This NUKEFACT presents a reactor rate diagram that you will find in no other text ... not because it's not important ... not because it wouldn't help the student's overview of reactor behavior ... not because it's obscene ... and certainly not because its underlying equation is unknown. No, nothing so simple. It's just another example of the disorganized, incomplete, and fragmented treatment of reactor behavior that has survived for 50 years ... and the reason that this Web Site exists.
The General Equation for Reactor Rate, as introduced in NUKEFACT #18, has been used in the U.S. nuclear industry for several years. As a teaching tool, it does a reasonable job of defining reactor rate for any mode of reactor operation, from shutdown to full power. With a considerable amount of calculation, it can also be used to construct a General Reactor Rate Diagram. Herein, we take the easy route, using The PWR Reactor Trainer to generate the General Reactor Rate Diagram. This diagram is a composite of the rate diagrams for the Sub-Critical (S-C) region, as shown in NUKEFACT 18, and for the Delayed-Critical (D-C) region, as shown in NUKEFACT #17. We start with Figure 20.1, which is the stable rate portion of the General Reactor Rate Diagram.
The vertical axis is reactor rate in decades-per-minute (DPM) and the horizontal axis is reactivity, rho. For negative reactivity, the reactor rate curve has two branches. The upper branch is the S-C stable rate curve extending from shutdown reactivity, rho = -0.0300, to criticality, as represented by a horizontal line at SUR = 0 DPM. The lower branch with a gradual upward curvature represents the subcritical portion of the D-C stable rate curve, extending from rho = -0.0300 to criticality. For positive reactivity, the reactor rate is represented by a single curve, which is the supercritical portion of the D-C stable rate curve. Here the reactor rate is positive and increases with the magnitude of positive reactivity. The subcritical and supercritical portions of the D-C stable rate curve combine to form the complete D-C stable rate curve. The D-C stable rate curve has been extended further for negative reactivity than previously shown, reaching a limit of SUR = -0.3 DPM for large negative reactivity values.The equivalent stable rate diagram scaled for reactor period displays the same stable rate curves.
In Figure 20.2, transient rate curves were generated so as to form the complete General Reactor Rate Diagram.
The equivalent general reactor rate diagram scaled for reactor period displays the same transient curves. The transient rate curves were generated in the following sequence:
1. Ramp-out starts from equilibrium multiplication at rho = -0.0300 with rho-dot = +2x10-4 delta-rho/sec and is continuous to a supercritical condition of rho = +0.0020.
As ramp-out is initiated, reactor rate immediately moves upscale, from 0 DPM on the S-C stable rate curve to +0.13 DPM, and then gradually increases as ramp-out continues. On termination of ramp-out at rho = +0.0020, reactor rate immediately moves downscale, and then gradually decays to the D-C stable rate curve, at +1.6 DPM. The transient curve segment from rho = -0.0300 to criticality is the ramp-out curve for the S-C region. The curve segment from criticality to rho = +0.0020 is the ramp-out curve for supercriticality in the D-C region.
2. Power is allowed to rise to 1x10-6 amps (IR) so as to render the non-fission source negligible by several decades, where ramp-in is initiated at rho-dot = -2x10-4 delta-rho/sec and is continuous to the subcritical limit of rho = -0.0300.
As ramp-in is initiated, the reactor rate immediately moves downscale from the D-C stable rate curve, quickly reaches 0 DPM at rho = +0.0020, and then goes negative. On termination of ramp-in at the reactivity limit, reactor rate moves upscale to the D-C stable rate curve, at -0.3 DPM. Since power remains above the non-fission source threshold, the curve segment from rho = +0.0020 to -0.0300 is the ramp-in curve for the D-C region.
3. Ramp-out is again initiated from rho = -0.0300 and is continuous to rho = -0.0010.
As ramp-out is initiated, reactor rate immediately moves upscale, from -0.3 DPM on the D-C stable rate curve to -0.1 DPM, and then gradually moves positive as the ramp-out continues. On termination of ramp-out, reactor rate immediately moves downscale, and then gradually decays to the D-C stable rate curve, at -0.1 DPM. This curve segment, from rho = -0.0300 to rho = -0.0010 is the ramp-out curve for subcriticality in the D-C region.
4. Power is allowed to decay to its equilibrium level, where ramp-in is initiated at rho-dot = -2x10-4 delta-rho/sec and is continuous to rho = -0.0300.
As ramp-in is initiated, the reactor rate immediately moves downscale from 0 DPM on the S-C stable rate curve to -0.7 DPM, then curls and gradually decreases in magnitude as ramp-in continues. On termination of ramp-in, reactor rate immediately moves upscale to the S-C stable rate curve. This curve segment, from rho = -0.0010 to rho = -0.0300 is the ramp-in curve for the S-C region.
As might be expected from the relative position of two branches of the stable rate curve, the transient rate curves for the D-C region lie below the corresponding curves for the S-C region. Figure 20.2 represents the General Reactor Rate Diagram, displaying stable and transient rates for both the S-C region and the D-C region.
