This study characterized the magnitude, spatial profile, and frequency spectrum of thermal striping at a junction using a novel sodium-deployable optical fiber temperature sensor. Additionally, this study revealed for the first time the capability of performing cross correlation velocimetry (CCV) with an optical fiber to acquire fluid flow rates in a pipe. Optical fibers were encapsulated in stainless steel capillary tubes with an inert cover gas for high-temperature sodium deployment. Plots of temperature oscillation range as a function of two-dimensional space highlighted locations prone to mechanical failure for particular flow momentum ratios. The effect of inlet sodium temperature differential and bulk flow rate on thermal striping behavior was also explored. The power spectral density (PSD) revealed that the striping temperature oscillations occurred at frequencies ranging from 0.1 to 6 Hz. Finally, the bulk flow rate of liquid sodium was calculated from thermal striping's periodic temperature oscillations using cross correlation velocimetry for flow rates of 0.25–5.74 L/min.

## Introduction

The thermal-hydraulic properties of liquid sodium make it an attractive candidate for use as a coolant in generation-IV nuclear reactors. With a high-thermal conductivity and low-Prandtl number, sodium provides efficient heat transfer in the core and heat exchangers of the reactor. However, these particular hydrodynamic properties of sodium also promote the phenomenon known as thermal striping. Thermal striping is characterized by temperature oscillations occurring on the order of 0.1–10 Hz at hot/cold stream junctions [1]. This oscillating temperature field is created by jet instabilities and turbulence in the flows and exacerbated by sodium's low-Prandtl number. These rapid and continuous temperature perturbations may result in damage to proximal reactor structures due to increased thermal stress cycling. This is due to the austenitic steel construction material possessing a high-thermal expansion coefficient and relatively low-thermal conductivity, as compared to sodium.

While thermal striping has been studied with conventional thermocouples, new advancements in temperature sensors provide unprecedented spatial and temporal resolutions of this phenomenon. This high-fidelity data can help optimize the reactor geometry and hydraulic parameters to mitigate thermal striping damage.

Measuring thermal striping has been a difficult task with more traditional methods due to limited spatial resolution and potential flow obstructions. However, recent advancements in fiber-optic sensors allow quasi-continuous measurement of temperature profiles of a system using swept-wavelength interferometry of Rayleigh backscattered light [2]. Luna Innovations' ODiSI-B optical fiber interrogator was chosen to investigate the thermal striping phenomenon. This system has a spatial resolution of 0.653 mm and a sensing frequency of 23.8 Hz. This sensing frequency gives a Nyquist frequency of 11.9 Hz. Thus, striping's temperature oscillation frequency range of 0.1–10 Hz predicted in the literature should be adequately captured without aliasing [1,3,4]. Corning's 245 μm diameter SMF-28 single mode optical fiber was used throughout this work to acquire temperature profiles. The small footprint of the optical fibers minimizes the impact on the thermal hydraulics of the system. This impressive spatial and temporal resolution of fiber-optic temperature sensors allows observation of thermal-hydraulic phenomena which occur over small lengths at high frequencies.

In this study, thermal striping at a 90-deg junction of two nonisothermal flows was explored with optical fibers for the first time. A novel method of encapsulation of the fibers in a protective capillary tube with inert cover gas was developed. Temperature oscillation range data from three optical fibers were interpolated for a variety of flow momentum ratios between hot and cold streams in the turbulent regime. This facilitated the prediction of the location and magnitude of thermally induced stress in a system component with unprecedented resolution not attainable with conventional methods of temperature sensing (e.g., thermocouples). Frequency characteristics of the thermal striping were also explored to determine the periodicity of the phenomenon.

As a demonstration of an auxiliary feature of the optical fiber sensor, cross correlation velocimetry (CCV) was performed on the optical fiber temperature data to calculate bulk flow rate which was compared to the electromagnetic flowmeters (EMFM) installed in the experimental system. This represents the first use of optical fiber temperature sensors to determine bulk fluid flow in a system.

This paper begins with the “Background" section which introduces the relevant literature published with respect to thermal striping, optical fiber temperature sensors, and cross correlation velocimetry. The “Experimental Setup” section then introduces the deployment method for optical fibers in sodium and describes the geometry of the thermal striping test section. The “Methods” section of this paper derives the flow momentum ratio equation used to characterize flow shapes and details the process of cross correlation velocimetry. The “Testing Parameters” section provides the flow conditions tested for thermal striping analysis and cross correlation velocimetry. Finally, the “Results” section presents the analysis of thermal striping and cross correlation velocimetry of sodium at a junction.

## Background

### Thermal Striping.

There have been many industrial case studies and experiments performed to analyze thermal striping as a failure mechanism in a liquid sodium system. In France's SPX-1, the failure of a circumferential weld downstream from a mixing tee in an auxiliary pipe of the secondary circuit was traced to thermal striping [5]. Additional recorded industrial failures include thermal striping-induced cracking in a Phenix sodium pump vessel in France, control rod tube in the Prototype Fast Reactor in the UK, and a cold trap in the BN-600 reactor in Russia [3].

The first experimental studies on thermal striping commenced in 1982 with a project that characterized the conditions under which the thermal striping caused damage to various structural configurations [6]. Further experimentation was performed by Kawamura et al. [7] and Yuki et al. [8] which focused primarily on thermal striping in tee junctions. Qian et al. found general characteristic equations to predict fluid flow shape at a junction which can be used to locate the spatial position of thermal striping oscillations [9]. These equations were modified to represent the 90 deg junction geometry used in this work.

The frequency behavior of thermal striping was explored by Ogawa et al. [4] and the effect of thermal striping frequency on surrounding structure by Jones and Lewis [1]. They found that the relatively slow transient thermal response of the structural component dampens high frequency thermal oscillations from fluid to structure. Thus, the literature suggests that lower frequency thermal striping behavior is more malignant as the full range of temperature oscillation may be realized in the structure leading to greater thermal strain. While a detailed study of how the thermal striping temperature oscillations transfer to the surrounding structure is outside the scope of this work, it is important for validation of the fiber data that their frequency spectra match previously published studies using thermocouples.

### Optical Fiber Temperature Sensors.

The fiber sensors functioned by means of optical frequency domain reflectometry to monitor temperature. Each optical fiber possesses unique and permanent microscopic scattering sites in the fiber core caused by intrinsic variations in the density of the glass. This defines a Rayleigh backscatter profile which will remain permanent barring a thermomechanical change in the fiber. During temperature changes the Rayleigh backscatter profile of the fiber is stretched or compressed creating a shift in frequency of the backscattered light [2]. This shift in frequency can be used to determine the local thermomechanical state of the fiber at a continuous set of locations, known as gauges.

Light frequency shift determination was done using Fourier domain reflectometry. The backscattered light from the fiber was collected with a photodiode and Fourier transformed from the time domain to the frequency domain, producing a pattern dependent on frequency. Then, frequency shifts with respect to an unstrained reference state can be determined via a cross correlation. The spectral shift was converted to temperature using a calibration curve found by Wood et al. for Corning's SMF-28 single mode optical fiber, see the following equation [10]:
$T=(−1.33×10−4)S2−(0.748)S−0.229$
(1)

where $T$ is the temperature in degrees centigrade, and S is the frequency shift in GHz. The ODiSI-B has a manufacturer's rated temperature repeatability of ±1.6 °C.

### Cross Correlation Velocimetry.

Given the high spatial and temporal resolution of the optical fibers, one can perform CCV on the temperature as a function of time and space to obtain the average flow rate. This technique works by finding the time separation of a distinct temperature pattern between two temperature sensors with a cross correlation. Given the sensors are spaced at a known distance in a flow stream, the velocity can then be calculated. This technique was developed by Cox in 1977 to study velocity in turbulent flames [11]. It has since been applied successfully to calculate water flow rate in an experimental scale model of a boiling water reactor with an array of thermocouples [12]. The oscillatory nature of the temperature in thermal striping provided a good application for CCV in this work.

## Experimental Setup

### Optical Fiber Deployment in Sodium.

In order to protect the optical fiber from damage due to sodium–silica interaction and moisture from the laboratory it was sealed from the environment. A method for encapsulating the Corning's acrylate coated SMF 28 optical fiber in a type 316 stainless steel capillary tube is depicted in Fig. 1. This design allows for hermetic sealing, ensuring moisture does not induce and propagate microcracking of the silica cladding and core at high temperature [13]. A vacuum of <150 mTorr was pulled on each fiber capillary tube during loop heat up to remove the off gassed acrylate fiber coating and any residual moisture from the fiber environment. When the loop was at an operating temperature (>250 °C) for at least 5 h, 138 kPa gauge pressure helium cover gas was then allowed to flow into the capillary. Helium was used as it is inert and provides high thermal diffusivity, thus optimizing heat transfer.

The 316 stainless steel capillary tube used to house the fiber in this experiment was from Valco Instruments Co. (Houston, TX) and had an outer diameter of 0.80 mm and an inner diameter of 0.51 mm. The manufacturer uses a hexane-based solvent to clean the inner wall of the capillary tubing to eliminate any contaminants which may damage the silica fiber. The capillary was fixed at either end via a silver solder joint to a 3.18 mm outer diameter, 1.02 mm inner diameter stainless steel tube which was swaged into place on the system by a 3.175 mm (1/8 in) Swagelok union, see Fig. 1.

### Thermal Striping Test Section.

The experimental liquid sodium loop located at the University of Wisconsin-Madison was used to acquire thermal striping data, see Fig. 2. A fraction of the sodium from the main loop was diverted to a diagnostic loop where the striping section was located. The striping section can be seen labeled in the diagnostic loop of the schematic in Fig. 2, and a more detailed drawing of the striping section can be found in Fig. 3.

The striping section directs two streams of sodium at independently variable flow rates and temperatures to impinge upon one another at a 90-deg angle to facilitate the thermal striping behavior. Three optical fibers were mounted concentrically in capillaries in the main mixing tube and two-angled branch tubes as seen labeled fiber A1, A2, and A3 in Fig. 3. In order to accurately locate the capillary tubes once installed, an X-ray image was taken of the capillaries and used to orient temperature data in later analyses.

The flow through each leg of the striping section was fine-tuned with separate spherical stem type, welded bellows sealed valves from Swagelok, part number SS-4UW-TW. A counter flow pressurized air heat exchanger cooled the cold side sodium, labeled “striping cooler” in Fig. 2. The flow rate of the pressurized air was set with a variable orifice valve. The orifice position was continuously determined via a proportional-integral-derivative feedback loop with a wetted 1.59 mm K type sheathed ungrounded thermocouple providing the process variable. This thermocouple is labeled “Cold TC” in Fig. 2. The hot sodium leg temperature was monitored with a thermocouple of the same type, labeled “Hot TC” in Fig. 2.

The flow rate through the main loop and each leg of the diagnostic loop was monitored with permanent magnet type flowmeters. Voltage induced by the sodium flowing through the EMFMs was read with 1.59 mm diameter diametrically opposed 316 stainless steel wires which were spot welded to the flow channel. The voltage was converted to flow rate using the following equation [14]:
$Q=πDH4BVmK1K2K3$
(2)

where $Q$ is the volumetric flow rate, $DH$ is the hydraulic diameter of the pipe, $B$ is the magnetic field, $Vm$ is the measured voltage, and the three $K$ factors are nonlinear correction functions which account for geometric and temperature effects particular to the system. The magnetic field of each flowmeter was read inside of the tube between the two flowmeter magnets with a FW Bell Model 4048 gaussmeter prior to loop filling.

In order to verify the theoretical flow rate given in Eq. (2), a Micromotion F025A Coriolis flowmeter was installed in the diagnostic loop in place of the striping section. The flow rates through each leg of the diagnostic loop were varied from 0.38 to 1.5 L/min for sodium temperatures of 200 °C, 260 °C, and 300 °C. Note that the size of the Coriolis flowmeter and its temperature restriction of <350 °C prevented installing in series with the striping section during striping experiments. The theoretical EMFM reading for both sodium streams, as predicted by Eq. (2), as a function of Coriolis flowmeter reading can be found in Fig. 4. The manufacturer's rated uncertainty for volumetric flow rate for the Coriolis flowmeter was 0.2%, and the calculated EMFM volumetric flow rate uncertainty was 3.65%.

Linear fits have been included in Fig. 4. Notice that the hot and cold side flowmeter theory according to Eq. (2) predicts flowrates 1.471 and 1.458 greater than Coriolis flowmeter reading, respectively. These values define calibration factors, EMFM readings were multiplied by the inverse of 1.471 and 1.458 for the hot and cold side flowmeter reading, respectively, to acquire accurate flowrate readings. This discrepancy was likely due to a higher magnetic field provided by the permanent magnets than measured with the gaussmeter. The nonlinear $K$ factors seem to capture temperature and geometric effects quite well given high coefficients of determination for the linear fits as well as minimal disparity in flow rate between sodium temperatures.

The two 45-deg angled branch tubes of the striping section had an inner diameter of 0.94 cm, while the larger main mixing tube had an inner diameter of 2.21 cm. The dimensionless entry length for turbulent flow can be used as an estimate to determine if flow is fully developed in the branch tubes at a particular Reynolds number, see the following equation [15]:
$leDH=4.4(Re)1/6$
(3)

where $le$ is the entry length, and $DH$ is the hydraulic diameter (inner tube diameter). One can see in Fig. 3 that the straight section of the branch tubes before connecting to the main mixing tube was 8.82 cm. Using this straight section as the entry length, one can calculate the maximum Reynolds number for fully developed flow to be only ∼94. Thus, the turbulent flow throughout these experiments was considered undeveloped or developing. This may have affected thermal striping behavior.

## Methods

### Categorization of Flow Shape at Junction.

It is important to predict and locate the position of thermal striping-induced temperature oscillations at a flow junction because some regions are more sensitive to rapid temperature fluctuations than others. When high temperature oscillations occur in the bulk sodium, they are a benign thermal phenomenon. Conversely, when close to a mechanical containment they can induce high cycle thermal fatigue.

In order to classify flow patterns at the 90-deg intersection, momentum rates were calculated using Eqs. (4) and (5) for the hot and cold streams, respectively,
$MH=π4DH2VH2ρH$
(4)

$MC=π4DC2VC2ρC$
(5)

where D, V, and ρ are defined as the hydraulic diameter, velocity, and density of the hot and cold inlet streams.

Momentum flow ratio of hot to cold flow at the junction can be found with the following equation:
$MR=MHMC=VH2ρHVC2ρC$
(6)

These flow equations are based on characteristic equations for T-junction intersections found in a report by the Japan Society of Mechanical Engineers [16]. Note that the momentum ratio for a T-junction is defined as the main tube flow divided by a branch flow. Table 1 provides categorization of T-junction flow, with categories for wall, re-attached, turn, and impinging jet as a function of momentum ratio [9]. An illustration detailing the flow pattern of the jet categories for the geometry in this work is included in Fig. 5.

### Cross Correlation Velocimetry.

The method of CCV utilizes the transport of a small volume of fluid at a particular temperature across temperature sensors to determine flow rate. In order to perform CCV analysis, a reference temperature gauge is chosen at the origin of a distinct temperature oscillation. A plot with sample data showing temperature versus time data for fiber A1 at a reference gauge 3.92 mm downstream from the fiber cross point and a subsequent gauge 6.53 mm downstream of this reference gauge is seen in Fig. 6. Temperature oscillations produced by thermal striping create a temperature variation which is transported by the bulk sodium flow. Thus, one can imagine shifting the downstream gauge data in time over to match the reference gauge to acquire high correlation between these data sets. This time shift is referred to as “lag” in time series analysis.

This process can be automated using the equation for cross correlation, see the following equation [17]:
$C12(τ)=1P−τ∑n=1P−τT1nT2n+τ$
(7)

where C is the cross correlation value, P is the measurement time period, τ is the lag, and T is the gauge temperature measurement.

Thus, the correlation values for time lag can be calculated with respect to reference for a series of down-stream gauges, as seen in Fig. 7. High correlation can be seen in Fig. 7 at particular distances with respect to reference for lag values. The frequency of the optical fiber reading is 23.8 Hz, thus the minimum lag value able to be calculated is 42 ms. The gauge with the highest correlation at a particular lag value can then be used to calculate velocity with the following equation:

(8)

where $X$ is the spatial location of a particular gauge.

## Testing Parameters

Flows which represent impinging, turn, re-attached, and wall jets were created to study thermal striping. This was done by varying the hot and cold sodium flow rates to produce momentum ratios which fall in the range of each flow category given in Table 1. The parameters for this experiment are included in Table 2 for reference. The momentum ratios were varied from 0.22 to 23.10 in order to capture each flow category. For tests 1–8, the temperature differential was kept at a constant gradient of around 90 °C, while the velocity of the hot stream was adjusted. Test 9 possessed a temperature gradient of 58 °C between the hot and cold flows. Tests 10–15 assessed the effect of temperature differential; the hot and cold flow rates were kept constant, while the temperature gradient was varied from 37 °C to 95 °C. Temperature-dependent density and viscosity values of sodium used to calculate Reynolds numbers and momentum ratios in this work were from an Argonne National Laboratory report [18]. Tests 1–15 possessed an acquisition period of 10 s each.

Temperature data from fiber A1 were used for CCV as it was situated parallel to bulk sodium flow in the mixing tube. The parameters used for calculation of sodium flow rate by CCV are given in Table 2. The temperature differential between sodium streams and the mixing tube flow rate was set at 65 °C and 50 °C for tests 16–25 and 26–37, respectively. A momentum ratio of 0.7 was kept constant in all tests as this ratio was empirically found to provide large magnitude temperature oscillations in the mixing tube center. These large oscillations provided good signal to noise ratio for CCV analysis. In addition, the effect of bulk flow rate on thermal striping behavior was explored with tests 16–37. A data acquisition period of 60 s was used for tests 16–37.

## Results

### Thermal Striping Characterization at Junction.

Two-dimensional contour plots showing the maximum range of temperature oscillations seen for tests 1–9 have been included in Fig. 8. The tests are labeled with their respective momentum ratio. These 2D plots were created from the 1D fiber data by performing an interpolation between the data from fibers A1, A2, and A3. This was done by creating a 50 × 110 (x by y) cell mesh with spatial coordinates spanning 2.2 cm in the x direction and 5 cm in the y direction. These dimensions represent the 2.2 cm inner diameter of the mixing tube and the corresponding vertical 5 cm span of the fibers, see Fig. 3. Temperature data were then interpolated onto the mesh using a natural neighbor interpolation included with MathWorks' matlab software [19]. Spatial coordinates of the optical fiber were acquired from the X-ray images and were used to position temperature data on the generated meshes. In Fig. 8, the normalized temperature range has been plotted for tests 1–9. The normalized temperature range is defined in the following equation:

$θrange=Tmax−TminΔT$
(9)

where $Tmax$ and $Tmin$ are the maximum and minimum temperatures at each gauge recorded over the acquisition period, and $ΔT$ is the branch sodium temperature difference. Recall that during these tests the momentum ratio was varied, while the temperature differential between sodium streams was kept constant. The momentum ratio has been labeled for each test in Fig. 8.

One can see that a momentum ratio of 0.22 results in large temperature oscillations toward the hot side mixing tube wall. This is representative of the shape of an impinging jet with a momentum ratio less than 0.35, as predicted by Table 1. A lower momentum ratio should produce oscillations even closer to the hot side wall. This flow regime could be characteristic of mechanical failures on the far side of an impinging flow. Thus, it would be prudent to perform component inspection on the opposite side of the branch to main tube interface when operating at momentum ratios less than 0.35 for extended periods of time.

Temperature oscillations occur with maximum intensity near the center of the mixing tube for the turn jet flow category, as seen for momentum ratios from 0.45 to 0.99 in Fig. 8. If a mechanical component were situated at the tube center, this would be cause for concern as thermal oscillation range is quite large with a maximum normalized temperature range of ∼0.7. However, turn jet flows are optimal in preventing thermal striping-induced fatigue in the junction walls as the high magnitude temperature oscillations occur in the bulk fluid.

Momentum ratios of 1.65 and 2.62 demonstrate the re-attachment behavior on the cold side of the tube with relatively high oscillation range. This flow condition could yield high thermally induced stress downstream of the junction on the cold inlet side. With respect to a momentum ratio of 1.65, one can see in Fig. 8 that the normalized temperature oscillation range is at ∼0.30 next to the main tube wall at a position of around 2 entry tube diameters downstream of the branch entry. This magnitude of temperature oscillation could lead to thermal fatigue and possibly failure in the mechanical structure.

As the momentum ratio was increased to 23.10, the flow oscillations became constrained to the cold stream wall. With a normalized temperature range of ∼0.35 next to the junction wall, this flow shape is troublesome. This is typically a weak area in a system given that a weld is usually located at this location. This weld may be under thermal creep and fatigue stresses from other sources such as thermal expansion of the structure. Oscillations also seem to be occurring far upstream of the cross point in Fig. 3; similar upstream behavior was seen by Tanaka et al. in computer simulations of thermal striping at a T-junction [20]. Using Eqs. (4)(6), one can calculate the momentum ratio in the Tanaka experiment as ∼8, thus also classifying it as a wall jet. These oscillations upstream were attributed to intermittent reverse flow from the branch pipe (cold stream) upstream. Thermal fatigue at the upstream edge of the branch pipe should be checked if this were an industrial component.

In order to determine the temperature differential effect at constant flow rate on thermal striping behavior, tests 10–15 from Table 2 were performed. Interpolated contour plots depicting temperature oscillation range have been given in Fig. 9 for each temperature differential. The sodium inlet temperature differential is included in the label for each contour plot. One can see the increase of striping magnitude as the temperature differential increases, while the characteristic turn jet shape is maintained. The maximum temperature oscillation range calculated for a particular gauge on fiber A1 was plotted as a function of sodium stream temperature differential for tests 10–15, Fig. 10. A linear trend line fitted to this plot shows a ratio of approximately 0.61 for temperature oscillation range to stream temperature differential, showing a damping effect of the oscillation range with respect to stream temperature range.

The maximum normalized temperature range calculated over the entire acquisition period was plotted as a function of main mixing tube Reynolds number in Fig. 11 for tests 16–37. One can see the normalized oscillation range asymptotes in the turbulent regime at Re > 5000, thus showing a reduced dependence of thermal striping temperature range on Re above this critical value.

### Frequency Analysis.

A frequency analysis reveals the number of temperature range cycles over a component lifetime and the effectiveness of the temperature oscillations in propagating from fluid to structure. In order to give an example of temperature as a function of time and space in thermal striping, data from test 4 were explored. The mean temperature was calculated for each gauge in fiber A1 over the 10-s experiment period. The normalized temperature difference from mean, Eq. (10), for each gauge was then plotted as a function of time in Fig. 12, where zero on the y-axis is located at the fiber cross point

$θdiff=T−TmeanΔT$
(10)

A periodic nature of temperature oscillation is evident in the data, as $θdiff$ varies from −0.35 to 0.35 at seemingly regular intervals. The power spectral density (PSD) for fibers A1, A2, and A3 at the gauge location of maximum temperature oscillation for each fiber in test 4 is plotted in Fig. 13.

The PSD reveals the frequency components present in the temperature signal. White noise is apparent from frequencies of 0.1–6 Hz with a drop in spectral power from around 6 Hz to the Nyquist frequency of 11.9 Hz. This frequency distribution is similar to those found in other striping experiments which used thermocouples [3,4]. A spike in spectral power is seen at 5.9 Hz which seems to match the visibly apparent frequency of temperature oscillations of Fig. 12. In order to further analyze this, an autocorrelation was performed on the fiber A1 temperature versus time data used in Fig. 13. The result of this autocorrelation can be found in Fig. 14. Notice that the first nonzero lag value with a positive peak in correlation is at 0.168 s. Calculating the inverse of this yields ∼5.9 Hz, which matches the peak in the PSD, as expected. Also notice in Fig. 14 that the subsequent positive correlation spikes are multiples of 0.168 s, and any negative correlation trough is halfway between these peaks. Ogawa et al. found a prominent frequency peak at 6 Hz during thermal striping experiments at a T-junction using thermocouples in water for a variety of flow configurations [4].

### Cross Correlation Velocimetry.

CCV was performed on optical fiber A1. This fiber was chosen as it was situated parallel to the bulk sodium flow in the mixing tube. The optical fiber gauge located 3.9 mm downstream from the fiber cross point was used as a reference gauge for which subsequent gauges downstream were cross correlated with respect to reference as described in the “Methods” section. This reference position was chosen empirically as it was the site of maximum normalized temperature range. Equation (7) was used to find the gauge with the highest correlation with respect to reference at the fifth nonzero lag value. This fifth nonzero lag value corresponds to five times the inverse acquisition frequency of the system (5 × 1/23.8 = 0.21 s). Using this fifth lag value and the gauge number with highest cross correlation to reference, the bulk sodium velocity may be found via Eq. (8). The use of the fifth nonzero lag value to calculate CCV was found empirically to give good results over the entire range of flow rates tested here (0.25–5.76 L/min). This entire process was written into a computer script using Mathworks' matlab programming language. Using this program, the user may input the optical fiber temperature file and location of a reference gauge, and the program will output the predicted flow rate.

Figure 15 shows the CCV-calculated flow rate versus the electromagnetic flow meter reading. Recall the flow parameters for tests 16–37 which can be found in Table 2, and each CCV reading had a temperature acquisition period of 60 s. A linear one-to-one fit for CCV versus electromagnetic flowmeter was plotted, and a high coefficient of determination of 0.977 was found. No noticeable difference in accuracy of CCV was seen between a sodium stream temperature differential of 65 °C and 50 °C.

At flow rates <1.3 L/min, the Reynolds number of the mixing tube was <4000 yielding laminar to transitional turbulent flow. As can be seen in Fig. 15, CCV still predicted the flow rate of the sodium well. Thus CCV may be applied to temperature oscillations transported by turbulent eddies and by bulk fluid advection in laminar flow.

## Discussion

### Thermal Striping Characterization at Junction.

This paper demonstrated, for the first time, a novel capillary encapsulated optical fiber temperature sensor locating and quantifying thermal striping. The industrial deployment of these high temporal/spatial resolution and relatively un-obtrusive sensors into sodium-cooled reactor pipe-to-pipe and pipe-to-pool interfaces allows characterization of the magnitude and frequency of thermal striping in a particular component. This will ultimately increase safety and reduce cost as efficiency of applying appropriate engineering safety factors in precise areas of high thermal striping is increased.

To avoid thermal stress failure of an SFR component, one must either avoid system parameters which induce thermal striping or implement mechanical safeguards to avoid fatigue. This paper demonstrated that the flow rate of two streams meeting at different temperatures played a significant role in determining the location of temperature oscillation. It was shown that the momentum ratio derived in this paper could be used to predict the general location of thermal striping-induced temperature oscillations at a junction of two perpendicular flows. This can be used to determine whether or not preventative measures, either operational or mechanical, need to be implemented to prevent thermal stress-induced failure.

### Cross Correlation Velocimetry at Junction.

It was shown for the first time that cross correlation velocimetry may be performed on optical fiber temperature data. Nonisothermal sodium meeting at a junction was ideal for CCV given that there is a temperature differential which produces an oscillating temperature field close to the sensor. Given an optical fiber sensor has already been installed to acquire temperature at a junction, this could prove an efficient method to determine flow rate at the site of two converging flows.

## Conclusion

This paper utilized a novel technique to deploy optical fiber temperature sensors in liquid sodium in order to analyze thermal striping at temperatures up to 637 °C. A method for analyzing the optical fiber data in two dimensions and characterizing the flow based on flow momenta and high temperature oscillation regions was presented. The effect of sodium junction temperature differential and Re on striping was quantified. The frequency spectrum of thermal striping behavior was successfully harvested from the fibers, which matched the previously published literature which used thermocouples. This proves fiber frequency spectra from fibers can determine the effectiveness of the thermal striping on inducing thermal fatigue in nearby structures. Finally, the optical fiber temperature data were cross correlated to obtain the accurate bulk flow rate of sodium in a tube as compared to calibrated electromagnetic flow meters.

The results from this work can be used to optimize the geometry and flow specification of sodium reactor piping to avoid component failure. The deployment method of the optical fiber has a wide range of engineering applications where system conditions would otherwise destroy the fragile fiber, providing the ability to monitor the thermal hydraulics of an industrial system in real-time.

## Funding Data

• Nuclear Energy University Programs (13-4955 and 16-10268)

## Nomenclature

• B =

magnetic field

•
• C =

cross correlation value

•
• CCV =

cross correlation velocimetry

•
• DH =

hydraulic diameter

•
• EMFM =

electromagnetic flowmeter

•
• K =

electromagnetic flowmeter constant

•
• L =

hydraulic entry length

•
• M =

momentum ratio

•
• P =

measurement time period

•
• PSD =

power spectral density

•
• Q =

volumetric flow rate

•
• Re =

Reynolds number

•
• S =

backscatter frequency shift

•
• T =

temperature

•
• V =

velocity

•
• Vm =

measured flowmeter voltage

•
• X =

spatial position of fiber gauge

•
• ΔT =

inlet sodium temperature difference

•
• θrange =

normalized temperature range

•
• θdiff =

normalized temperature differential

•
• ρ =

density

•
• τ =

lag

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