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Experimental determination thermo physical characteristics of balled biomass
Energy 45 (2012) 350e357
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Energy journal homepage: www.elsevier.com/locate/energy
Experimental determination thermo physical characteristics of balled biomass Aleksandar Eric a, Dragoljub Dakic b, Stevan Nemoda a, Mirko Komatina c, *, Branislav Repic a a
Univ. of Belgrade, Vinca Institute of Nuclear Sciences, P.O. Box 522, Belgrade 11001, Serbia Univ. of Belgrade, Faculty of Mech. Engineering, Innovation Centre, Kraljice Marije 16, 11120 Belgrade 35, Serbia c Univ. of Belgrade, Faculty of Mech. Engineering, Kraljice Marije 16, 11120 Belgrade 35, Serbia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 September 2011 Received in revised form 31 January 2012 Accepted 26 February 2012 Available online 30 March 2012
The paper presents the results of an experimental investigation conducted to determine the permeability coefficients and the stagnant thermal conductivity i.e. the thermo physical properties deemed to be the most important features of the bed material when considering combustion in pusher-type furnaces (i.e. combustion of biomass bales in cigar burners). The appropriate experimental methods have been developed and suitable experimental apparatus designed and constructed in order to determine permeability and stagnant thermal conductivity coefficient of the soybean straw bales. The experimental investigation conducted was aimed at examining the effects of relevant biomass bale parameters on the aforementioned coefficients. Based on the numerous measurements performed, correlations were obtained that are deemed highly important for optimization of the biomass bale combustion, as well as for modeling the transport phenomena occurring in the porous bed formed during biomass bales combustion in cigar burners. Data collected during the course of research investigation were used to develop a detailed CFD model of straw bales combustion in cigar burners. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Balled biomass Permeability Stagnant thermal conductivity
1. Introduction The use of renewable energy sources is becoming increasingly important [1], mainly due to the continuously rising prices of fossil fuels, resource depletion and global attempts to achieve the maximum feasible CO2 emission reduction. The research activities in this area are very complex, requiring the theoretical and experimental investigation to be performed if reliable data are to be obtained. A 1.5 MW industrial-scale hot water boiler was constructed and installed in the Agricultural Corporation Belgrade in order to facilitate research in the field mentioned. The boiler operation is based on the combustion of waste soybean straw bales, thereby providing the energy needed to heat 1 ha (10,000 m2) of greenhouse area. The combustion in the boiler is based on the socalled “cigarette” combustion module [2e4], with the straw bales used as combustion the fuel [5,6]. The specified combustion module is characterized by complex heat and mass transfer processes. In order to be able to properly examine transport phenomena occurring in a porous bed formed by the soy straw bales, thermo
* Corresponding author. Tel.: þ381 11 3302354; fax: þ381 11 3370364. E-mail addresses: [email protected] (A. Eric), [email protected] (D. Dakic), [email protected] (S. Nemoda), [email protected], mkomatina@ mas.bg.ac.rs (M. Komatina), [email protected] (B. Repic). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.063
physical properties of the biomass bales need to be known. Literature review has indicated a lack of sufficient data on the permeability and thermal conductivity of this sort of material [2,3]. In order to be able to determine previously specified thermo physical characteristics, appropriate experimental investigation need to be conducted. The experimental data are deemed necessary for optimization and modeling of physical processes occurring during the soy straw bale combustion. Permeability is a property of porous media taken into account by the pressure gradient term Vp in the momentum equation. The pressure gradient Vp is modeled through the Forchheimer equation [7]:
Dp m r w þ w2 ¼ Dx K1 K2
(1)
Equation (1) is characterized by the two proportionality coefficients, namely the viscous coefficient m/K1 and the inertial coefficient r/K2, where K1 and K2 represent viscous and inertial permeability respectively, both coefficients considered constant and independent on the flow direction, depending only on the characteristics of the porous matrix of the material analyzed. The viscous coefficient is significant in the case of flows characterized by low Reynolds number at the pore level (Red ¼ 1e10) [8]. The inertial coefficient becomes dominant at higher Reynolds numbers, since the inertial effects become more pronounced.
A. Eric et al. / Energy 45 (2012) 350e357
m r s
Nomenclature A d Gr h K1 K2 L l Nu p Pr Q Red SD T U V x w
surface area, [m2] diameter of the porous bed, [m] Grashof number, [e] height of the cone, [m] viscous permeability, [m2] inertial permeability [m] height of porous bed [m] height of cylinder [m] Nusselt number, [e] pressure, [Pa] Prandtl number, [e] heat flux, [W] Reynolds number based on the Darcy velocity, [e] standard deviation, [%] temperature, [ C] expanded measurement uncertainty, [%] volume, [m3] coordinate, [m] superficial velocity, [m/s]
Greek symbols convective heat transfer coefficient, [W/(m2K)] ε porosity, [e] l thermal conductivity, [W/(mK)] Thermal conductivity of biomass bales represents a complex thermal property which depends on many factors such as: geometry of porous medium (porosity, size and shape of the pores, pore curvature radius, percentage of closed pores etc.), thermal conductivity of gas and solid-phase, hydrodynamic properties of gas-phase (velocity, pressure and temperature), flow characteristics (laminar or turbulent flow) etc. Based on the specified parameters, effective thermal conductivity in case of laminar fluid flow may be considered to be composed of two main components i.e. stagnant thermal conductivity and thermal dispersion conductivity. Stagnant thermal conductivity represents a thermal conductivity of porous media under stagnant gas-phase conditions. In such case, the stagnant thermal conductivity is qualitatively and quantitatively affected by the following characteristics of porous media: porosity (ε), solid-phase thermal conductivity (ls), gas-phase thermal conductivity (lf), as well as pore and solid matrix distribution subject to heat flow direction (temperature gradient). If heat transfer in the porous medium is assumed by simultaneous conduction through the pores and the solid matter, stagnant thermal conductivity can be expressed by the following equation [8]
(2)
Another matrix orientation, characterized by the alternating distribution of pores and solid matter in the direction of the heat flow, may be expressed using the following equation [8]:
1=lo ¼ ð1 εÞ=ls þ ε=lf
(3)
For practical applications, another correlation between ls and lf coefficients is proposed to be utilized in stagnant heat conductivity calculations [8]: ε lo ¼ l1ε ,lf s
dynamic viscosity, [Pa s] density, [kg/m3] time, [s]
Subscripts and superscripts eff effective i, j direction s solid f fluid o stagnant ok ambient sp external sr mean Dp pressure difference V volume s time T temperature r density m dynamic viscosity Prandtl number of fluid Prf Prandtl number of wall PrA l thermal conductivity b coefficient of temperature expansion n kinematic viscosity in inner out external
a
lo ¼ ð1 εÞls þ εlf
351
(4)
However, the above correlation does not provide satisfactory results when the difference between ls and lf coefficients is
particularly large (an order of a magnitude). Still, problems encountered in practice are usually not so precisely defined, meaning that a straightforward implementation of the above shown equation may lead to incorrect or inaccurate results. Therefore, the stagnant thermal conductivity is usually determined experimentally. Bearing all the above in mind, the main objective of the research investigation conducted and presented herein was to determine functional dependency of permeability and thermal conductivity coefficient on porosity. The functional correlations obtained were to be used when optimizing the biomass bale combustion. Within the conducted research investigation the biomass bales were modeled as the soy straw bales. 2. Experimental investigation Experimental method used in the investigation conducted was developed to obtain reliable data on Forchheimer coefficients and thermal conductivity to be obtained. Appropriate experimental setup was designed and constructed in order to enable porosity of the analyzed sample (having a constant mass) to be varied in a preselected range. This was achieved by changing the volume of working unit provided in the experimental apparatus designed. Due to specific properties of the porous matrix of biomass bales, an assumption on isotropic nature of the biomass sample was deemed scientifically justified. In addition, it was assumed that porosity variations, achieved by changing the sample volume in a single direction (axially), did not cause anisotropic behavior of the sample. Working unit provided within the experimental apparatus was large enough to accommodate 1 kg of free-form biomass sample, which was deemed as sufficient to significantly reduce the effect of potentially anisotropic features of the sample. 2.1. Permeability measurements The experimental setup used in the research is shown in Fig. 1. The setup consists of three integral units: working unit, an air flow
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A. Eric et al. / Energy 45 (2012) 350e357
Fig. 1. Experimental setup used in the permeability measurements.
supply and measuring system and a pressure drop measuring system. The working unit is a cylindrical vessel used to accommodate the biomass sample (item no. 1). A predetermined quantity of soy straw is compressed in the working cylinder (item no. 3) by the means of an inner disc (item no. 2) and screws (item no. 7). In that manner, a pre-selected volume of the soy straw bed may be prepared, thus resulting in the desired sample porosity. The inner disc is movable and its position relative to the upper plate may be easily altered. Air is fed into the distribution cylinder (item no. 6) by the air supply pipeline (item no. 9). Air flow is then directed into the cylinder which effects the cross-sectional flow equalization (item no. 4). The air flow, characterized by a uniform cross-sectional velocity profile, then enters into the working cylinder. The working cylinder is equipped with a static pressure measuring port ps (item no. 8), which enables measurement of the static pressure of the air flow before the fluid enters the biomass bed. The air continues to flow upwards along the working cylinder, passing through a perforated inner disc and a Dl thick biomass bed, leaving the vessel through a perforated plate into the atmospheric (pa) environment. The air flow supply and measuring system comprises an air fan (item no. 16), a voltage variation device (item no. 15) used for air flow regulation, a gas meter (item no. 14) used for gas flow metering and a rotameter (item no. 13) used for air flow control. Pressure drop through the soy straw bed is measured by the means of a digital micro-manometer. The porosity of the sample was discretely varied over the range of 0.62e0.78, in a manner described earlier i.e. by reducing the sample volume. The sample porosity values analyzed in the first set of measurements performed were as follows: 0.62; 0.68; 0.71; 0.74; 0.77; 0.78. The experiments were carried out in order to simulate cases of various densities of compressed soy residues, while the moisture content of the residues was kept constant and equal to 0.0948. During the experiments performed, air volumetric flow rate and pressure drop across the layer of the soybean bale were
continuously measured. By dividing the volume DV of air which had passed through the experimental setup by relevant time period Ds, a volumetric flow rate of the air stream is obtained. When the volumetric flow rate is divided by the surface area of the biomass bed A ¼ d2p/4, flow velocity across the bed (superficial velocity) w is obtained. Pressure gradient generated across the bed Dp/Dx is calculated by dividing the mean pressure drop, recorded by the manometer, by the biomass bed thickness. The functional dependence of the superficial velocity upon the pressure gradient, based on Equation (1), can be expressed by the following, general-type relation:
y ¼ Ax þ Bx2
(5)
By fitting a second-order polynomial to the experimental data (applying a least-squares fit), coefficients K1 and K2 can be easily determined for the known density and viscosity of the gas flow [9] (r ¼ 1.205 kg/m3 and m ¼ 18.1 106 Pa s). The implementation of the previously described procedure during the first set of measurements performed enabled A and B coefficients (i.e. the Forchheimer coefficients) to be obtained. The values obtained, corresponding to the selected sample porosity level, are shown in Fig. 2 and Table 1. By fitting the higher-order functions, selected by an analogy with the Ergun’s permeability coefficients, to the experimentally determined porosity dependence of A and B coefficients (Table 1), yields:
K ¼ a
εm ð1 εÞn
(6)
where coefficient a generally depends upon the straw diameter (for K2) or the square of straw diameter (for K1), and m and n are the corresponding exponents. The value of a is considered constant, since it is assumed that the straw diameter remains unchanged i.e. constant throughout the experiments performed with the soya straw bales. The functional dependence of viscous and inertial
A. Eric et al. / Energy 45 (2012) 350e357
353
Table 1 Viscous and inertial permeability values. Porosity ε, [e]
0.62 0.68 0.71 0.74 0.77 0.78
Proportionality coefficients Viscous, A
Inertial, B
100 60 45 40 28 30
4200 3200 2000 1500 1180 1250
Viscous permeability, K1 107 [m2]
Inertial permeability, K2 103 [m]
1.81 3.01 4.02 4.52 6.03 6.46
0.286905 0.376563 0.6025 0.803335 0.964004 1.02119
permeability K1 and K2 on the porosity variations in the selected range may be expressed as follows:
K1 ¼ 2
ε2:9 ð1 εÞ
K2 ¼ 1:25
1:3
107 m2
ε4:4 ð1 εÞ0:6
(7a)
103 ðmÞ
(7b) Fig. 3. Variation of viscous permeability with porosity.
Fitting the correlation functions (7a) and (7b) to the experimentally obtained data yields the correlation curves shown in Figs. 3 and 4. The experimental results obtained indicate that, in general, increase in porosity causes an increase in permeability. The viscous permeability basically represents a permeability of the porous bed which increases with increasing porosity, primarily due to larger free cross-sectional area that becomes available for a fluid to flow through. In case of inertial flow regime, fluid flow through the pores causes a boundary layer to be formed on the pore walls. When porosity i.e. pore size increases, the impact of the boundary layer becomes less pronounced, resulting in a reduced flow resistance i.e. increased inertial permeability coefficient K2. The final result of experimental investigation performed in the first phase of the research conducted is the below presented form of Forchheimer equation, developed specifically for combustion of soy straw bales and with the permeability coefficients K1 and K2 replaced by the porosity term ε:
vp ¼ vx
m 2
ε2:9
r
wþ 7
10 ð1 εÞ1:3
1:25
ε4:4
w2 3
10 ð1 εÞ0:6
Fig. 2. Experimental data fitted by a second-order polynomial function.
(8)
2.2. Measurement uncertainty Forchheimer equation coefficients were determined using the data obtained by directly measuring of the following physical parameters: 1. Air flow pressure drop across the biomass layer, measured using ALNOR differential pressure manometer, characterized by measurement accuracy of 1% over the full measurement range of the instrument specified. 2. Volumetric flow rate of the air stream passing through the biomass layer, measured using ELSTER MEH gas meter, characterized by measurement accuracy of 0.7% over the full measurement range of the instrument specified. 3. Time needed for the measured air volume to pass through the biomass sample, measured by using a stop-watch characterized by measurement accuracy of 0.1%. 4. Ambient temperature, based on which density and kinematic viscosity are to be determined, measured using a measurement chain with a K-type thermocouple and a data acquisition
Fig. 4. Variation of inertial permeability with porosity.
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system, characterized by an overall measurement accuracy of 2.5%. Accuracy of ambient temperature measurement also affects the density calculation accuracy, which for the temperature range of 19.5e20.5 C (within 2.5% of recorded ambient temperature of 20 C), equals 0.21%. In similar manner, dynamic viscosity calculation accuracy is determined to be 2.7%. Based on the individual accuracy levels indicated above, an overall i.e. expanded measurement uncertainty may be obtained as follows [10,11]:
2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ul ¼ pffiffiffi, UD2 p þ UV2 þ Us2 þ UT2 þ Ur2 þ Um2 3 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffi, 12 þ 0:72 þ 0:12 þ 2:52 þ 0:212 þ 0:72 ¼ 3:32% 3 The overall measurement uncertainty was determined without taking into account a height difference associated with location of the pressure measuring point, as well as uncertainty introduced with adopted the porosity of the biomass sample. 2.3. Stagnant thermal conductivity measurements A comprehensive analysis of the commercially available devices, designed for measuring heat conductivity of different materials, has indicated that known setups are not suitable for investigation of the soy straw bales. The main reason lies in the fact that the volume of the representative soy straw bale sample, selected so as to be a representative of heat transfer phenomena occurring in the bales, would significantly exceed the working volume of the experimental apparatus. Therefore, the stagnant thermal conductivity experiments were performed using an apparatus especially designed for the specified purpose. The customemade apparatus enabled stagnant thermal conductivity of soy straw bales to be determined for different porosity levels of the material examined (Fig. 5). The apparatus was constructed so as to enable porosity variation of the constant mass biomass sample in a pre-selected range. The porosity variation of the sample was performed by
changing the volume of the working unit (item 4) within the apparatus constructed. Due to the very nature of the porous matrix of biomass bales, an assumption on the isotropic features of the samples was deemed scientifically justified. In addition, it was assumed that porosity variations, achieved by changing the volume of the sample in a single direction (axial), did not induce the anisotropic behavior of the sample analyzed. The working unit of the apparatus, indicated as the item no. 4 in Fig. 5, enables desired porosity of the soy straw sample to be achieved. This is accomplished by compressing the soy straw sample, placed in the area between the top (item no. 1) and the bottom plate (item no. 3), by the means of screws (item no. 5). The central cylinder (item no. 6) acts as a heat source. An inner cylinder is positioned at the supporting plate (item no. 2). The heat source is powered by an electric heater (item no. 8) with adjustable power output. In this manner, heat flow from the central cylinder to the outer cylinder is established. Surface temperatures of inner and outer cylinder are measured at points indicated in Fig. 5 as items no. 7 and no. 9, respectively. The conical end of the inner cylinder enables easier compression of the soy straw bale. An insulation layer is placed between the top plate and the working unit (cylinder) in order to prevent thermal bridging between the specified two apparatus components. In this manner, heat transfer between the inside and the outside cylinder, via heat conduction through top plate, is minimized. With respect to the bottom plate, the working cylinder and the bottom plate are preferably placed in such a relative position that their contact is attained only at a single point, since the case in question involves two spheres of different diameter (i.e. 199 mm diameter bottom plate and 205 mm diameter working cylinder). In this manner, heat transfer to the bottom plate is minimized. Based on this description, it is concluded that heat transfer between the inside and the outside cylinder is mainly dictated by heat conduction through the soy straw bed. Locations of temperature measurement openings provided on the experimental apparatus are indicated in Fig. 5 (items no. 7 and 9). In order to be able to examine the uniform temperature distribution all along the perimeter of both inside and the outside cylinder, an opening has been provided on the opposite side of each cylinder, in location where the associated temperature
Fig. 5. Experimental installation used in thermal conductivity measurements.
A. Eric et al. / Energy 45 (2012) 350e357
measurements are the most relevant for determining the stagnant thermal conductivity. Fig. 6 shows the experimental setup used to determine stagnant thermal conductivity. The thermal conductivity measurements are, as it was mentioned previously, based upon the measurements of outside and inside cylinder surface temperatures, as well as ambient temperature. Temperatures were measured using thermocouples (T1eT12) whose readings provided a basis for determining a heat transfer rate between the outside and the inside cylinders, which in the same time represented the amount of heat transferred through the biomass bed. The temperature data were acquired via the data acquisition system (item no. 8). In order to minimize the heat losses, the experimental apparatus was insulated by a layer of Styropor insulation (item no. 9). Surface temperature of the inside cylinder, which was not to exceed 100 C, was controlled by the means of voltage regulator (item 7). Basic equation used to determine the stagnant thermal conductivity was the Fourier law equation, which states that the heat transferred through a medium is proportional to the temperature gradient across the medium, whereby the proportionality coefficient is indeed the thermal conductivity of the medium in question [12]. For steady state heat conduction through a cylindrical wall, thermal conductivity is expressed as follows:
l ¼ Q_ ð2plDTÞln ðd2 =d1 Þ
(9)
where d2 and d1 represent outside and inside cylinders diameters, l is the length of the cylinders, Q_ is heat conducted through the sample and DT is the temperature gradient. In this manner, thermal conductivity can be easily determined by measuring the temperature difference between the inside and the outside cylinders, as well as the amount of heat transferred. This methodology was used to determine the thermal conductivity of soy straw bales, as presented herein. Heat transfer rate was calculated based on the estimated amount of heat transferred to the ambient surroundings. Calculation was conducted in two different manners, where one included the calculation of mean Nusselt number, generally defined by the expression [9]:
0:25 0:25 Prf =PrA jNuj ¼ 0:76 Gr,Prf
355
(10)
where Prf and PrA represent the Prandtl numbers corresponding to the bulk fluid temperature and temperature of the fluid in the vicinity of the wall, respectively. The heat transferred to the ambient surroundings i.e. the amount of heat conducted through the biomass sample, can then be determined using the following expression [8]:
Q_ ¼ aD2 pL T m Ta o
(11)
where a ¼ Nul/L, l e thermal conductivity of air at ambient temperature (Ta), D2 ¼ 0.215 m e outside wall diameter and Tom e mean outside wall temperature. It is important to note that due to high thermal conductivity of the wall, the temperature gradient across the wall was assumed to be zero i.e. the wall temperature was assumed constant. Tom was determined based on the weighted temperature data as measured at the related surface. For example, T10 is associated with a surface temperature of a cylinder characterized by a diameter of d2 ¼ 0.215 m and a height of l ¼ 0.09 m. In that manner, the mean wall temperature is expressed as follows:
Tom ¼ ðT10 ,0:09 þ T9 ,0:06 þ T8 ,0:06 þ T7 ,0:130 þ T6 ,0:160Þ=0:5
(12)
When determining DT in the Equation (9), it is important to note that another assumption was adopted, this one referring to the equality of the sample’s surface temperature and the temperature of the adjacent wall. The characteristic temperatures of the outside and inside surfaces of the biomass sample were assumed equal to the mean wall temperatures at corresponding wall portions, thereby enabling DT to be expressed as:
DT ¼ ½ðT2 þ T3 þ T4 Þ ðT8 þ T9 þ T10 Þ=3
(13)
As observed in Fig. 1, the inside cylinder was not entirely cylindrical in shape, but was provided with an h ¼ 0.04 m high cone at one end. For this reason, the value indicative of the inside “cylinder” length needed to be corrected accordingly. The correction was applied by adding another Dl ¼ 0.0218 m long cylinder to
Fig. 6. Experimental installation used in stagnant thermal conductivity measurements.
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A. Eric et al. / Energy 45 (2012) 350e357
the l1 ¼ 0.16 m cylindrical portion of the inner cylinder, whereby the surface area of the added cylinder was equal to the surface area of the cone. Thus, the length of the inside cylinder l in the Equation (9) was equal to l ¼ 0.1818 m. The outside diameter of the inside cylinder was d1 ¼ 0.076 m, while the inside diameter of the outside cylinder equaled d2 ¼ 0.205 m. Accuracy of the methodology used for determining the heat flux between the outside cylinder and the ambient surroundings was checked by performing simple simulation of natural convection heat transfer in large diameter cavity, modeled by the FLUENT flow modeling software. Since good agreement between the two methods was obtained, the simpler and less time consuming method, presented by Equations (9)e(13) above, was selected. The experimental validation of the methodology was performed by measuring the thermal conductivity of the porous medium of a known thermal conductivity. For this purpose, the expanded polystyrene (hereafter referred to as Styropor) has been used as the reference material, characterized by thermal conductivity of l ¼ 0.045 W/(mK). The indicated thermal conductivity of the selected reference material was comparable to the expected thermal conductivity of soy straw bale. A total of five sets of experiments were carried out with the soy straw bales samples, all by utilizing the previously described methodology and experimental setup. An additional set of experiments was performed with the Styropor sample to validate the methodology used i.e. to determine the absolute measurement error related to the experimental apparatus designed. The temperatures T1eT12 were selected in order as to be representative of the steady state regime, recorded after running the experimental setup for about 20 h. The experiments were performed at four different porosity levels, namely the porosity of 0.68 (reference porosity of soy straw); 0.45 (minimal indicative porosity associated with the using of apparatus designed); 0.78 (porosity of small bales) and 0.58 (the mean porosity). The temperatures obtained in the experiments performed, shown in Table 2, were used as a basis for determining the stagnant heat conductivity. The results of the thermal conductivity calculations, performed using the methodology that is presented herein, are outlined in Table 3 and in Fig. 7. The difference between the experimental results obtained from the measurements performed with the Styropor sample and a known Styropor thermal conductivity of l ¼ 0.045 W/(mK) was regarded as the absolute measurement error associated with the use of experimental apparatus designed. This error is probably due to flaws in thermal insulation and the effect of thermal bridges. Analysis of the results presented in Fig. 7 indicates that stagnant thermal conductivity of soy straw bale increases with increasing porosity in accordance with the following relation: Table 2 Temperatures used for determining heat conductivity. Temperature
Porosity Styropor
0.68
0.45
0.45a
0.58
0.78
T1, [ C] T2, [ C] T3, [ C] T4, [ C] T5, [ C] T6, [ C] T7, [ C] T8, [ C] T9, [ C] T10, [ C] T11, [ C] T12, [ C]
13.10 70.30 70.41 64.72 69.90 20.54 21.66 22.76 23.60 24.52 23.61 62.80
18.19 60.73 62.61 59.03 61.93 21.66 22.67 23.78 24.62 25.47 24.68 62.88
17.69 66.52 67.18 62.08 66.61 21.50 22.49 23.45 24.09 24.63 24.10 63.31
17.93 66.81 67.43 62.32 66.89 19.93 21.04 22.25 23.22 24.30 23.23 64.08
18.36 60.01 62.26 58.70 61.66 20.18 21.29 22.48 23.45 24.54 23.42 61.14
19.42 58.25 60.03 56.60 59.39 20.72 21.82 22.89 23.61 24.44 23.60 60.83
a
Tests were repeated in order to confirm reproducibility of the method used.
lo ¼ 0:01962 þ 0:19508εeff 0:12087ε2eff
(14)
Increase in the stagnant thermal conductivity associated with an increase in the porosity of soy straw bale can be explained in the following manner. Porous bed is comprised of open and closed pores. Closed pores prevent a forced fluid flow to be established through the pores, whereby the forced flow itself is deemed responsible for thermal dispersion effect. However, some fluid remains trapped in the closed pores and continues to circulate in the space enclosed by the pore walls. In this manner, heat is transferred from one pore wall to another via natural convection phenomenon, which additionally increases the effect of heat conduction. Based upon this assumption, an analogy can be made between the described phenomenon and the thermal dispersion effect, acknowledging that the thermal dispersion effect is much more complex due to a more intensive (forced) fluid flow. This leads to the conclusion that the analyzed phenomenon can be considered as “quasi-dispersion”. By decreasing the porosity of the soy straw sample used in the experiments performed, a reduction in the volume of the open pores is achieved, also resulting in additional splitting of the closed pores. In this manner, multiple smaller pores are formed instead of the larger diameter pores. Due to the reduced volume of the closed pores, fluid circulation inside the pores is reduced, thereby causing heat transfer rate between the pore walls to be reduced as well. This phenomenon may provide an explanation for an observation made during the experimental investigation, considering a decrease in thermal conductivity of the soy straw bale resulting from decreased sample porosity.
2.4. Measurement uncertainty Stagnant thermal conductivities of biomass bales have been determined based on the temperature measurements performed in accordance with the schematic shown in Fig. 6. Temperature was measured using K-type thermocouples, with data acquisition performed by the means of an appropriate data logger. Measurement uncertainty associated with the use of such measuring chain, comprising a K-type thermocouple and the appropriate data acquisition system, equals to 2.5%. Having in mind that data obtained from the inner and the outer cylinder surface temperature measurements were weighted, the overall measurement uncertainty needs to include standard deviations associated with specified temperature measurements, which in the case of inner cylinder temperature measurements equals maximally 2.36%, while in the case of outer cylinder temperature measurements equals maximally 1.51%. Furthermore, analysis performed has taken into account the fact that the heat transfer coefficient, indicative of the rate of heat transferred from the outer cylinder to the ambient surroundings, requires another five air flow parameters to be determined as well (namely, Prandtl number corresponding to the ambient air temperature far away from the wall, Prandtl number corresponding to the wall temperature, thermal conductivity, thermal expansion coefficient and kinematic viscosity). For measurement accuracy associated with the use of thermocouples utilized in the investigation performed, the following calculation uncertainties have been adopted for each of the previously indicated parameter: 0.015% for Prandtl number, 0.27% for thermal conductivity, 0.34% for thermal expansion coefficient and 0.6% for kinematic viscosity calculation. Based on the individual accuracy levels indicated above, an overall i.e. combined measurement uncertainty is obtained as follows [10,11]:
A. Eric et al. / Energy 45 (2012) 350e357
357
Table 3 Calculation of stagnant thermal conductivity of soy straw bales. Calculation parameters
DT, [K] Tair, [K] Tom , [K] Gr 103, [e] Nu, [e] a, [W/(mK)] Q_ , [W] l, [W/(mK)] lkor, [W/(mK)] a
Porosity Styropor
0.68
0.45
0.45a
0.58
0.78
51.00 286.1 289.3 64.057 62.235 3.1491 3.489 0.0606 0.01565
37.16 291.2 295.1 72.922 64.285 3.3814 4.661 0.1104 0.0948
42.00 290.7 294.6 73.129 64.331 3.3838 4.670 0.0986 0.0829
42.03 290.9 294.9 72.998 64.302 3.3822 4.663 0.0984 0.08276
36.68 291.3 295.2 71.639 64.000 3.3664 4.561 0.1094 0.0937
33.67 292.4 296.2 69.125 63.431 3.3365 4.376 0.1145 0.0989
Tests were repeated in order to confirm reproducibility of the method used.
Increased porosity causes an increase in the viscous and inertial permeability. The viscous permeability increase associated with increasing porosity primarily results from larger free surface that becomes available for fluid flow. Due to increased porosity, impact of pore boundary layer becomes less pronounced, resulting in increased inertial permeability. Experiments conducted have indicated that stagnant thermal conductivity decreases with decreased porosity of the analyzed sample. This can be attributed to decreased volume of the closed pores, reducing fluid circulation inside the pores and consequently resulting in reduced heat transfer between the pore walls. Acknowledgments
Fig. 7. Dependence of stagnant thermal conductivity on the porosity of soy straw bales.
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u
2
u UTin 2 UPrf 2 UTout 2 SDout 2 in u pffiffiffi þ SD p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi þ þ þ u 5 3 3 3 3 U ¼ 2,u ¼
2 2 2 u Ub Ul1 t UPrA 2 Un þ pffiffiffi þ pffiffiffi þ pffiffiffi þ pffiffiffi 3 3 3 3 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2
2 2
2 u 2:5 2:5 1:51 u pffiffiffi þ 2:36 pffiffiffi þ pffiffiffi þ pffiffiffi þ u 3 3 3 u 2,u
2
2
52 2 ¼ 5:16% ð0:015Þ 0:27 0:34 0:6 t pffiffiffi þ pffiffiffi þ pffiffiffi þ pffiffiffi 2, 3 3 3 3 The overall measurement uncertainty was determined without taking into account uncertainty introduced with adopted porosity of the biomass sample. 3. Conclusions Experimental methods have been developed for determining permeability coefficients and stagnant thermal conductivity of soy straw bales depending upon the porosity of the balled material. The semi-empirical correlations obtained were used to develop a detailed CFD model of straw bales combustion in cigar burners. Permeability coefficients were observed to exhibit hyperbolic dependence upon porosity.
The paper was developed through activities carried out within the scope of the following projects: “Applied research EU project Biom-Adria 2 e A Development and Improvement of Technologies, Methodologies and Tools For the Enhanced Use of Agricultural Biomass Residues“ and projects of Serbian Ministry of Science and Technological Development: III42011, TR 33042, OI 176006. References [1] Jovanovic M, Turanjanin V, Bakic V, Pezo M, Vucicevic B. Sustainability estimation of energy system options that use gas and renewable resources for domestic hot water production. Energy 2011;36:2169e75. [2] Bech N, Wolff L, Germann L. Mathematical modeling of straw bale combustion in cigar burners. Energy and Fuels 1996;10:276e83. [3] Miltner M, Makaruk A, Harasek M, Friedl A. CFD-modeling for the combustion of solid Baled biomass, Fifth international conference on CFD in the process industries CSIRO; 2006 December 13e15. Melbourne, Australia. [4] Mladenovi c R, Eri c A, Mladenovi c M, Repi c B, Daki c D. “Energy production facilities of original concept for combustion of soya straw bales”, 16th European Biomass Conference & Exhibition e From Research to Industry and Markets, Proceedings on DVD-ROM, ISBN 978-88-89407-58-1, 2e6 June 2008. Valencia, Spain. [5] Mladenovic R, Dakic D, Eric A, Mladenovic M, Paprika M, Repic B. The boiler concept for combustion of large soya straw bales. Energy 2009;34:715e23. [6] Delivand MK, Barz M, Gheewala SH. Logistics cost analysis of rice straw for biomass power generation in Thailand. Energy 2011;36. 1435e1441. [7] Kaviany M. Principles of heat transfer in porous media. New York: SpringerVerlag; 1991. [8] Nield DA, Bejan A. Convection in porous media. New York: Springer Science Business Media, Inc.; 2006. [9] Kozi c DJ, Vasiljevi c B, Bekavac V. Thermo-mechanics handbook in SI units. Belgrade: University of Belgrade, Mechanical Faculty; 1999 [in Serbian]. [10] Guide To the Expression Of Uncertainty In Measurement (GUM). BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML. International Organization of Standardization, Geneva Switzerland, 1st ed. 1993, Corrected and reprinted 1995. [11] EA 4/02 (rev.00): 1999 Expressions of The Uncertainty of Measurements in Calibration (including supplement 1 to EA-4/02)(previously EAL- R2). [12] Milin ci c D. Heat transfer. Belgrade: Academic Book; 1989 [in Serbian].
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Experimental determination thermo physical characteristics of balled biomass Aleksandar Eric a, Dragoljub Dakic b, Stevan Nemoda a, Mirko Komatina c, *, Branislav Repic a a
Univ. of Belgrade, Vinca Institute of Nuclear Sciences, P.O. Box 522, Belgrade 11001, Serbia Univ. of Belgrade, Faculty of Mech. Engineering, Innovation Centre, Kraljice Marije 16, 11120 Belgrade 35, Serbia c Univ. of Belgrade, Faculty of Mech. Engineering, Kraljice Marije 16, 11120 Belgrade 35, Serbia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 September 2011 Received in revised form 31 January 2012 Accepted 26 February 2012 Available online 30 March 2012
The paper presents the results of an experimental investigation conducted to determine the permeability coefficients and the stagnant thermal conductivity i.e. the thermo physical properties deemed to be the most important features of the bed material when considering combustion in pusher-type furnaces (i.e. combustion of biomass bales in cigar burners). The appropriate experimental methods have been developed and suitable experimental apparatus designed and constructed in order to determine permeability and stagnant thermal conductivity coefficient of the soybean straw bales. The experimental investigation conducted was aimed at examining the effects of relevant biomass bale parameters on the aforementioned coefficients. Based on the numerous measurements performed, correlations were obtained that are deemed highly important for optimization of the biomass bale combustion, as well as for modeling the transport phenomena occurring in the porous bed formed during biomass bales combustion in cigar burners. Data collected during the course of research investigation were used to develop a detailed CFD model of straw bales combustion in cigar burners. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Balled biomass Permeability Stagnant thermal conductivity
1. Introduction The use of renewable energy sources is becoming increasingly important [1], mainly due to the continuously rising prices of fossil fuels, resource depletion and global attempts to achieve the maximum feasible CO2 emission reduction. The research activities in this area are very complex, requiring the theoretical and experimental investigation to be performed if reliable data are to be obtained. A 1.5 MW industrial-scale hot water boiler was constructed and installed in the Agricultural Corporation Belgrade in order to facilitate research in the field mentioned. The boiler operation is based on the combustion of waste soybean straw bales, thereby providing the energy needed to heat 1 ha (10,000 m2) of greenhouse area. The combustion in the boiler is based on the socalled “cigarette” combustion module [2e4], with the straw bales used as combustion the fuel [5,6]. The specified combustion module is characterized by complex heat and mass transfer processes. In order to be able to properly examine transport phenomena occurring in a porous bed formed by the soy straw bales, thermo
* Corresponding author. Tel.: þ381 11 3302354; fax: þ381 11 3370364. E-mail addresses: [email protected] (A. Eric), [email protected] (D. Dakic), [email protected] (S. Nemoda), [email protected], mkomatina@ mas.bg.ac.rs (M. Komatina), [email protected] (B. Repic). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.063
physical properties of the biomass bales need to be known. Literature review has indicated a lack of sufficient data on the permeability and thermal conductivity of this sort of material [2,3]. In order to be able to determine previously specified thermo physical characteristics, appropriate experimental investigation need to be conducted. The experimental data are deemed necessary for optimization and modeling of physical processes occurring during the soy straw bale combustion. Permeability is a property of porous media taken into account by the pressure gradient term Vp in the momentum equation. The pressure gradient Vp is modeled through the Forchheimer equation [7]:
Dp m r w þ w2 ¼ Dx K1 K2
(1)
Equation (1) is characterized by the two proportionality coefficients, namely the viscous coefficient m/K1 and the inertial coefficient r/K2, where K1 and K2 represent viscous and inertial permeability respectively, both coefficients considered constant and independent on the flow direction, depending only on the characteristics of the porous matrix of the material analyzed. The viscous coefficient is significant in the case of flows characterized by low Reynolds number at the pore level (Red ¼ 1e10) [8]. The inertial coefficient becomes dominant at higher Reynolds numbers, since the inertial effects become more pronounced.
A. Eric et al. / Energy 45 (2012) 350e357
m r s
Nomenclature A d Gr h K1 K2 L l Nu p Pr Q Red SD T U V x w
surface area, [m2] diameter of the porous bed, [m] Grashof number, [e] height of the cone, [m] viscous permeability, [m2] inertial permeability [m] height of porous bed [m] height of cylinder [m] Nusselt number, [e] pressure, [Pa] Prandtl number, [e] heat flux, [W] Reynolds number based on the Darcy velocity, [e] standard deviation, [%] temperature, [ C] expanded measurement uncertainty, [%] volume, [m3] coordinate, [m] superficial velocity, [m/s]
Greek symbols convective heat transfer coefficient, [W/(m2K)] ε porosity, [e] l thermal conductivity, [W/(mK)] Thermal conductivity of biomass bales represents a complex thermal property which depends on many factors such as: geometry of porous medium (porosity, size and shape of the pores, pore curvature radius, percentage of closed pores etc.), thermal conductivity of gas and solid-phase, hydrodynamic properties of gas-phase (velocity, pressure and temperature), flow characteristics (laminar or turbulent flow) etc. Based on the specified parameters, effective thermal conductivity in case of laminar fluid flow may be considered to be composed of two main components i.e. stagnant thermal conductivity and thermal dispersion conductivity. Stagnant thermal conductivity represents a thermal conductivity of porous media under stagnant gas-phase conditions. In such case, the stagnant thermal conductivity is qualitatively and quantitatively affected by the following characteristics of porous media: porosity (ε), solid-phase thermal conductivity (ls), gas-phase thermal conductivity (lf), as well as pore and solid matrix distribution subject to heat flow direction (temperature gradient). If heat transfer in the porous medium is assumed by simultaneous conduction through the pores and the solid matter, stagnant thermal conductivity can be expressed by the following equation [8]
(2)
Another matrix orientation, characterized by the alternating distribution of pores and solid matter in the direction of the heat flow, may be expressed using the following equation [8]:
1=lo ¼ ð1 εÞ=ls þ ε=lf
(3)
For practical applications, another correlation between ls and lf coefficients is proposed to be utilized in stagnant heat conductivity calculations [8]: ε lo ¼ l1ε ,lf s
dynamic viscosity, [Pa s] density, [kg/m3] time, [s]
Subscripts and superscripts eff effective i, j direction s solid f fluid o stagnant ok ambient sp external sr mean Dp pressure difference V volume s time T temperature r density m dynamic viscosity Prandtl number of fluid Prf Prandtl number of wall PrA l thermal conductivity b coefficient of temperature expansion n kinematic viscosity in inner out external
a
lo ¼ ð1 εÞls þ εlf
351
(4)
However, the above correlation does not provide satisfactory results when the difference between ls and lf coefficients is
particularly large (an order of a magnitude). Still, problems encountered in practice are usually not so precisely defined, meaning that a straightforward implementation of the above shown equation may lead to incorrect or inaccurate results. Therefore, the stagnant thermal conductivity is usually determined experimentally. Bearing all the above in mind, the main objective of the research investigation conducted and presented herein was to determine functional dependency of permeability and thermal conductivity coefficient on porosity. The functional correlations obtained were to be used when optimizing the biomass bale combustion. Within the conducted research investigation the biomass bales were modeled as the soy straw bales. 2. Experimental investigation Experimental method used in the investigation conducted was developed to obtain reliable data on Forchheimer coefficients and thermal conductivity to be obtained. Appropriate experimental setup was designed and constructed in order to enable porosity of the analyzed sample (having a constant mass) to be varied in a preselected range. This was achieved by changing the volume of working unit provided in the experimental apparatus designed. Due to specific properties of the porous matrix of biomass bales, an assumption on isotropic nature of the biomass sample was deemed scientifically justified. In addition, it was assumed that porosity variations, achieved by changing the sample volume in a single direction (axially), did not cause anisotropic behavior of the sample. Working unit provided within the experimental apparatus was large enough to accommodate 1 kg of free-form biomass sample, which was deemed as sufficient to significantly reduce the effect of potentially anisotropic features of the sample. 2.1. Permeability measurements The experimental setup used in the research is shown in Fig. 1. The setup consists of three integral units: working unit, an air flow
352
A. Eric et al. / Energy 45 (2012) 350e357
Fig. 1. Experimental setup used in the permeability measurements.
supply and measuring system and a pressure drop measuring system. The working unit is a cylindrical vessel used to accommodate the biomass sample (item no. 1). A predetermined quantity of soy straw is compressed in the working cylinder (item no. 3) by the means of an inner disc (item no. 2) and screws (item no. 7). In that manner, a pre-selected volume of the soy straw bed may be prepared, thus resulting in the desired sample porosity. The inner disc is movable and its position relative to the upper plate may be easily altered. Air is fed into the distribution cylinder (item no. 6) by the air supply pipeline (item no. 9). Air flow is then directed into the cylinder which effects the cross-sectional flow equalization (item no. 4). The air flow, characterized by a uniform cross-sectional velocity profile, then enters into the working cylinder. The working cylinder is equipped with a static pressure measuring port ps (item no. 8), which enables measurement of the static pressure of the air flow before the fluid enters the biomass bed. The air continues to flow upwards along the working cylinder, passing through a perforated inner disc and a Dl thick biomass bed, leaving the vessel through a perforated plate into the atmospheric (pa) environment. The air flow supply and measuring system comprises an air fan (item no. 16), a voltage variation device (item no. 15) used for air flow regulation, a gas meter (item no. 14) used for gas flow metering and a rotameter (item no. 13) used for air flow control. Pressure drop through the soy straw bed is measured by the means of a digital micro-manometer. The porosity of the sample was discretely varied over the range of 0.62e0.78, in a manner described earlier i.e. by reducing the sample volume. The sample porosity values analyzed in the first set of measurements performed were as follows: 0.62; 0.68; 0.71; 0.74; 0.77; 0.78. The experiments were carried out in order to simulate cases of various densities of compressed soy residues, while the moisture content of the residues was kept constant and equal to 0.0948. During the experiments performed, air volumetric flow rate and pressure drop across the layer of the soybean bale were
continuously measured. By dividing the volume DV of air which had passed through the experimental setup by relevant time period Ds, a volumetric flow rate of the air stream is obtained. When the volumetric flow rate is divided by the surface area of the biomass bed A ¼ d2p/4, flow velocity across the bed (superficial velocity) w is obtained. Pressure gradient generated across the bed Dp/Dx is calculated by dividing the mean pressure drop, recorded by the manometer, by the biomass bed thickness. The functional dependence of the superficial velocity upon the pressure gradient, based on Equation (1), can be expressed by the following, general-type relation:
y ¼ Ax þ Bx2
(5)
By fitting a second-order polynomial to the experimental data (applying a least-squares fit), coefficients K1 and K2 can be easily determined for the known density and viscosity of the gas flow [9] (r ¼ 1.205 kg/m3 and m ¼ 18.1 106 Pa s). The implementation of the previously described procedure during the first set of measurements performed enabled A and B coefficients (i.e. the Forchheimer coefficients) to be obtained. The values obtained, corresponding to the selected sample porosity level, are shown in Fig. 2 and Table 1. By fitting the higher-order functions, selected by an analogy with the Ergun’s permeability coefficients, to the experimentally determined porosity dependence of A and B coefficients (Table 1), yields:
K ¼ a
εm ð1 εÞn
(6)
where coefficient a generally depends upon the straw diameter (for K2) or the square of straw diameter (for K1), and m and n are the corresponding exponents. The value of a is considered constant, since it is assumed that the straw diameter remains unchanged i.e. constant throughout the experiments performed with the soya straw bales. The functional dependence of viscous and inertial
A. Eric et al. / Energy 45 (2012) 350e357
353
Table 1 Viscous and inertial permeability values. Porosity ε, [e]
0.62 0.68 0.71 0.74 0.77 0.78
Proportionality coefficients Viscous, A
Inertial, B
100 60 45 40 28 30
4200 3200 2000 1500 1180 1250
Viscous permeability, K1 107 [m2]
Inertial permeability, K2 103 [m]
1.81 3.01 4.02 4.52 6.03 6.46
0.286905 0.376563 0.6025 0.803335 0.964004 1.02119
permeability K1 and K2 on the porosity variations in the selected range may be expressed as follows:
K1 ¼ 2
ε2:9 ð1 εÞ
K2 ¼ 1:25
1:3
107 m2
ε4:4 ð1 εÞ0:6
(7a)
103 ðmÞ
(7b) Fig. 3. Variation of viscous permeability with porosity.
Fitting the correlation functions (7a) and (7b) to the experimentally obtained data yields the correlation curves shown in Figs. 3 and 4. The experimental results obtained indicate that, in general, increase in porosity causes an increase in permeability. The viscous permeability basically represents a permeability of the porous bed which increases with increasing porosity, primarily due to larger free cross-sectional area that becomes available for a fluid to flow through. In case of inertial flow regime, fluid flow through the pores causes a boundary layer to be formed on the pore walls. When porosity i.e. pore size increases, the impact of the boundary layer becomes less pronounced, resulting in a reduced flow resistance i.e. increased inertial permeability coefficient K2. The final result of experimental investigation performed in the first phase of the research conducted is the below presented form of Forchheimer equation, developed specifically for combustion of soy straw bales and with the permeability coefficients K1 and K2 replaced by the porosity term ε:
vp ¼ vx
m 2
ε2:9
r
wþ 7
10 ð1 εÞ1:3
1:25
ε4:4
w2 3
10 ð1 εÞ0:6
Fig. 2. Experimental data fitted by a second-order polynomial function.
(8)
2.2. Measurement uncertainty Forchheimer equation coefficients were determined using the data obtained by directly measuring of the following physical parameters: 1. Air flow pressure drop across the biomass layer, measured using ALNOR differential pressure manometer, characterized by measurement accuracy of 1% over the full measurement range of the instrument specified. 2. Volumetric flow rate of the air stream passing through the biomass layer, measured using ELSTER MEH gas meter, characterized by measurement accuracy of 0.7% over the full measurement range of the instrument specified. 3. Time needed for the measured air volume to pass through the biomass sample, measured by using a stop-watch characterized by measurement accuracy of 0.1%. 4. Ambient temperature, based on which density and kinematic viscosity are to be determined, measured using a measurement chain with a K-type thermocouple and a data acquisition
Fig. 4. Variation of inertial permeability with porosity.
354
A. Eric et al. / Energy 45 (2012) 350e357
system, characterized by an overall measurement accuracy of 2.5%. Accuracy of ambient temperature measurement also affects the density calculation accuracy, which for the temperature range of 19.5e20.5 C (within 2.5% of recorded ambient temperature of 20 C), equals 0.21%. In similar manner, dynamic viscosity calculation accuracy is determined to be 2.7%. Based on the individual accuracy levels indicated above, an overall i.e. expanded measurement uncertainty may be obtained as follows [10,11]:
2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ul ¼ pffiffiffi, UD2 p þ UV2 þ Us2 þ UT2 þ Ur2 þ Um2 3 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffi, 12 þ 0:72 þ 0:12 þ 2:52 þ 0:212 þ 0:72 ¼ 3:32% 3 The overall measurement uncertainty was determined without taking into account a height difference associated with location of the pressure measuring point, as well as uncertainty introduced with adopted the porosity of the biomass sample. 2.3. Stagnant thermal conductivity measurements A comprehensive analysis of the commercially available devices, designed for measuring heat conductivity of different materials, has indicated that known setups are not suitable for investigation of the soy straw bales. The main reason lies in the fact that the volume of the representative soy straw bale sample, selected so as to be a representative of heat transfer phenomena occurring in the bales, would significantly exceed the working volume of the experimental apparatus. Therefore, the stagnant thermal conductivity experiments were performed using an apparatus especially designed for the specified purpose. The customemade apparatus enabled stagnant thermal conductivity of soy straw bales to be determined for different porosity levels of the material examined (Fig. 5). The apparatus was constructed so as to enable porosity variation of the constant mass biomass sample in a pre-selected range. The porosity variation of the sample was performed by
changing the volume of the working unit (item 4) within the apparatus constructed. Due to the very nature of the porous matrix of biomass bales, an assumption on the isotropic features of the samples was deemed scientifically justified. In addition, it was assumed that porosity variations, achieved by changing the volume of the sample in a single direction (axial), did not induce the anisotropic behavior of the sample analyzed. The working unit of the apparatus, indicated as the item no. 4 in Fig. 5, enables desired porosity of the soy straw sample to be achieved. This is accomplished by compressing the soy straw sample, placed in the area between the top (item no. 1) and the bottom plate (item no. 3), by the means of screws (item no. 5). The central cylinder (item no. 6) acts as a heat source. An inner cylinder is positioned at the supporting plate (item no. 2). The heat source is powered by an electric heater (item no. 8) with adjustable power output. In this manner, heat flow from the central cylinder to the outer cylinder is established. Surface temperatures of inner and outer cylinder are measured at points indicated in Fig. 5 as items no. 7 and no. 9, respectively. The conical end of the inner cylinder enables easier compression of the soy straw bale. An insulation layer is placed between the top plate and the working unit (cylinder) in order to prevent thermal bridging between the specified two apparatus components. In this manner, heat transfer between the inside and the outside cylinder, via heat conduction through top plate, is minimized. With respect to the bottom plate, the working cylinder and the bottom plate are preferably placed in such a relative position that their contact is attained only at a single point, since the case in question involves two spheres of different diameter (i.e. 199 mm diameter bottom plate and 205 mm diameter working cylinder). In this manner, heat transfer to the bottom plate is minimized. Based on this description, it is concluded that heat transfer between the inside and the outside cylinder is mainly dictated by heat conduction through the soy straw bed. Locations of temperature measurement openings provided on the experimental apparatus are indicated in Fig. 5 (items no. 7 and 9). In order to be able to examine the uniform temperature distribution all along the perimeter of both inside and the outside cylinder, an opening has been provided on the opposite side of each cylinder, in location where the associated temperature
Fig. 5. Experimental installation used in thermal conductivity measurements.
A. Eric et al. / Energy 45 (2012) 350e357
measurements are the most relevant for determining the stagnant thermal conductivity. Fig. 6 shows the experimental setup used to determine stagnant thermal conductivity. The thermal conductivity measurements are, as it was mentioned previously, based upon the measurements of outside and inside cylinder surface temperatures, as well as ambient temperature. Temperatures were measured using thermocouples (T1eT12) whose readings provided a basis for determining a heat transfer rate between the outside and the inside cylinders, which in the same time represented the amount of heat transferred through the biomass bed. The temperature data were acquired via the data acquisition system (item no. 8). In order to minimize the heat losses, the experimental apparatus was insulated by a layer of Styropor insulation (item no. 9). Surface temperature of the inside cylinder, which was not to exceed 100 C, was controlled by the means of voltage regulator (item 7). Basic equation used to determine the stagnant thermal conductivity was the Fourier law equation, which states that the heat transferred through a medium is proportional to the temperature gradient across the medium, whereby the proportionality coefficient is indeed the thermal conductivity of the medium in question [12]. For steady state heat conduction through a cylindrical wall, thermal conductivity is expressed as follows:
l ¼ Q_ ð2plDTÞln ðd2 =d1 Þ
(9)
where d2 and d1 represent outside and inside cylinders diameters, l is the length of the cylinders, Q_ is heat conducted through the sample and DT is the temperature gradient. In this manner, thermal conductivity can be easily determined by measuring the temperature difference between the inside and the outside cylinders, as well as the amount of heat transferred. This methodology was used to determine the thermal conductivity of soy straw bales, as presented herein. Heat transfer rate was calculated based on the estimated amount of heat transferred to the ambient surroundings. Calculation was conducted in two different manners, where one included the calculation of mean Nusselt number, generally defined by the expression [9]:
0:25 0:25 Prf =PrA jNuj ¼ 0:76 Gr,Prf
355
(10)
where Prf and PrA represent the Prandtl numbers corresponding to the bulk fluid temperature and temperature of the fluid in the vicinity of the wall, respectively. The heat transferred to the ambient surroundings i.e. the amount of heat conducted through the biomass sample, can then be determined using the following expression [8]:
Q_ ¼ aD2 pL T m Ta o
(11)
where a ¼ Nul/L, l e thermal conductivity of air at ambient temperature (Ta), D2 ¼ 0.215 m e outside wall diameter and Tom e mean outside wall temperature. It is important to note that due to high thermal conductivity of the wall, the temperature gradient across the wall was assumed to be zero i.e. the wall temperature was assumed constant. Tom was determined based on the weighted temperature data as measured at the related surface. For example, T10 is associated with a surface temperature of a cylinder characterized by a diameter of d2 ¼ 0.215 m and a height of l ¼ 0.09 m. In that manner, the mean wall temperature is expressed as follows:
Tom ¼ ðT10 ,0:09 þ T9 ,0:06 þ T8 ,0:06 þ T7 ,0:130 þ T6 ,0:160Þ=0:5
(12)
When determining DT in the Equation (9), it is important to note that another assumption was adopted, this one referring to the equality of the sample’s surface temperature and the temperature of the adjacent wall. The characteristic temperatures of the outside and inside surfaces of the biomass sample were assumed equal to the mean wall temperatures at corresponding wall portions, thereby enabling DT to be expressed as:
DT ¼ ½ðT2 þ T3 þ T4 Þ ðT8 þ T9 þ T10 Þ=3
(13)
As observed in Fig. 1, the inside cylinder was not entirely cylindrical in shape, but was provided with an h ¼ 0.04 m high cone at one end. For this reason, the value indicative of the inside “cylinder” length needed to be corrected accordingly. The correction was applied by adding another Dl ¼ 0.0218 m long cylinder to
Fig. 6. Experimental installation used in stagnant thermal conductivity measurements.
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A. Eric et al. / Energy 45 (2012) 350e357
the l1 ¼ 0.16 m cylindrical portion of the inner cylinder, whereby the surface area of the added cylinder was equal to the surface area of the cone. Thus, the length of the inside cylinder l in the Equation (9) was equal to l ¼ 0.1818 m. The outside diameter of the inside cylinder was d1 ¼ 0.076 m, while the inside diameter of the outside cylinder equaled d2 ¼ 0.205 m. Accuracy of the methodology used for determining the heat flux between the outside cylinder and the ambient surroundings was checked by performing simple simulation of natural convection heat transfer in large diameter cavity, modeled by the FLUENT flow modeling software. Since good agreement between the two methods was obtained, the simpler and less time consuming method, presented by Equations (9)e(13) above, was selected. The experimental validation of the methodology was performed by measuring the thermal conductivity of the porous medium of a known thermal conductivity. For this purpose, the expanded polystyrene (hereafter referred to as Styropor) has been used as the reference material, characterized by thermal conductivity of l ¼ 0.045 W/(mK). The indicated thermal conductivity of the selected reference material was comparable to the expected thermal conductivity of soy straw bale. A total of five sets of experiments were carried out with the soy straw bales samples, all by utilizing the previously described methodology and experimental setup. An additional set of experiments was performed with the Styropor sample to validate the methodology used i.e. to determine the absolute measurement error related to the experimental apparatus designed. The temperatures T1eT12 were selected in order as to be representative of the steady state regime, recorded after running the experimental setup for about 20 h. The experiments were performed at four different porosity levels, namely the porosity of 0.68 (reference porosity of soy straw); 0.45 (minimal indicative porosity associated with the using of apparatus designed); 0.78 (porosity of small bales) and 0.58 (the mean porosity). The temperatures obtained in the experiments performed, shown in Table 2, were used as a basis for determining the stagnant heat conductivity. The results of the thermal conductivity calculations, performed using the methodology that is presented herein, are outlined in Table 3 and in Fig. 7. The difference between the experimental results obtained from the measurements performed with the Styropor sample and a known Styropor thermal conductivity of l ¼ 0.045 W/(mK) was regarded as the absolute measurement error associated with the use of experimental apparatus designed. This error is probably due to flaws in thermal insulation and the effect of thermal bridges. Analysis of the results presented in Fig. 7 indicates that stagnant thermal conductivity of soy straw bale increases with increasing porosity in accordance with the following relation: Table 2 Temperatures used for determining heat conductivity. Temperature
Porosity Styropor
0.68
0.45
0.45a
0.58
0.78
T1, [ C] T2, [ C] T3, [ C] T4, [ C] T5, [ C] T6, [ C] T7, [ C] T8, [ C] T9, [ C] T10, [ C] T11, [ C] T12, [ C]
13.10 70.30 70.41 64.72 69.90 20.54 21.66 22.76 23.60 24.52 23.61 62.80
18.19 60.73 62.61 59.03 61.93 21.66 22.67 23.78 24.62 25.47 24.68 62.88
17.69 66.52 67.18 62.08 66.61 21.50 22.49 23.45 24.09 24.63 24.10 63.31
17.93 66.81 67.43 62.32 66.89 19.93 21.04 22.25 23.22 24.30 23.23 64.08
18.36 60.01 62.26 58.70 61.66 20.18 21.29 22.48 23.45 24.54 23.42 61.14
19.42 58.25 60.03 56.60 59.39 20.72 21.82 22.89 23.61 24.44 23.60 60.83
a
Tests were repeated in order to confirm reproducibility of the method used.
lo ¼ 0:01962 þ 0:19508εeff 0:12087ε2eff
(14)
Increase in the stagnant thermal conductivity associated with an increase in the porosity of soy straw bale can be explained in the following manner. Porous bed is comprised of open and closed pores. Closed pores prevent a forced fluid flow to be established through the pores, whereby the forced flow itself is deemed responsible for thermal dispersion effect. However, some fluid remains trapped in the closed pores and continues to circulate in the space enclosed by the pore walls. In this manner, heat is transferred from one pore wall to another via natural convection phenomenon, which additionally increases the effect of heat conduction. Based upon this assumption, an analogy can be made between the described phenomenon and the thermal dispersion effect, acknowledging that the thermal dispersion effect is much more complex due to a more intensive (forced) fluid flow. This leads to the conclusion that the analyzed phenomenon can be considered as “quasi-dispersion”. By decreasing the porosity of the soy straw sample used in the experiments performed, a reduction in the volume of the open pores is achieved, also resulting in additional splitting of the closed pores. In this manner, multiple smaller pores are formed instead of the larger diameter pores. Due to the reduced volume of the closed pores, fluid circulation inside the pores is reduced, thereby causing heat transfer rate between the pore walls to be reduced as well. This phenomenon may provide an explanation for an observation made during the experimental investigation, considering a decrease in thermal conductivity of the soy straw bale resulting from decreased sample porosity.
2.4. Measurement uncertainty Stagnant thermal conductivities of biomass bales have been determined based on the temperature measurements performed in accordance with the schematic shown in Fig. 6. Temperature was measured using K-type thermocouples, with data acquisition performed by the means of an appropriate data logger. Measurement uncertainty associated with the use of such measuring chain, comprising a K-type thermocouple and the appropriate data acquisition system, equals to 2.5%. Having in mind that data obtained from the inner and the outer cylinder surface temperature measurements were weighted, the overall measurement uncertainty needs to include standard deviations associated with specified temperature measurements, which in the case of inner cylinder temperature measurements equals maximally 2.36%, while in the case of outer cylinder temperature measurements equals maximally 1.51%. Furthermore, analysis performed has taken into account the fact that the heat transfer coefficient, indicative of the rate of heat transferred from the outer cylinder to the ambient surroundings, requires another five air flow parameters to be determined as well (namely, Prandtl number corresponding to the ambient air temperature far away from the wall, Prandtl number corresponding to the wall temperature, thermal conductivity, thermal expansion coefficient and kinematic viscosity). For measurement accuracy associated with the use of thermocouples utilized in the investigation performed, the following calculation uncertainties have been adopted for each of the previously indicated parameter: 0.015% for Prandtl number, 0.27% for thermal conductivity, 0.34% for thermal expansion coefficient and 0.6% for kinematic viscosity calculation. Based on the individual accuracy levels indicated above, an overall i.e. combined measurement uncertainty is obtained as follows [10,11]:
A. Eric et al. / Energy 45 (2012) 350e357
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Table 3 Calculation of stagnant thermal conductivity of soy straw bales. Calculation parameters
DT, [K] Tair, [K] Tom , [K] Gr 103, [e] Nu, [e] a, [W/(mK)] Q_ , [W] l, [W/(mK)] lkor, [W/(mK)] a
Porosity Styropor
0.68
0.45
0.45a
0.58
0.78
51.00 286.1 289.3 64.057 62.235 3.1491 3.489 0.0606 0.01565
37.16 291.2 295.1 72.922 64.285 3.3814 4.661 0.1104 0.0948
42.00 290.7 294.6 73.129 64.331 3.3838 4.670 0.0986 0.0829
42.03 290.9 294.9 72.998 64.302 3.3822 4.663 0.0984 0.08276
36.68 291.3 295.2 71.639 64.000 3.3664 4.561 0.1094 0.0937
33.67 292.4 296.2 69.125 63.431 3.3365 4.376 0.1145 0.0989
Tests were repeated in order to confirm reproducibility of the method used.
Increased porosity causes an increase in the viscous and inertial permeability. The viscous permeability increase associated with increasing porosity primarily results from larger free surface that becomes available for fluid flow. Due to increased porosity, impact of pore boundary layer becomes less pronounced, resulting in increased inertial permeability. Experiments conducted have indicated that stagnant thermal conductivity decreases with decreased porosity of the analyzed sample. This can be attributed to decreased volume of the closed pores, reducing fluid circulation inside the pores and consequently resulting in reduced heat transfer between the pore walls. Acknowledgments
Fig. 7. Dependence of stagnant thermal conductivity on the porosity of soy straw bales.
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u
2
u UTin 2 UPrf 2 UTout 2 SDout 2 in u pffiffiffi þ SD p ffiffiffi p ffiffiffi p ffiffiffi p ffiffiffi þ þ þ u 5 3 3 3 3 U ¼ 2,u ¼
2 2 2 u Ub Ul1 t UPrA 2 Un þ pffiffiffi þ pffiffiffi þ pffiffiffi þ pffiffiffi 3 3 3 3 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2
2 2
2 u 2:5 2:5 1:51 u pffiffiffi þ 2:36 pffiffiffi þ pffiffiffi þ pffiffiffi þ u 3 3 3 u 2,u
2
2
52 2 ¼ 5:16% ð0:015Þ 0:27 0:34 0:6 t pffiffiffi þ pffiffiffi þ pffiffiffi þ pffiffiffi 2, 3 3 3 3 The overall measurement uncertainty was determined without taking into account uncertainty introduced with adopted porosity of the biomass sample. 3. Conclusions Experimental methods have been developed for determining permeability coefficients and stagnant thermal conductivity of soy straw bales depending upon the porosity of the balled material. The semi-empirical correlations obtained were used to develop a detailed CFD model of straw bales combustion in cigar burners. Permeability coefficients were observed to exhibit hyperbolic dependence upon porosity.
The paper was developed through activities carried out within the scope of the following projects: “Applied research EU project Biom-Adria 2 e A Development and Improvement of Technologies, Methodologies and Tools For the Enhanced Use of Agricultural Biomass Residues“ and projects of Serbian Ministry of Science and Technological Development: III42011, TR 33042, OI 176006. References [1] Jovanovic M, Turanjanin V, Bakic V, Pezo M, Vucicevic B. Sustainability estimation of energy system options that use gas and renewable resources for domestic hot water production. Energy 2011;36:2169e75. [2] Bech N, Wolff L, Germann L. Mathematical modeling of straw bale combustion in cigar burners. Energy and Fuels 1996;10:276e83. [3] Miltner M, Makaruk A, Harasek M, Friedl A. CFD-modeling for the combustion of solid Baled biomass, Fifth international conference on CFD in the process industries CSIRO; 2006 December 13e15. Melbourne, Australia. [4] Mladenovi c R, Eri c A, Mladenovi c M, Repi c B, Daki c D. “Energy production facilities of original concept for combustion of soya straw bales”, 16th European Biomass Conference & Exhibition e From Research to Industry and Markets, Proceedings on DVD-ROM, ISBN 978-88-89407-58-1, 2e6 June 2008. Valencia, Spain. [5] Mladenovic R, Dakic D, Eric A, Mladenovic M, Paprika M, Repic B. The boiler concept for combustion of large soya straw bales. Energy 2009;34:715e23. [6] Delivand MK, Barz M, Gheewala SH. Logistics cost analysis of rice straw for biomass power generation in Thailand. Energy 2011;36. 1435e1441. [7] Kaviany M. Principles of heat transfer in porous media. New York: SpringerVerlag; 1991. [8] Nield DA, Bejan A. Convection in porous media. New York: Springer Science Business Media, Inc.; 2006. [9] Kozi c DJ, Vasiljevi c B, Bekavac V. Thermo-mechanics handbook in SI units. Belgrade: University of Belgrade, Mechanical Faculty; 1999 [in Serbian]. [10] Guide To the Expression Of Uncertainty In Measurement (GUM). BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML. International Organization of Standardization, Geneva Switzerland, 1st ed. 1993, Corrected and reprinted 1995. [11] EA 4/02 (rev.00): 1999 Expressions of The Uncertainty of Measurements in Calibration (including supplement 1 to EA-4/02)(previously EAL- R2). [12] Milin ci c D. Heat transfer. Belgrade: Academic Book; 1989 [in Serbian].