10.07.2015   Particle Image Velocimetry (PIV)

Boundary conditions

Local temperatures at the walls of the storage element are obtained from surface heat balances considering instantaneous solar irradiance gains {Gt — Gtrc/) on the front surface of the store, and heat losses coefficients of Ut and to account for thermal losses through

the front and the other sides of the store respectively. Non-slip conditions at the walls are assumed, i. e. и = v = 0.

From these assumptions, local temperatures at the front (x = L, y), back (x = 0, y), upper (x, y = L) and lower surfaces of the storage element result respectively from the

following expressions:

^° i < (re,//

= W) ~ (G* ~ Gfrcf ) —

dT

Xdy

(5)

i_x. y=w)

Ui(Ta —

d T

’ 1 h(.T,)/=0) ~~ "~~ЛХу

(rc,//=0)

(6)

‘•’,(‘/» —

dT

’ 1 h(.T=0,j/) — ~~~A~Qx

(rc=0,//)

(7)

Ui{T-

tv

1«y-.(x=L. V) —

(x=L, V)

(8)

where T„ is the ambient temperature.

Numerical model

The governing equations and boundary conditions are converted to algebraic equations by means of finite-volume techniques with fully implicit temporal differentiation, using bi­dimensional Cartesian grids in a staggered arrangement. Diffusive terms are evaluated using central differences scheme. For convective terms, the SMART scheme [3] is imple­mented using a deferred correction approach.

The domain where the computations are performed and a schematic of the mesh adopted is shown in Fig. 1. The mesh is represented by the parameter n. According to Fig. 1 b, control volumes are used (for example, when it means that the problem is solved on

100*40 control volumes). The size of the control volumes is maintained constant throughout x-direction, while the mesh is intensified near the front and back walls using a tanh-like function with a concentration factor of 1.5, see [7], so as to properly solve the boundary layer. This aspect is indicated in the figure with two solid triangles. The simulated time is discretized using a constant time increment Д!

The resulting algebraic equation systems are solved segregately using a multigrid solver [5] in a pressure-based SIMPLE-like algorithm [6]. For each time step, the iterative conver­gence procedure is truncated once the maximum increment of the variables and equation residuals are bellow to 10^5 and the normalised heat imbalance is lower than 1%.