FatiguePro Showerhead Model

In many cases the local temperature at a nozzle must be determined based on an instrument sensor which is some distance downstream of the monitored location. Due to thermal inertia of the piping and the distance between the sensor and the monitored location, there will be a time delay and a thermal response lag between the sensor and the monitored location.

The purpose of a "showerhead" model is to evaluate the transient temperature response of the feedwater piping/fluid system to varying input temperature and flow parameters. The showerhead model accounts for the upstream temperature transient, the advance of the feedwater flow, and the convective heat loss from the feedwater piping (including insulation) between the measured fluid temperature point and the monitored location. The objectives of the shower head model are as follows:

1. To account for the time delay between the plant temperature instruments and the monitored location.
2. To account for the heat transfer between the piping, fluid, and ambient air during the transport phenomenon.
3. To account for cooldown of the piping and fluid during stagnant flow conditions.

The analyzed piping system is broken down into multiple segments, each possessing n discrete elements, as shown in the figure below. Each segment represents a different pipe size. Each element consists of the fluid, piping and insulation in a segment of piping.

The next figure shows the thermal model of an element. The three temperature nodes represent the calculated temperatures in the fluid, piping and ambient air. Heat transfer theory is used to calculate the radial heat loss from the fluid to the air, including the effect of the insulation.

For each 10-second time step, the number of elements through which the fluid will flow is calculated from the input velocity. If the incoming fluid velocity is high enough that the fluid temperature gradient along the pipe can be neglected, then, for computational ease, all fluid temperature nodes are set to the temperature instrument value, and the heat transfer calculation is performed for the piping temperature nodes.

If there is a time gap in the input data, two cases are considered. If the ending fluid velocity in the previous hour was zero, then it is assumed that the fluid velocity remained zero for the intervening hours and that the fluid and piping nodes were the same temperature, cooling down with exponential decay. If the ending fluid velocity in the previous hour was non-zero, then it is assumed that the same non-zero velocity existed for the intervening hours, and the steady-state temperature distribution is calculated.

Ultimately what the showerhead model buys you is a significantly more realistic and less severe prediction of the remote fluid temperature. Note the figure below. When a step change in a temperature instrument occurs, the temperature change at the downstream nozzle is delayed because of the time it takes for the fluid to travel, and is rounded at the corner. The predicted fluid temperature forms the basis for computing the thermal shock component of stress. This results in a less severe stress response at the nozzle end than just using the raw instrument value.

SI has over 10 years of experience in developing innovative transfer functions for FatiguePro. We are committed to making high quality software that produces meaningful results for your engineering applications.