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Numerical analysis of entropy production on a LNG cryogenic submerged pump
Journal of Natural Gas Science and Engineering 36 (2016) 87e96
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Numerical analysis of entropy production on a LNG cryogenic submerged pump Hucan Hou a, Yongxue Zhang a, *, Zhenlin Li a, Ting Jiang b, Jinya Zhang a, Cong Xu c a
Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum-Beijing, Beijing 102249, China Huadian Distributed Energy Engineering Technology Co., Ltd., Beijing 100160, China c China Nuclear Power Engineering Co., Ltd., Beijing 100840, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 August 2016 Received in revised form 30 September 2016 Accepted 10 October 2016 Available online 11 October 2016
LNG cryogenic submerged pumps are the core component of LNG terminals and filling stations for mass transmission. A deep understanding of hydraulic behavior in LNG cryogenic submerged pumps is helpful to improve their performance. However, traditional analysis of hydraulic losses lacks intuitiveness. In this study, the irreversible energy loss was investigated based on entropy production theory, focusing on the magnitude and position of hydraulic loss of a two-stage LNG cryogenic submerged pump. Subsequently, a 3D steady flow field with a Reynolds stress turbulence model and energy equation model was conducted, and a UDF was used to calculate the entropy production. The results indicated that entropy production theory had advantages for evaluating the energy characteristics of the LNG pump. Turbulent dissipation and wall friction were considered to be the primary sources of generating irreversible hydraulic loss. Turbulent entropy production and wall entropy production accounted for approximately 73.25%e77.48% and 22.49%e26.72% of the entire production, respectively. At a 1.0Qd flow condition, STD and SW were 73.51% and 26.46%, respectively. The impeller at the second stage and guide vanes at the two stages (greater than 40 W/K) were the hydraulic loss domains, and the volumetric entropy production rate in impeller of the second stage was extremely high (average 10 000 W/m3K). The separation flow, shock phenomenon and vortex were considered to be hydrodynamic factors for the formation of entropy production. This research indicated that the entropy production theory can help to quantify irreversible energy loss and locate where and how it occurs, and even further to optimize pump performance. © 2016 Published by Elsevier B.V.
Keywords: LNG cryogenic submerged pump Entropy production theory Numerical simulation Energy loss
1. Introduction With the rapid growth of the Liquefied natural gas (LNG) industry worldwide, many LNG terminals have been produced in response to the growing natural gas demand (Coyle and Patel, 2005; Lovelady, 2008). As the core device, LNG cryogenic submerged pumps play the most important role in the LNG industry chain, including in liquefaction, shipping and receiving terminals. These pumps work at low temperatures, and designers consider high efficiency, low leakage and high reliability to keep the processes safe and economical. Currently, several types of cryogenic pumps, including high-pressure cryogenic pumps, liquid nitrogen
* Corresponding author. College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.jngse.2016.10.017 1875-5100/© 2016 Published by Elsevier B.V.
or helium cryogenic pumps and cryogenic submerged pumps, have been applied widely around the world (Brailovskii, 2000; Vaghela et al., 2012). Rush and Hall, 2001 discussed the typical uses of cryogenic submerged electric motor pumps built for the LNG industry and proposed various selection principles. Considering LNG pumps as one type of low specific speed centrifugal pump with a low efficiency and bad cavitation performance, Zhang et al., 2016 designed the impeller of a two-stage LNG submerged pump by a quasi-3D hydraulic design method based on S1 and S2 relative stream surface theory. Researchers worked to improve the pump anti-cavitation performance by providing a reasonable velocity moment distribution along the streamline. Investigations on LNG submerged pumps have recently drawn greater research attention. The typical single LNG submerged pump shown in Fig. 1 consists of three main components, including the inducer, impeller and guide vane. The high complexity of the pump structure makes its internal flow field fill with various types of flow behaviors, such as
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Fig. 1. Schematic of a single-stage LNG submerged pump.
boundary layer separation flow, secondary flow, recirculation flow, and so on. In addition, the present measurement and testing methods cannot accurately capture flow behaviors. Numerical simulation on the internal flow and performance of an LNG submerged pump by computational fluid dynamics (CFD) has been widely recognized and could offer enough flow field details. However, current studies mainly focus on hydraulic performance and key technologies (S. Zhu et al., 2012; Y. Zhu et al., 2012; Tan et al., 2007), and it is rare to find the distribution and characteristics of hydraulic loss for each component in the public literature, as they lack intuitiveness. As we known, pumps are always working at steady conditions. The second law of thermodynamics implies that an adiabatic and irreversible pumping process can lead to irreversible losses, i.e., hydraulic losses in fluid machinery. Entropy is a characteristic parameter that is used to describe such an irreversibility and can imply irreversible energy loss due to heat transfer and fluid viscosity. If the position and magnitude of energy loss occurring in a flow field can be captured in detail, the entire performance of a LNG submerged pump can be improved by changing geometrical parameters pointedly to obtain better flow patterns. Bejan, 1996 found the causes of entropy production during heat transfer and flow processes. Kock and Herwig, 2005, 2004 defined local entropy production methods and grouped them into four different mechanisms, including dissipation in a mean and fluctuating velocity field and heat flux in a mean and fluctuating temperature field. Hou et al., 2016 numerically analyzed the energy characteristics and entropy production distribution for an IS centrifugal pump by using the entropy production theory and believed that the exergy loss error was attributed to the high rotatability and curvature of the pump geometries in the impeller and volute. Wang et al., 2011 optimized the structural parameters of a centrifugal impeller, and the entropy production at the impeller and volute was reduced significantly. Few studies have been conducted on the entropy production of LNG submerged pumps, so the entropy production theory was first introduced for energy analysis of a two-stage LNG cryogenic submerged pump, which provides a completely new view on how to evaluate pump performance. Fig. 1 shows a single-stage LNG submerged pump consisting of an inducer and a single stage with one impeller and one guide vane. Generally, in order to reach high outlet pressure, two-stage or multi-stage LNG pumps are used. In this study, a two-stage LNG pump was considered, and a steady numerical simulation based on the Reynolds stress turbulence model and an energy equation model was used to obtain field distributions of temperature, velocity and pressure. Then, the local entropy production terms were embedded to calculate energy loss by User-defined Function (UDF). In actual LNG submerged pump operation, the temperature of the working medium changes little, and thus, entropy production due to heat transfer can be ignored (Li
et al., 2012). The flow is considered to be adiabatic, so the only contributory factor to energy dissipation is viscous dissipation and Reynolds stress (Griffin and Davies, 2004). 2. Entropy production theory Any actual irreversible physical process in energy conversion must be accompanied by energy dissipation. Researchers have determined that energy dissipation should have a relationship with entropy production. Theoretically, the flow fluid machinery, such as in a centrifugal pump, can be regarded as one type of energy conversion, which converts mechanical energy into dynamic energy and pressure energy. In this process, due to the viscous stress in the low Reynolds number region and the Reynolds stress in the high Reynolds number region, mechanical energy is inevitably converted into internal energy; this is called hydraulic loss. From the perspective of the second law of thermodynamics, entropy production is a perfect variable for measuring such hydraulic losses. As a one state variable, specific entropy has its own trans€rste portation equation for single-phase incompressible flow (Fo and Spurk, 1989).
.! vs vs vs vs q F F þu þv þw ¼ div þ þ Q r vt vx vy vz T T T2
(1)
where s is specific entropy; u, v and w are velocity components along the x, y and z directions in a Cartesian coordinate system, . respectively; q is heat flux density vector; and T is temperature. Like the Reynolds time-averaged process, the instantaneous variable can be separated into two parts, s ¼ s þ s0 , namely, the mean quantity part and the fluctuating part. Thus, the transportation equation is changed as follows.
0 .! vs vs vs vs q vu0 s0 vv0 s0 þu þv þw ¼ div r@ þ r vt vx vy vz T vx vy 1 vw0 s0 A F FQ þ þ 2 þ vz T T
(2)
In the equation above, the last two terms on the right hand side stand for the entropy production rate: the first term is the entropy production rate caused by viscous dissipation and the second term describes the finite temperature gradient due to the heat transfer process. The LNG cryogenic submerged pump investigated in this study is considered to have a constant temperature, so the entropy production rate by heat transfer is neglected. Entropy production due to viscous dissipation can be directly calculated (Gong et al., 2013). For an incompressible flow, the viscous dissipation function F is expressed.
H. Hou et al. / Journal of Natural Gas Science and Engineering 36 (2016) 87e96
"
" 2 2 # vu 2 vv vw vu vv 2 þ F ¼ 2m þ þ þm vx vy vz vy vx 2 2 # vu vw vv vw þ þ þ þ vz vx vz vy
(3)
As for turbulent flow, however, the specific entropy production rate can be separated into two terms after the Reynolds timeaveraged process: one with a mean term and the other with a fluctuating term (Kock and Herwig, 2007; Schmandt and Herwig, 2011).
Spro;D ¼ Spro;VD þ Spro;TD
(4)
where Spro,VD is the specific entropy production rate caused by time-averaged movement, called direct entropy production; Spro,TD is the specific entropy production rate caused by velocity fluctuation, called turbulent entropy production. Both terms are the local entropy production rates and can be defined as follows.
Spro;VD
Spro;TD
( " 2 2 # vu 2 vv vw vu vv 2 þ 2 ¼ þ þ þ vx vy vz vy vx T 2 2 ) vu vw vv vw þ þ þ þ vz vx vz vy
m
(5)
8 2 3 0 2 0 2 0 0 2 m < 4 vu0 2 vv vw 5 þ vu þ vv 2 ¼ þ þ T: vx vy vz vy vx
vu0 vw0 þ þ vz vx
2
vv0 vw0 þ þ vz vy
9 2 = ; (6)
For a steady CFD numerical simulation, the known velocity and temperature fields can be used to immediately determine Spro,VD. However, Spro,TD is still unknown, but may be related to the turbulence model. Kock and Herwig, 2004 proposed that this term could relate to the turbulent dissipation rate ε and the mean temperature T by all of the turbulence models in Fluent.
Spro;TD ¼
rε
(7)
T
Until now, local entropy production terms have been calculated directly by 3D steady turbulent flow numerical simulations using ANSYS 16.0-fluent. The overall entropy production of the computational domain can be calculated by volume integration. Considering the extremely steep gradient of velocity and temperature close to the wall boundary, the local entropy production rate appears to have a peak value. This value, as calculated by the Reynolds stress turbulence model, leads to unacceptable errors. Therefore, the entropy production rate in the near walls is calculated separately according to Ref. (Duan et al., 2014). Then, the corresponding exergy loss can be calculated as follows.
Z SVD ¼
Z Spro;VD dV
STD ¼
V
PVD ¼ Tr SVD
Z Spro;TD dV
V
PTD ¼ Tr STD
PW ¼ Tr SW
SW ¼
..
t$ v T
dA
(8)
A
(9)
After detailed analyses of the entropy production rate equations, the rate can be considered to be a field variable and can be calculated directly by UDF only when the 3D flow field is obtained. The
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entropy production theory has its own advantages for evaluating the hydraulic performance of fluid machinery and is presented in the following sections. Furthermore, the theory offers a quantitative analysis and a positioning analysis of energy dissipation (Gong et al., 2013). 3. Physical model and numerical method 3.1. Physical model This study uses a two-stage LNG pump as the study object; the pump was designed by quasi-3D flow theory and its impeller geometrical parameters can be found in Ref. (Zhang et al., 2016). The designed flow rate Qd is 430 m3/h, the head Hd is 256 m, the rotary speed nd is 2900 rpm, the shaft power Psd is 194.90 kW and the efficiency h is 70%. The density of LNG is r ¼ 455 kg/m3, and the viscosity m ¼ 0.139 cP. The main flow passage components are the inducer, two centrifugal impellers and two guide vanes, as shown in Fig. 2. The inducer (id) and two identical impellers (impeller in stage A and B to be shorted as impA and impB, respectively) share one common rotation axis, but the two identical guide vanes (guide vane in stage A and B to be shorted as gvA and gvB, respectively) in each stage are fixed on the pump body as stationary parts. 3.2. Grid generation and numerical settings As shown in Fig. 2, the flow domain of the LNG pump mainly consists of one inducer, two identical impellers and two identical guide vanes. Additionally, to reduce the boundary condition disturbance on the final flow field, inlet extension (ie) and outlet extension (oe) are introduced before the inducer and after the guide vane at stage B. Then, the grid on the corresponding flow domain is generated by ANSYS 16.0-meshing software in Fig. 3, and an unstructured tetrahedral grid is completed due to the high complexity and skewness of the geometry. At regions close to wall, especially on the blades or vane surfaces, the mesh refinement technique is used to capture the flow details. According to the Fluent User's manual, the yþ can reach a safe limit of 200 for the Reynolds stress turbulence model and standard wall function. Table 1 gives the average yþ of the key surfaces in the LNG pump, from which it is implied that the grid can meet the requirement of yþ. Flow in a LNG pump is complex turbulent flow with strong rotation and is commonly accompanied with separation flow. Thus, ANSYS 16.0-fluent is used to calculate the 3D turbulent flow field of the pump. The flow is assumed to be steady, and the medium LNG is viscous and incompressible. The Reynolds stress turbulence model, energy equation model and standard wall function are applied to close the RANS equations. The interactions between the rotors and stators are considered with the multiple reference frames (MRF) method. A SIMPLEC algorithm is used to calculate the coupling of pressure and velocity, and the pressure term is discretized with the PRESTO! method. The convection terms are discretized with a second order upwind scheme. The constant velocity inlet is set as inlet boundary condition and the outflow assuming to be fully developed flow is designed as outlet boundary condition. The nonslip and adiabatic boundary condition is given at the solid walls. The convergence criterion of the numerical calculation is set as a residual of 1e-4. 3.3. Grid independence investigation The grid independence was investigated at the designed flow condition shown in Table 2. The computational domain at each grid scheme keeps similar proportions of the grid number. The head and
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Fig. 2. Flow domains of the two-stage LNG pump.
Fig. 3. Calculation grid.
3.4. Performance comparison between the numerical and experimental results
Table 1 Average yþ of important surfaces. Regions
Average value
Regions
Average value
Inlet extension Inducer Impeller A Guide vane A
7.57 62.25 127.91 130.26
Impeller B Guide vane B Outlet extension
142.17 129.45 20.76
Table 2 Grid independence investigation. Schemes
Grid number (/106)
Efficiency h (%)
Error (%)
Head H (m)
Error (%)
1 2 3 4 5
1.87 3.56 5.40 6.79 8.21
68.98 67.13 66.23 66.03 65.82
1.85 0.90 0.20 0.21
268.42 261.55 258.61 257.96 257.27
2.63 1.14 0.25 0.27
efficiency are chosen to evaluate the effect of the grid size on the final solution. With an increasing grid number, the head and efficiency change very little and the error between each scheme is less than 2%. Thus, it is considered that further increasing the grid number has no effect on the calculation result. Grid scheme 4, with a total grid number of 6.79 million, is used for the numerical calculations. The simulation is performed on a workstation with 2 CPUs of Intel Xeon 2.4 GHz and RAM of 32 GB, and it usually takes about 11 h to finish a common case.
The hydraulic performance is calculated at eight flow rate conditions from 0.7Qd to 1.4Qd. The corresponding formulas for the head and efficiency are shown below.
H ¼ ðp2 p1 Þ=rg
(10)
h ¼ hh hm hv
(11)
where p1 and p2 stand for total pressure at the pump inlet and outlet, respectively; H is the head; h is the efficiency; hh ¼ rgQH/Mu is the hydraulic efficiency; hm ¼ 1e0.07(0.01ns)1.18 is the mechanical efficiency and hv ¼ 1e0.028(0.01ns)0.6 is the leakage efficiency (Zhang et al., 2016). The performance comparison between the numerical and experimental results is shown in Fig. 4. Generally, the head and shaft power curves by numerical calculations are in good agreement with the experimental results. The errors between the numerical and experimental results are relatively small. At the designed flow rate condition, the head error is only 1.02% and the shaft power error is 2.53%, which implies that the numerical simulation has enough degree of credibility. Meanwhile, the hydraulic efficiency curve and overall efficiency calculated by empirical formulas are also presented. Obviously, the hydraulic efficiency curve is located higher than the experimental curve in the figure because the mechanical efficiency and leakage efficiency are not considered. Taking the empirical formulas into consideration for
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the overall efficiency, the relative error still exists, but remains less than 5%, which is acceptable in the industry application described in Ref. (Zhang et al., 2016). 4. Results analysis based on the entropy production theory 4.1. Distribution of entropy production in a LNG pump for various flow conditions Fig. 5 presents the entropy production of each part for different flow rate conditions as calculated by the entropy production theory. Overall, the entropy production for all of the pump parts (“overall” curve) first decreases smoothly and then increases rapidly. At roughly the designed flow rate condition 1.0Qd, the entropy production is relatively low and the “overall” curve is much smoother, which corresponds to the smooth efficiency vs. flow rate curve described in Section 3.4. Fig. 5 indicates that for different pump domains, the amount of entropy production increases from part ie, id, impA, oe, impB, and gvB to part gvA. The entropy production in part ie, id and impA is relatively small (less than 10 W/K), while it is quite high in part impB, gvB and gvA (greater than 40 W/K). These sections produce the greatest flow in the overall flow passage. Curves for part gvA and gvB are more similar for the quantity of entropy production. The entropy production occurring in part impB is greater than that in part impA. Thus, the hydraulic loss in the LNG pump is mainly dissipated in the impellers and guide vanes; it tends occur more in stage B. It can be said that the guide vanes and the impeller at stage B determine the performance of the two-stage LNG pump and therefore should obtain a greater amount of attention during the designing or matching processes. In addition, the variation trend of entropy production for each part is not the same. The flow rate has little effect on part ie, id and impA. Instead, the entropy production in part oe and gvB slowly grows with the increasing flow rate, and it smoothly decreases with the increasing flow rate rise of part impB. Compared with the 0.7Qd condition, entropy production is increased by 93.68% for part gvB and 413.89% for part oe and decreased by 38.47% for part impB under the 1.4Qd condition. 4.2. Volumetric entropy production rate at parts for various flow conditions The volumetric entropy production rate is considered to be an
Fig. 5. Entropy production versus the flow rate conditions.
important variable to weigh the ability to generate irreversible energy loss. Fig. 6 shows the volumetric entropy production rate of different parts of the LNG pump for flow rate conditions from 0.7Qd to 1.4Qd. In part impB, the volumetric entropy production rate is the result of its entropy production divided by its volume. Specially, the “average” curve represents the result of the total entropy production in the pump divided by the entire pump volume under each flow condition, indicating the average level of irreversibility. Obviously from Fig. 6, all of the curves have the same shape as the curves in Fig. 5, but with different values. In all of the flow rate conditions, the average volumetric entropy production rate for the entire pump is approximately 2300 W/m3K. The average level for parts gvA, gvB and impB are 3800 W/m3K, 3600 W/m3K and 10 000 W/m3K, respectively. Particularly worth mentioning is part impB, whose average level is the sum total of that of the other parts. It can be concluded that part impB is where most of the irreversible energy loss is generated, followed by parts gvA and gvB, because the volumetric entropy production rates for the other parts are greater than the pump average level. Meanwhile, the mismatch between impB and gvA or gvB is quite apparent in the current pump geometry. To improve pump performance, the guide vanes and impeller at stage B should be designed to match, especially in impB. There are two feasible schemes to achieve this matching. One simple scheme is a multi-
Fig. 4. Performance comparison between the numerical and experimental results.
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Fig. 6. Volumetric entropy production rate versus flow rate conditions.
Fig. 7. Proportion of different entropy production versus the flow conditions.
stage matching design accomplished by adjusting the geometrical parameters of the stationary guide vanes or optimizing the clocking effect of each component. The other scheme is based on the hierarchical design of individually rotational impellers in later stages. Therefore, it can be concluded that the entropy production theory has its own advantages for localizing the location at which irreversible losses occur and weighing how serious the losses are quantitatively.
shaft power subtracted by the effective energy contributing to the pump head. As Fig. 8 shows, the average exergy loss calculated by the entropy production theory is 22.27 kW. The average energy loss calculated by the pressure drop method is 48.85 kW. Among all of the flow conditions, the exergy loss and energy loss perform in a similar variation trend, but the former is more stable and smoother. Meanwhile, the proportion between the two methods ranges from 43.16% to 47.93%, and the curve is relatively stable.
4.3. Analysis of various types of entropy production for different flow conditions
5. Flow field analysis of energy loss
Local entropy production is mainly divided into the following three types: direct entropy production due to viscous dissipation, turbulent entropy production due to turbulent dissipation and wall entropy production due to the boundary layer effect. To obtain a better understanding of the entropy production composition for various flow conditions, the proportion of each type of entropy production is presented in Fig. 7. The figure shows that direct entropy production accounts for only 0.04% (less than 0.1 W/K) of the entire production at all of the flow conditions, which is extremely small. The effect of the flow rate on viscous dissipation is neglected in this study. Instead, the effects of the flow rate on wall entropy production and turbulent entropy production are evident. Turbulent entropy production is almost three times greater than wall entropy production. The proportion of wall entropy production ranges from 22.49% to 26.72% and that of turbulent entropy production ranges from 73.25% to 77.48%. Thus, turbulent dissipation and wall friction are considered to be the main factors in generating irreversible energy loss, i.e., hydraulic loss in fluid machinery. At the designed flow condition 1.0Qd, STD and SW are 73.51% and 26.46%, respectively. Moreover, the wall entropy production grows smoothly first and then decreases with an increasing flow rate, while the turbulent entropy production first decreases and then increases. At the designed flow condition, both rates reach the greatest values, and the corresponding curves become more flat.
Compared with the traditional analysis method of pressure and velocity fields, the entropy production approach for analyzing energy loss is more intuitive, which helps to better understand complex flow and accurately locate where and how hydraulic losses occur. To locate the flow features in detail, the distribution of the volumetric entropy production rate is presented combined with a streamline or velocity vector distribution to explain the hydrodynamic factors of the hydraulic loss. As shown in Fig. 7, direct entropy production accounts for very little; thus, the visualization of the volumetric entropy production rate is mainly studied for turbulent and wall entropy production. Moreover, the volumetric entropy production rate in impB, gvA and gvB is relatively high, and
4.4. Energy loss analysis by entropy production and pressure drop methods Fig. 8 shows the energy loss calculated by entropy production theory and traditional pressure drop method, and the proportion between the two methods is also presented. The exergy loss is the result of PVD, PTD and PW, while the other loss is the direct result of
Fig. 8. Energy loss versus the flow conditions.
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the distributions are taken as examples to explain where and how the hydraulic loss occurs. 5.1. Distribution of the entropy production rate at the pump midspan section Fig. 9 shows the distribution of the turbulent volumetric entropy production rate at the mid-span section of the LNG pump under the 1.0Qd flow condition. The turbulent volumetric entropy production rate in impB, gvA and gvB is much higher than the others. Similarly, these parts are the main sources of hydraulic loss. Especially in impB, a large exergy loss region can be observed at the inlet close to the shroud wall. Additionally, the volumetric entropy production rate at parts gvA and gvB are at the same level, but the rate is hard to detect at parts impA and id. As shown in Fig. 10, the distribution of the wall entropy production rate at the mid-span section is also presented. Unlike the turbulent entropy production rate distribution, the wall entropy production rate at the guide vanes is quite small. On the contrary, the rate is relatively high at id, impA and impB, and large areas are observed close to the trailing edges or shroud sides because the wall friction induces entropy production, which is proportional to the velocity or shear stress at the near wall. The relative velocities at the shroud sides of id and the trailing edges of impA and impB are quite large. The average wall entropy production rate is 8.90 W/ m2K for id, 9.12 W/m2K for impA and 14.25 W/m2K for impB. 5.2. Distribution of the volumetric entropy production rate at impB The contour of the turbulent volumetric entropy production rate and streamlines at impB are presented under the 1.0Qd flow condition in Fig. 11. Obviously, the turbulent dissipation occurring in the blade suction side is much more serious than in the pressure side. A large loss area is observed at the leading edge close to the shroud wall. Meanwhile, to analyze the hydrodynamic factors causing the hydraulic losses, the streamlines inside the impB flow
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passage are also presented. It is found that the large loss region is always accompanied by one large vortex, as shown in Fig. 11 (b). The shock in the leading region gives rise to flow separation and, combined with the adverse pressure gradient effect, a large vortex is formed downstream that sparks the obvious hydraulic loss. This explains why the volumetric entropy production rate at the blade suction side is relatively high. 5.3. Comparative analysis of entropy production rate for impellers between stages From the analysis above, the entropy production occurring in the impeller at stage B is much higher than that at stage A. The turbulent volumetric entropy production rate and wall entropy production rates at part impA and impB are presented in Fig. 12, and the streamline and skin friction coefficient distributions are also displayed. Overall, the entropy production for impB is higher than that for impA from the perspective of turbulent entropy production or wall entropy production. It can be observed that the volumetric entropy production rate in impA is hard to observe in Fig. 12 (a), but it is obvious in impB at the same order of magnitude. The streamline distributions in Fig. 12 (b) imply that more vortexes appear in impB than in impA, which is the main reason for the high turbulent entropy production rate in impB. Of course, the shock phenomenon at the leading edge is also a production factor according to Fig. 10. The wall entropy production rate and skin friction coefficient are also given in Fig. 12 (c) and (d). It can be clearly seen that the wall entropy production rate in impB is slightly higher than that in impA, which is attributed to the friction close to the wall. Apparently, the distribution of the skin friction coefficient is very similar to the wall entropy production in the contour. Thus, high wall friction induces high entropy production. 5.4. Distribution of the volumetric entropy production rate at gvB Fig. 13 shows the contour of the turbulent volumetric entropy
Fig. 9. Contour of turbulent volumetric entropy production rate at the mid-span section.
Fig. 10. Contour of wall entropy production rate at the mid-span section.
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Fig. 11. Contour of volumetric entropy production rate and streamlines at impB.
Fig. 12. Comparative analysis of the entropy production rate between impellers.
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Fig. 13. Contour of the volumetric entropy production rate and streamlines at gvB.
production rate and the streamlines at gvB as well as the velocity vectors near the leading edge of each vane under 1.0Qd flow conditions. It is observed that the volumetric entropy production rate reaches the peak value at the leading edge of the outside guide vanes. The production rate is greatest at the flow passage and the shroud side of the inner guide vane as well. Meanwhile, the streamlines inside the inner flow passage imply that there is a strong flow vortex in each channel. The shock phenomenon also appeared close to the leading edge region. The flow angle and vane setting angle differences induce flow separation and compel disorderly flow. Thus, the volumetric entropy production rate in these regions is relatively high. 6. Conclusions Based on the entropy production theory, the energy characteristics of an LNG cryogenic submerged pump are investigated by means of numerical simulation in this study. A 3D steady turbulent flow field was calculated for eight flow conditions with a Reynolds turbulence model and an energy equation model. Subsequently, the local entropy production terms were embedded into software codes to analyze the energy loss. The accuracy of the numerical results was validated by experimental data, and many important conclusions can be drawn. a. Hydraulic loss mainly occurred in the guide vanes and impeller at stage B. In the LNG pump in all flow conditions, the entropy production of parts gvA, gvB and impB is high (greater than 40 W/K), while the production is relatively low (less than 10 W/K)
in the other domains. The entropy production curves for gvA and gvB are similar. b. The impeller at stage B is the most serious place for irreversible losses to occur. The volumetric entropy production rate in impB is extremely high (10 000 W/m3K) and is nearly the sum total of all of the other parts. In the current pump geometry, the mismatch between impB and gvA or gvB is quite apparent, indicating that the entropy production theory can be used to determine the location at which irreversible losses occur and weigh how serious they are quantitatively. c. Direct entropy production is extremely small compared with turbulent and wall entropy production, which are neglected in this study. Turbulent entropy production and wall entropy production account for the overall production at roughly 73.25%e77.48% and 22.49%e26.72%, respectively. Turbulent entropy production is practically three times greater than wall entropy production. At the 1.0Qd flow condition, STD and SW are 73.51% and 26.46%, respectively. d. The exergy loss and energy loss display a similar variation trend in the overall flow conditions; however, the former accounts for more than 43.16%e47.93% of the losses. e. From the flow field analysis, the separation flow, shock phenomenon and vortex are the hydrodynamic factors that produce irreversible energy loss. These factors induce a relatively high volumetric entropy production rate. Thus, the entropy production theory can be an effective way to capture bad flows and help locate where and how they occur. Furthermore, this theory can help to further optimize pump performance using the entropy production minimization principle.
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Acknowledgements
Subscripts & Superscripts
This work was supported by National Natural Science Foundation of China (Grant No. 51209217) and the Science Foundation of China University of Petroleum, Beijing (No. 2462015YQ0411).
ðÞ ()TD ()W ()’ ()VD
mean component about turbulent dissipation about wall fluctuating component about viscous dissipation
Nomenclature A H M ns p2 Ps Q .
q S Spro, ~ T uvw x, y, z g Hd nd p1 P Psd Qd s Spro t Tr V ! v
area head torque specific speed outlet total pressure shaft power flow rate heat flux density vector entropy production volumetric entropy production rate temperature velocity component coordinate gravity acceleration designed head rotary speed inlet total pressure exergy loss designed shaft power designed flow rate specific entropy total entropy production time ambient temperature volume wall velocity vector
Greek symbols ε turbulent dissipation rate hh hydraulic efficiency hv leakage efficiency r density F viscous dissipation term u angle velocity h efficiency hm mechanical efficiency m molecular viscosity t shear stress FQ entropy production term
References Bejan, A., 1996. Entropy minimization: the new thermodynamics of finite-size devices and finite-time processes. Appl. Phys. 79, 1191e1218. Brailovskii, Y., 2000. High-pressure pumps for cryogenic liquids: problems and prospects. Chem. Pet. Eng. 36, 90e93. Coyle, D.A., Patel, V., 2005. Processes and pump services in the LING industry. In: Texas A & M University International Pump Users Symposium, TAMU Pump Show, pp. 179e185. Duan, L., Wu, X., Ji, Z., 2014. Application of entropy generation method for analyzing energy loss of cyclone separator. CIESC J. 65, 583e592 (In Chinese). €rste, J., Spurk, J., 1989. Stro € mungslehre. Fo Gong, R., Wang, H., Chen, L., Li, D., Zhang, H., Wei, X., 2013. Application of entropy production theory to hydro-turbine hydraulic analysis. Sci. China Technol. S. C. 56, 1636e1643. Griffin, P., Davies, M., 2004. Aerodynamic entropy generation rate in a boundary layer with high free stream turbulence. J. Fluid Eng. 126, 700e703. Hou, H., Zhang, Y., Li, Z., 2016. A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method. Therm. Sci. 143. Kock, F., Herwig, H., 2007. Direct and indirect methods of calculating entropy generation rates in turbulent convective heat transfer problems. Heat. Mass Trans. 43, 207e215. Kock, F., Herwig, H., 2005. Entropy production calculation for turbulent shear flows and their implementation in CFD codes. Int. J. Heat. Fluid. Fl 26, 672e680. Kock, F., Herwig, H., 2004. Local entropy production in turbulent shear flows: a high-Reynolds number model with wall functions. Int. J. Heat. Mass Tran. 47, 2205e2215. Li, C., Yin, P., Ye, X., Zhang, L., 2012. Effect of abnormal blade incidence on internal entropy generation in axial-flow fans. J. Soc. Power Eng. 12, 947e953 (In Chinese). Lovelady, J., 2008. LNG pump applications with variable speed motor controls. In: Topical Conference on Natural Gas Utilization. American Institute of Chemical Engineers, New Orleans, La, pp. 152e159. Rush, S., Hall, L., 2001. Tutorial on cryogenic submerged electric motor pumps. In: International Pump Users Symposium, pp. 101e107. Schmandt, B., Herwig, H., 2011. Internal flow losses: a fresh look at old concepts. J. Fluid Eng. 133, 051201. Tan, H., Li, Y., Liang, Q., Li, H., 2007. Key technologies and research schemes for submerged pumps for liquefied natural gas. Mod. Chem. Ind. 12, 52e57 (In Chinese). Vaghela, H., Banerjee, J., Naik, H., Sarkar, B., 2012. Cryogenic pump at 4 K temperature level-basic hydro-dynamic design approach. Indian J. Cryog. 37, 134e139. Wang, S., Zhang, L., Ye, X., Wu, Z., 2011. Performance optimization of centrifugal fan based on entropy generation theory. Proc. CSEE 11, 86e91 (In Chinese). Zhang, J., Xu, C., Zhang, Y., Zhou, X., 2016. Quasi-3D hydraulic design in the application of an LNG cryogenic submerged pump. J. Nat. Gas. Sci. Eng. 29, 89e100. Zhu, S., Yuan, C., Zhuang, M., Lu, X., Liu, X., 2012. Hydraulic characterization of partial emission cryogenic nitrogen pump. Cryogenics 4, 34e37. Zhu, Y., Zhang, W., Wang, X., 2012. Research and development of LNG submerged pump for LNG car gas station. Mech. Sci. Technol. Aerosp. Eng. 31, 163e166.
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Numerical analysis of entropy production on a LNG cryogenic submerged pump Hucan Hou a, Yongxue Zhang a, *, Zhenlin Li a, Ting Jiang b, Jinya Zhang a, Cong Xu c a
Beijing Key Laboratory of Process Fluid Filtration and Separation, China University of Petroleum-Beijing, Beijing 102249, China Huadian Distributed Energy Engineering Technology Co., Ltd., Beijing 100160, China c China Nuclear Power Engineering Co., Ltd., Beijing 100840, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 August 2016 Received in revised form 30 September 2016 Accepted 10 October 2016 Available online 11 October 2016
LNG cryogenic submerged pumps are the core component of LNG terminals and filling stations for mass transmission. A deep understanding of hydraulic behavior in LNG cryogenic submerged pumps is helpful to improve their performance. However, traditional analysis of hydraulic losses lacks intuitiveness. In this study, the irreversible energy loss was investigated based on entropy production theory, focusing on the magnitude and position of hydraulic loss of a two-stage LNG cryogenic submerged pump. Subsequently, a 3D steady flow field with a Reynolds stress turbulence model and energy equation model was conducted, and a UDF was used to calculate the entropy production. The results indicated that entropy production theory had advantages for evaluating the energy characteristics of the LNG pump. Turbulent dissipation and wall friction were considered to be the primary sources of generating irreversible hydraulic loss. Turbulent entropy production and wall entropy production accounted for approximately 73.25%e77.48% and 22.49%e26.72% of the entire production, respectively. At a 1.0Qd flow condition, STD and SW were 73.51% and 26.46%, respectively. The impeller at the second stage and guide vanes at the two stages (greater than 40 W/K) were the hydraulic loss domains, and the volumetric entropy production rate in impeller of the second stage was extremely high (average 10 000 W/m3K). The separation flow, shock phenomenon and vortex were considered to be hydrodynamic factors for the formation of entropy production. This research indicated that the entropy production theory can help to quantify irreversible energy loss and locate where and how it occurs, and even further to optimize pump performance. © 2016 Published by Elsevier B.V.
Keywords: LNG cryogenic submerged pump Entropy production theory Numerical simulation Energy loss
1. Introduction With the rapid growth of the Liquefied natural gas (LNG) industry worldwide, many LNG terminals have been produced in response to the growing natural gas demand (Coyle and Patel, 2005; Lovelady, 2008). As the core device, LNG cryogenic submerged pumps play the most important role in the LNG industry chain, including in liquefaction, shipping and receiving terminals. These pumps work at low temperatures, and designers consider high efficiency, low leakage and high reliability to keep the processes safe and economical. Currently, several types of cryogenic pumps, including high-pressure cryogenic pumps, liquid nitrogen
* Corresponding author. College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing 102249, China. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.jngse.2016.10.017 1875-5100/© 2016 Published by Elsevier B.V.
or helium cryogenic pumps and cryogenic submerged pumps, have been applied widely around the world (Brailovskii, 2000; Vaghela et al., 2012). Rush and Hall, 2001 discussed the typical uses of cryogenic submerged electric motor pumps built for the LNG industry and proposed various selection principles. Considering LNG pumps as one type of low specific speed centrifugal pump with a low efficiency and bad cavitation performance, Zhang et al., 2016 designed the impeller of a two-stage LNG submerged pump by a quasi-3D hydraulic design method based on S1 and S2 relative stream surface theory. Researchers worked to improve the pump anti-cavitation performance by providing a reasonable velocity moment distribution along the streamline. Investigations on LNG submerged pumps have recently drawn greater research attention. The typical single LNG submerged pump shown in Fig. 1 consists of three main components, including the inducer, impeller and guide vane. The high complexity of the pump structure makes its internal flow field fill with various types of flow behaviors, such as
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Fig. 1. Schematic of a single-stage LNG submerged pump.
boundary layer separation flow, secondary flow, recirculation flow, and so on. In addition, the present measurement and testing methods cannot accurately capture flow behaviors. Numerical simulation on the internal flow and performance of an LNG submerged pump by computational fluid dynamics (CFD) has been widely recognized and could offer enough flow field details. However, current studies mainly focus on hydraulic performance and key technologies (S. Zhu et al., 2012; Y. Zhu et al., 2012; Tan et al., 2007), and it is rare to find the distribution and characteristics of hydraulic loss for each component in the public literature, as they lack intuitiveness. As we known, pumps are always working at steady conditions. The second law of thermodynamics implies that an adiabatic and irreversible pumping process can lead to irreversible losses, i.e., hydraulic losses in fluid machinery. Entropy is a characteristic parameter that is used to describe such an irreversibility and can imply irreversible energy loss due to heat transfer and fluid viscosity. If the position and magnitude of energy loss occurring in a flow field can be captured in detail, the entire performance of a LNG submerged pump can be improved by changing geometrical parameters pointedly to obtain better flow patterns. Bejan, 1996 found the causes of entropy production during heat transfer and flow processes. Kock and Herwig, 2005, 2004 defined local entropy production methods and grouped them into four different mechanisms, including dissipation in a mean and fluctuating velocity field and heat flux in a mean and fluctuating temperature field. Hou et al., 2016 numerically analyzed the energy characteristics and entropy production distribution for an IS centrifugal pump by using the entropy production theory and believed that the exergy loss error was attributed to the high rotatability and curvature of the pump geometries in the impeller and volute. Wang et al., 2011 optimized the structural parameters of a centrifugal impeller, and the entropy production at the impeller and volute was reduced significantly. Few studies have been conducted on the entropy production of LNG submerged pumps, so the entropy production theory was first introduced for energy analysis of a two-stage LNG cryogenic submerged pump, which provides a completely new view on how to evaluate pump performance. Fig. 1 shows a single-stage LNG submerged pump consisting of an inducer and a single stage with one impeller and one guide vane. Generally, in order to reach high outlet pressure, two-stage or multi-stage LNG pumps are used. In this study, a two-stage LNG pump was considered, and a steady numerical simulation based on the Reynolds stress turbulence model and an energy equation model was used to obtain field distributions of temperature, velocity and pressure. Then, the local entropy production terms were embedded to calculate energy loss by User-defined Function (UDF). In actual LNG submerged pump operation, the temperature of the working medium changes little, and thus, entropy production due to heat transfer can be ignored (Li
et al., 2012). The flow is considered to be adiabatic, so the only contributory factor to energy dissipation is viscous dissipation and Reynolds stress (Griffin and Davies, 2004). 2. Entropy production theory Any actual irreversible physical process in energy conversion must be accompanied by energy dissipation. Researchers have determined that energy dissipation should have a relationship with entropy production. Theoretically, the flow fluid machinery, such as in a centrifugal pump, can be regarded as one type of energy conversion, which converts mechanical energy into dynamic energy and pressure energy. In this process, due to the viscous stress in the low Reynolds number region and the Reynolds stress in the high Reynolds number region, mechanical energy is inevitably converted into internal energy; this is called hydraulic loss. From the perspective of the second law of thermodynamics, entropy production is a perfect variable for measuring such hydraulic losses. As a one state variable, specific entropy has its own trans€rste portation equation for single-phase incompressible flow (Fo and Spurk, 1989).
.! vs vs vs vs q F F þu þv þw ¼ div þ þ Q r vt vx vy vz T T T2
(1)
where s is specific entropy; u, v and w are velocity components along the x, y and z directions in a Cartesian coordinate system, . respectively; q is heat flux density vector; and T is temperature. Like the Reynolds time-averaged process, the instantaneous variable can be separated into two parts, s ¼ s þ s0 , namely, the mean quantity part and the fluctuating part. Thus, the transportation equation is changed as follows.
0 .! vs vs vs vs q vu0 s0 vv0 s0 þu þv þw ¼ div r@ þ r vt vx vy vz T vx vy 1 vw0 s0 A F FQ þ þ 2 þ vz T T
(2)
In the equation above, the last two terms on the right hand side stand for the entropy production rate: the first term is the entropy production rate caused by viscous dissipation and the second term describes the finite temperature gradient due to the heat transfer process. The LNG cryogenic submerged pump investigated in this study is considered to have a constant temperature, so the entropy production rate by heat transfer is neglected. Entropy production due to viscous dissipation can be directly calculated (Gong et al., 2013). For an incompressible flow, the viscous dissipation function F is expressed.
H. Hou et al. / Journal of Natural Gas Science and Engineering 36 (2016) 87e96
"
" 2 2 # vu 2 vv vw vu vv 2 þ F ¼ 2m þ þ þm vx vy vz vy vx 2 2 # vu vw vv vw þ þ þ þ vz vx vz vy
(3)
As for turbulent flow, however, the specific entropy production rate can be separated into two terms after the Reynolds timeaveraged process: one with a mean term and the other with a fluctuating term (Kock and Herwig, 2007; Schmandt and Herwig, 2011).
Spro;D ¼ Spro;VD þ Spro;TD
(4)
where Spro,VD is the specific entropy production rate caused by time-averaged movement, called direct entropy production; Spro,TD is the specific entropy production rate caused by velocity fluctuation, called turbulent entropy production. Both terms are the local entropy production rates and can be defined as follows.
Spro;VD
Spro;TD
( " 2 2 # vu 2 vv vw vu vv 2 þ 2 ¼ þ þ þ vx vy vz vy vx T 2 2 ) vu vw vv vw þ þ þ þ vz vx vz vy
m
(5)
8 2 3 0 2 0 2 0 0 2 m < 4 vu0 2 vv vw 5 þ vu þ vv 2 ¼ þ þ T: vx vy vz vy vx
vu0 vw0 þ þ vz vx
2
vv0 vw0 þ þ vz vy
9 2 = ; (6)
For a steady CFD numerical simulation, the known velocity and temperature fields can be used to immediately determine Spro,VD. However, Spro,TD is still unknown, but may be related to the turbulence model. Kock and Herwig, 2004 proposed that this term could relate to the turbulent dissipation rate ε and the mean temperature T by all of the turbulence models in Fluent.
Spro;TD ¼
rε
(7)
T
Until now, local entropy production terms have been calculated directly by 3D steady turbulent flow numerical simulations using ANSYS 16.0-fluent. The overall entropy production of the computational domain can be calculated by volume integration. Considering the extremely steep gradient of velocity and temperature close to the wall boundary, the local entropy production rate appears to have a peak value. This value, as calculated by the Reynolds stress turbulence model, leads to unacceptable errors. Therefore, the entropy production rate in the near walls is calculated separately according to Ref. (Duan et al., 2014). Then, the corresponding exergy loss can be calculated as follows.
Z SVD ¼
Z Spro;VD dV
STD ¼
V
PVD ¼ Tr SVD
Z Spro;TD dV
V
PTD ¼ Tr STD
PW ¼ Tr SW
SW ¼
..
t$ v T
dA
(8)
A
(9)
After detailed analyses of the entropy production rate equations, the rate can be considered to be a field variable and can be calculated directly by UDF only when the 3D flow field is obtained. The
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entropy production theory has its own advantages for evaluating the hydraulic performance of fluid machinery and is presented in the following sections. Furthermore, the theory offers a quantitative analysis and a positioning analysis of energy dissipation (Gong et al., 2013). 3. Physical model and numerical method 3.1. Physical model This study uses a two-stage LNG pump as the study object; the pump was designed by quasi-3D flow theory and its impeller geometrical parameters can be found in Ref. (Zhang et al., 2016). The designed flow rate Qd is 430 m3/h, the head Hd is 256 m, the rotary speed nd is 2900 rpm, the shaft power Psd is 194.90 kW and the efficiency h is 70%. The density of LNG is r ¼ 455 kg/m3, and the viscosity m ¼ 0.139 cP. The main flow passage components are the inducer, two centrifugal impellers and two guide vanes, as shown in Fig. 2. The inducer (id) and two identical impellers (impeller in stage A and B to be shorted as impA and impB, respectively) share one common rotation axis, but the two identical guide vanes (guide vane in stage A and B to be shorted as gvA and gvB, respectively) in each stage are fixed on the pump body as stationary parts. 3.2. Grid generation and numerical settings As shown in Fig. 2, the flow domain of the LNG pump mainly consists of one inducer, two identical impellers and two identical guide vanes. Additionally, to reduce the boundary condition disturbance on the final flow field, inlet extension (ie) and outlet extension (oe) are introduced before the inducer and after the guide vane at stage B. Then, the grid on the corresponding flow domain is generated by ANSYS 16.0-meshing software in Fig. 3, and an unstructured tetrahedral grid is completed due to the high complexity and skewness of the geometry. At regions close to wall, especially on the blades or vane surfaces, the mesh refinement technique is used to capture the flow details. According to the Fluent User's manual, the yþ can reach a safe limit of 200 for the Reynolds stress turbulence model and standard wall function. Table 1 gives the average yþ of the key surfaces in the LNG pump, from which it is implied that the grid can meet the requirement of yþ. Flow in a LNG pump is complex turbulent flow with strong rotation and is commonly accompanied with separation flow. Thus, ANSYS 16.0-fluent is used to calculate the 3D turbulent flow field of the pump. The flow is assumed to be steady, and the medium LNG is viscous and incompressible. The Reynolds stress turbulence model, energy equation model and standard wall function are applied to close the RANS equations. The interactions between the rotors and stators are considered with the multiple reference frames (MRF) method. A SIMPLEC algorithm is used to calculate the coupling of pressure and velocity, and the pressure term is discretized with the PRESTO! method. The convection terms are discretized with a second order upwind scheme. The constant velocity inlet is set as inlet boundary condition and the outflow assuming to be fully developed flow is designed as outlet boundary condition. The nonslip and adiabatic boundary condition is given at the solid walls. The convergence criterion of the numerical calculation is set as a residual of 1e-4. 3.3. Grid independence investigation The grid independence was investigated at the designed flow condition shown in Table 2. The computational domain at each grid scheme keeps similar proportions of the grid number. The head and
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Fig. 2. Flow domains of the two-stage LNG pump.
Fig. 3. Calculation grid.
3.4. Performance comparison between the numerical and experimental results
Table 1 Average yþ of important surfaces. Regions
Average value
Regions
Average value
Inlet extension Inducer Impeller A Guide vane A
7.57 62.25 127.91 130.26
Impeller B Guide vane B Outlet extension
142.17 129.45 20.76
Table 2 Grid independence investigation. Schemes
Grid number (/106)
Efficiency h (%)
Error (%)
Head H (m)
Error (%)
1 2 3 4 5
1.87 3.56 5.40 6.79 8.21
68.98 67.13 66.23 66.03 65.82
1.85 0.90 0.20 0.21
268.42 261.55 258.61 257.96 257.27
2.63 1.14 0.25 0.27
efficiency are chosen to evaluate the effect of the grid size on the final solution. With an increasing grid number, the head and efficiency change very little and the error between each scheme is less than 2%. Thus, it is considered that further increasing the grid number has no effect on the calculation result. Grid scheme 4, with a total grid number of 6.79 million, is used for the numerical calculations. The simulation is performed on a workstation with 2 CPUs of Intel Xeon 2.4 GHz and RAM of 32 GB, and it usually takes about 11 h to finish a common case.
The hydraulic performance is calculated at eight flow rate conditions from 0.7Qd to 1.4Qd. The corresponding formulas for the head and efficiency are shown below.
H ¼ ðp2 p1 Þ=rg
(10)
h ¼ hh hm hv
(11)
where p1 and p2 stand for total pressure at the pump inlet and outlet, respectively; H is the head; h is the efficiency; hh ¼ rgQH/Mu is the hydraulic efficiency; hm ¼ 1e0.07(0.01ns)1.18 is the mechanical efficiency and hv ¼ 1e0.028(0.01ns)0.6 is the leakage efficiency (Zhang et al., 2016). The performance comparison between the numerical and experimental results is shown in Fig. 4. Generally, the head and shaft power curves by numerical calculations are in good agreement with the experimental results. The errors between the numerical and experimental results are relatively small. At the designed flow rate condition, the head error is only 1.02% and the shaft power error is 2.53%, which implies that the numerical simulation has enough degree of credibility. Meanwhile, the hydraulic efficiency curve and overall efficiency calculated by empirical formulas are also presented. Obviously, the hydraulic efficiency curve is located higher than the experimental curve in the figure because the mechanical efficiency and leakage efficiency are not considered. Taking the empirical formulas into consideration for
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the overall efficiency, the relative error still exists, but remains less than 5%, which is acceptable in the industry application described in Ref. (Zhang et al., 2016). 4. Results analysis based on the entropy production theory 4.1. Distribution of entropy production in a LNG pump for various flow conditions Fig. 5 presents the entropy production of each part for different flow rate conditions as calculated by the entropy production theory. Overall, the entropy production for all of the pump parts (“overall” curve) first decreases smoothly and then increases rapidly. At roughly the designed flow rate condition 1.0Qd, the entropy production is relatively low and the “overall” curve is much smoother, which corresponds to the smooth efficiency vs. flow rate curve described in Section 3.4. Fig. 5 indicates that for different pump domains, the amount of entropy production increases from part ie, id, impA, oe, impB, and gvB to part gvA. The entropy production in part ie, id and impA is relatively small (less than 10 W/K), while it is quite high in part impB, gvB and gvA (greater than 40 W/K). These sections produce the greatest flow in the overall flow passage. Curves for part gvA and gvB are more similar for the quantity of entropy production. The entropy production occurring in part impB is greater than that in part impA. Thus, the hydraulic loss in the LNG pump is mainly dissipated in the impellers and guide vanes; it tends occur more in stage B. It can be said that the guide vanes and the impeller at stage B determine the performance of the two-stage LNG pump and therefore should obtain a greater amount of attention during the designing or matching processes. In addition, the variation trend of entropy production for each part is not the same. The flow rate has little effect on part ie, id and impA. Instead, the entropy production in part oe and gvB slowly grows with the increasing flow rate, and it smoothly decreases with the increasing flow rate rise of part impB. Compared with the 0.7Qd condition, entropy production is increased by 93.68% for part gvB and 413.89% for part oe and decreased by 38.47% for part impB under the 1.4Qd condition. 4.2. Volumetric entropy production rate at parts for various flow conditions The volumetric entropy production rate is considered to be an
Fig. 5. Entropy production versus the flow rate conditions.
important variable to weigh the ability to generate irreversible energy loss. Fig. 6 shows the volumetric entropy production rate of different parts of the LNG pump for flow rate conditions from 0.7Qd to 1.4Qd. In part impB, the volumetric entropy production rate is the result of its entropy production divided by its volume. Specially, the “average” curve represents the result of the total entropy production in the pump divided by the entire pump volume under each flow condition, indicating the average level of irreversibility. Obviously from Fig. 6, all of the curves have the same shape as the curves in Fig. 5, but with different values. In all of the flow rate conditions, the average volumetric entropy production rate for the entire pump is approximately 2300 W/m3K. The average level for parts gvA, gvB and impB are 3800 W/m3K, 3600 W/m3K and 10 000 W/m3K, respectively. Particularly worth mentioning is part impB, whose average level is the sum total of that of the other parts. It can be concluded that part impB is where most of the irreversible energy loss is generated, followed by parts gvA and gvB, because the volumetric entropy production rates for the other parts are greater than the pump average level. Meanwhile, the mismatch between impB and gvA or gvB is quite apparent in the current pump geometry. To improve pump performance, the guide vanes and impeller at stage B should be designed to match, especially in impB. There are two feasible schemes to achieve this matching. One simple scheme is a multi-
Fig. 4. Performance comparison between the numerical and experimental results.
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Fig. 6. Volumetric entropy production rate versus flow rate conditions.
Fig. 7. Proportion of different entropy production versus the flow conditions.
stage matching design accomplished by adjusting the geometrical parameters of the stationary guide vanes or optimizing the clocking effect of each component. The other scheme is based on the hierarchical design of individually rotational impellers in later stages. Therefore, it can be concluded that the entropy production theory has its own advantages for localizing the location at which irreversible losses occur and weighing how serious the losses are quantitatively.
shaft power subtracted by the effective energy contributing to the pump head. As Fig. 8 shows, the average exergy loss calculated by the entropy production theory is 22.27 kW. The average energy loss calculated by the pressure drop method is 48.85 kW. Among all of the flow conditions, the exergy loss and energy loss perform in a similar variation trend, but the former is more stable and smoother. Meanwhile, the proportion between the two methods ranges from 43.16% to 47.93%, and the curve is relatively stable.
4.3. Analysis of various types of entropy production for different flow conditions
5. Flow field analysis of energy loss
Local entropy production is mainly divided into the following three types: direct entropy production due to viscous dissipation, turbulent entropy production due to turbulent dissipation and wall entropy production due to the boundary layer effect. To obtain a better understanding of the entropy production composition for various flow conditions, the proportion of each type of entropy production is presented in Fig. 7. The figure shows that direct entropy production accounts for only 0.04% (less than 0.1 W/K) of the entire production at all of the flow conditions, which is extremely small. The effect of the flow rate on viscous dissipation is neglected in this study. Instead, the effects of the flow rate on wall entropy production and turbulent entropy production are evident. Turbulent entropy production is almost three times greater than wall entropy production. The proportion of wall entropy production ranges from 22.49% to 26.72% and that of turbulent entropy production ranges from 73.25% to 77.48%. Thus, turbulent dissipation and wall friction are considered to be the main factors in generating irreversible energy loss, i.e., hydraulic loss in fluid machinery. At the designed flow condition 1.0Qd, STD and SW are 73.51% and 26.46%, respectively. Moreover, the wall entropy production grows smoothly first and then decreases with an increasing flow rate, while the turbulent entropy production first decreases and then increases. At the designed flow condition, both rates reach the greatest values, and the corresponding curves become more flat.
Compared with the traditional analysis method of pressure and velocity fields, the entropy production approach for analyzing energy loss is more intuitive, which helps to better understand complex flow and accurately locate where and how hydraulic losses occur. To locate the flow features in detail, the distribution of the volumetric entropy production rate is presented combined with a streamline or velocity vector distribution to explain the hydrodynamic factors of the hydraulic loss. As shown in Fig. 7, direct entropy production accounts for very little; thus, the visualization of the volumetric entropy production rate is mainly studied for turbulent and wall entropy production. Moreover, the volumetric entropy production rate in impB, gvA and gvB is relatively high, and
4.4. Energy loss analysis by entropy production and pressure drop methods Fig. 8 shows the energy loss calculated by entropy production theory and traditional pressure drop method, and the proportion between the two methods is also presented. The exergy loss is the result of PVD, PTD and PW, while the other loss is the direct result of
Fig. 8. Energy loss versus the flow conditions.
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the distributions are taken as examples to explain where and how the hydraulic loss occurs. 5.1. Distribution of the entropy production rate at the pump midspan section Fig. 9 shows the distribution of the turbulent volumetric entropy production rate at the mid-span section of the LNG pump under the 1.0Qd flow condition. The turbulent volumetric entropy production rate in impB, gvA and gvB is much higher than the others. Similarly, these parts are the main sources of hydraulic loss. Especially in impB, a large exergy loss region can be observed at the inlet close to the shroud wall. Additionally, the volumetric entropy production rate at parts gvA and gvB are at the same level, but the rate is hard to detect at parts impA and id. As shown in Fig. 10, the distribution of the wall entropy production rate at the mid-span section is also presented. Unlike the turbulent entropy production rate distribution, the wall entropy production rate at the guide vanes is quite small. On the contrary, the rate is relatively high at id, impA and impB, and large areas are observed close to the trailing edges or shroud sides because the wall friction induces entropy production, which is proportional to the velocity or shear stress at the near wall. The relative velocities at the shroud sides of id and the trailing edges of impA and impB are quite large. The average wall entropy production rate is 8.90 W/ m2K for id, 9.12 W/m2K for impA and 14.25 W/m2K for impB. 5.2. Distribution of the volumetric entropy production rate at impB The contour of the turbulent volumetric entropy production rate and streamlines at impB are presented under the 1.0Qd flow condition in Fig. 11. Obviously, the turbulent dissipation occurring in the blade suction side is much more serious than in the pressure side. A large loss area is observed at the leading edge close to the shroud wall. Meanwhile, to analyze the hydrodynamic factors causing the hydraulic losses, the streamlines inside the impB flow
93
passage are also presented. It is found that the large loss region is always accompanied by one large vortex, as shown in Fig. 11 (b). The shock in the leading region gives rise to flow separation and, combined with the adverse pressure gradient effect, a large vortex is formed downstream that sparks the obvious hydraulic loss. This explains why the volumetric entropy production rate at the blade suction side is relatively high. 5.3. Comparative analysis of entropy production rate for impellers between stages From the analysis above, the entropy production occurring in the impeller at stage B is much higher than that at stage A. The turbulent volumetric entropy production rate and wall entropy production rates at part impA and impB are presented in Fig. 12, and the streamline and skin friction coefficient distributions are also displayed. Overall, the entropy production for impB is higher than that for impA from the perspective of turbulent entropy production or wall entropy production. It can be observed that the volumetric entropy production rate in impA is hard to observe in Fig. 12 (a), but it is obvious in impB at the same order of magnitude. The streamline distributions in Fig. 12 (b) imply that more vortexes appear in impB than in impA, which is the main reason for the high turbulent entropy production rate in impB. Of course, the shock phenomenon at the leading edge is also a production factor according to Fig. 10. The wall entropy production rate and skin friction coefficient are also given in Fig. 12 (c) and (d). It can be clearly seen that the wall entropy production rate in impB is slightly higher than that in impA, which is attributed to the friction close to the wall. Apparently, the distribution of the skin friction coefficient is very similar to the wall entropy production in the contour. Thus, high wall friction induces high entropy production. 5.4. Distribution of the volumetric entropy production rate at gvB Fig. 13 shows the contour of the turbulent volumetric entropy
Fig. 9. Contour of turbulent volumetric entropy production rate at the mid-span section.
Fig. 10. Contour of wall entropy production rate at the mid-span section.
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Fig. 11. Contour of volumetric entropy production rate and streamlines at impB.
Fig. 12. Comparative analysis of the entropy production rate between impellers.
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Fig. 13. Contour of the volumetric entropy production rate and streamlines at gvB.
production rate and the streamlines at gvB as well as the velocity vectors near the leading edge of each vane under 1.0Qd flow conditions. It is observed that the volumetric entropy production rate reaches the peak value at the leading edge of the outside guide vanes. The production rate is greatest at the flow passage and the shroud side of the inner guide vane as well. Meanwhile, the streamlines inside the inner flow passage imply that there is a strong flow vortex in each channel. The shock phenomenon also appeared close to the leading edge region. The flow angle and vane setting angle differences induce flow separation and compel disorderly flow. Thus, the volumetric entropy production rate in these regions is relatively high. 6. Conclusions Based on the entropy production theory, the energy characteristics of an LNG cryogenic submerged pump are investigated by means of numerical simulation in this study. A 3D steady turbulent flow field was calculated for eight flow conditions with a Reynolds turbulence model and an energy equation model. Subsequently, the local entropy production terms were embedded into software codes to analyze the energy loss. The accuracy of the numerical results was validated by experimental data, and many important conclusions can be drawn. a. Hydraulic loss mainly occurred in the guide vanes and impeller at stage B. In the LNG pump in all flow conditions, the entropy production of parts gvA, gvB and impB is high (greater than 40 W/K), while the production is relatively low (less than 10 W/K)
in the other domains. The entropy production curves for gvA and gvB are similar. b. The impeller at stage B is the most serious place for irreversible losses to occur. The volumetric entropy production rate in impB is extremely high (10 000 W/m3K) and is nearly the sum total of all of the other parts. In the current pump geometry, the mismatch between impB and gvA or gvB is quite apparent, indicating that the entropy production theory can be used to determine the location at which irreversible losses occur and weigh how serious they are quantitatively. c. Direct entropy production is extremely small compared with turbulent and wall entropy production, which are neglected in this study. Turbulent entropy production and wall entropy production account for the overall production at roughly 73.25%e77.48% and 22.49%e26.72%, respectively. Turbulent entropy production is practically three times greater than wall entropy production. At the 1.0Qd flow condition, STD and SW are 73.51% and 26.46%, respectively. d. The exergy loss and energy loss display a similar variation trend in the overall flow conditions; however, the former accounts for more than 43.16%e47.93% of the losses. e. From the flow field analysis, the separation flow, shock phenomenon and vortex are the hydrodynamic factors that produce irreversible energy loss. These factors induce a relatively high volumetric entropy production rate. Thus, the entropy production theory can be an effective way to capture bad flows and help locate where and how they occur. Furthermore, this theory can help to further optimize pump performance using the entropy production minimization principle.
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H. Hou et al. / Journal of Natural Gas Science and Engineering 36 (2016) 87e96
Acknowledgements
Subscripts & Superscripts
This work was supported by National Natural Science Foundation of China (Grant No. 51209217) and the Science Foundation of China University of Petroleum, Beijing (No. 2462015YQ0411).
ðÞ ()TD ()W ()’ ()VD
mean component about turbulent dissipation about wall fluctuating component about viscous dissipation
Nomenclature A H M ns p2 Ps Q .
q S Spro, ~ T uvw x, y, z g Hd nd p1 P Psd Qd s Spro t Tr V ! v
area head torque specific speed outlet total pressure shaft power flow rate heat flux density vector entropy production volumetric entropy production rate temperature velocity component coordinate gravity acceleration designed head rotary speed inlet total pressure exergy loss designed shaft power designed flow rate specific entropy total entropy production time ambient temperature volume wall velocity vector
Greek symbols ε turbulent dissipation rate hh hydraulic efficiency hv leakage efficiency r density F viscous dissipation term u angle velocity h efficiency hm mechanical efficiency m molecular viscosity t shear stress FQ entropy production term
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