Steam Turbine Expansion

"The present moment is the only thing of which anyone can be deprived, at least if this is the only thing he has and he cannot lose what he has not got." - Marcus Aurelius

 This post is a continuation of an earlier post about a Steam Turbine Outage.  The purpose of the continuation is to offer a deeper explanation of steam turbine expansion, and to share the resolution of a problem that one of my readers came across.  It's good information, and I'd like to thank Mike for sharing both the problem and the solution.  Let's begin with Differential Expansion.

Differential Expansion

Toward the end of the previous post linked above, I mentioned in passing the concept of differential expansion.  Differential expansion is the tendency of the steam turbine rotor to heat (and expand axially) more rapidly than the shell, due to the much greater mass of the shell.

Why differential expansion happens: The steam turbine rotor has very little mass compared to the shell, and the rotor is surrounded by steam.  The turbine shell has to contain the high pressure steam, and so it is quite thick - and the steam is heating it only from the inside.  As a result, the turbine shell and the rotor expand at different rates.  The rotor grows in length rather quickly compared to the shell.  

To compensate for this differential expansion, there are sometimes holds during a cold start for "heat soaking".  The purpose of a heat soak is to allow time for heat to spread through the turbine shell, allowing shell expansion to partially catch up to the rotor expansion.  This helps to avoid rubs caused by a long-rotor condition.

Below is an old-school diagram similar to those I used in the early days of my career.  These were used  to determine when and for how long to hold while warming the steam turbine during the start-up.  The hold period times would be based on initial temperature conditions of the steam and turbine casing prior to rolling the steam turbine.

Modern power plants are supplied with control systems that have a lot of processing power, and as a result these sort of graphs are no longer provided with steam turbines.  Instead, calculations are done on the fly in the background by the computer.  The operator only has to look at a number that reads out "% stress".  Once the turbine reaches 100% stress, the computer will place the steam turbine into a hold and the operator cannot load the turbine any further - until the indicated stress drops below 100%.

The steam turbine stress calculation takes into account the recent expansion rate of the turbine shell and rotor, several turbine shell metal temperatures, the steam inlet temperature, and what all those values have been doing for the past few hours.  It then calculates how much expansion is about to occur in the rotor and the shell, and decides whether it is OK to continue heating, or whether a pause is necessary.  

The stress calculation is much more flexible than the old and very conservative start-up curves.  With modern processors and algorithms, you can safely load a steam turbine rapidly and under a wide variety of dynamic conditions.   The the old start-up curves were only intended to cover a cold start-up following the annual outage, and the curves had huge safety margins.  The stress calculation offers a wide range of operational flexibility, which is important from a financial standpoint in a modern energy trading environment - when meeting energy prices can be the difference between profit and loss.  

While this stress calculation is going on out of sight of the operator, a good operator should have a decent understanding of the inputs, and what physical conditions the "% stress" number is actually working to describe - a long rotor condition and rubbing.

 Casing Expansion:

Recently, I was contacted by an operator at another power plant, who had read that previous post, and asked my opinion regarding a problem they were having.  They were experiencing seal steam leak-by during shut down periods at night.  When they performed a start up each morning as electrical demand on the grid went up, the steam turbine would vibrate as it neared 3600 RPM, and then it would trip.   

My initial thought was that the seal steam leakage was cooling off the shell and the rotor in localized areas while the turbine was offline, then as it heated up, conjectured that they might be seeing rubs as the High Pressure steam began heating up the turbine seals again.  Unfortunately, we went down the wrong track with that diagnosis, and I feel kinda bad that I didn't come up with the correct answer.  

This post is to explain that what they found - for interested readers.   Their problem was caused by locked up casing expansion.  

The shell (or casing) of the steam turbine is bolted down firmly at one end, but the other end is free to expand, because the turbine shell grows approximately one inch from a cold condition to normal operating temperature.

There are a couple of engineering techniques for supporting the free end of the turbine shell, while also allowing it to expand in an axial direction (along the shaft).  One technique is to support the free end on a slender frame or legs that can flex slightly as the turbine heats up.  

Below is an example of a flexible support on a very small turbine that might be used to power a pump.  The green flex plate at the bottom of the image supports the free end the turbine, while also allowing axial expansion caused by heating.  The bearing pedestal on the left is firmly bolted to the foundation.

The above solution works well enough on a short turbine, particularly where alignment is not too critical.  However the most common form of supporting the free end of a heavy industrial turbine is sliding feet inside a channel, and this is where the problem arose.

Below is an image of a turbine shell support foot in a sliding channel.  The foot for the turbine shell (top) slides left and right underneath the plate that is held down by three large bolts.

Below, close-up of the foot and channel:  The block with the purple arrow is the foot of the turbine.  Everything else is bolted to concrete.  The foot has slid to the right as the turbine shell came up to operating temperature.  Once the steam turbine comes offline and cools down for a couple of days, the shell will shrink, and the foot will slide left into the channel to where the arrow is pointing.

Below: Cold turbine, shell has contracted, and the foot has slid to the left.
 

Below are photos of the shell expansion monitor for the steam turbine.  There is a second monitor on the other side of the turbine, because the shell is supported on each side.  There are two channels to measure and monitor expansion.

As the steam turbine shell heats and expands during a cold start, it presses against the bolt, which pushes the shaft into the box.  Within the box is an LVDT - a Linear Variable Differential Transformer.  The LVDT measures the growth of the turbine shell as it heats up, and displays this growth on a monitor in the control room.

What can happen sometimes with these feet is that they become stuck inside the channels.  It's pretty rare - this is only the second time I've heard of it happening in forty years of interacting with power plant guys from all over the country.  

Once the free end feet become stuck, the shell must continue to expand, but it cannot.  The rotor will continue to grow as the turbine comes up to operating temperature.  If the feet do not manage to free themselves under the additional stress of expansion, a rub will occur between the rotor and the stator.  This causes vibration and the result is a turbine trip.  

These channels are equipped with grease fittings, and at our facility I believe greasing of the channels is done semi-annually. 

Lastly:  

Below is a chart of a few parameters that should be monitored during a turbine start-up.   This particular start is a warm one - less than 48 hours offline.  I will discuss a few of the relevant points below.

First up: Casing Expansion - the pink line.  If that line stopped rising during a turbine warm-up, it would indicate that the turbine shell feet were bound up in the channel.  It could also indicate sticky spots in the channels of the free end of the turbine if the trend were not a smooth climb upward.

Second:  The two yellow lines.  These lines trend the differential expansion for the High Pressure and Reheat turbine rotors with respect to the shell.  Notice that the rotor expands quickly, but then as the shell expansion begins to catch up (ie the rotor and the shell reach equilibrium temperature), the differential falls off again.

The blue line is RPM, nothing special there

The thin black line is stress.  You will notice that it goes way up just as the steam turbine comes online and starts making power (Dark black line at the bottom).  This jump in stress happens because rolling the turbine up to speed only takes a trickle of steam - the turbine is spinning in vacuum, so not much steam will roll it up to full speed.  However once the generator comes on line, it takes much more torque and steam to push against that resistance.  The added mass flow of steam heats the turbine much more rapidly, and as a result the stress goes up.

The white line is allowable loading rate.  As the stress goes up, the allowable loading rate drops.  It can drop all the way to zero, at which point you are stuck, and can't continue the start up.  It's best not to be here when your start up emissions permit time runs out.

That's about all for now as far as monitoring steam turbine expansion parameters during a start-up.  Yeah you have to monitor and control steam temperature and pressure, but that's a different post!