Thermal Model for Timber Fire Exposure with Moving Boundary

Fire exposure of timber leads to charring, surface cracking and timber burnout, shifting the external thermal load deeper into the timber domain. This phenomenon plays its role mainly in situations of longer fire exposure. The majority of current approaches and models assume initial geometry during the whole analysis, leading generally to the overestimation of the insulation effect of the charred layer and to a limited burnout. This paper presents a heat transport model which is supplemented with a moving boundary condition, a criterion for the finite element deactivation and the internal heat source. Comparison with experiments using a constant radiative load testifies that the moving boundary condition becomes important after approximately 10 min of fire exposure and rather leads to a constant charring rate observed in several experiments.

A Comparison of Time-Frequency Methods for Real-Time Application to High-Rate Dynamic Systems

High-rate dynamic systems are defined as engineering systems experiencing dynamic events of typical amplitudes higher than 100 gn for a duration of less than 100 ms. The implementation of feedback decision mechanisms in high-rate systems could improve their operations and safety, and even be critical to their deployment. However, these systems are characterized by large uncertainties, high non-stationarities, and unmodeled dynamics, and it follows that the design of real-time state-estimators for such purpose is difficult. In this paper, we compare the promise of five time-frequency representation (TFR) methods at conducting real-time state estimation for high-rate systems, with the objective of providing a path to designing implementable algorithms. In particular, we examine the performance of the short-time Fourier transform (STFT), wavelet transformation (WT), Wigner–Ville distribution (WVD), synchrosqueezed transform (SST), and multi-synchrosqueezed transform (MSST) methods. This study is conducted using experimental data from the DROPBEAR (Dynamic Reproduction of Projectiles in Ballistic Environments for Advanced Research) testbed, consisting of a rapidly moving cart on a cantilever beam that acts as a moving boundary condition. The capability of each method at extracting the beam’s fundamental frequency is evaluated in terms of precision, spectral energy concentration, computation speed, and convergence speed. It is found that both the STFT and WT methods are promising methods due to their fast computation speed, with the WT showing particular promise due to its faster convergence, but at the cost of lower precision on the estimation depending on circumstances.

Fuel Tank Vertical Sloshing during Aircraft Landing

In this article, the influence of the fuel sloshing on the tank under the landing condition is investigated to explain the skin deformation of wing tank. Based on the SPH method, a simplified fuel tank model of gas-liquid-solid three-phase is established. NanoFluidX, a fluid dynamics simulation tool, is used to calculate fuel sloshing through a given load and the pressure on the tank. The pressure on the lower wall of tank is then imported into the ABAQUS to calculate the stress distribution on the skin. A measured acceleration curve within 0.56s is used as the moving boundary condition of the fuel tank. It is found through simulation that the air has less influence on the pressure on the lower wall during the aircraft landing. By changing the liquid filling rate, the differences of the pressure on the lower wall are compared. Based on the above research, an empirical relationship among the wall pressure, the external load and the liquid filling rate is obtained.

Singular Perturbation Solution for a Two-Phase Stefan Problem in Outward Solidification

Mathematical modeling of phase change process in porous media can help ensure the efficient design and operation of thermal energy storage and pipe freezing. Numerical methods generally require high computational power to be applicable in practice. Therefore, it is of great interest to develop accurate and reliable analytical frameworks. This study proposes a singular perturbation solution for a two-phase Stefan problem that describes outward solidification in a finite annular space. The problem solves cylindrical heat conduction equations for both solid and liquid phases, with consideration of a moving boundary condition. Perturbation method takes the advantages of small Stefan number as the perturbation parameter, which intrinsically occurs in porous media. Furthermore, a boundary-fixing technique is used to remove nonlinearity in the moving boundary condition. Two different time scales are separately expanded and evaluated to facilitate the construction of a composite asymptotic solution. The analytical solution is verified against a general numerical model using enthalpy method and local volume-averaged thermal properties. The results indicate that the temperature profile of both phases can be well modeled by singular perturbation theory. The analytical solution is found to have similar conclusions to the numerical analysis with much lesser computational cost.

Mathematical Model of Pipeline Abandonment and Recovery in Deepwater

In offshore oil and gas engineering the pipeline abandonment and recovery is unavoidable and its mechanical analysis is necessary and important. For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. The mathematical model of pipeline abandonment and recovery is a moving boundary value problem, which means that it is hard to determine the length of the suspended pipeline segment. A novel technique for the handling of the moving boundary condition is proposed, which can tackle the moving boundary condition without contact analysis. Based on a traditional numerical method, the problem is solved directly by the proposed technique. The results of the presented method are in good agreement with the results of the traditional finite element method coupled with contact analysis. Finally, an approximate formula for quick calculation of the suspended pipeline length is proposed based on Buckingham’s Pi-theorem and mathematical fitting.

Lattice Boltzmann Simulation of Frost Formation Process

Compared with the conventional mathematical and physical models, the lattice Boltzmann (LB) method is an effective method to simulate the heat and mass transfer in porous media. Frost crystallization aggregation is a very complex process involving inconsistency of frost structures, crystal size distributions, the complex transient shapes, and other numerous influential factors. Assuming the frost is a special porous medium consists of ice crystals and humid air, a mesoscopic model is established to predict the behavior of frost formation based on the lattice Boltzmann equation. The moving boundary condition is adopted in the two-dimensional nine-speed (D2Q9) lattices. The influences of the cold flat surfaces temperature on frost formation process are investigated. The variation laws of frost density and frost layer height are obtained and discussed. Simulation results by the LB model are in agreement with the experiment data from the references.

Υπολογισμοί και μετρήσεις σταθερής τρισδιάστατης ροής με φερτά υλικά πέριξ υδραυλικών κατασκευών

Στην παρούσα ερευνητική εργασία παρουσιάζεται η αριθμητική προσομοίωση ροής με ελεύθερη επιφάνεια, γύρω από υδραυλικές κατασκευές. Βασικό της αντικείμενο αποτελεί η ανάπτυξη ενός πεπλεγμένου αριθμητικού σχήματος πεπερασμένων όγκων για την προσομοίωση δισδιάστατων και τρισδιάστατων σταθερών και ασταθών ροών με ελεύθερη επιφάνεια σε ανοικτούς αγωγούς με μη-ομαλή γεωμετρία, τόσο με σταθερό όσο και με μεταβλητό πυθμένα λόγω στερεομεταφοράς. Οι συντηρητικές εξισώσεις της κίνησης του ρευστού αποτελούν την βάση για την ανάπτυξη του δισδιάστατου αριθμητικού σχήματος ενώ στην περίπτωση μεταβλητού πυθμένα, οι παραπάνω εξισώσεις συνδυάζονται με μία νέα εξίσωση, αυτήν της διατήρησης της μάζας των φερτών, βάσει της οποίας υπολογίζεται η μεταβολή της στάθμης του πυθμένα του αγωγού σε συνδυασμό με τις μοναδιαίες στερεοπαροχές κατά τις δύο κατευθύνσεις ροής. Για την εκτίμηση των μοναδιαίων στερεοπαροχών υιοθετείται και παρουσιάζεται μία σειρά από εμπειρικές εξισώσεις υπολογισμού που ενσωματώνονται στο μοντέλο. Για την ανάπτυξη του τρισδιάστατου αριθμητικού μοντέλου επιλύονται οι εξισώσεις Navier-Stokes διατυπωμένες στις τρεις διαστάσεις. Παράλληλα, με την αξιοποίηση της τεχνικής της ψευδοσυμπιεστότητας δίδεται η δυνατότητα του άμεσου υπολογισμού της τιμής της πίεσης από την εξίσωση της συνέχειας. Ο καθορισμός της θέσης της ελεύθερης επιφάνειας του νερού βασίζεται στη συνθήκη του κινητού ορίου (moving boundary condition) και επιτυγχάνεται με την εισαγωγή της δισδιάστατης συντηρητικής εξίσωσης της συνέχειας. Οι παραπάνω εξισώσεις δισδιάστατης και τρισδιάστατης ροής μετασχηματίζονται σε ένα νέο τοπικό μη-ορθογώνιο σύστημα συντεταγμένων, προσδιορισμένο επί των ορίων του προβλήματος (non-orthogonal, body-fitted coordinate system). Με τον τρόπο αυτό επιτρέπεται η μετάβαση από τον φυσικό χώρο ροής στον υπολογιστικό χώρο ώστε να καταστεί δυνατή η προσομοίωση προβλημάτων με μη-ομαλή γεωμετρία. Επί των μετασχηματισμένων στο τοπικό σύστημα συντεταγμένων εξισώσεων, εφαρμόζεται το πεπλεγμένο αριθμητικό σχήμα πεπερασμένων διαφορών τόσο για τον δισδιάστατο όσο και για τον τρισδιάστατο χώρο ροής. Το προκύπτον αριθμητικό μοντέλο εφαρμόστηκε στην επίλυση ποικίλων προβλημάτων δισδιάστατης, σταθερής και ασταθούς ροής, δισδιάστατης ροής με φερτά υλικά γύρω από υδραυλική κατασκευή καθώς και τρισδιάστατης ροής με μη-υδροστατική κατανομή της πίεσης πάνω από εκχειλιστή διπλού τόξου. Τα αριθμητικά αποτελέσματα ελέγχονται με διαθέσιμα αποτελέσματα μετρήσεων, με αποτελέσματα μετρήσεων που διεξήχθηκαν για τον σκοπό αυτό καθώς και με αποτελέσματα άλλων αριθμητικών μοντέλων. Σε όλες τις περιπτώσεις προκύπτει ικανοποιητική σύγκριση, επιβεβαιώνοντας έτσι την αξιοπιστία του αναπτυχθέντος αριθμητικού μοντέλου.