Projectile motion | EPFL Graph Search

Projectile motion is a form of motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particular case of projectile motion on Earth, most calculations assume the effects of air resistance are passive and negligible. The curved path of objects in projectile motion was shown by Galileo to be a parabola, but may also be a straight line in the special case when it is thrown directly upward or downward. The study of such motions is called ballistics, and such a trajectory is a ballistic trajectory. The only force of mathematical significance that is actively exerted on the object is gravity, which acts downward, thus imparting to the object a downward acceleration towards the Earth’s center of mass. Because of the object's inertia, no external force is needed to maintain the horizontal velocity component of the object's motion. Taking othe

Numerical Simulations of the Apollo 4 Re-entry Trajectory

Ermioni Papadopoulou

Sample return capsules, as the Apollo Command Module have been widely used to ad- vance the knowledge and planning of manned lunar and planetary return missions. Such reentry vehicles undergo extreme thermal conditions, caused by shock-heated air during their super-orbital atmospheric re-entry. Such extreme conditions can result in failure of the aeroshell structure and loss of important payload. This technological challenge is ad- dressed by the use of ablative thermal protection systems (TPS), which dissipate the heat away from the vehicles front wall via ablative products release into the boundary layer. Additionally, such velocity and temperature magnitudes during reentry conditions intro- duce significant radiative heat loads, filling the shock layer with radiators that react with the ablative species injected by the capsule wall. Therefore, accurate numerical modeling techniques are required, so that the thermophys- ical, thermochemical environment of a reentry capsule can be successfully reproduced and predicted. The present work aims to numerically rebuild certain significant trajectory points, containing the peak heating points of the Apollo 4 terrestrial re-entry. This re- quires the coupling of the resolved flow-field with radiative and ablative effects in order to accurately predict the convective and radiative heat flux for each trajectory point. The results will be compared to previous calculations and existing flight data. The numerical simulations are performed in 2D thermal non-equilibrium with a compress- ible explicit Navier-Stokes solver, coupled to a radiation database and a thermal material response code to implement the ablative effects. The calculations are performed also in 3D, using a commercial implicit Navier-Stokes solver. The results will be used to reproduce the capsules trajectory and verify the accuracy of the associated Modeling Tools.

2014

Towards practical solutions for energy efficiency of large-scale industrial sites

Nasibeh Pouransari

This thesis investigates a set of advanced topics inspired from the heat integration and the pinch technology, all tied around the challenge of identifying energy savings in large-scale chemical industrial plants. In search for a general-purpose methodology for energy efficiency, it has been observed that some well established methods exist already, but either they are case specific or relatively short handed when it comes to dealing with the large size plants. A general multi-step methodology is proposed in this thesis and then continuously improved, with a particular focus on the industrial realism and the usability for large-scale problems. The general methodology has been first put in practice to identify energy savings options in real case applications with the purpose of identifying the challenges to be tackled. Different aspects of large scale systems integration are being tackled: we start by studying issues experienced during the data gathering stage and come up with a multilevel data extraction approach. It is based on the different representation of the process unit heat transfer interfaces that satisfy the same heat requirement and let us tune the required level of detail with respect to how detailed the energy requirement definition needs to be for the site scale integration. The combination of those heat requirement levels is then applied to the Total Site Integration (TSI), alleviating the difficulties of the data extraction for large-scale problems. The heat recovery targets of the total site are then explored to identify further energy savings by the introduction of advanced technologies such as the heat pump and the Mechanical Vapor Recompression (MVR). Following the heat recovery improvement target, the study investigates the integration of one of the major heat consumers in the chemical processes : the distillation columns. The thermodynamic optimization of distillation columns has been examined together with the TSI and the integration of advanced separation concepts like Dividing-Wall Columns has been investigated considering a holistic site scale approach. The retrofit of the Heat Exchanger Network (HEN) of large-scale plants has been studied next. The definition of the same heat requirement presenting different heat transfer units has been used to introduce the existing network into the optimization model. The purpose is to evaluate and to minimize the required modifications to the existing system. We have proposed a multi-objective optimization with the evolutionary algorithm and a Mixed Integer Linear Programming (MILP) model. The optimal Pareto-frontier has been generated with respect to the minimum operating cost, the investment cost, the number of required modifications and the thermal exergy destruction. This approach offers two main advantages: (i) it is helpful to predict the region of good solutions without going through numerous iterations between targeting levels, usually required in the classical heat integration methodology for the evaluation of the retrofit of existing facilities and (ii) it helps considerably reduce the size of the posterior HEN re-design problem by minimizing the number of streams to be considered. The concluding chapters consider ways to reduce the size and the computational complexities of the HEN design for industrial size problems, with a main focus on the Heat Load Distribution (HLD) subproblem.

EPFL2015

An Inertial Sensor-Based Method for Estimating the Athlete's Relative Joint Center Positions and Center of Mass Kinematics in Alpine Ski Racing

Kamiar Aminian, Benedikt Fasel

For the purpose of gaining a deeper understanding of the relationship between external training load and health in competitive alpine skiing, an accurate and precise estimation of the athlete's kinematics is an essential methodological prerequisite. This study proposes an inertial sensor-based method to estimate the athlete's relative joint center positions and center of mass (CoM) kinematics in alpine skiing. Eleven inertial sensors were fixed to the lower and upper limbs, trunk, and head. The relative positions of the ankle, knee, hip, shoulder, elbow, and wrist joint centers, as well as the athlete's CoM kinematics were validated against a marker-based optoelectronic motion capture system during indoor carpet skiing. For all joints centers analyzed, position accuracy (mean error) was below 110 mm and precision (error standard deviation) was below 30 mm. CoM position accuracy and precision were 25.7 and 6.7 mm, respectively. Both the accuracy and precision of the system to estimate the distance between the ankle of the outside leg and CoM (measure quantifying the skier's overall vertical motion) were found to be below 11 mm. Some poorer accuracy and precision values (below 77 mm) were observed for the athlete's fore-aft position (i.e., the projection of the outer ankle-CoM vector onto the line corresponding to the projection of ski's longitudinal axis on the snow surface). In addition, the system was found to be sensitive enough to distinguish between different types of turns (wide/narrow). Thus, the method proposed in this paper may also provide a useful, pervasive way to monitor and control adverse external loading patterns that occur during regular on-snow training. Moreover, as demonstrated earlier, such an approach might have a certain potential to quantify competition time, movement repetitions and/or the accelerations acting on the different segments of the human body. However, prior to getting feasible for applications in daily training, future studies should primarily focus on a simplification of the sensor setup, as well as a fusion with global navigation satellite systems (i.e., the estimation of the absolute joint and CoM positions).