Numerical investigation on fluid-thermal-electric performance of a thermoelectric-integrated helically coiled tube heat exchanger for coal mine air cooling

2.1.1 System description

Figure 1 depicts the proposed TE-integrated HCEX used for air cooling in underground mines. As can be seen from Figure 1(a), the air cooler works as the terminal device to achieve cold air near the working face in the generally used cooling and refrigeration system in underground mine. The proposed hybrid TE-integrated HCEX shown in Figure 1(b) plays the role of the air cooler in the cooling and refrigeration system in underground mine. It is composed of the HCEX, a series of TE modules, and the heat dissipator attached at the heat rejection side of the TE modules. In the TE-integrated HCEX, hot air is introduced into the shell side flow passage, and the cold water is supplied to the helically coiled tubes. The shell side hot air is cooled by both the cold water inside the helically coiled tubes through forced convection heat transportation as well as by the TE modules through the Peltier cooling effect.

Figure 1

Illustration of the TE-integrated HCEX used for air cooling in underground mines. (a) Typical mine air cooling system. (b) Proposed TE-integrated HCEX as air cooler. (c) Explosive view of TE-integrated HCEX.

The explosive view in Figure 1(c) shows the main components of the TE-integrated HCEX system. A typical TE module comprises lots of pairs of p-type and n-type legs, conductive metals and two electrically insulting ceramic layers. The p-type and n-type semiconductors are connected thermally in parallel between the hot and cold ceramic layers, and electrically in series by the interconnect conductive metals to receive the current from the external power supply. The cold side of TE modules is attached to the external shell wall of the HCEX, which is designed as a hexadecagon to better fit the square bulk TE modules to be attached. Meanwhile, as the TE module generally works with two heat exchangers attached to its hot and cold sides in order to enhance heat transfer and TE conversion performance, the hot side of the TE module need to dissipate heat to create a temperature gradient across the TE module via convective heat dissipator such as air-cooled heat sink by fan and pumped water-cooled channels by pumps. Considering that the underground air temperature is high and the cold-water cooling pipeline readily exists in the underground mine air cooling system, we herein use the water-cooling heat dissipator to remove heat at the hot side of the TE module. The water-cooling heat dissipator is represented by a series of rectangular fluid channel attached at the cold side of each column of TE module in Figure 1(c). Due to the TE effects, when electrical current is supplied, heat is extracted from the cold side of the TE module, which is attached to the object to be cooled, i.e., attached to the external shell wall of the helically coiled heat exchanger in this work, resulting in additional TE cooling capacity [30]. In this way, it is expected to improve the air-cooling capacity for the terminal air cooler used inside the confined space of the underground mine.

2.1.2 Geometrical parameters of system components

Figure 2 depicts the geometrical characteristics of the physical model of the conventional HCEX and the TE-integrated HCEX. The conventional HCEX without TE module is regarded as the baseline system. Figure 2(a) shows the geometrical structure of the conventional HCEX without TE module. The circumscribed circle diameter of the hexadecagon shell, D _shell, is 228.388 mm. The side length of the hexadecagon shell, L _side, is 44.556 mm. The effective heat exchange length of the HCEX, H, is 320 mm. The outer diameter of the helically coiled tube, D _t, is 12 mm. The longitudinal pitch of the helically coiled tube, P _l, is 19 mm. The helix angle of the heat exchange tube, β, is 6°. The winding diameter of one coil, D _coil, is 60 mm. Two layers of coiled tubes are considered in this work. There is one helically coiled tube in the innermost layer. Five helically coiled tubes are utilized in the second layer. They are coaxially arrayed along the radial direction in a symmetrical manner. The distance of the center axis between adjacent layers of coils, δ _layer, is 74 mm. The heat exchange tubes are made of copper.

Figure 2

Geometrical parameters of the HCEX with and without integration of TE modules for air cooling in underground mine. (a) Conventional HCEX without thermoelectric. (b) TE-integrated HCEX with FR varying from 50 to 100%.

Figure 2(b) depicts the geometrical structure of the TE-integrated HCEX. The specification for a TE module is 40 × 40 × 3.8 mm³. One TE module is comprised of 127 pairs of TE pellets. The TE material layer, ceramic substrate, and electrode are set as 1.6, 0.8, and 0.3 mm in thickness, respectively. The TE materials considered in this work are Bi₂Te₃, which is widely used commercially.

The filling ratio (FR) of the TE module is varied in this work so as to investigate its effect on the air-cooling performance, which is discussed in detail in Section 3. This work considers the TE layout designs including partially filled along the streamwise direction with FR of 50 and 75%, and fully filled TE modules with FR of 100%. The conventional HCEX, represented as Case 1, is regarded as the baseline case for comparison analysis. Each TE module sequence on the same hexadecagon side of the shell is series connected for electricity, and the adjacent two sequences of the TE modules mounted at the hexadecagon sides of the shell are parallel connected for electric.

For the TE-integrated HCEX, the position matrix for the TE module is represented by M for row and N for column, respectively. Under the condition of FR of 50% (Case 2), the layout of the TE modules, M × N, is 8 × 8, i.e., totally 64 pieces of TE modules. The layout position is symmetrically set on rows from M ₁ to M ₈ at the hexadecagon sides N ₁, N ₃, N ₅, N ₇, N ₉, N ₁₁, N ₁₃, and N ₁₅, with the other sides, i.e., N ₂, N ₄, N ₆, N ₈, N ₁₀, N ₁₂, N ₁₄, and N ₁₆, are free of TEs. Under the condition of partially filled TEs along streamwise direction with FR 75% (Case 3), the layout of the TEs, M × N, is 8 × 12, i.e., totally 96 pieces of TE modules. The layout position is symmetrically set on rows from M ₁ to M ₈ at hexadecagon sides N ₂ to N ₄, N ₆ to N ₈, N ₁₀ to N ₁₂, and N ₁₄ to N ₁₆, with the other sides (sides N ₁, N ₅, N ₉, and N ₁₃) are free of TEs. Under the condition of fully filled TE with FR of 100% (Case 4), the layout of the TEs, M × N, is 8 × 16, and the total number of the TE module is 128. That is, the external wall of the hexadecagon shell is all filled with TEs. The rectangular flow channel of the water-cooling dissipater attached to each column of TE module has same effective heat exchange length, H, as the hot side shell of the HCEX. The inner width of the rectangular flow channel is equivalent to the width of the TE module, which is 40 mm. The height of the rectangular flow channel is set as 5 mm. The material of the water-cooling heat dissipator is assumed to be made of aluminum.

2.2.1 Governing equations

As the focus of this work is to investigate the feasibility of improving the cooling capability for the conventional helically coiled tube heat exchanger by TE module with the energy transportation process mentioned above, the following approximations have been considered for the fluid-thermal-electric modeling:

1. The simulation of the hybrid TE-integrated HCEX in dehumidifying condition is considered in the present work. The thermal property parameters of dry air fluids are constant.

2. The air fluid flow through the HCEX is steady, fully developed turbulent, and incompressible.

3. The convective heat exchange in the rectangular cooling channel at the heat dissipation side of TE module as well as the tube side water-cooling inside the HCEX is represented by the third kind of boundary condition (BC).

4. The electrical resistivity and thermal conductivity of welding solder are considered to be negligible.

5. The hybrid TE-integrated HCEX is insulated from the external environment thermally and electrically at all the side walls.

The governing equations of the simulation domain for the required solution of fluid, thermal, and electrical fields include mass, momentum, energy, turbulent kinetic energy and energy dissipation rate, electrical current, and voltage equations. The mass, momentum, and energy conservation equations [34] for the fluid domain in the hot side air fluid channel are as follows:

Mass:

Momentum:

Energy:

where u is the velocity vector, m s⁻¹. T is the temperature, K. p represents the pressure, Pa. ρ is density of air fluid, kg m⁻³. λ is the thermal conductivity of air fluid, W m⁻¹ K⁻¹. μ is the dynamic viscosity, Pa s. c _p is the specific heat capacity, J kg⁻¹ K⁻¹.

In some similar studies, various options of k–ε turbulence model were successfully applied for HCEXs. Among them, the k–ε model (realizable) can improve the flow with higher strain rate and curve of flow stream, and thus improve the prediction precision of spiral flow. Our previous work [35] on model validation results for a spirally wound HCEX demonstrate that the k–ε model (realizable) is valid, which is in accordance with the modeling method reported by Zhou et al. [36] who also found that the k–ε model (realizable) can be employed in reasonably numerical prediction on thermal-hydraulic performance of shell side performance of HCEXs. Therefore, for the turbulence model of the air fluid inside the shell of the HCEX, the k–ε model (realizable) is adopted in the following numerical calculations to investigate the fluid flow and heat transfer performance of the helically coiled tube air cooler.

Transport equations for turbulent kinetic energy k, and energy dissipation rate ε in the realizable k–ε model [34] are as follows:

Turbulent kinetic energy:

Energy dissipation rate:

where μ t is calculated by μ t = ρ C μ k 2 ε , where C μ is the function of the mean strain and rotation rates, the angular velocity of the system rotation, and the turbulence fields. G k represents the generation of turbulent kinetic energy due to mean velocity gradients, which is evaluated by G k = μ t ⋅ S 2 , and S is defined by S = 2 S ij ⋅ S ij and S ij = 1 2 u i x j + u j x i . The model constants are C ₂ = 1.9, σ k = 1.0, and σ ε = 1.2, respectively. Readers can refer to Ref. [34] for a detailed fundamental theory for the realizable k–ε model.

The 3D partial differential equations governing the thermal-electric energy conversion phenomenon in the TE module can be described as follows [32,33]. The electrical current in the TE material and copper layers obeys the conservation law, which is calculated by

where J is the current density vector, A m⁻².

The constitutive current–voltage relationship is calculated by

where σ is the electrical conductivity, S m⁻¹. V is the electrostatic potential, V. α is the Seebeck coefficient, V K⁻¹.

The energy equation for the solid TE domain includes Fourier heat conduction, Joule heating, and Peltier and Thomson effects, which is described as:

The energy equation in the domain of the copper electrode where Joule heat is described as:

In the ceramic layers of the hot side and cold side plates, only heat conduction is considered. The corresponding heat equation is as follows:

where ρ e is the electrical resistivity, Ω m and λ s is the thermal conductivity of solid, W m⁻¹ K⁻¹.

As mentioned above, it is difficult to simulate 8,128–16,256 pairs of the semiconductor legs in detail. While the thermal resistance of these TE legs is connected in parallel and the electrical resistance is in series, Eqs. (11)–(13) based on the equivalent Seebeck coefficient, equivalent thermal, and electrical resistance between the TE module and the lumped one pair of TE leg can be derived [33].

where α p , n , λ p , n , ρ e , p , n represents the intrinsic Seebeck coefficient, thermal conductivity, and electrical resistivity for a single p-type or n-type TE leg, respectively. h _leg and A _leg are the height and cross-sectional area for a single TE leg. N _pn is the pair number of the TE leg for a TE module. α _E, λ _E, ρ _E, h _E, and A _E are the equivalent Seebeck coefficient, equivalent thermal conductivity, equivalent electrical resistivity, height and cross-sectional area for a TE module, respectively. Thus, the equivalent thermal-electrical properties of the TE module can be derived from those of the TE legs as Eqs. (14)–(16) [33].

The equivalent thermal-electrical properties are used in the above differential equations within the simulation domain of the TE modules during the numerical simulations.

2.2.2 Physical properties of materials

The physical properties of the materials considered in the numerical model are summarized in Table 1. The density of air is set as 1.225 kg m⁻³. The specific heat capacity of air is 1006.43 J kg⁻¹ K⁻¹, and the thermal conductivity of air is set as 0.0242 W m⁻¹ K⁻¹. The viscosity of air is 1.7894 × 10⁻⁵ Pa s. The physical properties of water used to estimate the representative convective heat transfer coefficient used for setting the third kind of BC of the above depicted water-cooling channel is as follows: the density of water is 999.7 kg m⁻³. The specific heat capacity of water is 4196 J kg⁻¹ K⁻¹, and the thermal conductivity of water is set as 0.58 W m⁻¹ K⁻¹. The viscosity of water is 1.306 × 10⁻³ Pa s.

During the numerical simulation, the equivalent property method is employed as it is computationally cost-effective to simulate tens to hundreds of pieces of TE modules, which has been introduced above. The equivalent parameters for the properties of the TE module are estimated by the intrinsic property values of p-type and n-type TE materials and structural specifications of the TE module, which are calculated by the correlations summarized in Table 1. Temperature-dependent intrinsic physical properties for TE materials are considered [37] in this work. The thermal conductivity of the conductive metal is set as 400 W m⁻¹ K⁻¹ and the electrical conductivity as 5.9 × 10⁸ S m⁻¹ [44]. The thermal conductivity of the Al₂O₃ ceramic is 49.2 W m⁻¹ K⁻¹ [38]. Besides, it is noted that the effects of electrical and thermal contact resistances of the welding solders used to connect the conductive metals and TE materials is small compared with the p-type and n-type TE materials, which is not considered at the energy conservation equation in the numerical work.

2.2.3 BCs

In this work, Chen’s numerical schemes and model framework are used by employing the specified current used for TE modules and the current direction is set in a way to guarantee that Peltier heat is absorbed at the cold side and released at the hot side [32]. Here the input working current for each column of TE module that is electrically connected in series varies from 1 to 9 A. Thus, the terminal-in electric BC of the TE module in each column is set as constant current density 87719.3–789473.7 A m⁻² according to Eq. (17).

where I is the working current, A and A ξ is the normal surface area at terminal-in boundary, m².

At the last TE module in each column, the terminal-out electric BC is treated as ground voltage

The air inlet BC is ascribed as uniform velocity inlet BC with prescribed inlet velocity and temperature. The inlet velocity is varied from 10 to 25 m s⁻¹ to examine the effect of different air flow rates supplied into the TE-integrated HCEX. The range of inlet air temperature is based on the practical environmental conditions in underground mine, which could be over 303.15 K (30°C) according to the mining depth and intensity [39]. For instance, the airflow temperature in the working face at the Pingdingshan No. 8 coal mine is 308.15 K (35°C) [40], and the temperature of the surrounding rock in the Zhao Lou mine of China at the −900 m mining layer reaches 316.15 K (43°C) [41]. Herein, the inlet temperature is calculated from 303.15 to 313.15 K to examine the effect of different air flow rates supplied into the TE-integrated HCEX. The outlet BC of air is assumed as fully developed outlet BC at 0 Pa. The conventional HCEX without TE module attached on the external shell wall is considered as the baseline case, whose external shell wall exposed to the surroundings are regarded as adiabatic. The TE modules used in the TE-integrated HCEX are attached to the shell walls, hence the coupled wall BC for the interface between the surface of the heat adsorption side (cold side) of TE module and external shell wall is employed.

Based on the heat transfer theory [42], the range of convective heat transfer coefficient of air is 20–100 W m⁻² K⁻¹ and the convective heat transfer coefficient of water is 1,000–15,000 W m⁻² K⁻¹, which is determined by the geometrical topology of fluid channel and the working fluid properties [10]. Thus, for an air-water based heat exchange system, the major thermal resistance is produced at the gas side channel, while the water side heat transfer coefficient is large and the BC can be treated by third kind of BC to simplify the model in similar investigations [33]. Thus, the wall BC of the helically coiled tube as well as the heat dissipation side of the TE module are set as the third kind of BC. The heat transfer coefficient of the rectangular water-cooling channel at the cold side of the TE modules depicted in Section 2.1 can be theoretically estimated by the Gnielinski formula [42].

The Konakov formula [42] can be used to calculate the value of flow resistance coefficient f.

The experimental verification range for Eqs. (19) and (20) is that the Re is 2,300-10⁶ and Pr_f is 0.6∼10⁵.

The convective heat transfer coefficient of the water-cooling channel can be determined by its relationship with the Nusselt number [42].

The pressure drop of the water-cooling channel can be determined by the relationship of flow resistance coefficient and pressure drop [42].

where H is the flow length of water-cooling flow channel, m; D _h is the hydraulic diameter of the flow channel, m; Re and Pr_f respectively represent the Reynolds number and Prandtl number of the working fluid; and f is the flow resistance coefficient of turbulent flow inside the flow channel.

Accordingly, for the above depicted water-cooling channel, considering a velocity magnitude range of the cold water with at the level of 0.3–0.6 m s⁻¹ (Re = 2,273–3,824), which is a reasonable operational velocity for water-based heat dissipater to constraint the pressure loss, ∆ p w , within 230 Pa. The convective heat transfer coefficient, h f , of the water-cooling flow channel is 1,000–2,000 W m⁻² K⁻¹, which falls in the range of similar work on water-cooling flow channel [33]. In a coal mine air cooler, the cooling water can be used as the cold side fluid of the TE module and the coolant temperature is generally within 283.15 K and the major thermal resistance is at the air side. Thus, according to the above estimated level of water-cooling heat transfer coefficient, the third kind of wall BC of the cold wall of the water-dissipator is set as 1,600 W m⁻² K⁻¹ and the estimated pressure drop value of the cold side channel is 170 Pa for the water-cooling BC in this work.

2.2.4 Model validation

The fluid-thermal-electric multiphysics coupled numerical model was implemented with ANSYS FLUENT platform and the model validation is performed by two steps. The first step is to validate whether the present numerical method is valid for the helically coiled heat exchanger. A thermal-hydraulic numerical model is established with the same specification of the experimentally tested sample which is a spiral-wound heat exchanger with helically coiled tubes inside the shell, which have been performed and described in our previous work [35]. Four sets of unstructured meshes for irregular shell side calculation domain with total grids of 599,264, 760,668, 971,899 and 1,503,612 have been used to conduct grid independence check for the shell side air fluid domain and finally the mesh with 971,899 grids is employed to ensure the accuracy of the calculation results and save the calculation time. The comparison result shows that the numerical results agree well with the experimental results, as shown in Figure 3(a). The deviation between the temperature difference between inlet and outlet and the experimental value is less than 6.4%. The average and maximum deviations between the air flow pressure drop of numerical and the experimental values are 9.6 and 14.8%, respectively. Hence, the setting of the mesh size investigated in the hybrid HCEX follows this grid density, with the maximum size of 15 mm for the overall grid division of the HCEX and the maximum size of the local grid division and densing processing of the heat exchange coil is limited within 5 mm in the ANSYS ICEM platform.

Figure 3

Code validation. (a) Validation for thermal-hydraulic performance [35]. (b) Validation for thermoelectric cooling UDF code against Jaegle’s result [44].

Second, in this model, in order to achieve the thermal-fluid-electrical coupling calculation, the equations governing the TE conversion phenomena are fulfilled with the external user defined functions (UDFs) to numerically calculate the TE-related scalars and source terms described in Eqs. (6)–(16). Thus, the second step is to perform code validation of the external UDFs for TE phenomenon in this hybrid device. The numerical model established here embedded the equivalent properties to the Chen’s finite-volume-method-based UDF methodology [32]. This method is applicable to both TE power generation as well as TE cooling process as the governing equations for thermal-electric conversion process is the same [43]. The Semi-implicit method for pressure linked equations (SIMPLE) algorithm is adopted for the coupling of pressure and velocity. Second-order upwind scheme is used for convective spatial discretization. The convergence criterion for mass continuity, and the velocity vectors in x, y, and z directions are all set as 10⁻⁵. The convergence criterion for energy equation is 10⁻⁸. For user defined scalars, including the current density, Seebeck electric potential, and Ohmic electric potential, the convergence criterion is respectively set as 10⁻¹⁵, 10⁻¹⁵, and 10⁻¹⁰. The validation of the numerical model with code for TE cooling process is illustrated in Figure 3(b) and the calculation result of the code is in good agreement with that of the previous study [44].

To guarantee uniform inlet flow and avoid reverse flow at outlet, the computational domain of the HCEX is prolonged more than ten times of the characterized length of the HCEX at the inlet and outlet, respectively (Figure 4). Considering the complexity of the geometrical model, hybrid mesh generation method is adopted. For the air fluid domain in the HCEX, the tetra-dominated unstructured grid was utilized. For the calculation domain of the TE modules, the orthogonal, non-uniform structured grid was employed. The total elements of the final hybrid mesh of the model of the TE-integrated HCEX with FRs of 50, 75, and 100% are 4,550,284, 5,211,244, and 5,872,279, respectively.

Figure 4

Mesh of the TE-integrated HCEX: (a) Overall view and (b) enlarged view of meshes of the TE modules and the helically coiled tubes.