One of the most critical aspects in the design of thermosyphon solar heater is the design of the absorber. It must be a very good heat exchanger, the flow must be equally distributed along all the tubes and the pressure drop of the thermal fluid due to flow resistance in the absorber must be minimised in order to enhance the thermosyphon effect. With the simple model, design and optimisation studies of the absorber cannot be carried out. On the other hand, the use of high level codes, CFD codes, for the modelling of the complete absorber are not still suitable due to the huge amount of computational resources needed to run a single test. In this section, a code for the modelling of the fluid flow in heat exchangers is explained. This code is being developed in the “Centre Tecnologic de Transferencia de Calor” of the Polytechnical University of Catalonia. It was mainly focused to heat exchangers for automotive applications. Currently it is being extended to be used in order applications such as the absorbers of the solar collector.

The heat exchanger is divided in n different CV in which the conservation laws of mass, momentum and energy are solved. Heat transfer coefficients from the walls of the heat exchanger to the thermal fluid, and pressure drop due two fluid flow resistance due to ex­pansions, contractions, elbows, wyes, friction in the walls.. are evaluated from correlations available in the literature, [10, 8, 13].

A unidimensional adaptation of the SIMPLE (Patankar [16]) methods has been imple­mented to solve the velocity-pressure coupling of the resulting algebraic equations.

This code is currently being used by the authors in order to investigate the fluid flow in different absorber configurations and to obtain the fluid flow parameters of the absorber which are required for the simple model, i. e. the pressure drop through the absorber in terms of the mass flow rate of the thermal fluid.

CFD model

This method represent the highest level of numerical simulation and it provides the values of all the relevant variables such as temperature, pressure and velocity, throughout the do­main of interest by means of the application of any discretization method. In this technique a continue variable in space and time is approached using a set of discreet values over all the studied domain. The method based on finite volumes is commonly employed in CFD and is the one used in this work.

The heat and mass transfer governing equations are continuity, momentum and energy. They constitute a set of non-linear, PDE’s and strongly coupled equations. They can be written in vectorial form, as follows:

V-v = 0 (4)

(5)

pcv (v-V)T = kV2T + V • qT (6)

where the Boussinesq equation of state, dp = —fipdT, has been applied. Here, T is the temperature, t the time, v the velocity, p is the dynamic pressure, Tre/ is the reference temper­ature, g is the gravity and p, f. t, A, and C), are respectively: density, viscosity, conductivity, thermal expansion coefficient and specific heat.

The last term in equation 6 is the energy generation per unit volume due to the imbalance between the absorbed and the emitted radiation. Radiation effects are taken into account via the radiative transfer equation (RTE) which is used to determine the intensity radiation field, I. The RTE considers the variation of the energy carried by a beam in direction due to its interaction with the medium where it is travelling on [5]. Then, the radiative heat
transfer equation is an integro-differential equation that properly describes such variation. For a given wavelength range in a purely absorbing (non scattering) medium, it reduces to

s-VI{r, s) = — k{I{r, s)-IB{r)) (7)

which is a conservation optical balance equation. IB(f) stands for the thermal emission of a black body at a temperature of T(r) for the given wavelength range, and & is the absorption coefficient. Once the intensity radiation field is known, the energy generation or loss due to radiation is calculated as:

рос p

(8)

Jo J 4?r

In general terms, the principal problem in the solution of Navier-Stokes equations is the handling of the coupling between momentum and continuity equations and the fact that it does not exist a specific equation for pressure. Then, the complexity for evaluating RTE equation adds an extra difficulty to the problem.

The method employed to couple pressure-velocity field is one of the SIMPLE(Semi-Implicit Method for Pressure-Linked Equations)[16] family. This resolves in a segregated way mo­mentum equation (5), with a guessed pressure. Then, velocities and pressure are corrected fulfilling continuity equation (4). So it is necessary to derive a pressure-correction equation using equations (4) and (5) [16].

If participant medium to radiation is considered, RTE equation has to be solved using some technique like Discrete Ordinates Method (DOM) [5]. The object of the DOM is to solve equation (7) for a chosen set of N ordinates in such manner that any integral magnitude in relation to the intensity radiation field may be changed by a weighted summation of the integrand at selected points (ordinates) of the integration domain.

Once momentum equations (5) are solved the procedure to resolve energy equation (6) is as follows. Firstly, a temperature field is supposed. Then, the RTE is solved using DOM, assuming that the temperature is not modified by radiation field. Thus, the energy generation or loss per unit volume is calculated using equation (8). The next step is to solve equation (6), given as an additional source term, that varies on each iteration due to it depends on the temperature field. With the new thermal field, the RTE is solved again until convergence is accomplished.

Due to the elliptic nature of the governing equations with respect to the spatial coor­dinates, boundary conditions have to be specified at all external boundaries to take into account the interactions with the environment.

In order to assure that the numerical solution are an appropriate approximation of the mathematical model, the authors use a post processing tool based on the generalised Richardson extrapolation for h-refinement studies [2]. From this method, estimations of the numerical uncertainty of the solutions are calculated.