Saba Metallurgical and Plant Engineering Services, LLC
Finite Element Analysis
LinearElastic Stress Analysis  This is a static analysis that considers only the linear portion of the material stressstrain curve. Basic benefits include speed of solution and ability to use a high mesh refinement, and/or high midnode counts. Main negatives include being limited to stresses below the proportional limit of the curve, and requiring stress linearization in the design process. Limiting design stress intensities (Pm, Pm+Pb, Pm+Pb+Q) are not always at the highest stress shown on the model and requires diligent examination of the model. Examples of SMPES, LLC's work using LinearElastic Stress Analysis follow:  
This mobile storage tank is evaluated using plate elements in a linear elastic stress analysis. The mesh is hand created. That is, each line is created manually by either direct entry or copy and pasting. Algor, in their results tab, for plate elements, has a direct evaluation of membrane stress intensity (Pm) and membrane plus bending stress intensity (Pm+Pb), which are used against ASME Code allowables. The maximum tresca stress intensity value found using the probe search in Algor is used to evaluate for fatigue. The Algor maximum value tag could also be used to identify this highest stress intensity value. 

A different mobile tank was analyzed for structural strength of the floor and reinforcement beams. Again, the mesh was entirely hand made and maximum stress intensities were evaluated against Pm and Pm+Pb Code criteria. Loading was only applied to the floor in this analysis.


Stress Linearization  In order to evaluate stress intensities for design purposes, linear elastic stresses require stress linearization. ASME VIII Div. 2 Code requires the average membrane stress intensities across a crosssection to be less than a specified value (Sm). Also, the Code limits membrane plus bending (Pm+Pb) across a crosssection to be less than a specified value (1.5Sm). In order to obtain these average stress intensities across the cross section, stress linearization is employed. This process unfortunately requires due diligence and patience as the maximum Pm and Pm+Pb are not necessarily at the highest stress intensity on the model. Two nodes on opposite sides of a crosssection are selected. Algor has an automatic stress linearization feature that allows calculation of Pm and Pm+Pb from direct entry of these two nodes.  
A heat exchanger is evaulated for maixmum stress intensities in the shell adjacent to the tubesheettoshell juncture. Various nodal cross section points are investigated. The above image shows the location and the seven data points used to calculate the linearized stress intensities. Typically, at a minimum, three elements across the crosssection are required to properly capture bending stresses; however, midnodes are used instead for this purpose.


NonLinear Stress AnalysisPlastic Collapse With Mechanical Event Simulation  Accounting for material nonlinearality means accounting for the material stressstrain curve properties outside of a purely linear elastic range. There are different ways of accounting for this nonlinearality. Either a straight line hardening coeffient can be used to approximate the material hardening effect, or curve data can be used to provide a truer means of matching the actual stressstrain curve profile. A hardening coefficient essentially creates two straight lines to represent the material curve, one for the linear elastic portion and the other to represent the nonlinear portion of the curve. Curve data is based on a set up data points of stress versus strain, which will eventually create a multitude of straight line between these data points. Thus, the more data sets, the more representative it will be of the real curve. Next, in the nonlinear analysis, the FE analysis can consider geometry changes, which is where much of the added time in a nonlinear analysis comes from because a stiffness matrix is recalculated at each step. A step is dependent upon user data input as to how often this matrix should be recalculated. With nonlinear analysis, there is also consideration for small and large displacements. For example, a long plastic object will have large displacements. Thus, large displacement theory is necessary to get proper results. Mechanical Event Simulation (MES) allows for actual motion which can lead to impact, inertial effects, and more realistic surfacetosurface effects. The following are two examples of SMPES's work involving nonlinear FEA with MES: 

A medical device company contact asked to evaluate one of their VBR in conjunction with a plate and screw system. SMPES used nonlinear plastic collapse (material curve data) FEA with MES to evaluate this design. A spinal column was modeled to implant the VBR and then to attach the plate screws. MES is used along with a displacement plot to determine unstable deformation, which indicates plastic collapse. The model is also used to capture peak stresses for evaluating fatigue. 



A three chamber pressure vessel tower was completely modeled to evaluate 1) if the vessel could be lifted in one piece from the ground up, and 2) to calculate the loads on the tangential nozzles due to hurricane winds. A mechanical event simulation was performed to study the stress intensities of the shells during lifting. During the lift siginificant yielding was determined and the thus it was deemd that the tower needed to be lifted in at least two pieces. A second mechanical event simulation was performed to capture loading on the top two tangential nozzles. Hand calculations were used, using standard formulas for cylinders, to determine the wind load and wind vortice frequency on the tower. These loads and frequency of loading were prescribed in the setup over several cycles. Embedded graphs associated with the tangential nozzle base nodal points are used to graph the variable X, Y, and Z loading of the nozzle. Using the graphs, the frequency of the load peaks is also used to calculate the various directional natural frequencies of the piping system associated with that nozzle. When observing movie clips of the pipes swaying in the wind, the differences between the wind vortice forcing frequency and piping natural frequency is readily observed. This model is made using Algor's PV Designer, in conjunction with the use of added beam, pipe, and shell elements. Beam elements are used for the structural supports. Shell elements are used for the platforms. The final tangential nozzle loads determined from this MES where used in the design model created in the PVElite software package.
 
Computation Fluid Dynamics (CFD)  Fluid analysis is performed using CFD. Fluid velocity and/or pressure profiles can be generated by analyzing effects of differential pressure, prescribed velocities, and fan curves. CFD requires an immense amount of setup and patience in order to acquire results. Much of the setup process requires obtaining a suitable mesh that accurately depicts the model without resulting in localized flow constraints. The Algor software automatically applies zero flow velocity constraints at fluid walls; however, how the flow is ramped up, what the convergence tolerances are, and how to handle turbulence are the primary adjustment factors. Computational time can be lengthy indeed. 

A thermal bypass tee is evaluated for maximum allowable stresses. CFD is used to determine flow velocities of the gas stream during steadystate flow, valve opening, and valve closing conditions. The velocity profile results from this CFD is used to automatically calculate internal convection coefficients in a thermal analysis. The image above shows the velocity and flow profile results for the selected streamline locations for the valve opening condition.

CFD is performed to study the flow characteristics of a vertical heat exchanger baffle and bustle configuration. This heat exchanger has a history of tube end cracking. The CFD results showed a stagnant location where the flows diverged in different directions to the exit bustle system. Investigation showed that this was the primary area of tubetotubesheet joint cracking. The boiler feedwater on the shell side is heated by a tubeside exothermic reaction, which generates steam on the shell side. This steam collects in a bubble at the area of stagnation causing a localized thermal hot spot on the top tubesheet. The CFD also showed that the exit nozzle side of the bustle created a strong flow pattern on that side of the bustle, but only minimal flow on the opposite side, thereby causing uneven bottomside heat convection coefficients and resultantly uneven temperatures along the entire tubesheet. This uneven temperature of the tubesheet leads to higher tubesheet bending stresses.


Combined CFDThermal Analysis  There are two means of determining thermal results in conjunction with CFD results, coupled and uncoupled. With coupled analysis, the CFD and thermal analysis run iteratively together and thus, the thermal changes affect the CFD results and so forth. With uncoulped analysis, the CFD is run and a solution is found and then the velocity results are imported into the thermal study in order to calculate convection coefficients. For studies that dependon natural circulation, a coupled analysis is required. For the most part, most studies can be achieve accurate results using uncoupled analysis. Due to the extra iteration time involved with coupled analysis, these solutions are much harder to obtain and require much more time.  
On continuation of the thermal bypass study, the previous CFD velocity results are used in this thermal analysis in an uncoupled fluidthermal study. Since the gas velocitities are relatively high relative to stagnation, temperature changes in the pipe are not expected to significantly alter the CFD results. Thus, use of an uncoupled study is warranted. The internal convection coefficients are automatically calculated based on the CFD flow velocities. Temperatures are applied at the two fluid inlets and allowed to mix and equibrilate. The outer pipe walls are insulated and deemed to have essentially zero heat flow out of the pipe. In the steadystate analysis, the steadystate thermal program is used and the inlets are identified to their incoming fluid temperatures. For the cases of valve opening and valve closing, the transient thermal program is used and load curves are used to "open" or "close" the valve in 1 second time. The program continues to run to study the cooling or warming affects over a couple minutes. Movie clips are created and results at different times can be used to study the existing thermal stresses using the stress analysis module.  
Saba Metallurgical & Plant Engineering Service, LLC. • Baton Rouge, LA 70820 • 2254054015