Research Article 
Corresponding author: Aleksandra V. Voronina ( avvoronina@mephi.ru ) Academic editor: Yury Korovin
© 2022 Aleksandra V. Voronina, Sergey V. Pavlov, Sergey V. Amosov.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Voronina AV, Pavlov SV, Amosov SV (2022) Ultrasonic monitoring of the VVER1000 FA form change. Nuclear Energy and Technology 8(2): 127132. https://doi.org/10.3897/nucet.8.89350

A procedure has been developed to determine the geometrical parameters of fuel assemblies (FA) by an ultrasonic pulseecho technique used for all types of lightwater reactor FAs. The measurement of geometrical parameters is achieved through the pairwise installation of ultrasonic transducers opposite the FA spacer grid faces at a distance of not more than a half of the transducer acoustic field nearregion length such that the acoustic axes of the pairwise transducers are parallel to each other. The advantages of the presented technique is that it enables monitoring of any FA modifications, including the VVER reactor assemblies with a different number of spacer grids.
The paper presents a mathematical model of the acoustic path developed in a geometrical acoustics approximation and its verification results. The model was used for computational and experimental studies of the ultrasonic test technique, and engineering formulas have been developed to calculate the errors of the transducermeasured distance to the FA surface. A code has been developed to simulate the FA form change monitoring and can be used to design new monitoring systems.
The developed technique to determine the VVER1000 FA geometrical parameters was introduced at units 1 and 2 of the Temelin NPP, the Czech Republic, for the TVSAT FA form change monitoring. The successful use of the proposed technique makes it possible to recommend it for use in inspection benches at other NPPs.
Ultrasonic technique, fuel assembly, form change, model, natural convection
In the process of irradiation in the reactor core, a fuel assembly (FA) is subjected to thermal, radiation and vibration impacts and loads. This leads to all kinds of strain, such as deflection, torsion and elongation, variation of the flattoflat dimension, and spacer grid (SG) warps. A deformed FA may result in abnormal operation of control rods and the control and protection system, so FA form change is a topical issue and requires special attention.
The FA form change as a result of service inside the reactor is investigated either in shielded boxes at material test centers or at inspection benches deployed in spent fuel pools (SFP) directly at NPPs. One example of a material test center is JSC SSC RIAR engaged, specifically, in testing irradiated VVER1000 FAs from all NPPs in Russia (
The inspection and repair bench developed for the NPP 2006 project uses contact differential transformer linear displacement transducers (
Despite the extensive use of ultrasonic techniques in technology, there are no currently common tools for developing ultrasonic FA geometry inspection systems. Besides, complexities arise with estimating the error in the obtained results when using ultrasonic techniques.
The paper describes a new ultrasonic pulseecho technique to identify the VVER FA form change in the NPP cooling pool successfully implemented at the Temelin NPP for the TVSA FA inspection. The paper also presents a mathematical model of the pulseecho technique acoustic path to measure the distance between the transducer and the FA surface and the model verification results. A code has been developed to simulate the FA form change process that can be also used to develop new measurement systems and FA monitoring techniques.
A method has been developed for the FA inspection in the NPP SFP to determine the FA geometry by ultrasonic technique that consists in the following (
The nearregion dimension, X_{б}, is equal to
X _{б} = R^{2}∙f/c, (1)
where R is the radius of the piezoelectric element, m; f is the UW frequency, Hz; and c is the speed of sound in the medium, m/s.
For example, for a transducer with a radius of R = 0.01 m that generates UWs with a frequency of f = 5 MHz, the nearregion dimension will be equal to X_{б} = 0.33 m.
With the investigated surface being at a distance not exceeding 0.7 Х_{б}, the amplitude of the reflected UW pulse echo does not practically change (
The system with ultrasonic transducers is moved along the FA longitudinal axis to determine the distance between the transducers and the SG faces using the following formula
S = c∙τ/2, (2)
where τ is the time of the UW propagation from the transducer to the FA and back, s.
The pairwise arrangement of the transducers allows determining the face rotation angle, α:
α = arctg(ΔS_{n}/L_{n}), (3)
where S_{n} is the deviation in the readings of the transducers installed opposite the n^{th} face, m; and L_{n} is the distance between the acoustic axes of the transducers installed opposite the n^{th} face, m.
The computed angle permits an allowance to be made in determining distance S and the error reduced in the UW angular incidence. The mentioned error is the result of the UW oblique reflection from the slanted surface. The distance measured with regard for the angular allowance will be
S = c∙τ∙[1 + 1/cos(2α)]^{–1}+ R∙tgα, (4)
where R is the radius of the piezoelectric element, m; and α is the face rotation angle computed using formula (3), degrees.
To employ the angular allowance, it is required to determine initially the distance from the transducers to the surface based on formula (2), determine further the face rotation angle, α, and the distance with regard for the allowance using formula (4), and then calculate again angle α. This approach used in measurements will make it possible to reduce the influence of the angular incidence on the technique results.
The torsion angle, ψ, for each FA crosssection can be determined by determining the rotation angle of all faces with respect to the FA upper or lower SG using formula
ψ = ψ_{0} – ψ_{i}, (5)
${\psi}_{i}=\frac{1}{n}\left(\sum _{1}^{n}arctg\frac{\Delta {S}_{n}}{{L}_{n}}\right)$ (6)
where ψ_{0} is the upper or lower SG rotation angle, degrees; ψ_{i} is the i^{th} SG rotation angle, degrees; and n is the number of the FA faces.
The deflection is calculated from the array of the SG surface point coordinates obtained in the inspection using algebraic computations.
This method can be used for all types of the lightwater reactor FAs, including squareshaped FAs.
A boundary layer occurs during the inspection of an irradiated FA near the FA surface due to the nuclear fuel decay heat. This layer is characterized by a temperature gradient growing in the upward direction along the FA longitudinal axis. The temperature profile in the natural convection conditions depends on the liquid flow pattern, the SFP water temperature, and the decay heat value.
Since ultrasonic speed depends on the wave propagation medium temperature, an error takes place in determining the distance between the transducer and the SG face. In addition, an error occurs depending on the UW angular incidence onto the surface. Besides, a refraction phenomenon, a curved UW propagation path, needs to be taken into account in a medium with a temperature gradient.
To determine the dependence of the distance measurement error on the factors described herein, a mathematical model of the ultrasonic technique acoustic path has been developed (
We shall introduce the following notation: τ_{1} (time for the UW propagation from the transducer to the boundary layer); τ_{2} (time for the UW propagation in the boundary layer); τ_{3} (time for the reflected UW propagation to the transducer after traveling through the boundary layer); Δτ_{A} (time defined by the pulseecho leadingedge recording technique); X (distance from the transducer to the inspected surface along the transducer’s acoustic axis), m; α (FA surface slope, degrees); δ_{t} (thickness of the thermal boundary layer, m); c (T_{∞}) (constant sound speed value at the SFP water temperature of T_{∞} far from the FA, m/s); T (x) (boundary layer temperature profile); f (UW frequency, Hz); k (ratio of threshold amplitude A_{0} and maximum signal amplitude, A_{max}).
The UW propagation time can be presented then by the following expression
$\tau ={\tau}_{1}+{\tau}_{2}+{\tau}_{3}+\Delta {\tau}_{A}=\frac{XR\xb7tg\alpha \frac{{\delta}_{t}}{\mathrm{cos}\alpha}}{c\left({T}_{\infty}\right)}\xb7\left(1+\frac{1}{\mathrm{cos}2\alpha}\right)+2\xb7{\int}_{0}^{{\delta}_{t}}\frac{dx}{c\left(T\right(x\left)\right)\xb7\sqrt{1{\left(\frac{\mathrm{sin}\alpha}{c\left({T}_{\infty}\right)}c\left(T\right(x\left)\right)\right)}^{2}}}+$
(7)
$+\frac{2{\mathrm{sin}}^{2}\alpha}{c{\left({T}_{\infty}\right)}^{2}\mathrm{cos}2\alpha}\xb7{\int}_{0}^{{\delta}_{t}}\frac{c\left(T\right(x\left)\right)dx}{\sqrt{1{\left(\frac{\mathrm{sin}\alpha}{c\left({T}_{\infty}\right)}c\left(T\right(x\left)\right)\right)}^{2}}}+\frac{1}{2\pi f}\xb7\mathrm{arcsin}\left(k\right)$.
The first three summands are determined from the UW propagation path in the medium between the transducer and the SG surface. The final summand characterizes the pulseecho recording method. Due to being steep, the pulseecho leading edge causes an additional distance determination error that depends on the threshold level of A_{0}, from which time τ is measured. When A_{0} increases, Δτ_{A} and, accordingly, the error increase (
According to (7), calculating the UW propagation time requires data on the boundary layer thickness and temperature profile. To determine the temperature profile in the natural convection conditions near the FA surface, one can use the results of the natural convection computational and experimental investigation or undertake numerical simulation using computational fluid dynamics (CFD) methods.
Based on semiempirical relations known in literature to determine the heatexchange characteristics during natural convection, a program was developed for calculating the speed of sound in water (
In the process of justifying the applicability of the developed acoustic path model, its verification procedure was undertaken (
Fig.
The influence of the slope on the ultrasonic measurement results is shown in Fig.
It can be seen that the error is the larger the larger is the slope. The experimental data numbered 1 (discs) are above the reference line, but the dependences of errors are identical. The data numbered 2 (squares) demonstrate the results of employing the angular allowance when calculating the distance between the transducer and the surface using formula (4). When the proposed allowance is used, the error is smaller and does not exceed 5 μm in a range of 0 to 3°. It can be concluded based on this that the given allowance needs to be used for the distance calculation since it makes it possible to reduce considerably the measurement error.
Investigating the influence of natural convection on the ultrasonic dimensional measurement results has shown that the error of measuring the distance from the transducer to the inspected item for a turbulent convection mode is several times as large as for a laminar mode and is defined primarily by the boundary layer thickness and water temperature drop. For a turbulent natural convection mode that starts at Ra > 4∙10^{13}, nomograms were obtained for determining the boundary layer thickness, the temperature drop, the origin of the turbulent mode coordinate near the FA surface, and the absolute error value for the measured distance between the transducer and the surface (
Fig.
Fig.
The nomograms were processed to obtain engineering formulas to calculate the measured distance error for a turbulent convection mode (
$\left\Delta X\right=\frac{q\xb7{y}^{2}}{\alpha}\xb7{\left({Ra}_{y}\right)}^{0.44}\xb7{10}^{2}+\chi \xb7{q}^{\gamma}\xb7{\left(\frac{y}{q}\xb7{10}^{3}\right)}^{\epsilon}\xb7{10}^{6}$, (8)
y _{т} = ω∙q^{−0.25} (9)
where ΔX is the absolute error value, m; y_{т} is the turbulent mode onset coordinate, m; y is the coordinate along the FA vertical axis, m; q is the heat flux density near the FA surface, W/m^{2}; Ra_{y} = Pr∙g∙β∙q∙y^{4}/(λν^{2}) is the local Rayleigh number; Pr is the Prandtl number; g is the free fall acceleration, m/s^{2}; β is the liquid bulk thermal expansion factor, 1/K; λ is the liquid conductivity factor, W/(m∙°С); and ν is the liquid kinematic viscosity factor, m^{2}/s.
The factors in formulas (8), (9) are determined depending on the SFP water temperature (
The decay heat value for the random burnup and FA cooling time values can be determined using different codes or calculated by linear interpolation of the decay heat values shown in (
A code has been developed based on the acoustic path mathematical model to simulate the VVER FA form change monitoring be ultrasonic technique (
The developed mathematical model and the code were used to simulate computationally and experimentally the VVER1000 FA form change monitoring process (
The diagram presents dependences of the transducermeasured distance error, ΔX, for different distances X between the transducers and the VVER1000 FA surface. The piezoelectric element radius was assumed to be equal to 9 mm, the resonant frequency was assumed to be equal to 5 MHz, while the distance between the transducer’s acoustic axes was selected as equal to 25 mm. The face deflection value was 20 mm, and the FA torsion angle was not more than 3°. The data were obtained for a turbulent mode with Ra = 3∙10^{16}, the water temperature being equal to 20 °C.
The dependence of the error on distance X is linear. It can be seen that the straight line oblique factor depends on the torsion angle. A torsion angle increase leads to the straight line slope increase the farther is the transducer from the SG surface, and the measured distance error is smaller. The presented calculated dependences demonstrate the results obtained without the angular allowance taken into account. As noted earlier, the allowance made permits reducing substantially the measurement error. As shown by the calculation results, the use of the allowance neutralizes the surface slope, while reducing the error to the values of the error defined by the FA decay heat. The values of this error in the diagram fit the data obtained for the angle equal to 0°.
The developed technique has been introduced in the TVSAT FA inspection bench at the Temelin NPP. About 40 TVSAT FAs of different modifications with a burnup of ~ 11 to ~ 52 MW·day/kgU were inspected. Most of the TVSATs were inspected practically a few days after having been withdrawn from the reactor core, while only some had been cooled in the SFP for about two years.
The process of the FA scanning in the bench using ultrasonic transducers for the deflection and torsion angle determination takes about 10 minutes, which proves ultrasonic inspection to be near realtime. A positive experience of using the developed technique at the Temelin NPP makes it possible to recommend it for being employed at other NPPs.