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Combined effects of different temperature and pressure loads on the “L”-type large-diameter buried pipeline
International Journal of Heat and Mass Transfer 111 (2017) 953–961
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Combined effects of different temperature and pressure loads on the ‘‘L”-type large-diameter buried pipeline Qian Xu ⇑, Junxiao Feng ⇑, Shuchen Zhang School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China
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Article history: Received 8 December 2016 Received in revised form 3 April 2017 Accepted 14 April 2017 Available online 22 April 2017 Keywords: Flow-heat-solid coupling Large-diameter buried pipeline Thermal stress Strength check
a b s t r a c t Large-diameter buried pipeline was widely used because of its energy-saving advantage and high efficiency. In this paper, ‘‘L”-type heat pipe network was taken as the research object, which was studied using the flow-heat-solid coupling method. The ANSYS Workbench platform was used to simulate heat transfer and the flow of the medium in the pipe network. The pressure and temperature of the flow field and the temperature, equivalent stress, and total deformation of the solid structure under different conditions were calculated, and the effects of different mediums on the variables of the temperature were compared. According to the theory of stress classification, stability analysis method was used to check the strength of the pipe network structure. Results show the stress and deformation of the anchorage section of the pipe network were mainly affected by the temperature of the fluid. When the pressure and temperature loads worked individually or simultaneously, maximum deformation occurred in the lateral region of the long arm near the elbow, and the maximum equivalent stress position changed according to the load change. When the medium temperatures were 60 °C and 80 °C, the strength of the pipe network structure satisfied the requirements according to the structural strength check analysis. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Directly buried installation, a kind of underground pipeline laying method, has been developed in the recent years because of its advantages of convenience, short construction time, and less construction cost [1–3]. Directly buried heating pipeline has been widely applied in district heating pipe networks in Sweden, Finland, Denmark, Germany, and other countries [4,5]. The heating pipeline load increases with the population. In addition, the pressure and diameter of buried pipelines also increase. In China, the heating pipe network pressures of some municipal main lines work to reach 2.5 MPa, the operating temperature of 150 °C, and diameter of DN1400 mm [6,7]. Several failure forms appear because of the flow-heat-solid coupling phenomenon in network systems, such as infinite plastic flow, cyclic plastic deformation, fatigue failure, and overall instability [8,9]. Pipeline steering parts (elbow, tee, taper pipe) bear larger pressure in fluid three-dimensional turbulent flow at high temperature and pressure, and they also increase the overall structure deformation [10]. Fluid structure interaction mechanics is a branch of fluid and solid mechanics that is mainly concerned with the behavior of
⇑ Corresponding author. E-mail addresses: [email protected] (Q. Xu), [email protected] (J. Feng). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.04.067 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
solids in the flow field and the influence of solid deformation on flow field. Many research related to heat transfer and the mechanical behavior of large-diameter buried pipe networks have been conducted. For example, Shi et al. [11] studied the structure strength based on Fluid-structure Interaction Heat transfer and thermal stress has been analyzed by Li et al. [12]. A methodology for the fatigue analysis of pipelines containing corrosion defects was proposed by Cunha et al. [13]. Rashidi et al. [14] and Rahman et al. [15] has studied the temperature distribution of pipeline through the finite element analysis. Heat losses from district heating network has been calculated by Danielewicz et al. [16] using a three-dimensional numerical model. Yuan et al. [17] studied the effect of pressure load on flow field in Workbench Platform. Previous pipe studies have mainly focused on either the flow field, temperature field, and structure stress separately, the computational results caused by the heat transfer and fluid pressure of the pipe network will deviate from the actual situation. But studies on the flow-heat-solid coupling of pipe networks are limited [18]. Meanwhile, flow-heat-solid coupling analysis method can accurately reflect the interaction of fluid and structure deformation [19]. Flow-heat-solid coupling analysis method has been receiving increasing attention in engineering practice. In directly buried heating pipe systems, the tube body is mostly made of stainless steel, and deformation of the structure system is generally smaller
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Nomenclature U Gk q k c1, c2 h T M C K X Y Z F E
Fi
fluid velocity vector, m/s turbulent production term total energy, J turbulent kinetic energy, J constants of the k-e model fluid enthalpy, J/kg temperature, K mass matrix damping matrix stiffness coefficient matrix solid displacement vector solid velocity vector solid acceleration vector force, N elastic modulus
Greek symbols q fluid density, kg/m3 t Poisson ratio re ; rk Prandtl numbers for k-e equations rt Prandtl number g dynamic viscosity, Pa s h first strain invariant ri normal stress, Pa si shear stress, Pa gt turbulent viscosity, Pa s l heat transfer coefficient
under the flow field action, but the stress is high. Stress concentration is more common in the most unfavorable conditions (anchorage segment) and the weakest link of the whole system. Further thermal stress changes the stiffness of the structure, induces structural deformation, and thus affects the stability and dynamic response of the structure, shortens the life of the system, and increases security risks. Therefore, thermal stress has important significance in pipe network system architecture analysis and research [20]. In this paper, the coupled flow and heat transfer inside the pipe wall at high temperature and pressure were simulated in three dimensions using the Computational Fluid Dynamics CFD Fluent software [21]. The pressure load on the pipe wall was determined from the fluid of high temperature and pressure based on the fluid calculation results. The transition from the fluid temperature and the pressure load to the structure of the model was achieved through the Workbench platform [21]. Subsequently, the unidirectional flow-heat-solid coupling of the large-diameter buried pipe was solved. The stress and strain distributions were comparatively analyzed under different fluid pressures and temperatures or combined load actions, and the strength of the pipe was checked. The analysis results could provide a basis for the structural strength design of large-diameter buried pipe networks [22]. 2. Fundamental theory Fluid theory: Continuity equation:
divðUÞ ¼ 0 ‘‘N-S” equation:
ð2Þ
‘‘k-e”equation: k equation
g divðqUkÞ ¼ div g þ t gradk þ gt Gk qe
rk
Solid theory: Based on the Hamilton principle of classical mechanics theory, the motion equation of the whole structure is established as follows:
MZ þ CY þ KX ¼ FðtÞ
ð3Þ
ð6Þ
The following assumptions should be met in the analysis: the K matrix must be continuous and the corresponding material should satisfy the linear elastic and small deformation theory. The F matrix is a static load, and the influences of the time variation of the load and inertia (such as mass and damping) were not considered. Thermal coupled heat conduction equation:
rD ¼ divðKgradTi Þ
ð7Þ
ðKgradTi Þ njC ¼ l½Ti Ta ðtÞC
ð8Þ
where r is the displacement matrix, D is the heat capacity matrix, i is used to distinguish the different items of different media, C is used to study the outer boundary of the area, l is the heat transfer coefficient, n is the outer normal vector, T0(x) is the distribution of the initial temperature of the system, and Ta(t) is a function of the time to obtain the temperature of the external environment interacting with the system. Stress–strain constitutive relation:
rij ¼ ð1Þ
@ ðqUÞ þ divðqUUÞ ¼ div½ðg þ gt ÞgradU þ F @t
volume force, N
E tE hdij eij þ 1þt ð1 þ tÞð1 2tÞ
ð9Þ
Force balance equation:
@ rx @ sxy @ sxz þ þ þ Fx ¼ 0 @x @y @z
ð10Þ
@ ry @ syx @ syz þ þ þ Fy ¼ 0 @y @x @z
ð11Þ
@ szx @ szy @ rz þ þ þ Fz ¼ 0 @x @y @z
ð12Þ
e equation
g e e2 divðqU eÞ ¼ div g þ t grade þ c1 gt Gk c2 q re k k
3. Numerical simulation
ð4Þ
Energy conservation equation:
g divðqUhÞ ¼ div g þ t gradh q
rt
ð5Þ
The solid model of the directly buried heating pipe network system was established using the Inventor software [23] and then imported into the Workbench analysis platform. The fluid region was established by the filling function in mechanics (fill). Internal flow is a three-dimensional, viscous, and turbulent flow, and the
Q. Xu et al. / International Journal of Heat and Mass Transfer 111 (2017) 953–961
movement law conforms to the N-S equation of the threedimensional Reynolds average. The calculation process included the energy, mass, and momentum conservation equations to obtain the temperature field inside the pipe network. Fluent (flow field calculation software) was used to calculate the pressure and temperature fields in the flow field under different temperature conditions. The total pressure inlet, mass flow outlet, and temperature of the inlet medium were set in the calculation process. The temperature load of the pressure field in the flow field can be applied to the solid field when data transmission is established between the flow field analysis module (Fluent) and the thermal stress analysis module (Thermal-Stress). The interface between the fluid and solid domains should be highly matched to guarantee that the pressure and temperature loads can be accurately transferred to specify the solid domain. Finally, the analysis of pipe network stress in the static-structure module was conducted. 3.1. Calculation model and mesh generation DN1400 mm caliber was selected as the research object. Its numerical calculation and experiment were performed. Elbow pipe was selected as the 1.5D bend radius large-diameter and connected with the straight pipe. The design parameters are shown in Table 1, and the pipe network structure is shown in Fig. 1. Grid division: The flow field, solid domain, and local enlarged drawing are shown in Fig. 2. As is shown in Fig. 2(a), the checkedge for grid independence was located at external surface of inlet pipe, and parallel to the Y axis. Four key points were selected at this edge to compare the equivalent stress values of various grid conditions. The interval length of each point is 8 m. Five kinds of grid partitions from sparse to dense were compared to increase the speed and accuracy of the simulation, which are shown in Table 2. The equivalent stresses of four points are shown in Fig. 3. The temperature showed less variation when the grid number increased from 300,000 to 700,000. When the number of grid was greater than 300,000, the results became not sensitive to the grid number, thus the grid was considered independent. Therefore, the selected computational grid number was 331,520. The convection field was divided into 215,760 elements using the ICEM-CFD software [24]. The structure domain used the grid partition function of Workbench ANSYS software, and the pipe body was divided into 115,760 elements.
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set to the pressure reference point using the standard k-e turbulence model and SIMPLEC algorithm [25]. The relative pressure was zero, and the convergence precision was 105. In addition, the pipe body structure load of the heating system included the internal pressure and heat transfer between the outer wall of the pipe and the covering soil, and the convection heat transfer coefficient was selected by the industry standard of ‘‘Institute of urban construction, Technical specification for directly buried hot-water heating pipeline in city CJJ/T 81-2014, China building industry press”. The material of the tube structure in the numerical simulation of the flow-heat-solid coupling was Q235B steel. The coefficient of thermal expansion was 12.5 106 m(m°C)1. The material properties included the density (7850 kgm3), elastic modulus (19.7 104 MPa), and Poisson’s ratio (0.3). The outside of the fluid and the inner side of the tube body were set as the interaction surfaces. The most unfavorable pipe network conditions were simulated, that is, the pipe network in the anchorage section, such that the inlet and outlet sides were set with no displacement constraints. 4. Analysis of results 4.1. Comparison of experimental parameters The experimental team cooperated with a manufacturer to design the corresponding experiments and measure the key working condition parameters of the whole pipe network in view of the research network to verify the accuracy of the numerical model. The experiment of the pipe network was set as a repetitive experimental study. Experiments were conducted five times under the same conditions, and the monitoring parameters were obtained through the average value. Therefore, the experimental error was very small and the results were accurate. The specific value of the experimental result at each instance was omitted in the paper because of space limitations. Thus, only the average values are shown in Table 3. The pipe network was simulated at the same time. The comparison of the experimental and simulation monitoring parameters is shown in Table 3. Specific parameters were selected from the inlet and outlet ends, and the average value of each end face was measured. The result errors of the experiment and simulation were within 2%, which was consistent with the accuracy of the engineering calculation, and the accuracy of the numerical model was proven.
3.2. Flow field boundary condition 4.2. Analysis of pressure and temperature fields in the fluid domain The flow field was calculated using Fluent. The inlet was set to the pressure inlet, and the pressure value was 1.6 MPa. The outlet was set to the pressure outlet, and the pressure value was 1.4 MPa. The solid wall surface was set to a no slip boundary condition. The wall roughness was set according to the actual condition based on the standard wall function treatment. The center of the inlet was
Table 1 Important design parameters. Design parameters
Design data
External diameter (D)/mm Wall thickness/mm Inlet straight pipe length (L1)/mm Outlet straight pipe length (L2)/mm Elbow arm length (L3)/mm Bending radius (R)/mm Internal pressure (P)/MPa Specific frictional head loss/(Pam1) Convective heat transfer coefficient/(Wm2K1)
1422 16 36,000 24,000 L3 = 1.5D = 2133 2133 1.6 300 1000
The pressure and velocity distributions in the system was obtained by simulating the temperatures of different media, as shown in Fig. 4. The pressure from the inlet to the outlet of the inlet straight pipe section decreased gradually. The internal pressure of the elbow was less than the straight pipe section of the elbow inlet and larger than the straight pipe section of the elbow. The surface pressure near the corner wall was small inside the elbow, and the high-pressure zone was located at the corner of the outer wall. Therefore, inner arch of elbow was also the most prone to cavitation. Thus, cavitation was also most likely to occur in this area. This shows that the temperature of the medium did not affect the internal pressure of the pipe network because the pressure value and distribution of the straight pipe and elbow were basically the same under different temperature conditions. The temperature field of the pipe network was studied only when the medium temperature was 140 °C because of space limitations. The temperature field distribution at the center of the pipe network is shown in Fig. 5. The flow boundary layer appeared on
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1- Elbow outlet cross section, 2- Elbow 45 cross section, 3- Elbow inlet cross section, 4- Elbow outlet arm cross section, 5- Elbow inlet arm cross section Fig. 1. Schematic diagram of the pipe network structure.
(a) The pipe body grid
(b) Flowing medium grid
(c) Local magnification of elbow body
Fig. 2. Grid partition graph.
Table 2 Five types of grid partition. Different grid partitions
1
2
3
4
5
Total number Convection field Structure domain
220,719 135,670 85,049
331,520 215,760 115,760
476,016 280,596 195,420
583,175 325,690 257,485
696,251 380,565 315,686
Table 3 Comparison of monitoring parameters.
Maximum equivalent stress (MPa)
90
85
80
75
No.2 point
70 No.3 point
65
60 200000
Monitoring parameters
Experimental results
Numerical simulation results
Inlet vertex velocity/(ms1) Inlet vertex temperature/K Outlet vertex temperature/K Inlet vertex gauge pressure/Pa Outlet vertex gauge pressure/Pa Inlet vertex stress/MPa Outlet vertex stress/MPa Elbow vertex stress/MPa
4.13 412.50 411.60 1,590,300 1,580,310 320.14 380.32 78.46
4.21 413.20 412.65 1,591,233 1,580,000 328.93 383.42 80.372
No.1 point
No.4 point
300000
400000
500000
600000
Grid number Fig. 3. Grid independent verification results.
700000
the solid wall, and the fluid velocity was lower than that of the main area because of the viscous effect of the medium. Therefore, the temperature near the wall was slightly lower than that of the main central area, and the whole temperature of the pipe network gradually decreased from the inlet end face to the end face of the
Q. Xu et al. / International Journal of Heat and Mass Transfer 111 (2017) 953–961
(a)100
(b)140
(c)180 Fig. 4. The pressure and velocity clouds in center section of pipe network and local magnification.
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4.3. Analysis of temperature field, structure stress, and deformation in solid state
Fig. 5. Distribution of temperature field in the center section of the pipe network (°C).
outlet. The inner wall of the elbow was measured at the lower part of the overall temperature, in which the lowest temperature point was 139.55 °C. The temperature gradually increased close to the outer wall, reached the maximum at the main area, and then gradually decreased.
This section focuses on the analysis of the stress and deformation of the pipe wall of the pipe network under different media temperatures. The stress field of the pipe network was studied only at the medium temperature of 140 °C because of space constraints. The temperature distribution of the outer surface of the pipe network at 140 °C is shown in Fig. 6. Fig. 6 shows that the temperature of the surface of the tube body is higher than that of the outer surface, and the temperature of the tube body decreases gradually from the entrance of the stage to the elbow. The heat speeded up because the turbulence strengthened. Thus, the temperature appeared to rise at the outlet of the elbow until the exit pipe section, and then gradually decreased. Inlet temperature was the highest, and outlet temperature was the lowest. The equivalent stress distribution of the pipe network under the design condition at 140 °C is shown in Fig. 7. The equivalent stress cloud of outer and inner surface of the inlet and outlet are shown in Fig. 8a, b, c, and d. The equivalent stress value of the pipe network was in the range of 11.46 MPa–84.9 MPa, and the stress concentration phenomenon occurred at the fixed section of the inlet outlet. The maximum equivalent stress of the pipe was 672.93 MPa, which occurred at the fixed part of the outlet pipe. This was because the stress concentration caused by the outlet straight pipe section anchorage cannot be released. Therefore, the sections, where the anchorage may appear in the pipe section, should be given more attention in the design process to ensure the longterm effective operation of the pipe network. The elbow was part of the release of stress components for the whole pipe network. Thus, the elbow stress was significantly less than the inlet and outlet pipe section stresses, and the equivalent minimum stress value appeared at the 45° center section of the
Fig. 6. Outer surface and inner surface temperatures of the pipe network (°C).
Q. Xu et al. / International Journal of Heat and Mass Transfer 111 (2017) 953–961
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Fig. 7. Equivalent stress distribution of the hot water pipe network (MPa).
Fig. 8. Distribution of equivalent stress distribution in the hot water pipe network section at 140 °C (MPa).
elbow. Fig. 8 shows that the equivalent stress on the inner wall of the same position is obviously larger than that on the outer wall. Therefore, the inner wall of the corrosion protection process should be given more attention during the engineering construction process to avoid the damage caused by fatigue and larger stress.
The total deformation of the pipe network at 140 °C is shown in Fig. 9. Fig. 9 shows that the maximum total deformation of the pipe network is at the outer surface of the elbow, close to the entrance wall. The minimum deformation is located at the entrance end face. The total deformation of the pipe network gradually increases
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Fig. 9. Total deformation distribution of the hot water pipe network at 140 °C (mm).
Table 4 The maximum equivalent stress and deformation under different temperature conditions. Temperature/°C
60 80 100 120 140 160 180
Maximum equivalent stress/MPa
Maximum deformation/mm
Pressure load
Temperature load
Coupled load
Pressure load
Temperature load
Coupled load
126.66 126.66 126.66 126.66 126.66 126.66 126.66
193.98 296.23 398.48 500.73 602.98 705.24 807.49
278.60 373.58 471.22 571.65 672.93 774.46 876.16
143.6 143.6 143.6 143.6 143.6 143.6 143.6
31.226 47.679 64.131 80.584 97.037 113.49 129.94
148.89 154.18 160.99 169.13 178.43 188.70 199.81
from the inlet end to the elbow, which is in line with the requirements of applied loads and constraints. 4.4. Influence of different medium temperatures on elbow stress and deformation In the design conditions of different media temperatures, the stress and deformation size and the distribution of the pipe body are separately under the pressure and temperature loads. The equivalent maximum stress and total deformation are shown in Table 4. Table 4 shows that the equivalent maximum stress and deformation of the pipe increase with the temperature of the medium, and the stress and deformation caused by the temperature load increase with the temperature. The pressure load did not change with the increase of the medium temperature. Thermal stress was greater than the stress value caused by pressure load, and the thermal deformation was less than that of the deformation caused by pressure load. Therefore, the influence of the structure caused by the temperature change should be considered during the analysis and calculation of the
pipe network under the condition of a certain working pressure and an abnormal structure temperature. The thermal stress load caused by the higher temperature may cause harm. In addition, the stress and the deformation under the combined action of two kinds of loads were not equal to the sum of the stress and the deformation of the two kinds of loads. This shows that pressure and temperature loads are not separate from each other, and the deformation and stress of the pipe network are coupled. 4.5. Strength check The stability analysis of the classification stress checking algorithm was used to check the strength of the pipe network structure. The stability analysis of the common action of primary stress and the two stresses was provided. Although the twostress corresponding to the finite plastic deformation will not cause damage, the strength condition of the limit analysis was set to less than three times that of the basic allowable stress considering the safety factor, that is, rr 6 3½r, to ensure the stable state of the hot water pipe network operation. The allowable stress
Q. Xu et al. / International Journal of Heat and Mass Transfer 111 (2017) 953–961
of the Q235B material was 125 MPa, and the maximum stress value of the pipe network was less than the allowable stress of the material at 60 °C and 80 °C. Therefore, the structure strength satisfied the requirement. However, the maximum stress value at 100 °C was 471.22 MPa, which was more than three times the allowable stress of the material. Thus, the structural strength did not satisfy the requirement, and the material of higher strength should be considered as a replacement. The maximum stress value was higher when the medium temperature was higher. Thus, the strength of the material should be considered in the design of the pipe network structure. 5. Conclusions (1) The stress and deformation of the anchor section of the ‘‘L”type heat pipe network were mainly affected by the temperature of the fluid, and the effect of pressure load was small. (2) Considering the temperature and pressure loads together, the maximum equivalent stress of the ‘‘L”-type heat pipe network was located at the entrance end face. The maximum equivalent stress was located at the outlet end when the temperature load was considered single. The maximum equivalent stress was located in the region near the short arm of the elbow when the fluid pressure load was considered single. (3) The pressure and temperature loads are not separate from each other, and the deformation and stress of the pipe network are coupled. Considering the temperature and pressure loads together or separately, the maximum deformation of the anchoring section of the ‘‘L”-type heat pipe network occurred in the elbow, close and outside the long arm of the region. (4) The medium temperature was up to 80 °C for the Q235B material when stability analysis was used to check the anchorage segment of the ‘‘L”-type heat pipe network. A new material of higher strength should be selected for pipe network or the stress of the import and export on the anchorage end should be released to ensure the safe operation of the pipe network when the temperature is higher than 80 °C.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Combined effects of different temperature and pressure loads on the ‘‘L”-type large-diameter buried pipeline Qian Xu ⇑, Junxiao Feng ⇑, Shuchen Zhang School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 8 December 2016 Received in revised form 3 April 2017 Accepted 14 April 2017 Available online 22 April 2017 Keywords: Flow-heat-solid coupling Large-diameter buried pipeline Thermal stress Strength check
a b s t r a c t Large-diameter buried pipeline was widely used because of its energy-saving advantage and high efficiency. In this paper, ‘‘L”-type heat pipe network was taken as the research object, which was studied using the flow-heat-solid coupling method. The ANSYS Workbench platform was used to simulate heat transfer and the flow of the medium in the pipe network. The pressure and temperature of the flow field and the temperature, equivalent stress, and total deformation of the solid structure under different conditions were calculated, and the effects of different mediums on the variables of the temperature were compared. According to the theory of stress classification, stability analysis method was used to check the strength of the pipe network structure. Results show the stress and deformation of the anchorage section of the pipe network were mainly affected by the temperature of the fluid. When the pressure and temperature loads worked individually or simultaneously, maximum deformation occurred in the lateral region of the long arm near the elbow, and the maximum equivalent stress position changed according to the load change. When the medium temperatures were 60 °C and 80 °C, the strength of the pipe network structure satisfied the requirements according to the structural strength check analysis. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Directly buried installation, a kind of underground pipeline laying method, has been developed in the recent years because of its advantages of convenience, short construction time, and less construction cost [1–3]. Directly buried heating pipeline has been widely applied in district heating pipe networks in Sweden, Finland, Denmark, Germany, and other countries [4,5]. The heating pipeline load increases with the population. In addition, the pressure and diameter of buried pipelines also increase. In China, the heating pipe network pressures of some municipal main lines work to reach 2.5 MPa, the operating temperature of 150 °C, and diameter of DN1400 mm [6,7]. Several failure forms appear because of the flow-heat-solid coupling phenomenon in network systems, such as infinite plastic flow, cyclic plastic deformation, fatigue failure, and overall instability [8,9]. Pipeline steering parts (elbow, tee, taper pipe) bear larger pressure in fluid three-dimensional turbulent flow at high temperature and pressure, and they also increase the overall structure deformation [10]. Fluid structure interaction mechanics is a branch of fluid and solid mechanics that is mainly concerned with the behavior of
⇑ Corresponding author. E-mail addresses: [email protected] (Q. Xu), [email protected] (J. Feng). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.04.067 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
solids in the flow field and the influence of solid deformation on flow field. Many research related to heat transfer and the mechanical behavior of large-diameter buried pipe networks have been conducted. For example, Shi et al. [11] studied the structure strength based on Fluid-structure Interaction Heat transfer and thermal stress has been analyzed by Li et al. [12]. A methodology for the fatigue analysis of pipelines containing corrosion defects was proposed by Cunha et al. [13]. Rashidi et al. [14] and Rahman et al. [15] has studied the temperature distribution of pipeline through the finite element analysis. Heat losses from district heating network has been calculated by Danielewicz et al. [16] using a three-dimensional numerical model. Yuan et al. [17] studied the effect of pressure load on flow field in Workbench Platform. Previous pipe studies have mainly focused on either the flow field, temperature field, and structure stress separately, the computational results caused by the heat transfer and fluid pressure of the pipe network will deviate from the actual situation. But studies on the flow-heat-solid coupling of pipe networks are limited [18]. Meanwhile, flow-heat-solid coupling analysis method can accurately reflect the interaction of fluid and structure deformation [19]. Flow-heat-solid coupling analysis method has been receiving increasing attention in engineering practice. In directly buried heating pipe systems, the tube body is mostly made of stainless steel, and deformation of the structure system is generally smaller
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Nomenclature U Gk q k c1, c2 h T M C K X Y Z F E
Fi
fluid velocity vector, m/s turbulent production term total energy, J turbulent kinetic energy, J constants of the k-e model fluid enthalpy, J/kg temperature, K mass matrix damping matrix stiffness coefficient matrix solid displacement vector solid velocity vector solid acceleration vector force, N elastic modulus
Greek symbols q fluid density, kg/m3 t Poisson ratio re ; rk Prandtl numbers for k-e equations rt Prandtl number g dynamic viscosity, Pa s h first strain invariant ri normal stress, Pa si shear stress, Pa gt turbulent viscosity, Pa s l heat transfer coefficient
under the flow field action, but the stress is high. Stress concentration is more common in the most unfavorable conditions (anchorage segment) and the weakest link of the whole system. Further thermal stress changes the stiffness of the structure, induces structural deformation, and thus affects the stability and dynamic response of the structure, shortens the life of the system, and increases security risks. Therefore, thermal stress has important significance in pipe network system architecture analysis and research [20]. In this paper, the coupled flow and heat transfer inside the pipe wall at high temperature and pressure were simulated in three dimensions using the Computational Fluid Dynamics CFD Fluent software [21]. The pressure load on the pipe wall was determined from the fluid of high temperature and pressure based on the fluid calculation results. The transition from the fluid temperature and the pressure load to the structure of the model was achieved through the Workbench platform [21]. Subsequently, the unidirectional flow-heat-solid coupling of the large-diameter buried pipe was solved. The stress and strain distributions were comparatively analyzed under different fluid pressures and temperatures or combined load actions, and the strength of the pipe was checked. The analysis results could provide a basis for the structural strength design of large-diameter buried pipe networks [22]. 2. Fundamental theory Fluid theory: Continuity equation:
divðUÞ ¼ 0 ‘‘N-S” equation:
ð2Þ
‘‘k-e”equation: k equation
g divðqUkÞ ¼ div g þ t gradk þ gt Gk qe
rk
Solid theory: Based on the Hamilton principle of classical mechanics theory, the motion equation of the whole structure is established as follows:
MZ þ CY þ KX ¼ FðtÞ
ð3Þ
ð6Þ
The following assumptions should be met in the analysis: the K matrix must be continuous and the corresponding material should satisfy the linear elastic and small deformation theory. The F matrix is a static load, and the influences of the time variation of the load and inertia (such as mass and damping) were not considered. Thermal coupled heat conduction equation:
rD ¼ divðKgradTi Þ
ð7Þ
ðKgradTi Þ njC ¼ l½Ti Ta ðtÞC
ð8Þ
where r is the displacement matrix, D is the heat capacity matrix, i is used to distinguish the different items of different media, C is used to study the outer boundary of the area, l is the heat transfer coefficient, n is the outer normal vector, T0(x) is the distribution of the initial temperature of the system, and Ta(t) is a function of the time to obtain the temperature of the external environment interacting with the system. Stress–strain constitutive relation:
rij ¼ ð1Þ
@ ðqUÞ þ divðqUUÞ ¼ div½ðg þ gt ÞgradU þ F @t
volume force, N
E tE hdij eij þ 1þt ð1 þ tÞð1 2tÞ
ð9Þ
Force balance equation:
@ rx @ sxy @ sxz þ þ þ Fx ¼ 0 @x @y @z
ð10Þ
@ ry @ syx @ syz þ þ þ Fy ¼ 0 @y @x @z
ð11Þ
@ szx @ szy @ rz þ þ þ Fz ¼ 0 @x @y @z
ð12Þ
e equation
g e e2 divðqU eÞ ¼ div g þ t grade þ c1 gt Gk c2 q re k k
3. Numerical simulation
ð4Þ
Energy conservation equation:
g divðqUhÞ ¼ div g þ t gradh q
rt
ð5Þ
The solid model of the directly buried heating pipe network system was established using the Inventor software [23] and then imported into the Workbench analysis platform. The fluid region was established by the filling function in mechanics (fill). Internal flow is a three-dimensional, viscous, and turbulent flow, and the
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movement law conforms to the N-S equation of the threedimensional Reynolds average. The calculation process included the energy, mass, and momentum conservation equations to obtain the temperature field inside the pipe network. Fluent (flow field calculation software) was used to calculate the pressure and temperature fields in the flow field under different temperature conditions. The total pressure inlet, mass flow outlet, and temperature of the inlet medium were set in the calculation process. The temperature load of the pressure field in the flow field can be applied to the solid field when data transmission is established between the flow field analysis module (Fluent) and the thermal stress analysis module (Thermal-Stress). The interface between the fluid and solid domains should be highly matched to guarantee that the pressure and temperature loads can be accurately transferred to specify the solid domain. Finally, the analysis of pipe network stress in the static-structure module was conducted. 3.1. Calculation model and mesh generation DN1400 mm caliber was selected as the research object. Its numerical calculation and experiment were performed. Elbow pipe was selected as the 1.5D bend radius large-diameter and connected with the straight pipe. The design parameters are shown in Table 1, and the pipe network structure is shown in Fig. 1. Grid division: The flow field, solid domain, and local enlarged drawing are shown in Fig. 2. As is shown in Fig. 2(a), the checkedge for grid independence was located at external surface of inlet pipe, and parallel to the Y axis. Four key points were selected at this edge to compare the equivalent stress values of various grid conditions. The interval length of each point is 8 m. Five kinds of grid partitions from sparse to dense were compared to increase the speed and accuracy of the simulation, which are shown in Table 2. The equivalent stresses of four points are shown in Fig. 3. The temperature showed less variation when the grid number increased from 300,000 to 700,000. When the number of grid was greater than 300,000, the results became not sensitive to the grid number, thus the grid was considered independent. Therefore, the selected computational grid number was 331,520. The convection field was divided into 215,760 elements using the ICEM-CFD software [24]. The structure domain used the grid partition function of Workbench ANSYS software, and the pipe body was divided into 115,760 elements.
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set to the pressure reference point using the standard k-e turbulence model and SIMPLEC algorithm [25]. The relative pressure was zero, and the convergence precision was 105. In addition, the pipe body structure load of the heating system included the internal pressure and heat transfer between the outer wall of the pipe and the covering soil, and the convection heat transfer coefficient was selected by the industry standard of ‘‘Institute of urban construction, Technical specification for directly buried hot-water heating pipeline in city CJJ/T 81-2014, China building industry press”. The material of the tube structure in the numerical simulation of the flow-heat-solid coupling was Q235B steel. The coefficient of thermal expansion was 12.5 106 m(m°C)1. The material properties included the density (7850 kgm3), elastic modulus (19.7 104 MPa), and Poisson’s ratio (0.3). The outside of the fluid and the inner side of the tube body were set as the interaction surfaces. The most unfavorable pipe network conditions were simulated, that is, the pipe network in the anchorage section, such that the inlet and outlet sides were set with no displacement constraints. 4. Analysis of results 4.1. Comparison of experimental parameters The experimental team cooperated with a manufacturer to design the corresponding experiments and measure the key working condition parameters of the whole pipe network in view of the research network to verify the accuracy of the numerical model. The experiment of the pipe network was set as a repetitive experimental study. Experiments were conducted five times under the same conditions, and the monitoring parameters were obtained through the average value. Therefore, the experimental error was very small and the results were accurate. The specific value of the experimental result at each instance was omitted in the paper because of space limitations. Thus, only the average values are shown in Table 3. The pipe network was simulated at the same time. The comparison of the experimental and simulation monitoring parameters is shown in Table 3. Specific parameters were selected from the inlet and outlet ends, and the average value of each end face was measured. The result errors of the experiment and simulation were within 2%, which was consistent with the accuracy of the engineering calculation, and the accuracy of the numerical model was proven.
3.2. Flow field boundary condition 4.2. Analysis of pressure and temperature fields in the fluid domain The flow field was calculated using Fluent. The inlet was set to the pressure inlet, and the pressure value was 1.6 MPa. The outlet was set to the pressure outlet, and the pressure value was 1.4 MPa. The solid wall surface was set to a no slip boundary condition. The wall roughness was set according to the actual condition based on the standard wall function treatment. The center of the inlet was
Table 1 Important design parameters. Design parameters
Design data
External diameter (D)/mm Wall thickness/mm Inlet straight pipe length (L1)/mm Outlet straight pipe length (L2)/mm Elbow arm length (L3)/mm Bending radius (R)/mm Internal pressure (P)/MPa Specific frictional head loss/(Pam1) Convective heat transfer coefficient/(Wm2K1)
1422 16 36,000 24,000 L3 = 1.5D = 2133 2133 1.6 300 1000
The pressure and velocity distributions in the system was obtained by simulating the temperatures of different media, as shown in Fig. 4. The pressure from the inlet to the outlet of the inlet straight pipe section decreased gradually. The internal pressure of the elbow was less than the straight pipe section of the elbow inlet and larger than the straight pipe section of the elbow. The surface pressure near the corner wall was small inside the elbow, and the high-pressure zone was located at the corner of the outer wall. Therefore, inner arch of elbow was also the most prone to cavitation. Thus, cavitation was also most likely to occur in this area. This shows that the temperature of the medium did not affect the internal pressure of the pipe network because the pressure value and distribution of the straight pipe and elbow were basically the same under different temperature conditions. The temperature field of the pipe network was studied only when the medium temperature was 140 °C because of space limitations. The temperature field distribution at the center of the pipe network is shown in Fig. 5. The flow boundary layer appeared on
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1- Elbow outlet cross section, 2- Elbow 45 cross section, 3- Elbow inlet cross section, 4- Elbow outlet arm cross section, 5- Elbow inlet arm cross section Fig. 1. Schematic diagram of the pipe network structure.
(a) The pipe body grid
(b) Flowing medium grid
(c) Local magnification of elbow body
Fig. 2. Grid partition graph.
Table 2 Five types of grid partition. Different grid partitions
1
2
3
4
5
Total number Convection field Structure domain
220,719 135,670 85,049
331,520 215,760 115,760
476,016 280,596 195,420
583,175 325,690 257,485
696,251 380,565 315,686
Table 3 Comparison of monitoring parameters.
Maximum equivalent stress (MPa)
90
85
80
75
No.2 point
70 No.3 point
65
60 200000
Monitoring parameters
Experimental results
Numerical simulation results
Inlet vertex velocity/(ms1) Inlet vertex temperature/K Outlet vertex temperature/K Inlet vertex gauge pressure/Pa Outlet vertex gauge pressure/Pa Inlet vertex stress/MPa Outlet vertex stress/MPa Elbow vertex stress/MPa
4.13 412.50 411.60 1,590,300 1,580,310 320.14 380.32 78.46
4.21 413.20 412.65 1,591,233 1,580,000 328.93 383.42 80.372
No.1 point
No.4 point
300000
400000
500000
600000
Grid number Fig. 3. Grid independent verification results.
700000
the solid wall, and the fluid velocity was lower than that of the main area because of the viscous effect of the medium. Therefore, the temperature near the wall was slightly lower than that of the main central area, and the whole temperature of the pipe network gradually decreased from the inlet end face to the end face of the
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(a)100
(b)140
(c)180 Fig. 4. The pressure and velocity clouds in center section of pipe network and local magnification.
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4.3. Analysis of temperature field, structure stress, and deformation in solid state
Fig. 5. Distribution of temperature field in the center section of the pipe network (°C).
outlet. The inner wall of the elbow was measured at the lower part of the overall temperature, in which the lowest temperature point was 139.55 °C. The temperature gradually increased close to the outer wall, reached the maximum at the main area, and then gradually decreased.
This section focuses on the analysis of the stress and deformation of the pipe wall of the pipe network under different media temperatures. The stress field of the pipe network was studied only at the medium temperature of 140 °C because of space constraints. The temperature distribution of the outer surface of the pipe network at 140 °C is shown in Fig. 6. Fig. 6 shows that the temperature of the surface of the tube body is higher than that of the outer surface, and the temperature of the tube body decreases gradually from the entrance of the stage to the elbow. The heat speeded up because the turbulence strengthened. Thus, the temperature appeared to rise at the outlet of the elbow until the exit pipe section, and then gradually decreased. Inlet temperature was the highest, and outlet temperature was the lowest. The equivalent stress distribution of the pipe network under the design condition at 140 °C is shown in Fig. 7. The equivalent stress cloud of outer and inner surface of the inlet and outlet are shown in Fig. 8a, b, c, and d. The equivalent stress value of the pipe network was in the range of 11.46 MPa–84.9 MPa, and the stress concentration phenomenon occurred at the fixed section of the inlet outlet. The maximum equivalent stress of the pipe was 672.93 MPa, which occurred at the fixed part of the outlet pipe. This was because the stress concentration caused by the outlet straight pipe section anchorage cannot be released. Therefore, the sections, where the anchorage may appear in the pipe section, should be given more attention in the design process to ensure the longterm effective operation of the pipe network. The elbow was part of the release of stress components for the whole pipe network. Thus, the elbow stress was significantly less than the inlet and outlet pipe section stresses, and the equivalent minimum stress value appeared at the 45° center section of the
Fig. 6. Outer surface and inner surface temperatures of the pipe network (°C).
Q. Xu et al. / International Journal of Heat and Mass Transfer 111 (2017) 953–961
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Fig. 7. Equivalent stress distribution of the hot water pipe network (MPa).
Fig. 8. Distribution of equivalent stress distribution in the hot water pipe network section at 140 °C (MPa).
elbow. Fig. 8 shows that the equivalent stress on the inner wall of the same position is obviously larger than that on the outer wall. Therefore, the inner wall of the corrosion protection process should be given more attention during the engineering construction process to avoid the damage caused by fatigue and larger stress.
The total deformation of the pipe network at 140 °C is shown in Fig. 9. Fig. 9 shows that the maximum total deformation of the pipe network is at the outer surface of the elbow, close to the entrance wall. The minimum deformation is located at the entrance end face. The total deformation of the pipe network gradually increases
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Fig. 9. Total deformation distribution of the hot water pipe network at 140 °C (mm).
Table 4 The maximum equivalent stress and deformation under different temperature conditions. Temperature/°C
60 80 100 120 140 160 180
Maximum equivalent stress/MPa
Maximum deformation/mm
Pressure load
Temperature load
Coupled load
Pressure load
Temperature load
Coupled load
126.66 126.66 126.66 126.66 126.66 126.66 126.66
193.98 296.23 398.48 500.73 602.98 705.24 807.49
278.60 373.58 471.22 571.65 672.93 774.46 876.16
143.6 143.6 143.6 143.6 143.6 143.6 143.6
31.226 47.679 64.131 80.584 97.037 113.49 129.94
148.89 154.18 160.99 169.13 178.43 188.70 199.81
from the inlet end to the elbow, which is in line with the requirements of applied loads and constraints. 4.4. Influence of different medium temperatures on elbow stress and deformation In the design conditions of different media temperatures, the stress and deformation size and the distribution of the pipe body are separately under the pressure and temperature loads. The equivalent maximum stress and total deformation are shown in Table 4. Table 4 shows that the equivalent maximum stress and deformation of the pipe increase with the temperature of the medium, and the stress and deformation caused by the temperature load increase with the temperature. The pressure load did not change with the increase of the medium temperature. Thermal stress was greater than the stress value caused by pressure load, and the thermal deformation was less than that of the deformation caused by pressure load. Therefore, the influence of the structure caused by the temperature change should be considered during the analysis and calculation of the
pipe network under the condition of a certain working pressure and an abnormal structure temperature. The thermal stress load caused by the higher temperature may cause harm. In addition, the stress and the deformation under the combined action of two kinds of loads were not equal to the sum of the stress and the deformation of the two kinds of loads. This shows that pressure and temperature loads are not separate from each other, and the deformation and stress of the pipe network are coupled. 4.5. Strength check The stability analysis of the classification stress checking algorithm was used to check the strength of the pipe network structure. The stability analysis of the common action of primary stress and the two stresses was provided. Although the twostress corresponding to the finite plastic deformation will not cause damage, the strength condition of the limit analysis was set to less than three times that of the basic allowable stress considering the safety factor, that is, rr 6 3½r, to ensure the stable state of the hot water pipe network operation. The allowable stress
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of the Q235B material was 125 MPa, and the maximum stress value of the pipe network was less than the allowable stress of the material at 60 °C and 80 °C. Therefore, the structure strength satisfied the requirement. However, the maximum stress value at 100 °C was 471.22 MPa, which was more than three times the allowable stress of the material. Thus, the structural strength did not satisfy the requirement, and the material of higher strength should be considered as a replacement. The maximum stress value was higher when the medium temperature was higher. Thus, the strength of the material should be considered in the design of the pipe network structure. 5. Conclusions (1) The stress and deformation of the anchor section of the ‘‘L”type heat pipe network were mainly affected by the temperature of the fluid, and the effect of pressure load was small. (2) Considering the temperature and pressure loads together, the maximum equivalent stress of the ‘‘L”-type heat pipe network was located at the entrance end face. The maximum equivalent stress was located at the outlet end when the temperature load was considered single. The maximum equivalent stress was located in the region near the short arm of the elbow when the fluid pressure load was considered single. (3) The pressure and temperature loads are not separate from each other, and the deformation and stress of the pipe network are coupled. Considering the temperature and pressure loads together or separately, the maximum deformation of the anchoring section of the ‘‘L”-type heat pipe network occurred in the elbow, close and outside the long arm of the region. (4) The medium temperature was up to 80 °C for the Q235B material when stability analysis was used to check the anchorage segment of the ‘‘L”-type heat pipe network. A new material of higher strength should be selected for pipe network or the stress of the import and export on the anchorage end should be released to ensure the safe operation of the pipe network when the temperature is higher than 80 °C.
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