The Delayed-Critical Reactor Rate Diagram of recent NUKEFACTs consists of three curves, a stable rate curve bounded by two transient rate curves which are associated with ramp-out and a ramp-in. The stable rate curve provides the reactor rate for a specified constant off-critical reactivity condition, i.e. with rho-dot equal to zero. A stable (constant) rate exists for exponential power change with time. The transient rate curves provide the reactor rate for a specified rate of reactivity change, namely ±2x10-4 delta-rho/second. A transient (changing) rate exists when power change is not exponential with time. The magnitude of ramp contribution to reactor rate is independent of the direction of the ramp. However, the displacement of the ramp from the stable rate does depend on the magnitude of rho-dot. Technically, the ramp curves apply only at the instant a ramp is initiated off an existing stable rate, or off criticality. Once a ramp is underway, the non-exponential power change causes the precursor inventory to diverge from the stable rate mix assumed for the transient rate curves.
Even so, besides presenting precalculated reactor rates for specific nuclear states, the Reactor Rate Diagram provides a good approximation of reactor rate behavior during short duration reactivity ramps. Typically, a simple ramp sequence consists of three parts:
1. initial constant reactivity (stable rate)
2. reactivity ramp at constant rho-dot (transient rate)
3. final constant reactivity (stable rate)
To illustrate, we use Figure 12.1, an enlarged section of the D-C Reactor Rate Diagram.
Initially, reactivity is constant at rhoi and power is changing at stable rate A. Introduction of rho-dot causes the rate to immediately shift vertically to the appropriate ramp curve at transient rate B. Then, as the ongoing ramp produces reactivity change, reactor rate tracks to the right along the ramp-out curve, or left along the ramp-in curve, to transient rate C. Termination of rho-dot, results in constant reactivity and causes the rate to shift vertically back to stable rate D. The final reactivity is constant at rhof and power continues to change at stable rate D. And since rho-dot is constant, the reactivity scale of the Rate Diagram can be converted to a time scale during the interval of rho-dot application. The relationship between reactivity and time is:
For initial and final stable rates, point A becomes line A-A and point D becomes line D-D, respectively. Here, the initial rate is constant for time prior to the ramp and the final rate is constant for time after the ramp. The curvature with time of the reactor rate segment B-C reflects the shape of the ramp curve on the Reactor Rate Diagram. To conform to convention, the leftward reactivity movement from negative rho-dot (ramp-in) on the Diagram is reversed, so that elapsed time proceeds from left to right on Figure 12.2.
The reactor rate behavior with time on Figure 12.2 represents the same behavior exhibited on the rate meters in the Control Room during an off-critical ramp change in reactivity. This is the general character of response whether your meter scale is Startup Rate or Reactor Period. Since a stable rate can only exist for power levels between initial attainment of criticality and the Point-of-Adding-Heat (typically about 1% reactor power), the behavior illustrated in Figure 12.2 applies only over this range in power.
Taking ramp-out of a control rod as an example, meter response in the Delayed-Critical region is as follows: