Abstract:
A method for determining the transit time and flowrate of coolant traversing a cooling channel of a nuclear reactor fuel element from the effective center of the fuel element to a point where the cooland exits therefrom.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a method for measuring the coolant flow rate of a fuel element and to apparatus for practicing the method. 
     In water or liquid metal cooled reactors, each fuel element comprises a plurality of metal clad fuel rods which are arranged in a common wrapper tube in such a manner that a cooling channel is formed which has a cross section that is sufficient for removing the thermal energy. The operational safety of the reactor and the optimum performance of each fuel element is critically dependent on the mass flow rae with which the coolant flows through its cooling channel with respect to the power produced in the fuel element. Thus, it is necessary to continuously measure the coolant flow rate and the power of each fuel element, and to perform these measurements redundtantly so as to exclude erroneous operations. 
     Although flow meters for measuring the rate of flow of liquid metals are known, their installation is generally limited to locations in the main coolant lines. This limitation is due to their complicated design, tendency to malfunction, relatively large space requirement and limited service life. 
     It is also known to monitor the coolant flow rate of reactors indirectly by continuously measuring the coolant exit temperature at the fuel element outlet. However, the coolant exit temperature depends not only on the coolant flow rate but also on the fuel element power which is influenced by the operating conditions and the duration of operation. 
     It is further known from the publication Atomwirtschaft (Atomic Energy Economics), December 1973, pages 580-582 that the velocity of vapor bubbles developing in the coolant of boiling water reactors may be determined by correlation methods. This technique requires a plurality of neutron detectors which are arranged within the fuel element one on top of the other when seen in the direction of flow. The actual coolant velocity, however, is less than the velocity measured by this method due to slippage of the vapor bubbles, and the method can be used only with the two-phase streams found in boiling water reactors. 
     In another prior art measuring method of this type, which is discussed in the book, Progress in Nuclear Energy, Volume 1, pp. 553-563, Pergamon Press 1977, Vol. 1, two thermocouples spaced at a distance of about 10 cm are positioned in a closed flow channel in the direction of coolant flow. 
     It is an object of the present invention to provide a method and apparatus which make it possible, without additional incore instruments and without using flow meters, to continuously measure the coolant flow rate of every fuel element and to detect cooling malfunctions at the time they develop. This permits malfunctions to be immediately corrected thereby preventing seriou damage to the reactor. 
     SUMMARY OF THE INVENTION 
     In accordance with the present invention, a method is provided for determining the transit time and flow rate of coolant traversing a cooling channel of a nuclear reactor fuel element from the effective center of the fuel element to a point where the coolant exits therefrom. The method comprises the steps of continuously measuring the temperature of the coolant exiting the fuel element, continuously measuring the temperature of the coolant before it enters the fuel element, generating a measured temperature rise signal corresponding to the difference between the coolant outlet temperature and the coolant inlet temperature; continuously measuring the neutron flux of the core of the reactor by means of at least one neutron detector to generate a neutron flux signal, converting the neutron flux signal to a simulation signal representing a temperature rise in the undelayed simulated coolant outlet temperature, corresponding to the temperature rise of the measured temperature signal, comparing the measured temperature rise with the simulated rise in the undelayed simulated coolant temperature, and determining the time shift of the measured coolant temperature rise with respect to the undelayed simulated coolant temperature rise. The time shift determined in this way corresponds to the transit time of the coolant between the effective center of the fuel element and the point where the coolant exits from the fuel element. 
     The invention further comprises apparatus for carrying out this method which includes a fuel element simulator which receives the neutron flux signal and converts it to a signal corresponding to the rise in the simulated coolant temperature. This apparatus also includes a first correlator for forming a crosscorrelation function from the ac component (noise) of the measured temperature of the coolant exiting the fuel element and the ac component of the simulated coolant temperature, and a second correlator for forming an autocorrelation function from the ac component of the simulated coolant temperature. The time shift between the cross and autocorrelation functions corresponds to the transit time. The method comprises the steps of continuously measuring the temperature of the coolant exiting the fuel element (&#34;outlet temperature&#34;), continuously measuring, the temperature of the coolant before it enters the fuel element (&#34;inlet temperature&#34;), generating a measured temperature rise signal corresponding to the difference between the coolant outlet temperature and the coolant inlet temperature; continuously measuring the neutron flux of the core of the reactor by means of at least one neutron detector to generate a neutron flux signal, converting the neutron flux signal to a simulation signal simulating an undelayed (promt) signal of the temperature rise of the coolant, when traversing the fuel element, comparing the measured temperature rise with the simulated one, and determining the time shift of the measured coolant temperature rise with respect to the undelayed simulated coolant temperature rise. The time shift determined in this way corresponds to the transit time of the coolant between the effective center of the fuel element and the point where the coolant outlet temperature is measured (top of fuel element). 
     The invention further comprises apparatus for carrying out this method which includes a fuel element simulator which receives the neutron flux signal and converts it to a signal corresponding to a simulated coolant temperature rise. This apparatus also includes a first correlator for forming a crosscorrelation function from stochastic fluctuations (noise) in the measured temperature of the coolant exiting the fuel element and fluctuations in the simulated coolant outlet temperature, and a second correlator for forming an autocorrelation function from the noise in the simulated coolant temperature rise. The time shift between the cross and autocorrelation functions corresponds to the transit time. 
     There are several advantages realized with the present invention. First, by using only a power proportional signal and a temperature signal, the transit time of the coolant in the coolant channel of the fuel element can be measured thereby obtaining a flow measurement without the use of a flow meter. Second, in fast reactors, all measuring signals are obtained by the use of the normally available operating instruments, additional incore instruments not being required. Third, falsification of the measured values which occur in conventional indirect flow rate measurements via temperature rise measurements because of changes in the fuel element power are eliminated. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a fuel element showing measuring points and measured values. 
     FIG. 2 is a graph of correlation functions vs delay time. 
     FIG. 3 is a block diagram illustrating apparatus for measuring the transit time of coolant within a fuel element. 
     FIG. 4 is a circuit diagram of a fuel element simulator. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In FIG. 1, a fuel element 1 having a length L and at least one time constant τ BE  is shown in simplified form. The coolant inlet temperature T E  is measured by a thermocouple 50 at (or upstream) the lower end 2 of the fuel element and the coolant outlet temperature T A  by a thermocouple 52 having a time constant τ TH  at its upper end 3. When a plurality of fuel elements are grouped together, the coolant inlet temperature T E  may be measured continuously at least once for all of the fuel elements in the group, once for each sub-group of fuel elements, or it may be measured for each fuel element individually. The coolant outlet temperature T A  is measured continuously at least once at each fuel element exit. 
     In accordance with a permissible simplification, the power P of the fuel element 1 is considered to be concentrated at the locus of the center of power S p , power center S p  being the effective center of the fuel element which is a distance L/2 from the upper end 3. The power P of fuel element 1 is proportional to the neutron flux Φ and is measured by at least one neutron flux detector whose position need not coincide with the position of the fuel element. The coolant outlet temperature T A  is changed by fluctuations in the reactor power P (particularly power noise), changes in the reactor power or in the neutron flux, and changes in the coolant inlet temperature. 
     The neutron flux signal is converted by a fuel element simulator 4 into an equivalent increase ΔT S  in the undelayed simulator coolant outlet temperature T S   corresponding to the temperature rise of the coolant when passing the fuel element according to the equ. T s  =T E  +ΔT s . 
     The coolant requires a transit time τ to travel from the center of power S P  to the point where the coolant outlet temperature T A  is measured, a path having a length L/2. The volume V o  of the cooling channel between the center of power S P  and the point at the upper end 3 of the fuel element 1 where the coolant exit temperature T A  is measured is constant. Thus, the coolant flow rate V in cubic centimeters per second is the quotient of the volume V o  of the cooling channel in cubic centimeters and the transit time τ in seconds of the coolant through a cooling channel of length L/2; that is, 
     
         V=V.sub.o /τ 
    
     The transit time τ can be measured by comparing the correlated alternating (ac) components of ΔT A  =T A  -T E  and ΔT S  i.e. the temperature rise of the measured and simulated coolant outlet temperatures T A  and T S . 
     FIG. 2 shows the correlation functions of two different types of fuel elements used in a sodium cooled reactor. The lower pair of curves depicts, for a first type of fuel element, a first autocorrelation function AKF 1 formed from the alternating voltage component of the simulated coolant outlet temperature T S . It also shows a first crosscorrelation function KKF 1 of the alternating voltage component of the simulated coolant outlet temperature T S  and the measured coolant outlet temperature T A . The ordinate scale for the correlation function KF 1 for the first type of fuel element is given in the left-hand margin in units of K 2  (K=deg. Kelvin). 
     The autocorrelation function AKF 1 and the crosscorrelation function KKF 1 are displaced with respect to each other by τ 1  =0.81 second in a direction parallel to the abscissa. This shift in time can be determined with great accuracy at parallel sections of the ascending and descending edges immediately adjacent the maxima. 
     The upper pair of the curves shows for a second type of fuel element an autocorrelation function AKF 2 and a crosscorrelation function KKF 2. The ordinate scale for the correlation functions KF 2 is shown for the second type of fuel element in the right-hand margin and the time shift is τ 2  =1.6 seconds. 
     There is a phase shift φ(ω) between the neutron flux signal and the output of thermocouple 52 corresponding to the delayed coolant outlet temperature T A . This phase shift includes a first component φ(ω) BE  =arctan (-ωτ BE ) caused by the fuel element 1, a second component φ(ω) v  =-ωτ caused by the transit time τ of the coolant and a third component φ(ω) TH  =arctan (-ωτ TH ) caused by the thermocouple 52 used for measuring the coolant outlet temperature T A , where ω is the angular frequency of the signal.* 
    
     A block diagram of a circuit arrangement for measuring the transit time τ is shown in FIG. 3. A signal T E  (t) corresponding to the coolant inlet temperature T E  is coupled to a first input 11 of a comparator 10 and a signal T A  (t) corresponding to the coolant outlet temperature T A  is fed to comparator 10 at a second input 12. The signal ΔT A  (t)=T A  (t)-T E  (t) corresponding to the coolant temperature rise is generated at an output 13 of comparator 10. 
     In a second comparator 14, a signal T E  (t) corresponding to the coolant inlet temperature is introduced at a first input 15 and a signal T Aref  (t) corresponding to the coolant outlet temperature T Aref  of a reference fuel element is coupled to a second input 16. A signal ΔT Aref  (t)=T Aref  (t)-T E  (t) corresponding to the temperature rise of the reference fuel element is generated at an output 17 of comparator 14. 
     A neutron flux signal Φ(t) is fed to the fuel element simulator 4 via an input 18, and a simulation signal ΔT S  (t) which corresponds to the rise of the undelayed simulated coolant outlet temperature T S  generated at output 19. 
     Output 13 of the first comparator 10 is connected with a first input 20 of a first correlator 21. A second input 22 of the first correlator 21 is coupled, through a switch 23, to either the output 17 of the second comparator 14 or the output 19 of the fuel element simulator 4. Depending on the position of switch 23, correlator 21 forms the crosscorrelation function KKF of either (1) the measured coolant temperature rise ΔT A  and the undelayed simulated coolant temperature rise ΔT S , or (2) the coolant temperature rise ΔT A  and the coolant temperature rise ΔT Aref  of the reference fuel element. 
     A second correlator 26 has first and second inputs 24 and 25 coupled to switch 23. Depending on the position of switch 23, correlator 26 forms the autocorrelation function AKF of either the undelayed simulated coolant temperature rise ΔT S  or of the measured coolant temperature rise ΔT Aref  of the reference fuel element. 
     The crosscorrelation function KKF is generated at the output 27 of correlator 21 and the autocorrelation function AKF is generated at the output 28 of correlator 26. Both outputs 27 and 28 are connected with a comparator 29 which compares the time position of the two correlation functions KKF and AKF and determines the transit time τ. 
     The correlation functions AKF and KKF are generally defined as the average square module of two stochastic functions (noise signals) as a function of a variable delay time τ (shift) between the two stochastic functions. The auto or cross correlation functions are obtained for identical or different stochastic functions, respectively. 
     The correlators 21 and 26 are commercially avaible devices which perform the necessary shift and multiply operations and form the average of the obtained square modules for a certain number of delay time intervalls (as for instance model 3721 manufactured by Hewlett Peckard company). It is also possible to calculate the correlation functions in a general purpose mini- or micro computer (Hewlett Packard model 2100, for instance). 
     The output of comparator 29 is coupled to a dividing circuit 54 which divides a constant input coupled through a switch 56 synchronized with switch 23 by the output τ of comparator 29. When switches 23 and 56 are in the positions shown the output V, corresponding to the flow rate of the cooling channel of the fuel element being measured, is equal to V ref  τ ref  /τ, where V ref  is the known flow rate of the reference fuel element and τ ref  is the known transit time for the reference fuel element. When switch 23 and 56 are switched to their other positions, the output V is equal to V o  /τ. Thus, two methods may be used to determine the flow rate of coolant through the fuel element under test. In connection with the measurement employing the reference fuel element, it shall be understood that the reference fuel element has the same time constants and a cooling channel of the same geometry and coolant volume as the fuel element whose flow rate V is to be measured. 
     The whole circuit of FIG. 3 can also be realized by a small computer such as a type HP2100 manufactured by Hewlett Packard company. This would provide more flexibility and capacity to measure coolant flow rates of all the fuel elements of a reactor core simultaneously. Also the function of the &#34;comparator&#34; 29 can be performed by the computer, i.e. to adjust a fixed time delay τ s  of the simulated signal ΔT s  in such a way that the dislocation of the cross correlation function in comparison with the autocorrelations function disappears. In this case τ s  is equal to the coolant transit time being used to determine the coolant flow rate. 
     FIG. 4 shows the circuit diagram of the fuel element simulator 4 with which the power proportional neutron flux signal Φ is converted into an equivalent signal for simulating the simulated temperature rise ΔT S . The neutron flux signal Φ is measured by means of a neutron detector which may be disposed either inside or outside the reactor core. With an almost constant coolant inlet temperature T E , the variation in the coolant outlet temperature T A  of each fuel element caused by stochastic fluctuations of the reactor power (power noise) is measured, and from this variation (noise) in the coolant outlet temperature there is obtained for each fuel element the interrelationship between the neutron flux and the coolant temperature. 
     The interrelationship between reactor power noise and outlet temperature noise or more generally between reactor power and temperature rise of the coolant passing a fuel element is given by the transfer function H(ω) between the neutron flux φ(ω) (input) and the temperature rise ΔT A  (ω)=T A  (ω)-T E  (ω) (output) according to the equation 
     
         ΔT.sub.A (ω)=H(ω)·φ(ω) 
    
     The transfer function H(ω) can be determined by standard noise analysis techniques, for instance, i.e. measuring the auto- and crosspower spectral density functions of the corresponding signals and dividing the cross power spectrum by the autopower spectrum of the neutron signal (c.f. J. S. Bendat, Principles and Applications of Random Noise Theory; John Wiley and Sons, Inc., New York, 1958). 
     The theory for modeling fuel elements by low-pass filters is given in the publication: Simulation of Fuel Element Thermal Hydraulics for Sensitive Monitoring of Coolant Flow by M. Edelmann (in: Proc. IAEA/NPPCI Specialists&#39;s Meeting on Procedures and Systems for Assisting an Operator during Normal and Annomalous Nuclear Power Plant Operation Situations, Munich, Dec. 5-7, 1979). 
     From the measured transfer function the fuel element and thermocouple time constants as well as the transit time of the coolant can be derived by fitting the theoretical transfer function to the measured one using conventional least-squares methods. Whereas the gain of the transfer function depends only on the time constants of fuel element and thermocouple, the phase angle of the (complex) transfer function is additionally depending on the delay time τ of the measured outlet temperature T A  (ω) with respect to the simulated signal T s  (ω). This delay in the measured signal is equivalent to an additional phase shhift φ v  (ω)=-ωτ in the transfer function. Thus the slope of the linear part of the phase angle (-τ) which is predominant at higher frequencies gives the delay time needed to determine the coolant flow rate through a fuel element. 
     In a larger reactor core with a plurality of spatially dispersed neutron detectors, the detector which has the signal of the highest correlation with the outlet temperature signal of a fuel element to be simulated (i.e. the nearest one, in general) is used to simulate that particular fuel element outlet temperature. 
     Preferably, only the alternating current component of the signals is utilized. Under normal operation conditions the power noise is sufficient for the measurement, otherwise small changes in power are induced by moving the control rod. 
     The neutron flux signal Φ is fed to the input 30 of a first lowpass filter of the first order with which the thermal hydraulic performance of the fuel elements can be simulated to a good approximation. The first lowpass filter consists of a first adjustable input resistor 31 and a first operational amplifier 32 in whose feedback branch there is connected a first RC member 33 including a potentiometer R 1  and a capacitor C 1 . Potentiometer R 1  is set to provide a first time constant τ 1BE  =R 1  ·C 1  corresponding to the time constant of the fuel element. 
     In certain applications it may be of advantage to connect after the first lowpass filter a basically identical second lowpass filter for setting a second time constant τ 2BE  =R 2  ·C 2 , consisting of an adjustable second input resistor 34, a second operational amplifier 35, a potentiometer R 2  and a capacitor C 2 . Potentiometer R 2  is set to a value which enables the first and second lowpass filters to more closely approximate the thermal hydraulic behaviour of the fuel element. This second low-pass filter is not needed, if its time constant τ 2  BE is much smaller than the first time constant τ 1BE  of the fuel element or the time constant τ 3  TH of the thermocouple or if the power noise producing the outlet temperature noise is restricted to frequencies below the corner frequency ω 2  =1/τ 2BE , of the second low-pass filter. 
     If the thermocouples employed cause the temperature signal to be band limited, a third lowpass filter can be connected thereto which includes a third settable input resistor 37, a third operational amplifier 38, a third potentiometer R 3  and a third capacitor C 3 . The potentiometer R 3  is set to simulate the time constant τ 3TE  =R 3  ·C 3   which is caused by the thermocouple 52 with which the coolant outlet temperature T A  is measured. 
     It will be understood that the above description of the present invention is susceptible to various modifications, changes and adaptations, and the same are intended to be comprehended within the meaning and range of equivalents of the appended claims.