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Estudo comparativo entre os modelos LES e DES para simulação de escoamento compressível turbulento.; A comparative study using les and des models for turbulent compressible flow simulation.

Pedrão, Nelson
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 25/05/2010 PT
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66.36%
Neste trabalho foi realizado um estudo utilizando os modelos de turbulência Simulação das Grandes Escalas, Large Eddy Simulation (LES), e Simulação dos Vórtices Desprendidos, Detached Eddy Simulation (DES), para simular o escoamento compressível interno em um duto contendo válvulas controladoras na saída dos gases de combustão de um reator de craqueamento catalítico fluido, com o objetivo de comparar o desempenho numérico e computacional de ambas as técnicas. Para isso foi utilizado um programa comercial de dinâmica dos fluidos computacional, Computational Fluid Dynamics (CFD), que possui em seu código os dois modelos de turbulência.; In the present work a study was conducted using Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) turbulence models in order to simulate the internal compressible flow in a duct containing the flue gas discharge control valves of a fluid catalytic cracking reactor so as to compare the numerical and computational behavior of both techniques. A commercial Computational Fluid Dynamics (CFD) software, which includes these turbulence models in its code, was used.

Análise da estabilidade global de escoamentos compressíveis; Global instability analysis of compressible flow

Gennaro, Elmer Mateus
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 08/08/2012 PT
Relevância na Pesquisa
56.51%
A investigação dos mecanismos de instabilidade pode ter um papel importante no entendimento do processo laminar para turbulento de um escoamento. Análise de instabilidade de uma camada limite de uma linha de estagnação compressível foi realizada no contexto de teoria linear BiGlobal. O estudo dos mecanismos de instabilidade deste escoamento pode proporcionar uma visão útil no desenho aerodinâmico das asas. Um novo procedimento foi desenvolvido e implementado computacionalmente de maneira sequencial e paralela para o estudo de instabilidade BiGlobal. O mesmo baseia-se em formar a matriz esparsa associada ao problema discretizado por dois métodos: pontos de colocação de Chebyshev-Gauss-Lobatto e diferenças finitas, além das combinações destes métodos. Isto permitiu o uso de bibliotecas computacionais eficientes para resolver o sistema linear associado ao problema de autovalor utilizando o algoritmo de Arnoldi. O desempenho do método numérico e código computacional proposto são analisados do ponto de vista do uso de métodos de ordenação dos elementos da matriz, coeficientes de preenchimento, memória e tempo computacional a fim de determinar a solução mais eficiente para um problema físico geral com técnicas de matrizes esparsas. Um estudo paramétrico da instabilidade da camada limite de uma linha de estagnação foi realizado incluindo o estudo dos efeitos de compressibilidade. O excelente desempenho código computacional permitiu obter as curvas neutras e seus respectivos valores críticos para a faixa de número de Mach 0 '< OU =' Ma '< OU =' 1. Os resultados confirmam a teoria assintótica apresentada por (THEOFILIS; FEDOROV; COLLIS...

Instabilidade hidrodinâmica linear do escoamento compressível em uma cavidade; Linear hidrodinamic instability of compressible lid-driven cavity flow

Bergamo, Leandro Fernandes
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 28/04/2014 PT
Relevância na Pesquisa
56.57%
Os mecanismos de instabilidade hidrodinâmica têm um papel importante no processo da transição do escoamento de laminar para turbulento. A análise da instabilidade hidrodinâmica em uma cavidade com tampa deslizante foi realizada através da decomposição em modos globais (biglobal) para avaliar o efeito da compressibilidade neste fenômeno. O escoamento base foi obtido através de simulação numérica direta (DNS). Para tal, foi desenvolvido um código DNS compressível com discretização espacial por diferenças finitas compactas de alta resolução espectral e capacidade de processamento paralelo, com um método de decomposição de domínio que mantém a precisão das diferenças finitas compactas. O escoamento base é usado para montar o problema de autovalor oriundo das equações de Navier-Stokes linearizadas para a perturbação, discretizadas por diferenças finitas explícitas. O uso de diferenças finitas em conjunto com a implementação em matrizes esparsas reduz sensivelmente o uso de memória. Através do algoritmo de Arnoldi, a ordem do problema de autovalor é reduzida e os autovalores de interesse são recuperados. Os resultados indicam o efeito estabilizante da compressibilidade nos modos dominantes da cavidade e revelam modos inerentes ao escoamento compressível...

Unicidade de soluções fracas das equações de Navier-Stokes para fluidos compressiveis; Uniqueness of weak solutions of the Navier-Stokes equations of compressible flow

Ariane Piovezan Entringer
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 05/06/2009 PT
Relevância na Pesquisa
56.49%
Este trabalho consiste de uma exposição detalhada do resultado provado no artigo Uniqueness of Weak Solutions of the Navier-Stokes Equations of Multidimensional, Compressible Flow de D. Hoff (SIAM J. Math. Anal - 2006) sobre a unicidade de solução fraca e a dependência contínua da solução fraca nos dados iniciais para as equações de Navier-Stokes para fluídos compressíveis...Observação: O resumo, na integra, podera ser visualizado no texto completo da tese digital; Uniqueness of Weak Solutions of the Navier-Stokes Equations of Multidimensional, Compressible Flow of D. Hoff (SIAM J. Math. Anal - 2006) about uniqueness and continuous dependence on initial data of weak solutions of the Navier-Stokes equations of compressible flow...Note: The complete abstract is available with the full electronic digital thesis or dissertations

Estrutura lagrangiana para fluidos isentrópicos compressíveis no semiespaço com condição de fronteira de Navier; Lagrangean structure for isentropic compressible fluid in halfspace with the Navier boundary condition

Edson Jose Teixeira
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 23/04/2014 PT
Relevância na Pesquisa
46.47%
Neste trabalho estudamos a estrutura lagrangiana para o campo de velocidade solução das equações de Navier-Stokes para um fluido isentrópico compressível no semiespaço do R3, com a condição de fronteira de Navier. Consideramos a solução deste modelo obtida por David Hoff no artigo Compressible Flow in a Half-Space with Navier Boundary Conditions}, J. Math. Fluid Mech. 7 (2005) 315-338. Demonstramos que se a velocidade inicial pertence ao espaço de Sobolev H8 com 8 >1/2, então as curvas integrais do campo de velocidade, ou seja, as trajetórias de partículas, existem e são únicas, e mostramos também algumas propriedades desse fluxo.; In this work we study the Lagrangian structure for the velocity field of the Navier-Stokes equations for isentropic compressible fluid in the halfspace in R3 with the Navier boundary condition. We consider the solution of this model obtained by David Hoff in the paper (Compressible Flow in a Half-Space with Navier Boundary Conditions}, J. Math. Fluid Mech. 7 (2005) 315-338. Our main result states that if the initial velocity belongs to the Sobolev space H8, with 8 >1/2, then the integral curves of the velocity field, i.e. the particles paths, there exist and are unique. We also show some properties of this flow map.

Turbulent momentum and passive scalar transport in supersonic channel flow

Friedrich,Rainer; Foysi,Holger; Sesterhenn,Joern
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2006 EN
Relevância na Pesquisa
46.51%
Direct numerical simulations of compressible turbulent channel flow including passive scalar transport have been performed at five Mach numbers, M, ranging from 0.3 to 3.5 and Reynolds numbers, Re, ranging from 181 to 1030. The Prandtl and Schmidt numbers are 0.7 and 1.0, respectively, in all cases. The passive scalar is added to the flow through one channel wall and removed through the other, leading to an S-shaped mean scalar profile with non-zero gradient in the channel centre. The paper describes the set of compressible flow equations, which is integrated using high-order numerical schemes in space and time. Statistical equations are presented for fully developed flow, including budgets for the Reynolds stresses, the turbulent scalar fluxes and the scalar variance. Results are presented for second order moments and the terms in the mentioned balance equations. Outer scalings are found suitable to collapse incompressible and compressible data. The reduction in the near-wall pressure-strain and pressure-scalar gradient correlations due to compressibility is explained using a Green-function-based analysis of the fluctuating pressure field.

A numerical model for thin airfoils in unsteady compressible arbitrary motion

Hernandes,Fabiano; Soviero,Paulo Afonso de O.
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/09/2007 EN
Relevância na Pesquisa
56.43%
A numerical method based on the vortex methodology is presented in order to obtain unsteady solution of the aerodynamic coefficients of a thin airfoil in either compressible subsonic or supersonic flows. The numerical model is created through the profile discretization in uniform segments and the compressible flow vortex singularity is used. The results of the proposed model are presented as the lift and the pressure coefficient along the profile chord as a function of time. The indicial response for the unit step change of angle of attack and unit sharp-edged gust response of the profile are also obtained numerically. The results yielded by the present methodology are also compared with solutions available in the literature.

An edge-based unstructured mesh formulation for high speed tridimensional compressible flow simulation

Ventura,D. M.; Lyra,P. R. M.; Willmersdorf,R. B.; Silva,R. S.; Antunes,A. R. E.
Fonte: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM Publicador: Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/03/2012 EN
Relevância na Pesquisa
46.43%
Numerical simulation of realistic compressible flows is very important and requires accurate and flexible tridimensional formulations, which should furthermore be robust and efficient. In this work we describe the development of a computational tool for numerical simulation of inviscid compressible 3-D fluid flow problems. This tool uses as the main building block an edge-based Galerkin FEM (Finite Element Method) together with a MUSCL (Monotonic Upstream-centered Schemes for Conservations Laws) approach to get a higher-order scheme with LED (Local Extremum Diminishing) property. The code is particularly developed for the simulation of supersonic and hypersonic flow regimes and several important (sometimes unavoidable) numerical procedures incorporated to increase its robustness are described. Some aspects related to the adoption of an edge-based data structure and other implementation issues are also described. Finally, some numerical model problems are analyzed and compared with results found in the literature demonstrating the effectiveness of the developed tool.

Least Median of Squares Filtering of Locally Optimal Point Matches for Compressible Flow Image Registration

Castillo, Edward; Castillo, Richard; White, Benjamin; Rojo, Javier; Guerrero, Thomas
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
46.59%
Compressible flow based image registration operates under the assumption that the mass of the imaged material is conserved from one image to the next. Depending on how the mass conservation assumption is modeled, the performance of existing compressible flow methods is limited by factors such as image quality, noise, large magnitude voxel displacements, and computational requirements. The Least Median of Squares Filtered Compressible Flow (LFC) method introduced here is based on a localized, nonlinear least squares, compressible flow model that describes the displacement of a single voxel that lends itself to a simple grid search (block matching) optimization strategy. Spatially inaccurate grid search point matches, corresponding to erroneous local minimizers of the nonlinear compressible flow model, are removed by a novel filtering approach based on least median of squares fitting and the forward search outlier detection method. The spatial accuracy of the method is measured using ten thoracic CT image sets and large samples of expert determined landmarks (available at www.dir-lab.com). The LFC method produces an average error within the intra-observer error on eight of the ten cases, indicating that the method is capable of achieving a high spatial accuracy for thoracic CT registration.

2.141 Modeling and Simulation of Dynamic Systems, Fall 2002; Modeling and Simulation of Dynamic Systems

Hogan, Neville John
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
EN-US
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46.36%
Mathematical modeling of complex engineering systems at a level of detail compatible with the design and implementation of modern control systems. Wave-like and diffusive energy transmission systems. Multiport energy storing fields and dissipative fields; consequences of symmetry and asymmetry. Nonlinear mechanics and canonical transformation theory. Examples will include mechanisms, electromechanical transducers, electronic systems, fluid systems, thermal systems, compressible flow processes, chemical processes. Description from course home page: This course deals with modeling multi-domain engineering systems at a level of detail suitable for design and control system implementation. Topics covered include network representation, state-space models; multi-port energy storage and dissipation, Legendre transforms, nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms and control-relevant properties. Application examples may include electro-mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission.

Compressible modes in a square lid-driven cavity

Bergamo, Leandro Fernandes; Gennaro, Elmer Mateus; Theofilis, Vassilis; Medeiros, Marcello Augusto Faraco
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica Formato: 125-134
ENG
Relevância na Pesquisa
46.47%
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); This paper studies the effect of compressibility on the linear stability of a two-dimensional lid-driven cavity flow in the subsonic regime. The base flow is generated by high fidelity direct numerical simulation and a biglobal mode instability analysis is carried out by a matrix forming approach. The eigenvalue problem is discretized by high-order finite differences and Arnoldi algorithm is used to reduce the size of the problem. The solution procedure uses sparse matrix techniques. Influence of Mach number on the modes known from incompressible calculations is presented, showing that compressibility has a stabilizing effect. New modes that appear only for compressible flows are presented and their relationship with duct acoustics is investigated.

L^p estimates for quantities advected by a compressible flow

Mellet, A.; Vasseur, A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/08/2006
Relevância na Pesquisa
46.4%
We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration of some pollutants. Because of the diffusion term, one expects the equations to have a regularizing effect. However, in their Euler form, the equations describe the evolution of the quantity multiplied by the density of the flow. The parabolic structure is thus degenerate near vacuum (when the density vanishes). In this paper we show that we can nevertheless derive uniform $L^{p}$ bounds that do not depend on the density (in particular the bounds do not degenerate near vacuum). Furthermore the result holds even when the density is only a measure. We investigate both the scalar and the system case. In the former case, we obtain $L^{\infty}$ bounds. In the latter case the quantity being investigated could be the velocity field in compressible Navier-Stokes type of equations, and we derive uniform $L^p$ bounds for some $p$ depending on the ratio between the two viscosity coefficients (the main additional difficulty in that case being to deal with the second viscosity term involving the divergence of the velocity). Such estimates are, to our knowledge...

Scalar transport in compressible flow

Vergassola, M.; Avellaneda, M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/11/1996
Relevância na Pesquisa
46.59%
Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport generally takes place when both the solenoidal and the potential components of the velocity do not vanish, despite of the fact that it has zero average value. The calculation of the effective ballistic velocity $V_b$ is reduced to the solution of one auxiliary equation. An analytic expression for $V_b$ is derived in some special instances, i.e. flows depending on a single coordinate, random with short correlation times and slightly compressible cellular flow. The effective mean velocity $V_b$ vanishes for velocity fields which are either incompressible or potential and time-independent. For generic compressible flow, the most general conditions ensuring the absence of ballistic transport are isotropy and/or parity invariance. When $V_b$ vanishes (or in the frame of reference moving with velocity $V_b$), standard diffusive transport takes place. It is known that diffusion is always enhanced by incompressible flow. On the contrary, we show that diffusion is depleted in the presence of time-independent potential flow. Trapping effects due to potential wells are responsible for this depletion. For time-dependent potential flow or generic compressible flow...

Global existence and incompressible limit in critical spaces for compressible flow of liquid crystals

Bie, Qunyi; Cui, Haibo; Wang, Qiru; Yao, Zheng-an
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/07/2015
Relevância na Pesquisa
46.36%
The Cauchy problem for the compressible flow of nematic liquid crystals in the framework of critical spaces is considered. We first establish the existence and uniqueness of global solutions provided that the initial data are close to some equilibrium states. This result improves the work by Hu and Wu [SIAM J. Math. Anal., 45 (2013), pp. 2678-2699] through relaxing the regularity requirement of the initial data in terms of the director field. We then consider the incompressible limit problem for ill prepared initial data. We prove that as the Mach number tends to zero, the global solution to the compressible flow of liquid crystals converges to the solution to the corresponding incompressible model in some function spaces. Moreover, the accurate converge rates are obtained.

Incompressible limit for the compressible flow of liquid crystals

Wang, Dehua; Yu, Cheng
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/08/2011
Relevância na Pesquisa
46.42%
The connection between the compressible flow of liquid crystals with low Mach number and the incompressible flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the compressible flow of liquid crystals to the weak solutions of the incompressible flow of liquid crystals is proved when the Mach number approaches zero; that is, the incompressible limit is justified for weak solutions in a bounded domain.

A stable FSI algorithm for light rigid bodies in compressible flow

Banks, J. W.; Henshaw, W. D.; Sjogreen, B.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.36%
In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problem of a shock impacting an ellipse of zero mass.; Comment: 32 pages, 20 figures

Conservative regularization of compressible flow

Krishnaswami, Govind S.; Sachdev, Sonakshi; Thyagaraja, Anantanarayanan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 06/10/2015
Relevância na Pesquisa
46.42%
Ideal Eulerian flow may develop singularities in vorticity w. Navier-Stokes viscosity provides a dissipative regularization. We find a local, conservative regularization - lambda^2 w times curl(w) of compressible flow and compressible MHD: a three dimensional analogue of the KdV regularization of the one dimensional kinematic wave equation. The regulator lambda is a field subject to the constitutive relation lambda^2 rho = constant. Lambda is like a position-dependent mean-free path. Our regularization preserves Galilean, parity and time-reversal symmetries. We identify locally conserved energy, helicity, linear and angular momenta and boundary conditions ensuring their global conservation. Enstrophy is shown to remain bounded. A swirl velocity field is identified, which transports w/rho and B/rho generalizing the Kelvin-Helmholtz and Alfven theorems. A Hamiltonian and Poisson bracket formulation is given. The regularized equations are used to model a rotating vortex, channel flow, plane flow, a plane vortex sheet and propagating spherical and cylindrical vortices. Some wider issues and implications for systematic analyses of fluid and plasma dynamic systems arising from our work are briefly discussed.; Comment: 29 pages, 8 figures

Three-dimensional instabilities in compressible flow over open cavities

Brès, Guillaume A.; Colonius, Tim
Fonte: Instituto de Tecnologia da Califórnia Publicador: Instituto de Tecnologia da Califórnia
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em 25/03/2008
Relevância na Pesquisa
46.44%
Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and...

A dilating vortex particle method for compressible flow

Eldredge, Jeff D.; Colonius, Tim; Leonard, Anthony
Fonte: Instituto de Tecnologia da Califórnia Publicador: Instituto de Tecnologia da Califórnia
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em 20/09/2002
Relevância na Pesquisa
46.4%
Vortex methods have become useful tools for the computation of incompressible fluid flow. In this work, a vortex particle method for the simulation of unsteady two-dimensional compressible flow is developed. By decomposing the velocity into irrotational and solenoidal parts, and using particles that are able to change volume and that carry vorticity, dilatation, enthalpy, entropy and density, the equations of motion are satisfied. Spatial derivatives are treated using the method of particle strength exchange with high-order-accurate, non-dissipative kernels. The new vortex method is applied to co-rotating and leapfrogging vortices in compressible flow, with the far acoustic field computed using a two-dimensional Kirchhoff surface.

Two-fluid mathematical model for compressible flow in fractured porous media

Khlaifat,A. L.
Fonte: Latin American applied research Publicador: Latin American applied research
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/07/2008 EN
Relevância na Pesquisa
56.36%
A three-dimensional isothermal transient compressible two phase flow of liquid and gas in a low permeability fractured porous media model has been developed from the general mass and momentum balances using volume averaging techniques. The emphasis of the paper is on the available analytical and semi-empirical correlations and closure relations. The interfacial mass and momentum transfer terms in the averaged formulation are explained. The assumptions used in the model's formulation are that a condition of capillary equilibrium exists throughout the media, momentum transfer between mobile fluid phases is negligible in the porous media and exists in the fracture, and fluid phase change has been neglected. The pore size distribution of the studied porous media was represented by three mean pore diameters: liquid pore network, gas pore network, and fractures. An average pore diameter and length for each network were determined using the gamma distribution function. The model was validated and solved for a hypothetical porous media and fractured domain.