Modeling Steam Generators

Assignment :

Finish HW10

Steam generators come in many configurations and are used well beyond the nuclear industry.  For nuclear power plants, there are three dominant types: U-Tube; Once-through; and Horizontal Tube.  U-Tube are the most prevalent.  Once-through steam generator were used on B&W plants, but lost favor due to TMI and the attention that it brought to the lower secondary water inventory of this design.  Horizontal tube steam generators occur in Russian reactors (VVER).  This discussion will focus on U-Tube steam generators, but most of what I say can be applied to all designs.

During Loss of Coolant Accidents (LOCAs), steam generators can provide significant cooling, although conditions can exist where the pressure in the secondary side is greater than the pressure in the primary, and heat flows into the primary.  One important cooling source is "Reflux Cooling".  In this situation steam travels from the core to the steam generator tubes.  Some or all of the steam is condensed in the upward path through the U-Tubes and flows back down into the hot leg, returning to to the reactor vessel via horizontally stratified counter-current flow.  A similar counter-current flow can occur in single phase during severe accidents with hot steam flowing out from the hot leg through some tubes and returning cooler to the hot leg via other tubes.  The hot and cold streams mix to some degree in the steam generator inlet plenum.  If insufficient mixing occurs, temperatures in the hottest flow can result in tube failure and release of radiation outside of containment.

When simulating a steam generator the primary is generally modeled with a single 1-D component covering the inlet and outlet plenums, and average tube geometry. For the tubes the hydraulic diameter must be that of an individual tube, but the modeled flow area and wall area must be total for all tubes. For accidents where voiding at the top of the U-tubes has an important impact on results, you should consider using at least three 1-D flow paths to model long, medium, and short tubes in the bundle.  This is particularly valuable when cooling during some phase of the transient depends on natural circulation in the loops with the steam generator secondary as the heat sink.  Another key consideration is the number of tubes modeled.  You need to know that the stress-corrosion cracking requires utilities to plug tubes during outages.  Number of actual tubes in use varies from plant to plant, and over time for a given plant.

The secondary side of the steam generator is normally modeled with 1-D dimensional flow, but the flow topology is more complex. In addition to the boiling tube bundle region, it is necessary to model the steam dome, the downcomer, feedwater connection, and beginning of the steam line. TRACE and RELAP5 have options to model the complete secondary side. However, you should realize that this capability has never been seriously exercised. In particular the turbine models may have problems preserving proper energy balance, and wall condensation processes in condensers could restrict time step sizes.

One feature of steam generators is an adjustable gate at the bottom of the downcomer to permit tuning of the recirculation flow. When modeling a steam generator, you will need to introduce and adjust a loss coefficient at this point to obtain the appropriate recirculation flow through the downcomer.  You will normally be asked to match a quoted "recirculation ratio" for the steam generator.  This is the ratio of mass flow recirculated to the downcommer to the mass flow of steam exiting the steam generator.  Normally this ratio is substantially greater than one, insuring that liquid entering the tube bundle is very close to the saturation temperature, even though the feedwater flow is significantly subcooled.

One problem with the use of 1-D modeling in the secondary is non-physical thermal stratification during some accidents. Watch the output of the secondary for colder temperatures at higher elevations in the bundle region. If the accident can be shown to be particularly sensitive to steam generator heat transfer, you might consider using a 3-D model for the secondary, or a carefully selected pair of cross-connected pipes in the bundle region. This will create a circulation path, and will at least produce a more uniform temperature distribution. Correct circulation velocities are possible, but not likely in the cross-junction model. The 3-D model has a better chance of modeling the balance of gravitational buoyancy and frictional damping forces, to obtain a good circulation pattern. However, I am not aware of anyone who has spent the necessary time including good cross-flow loss coefficients in a 3-D steam generator model. 

Remember that modeling natural circulation in a tube (or rod) bundle is a special case for the TRACE 3-D flow model. It has a chance of working because damping forces are a result of wall and form losses. TRAC has no chance of modeling circulation in an open 3-D region because it only solves the Euler equations. No attempt is made to specifically include viscous or turbulent damping forces.

Study and test the two classes of steam generator models that I have provided. The deck stgen.inp provides a generic model of a Westinghouse steam generator, including all important features.  Unfortunately, it does not lend itself to quick renodalization of the tubes and boiler region (I'll discuss this in class), so I have also created a variant stgenSS3.inp that is easier to renodalize. The deck stgen1.inp is a simpler model of a scaled experiment.

At this point you have examples (and perhaps knowledge) of enough bits and pieces to assemble the PWR model necessary for your final project. Do yourself a big favor and start working aggressively on the project NOW. If you do, you will have ample time and opportunity to finish before the last week of classes, giving you time to concentrate on final exams in other classes. If you ignore this advice, don't blame me for all-night work sessions at the end of the semester.

Your starting point should be a text book or SAR for a general description of geometry and operating conditions of a typical PWR. Next scale and assemble components from class examples to create an initial model of the system.  Learn to use the duplicate feature in SNAP to create multiple loops, but also exercise caution and check components created by SNAP.

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