Finite element methods for flow in porous media

This thesis studies the application of finite element methods to porous flow problems. Particular attention is paid to locally mass conserving methods, which are very well suited for typical multiphase flow applications in porous media. The focus is on the Brinkman model, which is a parameter dependent extension of the classical Darcy model for porous flow taking the viscous phenomena into account. The thesis introduces a mass conserving finite element method for the Brinkman flow, with complete mathematical analysis of the method. In addition, stochastic material parameters are considered for the Brinkman flow, and parameter dependent Robin boundary conditions for the underlying Darcy flow. All of the theoretical results in the thesis are also verified with extensive numerical testing. Furthermore, many implementational aspects are discussed in the thesis, and computational viability of the methods introduced, both in terms of usefulness and computational complexity, is taken into account

Effect of natural gas direct injection (NGDI) on the performance and knock behavior of an SI engine

The unique properties of natural gas (NG), including high availability and lower cost compared with other fossil fuels, make it attractive in internal combustion engine (ICE) application. NG is composed mainly of methane and has greater knock resistance than gasoline, enabling higher compression ratios (CR). In contrast with the distinctive advantages, the NG fueled engines suffer from lower power and torque outputs. To address the subject, this study proposes an approach employing NG direct injection (NGDI) strategy (with higher volumetric efficiency unlike port injection), enabling a higher CR irrespective of knock limit. This work applies reactive computational fluid dynamics (CFD) to investigate spark ignited co-combustion of direct-injected NG with port-admitted gasoline. The results are validated against experimental data. In all simulated cases, the equivalence ratio (i.e., ∅ = 1) and the total input energy are kept constant. Engine performance is evaluated for three CRs (10.5, 11.5, and 12.5:1), five proportion of CNG (RCNG) and at part- and full-load conditions at an engine speed of 1500 rpm. Results indicated that while running RCNG = 100 % with a CR of 10.5:1, carbon monoxide (CO) and carbon dioxide (CO2) emissions were decreased by 29.3 % and 23.5 % respectively, compared to RCNG = 0 %. The corresponding emission reduction at CR = 11.5:1 was 27.1 % and 24 %; at CR = 12.5:1 they were 29.6 % and 23.5 % respectively. At each CR, the knock intensity at full load fell significantly as the percentage of NG increased. At a CR of 12.5:1, ringing intensity (RI) at full load decreased by 88.6 % when using RCNG = 100 %, instead of RCNG = 0 %. Under the same conditions, RCNG = 25 % cut RI by 56 %.© 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).fi=vertaisarvioitu|en=peerReviewed

The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem

We present the formulation and the numerical analysis of the Brinkman problem derived in Allaire (Arch Rational Mech Anal 113(3): 209-259,1990. doi: 10.1007/BF00375065 , Arch Rational Mech Anal 113(3): 261-298, 1990. doi: 10.1007/BF00375066 ) with a lognormal random permeability. Specifically, the permeability is assumed to be a lognormal random field taking values in the symmetric matrices of size $$d\times d$$ , where $$d$$ denotes the spatial dimension of the physical domain $$D$$ . We prove that the solutions admit bounded moments of any finite order with respect to the random input's Gaussian measure. We present a Mixed Finite Element discretization in the physical domain $$D$$ , which is uniformly stable with respect to the realization of the lognormal permeability field. Based on the error analysis of this mixed finite element method (MFEM), we develop a multi-level Monte Carlo (MLMC) discretization of the stochastic Brinkman problem and prove that the MLMC-MFEM allows the estimation of the statistical mean field with the same asymptotical accuracy versus work as the MFEM for a single instance of the stochastic Brinkman problem. The robustness of the MFEM implies in particular that the present analysis also covers the Darcy diffusion limit. Numerical experiments confirm the theoretical result

Numerical Computations with H(div)-Finite Elements for the Brinkman Problem

The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant permeability. A hybridization technique for the problem is presented, complete with a convergence analysis and numerical verification. Finally, the numerical convergence studies are complemented with numerical examples of applications to domain decomposition and adaptive mesh refinement.Comment: Minor clarifications, added references. Reordering of some figures. To appear in Computational Geosciences, final article available at http://www.springerlink.co

Komposiittilaminaattien analyysi elementtimenetelmällä

Komposiittirakenteet ovat nykyään käytännön teollisuussovelluksissa yhä yleisempiä, ja niiden tehokas mallintaminen asettaa uusia haasteita laskennallisen mekaniikan näkökulmasta. Tässä työssä käsitellään komposiittilaminaattirakenteiden mallintamista Reissner-Mindlin laattateorian avulla, ja teoriaa sovelletaan paperin kupruiluun. Osana tätä työtä on Numerola Oy:n Numerrin-ohjelmistoon lisätty tarvittavat elementit ja luotu paperin mallintamiseen soveltuva malli. Aluksi muotoillaan klassisen laminaatioteorian mukainen matemaattinen malli, jossa laattatehtävä kytketään tasoelastisuustehtävään konstitutiivisen yhteyden avulla. Edelleen johdetaan tehtävän heikko muoto, sekä osoitetaan tehtävä hyvin määritellyksi ja stabiiliksi. Tehtävä ratkaistaan elementtimenetelmällä käyttäen laattatehtävälle MITC-elementtejä, joiden konstruktio esitellään yksityiskohtaisesti, ja johdetaan a priori virhearviot koko tehtävälle. Lopuksi esitellään paperin mallintamiseen soveltuva materiaalimalli, joka ratkaistaan käyttäen Numerrin-ohjelmistoa, sekä lasketaan muutamia numeerisia esimerkkejä. Tuloksiin perustuen komposiittilaattamallin voidaan todeta soveltuvan varsin hyvin paperin mallintamiseen, ongelmaksi havaitaan muodostuvan kuitenkin ennen kaikkea tehtävän laskennallinen vaativuus

Finite Element Analysis of Composite Plates with an Application to the Paper Cockling Problem

Summary In this work, we present a model for the laminated composite plate problem based on the Reissner-Mindlin model and classical lamination theory. The weak problem based on this model is solved with the finite element method using the MITC element family. Detailed a priori estimates are given for the mixed finite element formulation of the problem. Finally, we present an application of the model to the paper cockling problem

Wärtsilä Digital Design Platform

We present a methodology for systematically using an SPDM platform as the cornerstone of product development. The target is to base product development on clearly defined targets and requirements in different phases of the product development lifecycle. This is achieved by means of a data-centered approach where all data is retained in a digital form in the platform. Instead of reporting, users are provided with different views to the same data. We will demonstrate how a static document-based validation system can be replaced by a common validation data platform. In addition, we aim to base the validation requirements on a reliability analysis workflow. In this case, the platform is used not only to handle the simulation data but to encompass the whole product validation scope. To this end, we show how to couple requirements to the simulations and handle all the design decision data together with the simulations and use these to drive the design. In addition, we present ways to replace simulation reports with dynamic dashboards. To complete the loop, we touch the topic of PLM integration as a tool for assuring completeness of validation data in the product lifecycle. The motivation for the activity is a dramatic reduction in product development time based on a possibly somewhat longer concept phase but less iterations during the detail design phase. We will also present decision making based on data stored in the platform as well as demonstrate the data-centered approach to validation data. In addition, other benefits such as the re-use of data and simulation workflows along with the automatically handled data management are demonstrated. To conclude, some end user opinions and experiences in adopting a new system will be presented. Future developments will include moving also the physical testing data and coupling that with the corresponding simulations and validation requirements

Cylinder Head Design of Experiment by using the Wartsila Digital Design Platform

Cylinder Head Design of Experiment (DOE) was carried out by using the Wartsila digital design platform. The overall goal has been to create a simulation process to perform a complete cylinder head thermal-structural calculation and create a DOE over that process to vary the inputs, the geometrical parameters under optimization, in a fully automatic workflow. The outputs, uploaded to the DOE activity, were used to rank the input effects on the output response, to capture response sensitivity to input changes, to identify parameter interactions and, at the end, to estimate the optimal design

Full scale fatigue testing of crankshaft

This article outlines full-scale fatigue testing of crankshafts, in particular with the resonance fatigue testing method. The focus of the paper is the practical implementation of the method

Concept Calculation Tool for Dynamics of Generator Set Common Baseframe

The Natural frequency and vibration response calculation process of a generator set was automatized so that it can be used in a generator set common base frame concept design. The implementation of automatization was to be done so that no profound knowledge about the finite element method is needed to execute calculations and that computation times are short. Substructuring is used for certain parts of the generator set model to reduce the computation times for more a efficient concept design process. The common base frame concept design is implemented to the process by using a design tool in which the finite element model generation from parametric geometry is automatized. Generator set finite element model generation, natural frequency and vibration response calculations and post-processing of analysis results were implemented by developing a calculation tool for this purpose. The calculation tool is an independent application that uses Abaqus simulation software to execute analyses