On the influence of wind on cavity receivers for solar power towers: An experimental analysis

Applied Thermal Engineering 87 (2015) 724e735

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research paper

On the influence of wind on cavity receivers for solar power towers: An experimental analysis Robert Flesch a, *, Hannes Stadler a, Ralf Uhlig b, Bernhard Hoffschmidt c a

Institute of Solar Research, German Aerospace Center, Karl-Heinz-Beckurts Straße 13, D-52428 Jülich, Germany Institute of Solar Research, German Aerospace Center, Pfaffenwaldring 38-40, D-70569 Stuttgart, Germany c €he, D-51147 Ko €ln, Germany Institute of Solar Research, German Aerospace Center, Linder Ho b

h i g h l i g h t s
Analysis of the influence of wind on cavity receivers.
Usage of a similarity approach to scale the results to large receivers for solar power towers.
Receivers with high inclination angles are more susceptible to wind.
In some cases wind reduces the losses below the level of natural convection.
Distribution of the heat losses on different sections gives insight in the heat loss mechanisms.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 February 2015 Accepted 9 May 2015 Available online 4 June 2015

The influence of wind on the convective losses of cavity receivers for solar power towers was analyzed experimentally in a cryogenic wind tunnel. At an ambient temperature of 173  C a Grashof number of Gr ¼ 3.9$1010 can be reached. Six different wind directions ranging from head-on to rearward flow, five wind speeds up to Re ¼ 5.2$105 and four inclination angles of the cavity in the range of f ¼ 0 …90 were analyzed. With a similarity approach the results can be transferred to a receiver in normal ambient conditions with an inner diameter of 2.4 m and a wall temperature of approximately 730  C. The methodology and its restrictions are discussed in detail. The experiments show that the influence of wind on large horizontal receivers is small. However, with increasing inclination angle the receiver becomes more susceptible to wind, although the convective losses never exceed those of the horizontal cavity. In some cases a reduction of the convective losses under the level of natural convection was observed if wind is present. Additionally, local information about the heat losses of different heater sections are presented, which are used to analyze the heat loss mechanisms inside the cavity. A shrinking of the stagnant zone is found to be the main reason for the increasing losses. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Concentrating solar power Wind tunnel Open cavity receiver Mixed convection Wind

1. Introduction In solar thermal power plants solar radiation is concentrated with mirrors. The concentrated sunlight is used to produce heat. In contrast to other forms of energy heat can be stored easily. Therefore, the produced heat can be used directly to drive a conventional power plant or it can be stored first and used in periods when no sunlight is available. Thus, the technology is capable of producing dispatchable electricity.

* Corresponding author. E-mail address: robert.fl[email protected] (R. Flesch). http://dx.doi.org/10.1016/j.applthermaleng.2015.05.059 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

Based on its concentrator solar power plants can be divided into three groups.
parabolic trough and fresnel systems
dish systems
solar power towers. The focus of the first system is a line in which the collector pipe is placed. In the two latter systems the sunlight is concentrated onto the so called receiver, a surface of small dimensions compared to the concentrator. Here, a cavity is one favorable design for the receiver, because radiative losses can be minimized. The cavity receiver consists of an enclosure which has an opening on one side e the so called aperture. The solar radiation enters the cavity through the

R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

Nomenclature R

universal gas constant

Gr ¼

bref ðTwall T∞ ÞgL3cav r2ref mref 2

Grashof number

Nu ¼ a/kref$Lcav Nusselt number PT ¼ bref$(TwT∞) dimensionless temperature spread m cp Pr ¼ refk ref Prandtl number ref Re ¼ rrefLcavuwind/mref Reynolds number a angle of wind direction bref volumetric thermal expansion f inclination angle nref kinematic viscosity at film temperature k conductivity cpref heat capacity at film temperature measured conductive losses Q_ cond

Q_ conv Q_ rad

m mref r rref S

convective losses calculated radiative losses dynamic viscosity viscosity at film temperature density field density at film temperature rate-of-shear tensor

aperture and is absorbed by the enclosing walls. The walls either consist of tubes or they can be covered with a directly irradiated medium e e.g. particles. The cavities used for solar power towers and for dish systems are similar except in size. The typical inner length of a cavity for a solar power tower is larger than 1 m whereas the typical size of a cavity used for dish systems is less than 1 m. As the temperature of the walls inside the cavity is higher than the temperature of the surrounding, part of the absorbed energy is lost due to radiation Q_ rad , convection Q_ conv and conduction Q_ cond through the structure (Fig. 1). The conductive losses are small if an appropriate insulation is used and they can be calculated with adequate accuracy. The calculation of the radiative losses is a more complex phenomenon, but due to tools like ray tracing they can be simulated, too. Convection, however, is a highly nonlinear and

Fig. 1. The diagram shows the different heat loss mechanisms which reduce the usable share of the absorbed solar radiation Q_ solar .

~ d i T~

wall

T~ ∞ ~ wind u g u Atot di fR h Lcav p Ptotal T Tref T+ T∞ Twall uref uwind kref

725

scaled inner diameter model wall temperature model ambient temperature wind velocity in cryogenic wind tunnel acceleration of gravity velocity field total heated area inside the cavity inner diameter of cavity resistance ratio enthalpy field length of the cavity pressure field measured electric power temperature field film temperature dimensionless Temperature temperature of the environment temperature of the cavity receiver walls reference velocity wind velocity conductivity at film temperature

complex problem, especially when external effects like wind are taken into account. As it is crucial to have an estimate for the convective losses, several studies dealt with an analysis of the convective losses of cavity receivers. Since dish systems track the sunlight, the receiver moves. Therefore, its inclination angle defined as the angle between the normal of the aperture and the horizontal direction varies over the day. However, for cavity receivers of solar power towers this angle is fixed, but it is used as an optimization parameter in the design phase. In case of natural convection the basic mechanisms have already been described by Eyler in 1979 [2] and Clausing in 1981 [1]. The hot air is trapped in the upper part of the cavity. The inner volume of the cavity can be divided into two zones as shown in Fig. 2 [1]. The upper part is the so-called stagnant zone. Here, the temperature is close to the wall temperature and the air is stably stratified. The lower part is the so-called convective zone. The cold air entering this zone through the aperture opening, is heated up and leaves the cavity through the upper part of the aperture. The boundary between the two zones can be approximated with the horizontal plane which goes through the upper lip of the aperture. Kraabel [3] actually measured the losses caused by natural convection of a cubical cavity with an inner length of approximately 2 m. One side of the cube was missing. The others were heated electrically up to a maximum temperature of 815  C. The heat transfer coefficient at the cavity walls was found to be independent of the length scale. This is an indication for a turbulent flow inside the cavity. The influence of the aperture position and size was investigated by Clausing et al. [4]. The experiments were performed in a cryogenic environment under similarity conditions to reach higher Grashof numbers for a small-scale model. Evidence of the stagnant zone in the upper part of the cavity was shown. Hess and Henze [5] performed experiments with a heated cavity inside a water tank. Due to the higher density of the water, higher Grashof numbers could be achieved. Dye flow visualization was used to analyze the flow pattern inside the cavity, including the transition to turbulence.

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R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

Fig. 2. Schematic view of a cavity. According to Clausing [1] two zones can be identified. The stagnant zone with a very high temperature in the upper part and the convective zone in the lower part.

as well and used their model to show, that the losses can be reduced by decreasing the size of the aperture opening. In one experimental analysis by Wu et al. [16] the influence of a rotation on the heat loss of a receiver with the same geometry was found to be small. The numerical studies performed by Paitoonsurikarn et al. [17] and Xiao et al. [18] analyzed the influence of wind on this receiver. Both came to similar results: In the majority of the analyzed cases wind increased the convective losses. In some particular cases the losses with wind were lower than in case of natural convection. Prakash et al. [19] observed a similar effect while measuring the losses for a cavity receiver with an inner diameter of 0.33 m. An additional validation of CFD simulation was performed by Wu et al. [20] with a slightly enlarged version of the receiver from Taumoefolau et al. [13]. They used a constant heat flux boundary condition and included radiation in their model, but no wind. The CFD results were in good agreement with the experimental data. In a subsequent study the influence of wind on this receiver was analyzed experimentally [21]. Due to very low wall heat fluxes the wall temperature was below 100  C in most of the cases. Wu et al. [21] observed a monotonically increasing Nusselt number with increasing wind speed. Fig. 3 provides an overview about the previous studies. The different studies were ordered by the dimensionless temperature spread PT ¼ TwallT∞/0.5$(Twall þ T∞) and the Grashof number Gr ¼

In contrast to the studies described so far, where a model receiver was used, McMordie measured the losses of a cavity receiver in a solar power tower [6]. The receiver was not irradiated. A hot fluid passed through the receiver in reverse direction and the losses were estimated from the occurring temperature drop. The measurements were performed on days with different wind conditions, but no significant influence of wind on the losses was observed. Since the receivers of interest are large, an experimental analysis requires a high effort. With increasing computational power nowadays it is possible to analyze the convective losses with CFD simulations. Fang et al. [7] conducted a simulation of the influence of wind on an almost horizontal receiver. In the simulations wind increased the losses. The effect was explained by an increased heat transfer coefficient due to higher velocities inside the cavity. Tan et al. [8] showed that wind can reduce the losses below the value of natural convection. The effect was used as a measure to reduce convective losses with an air curtain. Liovic et al. [9] performed experiments and simulations for a downwards facing cavity. The simulations were validated with data of thermocouples which were located outside of the receiver. The simulations showed that wind causes an increase of the convective losses. The influence of wind on cavity receivers with different inclination angles is analyzed numerically by Flesch et al. [10]. The effect of wind was found to depend strongly on the cavity orientation. For horizontal receivers wind had only a small influence whereas it had a huge impact on cavities with a high inclination angle. Since the receivers designed for dishes are smaller and can be analyzed with lower effort, a larger number of studies deal with the convective losses of cavities used in dish systems. The convective losses with and without wind were measured for a receiver with an inner diameter of 0.66 m by Stine and McDonald [11] and Ma [12]. Wind caused a significant increase of the losses. The losses of a small scale receiver with an inner diameter of 0.07 m were measured by Taumoefolau et al. [13] without wind. This geometry was used in several subsequent studies, especially in order to validate CFD simulations. By performing a CFD simulation, Paitoonsurikarn et al. [14] showed that CFD simulation can be used to predict the losses caused by natural convection for this geometry. Wu et al. [15] validated their CFD model with the experimental data

bref ðTwall T∞ ÞgL3cav r2ref . mref 2

In the Grashof number, bref denotes the

volumetric expansion coefficient and nref the kinematic viscosity, both taken at the reference temperature Tref ¼ 0.5$(Twall þ T∞) with the ambient temperature T∞. The longest inner dimension (diameter or length) was taken as reference length Lcav. If the results were obtained numerically the name of the study is printed in italic font. The name of the studies in which wind was taken into account are underlined. For large cavity receivers used in power towers with Gr > 1$1010 eight studies have been performed in total, of which five included wind. Only in one of these five studies, the one performed by McMordie [6], an experimental approach was chosen. Since the results of CFD simulations entail a certain uncertainty due to the required usage of turbulence models, a validation of the results is favorable. But as claimed by Yuan et al. [22] and Flesch et al. [10],

Fig. 3. Summary of the analysis on the convective losses of cavity receivers. The names of the studies which include the influence of wind are underlined. Italic font is used for the names of the analyses which were performed numerically.

R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

not enough reliable data for a validation are available, especially if wind shall be taken into account. Therefore, this study aims to perform an experimental analysis of the convective losses of a large cavity receiver with and without wind.

In experimental fluid mechanics a similarity approach is often used. The parameters which influence the result are transformed into dimensionless numbers. By this it is possible to reduce the number of independent variables and to transfer the results obtained with a small scale experiment to a large scale application. The general approach is described in this section and the governing dimensionless numbers for the present problem are derived from the governing equations. The problem is described by the steadystate equation for mass conservation

V$ðruÞ ¼ 0

(1)

and the NaviereStokes equation


 V$ ruuu ¼ Vp þ V$ðmSÞ þ g$r:

(2)

These two equations describe the connection between the velocity field u and the pressure field p, where r denotes the fluid density, m the dynamic viscosity and



 
 2  V$uI þ Vu þ ðVuÞu 3

(3)

the rate-of-shear tensor. The identity matrix is symbolized by I. As the flow of interest includes heat transfer, the energy equation must be taken into account. Since the heat transfer is dominant, all other contributions to the energy equation can be neglected. This leads to

V$ðruhÞ ¼ V$ðkVTÞ:

(4)

In this equation h stands for the enthalpy of the fluid, T for the temperature, and k for the conductivity of the fluid. The equations can be dedimensionalized, when each dimensionful quantity is divided by a reference value. In case of the velocity, the division leads to u+ ¼ u/uref and in case of the acceleration of gravity to g+ ¼ g/g. The unit vector g+ gives the direction of the acceleration of gravity. The temperature field is transformed by

T+ ¼

T  T∞ : Twall  T∞

(5)

The differential operator must be dedimensionlized as well

V+ ¼ Lcav $V:

þ


 V+ $ r+ u+ h+ ¼


 mref V+ $ m+ S+ rref Lcav u∞

Lcav g + + g $r u2ref

(8)

+

+

For fluid properties r ¼ r/rref, m ¼ m/mref, k ¼ k/kref, h+ ¼ h=cpref ðTwall  T∞ Þ the property value in the reference state at the temperature Tref ¼ 0.5$(Twall þ T∞) is used. Since the problem is independent of the absolute value of the pressure, the dynamic pressure ru2ref is used as reference value for the pressure. The continuity equation (Eq. (1)) remains in the same form, after the dedimensionalization is applied

(7)

The dimensionless NaviereStokes equation (Eq. (2)) becomes


 kref V+ $ k+ V+ T + : cpref Lrref u∞

(9)

The prefactors can be linked to common dimensionless numbers



  1 Gr V+ $ r+ u+ u+u ¼ V+ p+ þ V+ $ m+ S+ þ 2 g + $r+ ; Re Re $PT (10) which are the Reynolds number Re and the Grashof number Gr and the dimensionless temperature spread PT ¼ bref$(TwT∞). In the energy equation the Prandtl number Pr appears as additional parameter


 V+ $ r+ u+ h+ ¼


 1 V+ $ k+ V+ T + : Re$Pr

(11)

With Eqs. (10) and (11) the principle of the similarity approach can be demonstrated. If the dimensionless numbers in these two equations are kept constant while the model is scaled for the experiment, real application and scaled model are described by the same dimensionless equations and therefore these equations give the same dimensionless result. In order to keep similarity, the dimensionless boundary conditions must be the same as well. The heat transfer at the walls can be expressed by

vT k$ ¼ a$ðTwall  T∞ Þ vn

(12)

with the temperature gradient normal to the wall vT/vn. This equation becomes

vT + a$Lcav k+ $ + ¼ ; kref vn

(13)

when the dedimensionalization is applied. At this point the Nusselt number Nu ¼ a$Lcav/kref with the heat transfer coefficient a must be introduced. The Nusselt number represents the heat transfer across the boundary. However, in case of temperature variations, the variation of the fluid properties with the dimensionless temperature must be the same in real scale application and small scale experiment. With the assumption of perfect gas behavior with negligible compressibility due to pressure variations, the density can be expressed as

(6) +


 V+ $ r+ u+ ¼ 0:


 V+ $ r+ u+ u+u ¼ V+ p+ þ

and the energy equation (Eq. (4))

2. Theory

S¼

727

r+ ¼

r T 1 : ¼ ref ¼ rref T PT $T +  0:5$PT þ 1

(14)

In the last step, the reference state Tref ¼ 0.5$(Twall þ T∞) is used. If the dimensionless temperature spread PT is kept the same, the similarity condition is fulfilled for the density. For the other fluid properties, like cp, k and m it is not possible to derive dimensionless numbers which guarantee the similarity in the whole temperature range at the same time. The same holds true for the Prandtl number, which depends only on temperature and the used fluid. The influence of this will be discussed in the following section.

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R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

3. Methods As shown in the previous section, similarity can be achieved except for some fluid properties if the dimensionless numbers Gr, Re and PT are kept constant. In order to perform the experiment with a small scale model, it is convenient to increase the density e.g. by decreasing the temperature. Unfortunately, it is not possible to model a whole tower with a built in cavity, because the scaling factor is limited due to the unfavorable exponent of the length scale in the Grashof number. Therefore, a sole cavity without tower was built and analyzed in a cryogenic wind tunnel. If the ambient temperature is lowered down to 173  C, a geometric scaling factor of approximately 3.5 can be reached. The inner surfaces were heated up to a temperature of approximately 60  C. For the reference size Lcav the inner diameter di of the cavity is used. The atmosphere inside the cryogenic wind tunnel consists of pure nitrogen. In the similarity calculation the thermodynamic properties published by Span et al. [23] and the transport properties published by Lemmon and Jacobsen [24] for air and nitrogen are used. With the volumetric expansion coefficient at the reference temperature bref ¼ 4.6$103 1/K and the temperature difference of 233 K we obtain a dimensionless temperature spread of approximately PT ¼ 1.1. With the same dimensionless number the wall temperature for the scaled application can be calculated for a given ambient temperature. The geometric scaling factor for an ambient temperature of 25  C to the given temperatures in the cryogenic wind tunnel is derived from the condition of an equal Grashof number in experiment and application with respect to the constant temperature spread PT

di ¼ de i

~ rref mref rref m ~ ref

!2 3

¼

kg 5 kg 1:6 m 3 $3:3$10 ms

!23

kg 5 kg 0:53 m 3 $1:4$10 ms

¼ 3:6:

(15)

The equality of the Reynolds number leads to the scaling factor for the wind speed

~~ r m uwind d ¼ i ref ref ¼ ~ ~ ref uwind di rref m

sffiffiffiffi di ¼ 1:9: de

(16)

i

The experimental parameters and their scaled equivalents are summed up in Table 1. As mentioned before, it is not possible to have similar variation of the fluid property values k, m and cp with the dimensionless temperature. The variation with the temperature is shown in Fig. 4 for the experiment and the scaled application in the temperature range specified in Table 1. Since the dimensionless temperature spread was adjusted to match the similarity condition, the variation of the density (Fig. 4a) is very similar in both cases. The difference between both densities is below 1%. This deviation is related to the non-perfect behavior of the gaseous nitrogen in the cryogenic wind tunnel. For the other properties no additional parameter can be adjusted to enforce similarity over the whole temperature range. As a result, deviations up to maximum 10% occur. Usually, variations of the fluid properties are neglected in most of the correlations used for heat transfer calculations, as the influence of the temperature

Table 1 Experimental parameter and their equivalent in the reals scale application.

Inner diameter Maximum wind speed Wall temperature Ambient temperature

Model

Application

Dimensionless

~ ¼ 0:66 m d i ~ wind ¼ 7 m u s ~ T wall ¼ 60:4 + C ~ T ∞ ¼ 173 + C

di ¼ 2.4 m uwind ¼ 13.3 m/s Twall ¼ 730  C T∞ ¼ 25  C

Gr ¼ 3.9$1010 Re ¼ 5.2$105 PT ¼ 1.1

spread is not included. Thus, we assume that the resulting difference between application and scaled experiment is smaller than the differences in the fluid property variations. Moreover, a difference between application and experiment is tolerable, as the present study aims to analyze the changes in the convective losses due to wind rather than to evaluate the losses of a specific design. Fig. 5 shows a sketch of the model cavity including dimensions. The outer part of the model cavity consists of a cryogenic storage dewar. The dewar provides a good thermal insulation combined with a short thermal time constant. A cylinder with bottom made of 10 mm thick aluminum was placed inside of the dewar. The aluminum cylinder is equipped with foil heaters on its outer surface. The bottom of the cylinder is equipped with a heater as well. ICA cables are led through the spacing between inner aluminum cylinder and the inner wall of the dewar to the front. A ring made of PTFE holds the inner cylinder in position and reduces the conductive losses through the flange of the dewar. The interior is held together by a ring made of compressed laminated wood, which is screwed onto the flange of the dewar. This material combines a low conductivity with resistance to very low temperatures. A channel for the cables is located at the back of the aperture ring (shown in the lower part of Fig. 5). The whole cavity is mounted on a frame as shown in Fig. 6. The inclination angle f can be varied with a stepper motor. The frame is placed on an automatic turntable which is used to analyze different wind directions a. The heaters are divided into five different sections. Fig. 7 is used to illustrate the different sections on the cylinder. Cutting the cavity horizontally and by flipping the two parts up and downwards, respectively, leads to the presented view. Each section, the upper front, the upper back, the bottom, the lower back and the lower front can be heated individually. Six thermocouples are used for each rectangular section on the cylinder to measure the temperature. The temperature of the circular section at the back of the cavity is measured by a total of nine thermocouples. All thermocouples are placed into holes with 8 mm depth. The average of the temperatures of all thermocouples in the specific section is used as controlled variable. In order to obtain the desired average temperature, the control unit adjusted the electric power, and accordingly the heating power, with a thyristor power controller. The electric power required to keep the desired temperature was measured with an effective power measuring transducers. Part of the electrical power consumption is caused by the resistances of the feed cables. The part consumed by the foil heaters is calculated with the ratio of heater resistance to total resistance fR. The electrical power transformed into heat inside the heaters equals the total losses of the cavity, composed of radiation, conduction through the insulation of the dewar, and the convective losses. Since only the convective losses are of interest, the other contributing losses must be subtracted. This can be expressed by the following formula

Q_ conv ¼ fR $Ptotal  Q_ cond  Q_ rad :

(17)

The radiative losses are calculated with a simple view factor approach. For the cavity walls a constant emissivity of 0.4 is used. All inner surfaces are assumed to have the same temperature. This rough estimation for the radiation losses is applicable due to the low wall temperature. The total radiation losses of about 30 W contribute only less than 1% to the total losses in the vast majority of the analyzed cases. Only in case of high inclination angles combined with no wind or very small wind speeds, when the convective losses are close to zero, the share of the radiation losses is higher. In order to measure the conductive losses, the aperture opening was blocked with a cover. The electric power transformed to heat in this case equals the conductive losses. The described

R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

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Fig. 4. Difference in the variation of the dimensionless fluid properties between air and the nitrogen in the cryogenic wind tunnel (KKK).

measurement was performed in the cryogenic environment for all different inclination angles without wind and for head-on and sideon wind with a speed of 5 m/s. From the measured losses effective heat transfer coefficients are calculated for each case. For the other analyzed wind velocities the

heat transfer coefficient is calculated with linear interpolation. The resulting conductive heat losses are in the range of 290 W to 520 W. Finally, from the convective heat losses the Nusselt number

Nu ¼

~ ~_ $d Q conv i

~ ~ ~ ~ Atot $ T wall  T ∞ $k ref

(18)

is calculated with the total heated inner surface Atot ¼ 1.73 m2 and the conductivity at reference temperature ~ kref ¼ 1:97$102 W=m2 K. 3.1. Accuracy

Fig. 5. Sketch of the cavity receiver model.

Eq. (17) shows, that three different terms are measured or evaluated to calculate the convective losses: the measured electricity transformed to heat fR$Ptotal, the measured conductive losses Q_ cond and the calculated radiative losses Q_ rad . The accuracy of these three terms is analyzed to estimate the resulting error of the convective losses. For the first term the accuracy of the power measurement system, of the resistance measurement (listed in Table 2) and of the temperature measurement must be taken into account. From the absolute error of the power measurement the relative error is calculated. After that, the error of the resistance measurement and the power measurement can be used directly. In order to evaluate the influence of the temperature measurement error, the derivative of the convective losses with respect to the temperature is required. This derivative is obtained experimentally: Another measurement at a slightly lower temperature level was taken. The convective heat losses at this temperature are calculated with Eq. (17), too. The derivative used in the error estimation is approximated by the difference quotient. The difference quotient is used to calculate the error related to the temperature measurement error.

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R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

Fig. 6. Model cavity in the test section of the cryogenic wind tunnel Cologne. The pictures shows the definition of the inclination angle f and the wind direction a. An inclination angle f ¼ 0 represents a horizontal cavity and a ¼ 0 head-on wind.).

As the conductive losses, the second term in Eq. (17), are measured as well, the accuracy of the measurement system must be considered once again. As applied for the first term, the accuracy of the resistance measurement and of the power measurement can be used directly. In contrast to the upper approach, no second measurement is used to evaluate the error caused by the temperature measurement. From the conduction measurement, the heat transfer coefficient for the conductive transport through the cylinder is calculated. The heat transfer coefficient is assumed to be independent of the temperature. Therefore, the influence of the temperature measurement error on Q_ cond can be calculated directly. Finally, the error of the radiation loss calculation, the third term, must be estimated. To do so, the losses are reevaluated. This time, the back of the aperture ring was assumed to have ambient temperature. Additionally, the higher temperature difference and an effective emissivity of 0.45 is used. With these assumptions the radiative losses are approximately 60 W higher than the used value. The difference is used as estimation for the radiation loss error. The different errors are summed up and the resulting errors are shown with an error bar in the following plots.

Fig. 7. Layout of the different heating section. Cutting the cavity horizontally and by flipping the two parts up and downwards leads to the presented view. The circles indicate the position of the thermocouples.

ordinate. The flow velocity applied in the wind tunnel is used on the lower abscissa. Its dimensionless representation Re2/Gr is shown on the upper abscissa. In case of a horizontal receiver it is evident that wind has only a small influence on the losses. Small wind speeds lead to slightly higher losses. In the range of ~ wind ¼ 2  5m=s the losses remain nearly constant. Only for very u high wind speeds the losses start increasing again. Some of the experiments were performed twice in order to proof reproducibility, therefore, for some parameter combinations two points are shown. Inclining the cavity to f ¼ 30 lowers the convective losses caused by natural convection effectively. Wind in this case actually reduces the losses below the level of natural convection. The losses ~ wind ¼ 3m=s. For higher reach a minimum somewhere around u wind speeds the losses increase almost linearly with wind speed. If the receiver is inclined to f ¼ 60 , the losses decrease furthermore. Once again, the losses undergo a minimum with increasing wind speed. In this case, the minimum is at lower wind speeds ~ wind ¼ 1m=s). For higher wind speeds the losses increase (u

4. Results 4.1. Integral results Fig. 8 shows the influence of head-on wind (a ¼ 0 ) on the losses of cavities with different inclination angles. The heat losses are represented by the dimensionless Nusselt number on the left ordinate. The dimensionalized values are shown on the right

Table 2 Error sources in the experimental setup. Type

Source

Magnitude

Absolute error

Power measurement Temperature difference Resistance measurement

89.7 W 4.1  C 2.1%

Relative error

R. Flesch et al. / Applied Thermal Engineering 87 (2015) 724e735

Fig. 8. Influence of head on wind of different wind speeds on cavities with different inclination angles.

monotonically. For a face-down receiver (f ¼ 90 ) the losses caused by natural convection are close to 0 W and therefore little lower than in the case of f ¼ 60 . If wind is present, the losses of the facedown receiver increase almost linearly with wind speed. As the slope is higher than in the other three cases, the face-down receiver ~ wind ¼ 7m=s has the highest losses of exposed to a wind speed of u all described cases. The influence of side-on wind (a ¼ 90 ) is shown in Fig. 9. Compared to the head-on (a ¼ 0 ) wind, side-on wind has a higher impact on the losses of a horizontal receiver. With increasing wind speed, the losses increase at first, before the decrease and reach a ~ wind ¼ 3m=s as well. After that velocity the losses minimum at u increase with wind speed. The influence of wind on a receiver with f ¼ 30 is similar. However, the minimum is not as distinct as for a ~ wind ¼ 3m=s are still horizontal receiver. Therefore, the losses at u higher than in case of pure natural convection. In case of f ¼ 60 the

Fig. 9. Convective heat losses plotted against the wind speed for side-on wind and different inclination angles.

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losses increase monotonically with wind speed. In Fig. 9 the facedown receiver is shown once again. In this case, all wind directions are equivalent. Therefore, this case was only analyzed with the supporting turntable in the a ¼ 0 position, in order to minimize the influence of the frame. As mentioned above, the losses of the face-down receiver increase monotonically with wind speed. In contrast to the head-on wind case, the slope of the losses of the face-down receiver at the high wind speeds is very similar for all inclination angles. In order to analyze the influence of the wind direction in more detail, the influence of the turntable angle a on the losses of a horizontal receiver is shown in Fig. 10. The majority of the points are difficult to distinguish as they lie close to each other, except for ~ wind ¼ 7m=s and a ¼ 60 with the case of a ¼ 90 with u ~ wind ¼ 3m=s or u ~ wind ¼ 5m=s, respectively. In the first case the u highest losses were measured, whereas wind reduces the losses below the level of natural convection in the two latter cases. Altogether, the statement, that wind has only a limited influence on the losses holds true for all wind directions ranging from head-on to rearward flow for horizontal receivers. The results change as shown in Fig. 11 if the cavity is inclined. As it was described above, wind coming from the side causes higher losses for every analyzed wind speed compared to the natural convection case. Additionally, in the present case, the combination of the wind direction a ¼ 60 and high wind speeds is increasing the losses significantly. Only for the intermediate speeds a reduction is observable. Wind coming from the back of the cavity does not have a huge impact on the losses. The observed changes between the horizontal cavity and the cavity with f ¼ 30 continue when the inclination angle is increased furthermore. The results for a cavity with an inclination angle f ¼ 60 are shown in Fig. 12. Wind, even at very low speed, increases the losses of the cavity in the vast majority of these cases. The highest losses occur once again for side-on wind. In contrast to the previous two cases, wind coming from the back causes higher losses as well. 4.2. Spatially resolved results In order to gain a deeper understanding of the relevant phenomena which influence the convective losses under windy conditions, the heaters inside of the cavity were divided into different sections. The convective losses of the different sections give information about the local distribution of the heat losses. Fig. 13a shows the distribution of the heat losses on the different sections for a horizontal cavity exposed to head-on wind of different wind speeds. The total heights of the columns represent the heat losses of the whole cavity receiver. Therefore, the corresponding Nusselt numbers equal those of the horizontal receiver in Fig. 8. Additionally, the contributing share of the different section to the losses is shown. If no wind is present, the lower sections, namely section 3 and 4, contribute the highest share of the total convective losses. In contrary, the losses of the two sections located in the upper part of the cavity (section 0 and section 1) are lower. If wind is present, the heat losses of the different sections and therefore the total convective losses do not change significantly (Fig. 13b). If the receiver inclination angle is increased to f ¼ 30 , only the lower two sections contribute to the losses. As described above, wind reduces the losses below the level of natural convection, which comes along with lower heat losses in each of the lower two sections (Fig. 13c). For a cavity with an inclination angle of f ¼ 60 only section 4 contributes to the losses in case of natural convection. Wind blowing with 1 m/s from the head-on direction reduces the losses of this section. If the wind speed increases furthermore, the losses

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Fig. 10. Influence of the wind direction on the convective losses in case of a horizontal receiver for different wind speeds.

Fig. 11. Convective losses of cavity receiver with inclination angle f ¼ 30 for different wind directions and wind speeds.

Fig. 12. Convective heat losses plotted against the wind direction for different wind speeds.

of section 4 increase again. For wind speeds higher than ~ wind ¼ 4m=s section 0 and 3 start contributing to the heat losses. u After that velocity the heat losses of section 4 stay relatively constant. At the highest wind speed heat is transferred from every section to the fluid. The same effect is observable with the face-down receiver (Fig. 13d). At first, the losses of section 0 and 4 are increasing with ~ wind ¼ 3m=s section 1 and 3 start wind speed. Beyond u

contributing to the losses whilst the losses of section 0 and 4 remain almost constant. The basic influence of wind on the losses is the same for the other wind directions, too. With increasing wind speed more sections contribute to the losses. If wind at intermediate speeds reduces the losses below the level of natural convection, the mean heat transfer coefficient of the contributing sections is reduced. The wind direction has an impact on the wind speed at which more

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Fig. 13. Bar plot of the heat losses of the different section for head-on wind.

sections start increasing the losses (see Fig. 14). If wind has a higher impact on the losses, this velocity is lower as it can be seen e.g. by the comparison of Fig. 14b with Fig. 13c. However, the constant maximum value which a section reaches for high wind speed is almost independent of the direction. 5. Discussion As described in the previous section, wind has two main effects on the losses. In some cases wind results in a local minimum at intermediate wind speeds, which can be below the level of natural convection. In the other cases wind causes an increase of the losses. An analysis of the distribution of the losses helps to explain these two effects. From the distribution of the heat losses in the different sections, the existence of the stagnant zone is clearly evident. The losses of the sections which lie in the upper part of the cavity, namely section 0 and section 1, are significantly lower than those of the other sections. Especially in the cases with a high inclination angle and natural convection, this phenomenon is clearly

observable. If wind is present, the losses of the upper section are still lower than those of the lower sections which indicates that the stagnant zone is still present. However, its extend seems to be smaller than in the cases without wind. The shrinking of the stagnant zone with wind explains the increasing heat losses with increasing wind speed. The sections which lie inside of the stagnant zone do not contribute to the convective losses. If wind is present and increasing the losses, part of the sections which were in the stagnant zone before start contributing to the convective heat losses (Fig. 15). As shown in Figs. 13 and 14 the losses of the different sections remain almost constant after a critical velocity. Therefore, the heat transfer coefficient is not influenced by wind. If only part of a section lies in the stagnant zone, the heat losses of this section are increasing with wind speed, even though the heat transfer coefficient remains constant. Due to the shrinking of the stagnant zone, the part of the section which contributes to the losses is increasing. At the critical wind speed for this section, the entire section contributes to the losses and therefore its heat loss does not increase further. However, the heat loss of the cavity

Fig. 14. Distribution of the heat losses over the different section in case of side-on wind.

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Fig. 15. Influence of wind on distribution of the heat losses over the different sections: when the stagnant zone shrinks, the boundary between the two zones moves upwards (dashed, dotted and dash-dotted line). As long as only a part of one section lies inside the convective zone, its losses increase when the boundary moves upwards. When almost the whole section is in the convective zone (dotted line - the threedimensionality of the sections must be kept in mind), the losses of the lower (green) section remain nearly constant and the next section (blue) starts contributing to the losses. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

increases furthermore as the next section starts contributing to the losses. When the inclination angle of the receiver increases, the layer between stagnant and convective zone lies closer to the opening. Due to the smaller distance between opening and convective zone, wind seems to disturb the stratified air more easily and therefore the receiver is more susceptible to wind. The second effect, which is the local minimum of the heat losses in some cases at intermediate wind speeds, is associated with a reduction of the losses in all sections which contribute to the losses. There are two possible explanations. Firstly, an increase of the size of the stagnant zone and secondly, an increased temperature in the convective zone. The first explanation can be ruled out as the losses of all sections are reduced by wind as it can be seen in Figs. 13b and 14a. An increasing stagnant zone would decrease the losses of one section before it would influence the next section as it happens when wind is increasing the losses. Therefore, wind seems to increase the temperature in the convective zone. Even if the wind speed is increasing, the temperature in the lower zone seems to stay higher than in the no wind case at first. Therefore, the losses of the sections in the convective zone are lower than in case of natural convection. Another interesting thing can be seen from the nondimensional axis, shown at the top abscissa in Figs. 8 and 9. The minima of the convective losses occur at velocities where the ratio Re2/Gr, which is known as the inverse Richardson number, is in the order of one. This ratio can be interpreted as the ratio of inertial force to buoyant force. If it is equivalent to one, both effects have the same order of magnitude. The general findings of the present analysis is in accordance with the results of the preceding numerical study presented in Ref. [10], where a similar geometry was simulated. The increasing influence of wind with increasing inclination angle and the reduction phenomena are described in this analysis as well. An analysis of mean temperature distributions inside the cavity

showed a shrinking stagnant zone with increasing wind speed which causes higher losses. The reducing effect of wind was explained by a natural air curtain which inhibits the hot air from leaving the cavity and, therefore, causes a temperature rise in the convective zone. An analysis of the distribution over the different sections revealed both influences on the heat losses in the present study as well. The experiment confirms the result presented in Ref. [6] that the influence of wind on large scale receivers is small. However, the present analysis shows that this statement is only valid for horizontal receivers. The universality of McMordie's findings were questioned before by the analysis of an almost face-down receiver in Ref. [9], where a shrinking size of the stagnant zone with wind was observed as well. The numerical results presented in Ref. [7], where an increasing heat loss of a horizontal cavity due to an increasing heat transfer coefficient is described, are in contrast to the present analysis. This might be related to the different geometries, as the aperture ring reduces the diameter of the opening in the present study. Therefore, the inner cavity is protected against higher velocities which would lead to higher heat transfer coefficients at the inner walls. The results presented for small scale cavities are different as well (e.g. Refs. [12,17,18]). In case of a small scale cavity, wind causes significantly higher losses even for a horizontal receiver. A possible explanation for this differences is that small scale receivers are more susceptible to wind than large scale receiver. This assumption was previously made by Ma as well [12]. It is supported by the Richardson number Re2 =Grfu2wind =d, which is larger in case of small receivers. Therefore, the influence of wind compared to the influence of the natural convection is higher in case of a small scale receiver and forced convection is dominant. As the inverse Richardson number is higher for the smaller receivers analyzed in literature, a reduction was observed experimentally only by Prakash [19], who focused on very small wind velocities. It might be possible to extrapolate the observed trend. Then, the influence of wind will become smaller with increasing receiver size. However, if the larger receiver analyzed in the present study is turned downwards, it becomes susceptible for wind, too. One possible explanation is the smaller distance between opening and the layer between the two zones (Fig. 16). This comes along with a smaller buoyancy length and therefore the effect of wind becomes more dominant compared to buoyancy at the same wind speed. Although, the receiver becomes more susceptible to wind with increasing inclination angle, an inclined receiver performs still better than a horizontal one at the same wind speed in the majority of the cases. Therefore, inclining the receiver is still an effective way to reduce convective losses. 6. Conclusion and outlook The influence of wind up to Re ¼ 5.2$105 on a cavity receiver with Gr ¼ 3.9$1010 was analyzed in a cryogenic wind tunnel. The experiment shows that wind has only a small impact on horizontal receivers, but the impact is increasing for receivers with higher inclination angles, where the losses increase with wind speed. In some cases wind actually reduces the losses below the level of natural convection. The minimum occurs where the buoyant and the external forces created by wind are in the order of unity. An analysis of the distribution of the heat losses over five different zones revealed two different mechanisms. Wind increases the losses by decreasing the size of the stagnant zone, whereas the reduction comes along with a decrease of the temperature difference between wall and the convective zone. The measurements of the presented experiment are compared to results available in literature. The general findings are in

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Fig. 16. Influence of the inclination angle on the buoyancy length and the position of the layer between stagnant and convective zone in case of natural convection.

accordance to several published results, giving more confidence in the numerical simulations or expanding the findings presented in literature. In the future the presented data can be used to validate numerical models, which can be used afterwards to simulate influence of wind on cavities in solar power towers. As the reducing effect of wind is experimentally verified by the present study, it emphasizes, that cavities should be designed in a way, that wind is redirected to flow parallel to the aperture plane in order to have a positive or at least not negative influence of wind. Acknowledgements This work was carried out with financial support from the Ministry of Innovation, Science and Research of the State of North Rhine-Westphalia (MIWF NRW), Germany under contract 3232010-006 (Start-SF). We want to thank the whole team of the cryogenic wind tunnel Cologne for their support during preparation and execution of the experiment. References [1] A.M. Clausing, An analysis of convective losses from cavity solar central receivers, Sol. Energy 27 (1981) 295e300. [2] L.L. Eyler, Predictions of Convective Losses from a Solar Cavity Receiver, Technical Report, Battelle Pacific Northwest Labs, Richland, WA (USA), 01.01.1979. [3] J. Kraabel, An experimental investigation of the natural convection from a side-facing cubical cavity, in: Y. Mori, W.J. Yang (Eds.), American Society of Mechanical Engineers, Japan Society of Mechanical Engineers, ASME-JSME Thermal Engineering Joint Conference, ASME-JSME Thermal Engineering Joint Conference: Proceedings, vol. 1, Japan Society Of Mechanical Engineers, 1983, pp. 299e306. [4] A.M. Clausing, J.M. Waldvogel, L.D. Lister, Natural convection from isothermal cubical cavities with a variety of side-facing apertures, J. Heat Transf. 109 (1987) 407. [5] C.F. Hess, R.H. Henze, Experimental investigation of natural convection losses from open cavities, J. Heat Transf. 106 (1984) 333e338. [6] R.K. McMordie, Convection heat-loss from a cavity receiver, J. Sol. Energy Eng. Trans. ASME 106 (1984) 98e100. [7] J.B. Fang, J.J. Wei, X.W. Dong, Y.S. Wang, Thermal performance simulation of a solar cavity receiver under windy conditions, Sol. Energy 85 (2011) 126e138. [8] T. Tan, Y. Chen, Z. Chen, N. Siegel, G.J. Kolb, Wind effect on the performance of solid particle solar receivers with and without the protection of an aerowindow, Sol. Energy 83 (2009) 1815e1827.

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