In both heat transfer models, pressure loss is modeled using the porous media model in Ansys Fluent. For the dual cell model (The Dual Cell Model), pressure loss is used for both streams, while for the macro model, it is used only for the primary side.

The loss coefficients of the porous media model are computed using curve fitting of the pressure-versus-flow rate data outside of Ansys Fluent, which you will specify for the cell zone conditions. However, in some cases, the data for curve-fitting is not available. The macro model provides an additional means of getting the coefficients if the data is not available. The coefficients can also be automatically computed (and updated) using a known pressure loss coefficient as a function of some geometric parameters, the theory of which is defined below:

(6–1)

The pressure loss coefficient is computed from

(6–2)

and are empirical quantities obtained from experimental data. You will need to specify these parameters based on graphs that are closest to the heat exchanger configuration that you are setting up [297], [295]. These parameters are used to set up large resistances in the two non-streamwise directions, effectively forcing the primary fluid flow through the core to be unidirectional.

In Equation 6–2, the core friction factor is defined as

(6–3)

and are empirical quantities obtained from experimental data. You will need to specify the core friction coefficient and exponent based on graphs that are closest to the heat exchanger models that you set up [297], [295].

The Reynolds number in Equation 6–3 is defined as

(6–4)

For a heat exchanger core, the hydraulic diameter can be defined as

(6–5)

where is the flow length of the heat exchanger. If the tubes are normal to the primary fluid flow, then is the length in the primary fluid flow direction. Note that can be calculated from

(6–6)

where is the primary fluid velocity and is the ratio of free-flow area to core frontal area.

The heat-exchanger effectiveness, , is defined as the ratio of actual rate of heat transfer between the primary and auxiliary fluids to the maximum possible rate of heat transfer. The maximum possible heat transfer is given by

(6–7)

where and are the inlet temperatures of the primary and auxiliary fluids and

(6–8)

Thus, the actual rate of heat transfer, , is defined as

(6–9)

The value of depends on the heat exchanger geometry and flow pattern (parallel flow, counter flow, cross flow, and so on). Even though the effectiveness of the primary fluid is computed using uniform conditions on the entire heat exchanger core, it will be applied to a small portion of the core represented by a computational cell. This can make it less accurate for some heat exchanger cores, where there is a strong variation in the primary flow.

For the simple-effectiveness-model, you provide effectiveness values for the heat exchanger you are simulating, specifying how this quantity changes with velocity. For the ntu-model, you provide the heat exchanger performance data (heat rejection / transfer data versus primary flow rate) based on uniform test conditions, and Ansys Fluent calculates the effectiveness of the entire heat exchanger from the ratio of heat capacity and the number of transfer units using the relation

(6–10)

where is the ratio of to .

The heat exchanger performance data should be specified for a number of auxiliary flow rates so that Ansys Fluent can compute the number of transfer units versus the primary fluid flow rate for a number of auxiliary fluid flow rates. This NTU, which is based on the full heat exchanger and uniform conditions, is scaled for each macro using the ratio of their volumes and minimum heat capacities.

For each macro, the primary fluid inlet temperature is calculated using the mass average of the incoming primary fluid temperatures at the boundaries. This automatically takes into account any reverse flow of the primary fluid at the boundaries.

Note that the previous equations are for crossflow (unmixed) conditions; the macro model can only simulate crossflow, as opposed to coflow and counterflow cases.

Heat rejection is computed for each cell within a macro and added as a source term to the energy equation for the primary fluid flow. Note that heat rejection from the auxiliary fluid to primary fluid can be either positive or negative.

For the simple-effectiveness-model, the heat transfer for a given cell is computed from

(6–11)

For the simple-effectiveness-model, the heat rejection from a macro is calculated by summing the heat transfer of all the cells contained within the macro

(6–12)

For the ntu-model, the heat transfer for a macro is calculated from

(6–13)

For the ntu-model, the heat transfer for a given cell is computed from

(6–14)

For both heat exchanger models, the total heat rejection from the heat exchanger core is computed as the sum of the heat rejection from all the macros:

(6–15)

The auxiliary fluid inlet temperature to each macro ( in Equation 6–11 and Equation 6–13) is computed based on the energy balance of the auxiliary fluid at a previous macro computation. For a given macro,

(6–16)

where and are the inlet and outlet enthalpies of the auxiliary fluid in the macro. The auxiliary fluid outlet temperature from the macro is calculated as

(6–17)

The values of and then become the inlet conditions to the next macro.

The first row of macros (Macros 0, 1, and 2 in Figure 6.2: Core Discretized into 3x4x2 Macros) are assumed to be where the auxiliary fluid enters the heat exchanger core. When the fixed total heat rejection from the heat exchanger core is specified, the inlet temperature to the first row of macros is iteratively computed, so that all of the equations are satisfied simultaneously. When a fixed auxiliary fluid inlet temperature is specified, the heat transfer for the first row of macros are used to calculate their exit enthalpy, which becomes the inlet condition for the next row macros. At the end of each pass, the outlet enthalpy of each macro (in the last row) is mass averaged to obtain the inlet condition for the next pass macros.

If the optional macro heat exchanger group is used, a single heat exchanger may be consist of multiple fluid zones. In this case, the auxiliary fluid is assumed to flow through these zones in parallel. Thus, after taking into account any auxiliary stream effects, the auxiliary fluid inlet mass flow rate is automatically apportioned to each zone in the group as follows:

(6–18)

where is the total auxiliary mass flow rate for the heat exchanger group. refers to the volume of the ^th finite volume cell within the ^th fluid zone. Within each zone, the auxiliary fluid flows through each macro in series as usual.

At the outlet end of the group, the parallel auxiliary fluid streams through the individual zones are recombined, and the outlet auxiliary fluid enthalpy is calculated on a mass-averaged basis:

(6–19)

With user-defined functions, the simple-effectiveness-model allows you to simulate two-phase auxiliary fluid flows and other complex auxiliary fluid enthalpy relationships of the form

(6–20)

where is the absolute pressure and is the quality (mass fraction of vapor) of a two-phase vapor-liquid mixture. When pressure-dependent auxiliary fluid properties are used, the mean pressure within each macro is calculated and passed to the user-defined function as

(6–21)

To learn how to use the macro heat exchanger models, refer to Using the Ungrouped Macro Heat Exchanger Model and Using the Grouped Macro Heat Exchanger Model in the User's Guide.