liquid sloshing.

Transient Liquid Sloshing in Partially-Filled Tank Vehicles

To investigate the accuracy and the scope of application of the QS method in transient liquid sloshing, 3 different tanks are selected as the research object. The liquid fill level is set at 0.6 and the constant lateral acceleration changes from 0.1 g to 0.4 g. The transient liquid sloshing is simulated by FLUENT and the relevant QS results are solved at the same conditions. The mean and maximum values for transient liquid sloshing effect are compared with the corresponding QS results. It was found that the mean values in a cycle are quite close to the QS calculation results. Furthermore, the QS method can only be used when the external excitation is constant and smaller. For lateral acceleration which is constant but large, and time-variation ones, the QS method is not suitable.

Investigation of Tank Pressurization and Pressure Control—Part I: Experimental Study

Self-pressurization and pressure control of cryogenic storage tanks have important design consequences for propellant and life support systems currently being planned for long duration space missions. During self-pressurization, the tank's liquid fill level and the heat load from the surroundings can have significant effects on the tank's thermal stratification and pressurization rate. When controlling pressure with a mixing jet, the velocity and temperature of the jet are important design parameters affecting the thermal destratification and pressure reduction time constants. In this work, a small-scale ground-based experiment was performed, as a precursor to a microgravity experiment, to investigate the effects of these variables on the pressurization and pressure control time constants in the tank and to assess the feasibility of using a forced jet mixer for reduced boil-off pressure control. Local pointwise temperature and pressure measurements, together with qualitative contours of the thermal field in the liquid, vapor, and wall region, were made to identify and characterize important self-pressurization and pressure control trends in 1 g.