# Core Heat Conduction Calculation

### Assignment :

Continue Homework 7 and Homework 8.  Read the TRACE Theory Manual Section on the conduction equation.
To prepare for this lecture you should read the ME 540 lecture on finite volume methods.

The last heat transfer lecture was about how codes like TRACE or RELAP5 model the transport of heat between metal and fluid. Today we need to extend the discussion to the conduction problem within the heat structure. I hope to show you that understanding and intellegently using these features can have a significant effect on the results.

When you think of heat conduction in a Nuclear Power plant, your natural inclination is to focus on the fuel rods. We will in fact do just that in this class. However, in an actual plant simulation, remember that a tremendous amount of energy is stored in all the heated metal of the system. Failure to account for this stored heat will generally result in significant errors in the prediction of accident scenarios. Accurate modeling of stored heat includes both conduction solutions for all metal mass, and adequate conduction mesh refinement near the interior surfaces of this metal. A conduction mesh that is too coarse near the surface contacting the fluid will significantly underestimate the temperature derivative (and hence heat flux) just inside the metal surface after a rapid change in fluid temperature.

Modeling of fuel rod conduction in TRACE is accomplished through the  Heat Structure (HTSTR) component, using a fairly standard finite volume method. However, the calculation is complicated significantly by the presence of several materials within the rod ( oxide pellets, gas gap, and zirc cladding).

Given basic rod bundle geometry (rod pitch and diameter, and number of rods) you should be able to calculate the available area for axial fluid flow. You should also be able to calculate a hydraulic diameter based on wetted perimeter of the bundle. You should also learn the "secret" TRACE hydraulic diameter for best bundle heat transfer (diagonal surface to surface distance between rods in the bundle).  This second method is often more appropriate if you learn that data from heated tube experiments rather than rod (or tube) bundle experiments has been used for the heat transfer coefficients used in a bundle.

Although we won't cover any details you should also know that convective heat transfer is not the only mechanism that must be considered. Particularly, when dealing with BWR cores or hot voided PWR cores, you will need to consider contributions of infrared radiation. This provides direct transport of heat from rods to liquid drops, between rods with different surface temperatures, and in BWRs transfer between the rod surfaces and the channel can wall. Understand that "view factors" give you a way to calculate how much radiation can be transported between specific portions of metal. They are obtained by tracing all possible light rays from one type surface to points on another surface. The good news here is that in standard fuel bundle configurations TRACE can compute the necessary view factors for you.  Take a graduate course in radiation heat transport for details on methods for calculating view factors.

It is important to understand the impact of your finite volume mesh on the results of the simulation:

• Think about a combination of the conduction finite volume mesh and the hydrodynamic mesh. TRACE's choice of grids normally results in a direct alignment one volume of metal with each hydrodynamic cell. During the transition into nucleate boiling from film boiling an entire axial mesh zone worth of metal rapidly increases the rate of energy deposition to the adjacent fluid, significantly increasing the vapor mass flow. In the presense of any normal flow losses at the top of the core, this results in a rapid increase in local pressure that is related to a numerical and not physical cause. This problem can be mitigated with the use of a finer axial conduction mesh and/or water level tracking.
• Use of the conduction finite volume equations begins by dividing the cylinder into finite radial volumes centered on the temperature nodes and, integration of the differential equation over the volumes to relate mean cell temperatures to cell edge heat fluxes.
• We evaluate the cell edge heat fluxes from a standard central difference method.
• Note that the TRACE use of the volume average equations at the wall can cause more inaccuracy than the implementation at interior nodes. This is because a very rapid change in temperature may exist at the metal surface during a transient. Users should perform nodalization sensitivity studies to be certain that the radial mesh near a metal surface is sufficiently fine, if details of transient heat conduction are important.
• A difference method using slightly more care in the evaluation of cell center and cell edge temperatures can largely solve this problem.
• Make sure you understand the mesh diagrams and associated difference equations provided during the lecture and in the Theory Manual.

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