# Category CONVERSION

## Review of Radiation Transfer Method

As stated at the beginning of the chapter, the radiation transfer method assumes isotropic radiation and uniform fluxes incident and leaving a surface. The isotropic assumption is necessary in order to remove the intensity, i, from the double integral that determines the radiation flux leaving a surface [equation (6.4)]. This results in the double integral becoming merely a geometrical factor, the view-factor. Without the isotropic assumption, the method would be very cumbersome since not only would the double integral depend upon the intensity, but the radiation transfer equation [equation (1.139)], which determines the intensity, would depend upon direction, 0, as well as distance, s...

## Dependence of TPV Performance upon Input Power

Consider the system shown in Figure 8.1 with the gap between the reflector and the PV arrays removed so that wE = wC3 = 10cm, wC1 = 6cm, wC2 = 9cm, and h = 0.2cm. Also, assume the same properties as used in Figure 8.2. Using the Mathematica program in Appendix F the efficiencies, temperature, and electrical power output have been calculated as a function of the thermal input power, QE + Qb. These results are shown in Figure 8.6.

 100 150 200 250 Thermal input power, Q +Q Watts

Figure 8.6a) – Effect of thermal input power on cavity efficiency, q, approximate cavity efficiency, q (eq. 8.55), PV efficiency, qpv,

and TPV efficiency, ■q of a planar, square geometry TPV

system with the same conditions as in Figure 8...

## TPV System with Selective Emitter and Back Surface Reflector (BSR)

Combining a selective emitter with a back surface reflector (BSR) on the PV arrays is a method of spectral control that makes possible large cavity efficiency. A rare earth selective emitter provides large emittance for the range of wavelengths that are

hc

convertible by the PV arrays. Also, in the range Xg < X < 5 pm, where Xg = —- is the wavelength corresponding to the PV bandgap energy, the emittance is small. For X > 5 pm the emittance becomes large again. However, a BSR has large reflectance for X > 5pm. As a result, the majority of these photons are not lost but are reflected back to the emitter where they are absorbed.

Consider the planar geometry system of Figure 8.1 that uses an erbium aluminum garnet, Er3Al5O12, emitter with the optical properties given in Figure 3.6...

## Importance of Filter Absorptance

As already mentioned, the large value of the radiation flux incident on the filter-PV array means that a significant absorptance loss will occur even for small values of the filter spectral absorptance. Consider the interference-plasma filter presented in Chapter 4 (Figure 4.22). That filter has very low absorptance (« 0.01) at all wavelengths except in the band-pass region around X = 1500nm where it reaches a maximum of 0.15. Using the optical properties of this filter and the emitter and PV array properties used for Figure 8.2, the system performance has been calculated using the Mathematica program. These results are shown in Figure 8.3.

As a result of the filter absorptance, 70W of power is lost from the system. The large reflectance (> 0...

The leakage of radiation from the optical cavity through the 0.05cm gap between the PV arrays and the reflector can be prevented by connecting the reflector to the PV arrays. Obviously, this will result in thermal conduction from the hot reflector to the cold PV arrays. However, this conduction loss can be minimized by using a very thin material to connect the reflector and the PV arrays. Consider an optical cavity with no gaps between the reflector and the emitter, and the emitter and the reflector and the PV arrays. Thus, the emitter width, wE = wC3 = 10cm in Figure 8.1. Using the same properties as used for Figure 8.2, the program in Appendix F was used to calculate the performance...

The basic radiation transfer equation is given by equation (6.5),

Qab = TabqoaFabAa W/nm (8.2)

where Qab is the radiation power incident on area Ab that originates at area Aa. Also, xab is the transmittance of the media between Aa and Ab, qoa is radiation power per unit area per wavelength leaving Aa and Fab is the view-factor from area Aa to area Ab. Equation (8.2) assumes qoa is uniform across Aa. In addition, assume the radiation fluxes arriving at an area, qi, are also uniform across the area. In that case, Qia = qiaAa, where qia is the total incident flux on area Aa. Also, the view-factor relation given by equation (6.7)

applies. Thus, applying equation (8.2) and equation (6.7) to the radiation leaving all areas that view area Ab the following is obtained.

qib = ^bqoaFba (8.3)

a

Also...

## TPV System Performance

Preceding chapters have concentrated on two objectives. The earliest chapters explained and quantified the performance of the major components of a TPV system. Later chapters developed the analysis to calculate the performance of a TPV system. Therefore, the major objective of this chapter is to describe the radiation transfer method for determining the performance of a TPV system.

The performance is a function of the thermal power input, the geometry of the optical cavity, and the optical properties of the various components. In Chapter 6 radiation transfer theory was applied to obtain the radiation fluxes leaving the surfaces of the optical cavity. These results are used to calculate TPV system performance. The two major assumptions of the radiation transfer analysis are the following...

## Derive equation (7.21) for a planar filter TPV system from equation (7.13) using the following approximations

1) for 0 < X < X& pC « 0 and pfFE, CFCE, ^ 1

2) for Xg < X < да, г2 « pf pj

7.2 Derive equation (7.34) for a cylindrical filter TPV system with a blackbody emitter from equation (7.33) using the following approximations.

1) for 0 < X < Хг, pC « 0 and pf [F22 + FE, CFCE, ] ^ 1

2) for Хъ < X < то, і;2 « pfpj

Show that equation (7.33) reduces to the planar filter TPV system result [equation (7.21)] if pfF22 ^ 1.

7.3 Derive equation (7.45) using the radiation transfer theory results of section 6.2 [equations (6.5), (6.7), (6.30), (6.31)].

7.4 Derive equation (7.78) for the radiation flux leaving the PV cells, qoC, when only the emitter emissive power terms are retained in the source terms SE and SC in equation (7.75).

7.5 Use equation (7.77) in (6...