Cloud this.. Cloud that... What about Cloud Simulations? Cloud FEA/CFD?

Firstly, sorry for the long silence and no recent posts in a while.  Too many things happened...with the latest being me under the surgeon's needle.  I had a cervical disc hernia and it was so bad that no simulation could help ;)  I needed to undergo surgery.  I am slowly recovering now... but need your help on a question that has been on my mind lately:

Do you think Cloud FEA/CFD will actually see the daylight?  I have created a poll on this recently and already have seen some great comments and interest on this topic.  I would love to hear from you! Here you go:
Poll: Cloud Computing for FEA/CFD? Do you like it?

Once I have this poll completed (in 28 days from today), I plan to update this post (or publish a new post) with a final report and analysis of what the simulation community thinks.

I am really interested in hearing what you have to say!

Get started with Entry-Level HPC and ANSYS

Ansys Mechanical has supported and been tightly integrated in the High Performance Computing (HPC) arena for many years and many versions. However, I've seen a quite some hesitation from users and companies to introduce HPC into their engineering simulation environment. Reasons generally come down to cost and complexity.

True, setting up a central cluster with many nodes is costly. The complexity of configuring it, optimizing it (for Ansys and the other array of applications that will share it), and maintaining it can be daunting.
However, I've worked with a large number of customers recently getting into "entry level HPC". Even though our primary workstations are getting more powerful (6-core processors are here, 12-core processors are coming soon) and we're able to run larger jobs on them, there's still a need to offload the job to an HPC environment. Let's face it - we've all closed our emails, web browsers, and office apps during those painfully slow solves to try a free up just a few more Mb's of ram, hoping the run won't crash.

What I consider "entry-level" is to have at minimum a 2nd workstation (or server), can be high or low end, expensive with lots of CPU/RAM/disk space, or inexpensive (assembled from all those spare components laying around). The idea here is to try HPC - a simple setup to send a solve over to a 2nd computer. If you have the compute power in your 2nd computer for high-end analysis, great! If not, get something set up to at least introduce yourself to the concepts and see how it works.

I recently worked with a customer who purchased a very high-end single-node compute server. Why just one? Simple answer... cost constraints. We were able to set it up, get the Ansys users up and running and accustomed to HPC (and adopting its advantages) and then when the budget allowed, the customer added additional compute nodes to the existing cluster.

Off-loading the solve can be done a number of ways, including Remote Solve Manager (RSM), batch scripts, Distributed Ansys, even simply using Remote Desktop. (Great discussion points for future topics!) This simple "entry level HPC" setup can free up your primary workstation during those intensive solves. It is amazingly convenient to build a model on my laptop, hit "Solve", shut down my laptop, go home, and come in the next morning with a fully solved model!

I love to hear your thoughts!

Jason.

Fracture Mechanics in Turbine Blade Analysis

I would like to take some time to start a discussion on fracture mechanics. The calculations for a basic fracture mechanics analysis are fairly simple, but they can play a very important role in failure analyses. This topic comes up quite frequently in turbine blade work.

So what is fracture mechanics? In short it’s a method of determining the time it takes a crack in a part to grow to failure under a specific loading condition. The crack growth stage of fatigue can make up a significant portion of a products life. This happens in products ranging from bicycles, to airplanes, to steam turbine blades.

At the heart of fracture mechanics is the stress intensity factor K defined as:

Where:

f(g) is a correction factor based on crack geometry. This value tends to be between 1 and 1.4.

a is the crack length

s is the remote stress

Fatigue crack growth is divided into 3 regions as shown in the figure below. In this figure, crack growth rate (da/dN) is plotted on the vertical axis in log scale and Stress Intensity Range (DK=K_max-K_min) is plotted on the horizontal axis in log scale. Region I is associated with crack threshold effects (the area where a crack first begins to grow), Region II is an area of linear growth (Paris region), and Region III exhibts extremely high/unstable crack growth.

For design purposes the focus is on Regions I and II. Crack growth is so fast in Region III that it does not have a significant effect on the total crack propagation life. Noted on the graph is DK_th, the threshold stress intensity which is determined through testing. This value marks the beginning of crack growth. K_c is the critical stress intensity and values higher than this predict fracture.

When performing a turbine blade analysis we often want to determine if a dynamic stress condition is severe enough to grow a crack (Refer to previous posts on blade analysis). To determine that, we run a fracture mechanics analysis for Region I of the above graph. If the stress condition and initial flaw size is not capable of growing a crack then we need not be concerned with removing the near resonant condition.

This analysis starts with calculating the stress intensity factor range:

In the case of an edge crack on a turbine blade airfoil the a correction factor f(g)=1.12 is typically used. Ds is the stress range, or dynamic stress for turbine blades (again refer to my last post on dynamic stress analysis). If DK is greater than DK_th, then a crack will propagate under the given loading condition.

One other thing to consider is the R ratio. Test results for DK_th values are very dependant on the conditions which they were tested at. A particular DK_th value will only apply to a loading condition that has the same R ratio as the test. The R ratio calculation is shown below:

Where s_m is the mean steady stress and s_d is the alternating or dynamic stress. If the R ratio for the DK_th test is different than calculated above, the DK_th will need to be adjusted to account for the difference. One common method for the compensation of DK_th is Walker’s Equation:

Where is the value at R=0, g is a material constant and is typically between 0.3 and 1. Steels are typically around 0.5. Using this relationship, and assuming that is a constant, you can calculate the DK_th value for any R ratio.

Thanks for reading,

Turbine Blade Dynamic Stress Analysis

Here is the second installment on our turbine blade analysis discussion. (Part one is here: Turbine Blade Modal Analysis)
This time I will focus on a dynamic stress analysis. Once you have created the interference diagram that was discussed in my last post, you will be able to identify conditions where resonance may occur. Typically I find any case where the resonant condition is less than 3% different from the forcing frequency (impulse line on interference diagram). I then run a dynamic stress analysis on each of those conditions using BLADE.

Resonant conditions were covered in my last post, but I think it is important enough to summarize it here. The dynamic amplitude and stress response of a structure depends on the following factors:

1. The natural frequencies of the system

2. The damping properties

3. The forcing amplitudes or stimulus ratio, defined as the ratio of the dynamic forces to the static steam loads on the blade

4. The phase angles, defined by the harmonic content (nodal diameter) of the modes.

The steam flow field is non-uniform due to nozzle asymmetry and irregular spacing geometry within the steam flow path. Other factors may include geometry variations of wakes, leakage flows and disturbances in the turbine structure such as joints and steam extractions. Since so many variables are involved and some of the fluid phenomena are still unknown, it is extremely difficult to estimate accurately the dynamic forces and consequently the stimulus ratio.

When calculating the alternating stresses using BLADE, I typically assume a 1% stimulus ratio so that results can be easily scaled. In practice the stimulus ratio varies for different machines and for different blade rows. When BLADE calculates these stresses it assumes that the system is at a resonant condition. Therefore, the resonant stresses that are output by BLADE need to be detuned (i.e. reduced) if the particular stimulus is not precisely at resonant frequency. For example let’s say the conditions that were selected to run a dynamic analysis on were within 1% of resonance and this occurs at 3500 Hz. This could lead to a significant detuning since the forcing frequency would be 35 Hz away from resonance.

The detuning of these resonant stresses is accomplished through the transmissibility function or sometimes referred to as the magnification factor. A derivation of the transmissibility function can be found in a mechanical vibrations text typically in the harmonic vibration chapter. For convenience here is the final result:

Where:

s_d= Dynamic Stress

s_r= Resonant Stress

h=Frequency Ratio (excitation frequency/natural frequency)

z =Critical damping ratio

Once the stress values are detuned you will now know the frequency and nodal diameter for each possible resonant condition and the dynamic stresses that occur there. With this you will be able to judge if this near resonant condition is significant and if a design needs to be modified to reduce the stresses or shift the frequencies to detune the resonant condition.

Thanks for reading and welcome your comments and suggestions.

Load incrementation of initially weak structures

I just worked on an FEA model which was essentially a flat, very thin plate of plastic with a pressure applied. Initially, I always use small displacement and linear contact (bonded) for debugging a model just to make sure that loads and boundary conditions are correct. This saves time because large deformation effects can introduce much longer solve times. The linear model solved fine.

When I turned on the large displacement option (nlgeom), the model failed to converge even after several cutbacks (bisections). I certainly did not expect to solve the model in one substep, but I thought the default bisection algorithm would find a converged solution. I was using automatic timestep control. I reduced the initial substep until I eventually obtained a solution, but by this point the subsequent substeps were so small that it would take many, many substeps to complete the load step.

I noticed that after the first substep converged, convergence for later substeps required only a few iterations. Therefore, I broke the load step into 2 separate steps. In the first step, the load was reduced to the value that converged earlier, about 1/1000th. In the second step, I specified the full load with a reasonably sized initial substep. The model had no trouble converging, even though the load had dramatically increased between steps. The reason is that the initial stiffness of the plate is bending only, because it was flat. Since it was a very thin plastic component, the bending stiffness is very low. The first step established some membrane stiffness as the plate tries to assume a more spherical shape. Once the load generates some membrane stress and there is membrane stiffness, subsequent predictions of displacement are more accurate.

I have also used this 2 step load strategy for preloading of bolts. Sometimes, not always, the contact resisting the preload has trouble converging with the full preload. Before contact is established, there is no stiffness resisting the preload. Then, the contact overcloses so much that the solver cannot resolve the overclosure efficiently.

Turbine Blade Modal Analysis

I have recently had the opportunity to work on a few steam turbine blade failure investigations and have found a whole new world of engineering simulation that I had not been exposed to. Analysis of turbine blades is its own animal and even though steam turbines have been in use in power generation for a very long time, the physics of power generation is so complex there are many areas that are still not well understood. Being new to turbine analysis I thought my experiences as I lean steam turbine analysis may be useful to others. The first topic I would like to describe has been fundamental to all of the turbine projects that I have been involved with: Modal analysis of a bladed disk row. In each investigation, modal analysis was used to calculate the natural frequencies and mode shapes for a particular stage of blades. This is a valuable tool in determining if the blades are operating near a resonant condition that could be responsible for a failure.

As you can find in any vibrations textbook, modal analysis is an eigenvalue procedure in which the eigenvalues of the equation of motion are the square of the natural frequencies and the eigenvectors are the mode shapes. For blade analysis, SimuTech Group uses an in-house developed code to run a modal Finite Element Analysis on turbine blades. This program is called BLADE.

A portion of the bladed disk is modeled in BLADE which usually consists of a 360°/N sector, where N is the number of blades in the row. The mass and stiffness matrices for the bladed disk sector are then reduced to a superelement containing selected fewer degrees of freedom. These selected degrees of freedom are called master degrees of freedom. They are selected in such a way as to be able to represent and predict the dynamic behavior of the bladed disk.

At operating speed, the rotating system stiffens because of the centrifugal effects. This stress stiffening causes the natural frequencies to be higher than their corresponding values calculated at zero RPM. The effect of the stress stiffening is evaluated and incorporated in the analysis.

If a rotating bladed disk is excited by a forcing which is fixed spatially, there are 3 conditions that need to be satisfied in order to produce a resonant condition:

1. The natural frequency of the blade row is equal to some per-rev forcing frequency

2. The number of nodal diameter of the natural mode equals the forcing harmonic number.

3. The excitation must be able to couple with the blade disk mode shape. For example, the forcing on the blade row must be in a direction that matches the mode shape deflection. If the forcing is along the axial direction of the turbine and the mode shape shows deflection only in the tangential direction, the mode can not be excited. Of course many modes contain components in both axial and tangential directions.

If all of the above conditions are met, resonance will occur. This natural frequency-forcing relationship is usually illustrated as an Interference diagram. In the Interference diagram, the natural frequency is plotted against the number of nodal diameters (harmonic content of a mode). An example of an interference diagram is shown above. The line through the origin is called the Impulse Line which corresponds to the operating speed. Whenever the Impulse Line intersects the natural frequency curves, a resonant condition may exist.

The Interference diagram is used to locate frequencies of interest for a more detailed stress analysis. Resonant stresses are calculated for these conditions and detuned as necessary to estimate the true dynamic stress in each blade. The dynamic stress will also depend on the damping present in the system as well as the stimulus ratio (the ratio of dynamic forcing to the steam bending force in the blade). Dynamic stress analysis is a discussion on its own and will likely be a topic of future entries.

Thanks for reading.

Limit load analysis

I worked on a 2007 ASME B&PV Code, Section VIII, Div 2 analysis of what was essentially an elbow casting with some additional detail. The more traditional approach would be to use stress linearization on an elastic analysis for stress categorization. However, since the elbow was thick-walled relative to the radius, stress linearization can be non-conservative because the stress distribution is non-linear. Think about the difference between a thick walled cylinder and. thin walled cylinder.

I used the limit load analysis method instead. The limit load analysis has established itself as the preferred method, subject to its limitations, to assess primary sizing (Protection Against Plastic Collapse). The limit load analysis eliminates the need for stress categorization because it is a pass-fail criterion. The material definition is elastic-perfectly plastic. So, the limit load analysis is trying to predict when a plastic hinge forms in a plate an uncontrolled deformation with result with any additional applied load.

The basis for the limit load is straightforward. A value of 1.5 is applied to the desired load (i.e. design pressure+static head+dead weight). Recall that a plastic hinge is formed in a rectangular cross-section beam with an elastic-perfectly plastic material when the moment is 1.5 X the moment required for initial yield. You can find this discussion in a Continuum Mechanics textbook in a section on Beams. I have the book by Shames and Cozzarelli, "Elastic and Inelastic Stress Analysis," which has a pretty good description of this derivation with lots of pictures. So, if you enter 1.5*S (in some cases 1.5S is equal to yield strength at temperature) as your FEA yield strength, and the model converges, you will not develop a plastic hinge in the component you are analyzing. There will likely be plastic strain, especially at structural discontinuities.

Bottom Line:
Did the analysis model converge at the desired load (i.e.1.5*Design Pressure)? If yes, Section 5.2, Protection Against Plastic Collapse is satisfied. If not, Section 5.2, Protection Against Plastic Collapse is NOT satisfied.

Advances in the capabilities of computers have enabled the method, since the limit load analysis will take longer to run than an elastic stress analysis. However, post-processing effort is reduced to near zero. Also, there is no question about whether or not the stress categorization line (stress cutline) is in the limiting location.

Jeff

Engineering Simulation blog... a beginning.

First question we asked ourselves is why blog? Does this help our customers? The simulation community? Does it help us?

Being an engineering simulation consulting firm and working with a wide range of customers in various industries, we see several unique simulation requirements, from leading edge to bleeding edge!  We have seen several times how what we learn in simulating for one industry can so easily be transferable to another industry; how simple tricks or having "been there, done that" would have saved us hours and hours of frustration (if not days!).  We also have done some "cool" projects which we love to share with anyone over a cocktail discussion.  We have a love-hate relationship with simulation... years of passion and also sometimes days of frustration!

So, that being said, we thought, blogging about our experiences, analyses and physics in general could be a great way to help the simulation community, our customers and also create our voice!  So, we plan to post interesting analysis stories, tricks, tips, macros, glitches, software patches (or atleast direct to the right resource), FEA vs. Testing, our perspectives and more.... If our experience, macros, resources etc., can save a few hours for a fellow analyst, we will consider our blog a success!

Let us "Engineer, Simulate and Innovate" together.

This blog is maintained by our engineering analysis group out of Rochester, NY office. 
Our blogging team (The SimuSquad) includes:
Jeff Heckman, Jason Zbick, Rolf Orsagh, Mike Sobol, Nick Lynn and Sriram "Rob" Atchutuni.