Chapter 6 Numerical Simulations
6.2 Numerical simulation of heat transfer in the context of building physics
Numerical models target in the description of a physical system through mathematical terms, and therefore rely on several basic assumptions.
Usually, it is important to validate the numerical simulations by mean of experimental results that may reflect the physic of the model. On the other hands, validation refers to an iterative procedure where the model outputs are compared to experimental data, until the errors are justified within the limits of confidence. Even though, a suitable validation
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should be provided by measuring of the models accuracy. Once a model is validated, it can be used in sensitivity and parametric analyses, where specific model parameters are varied and their respective impacts on the main variables investigated.
6.2.1 Finite Element Method (FEM)
The finite element method has been used by several authors in the context of incorporation of PCM in mortars for building envelopes (Lamberg et al. 2004, Ravikumar et al. 2008, Kheradmand 2012, Vaz Sá et al. 2012). All of these studies report that the finite element method can simulate the transient behaviour of phase change materials in the context of building physics. The key challenge in the modelling pertains to the modelling of the phase change of the PCM itself, for which specific methods will be discussed in Section 6.3. There is a wide choice of commercial FEM software, suited for implementing the PCM behaviour in the calculations, such as DIANA (Manie J 2010), ANSYS-APDL (Madenci et al. 2015), COMSOL (Robynne et
al. 2011). The most important shortcoming in standard FEM simulations of thermal
fields in building physics regards the simulation of the air behaviour itself in the sense that it flows and follows convective patterns. Such types of phenomena cannot be simulated with standard FEM. However, natural convection and even ventilation can play a relevant role in many practical applications, thus potentially demanding for more sophisticated approaches.
6.2.2 Computational Fluid Dynamic (CFD)
Computational Fluid Dynamics (CFD) models applied to building physics numerically solve a set of partial differential equations for the conservation of mass, momentum (Navier-Stokes equations), energy, chemical-species concentrations, and turbulence quantities. The solution provides the field distributions of air temperature for both indoor and outdoor spaces (Chen Q 2009). The CFD models have been widely used to study indoor air quality and thermal comfort in buildings (Chen Q 2009, Gómez et al. 2012, Gowreesunker et al. 2013). The accuracy of simulation depends on the grid resolution. Therefore, CFD models usually require much more computing time for calculations when compared with standard FEM approaches for temperature simulation. The available CFD models for predicting air temperature and distribution of air flow in buildings still bring uncertainties in predictions because of the complex air flow types such as laminar and turbulence. For example, Zhai et al. (2007) evaluated eight
109 turbulence models, that could be used for indoor environment modelling. They identified four indoor geometries, under forced, natural and mixed forced/natural ventilation and compared the numerical results with experimental data. They concluded that CFD models offer accurate results, but require much higher computing time and storage space. One of the difficulties in the modelling effort is to reproduce the programming of user defined functions (UDF) such as: the PCM effect, heat source according to the frame of the problem. Such optimization requires advanced simulation techniques that involve complex thermal exchange phenomena, leading many of currently existing simplified simulation approaches to provide results that deviate from experimental evidences (Cabeza et al. 2011). This method is important from the aspect of building physic modelling. Generally, for engineering problems, it is more important to obtain a solution where the general numerical solution accuracy is within the real‒life uncertainties of the adequate sensors (Gowreesunker et al. 2013) as opposed to having a solution with very small‒scale details. This allows for a quicker and more efficient use of the CFD tool for engineering purposes.
Gowreesunker et al. (2013) investigated the performance of PCM boards in a test cell equipped with a heating/cooling device. They modelled interior air and temperatures and then compared with experimental results. They concluded that the model was accurate enough in the air temperature values with acceptable range of errors (less than 1ºC). They also, validated a numerical model to investigate PCM building boards in a test cell. Using the model, they studied the effect of ventilation flow rates on the charging performance of the PCM boards. Employing numerical models can therefore prevent the construction of expensive experimental setups for parametric studies, as well as save considerable amount of time and resources.
In the models with large indoor spaces, the International Energy Agency (IEA) suggests that the air flow inside the space is crucial, and recommends the use of CFD for performance evaluations (Jeong et al. 2013).
6.2.3 Governing Equations
In order to predict air flow and temperature fields in indoor environments, CFD can be used by numerically solving the Navier-Stokes set of partial differential equations for mass, energy and momentum. These equations are linearized, discretized, and applied to finite volumes in the solvers to obtain a detailed solution, including velocity and
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temperature fields. In this thesis, the general transient heat balance equation (Incopera et
al. 2007) was applied for the numerical treatment of the heat transfer processes in the
studied models. All involved materials are considered homogeneous and isotropic. The effect of natural convection due to potential convective flows inside/outside the prototypes was considered through computational fluid dynamics(Gowreesunker et al. 2013): Continuity Equation: m u v w S x y z (6.1) Where Sis the source term; uis the velocity component along x-axes; v is the velocity
component along y-axes; and w is the velocity component along z-axes. Momentum Equations: 2 1 Air x Air u u u u P u v w u S t x y z x (6.2) 2
1
(
)
(
)
Air Air ref y
Air
v
v
v
v
P
u
v
w
v
g T T
S
t
x
y
z
y
(6.3) 2 1 Air z Air w w w w P u v w w S t x y z z (6.4) Where is the thermal expansion coefficient; gis the gravitational acceleration; P is the pressure; tis the time;Airis the dynamic viscosity for the air; Airis the density for the air; and the temperature Twill be computed from the energy equation.Energy equation: 2 2 2 ( ) ( ) ( ) ( ) ( p) E Air h h h h k T T T u v w S t x y z C x y z y x z (6.5)
111 The density of the air is calculated based on the compressible ideal gas flow law as follows:
Air
P
RT
(6.6)Where R is the universal gas constant.
In regard to boundary conditions applied to the temperature field computation, interaction with an ‘infinite’ surrounding air medium can be expressed through convective/radiative boundary fluxes, as shown in Eq. (6.7), where T is the temperature (ºC), Tsis the surface temperature (ºC) and heq is a convection/radiation coefficient that
depends on air speed (W/mK):
( )
eq s
qh TT (6.7)
Discretisation is a way to the process of breaking down the terms of the governing Equations (mentioned above) into simpler discrete algebraic forms in order to be solved. It can also refer to the breaking down of the flow domain into separate control volumes. For the purpose of illustration, Figure 6-1 shows schematic of mesh discretization, which allows the production of localised solution fields for a particular domain. In this figure, the cell centre values are labelled as 1, 2, 3, 4 and 5, while the face values are labelled as a, b, c and d. The approximate form of the governing equations is applied to each control volume and the face values are required to obtain a solution.
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