STP-PT-053 CRITERIA DOCUMENT FOR SHELL-AND-TUBE HEAT EXCHANGERS ACCORDING TO PART UHX OF ASME SECTION VIII DIVISION STP-PT-053 CRITERIA DOCUMENT FOR SHELL-AND-TUBE HEAT EXCHANGERS ACCORDING TO PART UHX OF ASME SECTION VIII DIVISION Prepared by: Francis Osweiller OSWECONSULT Date of Issuance: March 22, 2013 This report was prepared as an account of work sponsored by ASME Pressure Technologies Codes and Standards and the ASME Standards Technology, LLC (ASME ST-LLC) Neither ASME, ASME ST-LLC, the author, nor others involved in the preparation or review of this report, nor any of their respective employees, members or persons acting on their behalf, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe upon privately owned rights Reference herein to any specific commercial product, process or service by trade name, trademark, manufacturer or otherwise does not necessarily constitute or imply its endorsement, recommendation or favoring by ASME ST-LLC or others involved in the preparation or review of this report, or any agency thereof The views and opinions of the authors, contributors and reviewers of the report expressed herein not necessarily reflect those of ASME ST-LLC or others involved in the preparation or review of this report, or any agency thereof ASME ST-LLC does not take any position with respect to the validity of any patent rights asserted in connection with any items mentioned in this document, and does not undertake to insure anyone utilizing a publication against liability for infringement of any applicable Letters Patent, nor assumes any such liability Users of a publication are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility Participation by federal agency representative(s) or person(s) affiliated with industry is not to be interpreted as government or industry endorsement of this publication ASME is the registered trademark of the American Society of Mechanical Engineers No part of this document may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher ASME Standards Technology, LLC Two Park Avenue, New York, NY 10016-5990 ISBN No 978-0-7918-6876-8 Copyright © 2013 by ASME Standards Technology, LLC All Rights Reserved Criteria Document for Shell-and-Tube Heat Exchangers STP-PT-053 TABLE OF CONTENTS Foreword xi Abstract xii PART INTRODUCTION 1 SCOPE 2 HISTORICAL BACKGROUND 3 TYPES OF HEAT EXCHANGERS COVERED TYPES OF TS CONFIGURATIONS LOADING CASES STRUCTURE OF PART UHX 10 STRUCTURE OF THE DOCUMENT 11 NOTATIONS 12 References—Part 13 PART TUBESHEET CHARACTERISTICS 14 SCOPE (UHX-11.1) 15 NOTATIONS 16 DESIGN ASSUMPTIONS (UHX-11.2) 17 LIGAMENT EFFICIENCIES (UHX-11.5.1) 18 4.1 Introduction 18 4.2 Historical Background 19 4.3 LE in Part UHX (UHX-11.5.1) 20 EFFECTIVE ELASTIC CONSTANTS (UHX-11.5.2) 25 5.1 Introduction 25 5.2 Historical Background 25 5.3 The Square Pattern Problem 26 5.4 Synthesis of Results 27 5.5 Determination of EEC for the Full Range of μ* (0.1≤μ*≤1.0) 28 5.6 Determination of EECS for UHX Rules (UHX-11.5.2) 28 5.7 Conclusion 29 References—Part 33 PART ANALYTICAL TREATMENT OF FIXED TUBESHEET HEAT EXCHANGERS 34 SCOPE (UHX-13.1) 35 HISTORICAL BACKGROUND 36 GENERAL 37 3.1 TS Configurations (UHX-13.1) 37 3.2 Notations (UHX-13.3) 38 iii STP-PT-053 Criteria Document for Shell-and-Tube Heat Exchangers 3.3 Loading Cases (UHX-13.4) 42 3.4 Design Assumptions (UHX-13.2) 43 3.5 Basis of Analytical Treatment 44 3.5.1 General 44 3.5.2 Free Body Diagram 46 AXIAL DISPLACEMENTS AND FORCES ACTING ON THE TUBES AND ON THE SHELL 47 4.1 Axial Displacement and Force Acting on the Tubes (Figure 18) 47 4.2 Axial Displacement and Force Acting on the Shell 48 DEFLECTION AND LOADS ACTING ON THE TUBESHEET 51 5.1 Equivalent Plate Resting on an Elastic Foundation 51 5.2 Determination of Integration Constants A and B 55 5.3 Deflection 56 5.4 Net Effective Pressure 57 5.5 Rotation 57 5.6 Shear Force 57 5.7 Bending Moment 59 5.8 Conclusion 59 TREATMENT OF THE UNPERFORATED RIM 60 6.1 Edge Loads Applied on Shell and Channel at their Connection to the TS 60 6.2 Equilibrium of the Unperforated Rim 62 6.3 Edge Loads Va and Ma Applied to the Tubesheet 65 EQUIVALENT PRESSURE ACTING ON TUBESHEET 69 7.1 Definition 69 7.2 Determination of Pe 70 STRESSES IN THE HEAT-EXCHANGER COMPONENTS 74 8.1 TS Net Effective Pressure 74 8.2 TS Axial Displacement 74 8.3 TS Rotation 75 8.4 Stresses in the Tubesheet 76 8.5 Axial Membrane Stress in Tubes 79 8.6 Stresses in the Shell 80 8.7 Stresses in the Channel 83 8.8 How to use the Rules 84 DETERMINATION OF THE ALLOWABLE STRESS LIMITS 85 9.1 General Considerations 85 9.2 Allowable Stress Limit in the Tubesheet 86 9.3 Allowable Stress Limit in the Tubes 86 9.4 Allowable Membrane Stress Limit in the Shell 86 iv Criteria Document for Shell-and-Tube Heat Exchangers STP-PT-053 9.5 Allowable Membrane+Bending Stress Limit in the Shell 87 9.6 Allowable Membrane+Bending Stress Limit in the Channel 87 9.7 Conclusions 87 10 ADDITIONAL RULES 88 10.1 Effect of Different Shell Thickness and Material Adjacent to the TS (UHX-13.6) 88 10.2 Effect of Plasticity at Tubesheet-Shell-Channel Joint (UHX-13.7) 90 10.3 Effect of Radial Thermal Expansion Adjacent to the Tubesheet (UHX-13.8) 92 10.4 Calculation Procedure for Simply Supported Tubesheets (UHX-13.9) 95 10.5 Tubesheet Flange Extension (UHX-9) 96 10.6 HE Set-up with a Thin-Walled Expansion Joint (UHX-13.16) 97 10.7 HE Set-up with a Thick-Walled Expansion Joint (UHX-13.17) 97 11 CHECKING OF THE RESULTS 98 11.1 Comparison with FEA 98 11.2 Comparison with CODAP French Rules 100 11.3 Comparison with TEMA Rules 105 11.4 Comparison with Circular Plates Subject to Pressure 112 11.5 Conclusions 114 References—Part 115 PART FLOATING TUBESHEETS 116 SCOPE 117 HISTORICAL BACKGROUND 118 GENERAL 119 3.1 TS CONFIGURATIONS (UHX-14.1) 119 3.2 Notations 120 3.3 Loading Cases (UHX-14.4) 124 3.4 Design Assumptions (UHX-14.2) 125 3.5 Basis of Analytical Treatment 126 3.5.1 General 126 3.5.2 Free body diagram for ST TS 127 3.5.3 Free body diagram for FL TS 128 AXIAL DISPLACEMENTS AND FORCES ACTING ON THE TUBES AND ON THE SHELL 130 4.1 Axial Displacement and Force Acting on the Tubes (Figure 42) 130 4.2 Axial Displacement and Force Acting on the Shell (Figure 43) 131 DEFLECTION AND LOADS ACTING ON THE TUBESHEET 132 5.1 Equivalent Plate Resting on an Elastic Foundation (Figure 44) 132 5.2 Determination of Integration Constants A and B 133 TREATMENT OF THE UNPERFORATED RIM 134 6.1 Edge Loads Applied on Shell and Channel at their Connection to the TS 134 6.2 Equilibrium of the Unperforated Rim 134 v STP-PT-053 6.2.1 6.2.2 6.2.3 Criteria Document for Shell-and-Tube Heat Exchangers Due to Axial Loads 134 Due to Applied Moments 140 Edge Loads Va and Ma Applied to the Tubesheet 140 EQUIVALENT PRESSURE ACTING ON THE TUBESHEET 141 STRESSES IN THE HEAT-EXCHANGER COMPONENTS 142 DETERMINATION OF ALLOWABLE STRESS LIMITS 143 10 ADDITIONAL RULES 144 11 HOW TO USE THE RULES 145 11.1 Stationary TS 145 11.2 Floating TS 145 11.3 Calculation Procedure 145 11.4 Calculation Using a Fixed TS HE Software 146 References—Part 147 PART ANALYTICAL TREATMENT OF U-TUBE TUBESHEET HEAT EXCHANGERS 148 SCOPE 149 HISTORICAL BACKGROUND 150 GENERAL 151 3.1 TS Configurations (UHX-12.1) 151 3.2 Notations 151 3.3 Loading Cases (UHX-12.4) 154 3.4 Design Assumptions (UHX-12.2) 155 3.5 Basis of Analytical Treatment 155 3.5.1 General 155 3.5.2 Free Body Diagram 156 TREATMENT OF THE PERFORATED TUBESHEET 158 TREATMENT OF THE UNPERFORATED RIM 159 5.1 Edge Loads Applied on Shell and Channel at their Connection to the TS 159 5.2 Equilibrium of the Unperforated Solid Rim 159 STRESSES IN THE HEAT-EXCHANGER COMPONENTS 165 6.1 Stresses in the Tubesheet 165 6.2 Stresses in the Shell and Channel 165 6.3 Determination of Stresses using the Fixed TS Rules 166 DETERMINATION OF THE ALLOWABLE STRESS LIMITS 167 ADDITIONAL RULES 168 8.1 Effect of Plasticity at Tubesheet-Shell-Channel Joint (UHX-12.5) 168 HOW TO USE THE RULES 169 10 COMPARISON WITH TEMA RULES 170 10.1 TEMA Formula 170 vi Criteria Document for Shell-and-Tube Heat Exchangers STP-PT-053 10.2 Numerical Comparisons 170 References—Part 172 PART SUMMARY AND CONCLUSIONS 173 SUMMARY AND CONCLUSIONS 174 LIST OF ANNEXES Annex A —Values of Effective Elastic Constants from Various Authors 177 Annex B —Values of Effective Elastic Constants for the Full Range of μ (0.1≤μ*≤1.0) 179 B.1 Introduction 179 B.2 Curves (From [13] ) 179 B.3 Numerical Values (From [13] ) 180 B.4 Polynomials 185 Annex C —Poisson’s Ratio in Tubes and Shell 186 Annex D —Shell Pressure Acting on Expansion Joint Sidewalls 188 Annex E —Differential Pressure Acting on the Equivalent Solid Plate 189 Annex F —Solution of Differential Equation w(x) 191 Annex G —Coefficients Zd , Zv , Zw , Zm ; Qm , Qv ; Qα , Qβ ; Fm , Ft 193 Annex H —Radial Displacement and Rotation of the Shell at its Connection with the Ring 199 H.1 Radial Displacement Due to Internal Pressure Ps 199 H.2 Radial Displacement and Rotation due to Edge Loads Qs and Ms 200 H.3 Radial Displacement due to Internal Pressure and Edge Loads 200 H.4 Channel 201 Annex I —Shell-Ring Connection in Radial Direction 202 Annex J —Minimum Length of Shell and Channel when Integral with the TS 204 Annex K —Formulas for a Hemispherical Channel when Integral with the TS 206 K.1 Radial Displacement due to Internal Pressure Pc 206 K.2 Radial Displacement and Rotation due to Edge Loads Qs AND Ms 207 K.3 Radial Displacement due to Internal Pressure and Edge Loads 207 Annex L —Equilibrium of Ring Subjected to Edge Moments 208 Annex M —Direct Determination of the Equivalent Pressure 215 Annex N —Formulas to be used when Pe=0 219 N.1 Net Effective Pressure: q(x) 219 N.2 Axial Displacement: w(x) 219 N.3 Rotation: θ(x) 219 N.4 Bending Stress: σ(x) 219 N.5 Shear Stress: τ(x) 220 N.6 Axial Stress in Tubes: σt(x) 220 vii STP-PT-053 Criteria Document for Shell-and-Tube Heat Exchangers Annex O —Tabular and Graphical Representation of Coefficient Ft(x) 221 Annex P —Tabular and Graphical Representation of Coefficient Fm(x) 238 Annex Q —Tabular and Graphical Representation of Coefficient FQ(x) 249 Annex R —Calculation Sheet of a Fixed TS HE (EXAMPLE UHX-20.2.3) 261 Annex S —Determination of the Allowable Buckling Stress LimitS 262 Annex T —Common Intersection of Curves σt(x) 267 T.1 General 267 T.2 Determination of Common Intersection xo for σt(x) 267 T.3 Generalization to Other Stresses 268 Annex U —Determination of Stresses Using the Fixed TS Rules 269 Annex V —Calculation Using a Floating or Fixed TS HE Software 273 Annex W —UHX14 Example (2010 Edition) Stationary 274 Annex X —UHX14 – Example (2010 Edition) Floating 275 Annex Y —UHX13 – Example (2010 Edition) with General Equations 276 Annex Z —UHX12 – Example (2010 Edition) 277 Acknowledgements 278 Abbreviations and Acronyms 279 LIST OF TABLES Table 1—Values for E*/E and ν∗ for triangular pattern from Meijers [12] 26 Table 2—Values of E*/E and ν∗ for square pattern in pitch and diagonal directions from Slot and O’Donnell [7] 27 Table 3—Comparison of TEMA and ASME TS thicknesses for U-tube HEs 171 Table 4—Comparison of Effective Elastic Constants E* and ν∗ values by various theoretical methods for plane stress problem 177 Table 5—Values of Curves ν* as a function of μ* for ratios h/p=0.1, 0.15, 0.25, 0.5, 1.0 and 2.0 for TRIANGULAR pattern 181 Table 6—Values of Curves ν* as a function of μ* for ratios h/p=0.1, 0.15, 0.25, 0.5, 1.0 and 2.0 for SQUARE pattern 182 LIST OF FIGURES Figure 1—Three types of tubesheet heat exchangers Figure 2—Tubesheet configurations Figure 3—Ligament area in the actual tubesheet 18 Figure 4—Ligament orientation in the actual tubesheet 19 Figure 5—Ligament efficiency used in TEMA 20 Figure 6—TS equivalent diameter Do 20 viii Criteria Document for Shell-and-Tube Heat Exchangers STP-PT-053 Figure 7—TS with unperforated lanes 22 Figure 8—Tube expansion depth ratio ρ=lt,x/h 22 Figure 9—Pass partition groove on tube side of the TS 24 Figure 10—Pitch and diagonal directions for square pattern 27 Figure 11—Curves for the determination of E*/E and ν∗ (triangular pattern) 30 Figure 12—Curves for the determination of E*/E and ν∗ (square pattern) 31 Figure 13—Curves E*/E for square pattern obtained from polynomial approximation given in Figure 12 32 Figure 14 – Fixed tubesheet heat exchanger 35 Figure 15—Tubesheet configurations 38 Figure 16—Analytical model used in design method 45 Figure 17—Free body diagram of the analytical model 46 Figure 18—Axial displacement of tubes 47 Figure 19—Axial displacement of the shell 48 Figure 20—Loads acting on TS 51 Figure 21—TS displacement 52 Figure 22… 56 Figure 23—Ring equilibrium of the TS 62 Figure 24… 69 Figure 25—Bending stress distribution throughout the TS for Q3=0.0 and Xa=1, 3, 5, 7, 10 and 15 77 Figure 26—Shell with increased thickness adjacent to TSs 89 Figure 27—Temperature gradient at TS-shell-channel joint 93 Figure 28… 96 Figure 29—Minimum required thickness of the tubesheet flanged extension, h, 97 Figure 30—Comparison of tube stresses calculated per UHX and FEA (Example UHX-20.2.3) 99 Figure 31—Tube stress distribution obtained by UHX, CODAP and FEA throughout the TS from r =0 to r =ao 105 Figure 32—TEMA and ASME-CODAP coefficient F for X varying from X=0 to X=20 107 Figure 33—TEMA coefficient F 107 Figure 34—TEMA design range 108 Figure 35—Coefficient Fq as a function of X for SS and CL TS 110 Figure 36—Floating tubesheet heat exchangers 117 Figure 37—Stationary tubesheet configurations 119 Figure 38—Floating tubesheet configurations 120 ix Annex Z 1/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 U-TUBE Tubesheet Rules accord to UHX-12 (July 2010 Edition) highlighted in Yellow :most important data and results Case UHX-20.1.4 Geometric Data (from Fig.UHX-13.1) h := 3.5⋅ in For triangular pitch "Layout"=0 For square pitch "Layout"=1 Layout := ro := 12.75 ⋅ in Radius to outer tube A := 37.25 ⋅ in Outside Diameter of Tubesheet set Farenheit temp degF := R Configuration types: a, b, c, d, e, f "a" for shell/channel integral both sides "b" for shell integral, channel gask - TS extended Config := "e" "c" for shell integral, channel gask - TS not extended "d" for gasketed both sides "e" for channel integral, shell gask - TS extended "f" for channel integral, shell gask - TS not extended Bolt Circle Diameter C := 35⋅ in AL := 36.1⋅ in Total Untubed Lanes Area Tubesheet Corr Allow (Tubeside) h g := ⋅ in p := ⋅ in Tube Pitch Nt := 496 d t := 0.75⋅ in Number of Tubes tt := 0.085 ⋅ in Tube Thickness ρ := Tube expansion depth ratio ltx := ⋅ in Length of Expanded Portion of Tube Tube Outside Diameter ct := ⋅ in Tubesheet Corr Allow (Shellside) cs := ⋅ in Tubesheet Corr Allow (Shellside) SS := "NO" SS="YES" for Simply Supported TS calculation (for config a,b,c,e,f only) Ds := ⋅ in ts := 0.5⋅ in Shell ID Channel ID Dc := 31⋅ in tc := 0.625 ⋅ in Channel Thickness Shell Thickness Gs := 32.375⋅ in Shell Gasket Diameter Cs := ⋅ in Shell Corrosion Allowance Gc := ⋅ in G1 := ⋅ in Channel Gasket Diameter Cc := ⋅ in Channel Corrosion Allowance Contact mid-point TS/Flange CHAN := "CYL" "CYL" for Cylindrical Channel "HEMI" for Hemisherical Channel (for config a,e,f,only) Corroded thicknesses: Corroded diameters: h := h − cs − ct Tubesheet thickness Shell Thickness ts := ts − Cs h = 3.500 in tc := t c − Cc t c = 0.625 in Channel Thickness Ds := Ds + ⋅ Cs Dc := Dc + ⋅ Cc t s = 0.500 in 373 Shell ID Channel ID Ds = 0.000 in Dc = 31.000 in Annex Z 2/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 Loading conditions Ws := 656000⋅ lb shell flange design bolt load ( Wmax := max Ws , Wc channel flange design bolt load Wc := ⋅ lb ) Wmax = 656000.000 lb lb Shell Design Pressure Ps0 := 650 ⋅ in lb Tube Design Pressure Pt0 := 650 ⋅ in Design Pressures for the Seven Load Cases ⎛⎜ ⋅ lb ⎞ ⎜ in2 ⎟ Ps := ⎜ ⎟ P ⎜ s0 ⎟ ⎜ Ps0 ⎝ ⎠ ⎛⎜ Pt0 ⎞ ⎜ lb ⎟ Pt := ⎜ ⋅ ⎟ ⎜ in ⎟ ⎜ Pt0 ⎝ ⎠ ⎛ 0.000 ⎞ lb Ps = ⎜ 650.000 ⎜ ⎝ 650.000 ⎠ in ⎛ 650.000 ⎞ lb Pt = ⎜ 0.000 ⎜ ⎝ 650.000 ⎠ in Temperatures T := 400 ⋅ degF Tubesheet design temp Ta := 70⋅ degF Ambient temperature Ts := 400 ⋅ degF Shell design temp Tc := 400 ⋅ degF Channel design temp Tubesheet Material is SA-516 S := 20000 ⋅ lb Material Data TS allowable stress @ T lb E := 27.7⋅ 10 ⋅ in TS elastic modulus @ T in Tube Material is SA-179 lb StT := 13400 ⋅ in Tube allowable stress @ T t Shell Material is SA-516 lb Ss := ⋅ in Es := ⋅ lb in Tube elastic modulus @ T t in Shell allow stress @ T s lb Sys := ⋅ in Shell yield stress @ Ts Thin Shell elast mod @ Ts lb SPS.s := ⋅ in Shell allowable P+S stress @ Ts Shell Poisson' ratio ν s := 0.3 Channel Material is SA-516 lb Sc := 20000 ⋅ in lb Ec := 27.7⋅ 10 ⋅ ν c := 0.3 lb EtT := 27.7⋅ 10 ⋅ in Channel allow stress @ Tc lb Syc := 32500 ⋅ in Channel yield stress @ T c Channel elast modulus @ Tc lb SPS.c := 65000 ⋅ in Channel allowable P+S stress @ Tc Channel Poisson's ratio 374 Annex Z 3/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 Start of Calculations ( ) h'g := max h g − ct , h'g = 0.000 in ρ := ltx h ⎡ ⎛ EtT ⎞ ⎛ StT ⎞ ⎤ d* := max⎢d t − ⋅ tt⋅ ⎜ ⋅⎜ ⋅ ρ , d t − 2tt ⎥ d* = 0.636 in ⎣ ⎝ E ⎠⎝ S ⎠ ⎦ ( ρ = 1.000 ) UHX-12.5.1 Step Determine D , µ, µ* and h' g from UHX-11.5.1 : Do := ⋅ ro + d t Do = 26.250 in p p* := 1− ( ⋅ AL , 4Do ⋅ p π ⋅ Do ρ s := Ds Do Gs Do ρ c := Dc Do Gc Do ) p* = 1.035 ì 10 in à* := µ := if ( Config = "a" ) ∨ ( Config = "b" ) ∨ ( Config = "c" ) p* − d* p* p − dt p ρ s = 1.233 if ( Config = "d" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) if ( Config = "a" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) ρ c = 1.181 if ( Config = "b" ) ∨ ( Config = "c" ) ∨ ( Config = "d" ) M TS := Do ⋅ ⎡ ρ s − ⋅ ⎛ ρ s + 1⎞ ⋅ Ps − ρ c − ⋅ ⎛ ρ c + 1⎞ ⋅ Pt⎤ ⎝ ⎠ ⎝ ⎠ ⎦ 16 ⎣ ( ) ( ) 375 ⎛ −1.213 × 104 ⎞ ⎜ M TS = ⎜ 1.647 × 104 ⎟ lb ⎜ ⎟ ⎜ ⎝ 4.337 × 10 ⎠ µ* = 0.385 µ = 0.250 Annex Z 4/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 UHX-12.5.3 Step Calculate h/p If ρ changes, recalculate d* and µ* from UHX-11.5.1 Determine E*/E and ν* relative to h/p from UHX-11.5.2 h p = 3.500 µ* = 0.385 UHX-12.5.4 E* E = 0.4413 lb E* = 1.222 × 10 ν* = 0.318 in Step Calculate coefficients shell and channel parameters:β, k, λ, δ and ω : Use SS=YES for Simply Supported calculation in a nd step (see UHX-13.9) β s := 0.5 ⎡⎣( Ds + ts) ⋅ ts⎤⎦ β c := if SS = "NO" ∧ ( Config = "a" ∨ Config = "b" ∨ Config = "c" ) β s = 0.000 if SS = "NO" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) β c = 0.409 ⎡12⋅ ⎛ − ν 2⎞⎤ c ⎠⎦ ⎣ ⎝ in 0.25 0.5 ⎡⎣( Dc + tc) ⋅ tc⎤⎦ 1 in otherwise in k s := β s⋅ otherwise in 0⋅ SS = "NO" 0.25 ⎡12⋅ ⎛ − ν 2⎞⎤ s ⎠⎦ ⎣ ⎝ 0⋅ ( From right pages above ) Es⋅ ts 6⋅ ⎛ − ν s ⎝ k s = × 10 lb 2⎞ h's := h ⋅ β s k c := β c⋅ ⎠ h's = 0.000 × 10 ⎛⎜ h's ⎞ λ s := ⋅ k s⋅ ⎜ + h's + ⎠ ⎝ h ⋅ Ds Ec ⋅ t c 6⋅ ⎛ − ν c ⎝ h'c := h ⋅ β c 2⎞ k c = 5.064 × 10 lb ⎠ h'c = 1.431 × 10 ⎛⎜ h'c ⎞ λ c := ⋅ k c⋅ ⎜ + h'c + ⎠ ⎝ h ⋅ Dc lb λ s = 0.000 × 10 in λ c = 7.591 × 10 lb in δ s := νs ⎞ ⎛ ⎜1 − if SS = "NO" ∧ ( Config = "a" ∨ Config = "b" ∨ Config = "c" ) ⎠ 4Es⋅ ts ⎝ Ds ( ) −1 ⋅ in lb CHAN = "CYL" δ c := −1 δ s = × 10 in lb otherwise SS = "NO" νc ⎞ ⎛ ⎜1 − if SS = "NO" ∧ CHAN = "CYL" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) ⎠ 4Ec⋅ t c ⎝ Dc ⎛ − νc ⎞ ⎜ if SS = "NO" ∧ CHAN = "HEMI" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) 4Ec⋅ t c ⎝ ⎠ Dc ( δ c = 1.18 × 10 ) −1 ⋅ in lb −5 otherwise −1 in lb ( ) ω s := ρ s⋅ k s⋅ β s⋅ δ s⋅ + h's ω s = 0.000 in 376 ( ) ω c := ρ c⋅ k c⋅ β c⋅ δ c⋅ + h'c ω c = 7.013 in UHX-12.5.5 F := Annex Z 5/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 Step Calculate diameter ratio K and coefficient F : ⎡ − ν* ⋅ λ + λ + E⋅ ln( K) ⎤ if ( Config = "a" ) ⎢ (s c )⎥⎦ ⎣ E* ⎡ − ν* ⋅ λ + E⋅ ln( K) ⎤ if ( Config = "b" ) ∨ ( Config = "c" ) ⎢ (s )⎥⎦ ⎣ E* ⎡ − ν* ⋅ ( E⋅ ln( K) )⎤ if ( Config = "d" ) ⎢ ⎥ ⎣ E* ⎦ ⎡ − ν* ⋅ λ + E⋅ ln( K) ⎤ if ( Config = "e" ) ∨ ( Config = "f" ) ⎢ (c )⎥⎦ ⎣ E* K := A Do K = 1.419 F = 0.964 otherwise UHX-12.5.6 M* := Step Calculate moment M* acting on the unperforated ts rim : (MTS + ω c⋅ Pt − ω s⋅ Ps) ⎛ ⎜ MTS − ⎝ ⎛ ⎜ MTS − ⎝ ⎛ ⎜ MTS + ⎝ ⎛ ⎜ MTS + ⎝ ⎛ ⎜ MTS + ⎝ ω s⋅ Ps − ω s⋅ Ps − Gc − Gs ⋅ π ⋅ Do ω c⋅ Pt + ω c⋅ Pt − if ( Config = "a" ) C − Gc ⋅ Wc ⋅ π ⋅ Do G1 − Gc ⋅ π ⋅ Do ⎞ ⋅ Wmax ⎠ C − Gs ⋅ π ⋅ Do ⎞ if ( Config = "b" ) ⎠ ⋅ Wc ⎞ ⎠ if ( Config = "d" ) ⎞ if ( Config = "e" ) ⋅ Ws G1 − Gs ⋅ π ⋅ Do if ( Config = "c" ) ⎠ ⎞ ⋅ Ws ⎠ if ( Config = "f" ) 0lb otherwise 377 ⎛ 2.869 × 103 ⎞ ⎜ M* = ⎜ 2.691 × 104 ⎟ lb ⎜ ⎟ ⎜ ⎝ 1.934 × 10 ⎠ UHX-12.5.7 M* − M p := 15/05/2011 19:07 Step Calculate the max bending moments Mp ( at the periphery) , Mo ( at the center) : Do ( ⋅ F⋅ Ps − Pt 32 1+F ) ⎛ 8.332 × 103 ⎞ ⎜ M p = ⎜ 6.825 × 103 ⎟ lb ⎜ ⎟ ⎜ ⎝ 9.843 × 10 ⎠ ⎛ max⎛ Mo1 , Mp ⎞ ⎞ ⎠ ⎜ ⎝ M := ⎜ max⎛ M o , M p ⎞ ⎟ M = ⎠⎟ ⎜ ⎝ ⎜ max⎛ Mo , Mp ⎞ 3 ⎠⎠ ⎝ ⎝ M := Annex Z 6/12 UHX12-Case20.1.4(14may11)-(2010) ⎛ −1.489 × 104 ⎞ ⎜ Do ( ) M o := M p + ⋅ + ν* ⋅ ( Ps − Pt ) M o = ⎜ 3.005 × 104 ⎟ lb ⎜ ⎟ 64 ⎜ ⎝ 9.843 × 10 ⎠ ⎛ 1.489 × 104 ⎞ ⎜ ⎜ ⎟ lb ⎜ 3.005 × 10 ⎟ ⎜ ⎝ 9.843 × 10 ⎠ M o if SS = "OUI" ∧ ( Config = "a" ∨ Config = "b" ∨ Config = "c" ) M o if SS = "OUI" ∧ ( Config = "a" ∨ Config = "e" ∨ Config = "f" ) M otherwise UHX-12.5.8 Step Calculate the tubesheet bending stress σ : 6⋅ M σ := ⎛ 14887.535 ⎞ M = ⎜ 30045.009 lb ⎜ ⎝ 9842.828 ⎠ ( µ* ⋅ h − h'g ) ⎛ 18916.215 ⎞ lb σ = ⎜ 38175.417 ⎜ ⎝ 12506.372 ⎠ in σ max := max( σ ) σ max = 38175.417 σ allow := ⋅ S Calculate the minimum required thickness of the TS flanged extension for configurations b and e: h r := lb σ allow = 40000.000 1.9Wc C − Gc ⋅ if Config = "b" S⋅ Gc 2 in lb in h r = 1.589 in 1.9Ws C − Gs ⋅ if Config = "e" S⋅ Gs ⋅ in otherwise UHX-12.5.9 Step Calculate shear stress in the tubesheet τ : ⎛ 4875.000 ⎞ → lb ⎞ ⎛ Do ⎞ ⎯⎯⎯⎯ lb ⎛ τ := ⎜ ⋅⎜ ⋅ Ps − Pt τ = ⎜ 4875.000 τ max := max( τ ) τ max = 4875.000 ⎜ h 2 ⋅ µ ⎝ ⎠⎝ ⎠ in ⎝ 0.000 ⎠ in τ allow := 0.8⋅ S τ allow = 16000.000 If |Ps-Pt|>3.2Sµh/D o , the TEMA formula may be used, provided the data A p and Cp have been defined Ap := 510.7 ⋅ in Total area enclosed by C p ⎛ 4736.294 ⎞ → lb ⎞ ⎛ Ap ⎞ ⎯⎯⎯⎯ ⎛ τ := ⎜ ⋅ ⎜ ⋅ Ps − Pt τ = ⎜ 4736.294 ⎜ ⎝ µ ⎠ h ⎝ Cp ⎠ ⎝ 0.000 ⎠ in lb in ⎛ −650.000 ⎞ lb h lb Ps − Pt = ⎜ 650.000 3.2⋅ S⋅ µ ⋅ = 2133.333 ⎜ Do 2 in ⎝ 0.000 ⎠ in Perimeter of the tube layout measured stepwise in Cp := 80.1⋅ in increament of one tube pitch from the center-to-center of the outermost tubes (see Fig UHX-12.2) 378 Annex Z 7/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 UHX-12.5.10 Step 10 Calculate stresses in the shel and/or channel integral with the tubesheet (config.a,b,c): ⎛⎜ 0⋅ lb ⎞ ⎜ in2 ⎟ ⎜ ⎟ lb ⎜ ⎟ ⋅ σ zero := ⎜ in2 ⎟ ⎜ ⎟ ⎜ 0⋅ lb ⎟ ⎜⎝ in2 ⎠ ⎡ ⎤ Ds ⎢ ⎥ σ s.m := ⎢ ⋅ t ⋅ ( D + t ) ⋅ Ps⎥ if ( Config = "a" ) ∨ ( Config = "b" ) ∨ ( Config = "c" ) ⎣ s s s ⎦ σ zero otherwise ⎛ 0.000 ⎞ lb σ s.m = ⎜ 0.000 ⎜ ⎝ 0.000 ⎠ in ⎡ ⎤⎥ ⎤ h's ⎞ ⎡⎢ Do − ν* Do ⎛ ⎢ ⎥ σ sb := ⋅ k s⋅ β s⋅ δ s⋅ Ps + ⋅ ⋅ ⋅⎜1 + ⋅ ⎢ Mp + ⋅ ( Ps − Pt )⎥ ⎢ E* ⎠⎣ 32 ⎦ ⎥⎦ ts h ⎝ ⎣ σ s.b := ⎛ 0.000 ⎞ lb σ s.b = ⎜ 0.000 ⎜ ⎝ 0.000 ⎠ in σ sb if ( Config = "a" ) ∨ ( Config = "b" ) ∨ ( Config = "c" ) σ zero otherwise σ s := ⎯⎯⎯⎯⎯⎯⎯→ ⎛ 0.000 ⎞ lb σ s.m + σ s.b σ s = ⎜ 0.000 ⎜ ⎝ 0.000 ⎠ in ( ) ( ) lb σmaxs := max σ s σmaxs = 0.000 σ allows := 1.5⋅ Ss σ allows = 0.000 ⎡ ⎤ Dc ⎢ ⎥ σ c.m := ⎢ 4⋅ t ⋅ ( D + t ) ⋅ Pt⎥ if ( Config = "a" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) ⎣ c c c ⎦ in lb in ⎛ 7900.711 ⎞ lb σ c.m = ⎜ 0.000 ⎜ ⎝ 7900.711 ⎠ in σ zero otherwise ⎡ h'c ⎞ ⎡⎢ Do ⎯⎯⎯→ ⎤⎥ ⎤⎥ − ν* Do ⎛ ⎢ σ cb := ⋅ k c⋅ ( β c⋅ δ c⋅ Pt ) − ⋅ ⋅ ⋅⎜1 + ⋅ ⎢ Mp + ⋅ ⎛ ( Ps − Pt ) ⎞ ⎥ ⎠⎦⎥ ⎢ E* ⎠⎣ 32 ⎝ tc h ⎝ ⎣ ⎦ σ c.b := σ cb if ( Config = "a" ) ∨ ( Config = "e" ) ∨ ( Config = "f" ) ⎛ 39880.909 ⎞ lb σ c.b = ⎜ −56954.890 ⎜ ⎝ −2536.635 ⎠ in σ zero otherwise ⎛ 47781.621 ⎞ ⎯⎯⎯⎯⎯⎯⎯→ lb σ c := σ c.m + σ cb σ c = ⎜ 56954.890 ⎜ ⎝ 10437.346 ⎠ in ( ) ( ) σmaxc := max σ c σmaxc = 56954.890 lb σ allowc := 1.5⋅ Sc σ allowc = 30000.000 379 in lb in UHX-12.5.11 Step 11 Annex Z 8/12 UHX12-Case20.1.4(14may11)-(2010) 15/05/2011 19:07 Simplified Elastic-Plastic Procedure : > σ s ≤ SPS.s and σ c ≤ SPS.c - Configuration b , c -> σ s ≤ SPS.s - Configuration e , f -> σ c ≤ SPS.c NOTE : This option may be used when : - Configuration a E* s := Es⋅ 1.5⋅ Ss σs ⎛ min⎛ E* s1 , Es⎞ ⎞ ⎠ ⎜ ⎝ E* s := ⎜ min⎛ E* s2 , Es⎞ ⎟ ⎠⎟ ⎜ ⎝ ⎜ min⎛ E* s , Es⎞ ⎝ ⎝ ⎠⎠ From step : k s := β s⋅ k c := β c⋅ From step : From step : ⎛ 0.000 × ⎜ E* s = ⎜ 0.000 × ⎜ ⎜ ⎝ 0.000 × ⎛ 0.000 × ⎜ E* s = ⎜ 0.000 × ⎜ ⎜ ⎝ 0.000 × E* s⋅ t s 6⋅ ⎛ − ν s ⎝ 2⎞ E* c⋅ t c 6⋅ ⎛ − ν c ⎝ F := ⎠ 2⎞ ⎠ 10 10 0⎞ ⎛ 2.195 × ⎜ 1.5⋅ Sc E* c := Ec⋅ E* c = ⎜ 2.010 × ⎜ σc ⎜ ⎝ 4.696 × ⎛ min⎛ E* c1 , Ec⎞ ⎞ ⎛ 2.195 × ⎠ ⎜ ⎝ ⎜ ⎜ ⎟ E* , E ⎛ c c⎞ E* c := E* c = ⎜ 2.010 × ⎜ ⎝ ⎠⎟ ⎜ ⎜ min⎛ E* c , Ec⎞ ⎜ ⎝ 2.770 × ⎝ ⎝ ⎠⎠ ⎟ lb ⎟ in ⎠ 10 ⎞ 10 10 10 ⎟ lb ⎟ in ⎠ ⎛ 0.000 × 100 ⎞ ⎜ k s = ⎜ 0.000 × 100 ⎟ lb ⎜ ⎟ ⎜ ⎝ 0.000 × 10 ⎠ ⎛ 4.013 × 105 ⎞ ⎜ k c = ⎜ 3.676 × 105 ⎟ lb ⎜ ⎟ ⎜ ⎝ 5.064 × 10 ⎠ ⎟ lb ⎟ in 10 ⎠ 10 ⎞ 10 ⎟ lb ⎟ in 10 10 ⎠ ⎛ 0.000 × 100 ⎞ ⎜ ⎜ ⎟ lb ⎜ 0.000 × 10 ⎟ in ⎜ ⎝ 0.000 × 10 ⎠ ⎛ 6.015 × 106 ⎞ ⎜ ⎛⎜ ⋅ Dc h'c ⎞ lb λ c := ⋅ k c⋅ ⎜ + h'c + λ c = ⎜ 5.509 × 106 ⎟ ⎜ ⎟ ⎠ ⎝ in h ⎜ ⎝ 7.591 × 10 ⎠ ⎛⎜ ⋅ Ds h's ⎞ λ s := ⋅ k s⋅ ⎜ + h's + λs = ⎠ ⎝ h ⎡ − ν* ⋅ λ + λ + E⋅ ln( K) ⎤ if ( Config = "a" ) ⎢ (s c )⎥⎦ ⎣ E* ⎡ − ν* ⋅ λ + E⋅ ln( K) ⎤ if ( Config = "b" ) ∨ ( Config = "c" ) ⎢ (s )⎥⎦ ⎣ E* ⎡ − ν* ⋅ λ + E⋅ ln( K) ⎤ if ( Config = "e" ) ∨ ( Config = "f" ) ⎢ (c )⎥⎦ ⎣ E* otherwise ⎯⎯⎯⎯⎯⎯⎯⎯⎯→ ⎛ 8.332 × 103 ⎞ ⎜ ⋅ F⋅ ( Ps − Pt ) M = ⎜ 3⎟ M* − p ⎜ 6.825 × 10 ⎟ lb 32 M p := ⎜ 1+F ⎝ 9.843 × 10 ⎠ ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ ⎛ −1.515 × 104 ⎞ ⎜ ⎡⎢ ⎤⎥ Do M o := ⎢ M p + ⋅ ( + ν* ) ⋅ ( Ps − Pt ) ⎥ M o = ⎜ 3.135 × 104 ⎟ lb ⎟ ⎜ 64 ⎣ ⎦ ⎜ ⎝ 9.843 × 10 ⎠ Do 7⎞ 10 ⎛ max⎛ Mp , Mo ⎞ ⎞ 1 ⎠ ⎜ ⎝ M := ⎜ max⎛ M p , M o ⎞ ⎟ M = ⎠⎟ ⎜ ⎝ ⎜ max⎛ Mp , Mo ⎞ 3 ⎠⎠ ⎝ ⎝ 380 ⎛ 1.515 × 104 ⎞ ⎜ ⎜ ⎟ lb ⎜ 3.135 × 10 ⎟ ⎜ ⎝ 9.843 × 10 ⎠ ⎛ 0.877 ⎞ F = ⎜ 0.848 ⎜ ⎝ 0.964 ⎠ From step : σ := 6⋅ M ( Annex Z 9/12 UHX12-Case20.1.4(14may11)-(2010) µ* ⋅ h − h'g )2 ⎛ 19253.502 ⎞ lb σ = ⎜ 39838.016 ⎜ ⎝ 12506.372 ⎠ in 15/05/2011 19:07 σ max := max( σ ) σ max = 39838.016 σ allow := ⋅ S lb in σ allow = 40000.000 lb UHX12.6 Simply Supported Tubesheet Procedure This procedure applies only when the TS is integral with the shell or channel, i.e : - shell of configurations a,b,c - channel of configuration a,e,f SS = "NO" Calculation must be performed in phases : Phase 1) Perform Steps to 10 with SS="NON" (normal calculation) with the following modifications in Step 10: - minimum length requirement l smin of shell band for configurations a,b,c not apply - minimum length requirement l cmin of channel band for configurations a,e,f not apply if σs < SPS,s and σc < SPS,c , the shell and/or channel designs are acceptable Otherwise increase the thickness of the overstressed components (shell and/or channel) and return to Step Phase 2) Perform Steps to using SS="OUI" (Simply Supported calculation) for loading cases 1,2 and only If |σ| < 1.5S , the calculation procedure is complete Otherwise, increase the assumed tubesheet thickness h and repeat Steps to 8, using in Step : M=|M o | Note: If |σ| , E*SquPitch , E*TriPitch) E* := ⎛ Elay + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* 4⎞ ⋅E −0.3606 ⎞ E* = 4.894 × 10 sec −0.0600 ⎠ psi ft sec E* = 4.590 × 10 psi ft sec E* = 4.209 × 10 psi ft sec E* = 3.799 × 10 psi ft 1, 1, 1, 1, 1, ⎝ ⎠ 4⎞ ⎛ E* := Elay + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* ⋅ E 2, 2, 2, 2, 2, ⎝ ⎠ 4⎞ ⎛ E* := Elay + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* ⋅ E 3, 3, 3, 3, 3, ⎝ ⎠ 4⎞ ⎛ E* := Elay + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* + Elay ⋅ µ* ⋅ E 4, 4, 4, 4, 4, ⎝ ⎠ For h/p < 0.1,use h/p = 0.1.For values of h/p > 2, use h/p = 2.0 Otherwise perform a linear interpolation ⎛ E* ⎞ ⎜ ⎜ E* ⎟ interE* := ⎜ ⎟ ⎜ E* ⎟ ⎜ E* ⎝ 4⎠ ⎛⎜ 0.1 ⎞ 0.25 ⎟ hpratio := ⎜ ⎜ 0.5 ⎟ ⎜ 2.0 ⎝ ⎠ E* := si⎛⎜ h ⎝p > , E* , si⎛⎜ h ⎝p h = 3.5 p ≤ 0.10 , E* , interplin⎛⎜ hpratio , interE* , ⎝ h ⎞⎞⎞ p ⎠⎠⎠ sec E* = 3.799 × 10 ft lbf E* E in = 0.4413 νlay := si( Layout > , ν*SquPitch , ν*TriPitch) 4 4 4 ν* := νlay1 , + νlay1 , 2⋅ µ* + νlay1 , 3⋅ µ* + νlay1 , 4⋅ µ* + νlay1 , 5⋅ µ* ν* := νlay2 , + νlay2 , 2⋅ µ* + νlay2 , 3⋅ µ* + νlay2 , 4⋅ µ* + νlay2 , 5⋅ µ* ν* := νlay3 , + νlay3 , 2⋅ µ* + νlay3 , 3⋅ µ* + νlay3 , 4⋅ µ* + νlay3 , 5⋅ µ* ν* := νlay4 , + νlay4 , 2⋅ µ* + νlay4 , 3⋅ µ* + νlay4 , 4⋅ µ* + νlay4 , 5⋅ µ* ν* := νlay5 , + νlay5 , 2⋅ µ* + νlay5 , 3⋅ µ* + νlay5 , 4⋅ µ* + νlay5 , 5⋅ µ* ν* := νlay6 , + νlay6 , 2⋅ µ* + νlay6 , 3⋅ µ* + νlay6 , 4⋅ µ* + νlay6 , à* * = 1.208 ì 10 ν* = 1.429 × 10 −1 ν* = 1.739 × 10 −1 ν* = 2.521 × 10 −1 ν* = 2.992 × 10 −1 ν* = 3.179 × 10 For h/p lower than 0.1,use h/p = 0.1; for values of h/p higher than 2, use h/p = 2.0,otherwiseperform a linear interpolation: ⎛⎜ ν* ⎞ ⎜ ν* ⎟ ⎜ ⎟ ⎜ ν* ⎟ interν := ⎜ ⎟ ⎜ ν* ⎟ ⎜ ν* ⎟ ⎜ 5⎟ ⎜ ν* ⎝ ⎠ ⎛ 0.1 ⎞ ⎜ 0.15 ⎜ ⎟ 0.25 ⎟ ⎜ hpratio := ⎜ 0.50 ⎟ ⎜ 1.00 ⎟ ⎜ ⎝ 2.00 ⎠ h p = 3.5 ν* := si⎛⎜ h ⎝p ν* = 0.318 383 > , ν* , si⎛⎜ h ⎝p ≤ 0.10 , ν* , interplin⎛⎜ hpratio , interν , ⎝ h ⎞⎞⎞ p ⎠⎠⎠ UHX12-Case20.1.4(14may11)-(2010) 12/12 Ap := πro Ap = 510.705 in Cp := 2πro Cp = 80.111 in 384 Annex Z 15/05/2011 19:07 STP-PT-053 Criteria Document for Shell-and-Tube Heat Exchangers ACKNOWLEDGEMENTS The author would like to thank the members of the peer review committee who sent many valuable comments and provided helpful consulting in the development of this Criteria Document In particular Ramsey Mahadeen for his support and detailed reviews, Urey Miller for his help in stress classification considerations, Tony Norton for his comments on theoretical issues and performing FEA calculations, Guido Karcher for his support, Anne Chaudouet who spent so much time for checking the development of the formulas and Gabriel Aurioles who was very helpful for computer issues The author acknowledges CETIM for its financial support in the development of the Criteria Document appearing in PART 3, dedicated to fixed tubesheet heat exchangers The author further acknowledges, with deep appreciation, the activities of ASME ST-LLC and ASME staff and volunteers who have provided valuable technical input, advice and assistance with review and editing of, and commenting on, this document 385 Criteria Document for Shell-and-Tube Heat Exchangers ABBREVIATIONS AND ACRONYMS ASME – American Society of Mechanical Engineers C&S – Codes and Standards CL – Clamped EEC – Effective Elastic Constants FEA – Finite Element Analysis FL – Floating HE(s) – Heat Exchanger(s) LE – Ligament Efficiency ST – Stationary SG-HTE – Subgroup on Heat-Transfer Equipment TEMA – Tubular Exchanger Manufacturers Association TS(s) – Tubesheet(s) UHX – Unfired Heat Exchanger 386 STP-PT-053 A2381Q 387