Multistage rocket | EPFL Graph Search

A multistage rocket or step rocket is a launch vehicle that uses two or more rocket stages, each of which contains its own engines and propellant. A tandem or serial stage is mounted on top of another stage; a parallel stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched. By jettisoning stages when they run out of propellant, the mass of the remaining rocket is decreased. Each successive stage can also be optimized for its specific operating conditions, such as decreased atmospheric pressure at higher altitudes. This staging allows the thrust of the remaining stages to more easily accelerate the rocket to its final speed and height. In serial or tandem staging schemes, the first stage is at the bottom and is usually the largest, the second stage and subsequent upper stages are above

Three- or Two-Stage Stochastic Market-Clearing Algorithm?

Farzaneh Abbaspourtorbati, Antonio J. Conejo

As the power industry considers moving from a deterministic paradigm to a stochastic one to clear the day-ahead market in systems with significant stochastic production, the following question arises: how should a stochastic clearing algorithm be formulated? Our analyses indicate that a three-stage stochastic approach is clearly superior to a two-stage one. To show this, we propose a model that includes three stages: the first one represents the day-ahead market, the second stage, the intraday market, and the third one, the real-time operation. The objective is to clear the day-ahead market, but with a prognosis of the future: the intraday market and the real-time operation. To assess the impact of the intraday market on the day-ahead outcomes, we compare the results obtained from the proposed model with those of a simpler but more common two-stage model, which represents the day-ahead market and the real-time operation.

Ieee-Inst Electrical Electronics Engineers Inc2017

Application of the Rosenbrock methods to the solution of unsteady 3D incompressible Navier-Stokes equations

Simone Deparis, Michel Deville, Filippo Menghini, Luca Pegolotti, Alfio Quarteroni

We consider the Rosenbrock methods, namely a family of methods for Differential Algebraic Equations, for the solution of the unsteady three-dimensional Navier-Stokes equations. These multistage schemes are attractive for non-linear problems because they achieve high order in time, ensuring stability properties and linearizing the system to be solved at each timestep. Moreover, as they provide inexpensive ways to estimate the local truncation error, adaptive timestep strategies can be easily devised. In this work we test the Rosenbrock methods for the solution of three-dimensional unsteady incompressible flows. We derive the correct essential boundary conditions to impose at each stage in order to retain the convergence order of the schemes. Then, we consider two benchmark tests: a flow problem with imposed oscillatory pressure gradient whose analytical solution is known and the classical flow past a cylinder. In the latter case, we especially focus on the accuracy in the approximation of the drag and lift coefficients. In both benchmarks we test the performance of a time adaptivity scheme.

2018

Methodology using process integration for identifying suitable Organic Rankine Cycles for waste heat valorisation

Matthias Bendig, Daniel Favrat, François Maréchal

The identification of a suitable combined electricity production cycle depends on the heating and cooling requirements of the respective industrial process. Due to the large number of options an exhaustive enumeration of all the possibilities is not realistic. An optimisation based approach has to be adopted; it should be multi-objective and non-linear. The Methodology proposed is systematically generating a list of competing options, it follows the logic: - Analyse – Identifying heating and cooling requirements of the process. - Generate – Generation of options and scenarios how requirements can be satisfied. - Evaluate – Classify the generated options. During the different steps, several models are used. In order to identify the heating and cooling requirements of the process, Pinch analysis and the integration of the process have to be applied. The generation of the various options is done by a number of models. First an evolutionary algorithm fixes the decision variables for one option within the pre-defined constraints; a flow sheeting tool is used to calculate the thermodynamic states with the help of thermodynamic models. From the results, thermodynamic key performance indicators are calculated. A further model calculates the optimal thermal integration of the cycle configuration into the process; the results of this integration are used by sizing models to calculate the sizing of needed equipment. With the help of the sizes, cost models are used in order to calculate cost indicators and environmental models are used to calculate key environmental and LCA-indicators. With all the indicators related to every single configuration, the pareto-optimal solutions in regard to the pre-defined objectives are identified. As decision variables we identify the thermodynamic cycle configurations, in which the working fluid, fluid mixtures and compositions, multi stage or single stage cycles are proposed. In addition a second level of continuous decision variables, define the operating conditions for the selected cycle configuration. In addition to the objective function a set of performance indicators is proposed for the choice of the cycle as a decision support: 1. Quantitative indicators like efficiency (first and second principle), cost, CO2-equivalents, ozone depletion potential (ODP), LCA-Indicators 2. Qualitative criteria like flammability, toxicity

2013

Methodology using process integration for identifying suitable Organic Rankine Cycles for waste heat valorisation

Matthias Bendig, Daniel Favrat, François Maréchal

2013