Engineering task and calculation objective
The UHXb module calculates fixed tubesheets of shell-and-tube heat exchangers to ASME BPVC Section VIII Division 1, part UHX-13. In a fixed tubesheet exchanger both tubesheets are rigidly welded to the shell – tube bundle and shell form a statically indeterminate system in which pressure loads and restrained thermal expansion interact. Anyone who wants to calculate a tubesheet to ASME UHX must therefore consider shell, tubes, tubesheet, channel and, where present, an expansion joint together.
The module covers tubesheet configurations a through d per Figure UHX-13.1 (integral, gasketed, extended as a flange) and distinguishes the load cases design/operating, pressure test and special cases. The inputs include the shell-side and tube-side design pressures (each with maximum and minimum values), the design temperatures of tubesheet, shell, channel and tubes, as well as the mean metal temperatures and coefficients of thermal expansion along tube and shell – from which the equivalent pressure difference due to restrained thermal expansion results.
The results include the stress checks for tubesheet, tubes, shell and channel in all load case combinations, the effective bolt loads for gasketed configurations, and the required thickness of the tubesheet extension when it acts as a flange.
Standard and calculation basis: ASME BPVC VIII-1, UHX-13: 2021
Calculation workflow
- Define configuration and load cases: First the tubesheet configuration per Figure UHX-13.1 (integral or gasketed, on the shell side and/or channel side), the channel type (cylinder or hemispherical head) and the calculation case (design/operating, pressure test, other) are selected. Each combination of maximum and minimum shell-side and tube-side pressure produces its own load case.
- Determine the geometric and stiffness parameters of the bundle: From tube pitch, tube dimensions and the drilled pattern, the effective parameters of the perforated plate are determined (ligament efficiency, effective elastic constants). Shell, tube and channel stiffnesses feed into the dimensionless system parameters of the UHX theory.
- Calculate the thermal restraint loading: From the mean metal temperatures of tubes and shell and the associated coefficients of thermal expansion, the differential expansion between bundle and shell is determined. It acts like an additional equivalent pressure; an expansion joint in the shell reduces this restraint force through its spring rate.
- Determine internal forces and stresses per load case: Following the elastic model of the UHX-13 rules, the bending stresses in the tubesheet, the axial stresses in the tubes (including the buckling check of tubes in compression), and the stresses in shell and channel at the junction are calculated and compared with the allowable values.
- Verify bolt loads and the tubesheet extension: For gasketed configurations, the effective bolt loads and the gasket moment arm enter the calculation; for the tubesheet extension acting as a flange, the required thickness is determined for each load case, the largest value governing.
- Iterate until all checks are satisfied: If a component fails its check, the tubesheet thickness, wall thicknesses or the expansion joint design are adjusted and the calculation is repeated – the UHX rules also permit defined relief measures, such as taking credit for plastic reserves in shell and channel in certain load cases.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tubesheet configuration (figure UHX-13.1) | UHX-13.1) | – |
| Calculation case (design/operation, test, other) | other) | – |
| Channel type (cylinder/hemispherical head) | ctype | – |
| Calculation of radial differential | differential | – |
| Operation is different from design pressure ? | ? | – |
| Max. shell design pressure | Psd,max | MPa(p) |
| Min. shell design pressure | Psd,min | MPa(p) |
| Max. tube design pressure | Ptd,max | MPa(p) |
| Min. tube design pressure | Ptd,min | MPa(p) |
| Max. shell operation pressure | Psox,max | MPa(p) |
| Min. shell operation pressure | Psox,min | MPa(p) |
| Max. tube operation pressure | Ptox,max | MPa(p) |
| Min. tube operation pressure | Ptox,min | MPa(p) |
| Delta Psmax | ΔPsmax | MPa(p) |
| Delta Ptmax | ΔPtmax | MPa(p) |
| Delta Psmin | ΔPsmin | MPa(p) |
| Delta Ptmin | ΔPtmin | MPa(p) |
| Tubesheet design temperature | T | °C |
| Shell design temperature | Ts | °C |
| Channel design temperature | Tc | °C |
| Tube design temperature | Ttt | °C |
| Tubesheet | Tubesheet | – |
| Tube | Tube | – |
| Shell | Shell | – |
Calculation options
Tubesheet configuration (figure UHX-13.1)
a - integral with shell and channel · b - integral with shell and gasketed with channel and extended as a flange · c - integral with shell and gasketed with channel and not extendet as a flange · d1 - gasketed with shell and channel and without bolt loads · d2 - gasketed with shell and channel and with bolt loads
Calculation case (design/operation, test, other)
design/operation · hydrostatic test · pneumatic test · others
Channel type (cylinder/hemispherical head)
cylinder · hemispherical head
Calculation of radial differential
No · Yes
Operation is different from design pressure ?
No · Yes
Tube welded
welded · unwelded
Pattern (triangular/square)
triangular · square
Tube-to-tubesheet joint (extended/backwelded)
extended · backwelded
Frequently asked questions
Why must load cases with pressure on only one side also be calculated for fixed tubesheet exchangers?
Because shell and tubes are coupled, the differential pressure alone does not govern: every combination of maximum and minimum shell-side and tube-side pressure – including loss of one side – produces a different distribution of tube tension and compression forces. UHX-13 therefore requires checking all pressure combinations, each with and without the thermal restraint loading.
When is an expansion joint in the shell required?
When the restrained differential expansion between tube bundle and shell leads to inadmissible axial stresses in the tubes, exceeds the allowable tube-to-tubesheet joint load, or overloads shell or tubesheet. An expansion joint lowers the axial system stiffness; its spring rate enters the UHX calculation directly and must be consistent with the expansion joint design (e.g. per Appendix 26).
What is the mean metal temperature, and why is the design temperature not sufficient?
The restraint forces arise from the actual differential expansion in operation, i.e. from the metal temperatures of tubes and shell averaged over the length for the operating condition under consideration – not from the design temperatures used in the strength checks. Applying the design temperature of both sides across the board significantly over- or underestimates the thermal load depending on the operating mode; start-up and shut-down conditions can also govern.
Can tubes buckle under compressive loading, and how is this checked?
Yes. Depending on the load case, outer tubes or core tubes go into axial compression; UHX-13 limits the compressive stress via a buckling check using the governing unsupported length between the baffles. Excessive baffle spacing is a typical cause when the tube check fails even though the tubesheet itself is thick enough.