ANSYS FLUENT 12.0 Theory Guide - 6.2.2 Dual Cell Model Theory

The dual cell heat exchanger consists of two porous fluid zones, namely a primary zone and an auxiliary zone. The two zones are solved simultaneously and are coupled only through heat transfer. The common region in each zone, where heat transfer takes place, represents the heat exchanger core. The cores for both primary and auxiliary zones occupy the same physical space, as shown in Figure 6.2.1. The cells in the two cores should overlap completely in the physical space to ensure conservative heat transfer. Heat transfer occurs between cells in close proximity based on the cell centroid. In other words, a primary zone cell exchanges heat with one, and only one, auxiliary zone cell and vice versa. Therefore, if one of the core (say primary) mesh is too coarse or fine relative to the other core (say auxiliary) conservation of heat transfer is not ensured. Heat transfer calculations in the dual cell model are based on the NTU method.

**Figure 6.2.1:** Core with Matching Quad Meshes for Primary and Auxiliary Zones in a Cross-Flow Pattern

In a cross-flow pattern, the NTU values are calculated as in Equation 6.1-10. The equation is solved iteratively using the Newton-Raphson. For parallel flow, the NTU value is calculated as follows:

$NTU = \frac{-ln({1-\epsilon - \epsilon C_r})}{(C_r + 1)}$

(6.2-1)

$NTU_{C_r = 1} = \frac{\epsilon}{1-\epsilon}$

(6.2-2)

$NTU = \frac{1}{(C_r - 1)} ln\left[\frac{(1-\epsilon)}{(1-\epsilon C_r)}\right]$

(6.2-3)

Heat rejection is computed for each cell in the two cores (primary and auxiliary) and added as a source term to the energy equation for the respective flows. This is illustrated in Figure 6.2.2 and the following equations:

**Figure 6.2.2:** Core with Primary and Auxiliary Zones with Possible Overlap of Cells

$\dot m_{scaled,A} = \rho_{cell,A} \vec{V}_{cell,A} A_{inlet,A}$

(6.2-4)

$\dot m_{scaled,P} = \rho_{cell,P} \vec{V}_{cell,P} A_{inlet,P}$

(6.2-5)

$C_{min,scaled} = min[(C_{p,cell} \dot m_{scale})\vert _P , (C_{p,cell} \dot m_{scale})\vert _A]$

(6.2-6)

$NTU_{scaled} = [NTU_{full} (\dot m_{scaled,P} , \dot m_{scaled,A})]_{bilinear interpolation}$

(6.2-7)

$(UA)_{scaled} = NTU_{scaled} \;\; C_{min,scaled}$

(6.2-8)

$dq = q_{cell} = \frac{(UA)_{scaled} (T_{cell,A} - T_{cell,P})}{Volume_{cell}}$

(6.2-9)

where	$T_{cell,A}$	=	auxiliary cell temperature
	$T_{cell,P}$	=	primary cell temperature
		=	overall heat transfer coefficient
		=	total heat transfer area
	$C_{min,scaled}$	=	scaled minimum heat capacity rate

You can supply the NTU values, or it can be calculated using the supplied raw data and the effectiveness-NTU relation that you specify.

To learn how to use the dual cell heat exchanges model, refer to this section in the separate User's Guide.