Wire-mesh Sensor Research Articles

Characterization and visualization of gas–liquid two-phase flow based on wire-mesh sensor

Gas–liquid two-phase flow is prevalent in both industrial production and the natural environment, making the exploration of its flow behavior critically important. In this study, we design a wire-mesh sensor and measurement system to conduct dynamic experiments on vertical upward gas–liquid two-phase flow, obtaining multi-channel data under various conditions. We develop an integrated limited penetrable visibility graph network (ILPVGNet) to quantitatively assess the dynamic transition from slug flow to bubble flow using network metrics. The results demonstrate that this approach effectively integrates multi-channel measurements, revealing the evolution dynamics and internal coupling mechanisms of gas–liquid two-phase flow. To better observe fine flow structures and details, we perform visualization and super-resolution analysis on the multi-channel data, significantly enhancing image clarity and restoring detailed features, thereby improving our ability to intuitively analyze complex gas–liquid flow behaviors.

Improvement of a wire-mesh sensor based on the bubble-wire collision kinematics

While the wire-mesh sensor (WMS) has been widely used to measure the gas-phase distribution in gas–liquid two-phase flows with visually inaccessible conditions, there are still some issues to be improved such as the dependency on the bubble size and bubble-wire interaction pattern. In our previous work [Lee et al., Int. J. Multiphas. Flow, 139, 103,620 (2021)], we reported the development and validation of a set of two-layer WMS, which can simultaneously measure the velocity and size of O(10−2–100) mm bubbles. In this study, considering the above-mentioned issues, we improve the measurement accuracy of the WMS, in particular, for relatively small (less than 2 mm) bubbles that tend to have asymmetric interactions with wires. To achieve this, we devised a new parameter to address the effect of non-uniform distance (proximity) to the nodes that are affected by the bubbles to be measured. Depending on the bubble-wire interaction (i.e., bubble size), we found that the characteristic time and length scales of the bubble vary, which are correlated with the proximity of bubbles to nodes with high electrical sensitivity. By implementing this into the algorithm, compared to the previous setup, the accuracy of measuring the averaged void fraction and velocity of bubbles increased by approximately 10 % and 20 %, respectively. We believe that the present approach will be quite useful in enhancing the measurement accuracy of other types (dual-set, for example) of wire-mesh sensors.

Study on flow regime characteristics in 3×3 rod bundle channels based on wire mesh sensor

Abstract The characteristics and evolution of two-phase flow are of critical importance to the safety of pressurized water reactors. Based on the double-layer wire mesh sensors in this paper, the air-water two-phase flow experiment of the 3×3 rod bundle channels is carried out at room temperature and pressure. The results show that the critical bubble diameter range for the reversal of lateral lift direction is 4 to 5.8 mm. In addition, the time-averaged void fraction for bubbly flow reveals a wall peak distribution at lower superficial gas velocities and shifts to a core peak as these velocities increase. For cap flow, the cross-distribution of cap bubbles within adjacent subchannels triggers large-scale mixing of the liquid phase between adjacent subchannels. For slug flow, large-sized bubbles develop along the axis and cross subchannel gaps to aggregate into slug-shaped bubbles, with a more pronounced distribution of the central peak of void fraction. The drift-flux models are evaluated against the experimental data, and the Ozaki model demonstrates higher precision in estimating void fraction, exhibiting a deviation of 9.8% on average.

Intelligent predictions for flow pattern and phase fraction of a horizontal gas-liquid flow

In-situ measurement of phase fraction of a gas-liquid flow is closely related to the production efficiency in natural gas extraction. However, the measurement accuracy can be affected by the co-existed multiple flow patterns. This study proposes an intelligent strategy that identifies the flow pattern followed by a phase fraction prediction. For flow pattern recognition, we establish a bidirectional long short-term memory (BI-LSTM) network whose inputs are time-series phases of a Radio Frequency Sensor (RFS). The accuracy is 92.4 % over four classical flow patterns. The time-series phases of RFS are agreed well with the axial imaging from a Wire-Mesh Sensor (WMS). Two predictive models are developed for gas fraction: dimensionless analysis model (DAM) based on RFS and gas Froude number, and neural network model (NNM) with the phases of RFS and the recognized flow pattern. The mean absolute errors (MAE) are 3.2 % and 1.5 % for DAM and NNM, respectively. It is concluded that a NNM, incorporated with RFS and flow pattern by BI-LSTM, can intelligently predict gas fraction with high-accuracy. As the present strategy decouples the pattern recognition and gas fraction prediction into two networks, the complexity of a NNM is reduced which benefits the in-situ measurement practice.

Study on the hydrodynamics of structured packing: Liquid holdup and pressure drop of a novel 3D printed packing

SpiroPak is a patented innovative structured packing and can be used in process industries for chemical separation purposes. The core of its design is to ensure an uninterrupted flow path for both liquids and gases, leading to remarkably low-pressure drops but with substantial surface areas for efficient mass transfer. Experimental studies using the wire-mesh sensor technique have showcased SpiroPak's ability to eliminate the channelling effect that is observed in commercial packings. Furthermore, its wide-ranging liquid holdup capability encompasses the functionalities of conventional packings, offering clients the feasibility of diverse applications. In this study, the pressure-drop correlations for SpiroPak in this work are based on Stichlmair empirical formulas, with the coefficients of C1, C2 and C3 tuned through the curve fitting method. The primary objective of this study was to establish packing selection criteria based on the key hydraulic performance metrics, such as pressure drop and liquid holdup. By swiftly identifying suitable packing solutions, the method accelerates the pre-selection process, significantly reducing computational complexity and time expenditures at the early stages of research and development.

Numerical analysis and structural optimization of a DLC coated capacitance wire-mesh sensor for measuring liquid metal-gas two-phase distribution

The detection of liquid metal-gas two-phase distribution in lead-cooled fast reactor once steam generator tube rupture occurs is vital to the security assessment of the reactor core. In this paper, considering the high temperature, corrosiveness and high conductivity of the liquid metal, a diamond-like carbon coated capacitance wire-mesh sensor is proposed to detect the two-phase distribution in liquid metal. Based on the software COMSOL, a numerical model is firstly established that is quantificationally verified by experiment to study and optimize the performance of the coated WMS. The measurement accuracy of the sensor is investigated by ranging the AC excitation frequency and structure parameters of the system. The results show that the liquid metal has blocking effect on the small bubbles and the sensor has great measurement accuracy when the transverse and vertical interval are 2 mm while the exitation frequecy, coat thickness and electrode diameter show little effect. This research could guide the measurement in liquid metal-gas two-phase flow.

Experimental study of swirling flow pattern at the swirler outlet using a Wire-Mesh sensor

Entrained droplets and flow pattern change adversely affects separation performance of swirl-vane separators. Investigating gas–liquid distribution at swirler outlet, an experiment was conducted using a wire-mesh sensor positioned. Air and liquid superficial velocities ranged from 8.3 to 25.6 m/s and 0.1 to 1.4 m/s, respectively, covering swirling annular and swirling churn flow at swirler outlet. In swirling annular flow, liquid phase primarily exists as a stable thin film which facilitates efficient separation. In swirling churn flow, wall liquid film has unstable large amplitude disturbance waves. Disrupting liquid film leads to entrained droplets forming in gas center, increasing separation distance and hindering gas–liquid separation. The transition boundary from swirling churn to swirling annular is crucial. Increasing swirler angle shifts the transition boundary towards higher gas velocity at the same liquid velocity. A theoretical model based on interfacial shear stress and gas core blockage predicts the flow pattern transition at swirler outlet.

An experimental investigation on the fluid–structure coupling in horizontal pipes conveying two-phase intermittent flow

Two-phase flow is typically found in several industrial applications, such as in the production and transportation of oil and gas in the petrochemical industry, in the catalytic cracking and microreactors in the chemical industry, and in nuclear reactor cooling pumps. Measurement of two-phase flow features is usually necessary and has been done in several ways, including pressure probes, resistive sensors, gamma-ray, wire-mesh sensor and many others. However, these are either intrusive or invasive techniques, which might be of challenging application in industrial environments, or rely on a hazardous radioactive source. Vibration-based measurement of two-phase flow in pipes stands out as a non-invasive/non-intrusive approach and, consequently, multiphase-flow induced vibration in pipes has receiving increasing attention in recent years. In this work, the dynamic behaviour of a horizontal tube conveying an intermittent two-phase gas-liquid flow is investigated based on indirect approaches. The phenomenon of fluid–structure coupling is investigated using acceleration and pressure measurement. Moreover, the bubble size distribution is estimated from high-speed camera images and a deep learning model for image segmentation, along with its spectral content and time modulation. Focus is given at frequency bands around the cut-on frequencies of the circumferential wave modes of the pipe. An approach based on the estimation of frequency response function of the pressure and vibration at the liquid slug and elongated bubble is proposed, such that the coherence function can be used as quantitative measure of the coupling. Two experimental conditions with intermittent flow are investigated as representative cases. It is shown that there is a great vibration amplification at the cut-on frequencies of circumferential wave modes in pipes due to the corresponding structural wave and pressure coupling. Consequently, the frequency of passage of bubble can be estimated from the demodulation of vibration response filtered at the cut-on modes. The experimental results pave the way for innovative vibration-based measurement approaches.

Spatio-temporal void fraction visualization in air-water two-phase flow regime transitions by combination of convolutional neural network and long short-term memory implemented into multiple current-voltage (MCV-CNN_LSTM)

Spatio-temporal void fraction in air-water two-phase flow regime transitions has been visualized by combination of convolutional neural network and long short-term memory implemented into multiple -current-voltage (MCV-CNN_LSTM). The MCV-ML is composed of two components, which are MCV-CNN_LSTM training and evaluation. In the first component, four steps are carried out as 1) true void fraction α measurement was conducted by wire-mesh sensor (WMS) as objective variables, 2) simulated MCV voltage U calculation by simulation of MCV measurement for explanatory variable, 3) CNN_LSTM training instance generation, and 4) CNN_LSTM model training and testing. In the second component, two additional steps are experimentally conducted which are 5) actual MCV voltage V measurement by MCV for input of trained ML, and 6) spatio-temporal void fraction α prediction. For the dataset generation, the experiment was conducted on air-water two phase flow regime transitions in vertical pipe with an inner diameter of 25 mm and a length of 350 mm from the elbow. The superficial velocity of liquid and gas phase are varied to present the flow regime transition of bubbly to slug flow. As a result, the estimated spatio-temporal void fraction αˆ by MCV-CNN_LSTM enables the visualization of detailed gas distribution in vertical upward two-phase flow. The spatial averaged instantaneous void fraction measured by WMS and estimated by MCV-CNN_LSTM show qualitative agreement in normalized cross correlation (INCC) of 0.364 on its temporal variation.

Experimental investigation on steam-water flow patterns in a vertical narrow rectangular channel utilizing conductance scanning measurement

In order to tackle the challenges in two-phase flow measurement in narrow rectangular channels, especially under pressurized conditions, a novel conductance scanning sensor, consisting of two ceramic-substrate printed circuit (CSPC) boards, has been developed based on the concept of wire mesh sensor. A leak-tight structure was also fabricated to avoid leakage at the penetrations of lead wires through the sensor housing. Measurements have been carried out in a narrow rectangular channel, with inner the cross-sectional dimension 70 mm × 2 mm, under pressure between 0.20 and 0.90 MPa. In the experiment, bubbly, churn and annular flows have been observed, except for slug flow. Flow pattern maps have been proposed for the steam-water two-phase flow. Comparing with those in the literature, it can be found that as the channel width/gap increases, the flow pattern transition boundaries shift towards the higher vapor superficial velocity direction. Additionally, the transition criteria for narrow rectangular channels were investigated by separately evaluating the critical void fraction and the superficial velocity calculation correlations. Results show that the critical void fraction of bubbly to churn flow and churn to annular flow can be approximately estimated as 0.2 and 0.75, respectively. However, the existing correlations for superficial velocity calculation are not suitable for the steam-water flows with a void fraction less than 0.5.

Multidimensional measurement of air–water two-phase flow in particulate bed using refractive-index-matching method and wire-mesh sensor

Multidimensional measurement of air–water two-phase flow in particulate bed using refractive-index-matching method and wire-mesh sensor

Spatial distribution of void fraction in the liquid slug in vertical Gas-Liquid slug flow

Vertical slug flow is characterized by the intermittent passage of two structures, the Taylor bubble and the liquid slug. The Taylor bubble is an elongated gas bubble with a bullet shape that flows upward and fills most of the radial cross-section, leaving room for an annular downward flow of a liquid film. The liquid slug is composed of the liquid phase carrying small, scattered bubbles and flowing upwards. The liquid slug presents three main regions: the wake, the development and the fully developed one. The liquid slug has a high concentration of dispersed bubbles in the wake region because of the entrainment mechanism. The detachment point (Dt) is a stagnation point with almost no dispersed bubbles around it, occurring close to the wall in the wake region end. Experimental data for the gas fraction in three different pipe diameters (26, 40.8 and 50 mm) were gathered in the 14-meter-high vertical flow experimental facility of the NUEM/UTFPR MULTILAB. The gas fraction along the liquid slug was evaluated by using a capacitive wire-mesh sensor (WMS) for quantitative results and a high-speed camera was used to analyze qualitative results. A new correlation to predict the average volumetric gas fraction along the unit cell is proposed. Radial and axial gas fraction distribution were analyzed and the detachment point was identified. The Reynolds and Froude number influence on the Dt point was evaluated and a new correlation to predict the Dt location (LDt) is proposed.

Study of gas-liquid two-phase flow redistribution characteristics in the rod bundle channel using wire-mesh sensor

In subchannel analysis, the gas and liquid flow distribution phenomenon plays an important role in understanding rod bundle channels’ two-phase turbulent mixing mechanism. This paper obtained gas-liquid flow distribution data inside a vertical coupled subchannel rod bundle channel by utilizing a double-set wire-mesh sensor (WMS). To achieve evolutions of two-phase flow distributions, one subchannel was injected with gas and water called the donor channel, and the other injected with water is called the receptor channel. Four axial locations (Z/Dh = 28.95, 57.90, 86.86, and 115.81) were measured for each flow condition to obtain the evolution of the flow distribution. 36 flow conditions were acquired with 〈jg〉 from 0.073 to 1.02 m·s−1 and 〈jl〉 from 0.93 to 1.86 m·s−1 at Z/Dh = 115.81, including bubbly, cap-bubbly, and slug flow. The gas flow distributions were obtained by the cross-correlation calculation of the phase distribution data measured by a double-set WMS. The gas-phase flow rate relative errors acquired by WMS and rotameters are within ± 10%. To obtain the liquid flow distribution, the inter-subchannel equal-slip ratio assumption was introduced, which is according to the truth that two-phase flow characteristics between the adjacent subchannel are similar for most cases in this study. Further, obtained two-phase flow distribution data were verified and evaluated by Han et al.’s drift-flux model, and the relative errors for most cases are less than ± 20%. Results show that, under bubbly flow, the two-phase flow redistribution is weak. 90% of the gas was restricted in the donor channel, and the liquid flow was approximately distributed in both channels. With the increment of void fraction, two-phase flow redistributions are more severe. The liquid-phase recirculation flow was found in the receptor channel, under cap-bubbly and slug flow, which results in a higher gas-liquid flow in the donor channel than in the receptor channel. The rules of two-phase flow distributions indicate that the liquid-phase flow redistribution is more moderate than the gas phase. The drastic change in the gas-phase flow redistribution starts with the cap-bubbly flow. In addition, the current two-phase flow data indicates that the two-phase flow redistribution between the donor and the receptor channels does not follow the equal-volume principle postulated in the existing two-phase turbulent mixing model. Furthermore, current data also imply the relationship between void and mass flux distribution is not linear as assumed in the existing two-phase turbulent mixing model.

Validation of RANS-Based Turbulence Models Against High-Resolution Experiments and DNS for Buoyancy-Driven Flow with Stratified Fronts

To provide computational fluid dynamics (CFD)–grade experimental data for studying stratification, measurements on the High-Resolution Jet (HiRJet) facility at the University of Michigan have been conducted with density differences of 1.5 % and − 1.5 % , respectively. Fluid with a density different from the fluid initially present in the HiRJet tank was injected, and the propagation of the time-dependent density stratification was captured on a two-dimensional plane with the aid of the wire-mesh sensor technique for Reynolds numbers near 5000 and Richardson numbers near 0.29. Direct numerical simulations (DNSs) of the two cases have also been conducted to expand the multifidelity database. The novel experimental and DNS data were then used to assess the predictive capabilities of the Standard k − ε (SKE) model and the Reynolds Stress Transport (RST) model. In particular, the propagation speed and thickness of the stratification fronts were assessed by comparing the CFD results against the experimental and DNS data. It was found that the general trends of the stratified density fronts were well predicted by the CFD simulations; however, slight overprediction of the thickness of the stratification layer was found with the SKE model while the RST model gave a larger overprediction of the mixing. Examination of the turbulent statistics showed that the turbulent viscosity was largely overpredicted by the RST model compared to the SKE model.

Measurement of the water-vapor void fraction in a 4x4 unheated rod bundle

ABSTRACT In recent years, computational fluid dynamics (CFD) simulations have been used to evaluate the two-phase flow behavior inside fuel bundles for nuclear core design and accident management. Space – time distributions of the void fraction and interfacial velocity in bundle systems at high temperatures and pressures are important for validating CFD codes describing two-phase flow. However, such space – time distributions of the void fraction and interfacial velocity in bundle systems are difficult to obtain under high-temperature and high-pressure conditions. Thus far, we have developed an experimental apparatus with a 4 × 4 unheated rod bundle by adapting a through-rod wire mesh sensor to measure the void fraction and interfacial velocity distributions under high pressures and high temperatures. In this study, we measured distributions of the void fraction and interfacial velocity in a water–vapor system under high-pressure conditions up to 2.6 MPa and high temperatures, using the developed apparatus. We demonstrate that the experimental apparatus yields reasonable results for two-phase flow inside a fuel bundle. However, the analysis method used in this study could not properly estimate the interfacial velocity under some experimental conditions, highlighting the need to improve the method for analysis of the interfacial velocity.

Experimental investigation on two-phase cross-flow-induced vibration of a cylinder in a confined channel

Interactions between cylindrical structures and two-phase flows is a major concern for industrial applications, especially where cross-flows may cause damages, in heat exchangers for example. In order to understand the phenomenon of vibrations induced by two-phase flows, many experiments were conducted with reduced-scale models. In single-phase flow, the phenomenon has been characterized but is still a challenge numerically. In terms of two-phase flow, the effect of the two-phase flow regime adds more difficulties to explain the resulting phenomena in terms of vibrations. Experiments have been conducted focusing on vibrations mainly and flow pattern. To address this complex topic, the authors propose to study the impact of flow-pattern on vibration on a simpler geometry, presenting the advantages to be able to catch local scale phenomena and to be an interesting test case for CFD scale validation. The present paper focuses on a geometry which has been extensively studied in single-phase flow : flow-induced vibration of a single cylinder. An experiment with an upward air/water flow for void fractions, ranging from 10% to 80%, with two-phase flow characterization based on a wire-mesh sensor and a bi-optical sensor has been carried out in addition to vibration measurements. In terms of two-phase flow, the main behaviors for low void fractions, described in literature, are first reproduced and then extended to higher void fractions to be studied. In terms of vibration, the role of void fraction and flow-pattern is highlighted.

Measurement of film fluctuations and aerated characteristics during gas-liquid slug-churn flow transition by wire-mesh sensor

Vertical upward gas-liquid slug flows are frequently encountered in chemical processes and petroleum industries. The measurement of the film fluctuations and the aerated characteristics is of great significance for uncovering the mechanism of slug-churn flow pattern transitions. In this study, a conductance wire-mesh sensor (WMS) measurement system is designed based on a Field Programmable Gate Array (FPGA) to visualize the structures of vertical gas-liquid flows. Liquid film flooding is a significant factor prompting the transition from slug to churn flow. Based on the WMS data, the 3D film structures are derived to indicate film instability during the flow pattern transition. Three types of film fluctuations in stable slug flow, unstable slug flow, and churn flow are presented. Liquid slug aeration is another important factor contributing to the slug-churn flow transition. The spatial distribution and the diameters of the gas bubbles in the liquid slug are detected by the WMS. The coalescence behavior of the bubbles is uncovered. Finally, mechanistic models based on the film flooding and slug aeration are constructed to predict the boundary of the flow pattern transition. The performance of the film flooding model and slug aeration model in predicting the onset of churn flow is evaluated.

Unified two-component interfacial area concentration model for narrow channel two-phase flow

The conventional interfacial area concentration (IAC) models do not distinguish narrow and wide side interfaces when applied in narrow channels, which hinders accurate modeling of interfacial transfer mechanisms at different interfaces. In order to overcome such deficiency, void fraction data obtained in narrow-channel air-water flow with the flexible printed circuit (FPC) wire-mesh sensor (WMS) is analyzed to establish a two-component IAC model which consists of two essential parameters, i.e. the projected interfacial area concentration (PIAC) and projected interfacial length concentration (PILC). Based on the refined and sharpened void fraction distribution, the postprocessing algorithm is developed to obtain the PIAC and PILC for different flow patterns. Analysis of experimental data indicates that the PIAC is approximately proportional to void fraction, while variation of the PILC with void fraction is complicated. The ratio of PILC to PIAC, which characterizes topology of interfaces, shows distinct value in bubbly flow compared with other flow patterns. Such difference is attributed to the existence of large bubbles, typically with spanwise length over 70% of the channel width, in flow patterns other than bubbly flow. Hence, bubbles are separated into two groups with the critical ratio of bubble width to channel width in the model derivation. The semi-empirical PIAC and PILC models are derived for each bubble group. Based on volume fraction of two bubble groups, the unified PIAC and PILC models are obtained to realize the accurate prediction in all the flow patterns. The unified two-component IAC model and other IAC models are evaluated with the present IAC experimental data and the experimental data of Shen et al. (2012). The evaluation shows the superiority of the unified two-component IAC model and that the proposed unified two-component model can be applied in the narrow-channel air-water two-phase flow patterns with α¯≤0.9.

Periodic large-scale structural characteristics of two-phase flow in tight lattice bundles

This paper investigated the two-phase flow characteristics in a double sub-channel tight lattice (P/D = 1.06). Compared to the prototype, the test channel was magnified by 2.7 times. A self-developed 16 × 32 wire-mesh sensor was utilized to measure the phase distribution at two fully developed positions of the test channel (Z/Dh = 86.86, 115.8). The flow conditions are 0.036 m/s < jg < 1.04 m/s and 0.93 m/s < jl <1.86 m/s at Z/Dh = 115.8, including the bubbly flow (B), the cap-bubbly flow (CB), and the slug flow (S). Combined with the pseudo-side view of the flow pattern and the power spectrum, the coherent structure of the gas phase under the bubbly flow and the cap-bubbly flow was confirmed. For the bubbly flow, the coherent structure is in the form of bubble clusters consisting of discrete bubbles. These bubble clusters are staggered on both sides of the gap but do not traverse across the gap, which is speculated to be caused by the large-scale vortex of the liquid flow field. For the cap-bubbly flow, the coherent structure is in the form of cap-shaped bubbles. In this study, the cap-shaped bubbles are confined in the center of the subchannels and staggered in adjacent subchannels, which is attributed to the compact arrangement of rod bundles and the inter-subchannel liquid cross-flow caused by the cap-shaped bubbles. The characteristic parameters, including the pulsation frequency f, convection velocity v, wavelength λ, and amplitude A were defined to characterize the coherent structure. Data analysis results show that the coherent structure frequency under the bubbly flow increases with the increase of the liquid-phase velocity and the coherent structure frequency under the cap-bubbly flow increases with the increase of the gas-phase velocity. In addition, the coherent structure is suppressed under three flow conditions, including the bubbly flow with low liquid velocity (jl < 1.3 m/s), the B-CB transition, and the slug flow.

Experimental analysis and two-region mixing coefficients development for a wire-wrapped tight lattice bundle

Wire-wrapped tight lattice fuel assemblies are widely used in the design of advanced nuclear reactors for their advantages of higher power density and enhanced heat transfer capability. The flow mixing characteristics in this type of assembly are complicated due to the presence of the wire. In this study, a flow mixing experiment has been carried out in a 19-pin wire-wrapped tight lattice bundle with Reynolds numbers ranging from 5000 to 25,000. The mixing and crossflow effects were studied by injecting a tracer substance affecting the electrical conductivity of the fluid and measuring tracer concentration distributions using a wire-mesh sensor system. A set of flow mixing data has been obtained, and the experimental results indicate the mixing characteristics of a wire-wrapped bundle are insensitive to the Reynolds number. Combined with the measured data and the modified CTF code, the two-region mixing coefficients were determined by the least-square method and compared with the mixing coefficients in the literature. This work is an important supplement to the study of the mixing characteristics of wire-wrapped tight lattice bundles, and the data also can be used to validate the computational fluid dynamics codes and develop high-precision mixing models for subchannel analysis.