1、LOCAL HEATINGOF PIPING: THERMALANALYSISSTP-PT-079STP-PT-079 LOCAL HEATING OF PIPING: THERMAL ANALYSIS Prepared by: Cole Davis, M.Sc. Quest Integrity USA, LLC Date of Issuance: June 30, 2016 This report was prepared as an account of work sponsored by ASME Pressure Technology Codes it is therefore nec
2、essary to numerically approximate their So ak B an dH ea t B an dGr ad ien t C ontr ol B an dSTP-PT-079: Local Heating of Piping: Thermal Analysis 4 solutions with computational modeling. As a part of the numeric solution, some assumptions are necessary; these assumptions frequently include the Reyn
3、olds decomposition that breaks the velocity field into components of its mean and fluctuation. Employing this assumption leads to an inequality between equations and variables, which requires the use of a turbulence model 4. The k- turbulence model is formulated from the far field flow and therefore
4、 captures flow best in that region, however it often requires a wall function to capture turbulence near any boundary. The k- turbulence model is formulated in the near-wall region and therefore captures flow best in that region, however its accuracy is less in the far field flow. The k- SST turbule
5、nce model uses the k- turbulence model in the near-wall region and the k- turbulence model in far field flow. It combines the models using a blending function in the transition region to produce an accurate turbulence model for both far field flow and boundary layer flow 5. Although these models are
6、 primarily concerned with pipe temperatures, natural convection plays a significant role in overall heat transfer, therefore the k- SST turbulence model was implemented for the steady state CHT CFD analyses. Several other assumptions/physics were included in these models. Natural convection in the d
7、omain was modeled as an ideal gas, with temperature-dependent dynamic viscosity accounted for using Sutherlands Law. Temperature-dependent thermal conductivity was included in the material properties of air 6, pipe metal 7, and insulation 8. Gravitational effects were included to capture buoyancy ef
8、fects for natural convection. Conduction, convection, and surface-to-surface radiation effects were modeled to capture all applicable heat transfer mechanisms. An important factor in the analysis is the appropriate handling of the thermal contact between the layers. Heat flow between two contacting
9、solid bodies depends on thermal contact conductance, . The inverse of this quantity 1/ is referred to as thermal contact resistance. Heat flow, , in a solid body is governed by Fouriers Law: = where is the thermal conductivity, is the cross sectional area, and the thermal gradient is given by . Howe
10、ver, the heat flow through two contacting bodies is given by = ( )+(1 )+( )where the two bodies in contact are defined in Figure 2-3. STP-PT-079: Local Heating of Piping: Thermal Analysis 5 Figure 2-3: Two body thermal contact Note that the contact between bodies create a discontinuity in the temper
11、ature distribution. The heat flow across a contact boundary can be written as = The effect of contact resistance must be included to obtain the proper temperature distribution. In the case of the piping heating system, the contact resistance must be included between the heating layer and piping to o
12、btain the physical temperature distribution. Contact resistance (or conductance) is a function of the contact area between two bodies on a microscopic scale. For the piping system, this contact resistance is a function of the heating element size, element geometry, element layout (pattern), contact
13、pressure (“tightness” of the wrap), pipe size, and pipe surface condition (including roughness and cleanliness). Unlike the pipe, the insulation blanket can conform easier to the heating elements, resulting in a different contact resistance. When solving the CHT problem using CFD, the thermal contac
14、t resistance can be directly specified at a contact interface. Values of thermal contact resistance are difficult (or impossible) to determine analytically, and therefore are typically determined through experimental measurement. For this analysis, the thermal contact resistance value was the “tunin
15、g” parameter used to match the computational solution to experimental measurements. Using thermal contact resistance as a tuning parameter allows the heating layer to be treated as uniform, rather than having to include detailed element layouts in the models. Note that since the actual temperature d
16、istribution is a function of the thermal contact resistance, which is a function of the particular heating elements used, the results are strictly valid only for the exact equipment used for the heat treating experiments. Other heat treating providers, alternative equipment, or alternative designs c
17、ould impact the thermal resistance, and thus the resulting thermal distribution. It is suggested that the heat treating experiments be repeated using alternate equipment or an alternate provider. Heat flows from the heating element into the piping and to the insulation via conduction. Heat is then l
18、ost to the surroundings via natural convection and radiation. Heat is applied to the system through a prescribed power input governed by a series of temperature probes. These temperature probes correspond to thermocouples used for control zones during PWHT. The power input is then adjusted such that
19、 the STP-PT-079: Local Heating of Piping: Thermal Analysis 6 temperature probes achieve the prescribed PWHT temperature. The boundary conditions for the system are shown below. The top boundary of the ambient domain was modeled as a pressure outlet so that air could circulate in and out of the model
20、 as needed without adding convection in the area of interest. Figure 2-4: Piping Heating Configuration. Full-symmetry shown, half-symmetry modelled The use of the CFD solver allows the buoyancy-driven flow pattern throughout the system to determine the film coefficients. This is advantageous as the
21、natural convection heat flow can be directly computed, rather than estimated. In addition, this allows 3D effects (top vs. bottom vs. sides of piping) to be included. This is important to determine an accurate temperature distribution around the weld. During the heat treatment, the surrounding air (
22、especially inside) the pipe will be expected to heat locally, resulting in spatially varying sink temperatures for a steady state analysis. Using CFD-based analysis allows the air temperature to be directly computed, rather than using an estimated (likely uniform) sink temperature. Note that suffici
23、ent mesh refinement is required to accurately capture boundary layer convective effects. The y+ value provides a measure of mesh refinement in the boundary layer. It is defined as the distance from the wall normalized by the viscous length scale 4. A value of 50 or less is recommended and a value of
24、 5 or less is highly preferred to ensure boundary layer accuracy. In all cases the y+ value was significantly less than 50 and only exceeded one at a limited number of points remote from the area of interest. Calibration Model Cases Experimental PWHT simulation measurements were taken for two differ
25、ent nominal pipe diameters, eight inch and 14 inch pipes, in four HB configurations for the former and three HB configurations for the later. For every case the weld was not placed rather the joined pipes were placed with ends abutting. Temperature readings were taken at the 3, 6, 9, and 12 oclock l
26、ocations at or near the centerlines on the outside diameter (OD) and inside diameter (ID) and at the 6 and 12 oclock locations axially along the OD of the pipe at the edge of the SB, HB, and GCB for every configuration. These configurations can be seen in Appendix A: and a summary of the cases can b
27、e found in Figure 2-5. Temperature measurements were taken as the pipes were heated to a nearly steady state condition and then allowed to cool. For the purposes of the steady state CFD calibration models, the temperature profiles at steady state were extracted and used exclusively. The extracted pr
28、ofiles can be seen in Figure 2-6. P r esc ribe d T em p er a tu r eR ad ia tion + C on v e c tionR ad ia tion + C on v ec tionSTP-PT-079: Local Heating of Piping: Thermal Analysis 7 Figure 2-5: Calibration case summary Description Case ID OD (in) Wall thickness (in) HB length (in) GCB length (in) 14
29、 inch narrow band 1 14 1.25 20 30.5 14 inch medium band 2 14 1.25 36.75 47.5 14 inch wide band 3 14 1.25 48 59.72 8 inch narrow band 4 8.63 1.375 15 23 8 inch medium band 5 8.63 1.375 30.5 38.5 8 inch wide band 6 8.63 1.375 45.5 53.3 8 inch medium band with second layer of insulation extending the l
30、ength of GCB 7 8.63 1.375 30.5 50.5 Figure 2-6: Circumferential ID and OD temperature profiles at centerline. Case Oclock ID Temp (F) OD Temp (F) Case Oclock ID Temp (F) OD Temp (F) Case 1 12 1214 1250 Case 4 12 1230 1255 3 1202 1249 3 1224 1257 6 1199 1249 6 1225 1258 9 1198 1249 9 1224 1253 Case 2
31、 12 1226 1250 Case 5 12 1240 1250 3 1227 1250 3 1238 1250 6 1221 1250 6 1234 1250 9 1217 1250 9 1241 1250 Case 3 12 1237 1252 Case 6 12 1241 1250 3 1238 1248 3 1236 1250 6 1235 1250 6 1236 1250 9 1233 1249 9 1239 1250 Case 7 12 1242 1250 3 1240 1250 6 1236 1250 9 1243 1251 The CFD models were calibr
32、ated by setting the temperature probe control points mentioned in section 2.2 to the measured OD centerline temperatures measured in the data and listed in Figure 2-6. The contact resistance between the pipe and the heating band was adjusted until ID temperature probes matched the measured ID experi
33、mental data listed in Figure 2-6. Weight was given to matching the wide band data more closely than the narrow band data while erring on the conservative or greater temperature difference between OD and ID surfaces. Matching was achieved using four control zones similarly to the four control zones u
34、sed in the experimental cases. Temperature dependent thermal conductivity for the pipes was taken from ASME BPV Part 2 Section D 7. The 14 inch diameter experiment and CFD modeling were performed using 1Cr-1/2Mo material and STP-PT-079: Local Heating of Piping: Thermal Analysis 8 the eight inch diam
35、eter experiment and CFD modeling was performed using carbon steel. The CFD model interpolated between the table values for exact temperature thermal conductivity values. Prediction Model Cases The prediction models used the same models developed for the calibration cases with a few parameter changes
36、. For all of the prediction cases, material properties for P91 steel were used. The temperature-dependent thermal conductivity values were extracted from ASME BPV Part 2 Section D 7. Five different diameters with three thicknesses each were modeled. The SB was assumed to be three times the pipe thic
37、kness as given in ASME B36.10M 9. The GCB was calculated using the equation = +4, where R is the inside radius and t is the pipe thickness. This equation is found in AWS D10.10 1. The HB was iteratively changed until the maximum temperature difference in the soak band was no more than 15F. A summary
38、 of the pipe dimensions for each case can be seen in Figure 2-7. Figure 2-7: Prediction model geometry parameters Nominal diameter OD (in) Pipe schedule Thickness (in) SB (in) Pipe length (in) 6 6.625 80 0.432 1.296 132.5 120 0.562 1.686 132.5 160 0.719 2.157 132.5 10 10.75 80 0.594 1.782 215 120 0.
39、844 2.532 215 160 1.125 3.375 215 14 14 80 0.75 2.25 280 120 1.094 3.282 280 160 1.406 4.218 280 24 24 80 1.219 3.657 480 120 1.812 5.436 480 160 2.344 7.032 480 30 30 80 1.356* 4.068 600 120 2.015* 6.045 600 160 2.607* 7.821 600 Note: ASME B36.10M 9 does not specify a thickness for 30 inch diameter
40、 schedule 80, 120, 160 pipes so the proportional thicknesses were scaled from the 24 inch diameter pipe and the 30 inch diameter schedule 30 pipe. STP-PT-079: Local Heating of Piping: Thermal Analysis 9 3 RESULTS Calibration Model Cases The calibration cases were run to steady state while the therma
41、l contact resistance was adjusted to match the centerline ID temperature measurements from the experimental cases. The OD temperature probes were set to adjust the power input such that their value matched the experimental measurements at the same locations. The calibrated resistance value was found
42、 to be 0.0037 m2K/W. the calibrated centerline temperature profiles can be seen in Figure 3-1. The optimum value of resistance varied with each experimental case. Note that the most conservative value of resistance was used (Case 6) for subsequent analyses. Figure 3-1: Calibration centerline ID temp
43、eratures for thermal contact resistance of 0.0037 m2K/W Case o-clock ID CFD (F) ID Experimental (F) Case 1 12 1195.754 1214 3 1189.911 1202 6 1187.924 1199 Case 2 12 3 6 Case 3 12 1232.28 1237 3 1227.191 1238 6 1224.968 1235 Case 4 12 1199.439 1230 3 1195.749 1224 6 1193.333 1225 Case 5 12 3 6 Case
44、6 12 1240.318 1241 3 1238.18 1236 6 1236.866 1236 Case 7 12 3 6 As discussed with ASME, note that in the final calibration, run cases 2, 5, and 7 were omitted because of non-standard geometry irregularities. Prediction Model Cases The prediction model cases were run to nearly steady state. There did
45、 exist some minor transient flow in the models, however its nature is relatively small and should not affect the overall results of the models. Five different pipe diameters were investigated with three different pipe thicknesses per diameter. The temperature desired for proper PWHT in P91 steel is
46、between 1350 and 1400F, therefore the temperature STP-PT-079: Local Heating of Piping: Thermal Analysis 10 control probes were set to 1390F such that the minimum temperature in the SB exceeded 1350F. For 14 inch diameter and larger pipes, four control zones were used so that the temperature could be
47、 controlled at the 12, 3, and 6 oclock locations. For the six and ten-inch diameter pipes, two control zones were used so that temperature could be controlled at the 12 and 6 oclock locations. The HB and GCB were iteratively increased in length until the maximum temperature difference in the SB was
48、less than 15F. This occurred with four to six iterations per geometry. For all final HB lengths the minimum SB temperature exceeded the desired 1350F. The trend followed roughly a power relation between temperature differences desired to HB length required. To calculate the HB required for a 15F tem
49、perature difference (delta 15 points), for each case a linear interpolation was performed between the bounding iterations. This can be seen in Figure 3-2 through Figure 3-6. Figure 3-2: CFD SB delta T results for 6 inch schedule 80, 120, 160 P91 pipes 010203040506070800 5 10 15 20 25 30 35 40HB Length(in)Delta T ( F )HB l e ngt h (C FD ) v s . Del ta T for 6 .6 2 5 in P ipeS c h 80S c h 12 0S c h 16 0A W S D1 0.1 0 S c h 80A W
