Thermo-Photo-Voltaic Cell

The following example illustrates an application that maximizes surface-to-surface radiative fluxes and minimizes conductive heat fluxes.

A thermo-photo-voltaic (TPV) cell generates electricity from the combustion of fuel and through radiation. Figure 1 depicts the general operating principle. The fuel burns inside an emitting device that radiates intensely. Photovoltaic (PV) cells — almost like solar cells — capture the radiation and convert it to electricity. The efficiency of a TPV device ranges from 1 % to 20 %. In some cases, TPVs are used in heat generators to co-generate electricity, and the efficiency is not so critical. In other cases TPVs are used as electric power sources, for example in automobiles (Ref. 1). In those cases efficiency is a major concern.

Figure 1: Operating principle of a TPV device (Ref. 2), and an image of a prototype system (Ref. 3).

TPV systems, unlike typical electronic systems, must maximize radiation heat transfer to improve efficiency. However, inherent radiation losses — radiation not converted to electric power — contributes to the PV cells’ increased temperature. Further, heat transfer through conduction results in increased cell temperature. PV cells have a limited operating temperature range that depends on the type of material used. Solar cells are limited to temperatures below 80 °C, whereas high-efficiency semiconductor materials can withstand as much as 1000 °C. Photovoltaic efficiency is often a function of temperature with a maximum at some temperature above ambient.

To improve system efficiency, engineers prefer to use high-efficiency PV cells, which however can be quite expensive. To reduce system costs, engineers work with smaller-area PV cells and then use mirrors to focus the radiation on them. However, there is a limit for how much you can focus the beams; if the radiation intensity becomes too high, the cells can overheat. Thus engineers must optimize system geometry and operating conditions to achieve maximum performance at minimum material costs.

The following application, which uses the Heat Transfer with Surface-to-Surface Radiation interface, investigates the influence of operating conditions (flame temperature) on system efficiency and the temperature of components in a typical TPV system. The application can also assess the influence of geometry changes.

Model Definition

Figure 2 depicts the geometry and dimensions of the system under study. To reduce the temperature, the PV cells are water cooled on their back side (at the interface with the insulation).

Figure 2: Geometry and dimensions of the modeled TPV system.

Conduction is always present on the different boundaries. The model simulates the emitter with a specific temperature, Theater, on the inner boundary. At the outer emitter boundary, it takes radiation (surface-to-surface) into account in the boundary condition. It simulates the mirrors by taking radiation into account on all boundaries and applying a low emissivity. The inner boundaries of the PV cells and of the insulation also make use of radiation boundary conditions. However, the PV cells have a high emissivity and the insulation a low emissivity. Further, the PV cells convert a fraction of the irradiation to electricity instead of heat. Heat sinks on their inner boundaries simulate this effect by accounting for a boundary heat source, q, defined by

where G is the irradiation flux (W/m2) and ηpv is the PV cell’s voltaic efficiency. The latter depends on the local temperature, with a maximum of 0.2 at 800 K:

Figure 3 illustrates this expression for temperatures above 1000 K.

Figure 3: PV cell voltaic efficiency versus temperature.

At the outer boundary of the PV cells, the model applies convective water cooling by setting h to 50 W/(m2·K), and Tamb to 273.15 K. Finally, at the outer boundary of the insulation it applies convective cooling with h set to 5 W/(m2·K) and Tamb to 293.15 K.

Table 1 summarizes the material properties.

Table 1: Material properties.
Component	k (W/(m·K))	ρ (kg/m3)	Cp (J/(kg·K))	ε
Emitter	10	2000	900	0.99
Mirror	10	5000	840	0.01
PV Cell	93	2000	840	0.99
Insulation	0.05	700	100	0.1

The model calculates the stationary solution for a range of emitter temperatures (1000 K to 2000 K) using the parametric solver.

Finally, the geometry shown in Figure 2 allows taking advantage of sector symmetry and reflection to reduce the computational cost. As shown in Figure 4, the geometry can be divided in 8 sectors (delimited by blue lines), each containing a reflection plane (red line). The computational domain is thus reduced to one sixteenth of the geometry. Then, for surface-to-surface radiation modeling, the view factor computation on the reduced geometry takes into account the presence of all the surfaces of the full geometry.

Figure 4: Sectors of symmetry (blue lines) and reflection plane (red line) in one sector.

Results and Discussion

The results shows that the device experiences a significant temperature distribution that varies with operating conditions. Figure 5 depicts the stationary distribution on full geometry at operating conditions with an emitter temperature of 2000 K.

Figure 5: Temperature distribution in the TPV system when the emitter temperature is 2000 K.

As the upper plot in Figure 6 shows, the PV cells reach a temperature of approximately 1800 K. This is significantly higher than their maximum operating temperature of 1600 K, above which their photovoltaic efficiency is zero (see Figure 3).

It is interesting to investigate what the optimal operating temperature is. The lower plot in Figure 6 investigates at what temperature the system achieves the maximum electric power output. The optimal emitter temperature for this configuration seems to be between 1600 K and 1700 K, where the electric power (irradiation multiplied by voltaic efficiency) is maximum.

Figure 6: PV cell temperature (top) and electric output power (bottom) versus operating temperature.

The next step is to look at the temperature distribution at the optimal operating conditions (Figure 7).

Figure 7: Temperature distribution and surface irradiation flux in the system at an operating emitter temperature of 1600 K.

When the emitter is at 1600 K, the PV cells reach a temperature of approximately 1200 K, which they can withstand without any problems. Note that the insulation reaches a temperature of approximately 800 K on the outside, suggesting that the system transfers a significant amount of heat to the surrounding air.

The irradiative flux varies significantly along the circumference of the PV cell and insulation jacket. To further investigate this effect, Figure 8 plots the irradiative flux at this operating condition in one sector of symmetry. Clearly the variation it shows is related to the positions of the mirrors and is an effect of shadowing.

Figure 8: Irradiation flux along the TPV cells, insulation inner surface, mirrors and emitter.

This plot can help optimize the mirror geometry as well as help decide how large the PV cells should be and where they should be placed.

A general conclusion is that this type of modeling can shortcut the prototype development time and optimize the operating conditions for the finalized TPV device.

References

1. S. Christ and M. Seal, “Viking 27 — A Thermophotovoltaic Hybrid Vehicle Designed and Built at Western Washington University”, SAE Technical Paper 972650, 1997.

2. Courtesy of E. Fontes, Catella Generics AB, Sweden.

3. Courtesy of Dr. D. Wilhelm, Paul Sherrer Institute, Switzerland.

Heat_Transfer_Module/Thermal_Radiation/tpv_cell

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
T_heater	1000[K]	1000 K	Temperature, emitter inner boundary

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 40.

In the text field, type 360/16.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	5
Layer 2	24
Layer 3	1

Click

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2.

In the text field, type 5.

Locate the section. In the text field, type 20.

Click

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 6.

Locate the section. In the text field, type 20.

Click

Union 1 (uni1)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Clear the check box.

Click

Fillet 1 (fil1)

In the toolbar, click

On the object , select Points 3, 6, and 8 only.

It might be easier to select the correct points by using the window. To open this window, in the toolbar click and choose . (If you are running the cross-platform desktop, you find in the main menu.)

In the window for , locate the section.

In the text field, type 0.5.

Click

Circle 2 (c2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 37.

In the text field, type 360/48.

Locate the section. In the text field, type 360/24.

Locate the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	2

Click

Delete Entities 1 (del1)

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

On the object , select Domain 1 only.

In the toolbar, click

Click the

button in the toolbar.

The model geometry is now complete. It represents one sixteenth of the full geometry by taking advantage of the sector symmetry and reflection plane within each sector.

Materials

Insulation

In the toolbar, click

In the window for , type Insulation in the text field.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.05	W/(m·K)	Basic
Density	rho	700	kg/m³	Basic
Heat capacity at constant pressure	Cp	100	J/(kg·K)	Basic

PV Cell

In the toolbar, click

In the window for , type PV Cell in the text field.

Select Domain 5 only.

This is the PV-cell domain.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	93	W/(m·K)	Basic
Density	rho	2000	kg/m³	Basic
Heat capacity at constant pressure	Cp	840	J/(kg·K)	Basic

Mirror

In the toolbar, click

In the window for , type Mirror in the text field.

Select Domain 4 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	10	W/(m·K)	Basic
Density	rho	5000	kg/m³	Basic
Heat capacity at constant pressure	Cp	840	J/(kg·K)	Basic

Emitter

In the toolbar, click

In the window for , type Emitter in the text field.

Select Domain 2 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	10	W/(m·K)	Basic
Density	rho	2000	kg/m³	Basic
Heat capacity at constant pressure	Cp	900	J/(kg·K)	Basic