Finite element analysis

PIPING ENGINEERING AND PIPING DESIGN

This study is for educational purposes only. No commercial purposes intended.

free vibration

Modal analysis or free vibration for finite element analysis which involve only the stiffness of the material and mass of the geometry. In this case, we fix one one of the endpoint and check the number of degrees of freedom using the same dataset a coupled 6" 300# RF ANSI Flange fitted with stud bolts, nuts and washers with spiral wound gasket.

contact & target bodies

Preparation of the contact region. Note that in this case I used Frictional Type for type of contact with 0.15 factor for nuts and bolts, axial surface of nuts, bolts and washers. I used a frictionless contact on the gasket surface with flange's raised face. For the formulation, I used Augmented Lagrange.

The Augmented Lagrange method is a hybrid approach that combines the features of the Penalty method and the Lagrange Multiplier method to enforce contact constraints in finite element analysis. It aims to provide a balance between the accuracy of the Lagrange Multiplier method and the robustness and simplicity of the Penalty method. Note that the bolt in this assembly was not pre-stressed as we will cover the bolt tensioning later in this section. The intent of this simulation is to check the rigidness of the model for bolt tensioning. Note that we are just interested with the axial contact surface only and not including the surfaces on the bolt shaft and through holes of flanges, bolts and nuts to do the calculations.

deformation

With the computed degrees of freedom with fixed end, we obtained the following results.

PARTICIPATION FACTOR

With the computed degrees of freedom with fixed end, participation factor is used to understand how much each mode shape contributes to the dynamic response of a structure when subjected to a specific type of loading, such as base excitations or external forces. In this case, the highest value is located at Y-direction where, this axis tend to be affected by large stress when external force is applied.

static structural analysis

For 6" 300# the suggested bolt torque tension is 170 ft-lbs to maximum of 190 ft-lbs. Here, we used 244 N-m or the average of 180 ft-lbs. With 20 bar internal pressure, we can see that the applied torque is safe based on the contact stress.

Specification used in this study is saturated steam at 300 deg F at 20 bar (2 Mpa).

GASKET - Spiral Wound Gasket fitted with exfoliated graphite and Inconel 625 as a metal winding strip.

FLANGE - SA-182 (STD)

PIPE - ASTM A335 P11 ( STD)

Tensile Strength: 415 MPa (min)

Yield Strength: 205 MPa (min)

BOLTS - ASTM A193 Grade B7

Material: Chromium-molybdenum alloy steel

Tensile Strength: 125 ksi (860 MPa) minimum

Yield Strength: 105 ksi (720 MPa) minimum

Elongation: 16% minimum in 2 inches

Reduction of Area: 50% minimum

Hardness: 321 HB maximum (Brinell Hardness), 35 HRC maximum (Rockwell Hardness)

Young's Modulus (Elastic Modulus): Approximately 207 GPa (30 x 10⁶ psi)

Poisson's Ratio: Approximately 0.30

NUTS - ASTM A194 Grade 2H

Material: Carbon and alloy steel

Tensile Strength: Not directly specified, but must match the strength of the bolts used (typically matched with ASTM A193 Grade B7)

Proof Load: 150 ksi (1034 MPa) minimum

Hardness: 248-341 HB (Brinell Hardness), 24-38 HRC (Rockwell Hardness)

Young's Modulus (Elastic Modulus): Approximately 207 GPa (30 x 10⁶ psi)

Poisson's Ratio: Approximately 0.30

WASHERS - ASTM F436

Material: Hardened steel

Hardness:

Through-Hardened: 38-45 HRC (Rockwell Hardness)
Surface-Hardened: 44-50 HRC (Rockwell Hardness)

Young's Modulus (Elastic Modulus): Approximately 207 GPa (30 x 10⁶ psi)

Poisson's Ratio: Approximately 0.30

CONFIRMING THE MODEL DIMENSIONS

Based on the available charts and tables. In this case, we use 316L Stainless Steel with graphite as filler material with stiffness of 3000-4000 psi. To make the calculation conservative, we will take the minimum stiffness value. All values are taken as the average of vendor specifications for simplicity.

steady-state gas-liquid gasket leak test

Flange Type: (Integral Weld Neck)

Effective gasket width parameters:

Effective gasket seating width, b......(in.) 0.1585

Diameter of gasket load reaction, G....(in.) 7.3450

SAFETY FACTOR SUMMARY for the different Flange Models

analyzed. (SAFETY FACTOR = Allowed/Actual)

Flexibility/Gasket Compression Model (Leakage).. 12.56

ANSI B16.5/Equivalent Pressure (Stress)......... 2.52

ASME Model Operating (Stress)................... 4.10

ASME Model Seating (Stress)..................... 1.62

FLANGE FLEXIBILITY MODEL

BOLTED FLANGE CHARACTERISTICS:

Initial Tightening Stress in the Bolt

(Not the seating stress): 3000 lb./sq.in.

Approximate Torque required to induce the above initial

stress: 8 ft.lb.

GASKET COMPRESSION: COMPRESSION (in.)

After Initial Boltup (Ci)........... 0.0237916280

Loss-of due to Pressure (Cp)........ 0.0003788026

Loss-of due to Applied Moment (Cm).. 0.0000000000

Loss-of due to Applied Force (Cf)... 0.0000000000

Loss-of due to all loads (CL)....... 0.0003788026

Initial minus all Losses (Ci-CL).... 0.0234128255

For Leak-Proof Joint (Creq)......... 0.0190336667

Excess available (Ci-Creq) ......... 0.0047579613

LEAKAGE SAFETY FACTOR:

(If less than one then joint leakage is predicted.) (Allowed/Actual)

Pressure Only (Ci-Creq)/Cp ............. 12.56

Force Only (Ci-Creq)/Cf ................ 99999.00

Moment Only (Ci-Creq)/Cm ............... 99999.00

Pressure+Force+Moment (Ci-Creq)/CL ..... 12.56

EQUIVALENT PRESSURE MODEL

Equivalent Pressure (lb./sq.in.) ............ 290.00

ANSI B16.5 Flange Allowable Pressure Rating . 730.00

STRESS SAFETY FACTOR:

(If less than one then joint failure is predicted.) (Allowed/Actual)

ANSI B16.5/Equivalent Pressure ................. 2.52

ASME SECT VIII DIV 1 STRESS MODEL

ACCORDING TO A05 APP 2-14, THE FOLLOWING RIGIDITY

FACTORS SHOULD BE LESS THAN 1.0

ASME Rigidity Factor "J", Operating Case ....... 0.0778

ASME Rigidity Factor "J", Seating Case ......... 0.2191

CALCULATED STRESSES (lb./sq.in.)

OPERATING ALLOW SEATING ALLOW

--------- ----- ------- -----

Longitudinal Hub .. 6209 29400 17912 33450

Radial Flange ..... 3357 29400 9686 22300

Tangential Flange . 2953 29400 8520 22300

Maximum Average ... 4783 19600 13799 22300

Bolting ........... 5146 46000 10089 23000

STRESS SAFETY FACTOR:

(If less than one then joint failure is predicted.) (Allowed/Actual)

OPERATING SEATING

--------- -------

Longitudinal Hub .... 4.74 1.87

Radial Flange ....... 8.76 2.30

Tangential Flange ... 9.96 2.62

Maximum Average ..... 4.10 1.62

Bolting ............. 8.94 2.28

The molecular weight of a substance is a fixed property and does not change with temperature or pressure. The molecular weight of water (H₂O), given that our fluid is steam, is calculated based on the sum of the atomic weights of its constituent atoms:

Hydrogen (H): approximately 1.008 g/mol
Oxygen (O): approximately 16.00 g/mol

This value remains constant regardless of the temperature or pressure.

These conditions might change the phase of water, but the molecular weight remains the same.

Molecular Weight of H₂O=18.016g/mol≈0.0397 lb/lb-mol

Here, is the result of static analysis for initial bolt-up impact on the gasket face. with its initial compression. What we are trying to check is if there is a complete plasticity of the material or deformed part of the gasket during the compression. Note that in order to simulate an installation, we made one of the gasket side as fixed support while the other side was subjected to uniform varying pressure load during single initial bolt-up using a gasket Non Linear Unloading for multilinear isotropic hardening.

safety factor of 0.73 with internal pressure

Note that the results are based on internal pressure with preload bolts without any thermal load with very low safety factor to exaggerate defect of materials related to its mechanical properties.

This is the element meshing for different materials. Note that the fluid flow which is indicated by brown color was not used in calculation. The thermal mesh was generated for laminar and turbulence flow for initial boundary condition. On the left is further refinement of mesh topology for more detailed fluid characteristics on the inner wall and in the area of high stress concentration on contact surfaces.

Final mesh for thermal analysis for nuts, bolts, washers and flange, in the pipe side and fluid zone. Note that the mesh is more granular near the pipe wall to better capture the heat transfer.

A graph neural network model with temporal multi-head attention for transient physics by NVIDIA.

thermal analysis

Based on the 20 bar internal pressure, the saturated steam temperature properties are the following where the temperature is around 300 F (consult your steam tables or your Mollier chart). For this analysis, we will use the following data for heat convection for isothermal fluid (as an assumptions) to the flange and pipe material. The final mesh for fluid wall boundary and gasket material is also shown below. However, the simulation only take into account the operating condition of flanged connection and does not include the stress induced by bolt-tensioning. The graphics below only show how the temperature propagates from the fluid (inlet velocity of steam condensate) to the pipe wall and flange material through convection (by varying the inlet and outlet pressure).

For Flange Material:

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