Numerical Simulation of Compressible Multicomponent Flows

Abstract: France is a country where the sector of energy has a big importance. Seven out of the fourteen companies of the CAC40 (a french stock market index of the 40 biggest companies) are strongly involved in the energy sector: Total, GDF Suez, EDF, Legrand, Schneider Electric, Alstom, and Technip. This industry was also responsible for 1.7% of France's GDP in 2012. The term energy industry includes all the activities related to the treatment of the primary energies, from their production, importation, to their transformation into usable energy and their transport and distribution to the consumers. Fossil fuels represent about half of the primary energy consumed in France, most of which is imported as the country does not possess any major oil deposit or gas well, and the extraction of coal was stopped in 2004. Electricity represents the other half of the primary energy consumption. This electricity does not need to be imported. France is the eighth biggest electricity producer in the world. Large amounts of its production are even exported: in 2012 57 TWh were exported (10% of the total production). From the 80's the energy production in France has been dominated by the nuclear sector, and by 2014 77% of the electricity was produced in nuclear powerplants. This makes France the rst country in the world in terms of proportion of electricity produced with nuclear energy. However after the recent accident of Fukushima and the raising interest for renewable energies, the French government has decided to limit the yearly nuclear production to its current level (63.2 GW). It has also devised a plan to reduce the proportion of nuclear energy to 50% by 2025. Currently 58 nuclear reactors are in service on the territory and new generation reactors are being built to replace the old ones. So in spite of this political plan to reduce the importance of nuclear energy, it is still very important to study the technical aspects of nuclear energy generation. Understanding the various phenomenons that can occur during the process is of tremendous importance in order to prevent any severe accident. To understand the kind of issues that can appear on a nuclear power plant, let us say a few words about its working. A nuclear power plant is an industrial facility that uses the heat produced by nuclear reactions to produce electricity. Like in any thermal power plant the heat is used to vaporise water. The steam then drives a turbine linked to an electric generator. The 58 French reactors are Pressurized Water Reactors (PWR) owned by the company EDF (Electricite De France). This technology is the most used worldwide. PWR uses uranium as combustible. They work as follows. The ssion chain reaction produces heat that is transferred to the primary coolant loop inside the reactor. The primary coolant loop is a circuit of pressurized water at 155 bar (155 times the atmospheric pressure). After owing through the reactor, the water of this loop reaches a temperature of around 328C. Due to its high pressure, the water stays liquid even at that temperature. After the reactor, the pressurized water of the primary coolant loop ows through the steam generator to transfer heat to the secondary coolant loop. It is then pumped back into the reactor. The secondary coolant loop is also a circuit of water. In this one the water is rst transformed into pressurized steam inside the steam generator thanks to the heat transfer with the primary coolant loop. The pressurised steam is used to drive a turbine that is connected to an electric generator for the actual production of electricity. After the turbine the steam is transformed back into liquid water inside the condenser, and pumped to the steam generator. In the steam part of the secondary coolant loop, between the steam generator and the turbine, the gas has a very high density of energy. The ow in the pipes is turbulent and compressible. Shock waves, supersonic jet and other compressible phenomenons occur in the devices present in the loop, such as throttle valves. All this leads to a generation of noise and vibrations that often interact back with the ow. This coupling between ow features and acoustic waves can be very problematic when they resonate with the vibrational mode of the structure. It can lead to large discharge of energy by vibration, inducing premature deterioration or even rupture of the structure. To understand these phenomenons is of primary importance for the safety of EDF's nuclear power plants. Thus EDF decided in 2008 to create a numerical tool for the simulation of ows where compressible features and acoustic waves interact. The project was called Code Safari.  Simulating directly both the compressible features of the ow and its acoustic eld is very challenging. For example in a situation at ambient pressure it means being able to resolve variations around 1 Pa in a ow at 105 Pa. The di erence of scale between the compressible features of the ow and the acoustic waves makes it important that the numerical scheme used for the simulation be very accurate. It was decided to develop Code Safari based on a high-order centered nite-di erence scheme, with a shock capturing strategy [6]. With this scheme, Code Safari has demonstrated its capability to simulate ows with acoustic coupling [9], and was successfully applied in the study of several industrial issues. An other class of problem is of importance for EDF: the compressible and multiphase ows. For example one of the accidental scenario that is thoroughly investigated is the Loss Of Coolant Accident or LOCA. This acronym describes an accidental scenario where the primary coolant loop is compromised and some of the highly pressurised water starts to ow out. In that case the sudden loss of pressure in the pipes as well as the high temperature of the water causes it to transform into steam. At EDF this kind of accident is studied among other using Europlexus, a software developed by the CEA (Commissariat a l'Energie Atomique). Unlike Code Safari, this software is based on rst and second order accurate numerical schemes and is able to simulate multiphase compressible ows. However on one-phase ows it cannot resolve the ow features with as much precision as Code Safari would. On those situations the two softwares are very complementary: Europlexus calculates the general ow eld including the e ects of uid-structure interaction while Code Safari allows for a more precise understanding of the ne structures of the ow. But as soon as multi-phase ows are involved, Code Safari do not have the ability to run simulations. For this reason it was decided in 2014 to improve Code Safari and give it the ability to treat multiphase ows. The following work is the rst step of this project. The objective is to develop, implement, and test a new high-order numerical scheme adapted to multi-components ows. The rst part of this report will give the background information necessary to understand the second part, where the main features of the numerical scheme are described. In the nal part we present the results obtained with this numerical scheme on several benchmark tests.