Heat-transfer enhancement for corn straw slurry from biogas plants by twisted hexagonal tubes

Applied Energy 262 (2020) 114554

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Heat-transfer enhancement for corn straw slurry from biogas plants by twisted hexagonal tubes ⁎

Jingjing Chena,b, Zhong Haia, Xiaohua Lua, Changsong Wanga, , Xiaoyan Jib, a b

T

⁎

State Key Laboratory of Material-Oriented Chemical Engineering, Nanjing Tech University, Nanjing 211816, PR China Energy Engineering, Division of Energy Science, Luleå University of Technology, 97187 Luleå, Sweden

H I GH L IG H T S

rheologies with TS = 8% were determined systematically. • Temperature-dependent twisted hexagonal tube has the highest heat-transfer performance. • The and strong shear rate at sizable radial flow causes optimal performance. • Continuous • The twisted hexagonal tube can increase the net raw biogas production by up to 17.0%.

A R T I C LE I N FO

A B S T R A C T

Keywords: Corn straw slurry Twisted hexagonal tube CFD Shear rate Waste-heat recovery Biogas production

Heat-transfer geometries that enhance heat transfer performance for slurries increase the net raw biogas production in the bio-methane process. In this study, the precise temperature-dependent rheologies of corn straw slurry with 6 and 8% total solid were determined, collected, and modeled to conduct a numerical simulation via CFD, the first instance of such research. Subsequently, the reliability of the numerical results was verified with heat-transfer experiments. The heat-transfer performances of the circular, twisted square and twisted hexagonal tubes were estimated numerically, ultimately showing that the twisted hexagonal tube performed optimally with an enhancement factor of up to 2.0 in the turbulent region, compared to the circular tube. Based on the numerical results, the mechanism of heat-transfer enhancement was revealed, showing balanced radial mixing and the near-wall shear effect that leads to a strong and continuous shear rate under a considerable radial-flow intensity. An engineering equation was obtained for the performance evaluation, and the waste-heat recovery from corn straw slurry was analyzed, showing the twisted hexagonal tube can increase the net raw biogas production by up to 17.0% compared to the circular tube.

1. Introduction Bio-methane production process from anaerobic digestion (AD) has attracted worldwide attention. The AD process shows a drastically higher potential energy output/input ratio (up to 28/1) compared to other biological and thermo-chemical conversion processes [1]. Meanwhile, the effect of methane emission on global warming is 20 times higher than that of carbon dioxide. The AD process can prevent the self-decomposition of biomass in open environments and then avoid methane emissions, and the methane byproduct can be upgraded to the commercial energy products including electricity, heat, and compressed natural gas (CNG) [2]. Lignocellulosic biomass, for example, corn straw, is an abundant, organic material needed for the AD process. It is readily available from agricultural, forestry and municipality resources.

⁎

Owing to the growing demand from agricultural and environmental industries, AD of corn straw has been paid increasing efforts and is considered the most cost-effective industrial process for the decomposition of corn straw [3]. Generally, AD processes operating at a total solid (TS) content of less than 15% are classified as liquid AD [4], and considered superior due to its high reaction rate and short retention time. In practice, for a full-scale biogas plant fed with corn straw, in order to avoid problems such as acidification [5,6] and high agitation energy [7,8], a TS around 6–8% is extensively performed. AD operates under varying thermal conditions, and heat is generally provided by burning the produced biogas. It has been extensively accepted that the rate of biogas production can be dramatically increased (up to 144%) with thermophilic fermentation at 50–55 °C [9,10]. However, for AD under the thermophilic condition, the requirement for

Corresponding authors. E-mail addresses: [email protected] (C. Wang), [email protected] (X. Ji).

https://doi.org/10.1016/j.apenergy.2020.114554 Received 3 November 2019; Received in revised form 5 January 2020; Accepted 24 January 2020 0306-2619/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclature d50 τ γ μapp k n dh ds L S δ Q̇ c Q̇ h Q̇ ṁ s ṁ w Ti,s To,s Ti,w To,w Ki U g ρs cp,s λs C Ea R

f ΔP Nug Reg η Pr H Sw q th tw Qv,s Ths,in Ths,out A Vr ΔTm ΔcHCH4 Vbiogas AD TS THT TST CT CFD ZSV CSV WHRP NRBP PIBP

average diameter of particle, μm shear stress, Pa shear rate, s−1 apparent viscosity, kg/(m·s) consistency coefficient, Pa·sn flow-behavior index hydraulic diameter of tubes, m inner diameter of shell, m length of tube, m pitch of twisted tube, m wall thickness, m heat duty of tube side, W heat duty of shell side, W average heat duty, W mass flow rate of slurry, kg/s mass flow rate of water, kg/s inlet temperature of slurry, °C outlet temperature of slurry, °C inlet temperature of water, °C outlet temperature of water, °C heat-transfer coefficient of tube side, W/(m2·K) velocity vector, m/s gravity vector, m/s2 density of slurry, kg/m3 specific heat of slurry, kJ/(kg·K) thermal conductivity, W/(m·K) constant activation energy gas constant, 8.314 J/(mol·K)

friction coefficient, dimensionless pressure drop at unit length, Pa/m generalized Nusselt number, dimensionless generalized Reynolds number, dimensionless performance evaluation criterion Prandtl number twisted ratio swirl parameter heat flux, W/m2 hydraulic retention time, 20 days operating time, h volumetric flow rate, m3/s temperature of slurry at inlet, °C temperature of slurry at outlet, °C heat exchange area, m2 volume of anaerobic reactor, m3 logarithmic mean temperature difference, °C combustion heat of methane, 39745.5 kJ/m3 biogas production, m3/day anaerobic digestion total solid, wt. % twisted hexagonal tube twisted square tube circular tube Computational Fluid Dynamics zero shear viscosity, Pa·s critical shear viscosity, Pa·s waste-heat recovery process net raw biogas production potential increasing of biogas production

the effect of rheological properties on the pretreatment [22,23] and the agitation power when mixing [24,25] at a certain temperature. Limited research has been conducted on the heat transfer owing to a lack of temperature-dependent rheology. To develop a heat exchanger for corn straw as a working fluid, its rheological properties at different temperatures must be studied. For Newtonian fluids, different special designs can be used to enhance the heat-transfer performance substantially, for example, the overlapped helical baffles in the shell side of shell-and-tube heat exchangers [26], the wavy fin in compact heat exchangers [27], and the geometry of plate heat exchangers [28]. However, all these technologies are not recommended for the fluids with solids, such as corn straw slurry from AD, owing to the fouling and blocking problems. Hence, using the channels with both continuous, smooth configurations and disturbed flow, e.g., twisting a tube with a non-circular cross-section, is an effective option. Considerable numerical and experimental studies have been reported since the first twisted-tube heat exchanger was developed in the 1980s [29] for Newtonian fluids with low viscosity including water and air [30]. Dzyubenko and Yakimenko [31] found that the thermal-hydraulic efficiency in twisted elliptical tubes is higher than that of smooth tubes. Si et al. [32] displayed a superior heattransfer performance of twisted elliptical tubes at low Reynolds numbers and twist pitches. Yang and Li [33] concluded that the secondary flow near the inner wall is the mechanism for the heat-transfer enhancement in twisted elliptical channels. Tang et al. [34] proposed a new twisted geometry, twisted tri-lobed tube, and revealed that the heat-transfer performance of the twisted tri-lobed tube was 5.4% higher than that of the twisted oval tube. Indurain et al. [35] investigated the twisted tri-lobed tube with water as a working fluid, and their numerical results show that the heat transfer can be enhanced from 22 to 105% but with the increased pressure drops of 63 and 180%, respectively, compared to the circular tubes.

direct heating to achieve and maintain the operating temperature can account for over 70% of total energy utilization [11]. Additionally, most of the heat is wasted along with discharging streams from the AD reactor. Meanwhile, to avoid cross-infection caused by pathogens and to obtain a suitable fertilizer in a biogas plant, the substrates need to be pasteurized at 70 °C for at least 1 h before entering the digestion reactors [12,13], and such a sanitation process also demands a large amount of heat. In current practice, the streams in sanitation are heated to 70 °C with steam and then cooled to 50–55 °C before entering the AD reactor, resulting in more wasted heat. Therefore, a heat-recovery process that can use low-grade heat to achieve and maintain the temperature of the AD reactor can decrease the amount of biogas used for heating and increase the net production of biogas [10,14]. It has been reported that net raw biogas production (NRBP) can be increased by 5.3–17.4 % with a waste-heat recovery process [15,16], and the efficiency strongly depends on the heat-transfer coefficient of the associated heat exchangers [14,16,17]. However, conventional heat exchangers such as shell-and-tube (circular tube) heat exchangers (STHE) and spiral-plate heat exchangers show low heat-transfer performance [14,18]. Maintenance problems including build-up of solids over time and blocking of the heat exchangers also reduce the heat-transfer efficiency when slurries are the working fluids. This leads to high investment and operating costs. These problems require new developments in heat exchangers. The construction of heat exchangers is related to its working fluid. Ninety percent of the streams in the thermal cycle of AD are slurries, which show a very different fluid behavior from that of normal working fluids. A slurry is a shear-thinning fluid, and its viscosity, or, more accurately, the rheological properties, depends on temperature and the shear rate [19] and can be hundreds of times higher than that of water when the TS of slurries exceeds 7% [20,21]. Studies have been conducted on corn straw slurry, but most of the research was focused on 2

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analyzer (S3500, Microtrac Inc., USA). The detailed information is listed in Table 1.

Recently, an increasing number of studies on the heat-transfer performance of highly viscous or non-Newtonian fluids with twisted tubes have been reported. Bhadouriya et al. [36] investigated a “model” fluid with a Prandtl number Pr of 0.7–20. It was found that the twisted square tube (TST) showed a higher heat-transfer performance with less twisted pitches S. Khoshvaght-Aliabadi et al. [37,38] compared different twisted geometries including twisted elliptical, half-circular, square, rectangular, and triangular tubes for the heat transfer of Al2O3H2O nanofluid, engine oil (Pr = 50) and ethylene glycol (Pr = 150) and found that TST showed optimal performance. Omidi et al. [39] numerically calculated the flow and heat transfer of H2O–Al2O3 nanofluid ranging from 0 to 3% inside the twisted tri-lobed tube. In this study, an effective viscosity was used for simulating heat transfer, and this viscosity was impacted by temperature, the particle size, and the volumetric fraction of nanoparticles. In our previous study [40], the twisted geometries with equilateral polygon cross-sections were screened for a highly viscous and non-Newtonian fluid (manure slurry from biogas plants), and the twisted hexagonal tube (THT) had the highest heattransfer enhancement factor. This research, however, was based on manure slurry with CFD, and it is unclear whether the research observations were universal for other slurries. Based on the literature survey, for the twisted tubes, Newtonian fluids with low and high viscosities were extensively studied, and TST was found to be the best geometry for the high viscous fluids. For non-Newtonian fluids, only manure slurry was studied numerically, and the mechanism of heattransfer enhancement is still unclear. Additionally, the effect of the enhanced performance for twisted tubes on a total thermal cycle has not been investigated in order to quantitatively illustrate the potential of using these new geometries in a biogas plant. This work was to investigate the performance of the newly designed heat exchanger with twisted tubes for the heat transfer with corn straw slurry as a working fluid, to clarify the mechanism of heat-transfer enhancement, and to study the impact of the new heat exchanger on the total thermal cycle in a biogas plant. To achieve this, the temperaturedependent rheologies of corn straw slurry with TS = 8% were determined systematically. Combined with the results at TS = 6% determined in our previous work [25], the rheological properties of corn straw slurry were correlated with the operating conditions of temperature and shear rate. Based on the obtained rheology, the performances of the heat transfer for corn straw slurry flowing in a circular tube (CT), TST, and THT were investigated numerically and validated with new experimental results. The mechanism of heat-transfer enhancement was revealed based on the numerical results. An engineering equation was obtained for the performance evaluation. The new heat exchanger with optimal geometries was further integrated into an overall thermal cycle system as a waste-heat recovery process and combined with a biogas plant in order to quantitatively illustrate the contribution of heat-transfer enhancement to NRBP.

2.2. Measurements of rheology The rheological properties were tested, as in our previous work [25], with a viscometer (DV2TLV, Brookfield Engineering Laboratories Inc., USA). During testing, corn straw slurry samples were subjected to an increasing shear rate γ from 0.1 to 100 s−1 at a steady temperature ranging from 10 to 55 °C. Each test was repeated at least five times with fresh samples. According to Eq. (1), the characteristic parameters of consistency coefficient k and flow-behavior index n were calculated. For the heat-transfer process, the upper and lower limits of apparent viscosity μapp (Eq. (2)), i.e., the zero shear viscosity (ZSV) and critical shear viscosity (CSV), showed a great impact on the precision of the numerical results [16]. Specifically, ZSV must be fixed for the convergence of governing equations, and CSV needs to be tested and modeled precisely to predict the flow and heat transfer in the viscosity-boundary layer. In this work, ZSV and CSV were determined from the measured viscosities at each temperature, correlated with a polynomial to represent the temperature-dependence, and implemented into ANSYS for the CFD calculations.

τ = k γn

μapp =

τ = kγ n − 1 γ

(1) (2)

3. CFD modeling and experimental setup of heat transfer in tubes Numerical models of heat transfer need to be established for simulations via CFD, and experiments need to be conducted to validate the simulation. 3.1. Numerical modeling of CFD Even though CFD modeling of the heat transfer for Newtonian fluid with low viscosity in circular and twisted square tubes has been studied extensively, and that for the pig manure slurries was studied in our previous work [40], CFD modeling with corn straw slurry as a working fluid in the enhanced tubes has never been studied. In the following subsections, the following concepts were described: the numerical modeling, including the details of the computational domain; the definition of the boundary conditions, in conjunction with the numerical scheme; as well as the choice of mesh, depending on the working fluid. 3.1.1. Computational domain Considering the temperature-dependent rheological properties addressed in this study, the conjugated heat-transfer process was used to study the heat transfer in different geometries. This is illustrated in Fig. 2a. More specifically, a twisted tube (TST or THT) or CT and a cylinder shell were in the same axle wire. The tube side was for the

2. Materials and measurements The rheology of non-Newtonian fluids is crucial in conducting simulations of the flow and heat transfer via CFD. However, there is a lack of quantitative effects of temperature and shearing on the rheological properties of corn straw slurry. In this work, the properties of corn straw slurry were tested through experiments, in which the materials and the methods for experimental measurements were described as follows. 2.1. Materials of corn straw slurry In this study, corn straw slurry was a mixture of corn straw and sludge inoculums. Corn straw was pretreated with the standard methods [41] and mixed with the sludge inoculums from the Jiangpu biogas plant, as shown in Fig. 1. The particle size distributions for the sludge inoculum and corn straw slurry were obtained by a particle size

Fig. 1. Sludge inoculum from Jiangpu biogas plant in China. 3

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Table 1 Loading concentration and TS for the studied corn straw slurries.

TS wt.% Loading concentration g/L Average diameter d50 μm

Sludge inoculum

Corn straw slurry

2.4 23 55.2

8.0 57 461.3

Table 2 Geometric parameter of tubes used for simulation and experiments of heat transfer.

flowing of corn straw slurry, and the geometrical characteristics are listed in Table 2. On the shell side, the heat-transfer medium (water) was flowing. Considering the manufacturing constraints of industrial heat exchangers [36], this study investigated the twisted tubes with a pitch S ranging from 0.33 to 0.66 m.

Parameter

Value

hydraulic diameter of tubes dh (m) inner diameter of shell ds (m) length of tubes L (m) torque S (m) wall thickness δ (m)

0.051 0.060 1.00 0.33, 0.50, 0.66 0.001

Table 3 Mesh-independent test with Ki. Ki W/(m2·K)

3.1.2. Boundary conditions In simulations, the inlet temperature of slurry was set to be from 10 to 55 °C, considering thermophilic fermentation and sanitation used in biogas plants. The velocity of corn straw slurry was set to fall in the range of 1.15–2.5 m/s in order to keep the flow in the tubes in turbulent regions, and the velocity of water was set to be 1.5 m/s, considering the principles of engineering [42].

Mesh density (million) Types Tetra (TST) Hybrid (THT) Hexcore (CT)

1 – – 936

3 1150 1346 898

5 1015 1213 867

6 953 1205 861

8 947 1199 –

both the computational complexity and accuracy. The computation was performed using a personal computer with 16 2.6-GHz CPUs and 64 GB of RAM. Based on the above setting, convergence was achieved within 1000 iterations, during which the normalized residual remained a constant. The computation took less than 10 h for each simulation case.

3.1.3. Solving scheme The governing equations for numerical calculation were provided in part S1 of Supplementary material. In modeling, the following assumptions were made: the fluid flow was incompressible, and the specific heat capacity and the thermal conductivity of the fluid were temperature-independent owing to the narrow range of the studied temperatures (10–55 °C). For simulations, additional physical properties [16] including density, specific heat and thermal conductivity, were used (see part S2 in Supplementary material). The CFD simulation of the heat transfer for different tubes was conducted using ANSYS 12.0. To perform the simulation, the following items were selected in Fluent: pressure-based model, segregated algorithm, QUICK scheme for solving the momentum and energy equations, PRESTO! scheme for the pressure-correction equation, and the SIMPLEC algorithm. Viscous heating was considered in all cases. Considering the turbulent flow in the range of Re = 3000–20000 and the conjugated heat transfer, k-ω SST was applied as the turbulent model for both the shell and tube sides.

3.2. Heat-transfer experiments In order to determine the flow resistance (unit pressure drop ΔP) and heat-transfer performance (heat-transfer coefficient Ki), heattransfer experiments with THT were conducted as shown in Fig. 3. The THTs with S = 0.5 m were manufactured as shown in Fig. 3a, and they were cut and put into the heat-transfer apparatus. The details of the streams and testing-points are displayed in Fig. 3b. For the cold stream on the tube side, the velocity was set in the range of 1.15–2.5 m/s in order to keep the flow at the turbulent region, and the temperature was ranging from 10 to 55 °C in order to test the heat-transfer performance comprehensively. A hot stream of water flowed in a closed circuit of the shell and thermostatic water tank at a constant temperature of 70 °C and with a velocity of 1.5 m/s in the shell. The pressure drop between the inlet and outlet of tubes was measured with a manometer to obtain ΔP in THT. In order to obtain the heat-transfer coefficient of THT, four thermocouples, with an accuracy of 0.1 °C for each, were pre-calibrated and then used to detect the inlet and outlet temperatures of tubes and shells. Eqs. (3)–(6) [36] were used to conduct data processing to obtain Ki.

3.1.4. Choice of mesh As shown in Fig. 2b, c, and d, the meshes of TST, THT, and CT were constructed with a suitable tetra, hybrid (tetra mesh for shell and hexcore mesh for tube), and hexcore grid, respectively. For heat transfer, the dense mesh of boundary layers on both the inside and outside of the tube wall was established with y+ ≈ 1 [43]. In addition, the effect of the mesh density on the simulation results was detected with five different volumes (1, 3, 5, 6, 8 million). According to the results listed in Table 3 for the mesh-independent tests, a mesh with five million for TST and a mesh with six million for THT and CT were taken considering

Qċ = ṁ s cP, s (To, s − Ti, s )

(3)

Qḣ = ṁ w cP, w (Ti, w − To, w )

(4)

Fig. 2. Geometries for simulation, a. shell and tube for conjugated heat transfer, b. mesh of twisted square tube, c. mesh of twisted hexagonal tube, d. mesh of circular tube. For the mesh in b, c, and d, the red parts represent the shell side, and the blue parts represent the tube side. 4

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Fig. 3. Details of the experimental setup, a. twisted hexagonal tubes THT (S = 0.5 m), b. schematic diagram of heat-transfer experiments.

Q̇ =

Qċ + Qḣ = KAΔTm 2

4.1. Rheology of corn straw slurry (5) In order to ensure the accuracy of testing, a pre-test was conducted at 25 °C, and the results were compared with those in previous studies [44] as well as the results for manure [19]. Subsequently, the temperature-dependent rheology of corn straw slurry was measured. The determined rheological properties together with those from our previous work [25] were correlated with the power-law equation, and the characteristic parameters of consistency coefficient k and flow-behavior index n were obtained.

where ΔTm is the logarithmic mean temperature difference for the inlet and outlet in the tube and shell sides.

1 1 1 = + +R K Ki Ko

(6)

where Ko is the heat-transfer coefficient of shell side. It was estimated with the Gnielinski’s correlation in this work. R is the wall resistance, depending on the thickness δ and the thermal conductivity λ of the wall, i.e., R = δ/λ. In this work, δ was set to be 0.001 m, and the λ of stainless steel was taken from the previous study [33] with a value of 16.5 W/(m·K). In data processing, based on the temperatures and mass flow rates detected in this work, the heat duties in the tube and shell sides were calculated with Eqs. (3) and (4). Subsequently, the total heat-transfer coefficient K was calculated with Eq. (5). The heat-transfer coefficient of tubes Ki was then obtained with Eq. (6) based on the estimated Ko, R, and K.

4.1.1. Validation of set-up and comparison The rheology of corn straw slurry with TS = 8% was determined at 25 °C and different shear rates up to 100 s−1 in this work, and the determined results were compared with the Natalia V’s correlation [44]. The comparison is presented in Fig. 4 with an average deviation of 8.74%. The consistency indicates the reliability of the experimental measurements in this work. The types of particles in slurry have a primary impact on its

4. Results and discussion As the slurry with a TS around 6–8% is extensively performed in a full-scale biogas plant, corn straw slurry with TS = 6 and 8% was selected as the lower and upper limits of rheological properties in order to conduct a comprehensive investigation for practical applications. The AD process operates under the thermostatic conditions, and thus the feeding stream at the ambient temperature needs to be heated or preheated to the required temperature of the thermophilic AD (55 °C). Therefore, the rheological properties of corn straw slurry at temperatures ranging from 10 to 55 °C were studied in this work, and the performance of the heat exchangers was modeled with CFD and validated with experiments. In addition, the mechanism of heat-transfer enhancement for corn straw slurry with THT was revealed, and engineering equations were obtained for practical applications of THT. Finally, THT was combined with a complete thermal cycle in a biogas plant in order to illustrate the potential of waste-heat recovery.

Fig. 4. Rheological behavior of corn straw and manure slurries at T = 25 °C, TS = 8% 5

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rheology at the same TS. The diameter distributions of slurries with corn straw (461.3 μm, see Table 1) and those for manure (125–500 μm [22]) are in the same order of magnitude. However, as shown in Fig. 4, the slurry mainly containing corn straw shows a higher shear stress τ at low shear rates (γ ＜ 1) and lower τ at relatively high shear rates (γ ＞ 10) compared with the slurry of manure at the same TS (8%). This observation indicates that the rheological behavior of corn straw slurry is totally different from that of manure slurry. As a result, it is necessary to establish a reliable rheological model for corn straw slurry based on the new experimental measurements.

Table 4 Rheological parameters for the slurries at different temperatures. n

μapp / Pa·s

R2

This study, Corn straw slurry TS = 8%

10 15 25 35 45 55

1.57 1.38 1.14 1.05 0.923 0.754

0.178 0.194 0.228 0.244 0.273 0.312

0.035–1.6 0.033–1.4 0.033–1.1 0.032–1.0 0.032–0.92 0.032–0.75

0.994 0.992 0.997 0.992 0.992 0.994

Corn straw slurry, TS = 6% [25]

10 55 10 55

0.556 0.407 2.37 0.229

0.276 0.292 0.394 0.604

0.020–0.56 0.016–0.41 0.15–2.4 0.037–0.23

0.988 0.998 0.960 0.960

for corn straw slurry with TS = 8%,

k = 0.01041e

1413.8 T ,

R2 = 0.979

n = 0.002848(T − 273.15) + 0.1501,

(8)

R2

= 0.989

(9)

for corn straw slurry with TS = 6%,

k = 0.05060e

678.40 T

n = 0.0003471(T − 273.15) + 0.2725

(10) (11)

As listed in Table. 3, for corn straw slurry with different TSs, the values of n are in a similar range, indicating a similar non-Newtonian behavior, while the values of k for corn slurry with TS = 6 and 8% are in the ranges of 0.407–0.556 and 0.754–1.57, respectively. Hence, the values of μapp for corn straw slurry with TS = 6 and 8% are in the ranges of 0.032–1.6 and 0.016–0.56 Pa·s, respectively. This indicates that the rheology of corn straw slurry with different TSs is different, and corn straw slurry with TS = 8% shows a wider range of viscosity compared to that with TS = 6%. Meanwhile, for corn straw slurry with TS = 8%, the calculated consistency coefficient k and the flow-behavior index n show more temperature-dependent behavior. These results indicate that the flow and heat-transfer behaviors can be completely different for corn straw slurries with TS = 6 and 8%. In addition, k of corn straw slurry with TS = 8% shows a relatively weaker decreasing trend, as the temperature increases, when compared to manure slurry with TS = 8%. However, n of corn straw slurry increases from 0.178 to 0.312 when temperature increases from 10 to 55 °C, which is half the value of manure slurry. This suggests that corn straw slurry with TS = 8% shows a relatively stronger shear-thinning behavior compared to manure slurry. Therefore, μapp of corn straw slurry with TS = 8% is much more sensitive to the shear rate than that of manure slurry in the same shear rate range. Meanwhile, the viscosities of corn straw slurry at each TS at different temperatures approach to a lower limit when γ is greater than 1000 s−1 (Fig. 5b), and the corresponding viscosities were considered

4.1.3. Characteristic parameters of rheology for CFD modeling Based on the power-law relation between μapp and γ as shown in Fig. 5b, the characteristic parameters k and n were obtained as listed in Table 4 for corn straw slurry with TS = 8%. In order to establish a temperature-dependent model of k, the Arrhenius equation (Eq. (7)) was used [19–21], and the results can be expressed as Eq. (8). The flowbehavior index n can be expressed as Eq. (9) according to previous studies [19]. Similarly, for corn straw slurry with TS = 6%, the characteristic parameters k and n were obtained according to the power-law relation with the results listed in Table 4. The temperature-dependent k and n for corn slurry with TS = 6% can be expressed as Eqs. (10) and (11), respectively. For manure slurry with TS = 8%, it has been studied in our previous work [16], and the corresponding characteristic parameters k and n are also listed in Table 4 for comparison.

Ea RT

k

Previous model [14], Manure slurry TS = 8%

4.1.2. Rheology at different temperatures The rheologies for corn straw slurry with TS = 8% at temperatures from 10 to 55 °C and the shear rate ranging from 0.1 to 100 s−1 were determined in this work, and the results are listed in Table S1. For corn straw slurry with TS = 8%, the increase in temperature obviously reduces the shear stress τ and the corresponding apparent viscosity μapp. This is because corn straw slurry is a typical lignocellulosic biomass suspension, of which the strong cohesive forces between the molecules and the cross-linked network of substrate particles can be reduced and destroyed by the improved thermal motion when the slurry is heated. As shown in Fig. 5a, a significant reduction in the shear stress up to 61.3% at low shear rates (γ ＜ 1) and down to 10.7% at high shear rates (γ ＞ 10) can be achieved when the temperature increases from 10 to 55 °C. With Eqs. (1) and (2), the relation of μapp and γ can be obtained as displayed in Fig. 5b. Based on the linear relationship of the logarithmic μapp and the logarithmic γ in Fig. 5b, it can be stated that corn straw slurry is a pseudo-plastic fluid according to the power-law model, and the temperature has a significant impact on its rheology.

ln (k ) = ln (C ) +

T / °C

(7)

°C °C °C °C °C °C

°C °C °C °C °C °C

Fig. 5. Rheological behavior of corn straw slurry with TS = 8% at different temperatures, a. shear stress vs. shear rate, b. apparent viscosity vs. shear rate. 6

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as CSVs and fitted to the polynomial equation as listed in Table 5. In addition, the values of μapp at γ = 0.1 s−1 at different temperatures were considered as ZSVs and also correlated with the polynomial equation in Table 5. Eventually, the results of k and n, as well as those for ZSV and CSV, were implemented in the numerical research program ANSYS as userdefined functions to conduct further numerical simulations for corn staw slurry with TS = 6 and 8%.

geometries for corn straw slurry with TS = 6 and 8% are presented in Fig. 7c and d. It is obvious that the heat-transfer performance of THT is enhanced more compared to CT, while TST shows no difference or even a lower value in the heat-transfer coefficient compared to CT in the region with significant turbulence. Combined with the low value of fTHT/fCT, it can be concluded that THT is the optimal geometry for corn straw slurry. In order to quantify the effective heat-transfer enhancement of the twisted geometries, a comprehensive criterion η, which considers the flow resistance f and the heat-transfer performance Nu simultaneously, was further calculated based on Eq. (15) [33]. The values of η can be used to justify the feasibility of industrial applications. Based on the calculated results of η displayed in Fig. 7e and f, TST shows η ＜ 1 at large flow regime (TS = 6%: Reg ＞ 12,000 at Pr = 500 and Reg ＞ 6000 at Pr = 700, TS = 8%: Reg ＞ 6000 at Pr = 1000 and whole turbulent range at Pr = 3000), and thus it is not suitable for corn straw slurry. Considering that η of THT is in the range of 1.4–2.0 for corn straw slurry with TS = 6 and 8% at a turbulent region of Reg = 3000–20000, THT is a good choice to effectively enhance the heat transfer in a wide range of turbulent regions. It should be pointed out here that the analysis was based on corn straw slurry with TS = 6 and 8%, however, it corresponds to the nonNewtonian fluid with shear-thinning behavior with n ranging from 0.178 to 0.312 and μapp from 0.016 to 1.6 Pa·s. In practice, the raw materials for AD processes are always changing with location, climate, economic level, and AD technology. Even considering this unpredictability, the rheology for most of the slurry is shear-thinning, and their values of n and μapp are within the range studied in this work. Moreover, it is reasonable to describe the slurries with n and μapp instead of TS. Therefore, based on the analysis and combined with the above reasoning, it can be stated that THT is suitable to enhance heat-transfer for the non-Newtonian fluid with shear-thinning behavior, and n ranging from 0.178 to 0.312, and μapp from 0.016 to 1.6 Pa·s in a wide range of turbulent regions (Reg = 3000–20000).

4.2. Heat transfer of corn straw slurry in different types of tubes As shown in the previous section, corn straw slurry is a highly nonNewtonian suspension, and its viscosity is temperature-dependent and sensitive to shear rate. For such a working fluid, twisting a tube with a non-circular cross-section can be used to optimize the field of shear rate for the slurry flowing side and thus enhance the heat-transfer performance. In our previous work, THT was chosen as the optimal geometry for manure slurry. TST has been studied by others, and thus TST and THT were chosen for this study. For comparison, CT was used as a reference. 4.2.1. Validation of simulation The simulation indicates that THT has a geometry with a high heattransfer enhancement for manure slurry in the large turbulent region compared to CT and TST according to our previous study [40]. Hence, the flow and heat-transfer experiments were carried out based on a heat exchanger with THT in order to validate the simulation results of corn straw slurry. In the experiment, unit pressure drop ΔP and heat-transfer coefficient Ki were determined. The experimental results of ΔP are presented in Fig. 6a. As the velocity of flow on the tube side, U, is increased, the pressure drop ΔP increases. The deviation of ΔP between the numerical and experimental results is in a range of 4–25 %, with the average at 10%. Meanwhile, a comparison of the heat-transfer coefficient Ki from experiments and simulations is illustrated in Fig. 6b and the deviation is in the range of 4–16 % with the average at 7%. Generally, for CFD and heat transfer experiments, the deviation between simulations and experiments below 10% represents good numerical results [45]. In this work, the average deviations of pressure drop ΔP and heat-transfer coefficient Ki between the numerical and experiments results are 10% and 7%, respectively. Therefore, the numerical results are reliable.

Pr =

f=

μapp cp

2dh ΔP ρU 2

Nug =

4.2.2. Performance of different types of tubes Corn straw slurry with TS = 6 and 8% was chosen for performance evaluation and comparison based on the numerical simulations, and the corresponding Prandtl number Pr values are in the ranges of 500–700 and 1000–3000 according to Eq. (12), respectively. Firstly, f was calculated from the unit pressure drop ΔP obtained from simulations by Eq. (13), and the results are shown in Fig. 7a and b. It has been extensively acknowledged that, for twisted tubes, even though heat transfer can be enhanced, the pressure drop is also increased owing to a higher flow resistance compared to CT. The values of f for THT and CT were similar and they are lower compared to TST at different Pr values. In order to analyze the effect of the pressure drop on the performance of the twisted tube, f of CT (fCT) was used as a reference, and the ratios of f for the twisted tubes to fCT, i.e. fTHT/fCT and fTST/fCT, were calculated. For corn straw slurry in this study, the values of fTHT/fCT and fTST/fCT fell in the ranges of 0.7–1.21 and 1.08–2.28, respectively. For comparison, the values of fTST/fCT for water from Bhadouriya [36] were in the range of 1.60–1.94. The lower values of f/fCT for corn straw slurry indicate that the strong shear-thinning behavior of slurry makes the twisted geometries, especially THT, more effective in controlling the flow resistance, compared to water. Nug was calculated from the heat-transfer coefficient Ki based on the simulations shown in Eq. (14). The results of Nug vs. Reg of different

η=

(12)

λ

(13)

Ki dhn λ

(14)

Nug / NuCT (fg / fCT )1/3

(15)

4.3. Mechanism of heat-transfer enhancement In most chemical processes, the shear rate itself is not important except as a means of increasing the heat and mass transfer, and in general, a certain degree of shearing is required to attain sufficient heat and mass transfer rates and to achieve a homogeneous distribution of the transferred components. However, for the heat-transfer process, Table 5 The polynomial equations of ZSV and CSV as the function of temperature (T) for corn straw slurries with TS = 6 and 8%. ZSV or CSV = aT3 + bT2 + cT + d

TS

7

R2

a × 109

b × 106

c × 104

d × 10

8%

ZSV CSV

−70024.06 −3.054171

65197.98 2.875454

−202753.4 −9.041767

21093.11 1.004520

0.998 0.992

6%

ZSV CSV

−836.1898 −0.7335239

906.3160 0.7947616

−3392.208 −2.966402

453.1257 0.4073429

0.993 0.990

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Fig. 6. Convective heat-transfer performance of THT with TS = 8% corn straw slurry, a. unit pressure drop in tube ΔP, b. heat-transfer coefficient of tube side Ki.

both the radial-flow intensity in the bulk flow and the viscosity in the boundary layer determine the performance of heat exchangers, and the higher the radial-flow intensity in the bulk flow and the lower the viscosity in the boundary layer, the better the heat-transfer performance. Corn straw slurry is a typical non-Newtonian fluid with high and shear-thinning viscosity, which can obstruct the heat flow through the convection and form a thick viscosity-boundary layer. For such a non-Newtonian fluid, shear rate is an important factor in determining the viscosity and subsequently evaluating the heat-transfer performance, while the shear rate depends on the velocity gradient in the flow field, especially in the boundary layer. This means that the intensity and continuity of the shear rate in the boundary layer, as well as the radialflow intensity in the bulk flow are important pieces of information for analyzing the performance of the heat exchangers. However, the direct measurement of the local velocity (e.g., the radial-flow rate) and shear rate is complex. As a result, obtaining reliable numerical results of the velocity and shear rate is a key step in revealing the mechanism of heattransfer enhancement. In this part, in order to reveal the mechanism of heat-transfer enhancement for THT, the distributions of the radial-flow rate and shear rate, especially in the near-wall region, in different tubes (i.e., THT, TST, and CT) were investigated. Based on the analysis, the mechanism for heat-transfer enhancement was revealed.

4.3.2. Mechanism analysis Generally, for the twisted geometries, the secondary flow (or swirl motion) can be easily generated, promoting radial mixing in the bulk flow and enhancing the near-wall flow to promote heat transfer [33]. For the shear-thinning fluid, e.g., corn straw slurry, the viscosity will be influenced by the shear effect, and the strong and continuous shear effect in the boundary layer can decrease the viscosity in the region. Based on the CFD results shown in Fig. 8, for all the studied geometries, it is difficult to achieve a strong and continuous shear rate in the boundary layer and a strong convection in the bulk flow simultaneously for a shear-thinning fluid. Nevertheless, for THT, the radial mixing in the bulk flow and the shear effect in the near-wall region reached an optimal condition, i.e., the intensity and continuity of the shear rate in the boundary layer are greater than that of TST, while the radial-flow intensity in the bulk flow is stronger compared to CT, and thus the overall performance of THT is better than both CT and TST. Therefore, the strong and continuous shear effect formed in the near-wall region and the considerable radial-flow intensity kept in bulk flow is the intrinsic mechanism for THT to have optimal heat-transfer performance. 4.4. Engineering equations for practical applications of THT For engineering applications, the effective shear rate γeff is an important parameter for the design of hydrodynamic and transport processes, and it depends on shear effect in the boundary layer for the flow in tubes. According to mechanism analysis in the above section, for the shear-thinning fluid (corn straw slurry), a strong and continuous shear rate appears on the inner wall of the tube, which can be considered as the average shear rate γavg for ordinary fluids in ordinary tubes. However, a strong shear rate also extends to the bulk flow owing to its twisted geometries, which has not been considered in the conventional theory. Therefore, in this work, a correction term Δγ representing the extended part of the strong shear rate was used to estimate γeff from γavg (Eq. (16)), and then the actual value of viscosity in the flowing state (μeff) can be obtained with the rheological properties and Eq. (2) for engineering applications.

4.3.1. Radial-flow intensity and shear rate distribution in tubes The contours of the shear rate distribution and the radial-flow vectors of THT were compared with those of TST and CT. On the one hand, as displayed in Fig. 8, for TST and THT, the magnitude of their radial-flow vectors are two orders’ higher than that of CT, showing the presence of a strong secondary flow in TST and THT. Since CT corresponds to that with a very high number of edges, it can be concluded that the radial-flow intensity in the bulk flow increases with decreasing the number of edges, and the radial-flow intensity for TST is stronger than THT and much stronger than CT. On the other hand, nearly 25% of the near-wall region in TST experiences a low shear effect, and a relatively strong shear effect only appears in the bulk flow that is shown as the “green ring” in Fig. 8a. However, for THT and CT, the strong shear effect is continuous along the wall as shown in Fig. 8b and c as the “red” parts. These indicate that the intensity and continuity of the shear rate in the boundary layer depend on the number of edges for the twisted tube, and they increase with increasing the number of edges. Therefore, the intensity and continuity of the shear rate in the boundary layer for CT are stronger than those for THT and much stronger than those for TST. Combining the analyses of the radial-flow intensity and shear rate in the boundary layer with the number of edges for the twisted tubes, it was found that THT has a reasonable number of edges to keep the radial-flow intensity and shear rate in the boundary in a considerable level simultaneously.

γeff = γavg − Δγ

(16)

In order to further quantify how the shear rate affects the flow and heat-transfer process, the significance of Δγ was elaborated from the comparisons of γavg (see Table S2) and the average viscosity μavg (calculated with γavg) with γeff (calculated with μeff) and μeff (see Table S2) (4.4.1), respectively, and then an empirical equation was obtained to estimate γeff for THT based on the operating conditions of U/dh and the flow-behavior index n (4.4.2). 4.4.1. Effective shear rate and viscosity in tubes Both γavg and γeff in different tubes are shown in Fig. 9, and a significant difference between γavg and γeff (i.e., Δγ) can be observed. 8

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0.10

Pr = 500, CT Pr = 500, TST Pr = 500, THT

0.05

0.00 3000

Pr = 700, CT Pr = 700, TST Pr = 700, THT

9000

0.05

0.00 3000

15000

Reg

9000

b. TS = 8 % 5000

Pr = 700, CT Pr = 700, TST Pr = 700, THT

Nug

Nug

Pr = 500, CT Pr = 500, TST Pr = 500, THT

2500

0 3000

9000

Reg

Pr = 3000, CT Pr = 3000, TST Pr = 3000, THT

2500

Pr = 1000, CT Pr = 1000, TST Pr = 1000, THT

0 3000

15000

9000

Reg

1

1

Pr = 500, TST Pr = 500, THT Pr = 700, TST Pr = 700, THT

9000

Reg

15000

d. TS = 8 % 2

η

η

c. TS = 6 % 2

0 3000

15000

Reg

a. TS = 6 % 5000

Pr = 3000, CT Pr = 3000, TST Pr = 3000, THT

Pr = 1000, CT Pr = 1000, TST Pr = 1000, THT

f

f

0.10

Pr = 1000, TST Pr = 1000, THT Pr = 3000, TST Pr = 3000, THT

0 3000

15000

9000

Reg

e. TS = 6 %

15000

f. TS = 8 %

Fig. 7. Performance of TST, THT, and CT at different flow states and TSs, a and b: the friction coefficient f; c and d: the generaized Nusselt number Nug; e and f: performance evaluation criterion η.

Therefore, it is important to have the correction of Δγ. For THT, although γavg is lower than that in CT and TST, γeff is higher in a wide range of flow regions compared to CT and TST. This relatively smaller Δγ in THT compared to CT and TST causes a higher γeff and thereby a lower viscosity of corn straw slurry in THT, which agrees with the inference from the mechanism of heat-transfer enhancement. Based on the different shear rates (i.e., γavg and γeff), the corresponding viscosities can be estimated with Eq. (2), and the results are depicted in Fig. 9b for comparison. μeff is an order higher than that estimated from γavg, further indicating that Δγ should be considered to obtain γeff for an accurate prediction of μeff in order to evaluate the heattransfer process reliably.

4.4.2. Engineering equations of heat-transfer process for THT For γeff, Metzner and Reed [46] established a relationship to consider the effects of flow-behavior index n and flow parameter U/dh on effective shear rate for non-Newtonian fluid flowing in CT as expressed in Eq. (17) based on the experimental results. Following Eqs. (16) and (17), γeff in THT for corn straw slurry with TS = 6 and 8% was correlated based on the numerical results listed in Table S2 in Supplementary material. The correlation is illustrated as Eq. (18), where 1/n represents the impact of T and U/dh is the impact of the flow and geometry on the shear rate.

U 1 U γeff = C·g ⎛ ⎞ − f ⎛ ⎞·g ⎛ ⎞ ⎝ n ⎠ ⎝ dh ⎠ ⎝ dh ⎠ ⎜

9

⎟

⎜

⎟

(17)

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a.TST

b.THT

c.CT

Fig. 8. Flow vector of radial velocity Ur and shear rate γ distribution inside different tubes for corn straw slurry (TS = 8%) at Reg = 11000.

U 1 0.0470 ⎛ U ⎞ γeff = ⎛4.281 + 2.676⎞ − 4.700·⎛ ⎞ dh ⎝n⎠ ⎝ ⎠ ⎝ dh ⎠ ⎜

⎟

⎜

0.940

TS = 6%, corn straw slurry with TS = 8% was chosen to further study δNRBP for the Boden Biogas Plant.

⎟

(18)

With the quantified effective shear rate γeff and the numerical heattransfer performance under different conditions (see Table S3), the engineering equation can be obtained as Eq. (19). The accuracy of the engineering equations was further verified with plenty of experimental results (see Table S4) with an average deviation of 9% (see section S3 in Supplementary material). Based on Eqs. (2), (18), (12), (19)–(22), the heat-transfer performance can be obtained conveniently for process evaluation.

Nug = 0.288Sw 0.483Pr 0.688, R2 = 0.990

4.5.1. Waste-heat recovery with THT A typical type of waste-heat recovery process (WHRP), as shown in Fig. 10a, is increasingly applied in biogas plants, such as Sunderland Dairy Digester System (SDDS) [48] and the biogas plants in Boden and Borås in Sweden [10]. This WHRP was selected to perform the simulation in order to illustrate the effect of heat exchangers on the overall process performance. In the biogas production process, thermophilic fermentation (at 55 °C) with a reactor volume of 3000 m3, gas production rate of 2.32 m3/(m3·day) and hydraulic retention time of 20 days were chosen. Accordingly, the volumetric flow rates of the slurry Qv,s were set in the range of 30–50 m3/h considering the proper operating time tw (3–5 h) for one AD reactor. As shown in Fig. 10a, WHRP includes two pairs of heat exchangers (HE 1–2 and HE 3–5) with the same geometries under a countercurrent condition, in which the discharged slurry from the biogas plant is used to preheat the feed stream. The stream after sanitation is used to further heat the preheated feed stream. After these heat-exchange processes, the temperature of corn straw slurry is strictly controlled at 55 °C before entering the AD reactor. The heat-transfer medium, water, is circulated in these two heat exchangers by a pump. For the sanitation of the feed stream, a boiler with HE 4 is used to heat the raw slurry to 70 °C by burning the biogas from the AD. For WHRP, in order to quantitatively describe the impact of the heat exchangers (THT and CT) on production, δNRBP defined by Eqs. (23)–(25) was calculated according to the algorithm for solving the nonlinear heat balance equations described in our previous study [16], where the heat-transfer performance of THT defined by Eqs. (18) and (19) was applied, and δNRBP/A under different operating conditions was investigated. Here A represents the total heat exchange area of the heat exchangers HE 1-HE 5. For a full-scale biogas plant, multiple reactors can be operated and

(19)

where dimensionless number —swirl parameter Sw can be expressed as Eqs. (20) [36], (21), and (22) [43,47].

Reg

Sw =

H=

(20)

H S dh

Reg =

(21)

dhn U 2 − nρs μeff

(22)

4.5. Implementation of THT in waste-heat recovery in a biogas plant For the same waste-heat recovery process with THT, apparently, the type and the total solid (TS) of fluids can affect the value of increased net raw biogas production (δNRBP). In fact, both the type of fluids and their TSs can be reflected and considered with viscosity, the higher the viscosity, the lower the heat-transfer coefficient, and the lower the value of δNRBP. Since corn straw slurry with TS = 8% shows a wider range of viscosity and covers the most part for corn straw slurry with 300 200

0.30 ȝ (In flowing state) eff

100

0.25

μ (Pa·s)

γavg(s-1)

ǻȖ 15 10

Ȗeff CT TST THT

5 0

THT CT TST

0.35

Ȗavg

4000

8000

12000

16000

0.20 0.15 0.10 0.03

ȝavg (Calculate from Ȗavg)

0.02

20000

4000

8000

12000

16000

20000

Reg

Reg

a.

b.

Fig. 9. Detailed shear behavior of TS = 8% slurry at different flow rates, a. average shear rate, b. apparent viscosity. 10

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a. Streams and units in WHRP

b. Subsequent AD reactors shearing one heat utilization system Fig. 10. Waste-heat recovery process in a biogas plant.

to calculate ΔTm considering the complete counter-current condition.

share the same heat utilization system at staggered operating times in order to maximize the overall efficiency. The subsequent AD reactors sharing one WHRP were established, as illustrated in Fig. 10b. For performance evaluation, the potential increase of biogas production VPIBP was defined as Eq. (26), and VPIBP at a unit heat exchanger area VPIBP/A was investigated. Moreover, the economic criterion, i.e., the increased profit as determined in Eq. (27), for THT and CT in WHRP was calculated and analyzed.

δNRBP =

q·tw ξ ·Δc HCH 4·Vbiogas

tw =

VPIBP =

2.00x10

THT, Qv,s=50 m3/h

VPIBP /A (m 3/m 2·year)

THT, Qv,s=37.5 m3/h

δNRBP /A (m-2)

(27)

4.5.2. Sensitivity analysis and performance comparison The investment return for the system integrated with CT and THT

where the logarithmic mean temperature difference method was used

THT, Qv,s=30 m3/h CT, Qv,s=37.5 m3/h

9.0x10-4

6.0x10-4 0.03

(26)

tw

where UPB is the unit price of biogas. In this work, the value in 2017 [49] was used, and UPB = 33 €/(MW·h)

(24)

1.2x10-3

th Vbiogas δNRBP

Increased profit = ξ ·Δc HCH 4 · VPIBP · UPB

where ξ is the methane content (volumetric) in biogas, ξ = 65%, and Vbiogas is the produced biogas per day.

1.5x10-3

(25)

where t is the operating time per year for a biogas plant, t = 7200 h/ year

(23)

q = Ki AΔTm = ρcp, s Q v, s (Ths, in − Ths, out )

Vr th·Q v, s

4 3

THT, Qv,s=50 m /h 3

THT, Qv,s=37.5 m /h 3

THT, Qv,s=30 m /h

1.75x10

4

1.50x10

4

CT, Qv,s=37.5 m3/h

4

0.04

0.05

0.06

Area ratio A/Vr (m2/m3)

1.25x10 0.004

0.07

0.006

0.008

0.010 2

0.012 3

Area ratio A/Vr (m /m )

Fig. 11. Effects of investment of heat exchanger, area ratio A/Vr and volumetric flow rate of slurry Qv,s on δNRBP in the WHRP with THT and CT, a. δNRBP at unit heat exchange area δNRBP/A; b. the potential increase of biogas production at unit heat exchange area VPIBP/A. 11

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can be defined as δNRBP/A vs. area ratio A/Vr, where δNRBP /A and A/Vr represent the unit production and costs, respectively. A higher δNRBP /A at a lower A/Vr can be considered as a better option for WHRP in biogas plants. As shown in Fig. 11a, for THT, δNRBP /A decreases with increasing A/Vr, and there is an optimal operating volumetric flow rate of slurry (Qv,s = 37.5 m3/h) under the specific conditions in this study. Meanwhile, for CT, a peak value of δNRBP /A is obtained with a large investment of heat exchangers (A/Vr = 0.59 m2/m3), and this peak value of CT is 15% lower than that of THT at the same Qv,s. δNRBP for different types of WHRP in industry or previous studies are listed in Table 6. For the WHRP with CT, the results of δNRBP obtained in this work are consistent with those from the Boden Biogas Plant and Wang et al. [50], implying the method used in this work for process evaluation is reliable. The engineering data values are slightly lower than the results from the mathematical model, which is reasonable as the practical problems such as fouling and maintenance will result in low performance. As listed in Table 6, for WHRP with THT, δNRBP can be increased to 17.0% at the same investment level (A/Vr = 0.054 m2/ m3) for corn straw slurry with TS = 8% at the Boden Biogas Plant, indicating that the performance of THT is much better compared to CT. It should be pointed out that according to the results from Zhang et al. [15], the potential δNRBP can reach 17.4% when recovering the waste heat also from the upgrading process, which is a significant increased profits for biogas plants. This further indicates that WHRP with THTs is feasible and can be integrated with upgrading systems to further improve δNRBP. When subsequent AD reactors share one heat utilization system, A/ Vr decreases by an order of magnitude, and the cost of heat exchangers in WHRP is significantly reduced. For THT, there are peak values of VPIBP/A at different A/Vr when the operating volumetric flow rate Qv,s changed, which indicates that there is an optimal point of low investment of heat exchangers for high production. Meanwhile, Qv,s = 37.5 m3/h is still the optimal value for a higher VPIBP/A. It is obvious that VPIBP/A of THT can be enhanced by 50% at a lower A/Vr (A/Vr = 0.0057 m2/m3) compared to the maximum value for CT (A/ Vr = 0.0095 m2/m3), as presented in Fig. 11b. This indicates that WHRP with THTs is more suitable for biogas plants with full-scale reactors. The increased profits of WHRP under different operating conditions are summarized in Table 7. For CT with the same A/Vr, WHRP is infeasible because low-grade heat cannot be recovered with a low heat exchange area when the heat-transfer coefficient is low. However, as illustrated in Table 7, the increased profits of WHRP with CTs can be 0.5 million €/year with a high investment of heat exchangers (A/ Vr = 0.0096), while for WHRP with THTs, the increased profits can be up to 0.78 million €/year at the optimal Qv,s, which means that WHRP with THTs can achieve 47% higher increased profit and cut down on 40% of the investment for heat exchangers compared to WHRP with CTs. As a result, with regard to investment return, THT can be used to establish a compactable, low-cost, and high-efficient heat utilization system for biogas plants.

Table 7 Increased profits from WHRP with different heat exchangers and operating conditions. Type of heat exchangers for WHRP

Qv,s m3/h

A/Vr m2/ m3

VPIBP/A m3/ (m2·year)

Increased profits with WHRP million €/year

THT

50 30 37.5 37.5 37.5

0.0050 0.0053 0.0058 0.0058 0.0096

15,067 18,126 19,747 0 13,475

0.59 0.72 0.78 0 0.53

CT

from this work combined with that from our previous study, and verified with experimental results. The mechanism of heat-transfer enhancement was revealed from radial mixing and the near-wall shear effect. An engineering equation was also obtained and combined with a complete thermal cycle in a biogas plant in order to illustrate the potential of waste-heat recovery with the twisted hexagonal tube. The determined temperature-dependent rheology of corn straw slurry with TS = 8% shows that corn straw slurry is a pseudo-plastic fluid, and the temperature has a significant impact on its rheology. The twisted hexagonal tubes are superior in heat transfer with an enhancement factor up to 2.0 for corn straw slurry, which was confirmed with the experimental results. The balanced radial mixing and the nearwall shear effect leading to a strong and continuous shear rate under considerable radial-flow intensity is the intrinsic mechanism to achieve an optimal heat-transfer performance for the twisted tubes. Using the twisted hexagonal tubes, net raw biogas production can increase by up to 17.0% and the potential profits for biogas plants can reach 0.78 million €/year with a low investment in heat exchangers. The waste-heat recovery process with a twisted hexagonal tube has a considerable advantages of low cost and high efficiency. Additionally, the established methodology, from material properties to industrial process, as well as the clarification of heat-transfer enhancement mechanism can be applied for energy savings in other thermal cycling systems with various complex fluids and heat exchangers. Possible industrial applications include food, bioethanol, and civil sludge. CRediT authorship contribution statement Jingjing Chen: Conceptualization, Methodology, Software, Writing - original draft. Zhong Hai: Validation, Data curation. Xiaohua Lu: Conceptualization, Data curation, Supervision. Changsong Wang: Investigation, Supervision. Xiaoyan Ji: Conceptualization, Visualization, Writing - review & editing, Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

5. Conclusions Acknowledgements The heat-transfer enhancement of corn straw slurry with the twisted hexagonal tube was studied numerically, with the rheology determined

This work was supported by the National Natural Science

Table 6 Comparison of δNRBP with different heat exchangers for WHRP of biogas plants.

Boden Biogas Plant Literature 1 [15] Literature 2 [50] This study

Heat exchangers for WHRP

Area ratio A/Vr, m2/m3

Increase of biogas production δNRBP %

CT CT CT CT THT

0.054 NA NA 0.054 0.054

10.0 5.3–17.4 12.0 12.8 17.0

12

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Foundation of China (Grant Nos. 21838004 and 91934302) and the Swedish Energy Agency (Grant No. 45957-1).

[25]

Appendix A. Supplementary material [26]

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2020.114554.

[27]

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