Cellular Ceramics / 5

534 Part 5 Applications

Fig. 11 Photograph and sketch of 80 ppi/20 ppi silicon carbide foam absorber samples manufactured for laboratory-scale (left, 70 mm diameter) and 200 kW (middle, ca. 125 mm, two absorbers inserted into cups) efficiency tests (photographs by P.M. Rietbrock, DLR).

foams were first tested as volumetric solar absorbers in a project investigating solar CO2 steam reforming of methane [10, 11, 20]. Since then a number of materials have been tested on a laboratory scale [19]. Especially silicon carbide foams show excellent absorption and permeability properties. The permeability properties of various absorber materials can be seen in Fig. 10. To achieve a large specific surface area for a good solid-to-fluid heat transfer, foams with small cell dimensions must be employed. As an example, an 80 ppi foam material is shown in Fig. 11. It was tested in combination with a 20 ppi substrate, as shown on the right. The 80 ppi material serves as the absorbing and heat-transferring medium, and the 20 ppi material improves mechanical stability [21].

5.7.4.3

SiC Fiber Mesh

The SiC fiber mesh material shown in Fig. 12 originally was developed for burners. The material was tested as a solar absorber in the German project SOLPOR [22]. Samples were manufactured by Schott Glas in Mainz, Germany. The material is commercially available under the trade name Ceramat FN. It consists of silicon carbide fibers of 25 mm diameter glued together to form a layer 3.5 mm thick. The fibers are oriented in directions perpendicular to the direction of the air flow, which

Fig. 12 Silicon carbide fiber mesh material Ceramat FN manufactured by Schott Glas, Mainz, Germany (photograph by P.M. Rietbrock, DLR).

536 Part 5 Applications

square cross section and an open cell width of 1330 mm. The wall thickness is 195 mm. In contrast to extruded cellular monoliths and typical catalyst supports, each channel has a plane of 270 mm thickness arranged perpendicular to the channel direction. Each plane has a small hole of 150 mm diameter which serves as an orifice in each individual channel. This additional plane changes the fluid flow from pure Darcy flow to a more turbulent flow, which is an important prerequisite for an application as a volumetric absorber.

5.7.4.5

Material Combinations

A front material having high specific surface area, excellent absorption, and high porosity to achieve volumetric absorption of the concentrated solar radiation (Schott Ceramat FN, see Section 5.7.4.3) has been combined with a material having beneficial thermal conductivity properties and a quadratic pressure loss characteristic (SiC catalyst support, see Section 5.7.4.1). This combination is called advanced Hitrec. For tests in concentrated solar radiation, the two materials have been glued into a ceramic tube without directly connecting them. Figure 14 shows the combined absorber element.

Fig. 14 Absorber element made out of an SiC fiber mesh and a SiC catalyst support (advanced Hitrec; photograph by P.M. Rietbrock, DLR).

5.7.5

Absorber Tests

Efficiency and performance tests can be carried out at test sites at various research centers, from laboratory-scale dimensions up to large-scale tests of 3 MW and more [23, 24]. Generally, an installation capable of generating concentrated solar radiation is needed. Two of a number of important installations of this kind in Europe are Cesa 1 and the SSPS tower at the Plataforma Solar de Almer%a (PSA) in Spain with total powers of 3000 and 200 kW, respectively, and the Solar Furnace at the German Aerospace Centre (DLR) in Germany with a total power of 25 kW [25].

5.7 Solar Radiation Conversion 537

In general, the efficiency g of a solar absorber is defined as the useful power of the heat and the reaction enthalpy of the fluid mass flow generated by the absorber Puse, divided by the power of the concentrated radiation penetrating through the aperture of the absorber (power on aperture, POA)

To assess an absorber it is useful to also measure the temperature distribution of the front surface of the absorber, so that any hot spots or other irregularities can be detected.

In the case of an open-air receiver there is no chemical reaction, and heat is the only useful power. The general principle of measurement is shown in Fig. 15 along with a photograph of the top of the SSPS tower, where a 200 kW receiver test bed is installed. A fan forces ambient air to flow through the sample followed by an air/ water heat exchanger. The following quantities are monitored during the test: direct normal incidence (DNI, W m–2) of the solar radiation, the material front (peak) temperature, the air temperature at the outlet of the absorber, the air temperature at the outlet of the heat exchanger, the total air mass flow, the water mass flow of the heat exchanger, and the water temperatures at the heat exchanger inlet and outlet. From these values the power of the air flow and the power of the water flow at the outlet of the heat exchanger can be calculated. In addition to these continually measured data, periodic measurements are made. First, the solar flux density penetrating through the aperture area (POA) is measured. This aperture area corresponds to the diameter of the absorber sample. Second, the temperature distribution on the absorber front is measured. These two measurements are carried out several times during the experiment. At these times efficiency is calculated by (power water + power air)/POA with the POA value at this time and averages of the other quantities. The POA values have to be taken as representative for the time of averaging. Optical flux measurements are usually performed with a camera/target method, and the temperature distribution is measured with an infrared camera. One camera/target method is described in more detail by Neumann and Groer [25].

Fig. 15 Test bed used for measurement of open volumetric absorber efficiency in concentrated solar radiation (photograph by P.M. Rietbrock, DLR).

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As examples from a wide variety of materials tested [21, 22], results of efficiency measurements on four cellular ceramic materials are briefly presented here. These tests were conducted under solar radiation fluxes of around 1 MW m–2. With a 20 ppi silicon carbide foam, efficiencies of 80 % were achieved at air outlet temperatures of 700 C (Fig. 16). As mentioned above, smaller cell dimensions lead to improved heat transfer in the extinction volume. Thus, an 80 ppi silicon carbide foam was used as a 2 mm outer layer on a body of a 20 ppi silicon carbide foam material. The heat transfer surface area AV available is 5400 m2 m–3 for the 80 ppi foam as opposed to 1100 m2 m–3 for the 20 ppi foam. Consequently, the efficiency could be increased to values of more than 90 %. Because of its lower strength properties, the 80 ppi layer only serves as a functional material providing absorption and solid-to-fluid heat transfer.

Two further examples are shown in Fig. 17. An extruded silicon carbide catalyst carrier (Hitrec) consisting of parallel channels of 2 mm width and advanced Hitrec (see Section 5.7.4.5) with a front surface made of a fiber mesh material consisting of silicon carbide fibers of 25 mm diameter. Again the very different cell dimensions lead to differing values of the specific surface area AV of 1000 m2 m–3 (Hitrec) and 8000 m2 m–3 (fiber mesh). Consequently, advanced Hitrec shows improved efficiency values of up to 95 % compared to 80–85 % for the Hitrec material. However, operating the fiber mesh material and the 80 ppi foam at high temperatures causes oxidation problems, which become more severe with decreasing cell dimensions. The SiC catalyst support material has been additionally proven on a 3 MW scale in the European project SOLAIR [5].

Fig. 16 Results of the efficiency measurements on a sandwich-foam material (80 ppi/20 ppi) compared to a simple foam material (20 ppi). Photographs by P.M. Rietbrock, DLR.

5.7 Solar Radiation Conversion 539

Fig. 17 Efficiency properties of a silicon carbide catalyst carrier material (Hitrec) compared to advanced Hitrec (photographs by P.M. Rietbrock, DLR).

5.7.6

Physical Restrictions of Volumetric Absorbers and Flow Phenomena in cellular ceramics

Much theoretical and experimental research has been conducted on the properties and physical restrictions of the open volumetric absorber principle [18, 24, 26, 27]. Several independent experiments in the field of solar applications concerning the flow through porous materials have indicated a relationship between absorber temperature and resistance to flow [10, 13]. Local high solar flux leads to a lower mass flow and high material temperatures. Local low solar flux leads to a high mass flow with a low material temperature (Fig. 18). This means that the local absorber temperature can exceed the upper operating temperature of the material and lead to its destruction although the average air outlet temperature is low. The main cause of this behavior is the temperature-dependent increase in the viscosity of the fluid.

Several theoretical approaches [27] and numerical simulations [13, 18, 19] lead to a fairly good agreement between calculations and experiments, and general tendencies could be shown. The most important influence on flow stability comes from the pressure loss characteristic of the porous media. A linear dependency of the pressure drop on the flow velocity (Darcy flow) can lead to instabilities; a purely quadratic dependency (Dupuit, Forchheimer) can not. The problem is that in solar applications usually there is a mixture of both linear and quadratic behavior. In the following it is shown with a simple model under which conditions instabilities can occur in flow through porous media.

In flow through a porous structure the mass flow density is determined by the pressure difference between the two sides of the structure. In extended structures with large void spaces on both sides of the structure, the pressure difference is nearly the same across the whole structure, because there is instant pressure equal-

540 Part 5 Applications

Fig. 18 Instabilities in the flow through porous materials used in solar applications.

ization on both sides. Instability occurs when a certain pressure drop can cause different mass flow densities. In the following a one-dimensional model described by Kribus [27] is extended to find general conditions for instabilities in volumetric absorbers.

The pressure drop across the sample can be described by Darcy’s law in the Forchheimer extension:

where p denotes the pressure, x the coordinate in the direction of the flow, K1 and K2 the viscosity and the inertial coefficient, ldyn the dynamic viscosity, F the density of the fluid and U0 the velocity of the fluid.

If air is used as fluid, the ideal gas law can be taken as valid over a wide temperature range:

with the specific gas constant R = 287 J kg–1 K–1 and the air temperature T. The dependence of the dynamic viscosity on air temperature at high temperatures can be approximated by Eq. (23) [27]. The same result can be obtained by numerically fitting literature data, as given in Ref. [28].

5.7 Solar Radiation Conversion 541

This equation can be integrated by assuming a deep absorber for which the length is much larger than the hydraulic diameter of the structure and the temperature distribution along its length can be well approximated by the outlet air temperature. In practice the temperature rise of the fluid from inlet to outlet takes place in the first few millimeters, whereas absorber thicknesses are on the order of several centimeters for reasons of stability. This integration gives

where L denotes the length of the absorber, and T0 and Tout are the inlet and outlet temperatures of the air, respectively. Now consider an absorber and its energy balance neglecting radial heat transfer

where I0 is the solar radiation flux incident on the surface of the absorber, CPF the specific heat capacity of the air, r the Stefan–Boltzmann constant, and b a correction factor which describes the thermal losses through radiation. If b is smaller than 1, then the surface temperature of the outside of the absorber is lower than the air outlet temperature (“volumetric operation”) and the radiation losses are smaller. This is the case when the solar radiation can enter the inside of the porous structure and the incoming air cools the front surface well. If b > 1 the conditions are similar to those in a pipe absorber. The surface temperature is higher than the air outlet temperature (“nonvolumetric operation”).

Rearranging the energy balance for the mass flow density and inserting it into the integrated pressure drop equation gives:

For a better understanding the left-hand side can be seen as the product of the pressure drop and the mean pressure Dp pmean. In the case of a structure having a linear pressure drop relation, that is, K2 = ¥, the above equation becomes much simpler. A plot of the quadratic pressure difference versus temperature shows what happens in the case of instability (Fig. 19). If one or more temperatures and the corresponding mass flows are possible for the same pressure drop, there is an instability. In the graph lines of constant pressure drop are drawn, which intersect the curves with high solar flux at three points. Thus, for the same pressure drop different temperatures are possible. Parts of the absorber can have a low mass flow through them, and others a high mass flow. The low mass flow can lead to local overheating and thus to the destruction of the absorber.

Figure 19 shows the quadratic pressure drop as a function of the temperature for different solar fluxes and a material with purely linear pressure drop characteristic (K2 = ¥). One can see that instability only exists above a certain solar flux.

542 Part 5 Applications

Fig. 19 Quadratic pressure drop versus air temperature for different solar fluxes.

Looking at instability mathematically an ambiguity can only occur if the curve of the pressure drop shows a zero point in the derivative of the outlet temperature which lies in the physically relevant range between the maximum of the inlet temperature T0 and the maximum temperature Tmax, which is reached at zero mass flow:

This zero point of the derivative of the pressure difference depends only on Tout, T0, b, r, and I0. Setting the derivative to zero gives the following equation:

This equation can only be satisfied if the solar flux is above a critical value; below this value, there is no solution. The value can be obtained by solving the equation for I0 and finding the minimum of the obtained expression. The minimum occurs at Tout = 2.95 T0. The critical flux above which instabilities can occur is:

For example for b = 1 and T0 = 300 K this means a critical flux of 778 kW m–2.

This calculation is only valid for a porous medium with a purely linear pressure drop characteristic, that is, K2 = ¥. From a physical point of view the introduction of a quadratic term in the pressure drop equation considers the forming force of the porous medium on the fluid flow, while in the purely linear equation of Hagen– Poiseuille only friction forces are taken into account. Looking at the curves of the quadratic pressure drop difference for the case of K2 „ ¥, the trend for the case of constant solar flux can be seen in Fig. 20. A change in the pressure-drop characteristic of the absorber has a significant influence on the curves. The lower the value of K2 the less probable instabilities become. The values of K1 and K2 for the curves shown in the graph are of realistic magnitude. For example, the SiC parallel-channel catalyst support with a cell density of about 80 cpsi has K1 = 10–7 m2 and K2 = 0.011 m.