During Phase IV of the Memorial Tunnel Fire Ventilation Test Program, a general Computational Fluid Dynamics (CFD) code was customized and validated specifically for tunnel application. For transverse ventilation, a novel approach was developed for modeling the interaction between ventilation ducts and the tunnel. A network model, comprised of nodes and links, is used to represent the ducts while a field model is used to represent the tunnel. These models interact with each other through boundary conditions. The paper presents the details of the network model, the method for integrating this model with the basic field model, and the overall solution procedure. The general application of the CFD model to the Memorial Tunnel is discussed. Model predictions are compared with test data from selected fire tests for both steady-state and transient conditions. 1.0 INTRODUCTION The Memorial Tunnel Fire Ventilation Test Program (MTFVTP) evolved from the need to better understand the capabilities of tunnel ventilation systems during a fire emergency. The Memorial Tunnel, an abandoned road tunnel in West Virginia, was modified, retrofitted with new ventilation equipment, and instrumented to evaluate ventilation system performance during full-scale testing as a function of system type and capacity, and fire size. Ventilation systems tested included longitudinal ventilation using jet fans, natural ventilation, full transverse ventilation, partial transverse ventilation, and partial transverse ventilation supplemented with special extraction techniques. A total of 98 full-scale tests were carried out with fires ranging in intensity from 10 to 100 MW. The test program comprised four phases of work. The first three phases addressed test program development, test facility design and construction, testing and data evaluation. Phase IV focused on development and validation of a customized Computational Fluid Dynamics (CFD) code specifically for tunnel application. Data from the full-scale fire tests was used as the basis for validation. The CFD model is geared towards individuals concerned with fire/life safety in tunnels from a perspective of analysis, design, and operation of ventilation systems. The primary objective established for the model is the ability to simulate the interactive effects of a tunnel fire and the ventilation system to determine the unsafe regions of the tunnel, that is, the regions where the hazardous effects of the fire (smoke and high temperature) are confined, and how these regions are affected by the ventilation system configuration, capacity, and operation. The customized CFD code is based on an existing general-purpose computer program for the analysis of fluid flow, heat transfer, and related processes (IRI, 1996). The customization work included development, implementation, and validation of sub-models to address certain features required for the tunnel model. One such feature is the ability to model tunnel ventilation air ducts to address transverse ventilation systems. The requirements for this feature were many. The model had to be sufficiently flexible to address not only the ventilation configurations tested in the Memorial Tunnel but also possible extensions, variations, and combinations of these systems. The model had to be able to deliver each duct system’s flow capacity and distribution, and adjust them accordingly to account for the effects of a tunnel fire. The exchange of flow, heat, and smoke at the tunnel/duct wall interface had to be accounted for properly. In addition, this had to be accomplished without overburdening the computational process. To meet these requirements, a novel approach was developed. 2.0 DETAILS OF THE MATHEMATICAL MODEL In transverse ventilation systems, air is supplied to and exhausted from the tunnel through ventilation ducts. The supply and exhaust rates through the ventilation ducts are not known a priori; these depend not only on the characteristics of the duct systems but also on the conditions within the tunnel. A complete model for such systems, therefore, requires a method for calculating the fluid flow and heat transfer within the tunnel, a method for calculating the supply and exhaust rates for the ducts, and a procedure for interacting the two. A field model based on CFD is used to calculate the flow and heat transfer characteristics within the tunnel. A flow network model is used to calculate the flow and heat transfer through the ventilation ducts. A special procedure has been developed to couple these models so that they fully interact with each other. The specific details of these three components of the overall model for transverse ventilation systems are presented in the following sections. 2.1 Field Model for Tunnel (Tunnel Model) The tunnel model uses a numerical method to solve the three-dimensional, time-dependent equations (field equations) describing the laws of conservation for mass, momentum, energy, turbulence parameters, and species, subject to the given set of boundary conditions. It is based on the buoyancy-augmented k-ε turbulence model (Cox, 1995) and includes component models for representing fire, radiation heat transfer from fire, smoke movement, and wall roughness. 2.1.1 Governing Equations The governing equation for the transport of mass, momentum, energy, turbulence parameters and other quantities can be cast, using the Cartesian tensor notation, in the following general form (Patankar, 1980): S x x u x t i i i i + Γ + ∂ ∂φ ∂ ∂ φ ρ ∂ ∂ ρφ ∂ ∂ = ) ( ) ( (1) where φ is the general dependent variable, ρ is the fluid density, Γ is the generalized diffusion coefficient, and S is the source term. The density is calculated from the perfect gas law. The expressions for the diffusion coefficients and the source terms appearing in the transport equations are well known (see, for example, Cox, 1995) and are not presented here. 2.1.2 Boundary Conditions Tunnel Portals. The tunnel portals can be specified as inflow/outflow boundaries or as “free” boundaries with known values of pressure, depending on the physical situation being modeled. At an inflow boundary, values of all variables are specified. At an outflow boundary, the diffusion flux normal to the boundary is assumed to be zero and no other information is needed. At a free boundary, the value of pressure is specified. The given value of pressure is interpreted as total pressure at the inflow points and static pressure at the outlet points. Tunnel Walls. At a solid-fluid interface, the wall-function approach (Launder and Spalding, 1974) is used. The approach outlined by Jayatilleke (1969) is followed to account for the influence of wall roughness on the standard wall functions. 2.1.3 Solution Procedure The governing equations for the tunnel model are solved using the finite-volume method described by Patankar (1980). The implicit differencing scheme is used for the unsteady term in the equations. The convection-diffusion fluxes are approximated using the Power-law scheme. The coupling between the velocity and pressure fields is handled using the SIMPLER algorithm. The algebraic equations are solved using the TriDiagonal-Matrix Algorithm (TDMA). 2.1.4 Representation of Fire The fire is represented as a source of heat and mass. The heat release rate due to combustion is prescribed as a volumetric heat source in a postulated fire region. The model needs information on the flame size and shape and the volumetric heat release rate and its distribution. The heat release rate is computed from the rate of fuel consumption ( fu m ), the heating value of the fuel ( fu H ), and the combustion efficiency (η ), as η fu fu H m Q = (2) In the fire region, the energy equation includes an additional source term, which is calculated on a unitvolume basis as ) 1 ( , R fire fire h V Q S χ − = (3) where Vfire is the volume of the fire region and R χ is the fraction of the total heat released from the fire that is lost to the tunnel walls by radiation, without influencing the temperature distribution within the tunnel. 2.1.5 Representation of Smoke In the tunnel model, a separate conservation equation is solved for smoke. This equation contains a source term in the fire region where the combustion process takes place. The total rate of smoke production is calculated from the rate of fuel consumption and the stoichiometric ratio for the fuel, assuming complete combustion. On a unit-volume basis, this source term is calculated as fire fu smoke V s m S ) 1 ( + = (4) where s is the stoichiometric ratio (kg of air / kg of fuel) for the fuel. 2.2 Flow Network Model for the Ventilation Ducts A ventilation duct system is represented as a network of links and nodes. The values of pressure, temperature, and smoke concentration are stored at the nodes. At boundary nodes, the values of these variables are known. At the remaining nodes, these values are unknown and are calculated by the network model. Each link in the network represents a fluid path and is associated with an upstream and a downstream node. A link is characterized by the aerodynamic resistance, the flow rate, and the heat transfer coefficient. The details of the network model are presented. 2.2.1 Governing Equations The basic governing equations in a flow network model are the mass continuity equation at a node, the correct relationship between the pressure drop and the flow rate (momentum equation) for a link, and the energy equation at a node. The mass continuity equation for node i can be expressed as ( ) i J j ij ij m Q − = =1 ρ (5) J is the total number of links associated with node i. Here, ρ is the density, Q is the volumetric flow rate, and m is the external mass flow into node i. In Eq. (5) and subsequent equations, the subscript i denotes the value of the quantity at node i and the subscript ij indicates reference to the j link connected to the node i. The pressure drop-flow rate relationship for a link is expressed as ) ( ) ( ij ij ij Q