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The design of metal halide-based high flux solar simulators: Optical model development and empirical validation
Solar Energy 157 (2017) 818–826
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Solar Energy journal homepage: www.elsevier.com/locate/solener
The design of metal halide-based high flux solar simulators: Optical model development and empirical validation Jeffrey P. Roba, Nathan P. Siegel
MARK
⁎
Bucknell University, 1 Dent Dr., Lewisburg, PA 17837, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Solar Simulator Optics Ray tracing Flux
In this paper we present an experimentally validated process for the design of high flux solar simulators based on metal halide arc lamps, which are suitable for research applications including high temperature materials evaluation, concentrating solar power generation, and solar thermochemistry. The objective of our work is to facilitate the design of solar simulator hardware from commercially available components, with an emphasis on accurately predicting hardware performance in the design stage. The inputs to the design process include reflector geometry and surface properties, rated lamp power, and lamp dimensions. These inputs are incorporated in a ray tracing analysis along with a semi-empirical model of a metal halide arc source that accounts for arc shape and the spatial variation of emitted power within the arc volume. This lamp-specific optical model is then further generalized to be applicable to a range of commercially available metal halide lamps. The experimental validation of the design process is accomplished using a single simulator module, and a combination of optical flux mapping and calorimetry to compare the distribution of radiant power delivered by the module to design predictions. Our validation process includes data from four different metal halide lamps, spanning a power range from 1.5 kWe to 4.0 kWe. Design predictions for the generalized optical model agree with experimental data to within ± 20% for peak flux and ± 9% for total power delivered to a 6 cm diameter target.
1. Introduction High flux solar simulators are commonly used to provide high radiant flux (> 2000 kWth/m2), similar to focused sunlight in power distribution and spectrum, in a controlled, laboratory setting. Typical applications for high flux solar simulators include the experimental evaluation of materials and hardware related to solar power or solar thermochemical devices. Sarwar et al. (2014) present a detailed review of solar simulators designed and built for a variety of research applications over the last twenty years. Many modern solar simulators include multiple modules, each of which consists of a lamp and a reflector. The lamp, typically a xenon arc lamp, is positioned at the first focus of a truncated ellipsoidal mirror such that light from the lamp is reflected to the second focus which corresponds to the target plane at which the test article is placed (Fig. 1a). In a multi-lamp simulator the individual lamp/reflector modules are aimed at a common target point such that the radiant output from the each module in the array is summed, increasing the flux and total power delivered to the target (Fig. 1b). One of the first large, multi-lamp solar simulators to be constructed was designed and built by researchers at the Paul Scherrer Institut (PSI)
⁎
Corresponding author. E-mail addresses: [email protected] (J.P. Roba), [email protected] (N.P. Siegel).
http://dx.doi.org/10.1016/j.solener.2017.08.072 Received 2 June 2017; Received in revised form 18 August 2017; Accepted 27 August 2017 0038-092X/ © 2017 Elsevier Ltd. All rights reserved.
(Petrasch et al., 2007). The bulk of the analysis supporting the design of this system was dedicated to the determination of the optimal reflector shape for a specific focal length. The analysis itself was based on Monte Carlo ray-tracing software that was used to support parametric studies in which the geometric parameters of the reflector were varied and the resulting radiant transfer to the target plane evaluated. The stated design objective was to maximize the amount of radiant energy transferred to the target plane. The figure of merit for radiant energy transfer in this and subsequent analyses is the transfer efficiency, which is defined as the fraction of electrical power supplied to the lamp that is incident as radiant power on the target surface, in this case a 6 cm diameter circle positioned at the second focus of the ellipsoidal reflector. The PSI researchers determined that the transfer efficiency of the optimal mirror was 34%, and predicted that the mean flux incident on a 6 cm diameter target would be 5900 kW/m2 for a ten-lamp array. The prototype system performance exceeded these predictions, delivering a mean flux of 6800 kW/m2. The authors stated that one of the factors contributing to the disparity between predicted and measured results was the complexity involved with simulating the arc itself, which in this case was modeled as a diffusely emitting spherical surface source.
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Fig. 1. (a) An illustration of the single lamp/reflector module used in the experimental portion of this work, and (b) a three lamp simulator array with a single aim point located at the second focus of the ellipsoidal mirrors. The height of the single module is roughly 80 cm.
reflective secondary concentrator to provide a radiant heat input to a volumetric thermal energy storage system (Codd et al., 2010). The simulator used four metal halide stadium lights, with stock reflectors, aimed at a common target and further focused using a reflective sheet metal cone (i.e. a non-imaging secondary concentrator). The power delivered by this system was 51 Wth with a peak flux of 60 kWth/m2. The relatively lower peak flux value, as compared to the preceding Xebased systems, was in part due to the larger arc size of the metal halide lamps. In the preceding simulator development efforts the design emphasis was placed on the reflective components (mirrors and secondary concentrators) and on the spatial arrangement of modules, rather than on the arc source itself. While the use of a simplified arc source may not significantly affect the calculation of the optimal shape of an ellipsoidal reflector, it does reduce the accuracy of simulator performance predictions, which is important when designing a simulator for an application requiring a specific level of performance. In this paper, we present an optical model that improves the accuracy of simulator performance calculations by better accounting for the spatial variation of radiant emission within the arc of a metal halide lamp. Our arc model is based on direct measurements of the intensity variation within the arc volume, and does not require the use of fitting parameters to achieve good agreement with experimental data. We further generalize our results to enable the specification of an accurate metal halide arc source model using only the manufacturer-provided lamp geometry and lamp power rating as inputs.
The design objectives for the seven-lamp simulator developed by the University of Minnesota were to replicate the performance specifications of concentrating solar power collectors including the angular distribution of light incident on the target plane, the distribution of radiant flux, and the spectrum (Krueger et al., 2011). The design approach included a ray-tracing optical model in which reflector eccentricity was varied parametrically, and both transfer efficiency and flux uniformity used to determine the optimal reflector shape. The arc source was modeled as a uniform, cylindrical volumetric emitter. The predicted peak flux for the optimal configuration was reported as 3700 kWth/m2, with a total power delivered to a 6 cm diameter target of 7.5 kWth. The experimental characterization of this simulator was presented in a later work (Krueger et al., 2013). The results of that study show that the actual power delivered to a 6 cm diameter target is 9.2 kWth with a peak flux of 7300 kWth/m2. The difference between predicted and experimentally measured power delivery is 20%; the difference in the peak flux values is 65%. The solar simulator built by Georgia Tech is a seven lamp array that delivers approximately 6.2 kWth to a 4 cm diameter target at a peak flux of 6800 kWth/m2. Like the systems at PSI and UMN, this simulator includes custom built reflectors designed to maximize transfer efficiency. Design simulations incorporated optical ray tracing and a diffusely emitting, cylindrical model of the Xe arc source (Gill et al., 2015). These simulations, along with empirical data, were used to evaluate the specular error of the reflectors and the electrical to radiant energy conversion ratio by adjusting these parameters to achieve agreement between experimental and predicted performance. Two 45 kWe, 18 lamp simulators were recently built through a collaborative effort between the Australian National University (ANU) and Ecole Polytechnique Fédérale de Lausanne (EPFL). The design effort supporting these systems is well documented. Bader et al. present a general optical design process for multi-lamp simulators in which they describe the process by which both the reflector geometry and overall simulator configuration may be optimized to maximize radiative transfer to a target (Bader et al., 2015). Their initial optical model included an idealized cylindrical arc with ray emission determined with a probability distribution function. A subsequent publication by members of this team (Levêque et al., 2016) includes a more detailed description of the optical model and experimental data for the completed simulator. In this work the lamp source is described by an exponential probability distribution function in which emitted intensity can vary within the arc volume. The final form of this equation is determined by fitting model results to experimental data. The resulting agreement between model results and experiment, using fitting parameters for spatial intensity variation, mirror roughness, and lamp efficiency is within a few percent across the entire flux map. MIT produced a solar simulator based on metal halide lamps and a
2. Optical model development Our solar simulator design process begins with the development of an optical model using the commercially available Monte Carlo (MC) ray tracing software TracePro (2017). The optical model requires three elements to be defined: the reflector (geometry and properties), the target (geometry and properties), and the arc source (geometry and emission profile). The definition of each of these elements is implemented in a way that closely matches the properties of the commercially available components on which our simulator modules are based, making use of manufacturer-provided data or, in the case of the arc source, experimental data from our own characterization studies. 2.1. Optical considerations High flux solar simulators typically use truncated ellipsoidal reflectors to focus the light emitted by an arc at the first focus to a target plane at the second focus, as illustrated in Fig. 2. The fraction of the power input to the lamp (i.e. electrical power) that reaches the target plane as radiant power is called the transfer efficiency, and is often the 819
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Fig. 2. The optical configuration of a high flux solar simulator with an ellipsoidal focusing mirror.
2012). This is the approach that we have used in this work.
objective function used in simulator mirror design optimizations (Petrasch et al., 2007; Gill et al., 2015). The maximum value of the transfer efficiency can be no more than the view factor between the arc and the reflector surface, or the fraction of light from the lamp that strikes somewhere on the reflector surface. For the truncated reflector geometry used in this work the maximum transfer efficiency is calculated to be 0.7, using radiative view factors from Howell (2017). This value is further reduced by the ability of the reflector to focus light from a source of finite size to a target plane that is typically a disc of 6–10 cm in diameter located at the second focus of the ellipsoid, which is, in part, determined by the spectral reflectance and scattering behavior of the reflector. The peak flux delivered to the target, another commonly reported performance metric, is also influenced by the properties of the reflector and lamp. To illustrate this point, consider a reflector surface divided into infinitesimally small discrete elements, δAs . The size of the image projected on the target plane at the second focus of the ellipsoid from any one of these surface elements may be approximated as shown in Eq. (1).
dimage ≈ ϕref rST
2.2. Reflector model The reflector used in this work was purchased from Optiforms, Inc. (2017) and is an electroformed ellipsoid with an 813 mm inter-focal distance and consisting of a structural nickel substrate coated with a silver reflecting layer and topped with an aluminum oxide overcoat. The combined thickness of the silver and alumina layers is approximately 30–50 nm. The spectral reflectance of an electroplated mirror coupon provided by Optiforms was measured using a 410-Solar spectrophotometer from Surface Optics and Inc. (2017). The total spectral reflectance of the mirror is shown in Fig. 3 along with the emission profile of a metal halide arc lamp provided by Osram (Osram Sylvania, 2016). We assumed that the reflector could be accurately modeled with a single, spectrum-weighted reflectance applied across the entire lamp emission spectrum. The spectrum-weighted total reflectance was calculated from the data in Fig. 3 using Eq. (3). The geometry and properties on which our reflector model is based are summarized in Table 1.
(1)
ρspectrum − weighted =
where the divergence angle, ϕref , is estimated from the angular divergence of the incident radiation modified by a surface error, expressed in Eq. (2) as a “slope error”, which is the standard deviation of the difference between the actual local mirror surface normal vector, and the theoretical value defined by the geometry of the mirror.
ϕref = ϕinc + σSlope =
darc + σSlope rFS
∞ ∫0 ρmeasured (λ ) Pλ (λ ) dλ ∞ ∫0 Pλ (λ ) dλ
(3)
This calculation was done separately for the total reflectance, and for the specular component alone. The difference between these two values was used to estimate the amount of diffuse radiation as 0.4% of the total reflectance. The individual values for the specular and diffuse reflectance components were used to calculate a bi-directional reflectance function (BRDF) using the methods described in Harvey et al. (2012).
(2)
In Eq. (2), darc is the projection of the arc onto a plane normal to the direction of rFS, the distance from the focus to the mirror surface. Both the transfer efficiency and peak flux increase as dimage decreases. We can see from equations 1 and 2 that the minimum image size (and therefore peak flux) occurs for a perfectly smooth mirror (σslope = 0 ) when both the arc size, darc, and distance to the target plane, rst, are minimized.1 Expressing the effect of the mirror surface on the reflected beam using a slope error is a common convention within the solar energy community; however, it may also be represented with a description of the manner in which light is scattered from mirror, such as a bi-directional reflectance distribution function (BRDF) (Harvey et al.,
2.3. Lamp specific arc source model Arc lamps emit volumetrically, and it is important to consider the spatial variation of emission in order to create an accurate optical model of an arc lamp. Jacobsen (2004) and Jacobsen et al. (2010) developed a semi-empirical model for Xe flash lamps in which the arc is represented by several nested surface sources that vary with respect to emission intensity and spectrum. Their model was based on direct measurement of the spatial variation of intensity, and emission spectrum, within the arc. We have adapted this approach to simulate metal halide lamps. In our semi-empirical lamp model, shown schematically in Fig. 4 alongside a single surface source, each shell is a surface emitter, modeled as an ellipsoid, and is transparent to emission from the other shells. The radiant power emitted by each shell sums to the total power
1 The arc diameter for a 4 kW metal halide lamp is about 20 mm. A 4 kW Xe lamp may have an arc diameter as small as 7 mm. This allows Xe-based simulators to achieve greater peak flux at a given power level.
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Fig. 3. The spectral reflectance of the electroplated reflector used in this work displayed alongside an emission profile typical of metal halide arc lamps. The uncertainty in these data is ± 0.001 reflectance units.
Vn , and the luminous flux (e.g. luminosity) of the lamp, Φv , provided as a range by the manufacturer.
Table 1 Ellipsoidal reflector geometry and optical properties. The geometric parameters Ref. Fig. 2.
Prad [W] =
Optiforms E813-001 dv [cm] dt [cm] H [cm] dIF [cm] tNi/Al2O3 [nm] ρMH, S ρMH, D BDRF (A, B, g)
8.6 39.40 21.98 81.30 30–50 0.896 0.004 (0.00129, 0.015, 0)
Φv [lm] lm
∞
683[ W ] ∗ ∫0 Pn (λ ) Vn (λ ) dλ
(4)
where Pn is the normalized spectral emissive power having units of nm−1 and computed as
Pn (λ ) =
Pλ (λ ) ∞ ∫0 Pλ (λ ) dλ
(5)
where Pλ (λ ) is the spectral emissive power in W/nm provided by the Fig. 4. (a) Schematic of a nested ellipsoid source with rays of light emitted from each surface and (b) a schematic of a singular spherical source with rays of light emitted from its surface.
manufacturer in tabular form as a function of wavelength for a given lamp. The lamp efficiency is then calculated as
emitted by the lamp, and more closely approximates a volumetric emitter as the number of discrete shells increases. In order to fully define this arc model we must specify the geometry of each shell and the power emitted from it. The reported radiant output from commercially available arc lamps (Xe and MH) is typically expressed in lumens, which is a measure of irradiance weighted based on the ability of the human eye to perceive light. The radiative power emitted by the lamp, Prad [W], is calculated using Eqs. (4)–(6) to convert emission from photometric units [lm] to radiometric units [W], by considering the spectral response of the human eye expressed by the normalized luminous efficiency function,
ηlamp =
Prad Pe
(6)
where Pe is the electric power supplied to the lamp and is provided by the manufacturer. Using the preceding calculations we determine the radiant power, Prad , in Watts, from a given arc lamp using only data obtained from lamp manufacturers. We used four lamps in the development of our arc source model. These are listed in Table 2 along with their relevant optical properties. These lamps were chosen to span a range of output power, and to provide variation in arc gap, both of 821
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Table 2 Optical properties of the metal halide lamps used in this study.
Pe [W] ILU [lm] Darc [mm] Prad [W] ηlamp
Prad [W] =
Lamp 1 Osram 1500 W/ D7/60
Lamp 2 Osram 2500 HMI SE/XL
Lamp 3 Philips MSR Gold 2500/2
Lamp 4 Philips 4000 HR
1500 149250 7.5 1240 0.83
2500 223750 14 2070 0.83
2500 193000 9.5 2000* 0.8*
4000 380000 20 3290 0.82
∫1 +
n
In dVn ≅
∑ ⎛I1 (V1−0) + ⎝
I1 + I2 I + I3 (V2−V1) + 2 (V3−V2)… 2 2
In − 1 + In (Vn−Vn − 1)⎞ 2 ⎠
(7)
where Vn is the volume, in m , of the ellipsoid fit to each arc image in and In is the local intensity of the arc, in W/m3. We assume that the intensity of the arc in any image is related to intensity of the arc in the first by Eq. (8) 3
In = I1 ∗0.5n − 1
(8)
where the constant, 0.5, corresponds to the change in optical density due to the removal of a single ND-2 filter. The intensity of the first image, I1, can be calculated by combining Eqs. (7) and (8) with the known radiative power of the lamp:
* Estimated from data provided for similar lamps.
which significantly affect simulator performance. The parameter ILU is the average luminosity value supplied by the manufacturer. Prad is the radiative power output calculated at this luminosity value using Eqs. (4) and (5). This was done for all of the lamps except for Lamp 3. In this case we could not obtain data for spectral emissive power. As such, we assumed that Lamp 3 performed similarly to the others with regard to lamp efficiency, ηlamp , and estimated its radiative power to be 80% of the rated electrical power. The completion of the arc source model requires the definition of shell dimensions, and the emissive power applied to each shell. To measure shell dimensions, we developed an empirical technique in which a 12-bit CCD camera (AVT Manta) was used to obtain images of an arc through a stack of neutral density filters. Initially, we attached several ND filters to the camera lens to achieve high optical density. We then adjusted the electronic shutter of the camera to further regulate the amount of light reaching the detector. In this way we were able to adjust the equivalent optical density such that a continuous region of saturated pixels was visible between the lamp electrodes. The image acquired here represents the region of the arc volume having the highest radiant intensity. From there we sequentially removed a single ND 2 filter (50% reduction in optical density) to allow relatively more light to enter the camera, taking an image at each step. This process was continued until the arc size no longer increased due to being constrained by the quartz lamp envelope. We then processed the images to identify the shape of the region of saturated pixels in each image, which we fit to an ellipse. From this sequence of ellipses we measured the major and minor axes for each arc shell. A sequence of images from Lamp 3 is shown in Fig. 5. The imaging process was repeated for all four lamps. The power emitted from the surface of each shell in the arc model represents emission from a differential arc volume defined by any two adjacent images as shown in Fig. 5. The sum of the emission from the collection of shells equals the total emission from the arc as shown in Eq. (7)
I1 =
PR
(
∑ V1 +
1 + 0.5 (V2−V1) 2
+
0.5 + 0.25 0.5n − 2 + 0.5n − 1 (V3−V2)…+ (Vn−Vn − 1) 2 2
) (9)
The emission intensity for each shell can now be found with Eq. (8), and the power assigned to the surface of each shell calculated with Equation (10).
Pn = (Vn−Vn − 1)
In + In − 1 2
(10)
The shell geometry and power assignments for Lamp 3 are shown in Table 3. 2.4. Optical model results The preceding definitions for the reflector and arc source were used to build a complete solar simulator model in TracePro. This model also included a 6 cm diameter target located at the second focus of the ellipsoidal mirror, 813 mm distant from the center of the lamp. The target was modeled as a perfect absorber and the front surface used to generate flux maps from the optical simulations. A series of simulations were carried to generate theoretical flux maps for the lamps listed in Table 2. In all cases the total number of rays emitted from each shell was set to 75,000, the value needed to achieve a solution output independent of the number of rays included in the simulation. The crosssectional flux map for each of the four lamps is shown in Fig. 6, along with the flux map for a 2500 W lamp modeled with single spherical surface source of 9.5 mm in diameter (the arc gap of Lamp 3). All of the calculated flux maps were symmetric about the center of the flux map. One commonly used approach to modeling arc sources is to treat them as either spherical or cylindrical surface emitters of a size equal to the arc gap. This does not suitably represent the true nature of the emission from the arc, and leads to an inaccurate flux map prediction, which can be seen by comparing the flux map for Lamp 3 to that of the
Fig. 5. (a) The raw image data from the camera and (b) the processed data showing the outline of individual arc shells. The sequence moves from left to right with the image on the far left being the most intense region of the arc. The vertical line in the first image of (b) is 10 mm in length.
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of the light from the simulator module reflected from a Lambertian target placed at the focal plane. The intensity distribution present in this image can be related to the intensity distribution of the light incident on the target from the simulator module. The images obtained in this step have arbitrary units and must be scaled with a calibration factor to display flux maps having units of kW/m2. The scaling process requires the measurement of the power intercepted by a water-cooled calorimeter placed at the target plane, which is related, by the calibration factor, to the integral of the arbitrary flux values across the aperture of the calorimeter. This is a commonly used method of measuring the flux distribution in concentrating solar power applications, and its application to solar simulators is discussed in detail by Gill et al. (2015) and by Levêque et al. (2016) who use a flux gauge in place of a calorimeter. The experimentally measured flux maps include the following sources of uncertainty:
Table 3 Measured shell geometry and assigned properties for Lamp 3. Shell number
Minor radius [mm]
Major radius [mm]
Power [W]
Intensity [W/ mm3]
1 2 3 4 5 6 7 8 9
1.17 1.64 2.39 3.7 4.55 5.76 7.26 9 10.83
4.73 5.39 6.37 6.89 6.94 7.86 8.47 8.97 9.99
250.04 231.31 316.08 419.18 176.81 212.57 167.66 126.05 100.31
9.194 6.896 3.448 1.724 0.862 0.431 0.215 0.108 0.054
2000
Lamp 1-1500 W Lamp 2 - 2500 W 2500 W Spherical Arc
1200
Lamp 3 - 2500 W Lamp 4 - 4000 W
• Pixel gray value: ± • Pixel position: ± 7.5 × 10 cm • Coolant flow rate: ± 5 mL • Time (flow measurement): ± 1 s • Calorimeter coolant temperature: ± 0.2°C. 1 4096
Flux [kW/m2]
1000 800 600
Taken together and further accounting for thermal losses from the calorimeter, the total uncertainty for the measurement of flux distribution and total incident power was calculated, and is summarized, along with model predictions for simulator performance, in Table 5. The agreement between experimentally measured and predicted values for peak flux is within ± 12% for all lamps, and the agreement for power delivered to a 6 cm diameter target is within ± 9%. A comparison of the shape of the experimentally measured and simulated flux maps is shown in Fig. 7a for Lamp 3, and in Fig. 7b for Lamp 2. Qualitatively, the agreement between the experiment and prediction is good across most of the map, with a significant difference in the region near the peak for some of the lamps. The reason for this discrepancy is unknown, but could be a consequence of approximations made in the development of the arc model. One of these approximations is the idealized representation of the arc shells in the optical model; each shell was fit to an ellipsoid, for simplicity, even though the shells were not always ellipsoidal in shape. This approximation carries relatively more weight for the smallest shells, which most strongly affect the magnitude of the predicted peak flux value.
400 200 0
-3
-2
-1
0
1
2
3
Distance From Flux Map Center [cm] Fig. 6. The calculated flux distribution for all four lamps as well as for a 2500 W lamp modeled as a single surface, diffuse spherical emitter.
Table 4 Predicted performance of a single simulator module using a metal halide lamp. Lamp number
Peak flux [kW/m2]
Power to target [W]
Average flux [kW/m2]
Transfer efficiency [%]
1 2 3 4
888 414 835 393
608 616 849 711
215 218 300 252
39.8 25.4 34 18.1
−3
4. A generalized arc model The final step toward our objective of enabling simulator design from off the shelf components is to create an arc model that is not specific to any one lamp, but can accurately represent a range of metal halide lamps suitable for use in a high flux solar simulator. We begin by normalizing the experimentally measured arc size data, dividing the measured major and minor radius value for each arc “shell” by the
lamp modeled with a spherical surface source. The maps differ significantly, with a much higher peak flux realized when treating the source as a volumetric emitter. The results in Fig. 6 also show the effect of arc size on beam size and peak flux; the lamp having the lowest radiant power output produces the highest peak flux due to its relatively short arc gap. Larger arcs tend to produce more beam spread and lower overall flux at the target. A comparison of the flux maps for lamps 2 and 3 shows that an increase in arc gap from 9.5 mm (Lamp 3) to 14 mm (Lamp 2) results in a decrease in the peak flux of over 50%. The numerical output from the optical models for all of the lamps is summarized in Table 4.
Table 5 A comparison of experimentally measured simulator performance to predicted values. Power is integrated over a 6 cm diameter target. Lamp number
3. Experimental validation Our lamp-specific optical models were validated by comparing predicted flux maps (Fig. 6) to experimentally measured flux maps for a single-lamp simulator module. This simulator module is shown schematically in Fig. 1a, and described in detail in the supplement to the paper. The experimental procedure included two steps. In the first, a flux map for each lamp was acquired using a camera to obtain an image
1 2 3 4
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Experimental
Predicted
Percent difference [%]
Peak flux [kW/m2]
Power [W]
Peak flux [kW/ m2]
Power [W]
Peak flux
Power
795 370 860 400
618 565 914 760
888 414 835 393
608 616 849 711
11.1 11.2 2.9 1.8
1.6 8.6 7.3 6.7
± ± ± ±
55 20 30 20
± ± ± ±
43 33 30 37
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Fig. 7. (a) cross-sectional flux maps for Lamp 3 and (b) for Lamp 2. The experimentally measured maps are represented by an upper and lower curve corresponding to the limits of uncertainty in the experimental data.
major or minor radius of the quartz envelope, raised to some power, n, for the corresponding lamp as shown in Eq. (11).
Rnorm =
Rmeas n Rquartz
and the arc shell number for both the major and minor axis dimensions. These relationships, given in Fig. 8, allows the specification of the nested-shell arc dimensions for any metal halide lamp for which the dimensions of the quartz envelope are known. A detailed accounting of this procedure is presented in the supplement to this paper, along with a code that facilitates source calculations from manufacturer-provided data.
(11)
The collection of calculated values for Rnorm is then plotted and fitted with a polynomial to determine functional relationships between Rnorm
Fig. 8. (a) Normalized major and (b) minor axis values for each arc model shell and for all lamps.
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Fig. 9. (a) Flux maps for Lamp 2 and (b) Lamp 3 generated with the Lamp-Specific arc model and the General arc model plotted with the upper and lower bounds of the experimentally measured flux map data.
within ± 12% of the experimentally measured values for peak flux and ± 9% total power delivered. The model is based on treating the arc source as an assembly of nested elliptical shells, each emitting a fraction of the total lamp power and arranged in a way that simulates the spatial variation in emission intensity within the arc. The arc model was developed by experimentally measuring the size of isoflux surfaces within the arc for several metal halide lamps spanning a range of power output from 1500 W to 4000 W. Our overall objective was to enable the design of solar simulators from off the shelf components. To that end we have presented a general arc model in which the nested-shell arc source may be defined for any commercially available metal halide lamp in the 1500–4000 W power range, with the only required inputs being the dimensions of the quartz envelop of the lamp, and the electric power rating. This approach, when applied to the lamps that we experimentally evaluated, resulted in model predictions for peak flux that were within ± 20% of experimentally measured values, and within ± 9% for total power delivered to the target.
Table 6 A comparison between the general model results and experimentally measured peak flux and power delivered to a 6 cm target. Lamp number
1 2 3 4
Predicted
Percent difference [%]
Peak flux [kW/m2]
Power [W]
Peak flux
Power
858 451 818 429
627 616 869 701
7.6 19.7 5.0 7.0
1.4 8.6 5.0 8.1
The results in Fig. 8 allow the specification of up to eleven shells in a given arc source model. The actual number used is limited by the constraint that the largest shell be smaller than the interior dimensions of the quartz envelope of the lamp in question. The number of shells may also be limited by specifying that each shell must emit greater than 3% of the total lamp output. Our results have shown that including shells with emitted power less than 3% does not substantively affect the outcome of the optical model. The power assigned to each shell can be determined from the rated electrical power of the lamp and calculated using Eqs. (6)–(10). In this calculation the ratio of radiant power to electrical power set to 0.8 in Eq. (6), a value that is within the experimentally determined range for the lamps that we evaluated, and the ratio of intensity between subsequent shells set to 0.5 in Eq. (8). The combination of the shell dimensions calculated from the fitting functions presented in Fig. 8 and power assignments yield a complete, nested-shell arc model that requires as input only the known values for lamp dimensions and electric power consumption. We applied this generalized modeling approach to develop arc models for the lamps in Table 2. The resulting flux maps for Lamps 2 and 3 are shown in Fig. 9, and a comparison between the predicted and experimental peak flux and power delivered to a 6 cm diameter target is given, for all lamps, in Table 6. The results in Table 6 show that the agreement between predicted peak flux and the experimentally measured value increased relative to the lamp-specific model, but was within ± 20% for all lamps evaluated. The predicted power delivered was closer to the experimental value, within ± 9% for all lamps.
Acknowledgements This work was supported by the United States Department of Energy, Fuel Cell Technology Office [grant number DE-FOA-0000826]. Supplementary Information We have provided a document set containing additional information related to the design and construction of the 2500 W simulator module shown in Fig 1a, as well as a code and sample calculation of a nested shell arc source developed with our general modeling approach and manufacturer-provided lamp data. These documents are included as supplements to this paper, and can also be downloaded from the links contained in the document linked here (http://dx.doi.org/10.1016/j. enconman.2017.08.091) References Bader, R., Haussener, S., Lipiński, W., 2015. Optical design of multisource high-flux solar simulators. J. Sol. Energy Eng. 137, 021012. Codd, D.S., Carlson, A., Rees, J., Slocum, A.H., 2010. A low cost high flux solar simulator. Sol. Energy 84 (12), 2202–2212. Gill, R., Bush, E., Haueter, P., Loutzenhiser, P., 2015. Characterization of a 6 kW high-flux solar simulator with an array of xenon arc lamps capable of concentrations of nearly 5000 suns. Rev. Sci. Instrum. 86 (12), 125107. Harvey, J.E., Schröder, S., Choi, N., Duparré, A., 2012. Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles. Opt. Eng. 51 (1) pp. 013402-1.
5. Conclusions We have developed a lamp specific arc source model that can be used, in combination with optical ray tracing software, to predict the performance of solar simulators based on metal halide lamps to 825
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characterization of a new 45 kWe multisource high-flux solar simulator. Opt. Express 24 (22). Optiforms, Inc., 2017. Available at: < http://www.optiforms.com/ > . Osram Sylvania Inc., 2016. Spectral data HMI 2500W_SE. Petrasch, J., Coray, P., Meier, A., Brack, M., et al., 2007. A novel 50 kW 11,000 suns highflux solar simulator based on an array of xenon arc lamps. J. Sol. Energy Eng. 129 (4), 405–411. Sarwar, J., Georgakis, G., LaChance, R., Ozalp, N., 2014. Description and characterization of an adjustable flux solar simulator for solar thermal, thermochemical and photovoltaic applications. Sol. Energy 100, 179–194. Surface Optics, Inc., 2017. 410-Solar visible/NIR portable reflectometer. Available at:
Howell, J.R., 2017. A catalog of radiation heat transfer configuration factors. Available at: < http://www.thermalradiation.net/indexCat.html > . Jacobsen, D.A., 2004. Modeling the spectral shape of short-arc pulsed xenon flashlamps. In: Optical Science and Technology, the SPIE 49th Annual Meeting (pp. 295–302), October. International Society for Optics and Photonics. Jacobsen, D.A., Freniere, E.R., Gauvin, M., 2010. Accurate source simulation in modern optical modeling and analysis software. In: OPTO (pp. 75971E–75971E), February. International Society for Optics and Photonics. Krueger, K.R., Davidson, J.H., Lipiński, W., 2011. Design of a new 45 kWe high-flux solar simulator for high-temperature solar thermal and thermochemical research. J. Sol. Energy Eng. 133 (1), 011013. Krueger, K.R., Lipiński, W., Davidson, J.H., 2013. Operational performance of the University of Minnesota 45 kWe high-flux solar simulator. J. Sol. Energy Eng. 135 (4), 044501. Levêque, G., Bader, R., Lipiński, W., Haussener, S., 2016. Experimental and numerical
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Contents lists available at ScienceDirect
Solar Energy journal homepage: www.elsevier.com/locate/solener
The design of metal halide-based high flux solar simulators: Optical model development and empirical validation Jeffrey P. Roba, Nathan P. Siegel
MARK
⁎
Bucknell University, 1 Dent Dr., Lewisburg, PA 17837, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Solar Simulator Optics Ray tracing Flux
In this paper we present an experimentally validated process for the design of high flux solar simulators based on metal halide arc lamps, which are suitable for research applications including high temperature materials evaluation, concentrating solar power generation, and solar thermochemistry. The objective of our work is to facilitate the design of solar simulator hardware from commercially available components, with an emphasis on accurately predicting hardware performance in the design stage. The inputs to the design process include reflector geometry and surface properties, rated lamp power, and lamp dimensions. These inputs are incorporated in a ray tracing analysis along with a semi-empirical model of a metal halide arc source that accounts for arc shape and the spatial variation of emitted power within the arc volume. This lamp-specific optical model is then further generalized to be applicable to a range of commercially available metal halide lamps. The experimental validation of the design process is accomplished using a single simulator module, and a combination of optical flux mapping and calorimetry to compare the distribution of radiant power delivered by the module to design predictions. Our validation process includes data from four different metal halide lamps, spanning a power range from 1.5 kWe to 4.0 kWe. Design predictions for the generalized optical model agree with experimental data to within ± 20% for peak flux and ± 9% for total power delivered to a 6 cm diameter target.
1. Introduction High flux solar simulators are commonly used to provide high radiant flux (> 2000 kWth/m2), similar to focused sunlight in power distribution and spectrum, in a controlled, laboratory setting. Typical applications for high flux solar simulators include the experimental evaluation of materials and hardware related to solar power or solar thermochemical devices. Sarwar et al. (2014) present a detailed review of solar simulators designed and built for a variety of research applications over the last twenty years. Many modern solar simulators include multiple modules, each of which consists of a lamp and a reflector. The lamp, typically a xenon arc lamp, is positioned at the first focus of a truncated ellipsoidal mirror such that light from the lamp is reflected to the second focus which corresponds to the target plane at which the test article is placed (Fig. 1a). In a multi-lamp simulator the individual lamp/reflector modules are aimed at a common target point such that the radiant output from the each module in the array is summed, increasing the flux and total power delivered to the target (Fig. 1b). One of the first large, multi-lamp solar simulators to be constructed was designed and built by researchers at the Paul Scherrer Institut (PSI)
⁎
Corresponding author. E-mail addresses: [email protected] (J.P. Roba), [email protected] (N.P. Siegel).
http://dx.doi.org/10.1016/j.solener.2017.08.072 Received 2 June 2017; Received in revised form 18 August 2017; Accepted 27 August 2017 0038-092X/ © 2017 Elsevier Ltd. All rights reserved.
(Petrasch et al., 2007). The bulk of the analysis supporting the design of this system was dedicated to the determination of the optimal reflector shape for a specific focal length. The analysis itself was based on Monte Carlo ray-tracing software that was used to support parametric studies in which the geometric parameters of the reflector were varied and the resulting radiant transfer to the target plane evaluated. The stated design objective was to maximize the amount of radiant energy transferred to the target plane. The figure of merit for radiant energy transfer in this and subsequent analyses is the transfer efficiency, which is defined as the fraction of electrical power supplied to the lamp that is incident as radiant power on the target surface, in this case a 6 cm diameter circle positioned at the second focus of the ellipsoidal reflector. The PSI researchers determined that the transfer efficiency of the optimal mirror was 34%, and predicted that the mean flux incident on a 6 cm diameter target would be 5900 kW/m2 for a ten-lamp array. The prototype system performance exceeded these predictions, delivering a mean flux of 6800 kW/m2. The authors stated that one of the factors contributing to the disparity between predicted and measured results was the complexity involved with simulating the arc itself, which in this case was modeled as a diffusely emitting spherical surface source.
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Fig. 1. (a) An illustration of the single lamp/reflector module used in the experimental portion of this work, and (b) a three lamp simulator array with a single aim point located at the second focus of the ellipsoidal mirrors. The height of the single module is roughly 80 cm.
reflective secondary concentrator to provide a radiant heat input to a volumetric thermal energy storage system (Codd et al., 2010). The simulator used four metal halide stadium lights, with stock reflectors, aimed at a common target and further focused using a reflective sheet metal cone (i.e. a non-imaging secondary concentrator). The power delivered by this system was 51 Wth with a peak flux of 60 kWth/m2. The relatively lower peak flux value, as compared to the preceding Xebased systems, was in part due to the larger arc size of the metal halide lamps. In the preceding simulator development efforts the design emphasis was placed on the reflective components (mirrors and secondary concentrators) and on the spatial arrangement of modules, rather than on the arc source itself. While the use of a simplified arc source may not significantly affect the calculation of the optimal shape of an ellipsoidal reflector, it does reduce the accuracy of simulator performance predictions, which is important when designing a simulator for an application requiring a specific level of performance. In this paper, we present an optical model that improves the accuracy of simulator performance calculations by better accounting for the spatial variation of radiant emission within the arc of a metal halide lamp. Our arc model is based on direct measurements of the intensity variation within the arc volume, and does not require the use of fitting parameters to achieve good agreement with experimental data. We further generalize our results to enable the specification of an accurate metal halide arc source model using only the manufacturer-provided lamp geometry and lamp power rating as inputs.
The design objectives for the seven-lamp simulator developed by the University of Minnesota were to replicate the performance specifications of concentrating solar power collectors including the angular distribution of light incident on the target plane, the distribution of radiant flux, and the spectrum (Krueger et al., 2011). The design approach included a ray-tracing optical model in which reflector eccentricity was varied parametrically, and both transfer efficiency and flux uniformity used to determine the optimal reflector shape. The arc source was modeled as a uniform, cylindrical volumetric emitter. The predicted peak flux for the optimal configuration was reported as 3700 kWth/m2, with a total power delivered to a 6 cm diameter target of 7.5 kWth. The experimental characterization of this simulator was presented in a later work (Krueger et al., 2013). The results of that study show that the actual power delivered to a 6 cm diameter target is 9.2 kWth with a peak flux of 7300 kWth/m2. The difference between predicted and experimentally measured power delivery is 20%; the difference in the peak flux values is 65%. The solar simulator built by Georgia Tech is a seven lamp array that delivers approximately 6.2 kWth to a 4 cm diameter target at a peak flux of 6800 kWth/m2. Like the systems at PSI and UMN, this simulator includes custom built reflectors designed to maximize transfer efficiency. Design simulations incorporated optical ray tracing and a diffusely emitting, cylindrical model of the Xe arc source (Gill et al., 2015). These simulations, along with empirical data, were used to evaluate the specular error of the reflectors and the electrical to radiant energy conversion ratio by adjusting these parameters to achieve agreement between experimental and predicted performance. Two 45 kWe, 18 lamp simulators were recently built through a collaborative effort between the Australian National University (ANU) and Ecole Polytechnique Fédérale de Lausanne (EPFL). The design effort supporting these systems is well documented. Bader et al. present a general optical design process for multi-lamp simulators in which they describe the process by which both the reflector geometry and overall simulator configuration may be optimized to maximize radiative transfer to a target (Bader et al., 2015). Their initial optical model included an idealized cylindrical arc with ray emission determined with a probability distribution function. A subsequent publication by members of this team (Levêque et al., 2016) includes a more detailed description of the optical model and experimental data for the completed simulator. In this work the lamp source is described by an exponential probability distribution function in which emitted intensity can vary within the arc volume. The final form of this equation is determined by fitting model results to experimental data. The resulting agreement between model results and experiment, using fitting parameters for spatial intensity variation, mirror roughness, and lamp efficiency is within a few percent across the entire flux map. MIT produced a solar simulator based on metal halide lamps and a
2. Optical model development Our solar simulator design process begins with the development of an optical model using the commercially available Monte Carlo (MC) ray tracing software TracePro (2017). The optical model requires three elements to be defined: the reflector (geometry and properties), the target (geometry and properties), and the arc source (geometry and emission profile). The definition of each of these elements is implemented in a way that closely matches the properties of the commercially available components on which our simulator modules are based, making use of manufacturer-provided data or, in the case of the arc source, experimental data from our own characterization studies. 2.1. Optical considerations High flux solar simulators typically use truncated ellipsoidal reflectors to focus the light emitted by an arc at the first focus to a target plane at the second focus, as illustrated in Fig. 2. The fraction of the power input to the lamp (i.e. electrical power) that reaches the target plane as radiant power is called the transfer efficiency, and is often the 819
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Fig. 2. The optical configuration of a high flux solar simulator with an ellipsoidal focusing mirror.
2012). This is the approach that we have used in this work.
objective function used in simulator mirror design optimizations (Petrasch et al., 2007; Gill et al., 2015). The maximum value of the transfer efficiency can be no more than the view factor between the arc and the reflector surface, or the fraction of light from the lamp that strikes somewhere on the reflector surface. For the truncated reflector geometry used in this work the maximum transfer efficiency is calculated to be 0.7, using radiative view factors from Howell (2017). This value is further reduced by the ability of the reflector to focus light from a source of finite size to a target plane that is typically a disc of 6–10 cm in diameter located at the second focus of the ellipsoid, which is, in part, determined by the spectral reflectance and scattering behavior of the reflector. The peak flux delivered to the target, another commonly reported performance metric, is also influenced by the properties of the reflector and lamp. To illustrate this point, consider a reflector surface divided into infinitesimally small discrete elements, δAs . The size of the image projected on the target plane at the second focus of the ellipsoid from any one of these surface elements may be approximated as shown in Eq. (1).
dimage ≈ ϕref rST
2.2. Reflector model The reflector used in this work was purchased from Optiforms, Inc. (2017) and is an electroformed ellipsoid with an 813 mm inter-focal distance and consisting of a structural nickel substrate coated with a silver reflecting layer and topped with an aluminum oxide overcoat. The combined thickness of the silver and alumina layers is approximately 30–50 nm. The spectral reflectance of an electroplated mirror coupon provided by Optiforms was measured using a 410-Solar spectrophotometer from Surface Optics and Inc. (2017). The total spectral reflectance of the mirror is shown in Fig. 3 along with the emission profile of a metal halide arc lamp provided by Osram (Osram Sylvania, 2016). We assumed that the reflector could be accurately modeled with a single, spectrum-weighted reflectance applied across the entire lamp emission spectrum. The spectrum-weighted total reflectance was calculated from the data in Fig. 3 using Eq. (3). The geometry and properties on which our reflector model is based are summarized in Table 1.
(1)
ρspectrum − weighted =
where the divergence angle, ϕref , is estimated from the angular divergence of the incident radiation modified by a surface error, expressed in Eq. (2) as a “slope error”, which is the standard deviation of the difference between the actual local mirror surface normal vector, and the theoretical value defined by the geometry of the mirror.
ϕref = ϕinc + σSlope =
darc + σSlope rFS
∞ ∫0 ρmeasured (λ ) Pλ (λ ) dλ ∞ ∫0 Pλ (λ ) dλ
(3)
This calculation was done separately for the total reflectance, and for the specular component alone. The difference between these two values was used to estimate the amount of diffuse radiation as 0.4% of the total reflectance. The individual values for the specular and diffuse reflectance components were used to calculate a bi-directional reflectance function (BRDF) using the methods described in Harvey et al. (2012).
(2)
In Eq. (2), darc is the projection of the arc onto a plane normal to the direction of rFS, the distance from the focus to the mirror surface. Both the transfer efficiency and peak flux increase as dimage decreases. We can see from equations 1 and 2 that the minimum image size (and therefore peak flux) occurs for a perfectly smooth mirror (σslope = 0 ) when both the arc size, darc, and distance to the target plane, rst, are minimized.1 Expressing the effect of the mirror surface on the reflected beam using a slope error is a common convention within the solar energy community; however, it may also be represented with a description of the manner in which light is scattered from mirror, such as a bi-directional reflectance distribution function (BRDF) (Harvey et al.,
2.3. Lamp specific arc source model Arc lamps emit volumetrically, and it is important to consider the spatial variation of emission in order to create an accurate optical model of an arc lamp. Jacobsen (2004) and Jacobsen et al. (2010) developed a semi-empirical model for Xe flash lamps in which the arc is represented by several nested surface sources that vary with respect to emission intensity and spectrum. Their model was based on direct measurement of the spatial variation of intensity, and emission spectrum, within the arc. We have adapted this approach to simulate metal halide lamps. In our semi-empirical lamp model, shown schematically in Fig. 4 alongside a single surface source, each shell is a surface emitter, modeled as an ellipsoid, and is transparent to emission from the other shells. The radiant power emitted by each shell sums to the total power
1 The arc diameter for a 4 kW metal halide lamp is about 20 mm. A 4 kW Xe lamp may have an arc diameter as small as 7 mm. This allows Xe-based simulators to achieve greater peak flux at a given power level.
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Fig. 3. The spectral reflectance of the electroplated reflector used in this work displayed alongside an emission profile typical of metal halide arc lamps. The uncertainty in these data is ± 0.001 reflectance units.
Vn , and the luminous flux (e.g. luminosity) of the lamp, Φv , provided as a range by the manufacturer.
Table 1 Ellipsoidal reflector geometry and optical properties. The geometric parameters Ref. Fig. 2.
Prad [W] =
Optiforms E813-001 dv [cm] dt [cm] H [cm] dIF [cm] tNi/Al2O3 [nm] ρMH, S ρMH, D BDRF (A, B, g)
8.6 39.40 21.98 81.30 30–50 0.896 0.004 (0.00129, 0.015, 0)
Φv [lm] lm
∞
683[ W ] ∗ ∫0 Pn (λ ) Vn (λ ) dλ
(4)
where Pn is the normalized spectral emissive power having units of nm−1 and computed as
Pn (λ ) =
Pλ (λ ) ∞ ∫0 Pλ (λ ) dλ
(5)
where Pλ (λ ) is the spectral emissive power in W/nm provided by the Fig. 4. (a) Schematic of a nested ellipsoid source with rays of light emitted from each surface and (b) a schematic of a singular spherical source with rays of light emitted from its surface.
manufacturer in tabular form as a function of wavelength for a given lamp. The lamp efficiency is then calculated as
emitted by the lamp, and more closely approximates a volumetric emitter as the number of discrete shells increases. In order to fully define this arc model we must specify the geometry of each shell and the power emitted from it. The reported radiant output from commercially available arc lamps (Xe and MH) is typically expressed in lumens, which is a measure of irradiance weighted based on the ability of the human eye to perceive light. The radiative power emitted by the lamp, Prad [W], is calculated using Eqs. (4)–(6) to convert emission from photometric units [lm] to radiometric units [W], by considering the spectral response of the human eye expressed by the normalized luminous efficiency function,
ηlamp =
Prad Pe
(6)
where Pe is the electric power supplied to the lamp and is provided by the manufacturer. Using the preceding calculations we determine the radiant power, Prad , in Watts, from a given arc lamp using only data obtained from lamp manufacturers. We used four lamps in the development of our arc source model. These are listed in Table 2 along with their relevant optical properties. These lamps were chosen to span a range of output power, and to provide variation in arc gap, both of 821
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Table 2 Optical properties of the metal halide lamps used in this study.
Pe [W] ILU [lm] Darc [mm] Prad [W] ηlamp
Prad [W] =
Lamp 1 Osram 1500 W/ D7/60
Lamp 2 Osram 2500 HMI SE/XL
Lamp 3 Philips MSR Gold 2500/2
Lamp 4 Philips 4000 HR
1500 149250 7.5 1240 0.83
2500 223750 14 2070 0.83
2500 193000 9.5 2000* 0.8*
4000 380000 20 3290 0.82
∫1 +
n
In dVn ≅
∑ ⎛I1 (V1−0) + ⎝
I1 + I2 I + I3 (V2−V1) + 2 (V3−V2)… 2 2
In − 1 + In (Vn−Vn − 1)⎞ 2 ⎠
(7)
where Vn is the volume, in m , of the ellipsoid fit to each arc image in and In is the local intensity of the arc, in W/m3. We assume that the intensity of the arc in any image is related to intensity of the arc in the first by Eq. (8) 3
In = I1 ∗0.5n − 1
(8)
where the constant, 0.5, corresponds to the change in optical density due to the removal of a single ND-2 filter. The intensity of the first image, I1, can be calculated by combining Eqs. (7) and (8) with the known radiative power of the lamp:
* Estimated from data provided for similar lamps.
which significantly affect simulator performance. The parameter ILU is the average luminosity value supplied by the manufacturer. Prad is the radiative power output calculated at this luminosity value using Eqs. (4) and (5). This was done for all of the lamps except for Lamp 3. In this case we could not obtain data for spectral emissive power. As such, we assumed that Lamp 3 performed similarly to the others with regard to lamp efficiency, ηlamp , and estimated its radiative power to be 80% of the rated electrical power. The completion of the arc source model requires the definition of shell dimensions, and the emissive power applied to each shell. To measure shell dimensions, we developed an empirical technique in which a 12-bit CCD camera (AVT Manta) was used to obtain images of an arc through a stack of neutral density filters. Initially, we attached several ND filters to the camera lens to achieve high optical density. We then adjusted the electronic shutter of the camera to further regulate the amount of light reaching the detector. In this way we were able to adjust the equivalent optical density such that a continuous region of saturated pixels was visible between the lamp electrodes. The image acquired here represents the region of the arc volume having the highest radiant intensity. From there we sequentially removed a single ND 2 filter (50% reduction in optical density) to allow relatively more light to enter the camera, taking an image at each step. This process was continued until the arc size no longer increased due to being constrained by the quartz lamp envelope. We then processed the images to identify the shape of the region of saturated pixels in each image, which we fit to an ellipse. From this sequence of ellipses we measured the major and minor axes for each arc shell. A sequence of images from Lamp 3 is shown in Fig. 5. The imaging process was repeated for all four lamps. The power emitted from the surface of each shell in the arc model represents emission from a differential arc volume defined by any two adjacent images as shown in Fig. 5. The sum of the emission from the collection of shells equals the total emission from the arc as shown in Eq. (7)
I1 =
PR
(
∑ V1 +
1 + 0.5 (V2−V1) 2
+
0.5 + 0.25 0.5n − 2 + 0.5n − 1 (V3−V2)…+ (Vn−Vn − 1) 2 2
) (9)
The emission intensity for each shell can now be found with Eq. (8), and the power assigned to the surface of each shell calculated with Equation (10).
Pn = (Vn−Vn − 1)
In + In − 1 2
(10)
The shell geometry and power assignments for Lamp 3 are shown in Table 3. 2.4. Optical model results The preceding definitions for the reflector and arc source were used to build a complete solar simulator model in TracePro. This model also included a 6 cm diameter target located at the second focus of the ellipsoidal mirror, 813 mm distant from the center of the lamp. The target was modeled as a perfect absorber and the front surface used to generate flux maps from the optical simulations. A series of simulations were carried to generate theoretical flux maps for the lamps listed in Table 2. In all cases the total number of rays emitted from each shell was set to 75,000, the value needed to achieve a solution output independent of the number of rays included in the simulation. The crosssectional flux map for each of the four lamps is shown in Fig. 6, along with the flux map for a 2500 W lamp modeled with single spherical surface source of 9.5 mm in diameter (the arc gap of Lamp 3). All of the calculated flux maps were symmetric about the center of the flux map. One commonly used approach to modeling arc sources is to treat them as either spherical or cylindrical surface emitters of a size equal to the arc gap. This does not suitably represent the true nature of the emission from the arc, and leads to an inaccurate flux map prediction, which can be seen by comparing the flux map for Lamp 3 to that of the
Fig. 5. (a) The raw image data from the camera and (b) the processed data showing the outline of individual arc shells. The sequence moves from left to right with the image on the far left being the most intense region of the arc. The vertical line in the first image of (b) is 10 mm in length.
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of the light from the simulator module reflected from a Lambertian target placed at the focal plane. The intensity distribution present in this image can be related to the intensity distribution of the light incident on the target from the simulator module. The images obtained in this step have arbitrary units and must be scaled with a calibration factor to display flux maps having units of kW/m2. The scaling process requires the measurement of the power intercepted by a water-cooled calorimeter placed at the target plane, which is related, by the calibration factor, to the integral of the arbitrary flux values across the aperture of the calorimeter. This is a commonly used method of measuring the flux distribution in concentrating solar power applications, and its application to solar simulators is discussed in detail by Gill et al. (2015) and by Levêque et al. (2016) who use a flux gauge in place of a calorimeter. The experimentally measured flux maps include the following sources of uncertainty:
Table 3 Measured shell geometry and assigned properties for Lamp 3. Shell number
Minor radius [mm]
Major radius [mm]
Power [W]
Intensity [W/ mm3]
1 2 3 4 5 6 7 8 9
1.17 1.64 2.39 3.7 4.55 5.76 7.26 9 10.83
4.73 5.39 6.37 6.89 6.94 7.86 8.47 8.97 9.99
250.04 231.31 316.08 419.18 176.81 212.57 167.66 126.05 100.31
9.194 6.896 3.448 1.724 0.862 0.431 0.215 0.108 0.054
2000
Lamp 1-1500 W Lamp 2 - 2500 W 2500 W Spherical Arc
1200
Lamp 3 - 2500 W Lamp 4 - 4000 W
• Pixel gray value: ± • Pixel position: ± 7.5 × 10 cm • Coolant flow rate: ± 5 mL • Time (flow measurement): ± 1 s • Calorimeter coolant temperature: ± 0.2°C. 1 4096
Flux [kW/m2]
1000 800 600
Taken together and further accounting for thermal losses from the calorimeter, the total uncertainty for the measurement of flux distribution and total incident power was calculated, and is summarized, along with model predictions for simulator performance, in Table 5. The agreement between experimentally measured and predicted values for peak flux is within ± 12% for all lamps, and the agreement for power delivered to a 6 cm diameter target is within ± 9%. A comparison of the shape of the experimentally measured and simulated flux maps is shown in Fig. 7a for Lamp 3, and in Fig. 7b for Lamp 2. Qualitatively, the agreement between the experiment and prediction is good across most of the map, with a significant difference in the region near the peak for some of the lamps. The reason for this discrepancy is unknown, but could be a consequence of approximations made in the development of the arc model. One of these approximations is the idealized representation of the arc shells in the optical model; each shell was fit to an ellipsoid, for simplicity, even though the shells were not always ellipsoidal in shape. This approximation carries relatively more weight for the smallest shells, which most strongly affect the magnitude of the predicted peak flux value.
400 200 0
-3
-2
-1
0
1
2
3
Distance From Flux Map Center [cm] Fig. 6. The calculated flux distribution for all four lamps as well as for a 2500 W lamp modeled as a single surface, diffuse spherical emitter.
Table 4 Predicted performance of a single simulator module using a metal halide lamp. Lamp number
Peak flux [kW/m2]
Power to target [W]
Average flux [kW/m2]
Transfer efficiency [%]
1 2 3 4
888 414 835 393
608 616 849 711
215 218 300 252
39.8 25.4 34 18.1
−3
4. A generalized arc model The final step toward our objective of enabling simulator design from off the shelf components is to create an arc model that is not specific to any one lamp, but can accurately represent a range of metal halide lamps suitable for use in a high flux solar simulator. We begin by normalizing the experimentally measured arc size data, dividing the measured major and minor radius value for each arc “shell” by the
lamp modeled with a spherical surface source. The maps differ significantly, with a much higher peak flux realized when treating the source as a volumetric emitter. The results in Fig. 6 also show the effect of arc size on beam size and peak flux; the lamp having the lowest radiant power output produces the highest peak flux due to its relatively short arc gap. Larger arcs tend to produce more beam spread and lower overall flux at the target. A comparison of the flux maps for lamps 2 and 3 shows that an increase in arc gap from 9.5 mm (Lamp 3) to 14 mm (Lamp 2) results in a decrease in the peak flux of over 50%. The numerical output from the optical models for all of the lamps is summarized in Table 4.
Table 5 A comparison of experimentally measured simulator performance to predicted values. Power is integrated over a 6 cm diameter target. Lamp number
3. Experimental validation Our lamp-specific optical models were validated by comparing predicted flux maps (Fig. 6) to experimentally measured flux maps for a single-lamp simulator module. This simulator module is shown schematically in Fig. 1a, and described in detail in the supplement to the paper. The experimental procedure included two steps. In the first, a flux map for each lamp was acquired using a camera to obtain an image
1 2 3 4
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Predicted
Percent difference [%]
Peak flux [kW/m2]
Power [W]
Peak flux [kW/ m2]
Power [W]
Peak flux
Power
795 370 860 400
618 565 914 760
888 414 835 393
608 616 849 711
11.1 11.2 2.9 1.8
1.6 8.6 7.3 6.7
± ± ± ±
55 20 30 20
± ± ± ±
43 33 30 37
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Fig. 7. (a) cross-sectional flux maps for Lamp 3 and (b) for Lamp 2. The experimentally measured maps are represented by an upper and lower curve corresponding to the limits of uncertainty in the experimental data.
major or minor radius of the quartz envelope, raised to some power, n, for the corresponding lamp as shown in Eq. (11).
Rnorm =
Rmeas n Rquartz
and the arc shell number for both the major and minor axis dimensions. These relationships, given in Fig. 8, allows the specification of the nested-shell arc dimensions for any metal halide lamp for which the dimensions of the quartz envelope are known. A detailed accounting of this procedure is presented in the supplement to this paper, along with a code that facilitates source calculations from manufacturer-provided data.
(11)
The collection of calculated values for Rnorm is then plotted and fitted with a polynomial to determine functional relationships between Rnorm
Fig. 8. (a) Normalized major and (b) minor axis values for each arc model shell and for all lamps.
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J.P. Roba, N.P. Siegel
Fig. 9. (a) Flux maps for Lamp 2 and (b) Lamp 3 generated with the Lamp-Specific arc model and the General arc model plotted with the upper and lower bounds of the experimentally measured flux map data.
within ± 12% of the experimentally measured values for peak flux and ± 9% total power delivered. The model is based on treating the arc source as an assembly of nested elliptical shells, each emitting a fraction of the total lamp power and arranged in a way that simulates the spatial variation in emission intensity within the arc. The arc model was developed by experimentally measuring the size of isoflux surfaces within the arc for several metal halide lamps spanning a range of power output from 1500 W to 4000 W. Our overall objective was to enable the design of solar simulators from off the shelf components. To that end we have presented a general arc model in which the nested-shell arc source may be defined for any commercially available metal halide lamp in the 1500–4000 W power range, with the only required inputs being the dimensions of the quartz envelop of the lamp, and the electric power rating. This approach, when applied to the lamps that we experimentally evaluated, resulted in model predictions for peak flux that were within ± 20% of experimentally measured values, and within ± 9% for total power delivered to the target.
Table 6 A comparison between the general model results and experimentally measured peak flux and power delivered to a 6 cm target. Lamp number
1 2 3 4
Predicted
Percent difference [%]
Peak flux [kW/m2]
Power [W]
Peak flux
Power
858 451 818 429
627 616 869 701
7.6 19.7 5.0 7.0
1.4 8.6 5.0 8.1
The results in Fig. 8 allow the specification of up to eleven shells in a given arc source model. The actual number used is limited by the constraint that the largest shell be smaller than the interior dimensions of the quartz envelope of the lamp in question. The number of shells may also be limited by specifying that each shell must emit greater than 3% of the total lamp output. Our results have shown that including shells with emitted power less than 3% does not substantively affect the outcome of the optical model. The power assigned to each shell can be determined from the rated electrical power of the lamp and calculated using Eqs. (6)–(10). In this calculation the ratio of radiant power to electrical power set to 0.8 in Eq. (6), a value that is within the experimentally determined range for the lamps that we evaluated, and the ratio of intensity between subsequent shells set to 0.5 in Eq. (8). The combination of the shell dimensions calculated from the fitting functions presented in Fig. 8 and power assignments yield a complete, nested-shell arc model that requires as input only the known values for lamp dimensions and electric power consumption. We applied this generalized modeling approach to develop arc models for the lamps in Table 2. The resulting flux maps for Lamps 2 and 3 are shown in Fig. 9, and a comparison between the predicted and experimental peak flux and power delivered to a 6 cm diameter target is given, for all lamps, in Table 6. The results in Table 6 show that the agreement between predicted peak flux and the experimentally measured value increased relative to the lamp-specific model, but was within ± 20% for all lamps evaluated. The predicted power delivered was closer to the experimental value, within ± 9% for all lamps.
Acknowledgements This work was supported by the United States Department of Energy, Fuel Cell Technology Office [grant number DE-FOA-0000826]. Supplementary Information We have provided a document set containing additional information related to the design and construction of the 2500 W simulator module shown in Fig 1a, as well as a code and sample calculation of a nested shell arc source developed with our general modeling approach and manufacturer-provided lamp data. These documents are included as supplements to this paper, and can also be downloaded from the links contained in the document linked here (http://dx.doi.org/10.1016/j. enconman.2017.08.091) References Bader, R., Haussener, S., Lipiński, W., 2015. Optical design of multisource high-flux solar simulators. J. Sol. Energy Eng. 137, 021012. Codd, D.S., Carlson, A., Rees, J., Slocum, A.H., 2010. A low cost high flux solar simulator. Sol. Energy 84 (12), 2202–2212. Gill, R., Bush, E., Haueter, P., Loutzenhiser, P., 2015. Characterization of a 6 kW high-flux solar simulator with an array of xenon arc lamps capable of concentrations of nearly 5000 suns. Rev. Sci. Instrum. 86 (12), 125107. Harvey, J.E., Schröder, S., Choi, N., Duparré, A., 2012. Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles. Opt. Eng. 51 (1) pp. 013402-1.
5. Conclusions We have developed a lamp specific arc source model that can be used, in combination with optical ray tracing software, to predict the performance of solar simulators based on metal halide lamps to 825
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Howell, J.R., 2017. A catalog of radiation heat transfer configuration factors. Available at: < http://www.thermalradiation.net/indexCat.html > . Jacobsen, D.A., 2004. Modeling the spectral shape of short-arc pulsed xenon flashlamps. In: Optical Science and Technology, the SPIE 49th Annual Meeting (pp. 295–302), October. International Society for Optics and Photonics. Jacobsen, D.A., Freniere, E.R., Gauvin, M., 2010. Accurate source simulation in modern optical modeling and analysis software. In: OPTO (pp. 75971E–75971E), February. International Society for Optics and Photonics. Krueger, K.R., Davidson, J.H., Lipiński, W., 2011. Design of a new 45 kWe high-flux solar simulator for high-temperature solar thermal and thermochemical research. J. Sol. Energy Eng. 133 (1), 011013. Krueger, K.R., Lipiński, W., Davidson, J.H., 2013. Operational performance of the University of Minnesota 45 kWe high-flux solar simulator. J. Sol. Energy Eng. 135 (4), 044501. Levêque, G., Bader, R., Lipiński, W., Haussener, S., 2016. Experimental and numerical
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