A symmetry-preserving second-order time-accurate PISO-based method

A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. [35]. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method. Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods

Development of an implicit framework for the two-fluid model on unstructured grids

The two-fluid model is an efficient method for simulating multiphase flows, based on an averaged description of the phases as interpenetrating and interacting continua. It is particularly attractive for the simulation of dispersed gas-solid flows in which the large number of particles in practical devices can impose an insurmountable computational burden for particle tracking methods, given currently available computing resources. Whilst the two-fluid model is more efficient than particle tracking methods, it results in large, strongly coupled and highly non-linear systems of equations, placing a premium on efficient solution algorithms. Additionally, the constitutive models used to describe the solid phase introduce stiff source terms, requiring a robust solution algorithm to handle them. In this thesis a fully-coupled algorithm is developed for the two-fluid model, based on a Newton linearisation of the underlying equation system, resulting in an algorithm treating all inter-equation couplings implicitly. For comparison, a semi-coupled algorithm, based on a Picard linearisation of the two-fluid model is also implemented, yielding a smaller implicitly coupled pressure-velocity system and a segregated system for the transport of phase concentrations. Motivating this work is the highly non-linear nature of the two-fluid model and the stiff source terms arising in the models of the dispersed phase, these are treated explicitly in the semi-coupled algorithm and may impose stability limits on the algorithm. By treating these terms implicitly, it is expected that the fully-coupled solution algorithm will be more robust. The algorithms are compared by application to test cases ranging from academic problems to problems representative of industrial applications of the two-fluid model. These comparisons show that with increasing problem complexity, the robustness of the fully-coupled algorithm leads to an overall more efficient solution than the semi-coupled algorithm.Open Acces

Minimum-dissipation model for large-eddy simulation in OpenFoam -A study on channel flow, periodic hills and flow over cylinder

The minimum-dissipation model is applied to turbulent channel flows up to $Re_\tau = 2000$, flow past a circular cylinder at $Re=3900$, and flow over periodic hills at $Re=10595$. Numerical simulations are performed in OpenFOAM which is based on finite volume methods for discretizing partial differential equations. We use both symmetry-preserving discretizations and standard second-order accurate discretization methods in OpenFOAM on structured meshes. The results are compared to DNS and experimental data. The results of channel flow mainly demonstrate the static QR model performs equally well as the dynamic models while reducing the computational cost. The model constant $C=0.024$ gives the most accurate prediction, and the contribution of the sub-grid model decreases with the increase of the mesh resolution and becomes very small (less than 0.2 molecular viscosity) if the fine meshes are used. Furthermore, the QR model is able to predict the mean and rms velocity accurately up to $Re_\tau = 2000$ without a wall damping function. The symmetry-preserving discretization outperforms the standard OpenFOAM discretization at $Re_\tau=1000$. The results for the flow over a cylinder show that mean velocity, drag coefficient, and lift coefficient are in good agreement with the experimental data. The symmetry-preserving scheme with the QR model predicts the best results. The various comparisons carried out for flows over periodic hills demonstrate the need to use the symmetry-preserving discretization or central difference schemes in OpenFOAM in combination with the minimum dissipation model. The model constant of $C=0.024$ is again the best one

A generalised immersed boundary method for flows of dense suspension of solid particles

Immersed boundary method (IBM) provides computational advantages in approximating moving solid surfaces on fixed numerical meshes. It has been widely used for fully-resolved simulations of particulate flows. This thesis proposes a generalised formulation of IBM with improved applicability to flows with dense concentrations of particles and unstructured meshes. The new IBM formulation, which is based on the smooth-interface direct forcing approach, directly uses the algebraic discretised terms of the momentum equations in the evaluation of the forces on Lagrangian immersed boundary (IB) points, and evaluate the integral Lagrangian volumes based on these forces. Appropriate reconstructions of the boundary forces are adopted to ensure the compatibility with the momentum-weighted interpolation used for the finite-volume discretisation with a collocated mesh arrangement. A modified direct forcing formulation is also proposed, which results in an efficiency gain of a devised segregated flow-particle coupling scheme. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and arbitrary triangular/tetrahedral meshes, and the results are similar or better than other related methods that are mostly developed for Cartesian meshes. Accurate and stable enforcement of the no-slip condition on the IB at every time-step is demonstrated, even for flows with strong transient behaviour and high velocity and pressure gradients. Local continuity in the vicinity of the IB is also preserved, ensuring local and global mass conservation alongside the local no-slip condition. Adaptations devised for unstructured meshes results in an accuracy close to that obtained on Cartesian meshes. The framework is successfully applied in the simulations of fluidisation of dense particle bed and a rising pack of light particles, showing robust stability. The issues related to the interfering regularised forces of different particle surfaces are not significant using the present formulation, hence eliminate unphysical flow patterns between aggregated particles.Open Acces

A non-linear quasi-3D model for air management modelling in engines

El modelado se ha convertido en los últimos años en una herramienta esencial en el diseño de motores de combustión interna alternativos, ya que permite reducir considerablemente el tiempo y los costes de desarrollo. Las metodologías de diseño clásicas se basan en la fabricación de prototipos y la realización de pruebas de ensayo y error. Actualmente, la mayoría de estas pruebas han sido sustituidas por cálculos numéricos, de modo que sólo las opciones de diseño más prometedoras se prueban en realidad en banco motor. Durante años, los códigos unidimensionales de dinámica de gases en el dominio del tiempo han sido suficientes para modelar tanto las prestaciones y el consumo del motor como el ruido de admisión y escape. Sin embargo, para un nivel más exigente de diseño, una representación 1D puede no ser suficiente para describir con precisión el flujo en ciertos elementos. Esto es especialmente importante en el caso de silenciadores, donde la hipótesis unidimensional sólo se puede aplicar a geometrías simples. En el caso de las uniones de conductos es la existencia de estructuras tridimensionales de flujo complejas lo que establece el límite de la aplicabilidad de una descripción simple cero-dimensional. En vista de estas limitaciones, la primera opción sería el uso de un modelo de dinámica de fluidos computacional (CFD); sin embargo, su aplicación conllevaría un tiempo de cálculo excesivo. Una posible solución de compromiso viene dada por los modelos cuasi-3D, basados en esquemas tridimensionales, pero con ciertas simplificaciones capaces de reducir significativamente el tiempo de cálculo sin afectar excesivamente a la precisión. Tales soluciones se han convertido en estándar en los códigos comerciales y se han aplicado con éxito a los silenciadores, tanto para excitaciones acústicas en el régimen lineal como en condiciones reales de motor, típicamente no lineales. Esta tesis tiene como objetivo el desarrollo de un nuevo método numérico cuasi-3D en una malla escalonada, basado en la simplificación de la ecuación de la cantidad de movimiento, para ser incluido en un código unidimensional existente. Tal método, sin embargo, no está libre de inconvenientes. En particular, se ve afectado por la aparición de oscilaciones no físicas, especialmente en gradientes de presión significativos. De la revisión bibliográfica se determina que este comportamiento es típico en esquemas de segundo orden y se puede ver acentuado por las simplificaciones adoptadas. Tras estudiar las posibles soluciones aplicables a este problema, se desarrollan tres limitadores de flujo diferentes, basados en las metodologías MDT, FCT y TVD. Una vez definido el método numérico y asegurada su estabilidad, es necesario desarrollar las condiciones de contorno adecuadas que permitan su utilización. Con este objetivo, se desarrollan las condiciones de pulso de presión de entrada y de extremo anecoico, los cuales permiten simular un banco de impulso. No hay que olvidar, sin embargo, que el objetivo final es la conexión con un código unidimensional, por lo que hay que comprobar que el método numérico cuasi-3D creado es compatible con los unidimensionales existentes, mostrando algunos resultados preliminares. Finalmente, con el método ya completamente operativo, se procede a su validación en las aplicaciones para las que ha sido diseñado principalmente, las cuales son, modelado de silenciadores y uniones de conductos. Para el caso de los silenciadores, se modelan dispositivos de complejidad creciente, pasando por geometrías de sección constante hasta sistemas con geometrías reales. Los resultados obtenidos se validan con otras herramientas tanto lineales como no lineales. En el caso de las uniones de conductos, el objetivo principal es el de establecer el potencial del nuevo método numérico frente a los tradicionales unidimensionales, por lo que los resultados de ambos se comparan con datos experimentEngine modelling has become an essential tool in the design of internal combustion engines, allowing considerable reductions in development time and cost. Classical design methodologies are based on prototype manufacturing and trial-and-error tests, but currently, most of those tests have been replaced by numerical computations, so that only the most promising design options are actually tested on engine bench. For years, one-dimensional gas dynamics codes in the time domain have offered sufficiently good solutions for modelling both engine performance and intake and exhaust noise. However, for a more demanding level of design, a 1D representation may not be sufficient to describe accurately the flow in certain elements. This is especially important in the case of silencers. In the case of duct junctions, the existence of complex 3D flow structures is what sets the applicability limit for a simple zero-dimensional description. In view of these limitations, the first option would typically be the use of a computational fluid dynamics (CFD) model; however, the application of such a model to a complete intake or exhaust system entails an excessive computational time. A possible compromise solution is given by quasi-3D models, based on three-dimensional schemes, but with certain simplifications able to significantly reduce the calculation time without excessively affecting the accuracy. Such solutions have become standard in commercial codes and have been successfully applied to silencers with perforated tubes and absorbing material, both in the linear acoustic regime and in real engine conditions, typically non-linear. The objective of this thesis is the development a new quasi-3D numerical method in a staggered-grid, based on the simplification of the momentum equation, to be included in an existing one-dimensional code. Such method however, is not hassle free. In particular, it is affected by the appearance of non-physical oscillations, specially near significant pressure gradients. From the literature review it is determined that this behaviour is typical among second-order schemes and it can be aggravated by the simplifications adopted. After researching the possible solutions to face this problem, three different flux limiters are developed, based on the MDT, FCT and TVD methodologies. In the case of the two latter methods, its effectiveness is well established for finite differences schemes, thus defining a clear improving line for quasi-3D models. Once the numerical method is defined and its stability assured, proper boundary conditions that allow its use must be developed. With this objective, a pressure pulse inlet and an anechoic termination boundary condition are developed, which allow the simulation of an impulse test rig. It should not be forgotten, however, that the ultimate objective is the connection with a one-dimensional code, therefore the compatibility of the quasi-3D numerical method created with the existing one-dimensional methods has to be tested, showing some preliminary results. Eventually, with a fully operative method, the validation process for the applications which it has been mainly developed for, takes place, namely, mufflers and duct junctions modelling. In the case of mufflers, increasingly complex devices are modelled, from constant section geometries to real geometry systems. The results obtained are validated with both linear and non-linear tools. In the case of duct junctions, the main objective is to establish the potential of the new numerical method against the traditional one-dimensional schemes, consequently, results from both approaches are compared to experimental measures, obtaining promising results.El modelatge s'ha convertit en els últims anys en una eina essencial en el disseny de motors de combustió interna alternatius, ja que permet reduir considerablement el temps i els costos de desenvolupament. Les metodologies de disseny clàssiques es basen en la fabricació de prototips i la realització de proves d'assaig i error. Actualment, la majoria d'aquestes proves han sigut substituïdes per càlculs numèrics, de manera que només les opcions de disseny més prometedores es proven en realitat en banc motor. Durant anys, els codis unidimensionals de dinàmica de gasos en el domini del temps han sigut suficients per a modelar tant les prestacions i el consum del motor com el soroll d'admissió i escapament. No obstant això, per a un nivell més exigent de disseny, una representació 1D pot no ser prou per a descriure amb precisió el flux en certs elements. Açò és especialment important en el cas de silenciadors, on la hipòtesi unidimensional només es pot aplicar a geometries simples. En el cas de les unions de conductes és l'existència d'estructures tridimensionals de flux complexes el que establix el límit de l'aplicabilitat d'una descripció simple zero-dimensional. En vista d'estes limitacions, la primera opció seria típicament l'ús d'un model de dinàmica de fluids computacional (CFD); no obstant això, l'aplicació comporta un temps de càlcul excessiu. Una possible solució de compromís ve donada pels models quasi-3D, basats en esquemes tridimensionals, però amb certes simplificacions capaços de reduir significativament el temps de càlcul sense afectar excessivament la precisió. Tals solucions s'han convertit en estàndard en codis comercials i s'han aplicat amb èxit als silenciadors, tant per a excitacions acústiques en el règim lineal com en condicions reals de motor, típicament no lineals. Aquesta tesi té com a objectiu el desenvolupament d'un nou mètode numèric quasi-3D en una malla escalonada, basat en la simplificació de l'equació de la quantitat de moviment, per a ser inclòs en un codi unidimensional existent. Tal mètode, però, no està lliure d'inconvenients. En particular, es veu afectat per l'aparició d'oscil·lacions no físiques, especialment en gradients de pressió significatius. De la revisió bibliogràfica es determina que aquest comportament és típic en esquemes de segon ordre i es pot veure accentuat per les simplificacions adoptades. Després d'estudiar les possibles solucions aplicables a aquest problema, es desenvolupen tres limitadors de flux diferents, basats en les metodologies MDT, FCT i TVD. En el cas dels dos últims mètodes, la seua efectivitat està ben establida per als esquemes de diferències finites, la qual cosa definix una clara via de millora per als models quasi-3D. Una vegada definit el mètode numèric i assegurada la seua estabilitat, és necessari desenvolupar les condicions de contorn adequades que permeten la seua utilització. Amb aquest objectiu, es desenvolupen les condicions de pols de pressió d'entrada i d'extrem anecoic, els quals permeten simular un banc d'impuls. No cal oblidar que l'objectiu final és la connexió amb un codi unidimensional, per la qual cosa cal comprovar que el mètode numèric cuasi-3D creat és compatible amb els unidimensionals existents, mostrant alguns resultats preliminars. Finalment, es procedix a la seua validació en les aplicacions per a les que ha sigut dissenyat principalment, les quals són, modelatge de silenciadors i unions de conductes. Per al cas dels silenciadors, es modelen dispositius de complexitat creixent, passant per geometries de secció constant fins a sistemes amb geometries reals. Els resultats obtinguts es validen amb altres eines tant lineals com no lineals. En el cas de les unions de conductes, l'objectiu principal és el d'establir el potencial del nou mètode numèric front als unidimensionals tradicionals, per la qual cosa els resultats d'ambdós es comparen amb dades experimHernández Marco, M. (2018). A non-linear quasi-3D model for air management modelling in engines [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/103683TESI

Numerical Computation Of 2-d Laminar Flows In Complex Geometries

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2006Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2006İki boyutlu sürekli rejimde laminer akışların eğrisel kordinatlarda çözümünü gerçekleştirmek için bir yöntem geliştirilmiştir. İlgili denklemler sonlu hacimler yöntemi kullanılarak yapısal ve hücre merkezli bir ağ üzerinde ayrıklaştırılmışlardır. Kodun kesinliği, değişik duvar eğiklikleri için üzerinde akış olan bir kuyu içindeki ve Re=10, 20 ve 40 için dairesel bir silindirin üzerindeki akışların hesaplanmasıyla doğrulanmıştır. Bu çalışmada, ağ eğikliği kayda değer bir hal aldığı durum için sadeleştirilmiş basınç-fark denklem metodu, tam basınç-fark denklem metodu ve Cho ve Chung’ ın methodlarının yakınsama performanları analiz edilmektedir. Sonuçlar göstermektedir ki, SIMPLEC algoritmasıyla elde edilen sonuçlar SIMPLE algoritmasıyla elde edilenlerden oldukça üstündür. Hesaplama ağının çok eğik olmadığı durum için basınç-fark denkleminin çözümünde sadeleştirilmiş metodu kullanmak daha mantıklıdır. Diğer taraftan ağ eğikli arttıkça tam basınç-fark denklemi metodu αp için limitsiz bir aralıkta daha hızlı yakınsamaktadır. Cho ve Chung’ın metodu SIMPLEC algoritması kullanıldığında SIMPLE algoritmasıyla çözülen durumun aksine verimsiz bir performans göstermektedir.A numerical methodology has been developed to solve steady laminar flows in two dimensional domains using curvilinear coordinates. The finite volume procedure is employed to discretize the governing equations on a collocated and structured grid arrangement. The accuracy of the code is validated by calculating laminar flows in a lid-driven cavity with inclined walls with different angles and the steady flow past a circular cylinder for various Reynolds numbers from Re=10, 20 and 40. This study analyzes the convergence performances of the simplified pressure-correction equation, full pressure-correction equation and the treatment of Cho and Chung on the mass flux corrections when the grid non-orthogonality becomes appreciable. The proposed methods have been tested for typical non-orthogonal two-dimensional cavity flows. The results show that the SIMPLEC algorithm is superior to the SIMPLE algorithm when simplified and full pressure-correction equation methods are used. If computational grid is not severely non-orthogonal (β >45o), it is more logical to use simplified version than the full one. The computer program is simpler and less memory is needed. On the other hand, full pressure-correction equation method converges fastest in a limitless range of αp when the grid skewness increases. The Cho and Chung’s method serves inefficient performance if the SIMPLEC algorithm is employed. Although there is no limit to the ranges of αp values, the convergence rate of the method is low.Yüksek LisansM.Sc