3. Case study

The proposed method is applied on two types of heat exchangers, namely, a finned-tube heat exchanger and a helical-tube heat exchanger. These configurations were selected because they are compact, of relatively simple geometry and of easy modification of parameters. The open literature indicates that these types of heat exchangers are typically used in heat recovery from exhaust gases. The geometry of both exchangers consists of two concentric tubes: the hot gas flows at the internal tube and ethylene glycol flows in the annular space between tubes. The outer surface of the exchangers is isolated. Figures 2 and 3 show the helical-tube heat exchanger and the finned-tube heat exchanger, respectively. The only parameter that remains the same, as reference, for both types of heat exchangers is the linear length from inlet to outlet which is set to 1 m.

CFD techniques are used to analyze the performance of the units. The response variables of the CFD simulation are gas outlet pressure (PG), ethylene glycol outlet pressure (PEG), heat exchanger's surface area referred to the hot side (AG), heat exchanger's surface area referred to the cold side (AEG), heat flux from the hot side (QG"), and heat flux to the cold side (QEG"). For the design of experiments, the factors considered for the case of the helical-tube heat exchanger are internal

Figure 2. Helical-tube heat exchanger.

Figure 3. Finned-tube heat exchanger.

diameter (ID), external diameter (ED), mass flow rate of the gas (mass), and inlet gas temperature (temp). The range of parameters are shown in Table 1.

In the case of the finned-tube heat exchanger, where the fins are assumed to be straight, the parameters considered are fin height, fin thickness, fin density (FD), mass ratio between gas and ethylene glycol (mass ratio), and inlet gas temperature (temp). The range of the parameters are shown in Table 2.

The variables were selected based on the impact they have on the dimensions of the heat exchanger, as well as on the operating conditions over the range where maximum heat transfer will be achieved. These variables will allow to find the optimal conditions of the heat exchanger when determining new correlations for the Nusselt number to eliminate the risk of oversizing.

The factors chosen for the finned heat exchanger were taken from the work of Hatami et al. [7]. The mass ratio factor is the ratio between the two fluids, namely, gas and ethylene glycol. After trying different mass ratios, the best fit between CFD results and Minitab [13] regressions was obtained. To select the factors for the case of helical heat exchanger, six parameters were initially considered: internal diameter, external diameter, helix diameter, helix pitch, mass of gas, and temperature of gas. Some parameters were eliminated to get the minimum number of factors that could exhibit a good fitting to the simulated results. The parameters eliminated were helix diameter and helix pitch. The minimum number of factors required to get a good fit were internal diameter, external diameter, and temperature and mass of gas.

The experiment design indicates that 27 configurations to simulate the helicaltube heat exchanger are needed, while 46 are required for the finned-tube unit. Each one of these configurations was simulated using Ansys Fluent 2016 [14]. The simulations were made under the following considerations:

a. The standard k-ε model with standard wall function turbulent model was used for the gas side.


b.A laminar model was used at the ethylene glycol side (50 ≤ Re ≤ 250).

Table 1.

Design parameters for the helical-tube heat exchanger.


Table 2.

Design parameters for the finned-tube heat exchanger.

c. There is no phase change on either side.

d.The gas pressure drop must be lower than 10 kPa.

e. The y+ value must be around y+ > 30 and y+ < 300 (wall treatment) [15].

The density of the gas was determined using the incompressible ideal gas model because the Mach number in all cases was lower than 0.3. The density and viscosity of ethylene glycol were calculated using a user-defined function (UDF). In this way, the variation of density and viscosity with temperature was considered applying the equations

$$
\rho\_{\rm EG} = -0.9904 \ast temp + 1417 \tag{1}
$$

$$\eta\_{\rm EG} = \mathbf{3.724E4} \cdot \exp\left(-0.05021 \ast temp\right) + 0.2811 \exp\left(-0.01356 \ast temp\right) \tag{2}$$

For the thermal conductivity and viscosity of the hot gas, the equations used are

$$\mathbf{x}\_{GA} = \mathbf{6.22} \ast \mathbf{10} - \mathbf{5} \ast temp + 0.008116\tag{3}$$

$$\eta\_{GA} = \mathbf{3.755} \ast \mathbf{10} - \mathbf{5} \ast \exp\left(0.0002586 \ast temp\right)$$

$$- \mathbf{3.561} \ast \mathbf{10} - \mathbf{5} \ast \exp\left(-0.001614 \ast temp\right)\tag{4}$$

To validate the results of the CFD simulations, the following published correlations are used [10]:

Helical-tube heat exchanger Turbulent regime

$$\text{Nu}\_{s} = \frac{\text{PrRe}(\mathbf{f}\_{s}/8)}{\mathbf{1} + \mathbf{1}2.7\sqrt{\frac{\mathbf{f}\_{s}}{8}} \left(\mathbf{f}^{\dagger}\mathbf{\hat{r}}^{\dagger} - \mathbf{1}\right)} \left[\mathbf{1} + \left(\frac{\mathbf{d}\_{h}}{\mathbf{L}}\right)^{2/3}\right] \tag{5}$$

Laminar regime

$$\mathrm{Nu} = \left[ \left( \left( 364 + \frac{4.636}{\mathrm{x\_3}} \right) + 1.816 \left( \frac{\mathrm{De}}{\mathrm{x\_4}} \right)^{3/2} \right]^{1/3} \right] \tag{6}$$

Finned-tube heat exchanger Turbulent regime

$$\frac{\mathbf{Nu\_n}}{\mathbf{Nu\_{D-n}}} = \left[\frac{\mathbf{d\_i}}{\mathbf{d\_{im}}} \left(\mathbf{f} - \frac{\mathbf{2e}}{\mathbf{d\_i}}\right)\right]^{-0.2} \left.\frac{\mathbf{d\_i}\mathbf{d\_i}}{\mathbf{d\_{im}^2}}\right\vert^{0.5} \sec^3\theta \tag{7}$$

Laminar regime

$$\text{Nu} = 1.86 \left( \frac{\text{Pe}\_{\text{b}} \text{d}\_{\text{i}}}{\text{L}} \right)^{1/3} \left( \frac{\mu\_{\text{b}}}{\mu\_{\text{w}}} \right)^{0.14} \tag{8}$$

To determine the maximum exergy recovery, the expression used is

$$\frac{d\Phi\_{\rm CV}}{dt} = \Sigma \dot{\Phi}\_{\rm Q} + \Sigma \dot{\mathbf{m}}\_{i} \mu\_{i} - \Sigma \dot{\mathbf{m}}\_{\rm e} \mu\_{e} + \dot{\mathbf{W}}\_{\rm act} - \dot{\mathbf{I}}\_{\rm total} \tag{9}$$

Figure 4. Flow diagram for the simulation of the organic Rankine cycle.

The generation of power from a low temperature heat source can be achieved by means of an Organic Rankine Cycle. Figure 4 shows the diagram of the ORC cycle used for the simulation using HYSYS [11]. The working fluid is butane and the main components of the cycle are:

Pump (P-100): adiabatic efficiency 75%.

Heat exchanger (heater) (E-101): tube passes 2, shell passes 1, ΔP = 0. Turbine (K-100): adiabatic efficiency 75%. Heat exchanger (cooler) (E-100): Δ P = 0.
