A New Development of Cross-Correlation-Based Flow Estimation Validated and Optimized by CFD Simulation  
[PERSON]  
1 Department of Nuclear Engineering, University of Tennessee-Knoxville, Knoxville, TN 37996, USA; [EMAIL_ADDRESS] (J.B.C.) [PERSON]  
2 Department of Mechanical and Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA; [EMAIL_ADDRESS] 2 jhines2@utk. gasses. It is expected that reactor components interfacing with these coolants have to be operated under such harsh conditions for a long time without repair or replacement. For example, when the main coolant flow is a liquid metal such as sodium or lead-bismuth, which is high density with other chemical erosive issues [2], traditional flow meters cannot be operated safely for continuous, long periods of time. To allow for flexible measurement installation and operation under harsh environments, cross-correlation function (CCF) flow estimation is introduced as an inferential flow measurement methodology that can be applied in operating and advanced reactors to resolve issues that prevent direct flow measurement [3]. Previously, [PERSON] et al. [3] studied CCF flow estimation in a pool-type reactor, establishing the basis for it. Due to the fluid dynamic scaling, the measurement is not restricted to water; it can be applied to liquid metals [2], gases [4], and even non-Newtonian fluids such as surrogate fluids or blood [5]. It can also be extended to two-phase flows, including liquid-gas flow (oil mixed with nitrogen gas) [6], solid-gas swirl flow [7], or liquid-solid flow (water mixed with solid ceramic nodules) [8]. The CCF method for flow measurement was first studied by [PERSON] et al. in 1966 [9], and CCF flow estimation was applied in nuclear fields in the 1980s [10; 11]. CCF flow estimation infers the flow velocity by estimating the delay time between two adjacent sensors using the cross-correlation function and using knowledge of the relative sensor placement. The two adjacent sensors are installed in series in the direction of bulk flow and are not restricted by the pipeline structure. This means that the two sensors can be applied in pool-type or integral reactors. Further, the only restriction for the selection of the two sensors is a preference for a common sensor type to enable better cross-correlation estimation. This allows for the sensor selection to focus on sensors that are more reliable under the harsh operating conditions experienced in advanced reactors. Several sensor signals can be used as the source signals for CCF flow estimation, including temperature, neutron noise [12], voltage [13], or capacitance [6]. The temperature signal is widely selected for CCF flow estimation because the profile of the temperature fluctuation can reflect the profile of the flow rate [14]. Moreover, temperature sensors, such as thermocouples, which are robust and reliable in most flow estimation situations, can be operated under the expected harsh conditions and are typically required process instrumentation in reactor designs. Therefore, temperature sensors are selected for this study with a focus on thermocouple measurements. For these reasons, CCF flow estimation is being proposed and studied for potential implementation in advanced reactor concepts. Although CCF flow estimation is not restricted by geometry and pipes and can be operated under harsh conditions, the accuracy of this approach is impacted by signal resolution, the ratio of the correlated process noise to the uncorrelated measurement noise, and the sensor response time [15; 16]. Based on NRC efforts [17] to address the response time issue, prior work has applied the same brand and type of temperature sensors to alleviate potential response time issues in the experimental flow loop. This is due to the response time being directly impacted by dissimilar temperature sensor selection. A thermocouple (TC) is selected due to its small response time. The bare-wire TC generally has a smaller response time compared with Resistance Temperature Detectors (RTDs) [18].