Fluid Physics Research Articles

The Validity Analysis of Integration Between Science and Religion in Static Fluid Materials

Learning science and religion is a combination of knowledge or science with relevant verses of the Al-Qur’an. Education is not only a means of gaining general knowledge through subjects, but also covers aspects of life as a whole, including religious morals. Considering that natural phenomena are so vast, it would be a shame if students are not given enough integration between science and religion, one of which is in physics lessons. The researcher took the initiative to carry out the application of science and religion further in the hope of providing a solution, namely by teaching physics, fluid material, integrated with verses from the Al-Al-Qur’an. This study employs mixed or combined research (mixed methods) with the type of Explanatory Design. Specifically, data collection and analysis of quantitative data are done in the first stage, and then qualitative data are collected and analyzed in the second stage. The integration of science and religion for the fluid material used produces an average value that is categorized as very good. Apart from that, the material from the validation results uses 3 foundations, namely the theological basis (hadârat an-nas), philosophical basis (hadârat al-falsafah), and scientific basis (hadârat al-'ilm). So that the verses of the Al-Qur’an become the main source of the theological basis for the idea of integration by including religious elements, then the scientific or scientific basis which includes the basics of static fluid physics, and the philosophical basis which includes the field of philosophy to connect these two things.

On the continuous nature of phase change in near-critical carbon dioxide

Unique boiling behavior at near-critical conditions can leverage the large heat transfer coefficients associated with flow boiling while mitigating some of the disadvantages encountered in two-phase flows, presenting opportunities for enhancing the stability and effectiveness of cooling systems. Contemporary understanding treats subcritical boiling and supercritical heat transfer as two distinct regimes, separated by the critical point. Recent studies investigating microchannel flow boiling near the critical point challenge this notion, suggesting a significant alteration in subcritical phase change heat transfer mechanisms, predominantly driven by variations in thermophysical properties near the critical point. However, a generalized understanding of heat transfer behavior and the phase change physics near the critical point is lacking. The current work presents a new perspective to elucidate underlying fluid phenomena associated with near-critical (0.85<PR<1.02) microscale (Dh=500μm) phase change over parameterized experimental conditions (G=100−1000kgm−2s−1; q″=2−100Wcm−2). Through high-speed (8000fps) side-view microscopic imaging and simultaneous heat transfer measurements, unique flow behavior was discovered at PR>0.95, including supercritical-like phenomena and evidence of homogeneous nucleation which form the physical basis for altered heat transfer behavior. The visualized flow physics and heat transfer behavior suggest a continuous transition from subcritical phase change to supercritical mechanisms near the critical point. As homogeneous nucleation becomes the dominant phase change mechanism, the near-wall heat transfer condition transitions from nucleate boiling to single-phase vapor convection. However, due to significant thermophysical property variations near the critical point, this single-phase convection condition exhibits fluid physics and heat transfer behavior virtually indistinguishable from supercritical conditions. These insights significantly disrupt the conventional understanding of a sharp transition in fluid behavior at the critical point. The gradual change in flow boiling mechanisms near the critical point presents opportunities for application-specific tuning of heat transfer performance through pressure variation alone.

Review[sbnd]Recent developments on applying acoustic waves for efficiency improvements of different thermofluids systems

This review classified recent works using proper acoustic waves to develop more efficient thermofluids systems for different industrial equipment such as swirl combustor, jet in crossflow, gas flare, different types of heat exchangers, cooling mechanism, aircraft wings, and turbine blades. For the swirl combustor, the range of proper excitation Strouhal number and jet pulsation intensity depends on the type of fuel, geometry of burner, swirl number, and central and annular Reynolds numbers. The combined effects of early jet break up, and centrifugal force induced by proper acoustic waves can lead to higher jet spread rate that can induce higher levels of mixing of the fuel and air in swirl combustor, improving combustion efficiency. For the transverse jet, the range of proper excitation Strouhal number and jet pulsation intensity depends on the type of fuel, geometry, and angle and direction of the burner, and jet and cross flow Reynolds numbers. Proper acoustic excitation can force the transverse jet flow to synchronized shear layer vortices. This phenomenon can cause the new vortices to appear in the upwind shear layer region of the deflected jet; then the spread, penetration, entrainment, and dispersion of the jet significantly increases, improving combustion efficiency. For the aircraft wing, vertical acoustic excitation significantly improves the lift force when the sound frequency is equal to the period of flow fluctuation in the separated boundary layer. For the heat exchanger, the ultrasonic transducer can be installed on the walls of a heat exchanger with direct contact to the fluid, improving the heat transfer coefficient. The physics of fluids behind the efficiency improvements of all mentioned cases were also clarified. Moreover, the acoustically excited impinging jets with higher cooling efficiency applied in different areas are discussed. Proper acoustic forcing can decrease the rate of unstable frequencies of disturbances related to impinging jets over a short distance. This phenomenon can significantly enhance heat transfer and improve cooling efficiency. This review paper provides insight into how acoustic waves could improve the efficiency of thermofluids systems in a variety of applications. Acoustic excitation could have the potential capability to improve the efficiency of new applications such as wind, gas or steam turbines, some types of industrial chemical mixers with parallel plane jets, aircraft wings or those of unmanned aerial vehicles, more efficient combustion chambers, and less polluting gas flares. However, the feasibility of this concept requires further investigation by the community in the future.

Applications of Partial Differential Equations in Fluid Physics

Partial differential equations, or PDEs, assume a critical part in grasping and outlining different fluid physics peculiarities. They have an expansive scope of utilizations, from expecting weather patterns to consolidating ocean streams, fire cycles, and fluid streams into system plan. These equations oversee the way of behaving of fluid amounts like as speed, stress, temperature, and consistency. They portray complex collaborations like changes in precipitation, scattering, and fluid-solid associations. Partial differential equations are utilized to apply the developing methodology. The arrangement is equivalent to for the recently concentrated on examples of typical differential equations. There are two kinds of partial differential equations: nonlinear and straight. Some certifiable equations, for example, those in electrostatics, heat conduction, transmission lines, quantum mechanics, and wave hypothesis, feature the significance of partial differential equations (PDEs). To make sense of something other than one, two, or three pieces of the partial differential equations, we will check out at the speculative piece of those applications that utilization PDEs in this examination. In all parts of science and development, partial differential equations, or PDEs, are generally utilized. Partial differential equations handle most of genuine frameworks. A condition communicating a connection between a piece of no less than two free factors and the partial helpers of this cutoff concerning these free factors is known as a partial differential condition, or PDE.

Flight test results for microgravity active vibration isolation system on-board Chinese Space Station

The Fluid Physics Research Rack (FPR) is a research platform employed on-board the Chinese Space Station for conducting microgravity fluid physics experiments. The research platform includes the Microgravity Active Vibration Isolation System (MAVIS) for isolating the FPR from disturbances arising from the space station itself. The MAVIS is a structural platform consisting of a stator and floater that are monitored and controlled with non-contact electromagnetic actuators, high-precision accelerometers, and displacement transducers. The stator is fixed to the FPR, while the floater serves as a vibration isolation platform supporting payloads, and is connected with the stator only with umbilicals that mainly comprise power and data cables. The controller was designed with a correction for the umbilical stiffness to minimize the effect of the umbilicals on the vibration isolation performance of the MAVIS. In-orbit test results of the FPR demonstrate that the MAVIS was able to achieve a microgravity level of 1–30 μg0 (where g0 = 9.80665 m ∙ s−2) in the frequency range of 0.01–125 Hz under the microgravity mode, and disturbances with a frequency greater than 2 Hz are attenuated by more than 10-fold. Under the vibration excitation mode, the MAVIS generated a minimum vibration acceleration of 0.4091 μg0 at a frequency of 0.00995 Hz and a maximum acceleration of 6253 μg0 at a frequency of 9.999 Hz. Therefore, the MAVIS provides a highly stable environment for conducting microgravity experiments, and promotes the development of microgravity fluid physics.

Gust-induced flow perturbations on circular cylinder: Investigating the effects and characteristics

This paper delves into the fascinating realm of gust flow past a circular cylinder, unveiling the dynamic interactions and key features that influence the system's behavior. In this study, ANSYS Fluent is used to perform numerical simulations based on finite volume method. The aim is to investigate the temporal evolution of the aerodynamic forces at different Reynolds numbers (Re) at different gust frequencies. In this study, gusts are generated by harmonically changing the direction of the inlet velocity at different frequencies. Unlike uniform flow, vortices are shed simultaneously from the upper and lower surface of cylinder, sometimes with equal strengths and sometimes with varying strengths depending upon the gust frequency. Cl, Cd and Strouhal number values increase with gust frequency corresponding to any Reynolds number. However, the values remain less than no-gust case under similar flow situations. Fast Fourier transform analysis has been used to examine the energy spectrum and kinetic energy contours of vorticity and turbulence to gain further insight into fluid physics. The results of this study provide valuable insight into the physics of gust flow and circular cylinders.

Direct measurement of the inertial-convective subrange above ocean surface waves

The −5/3 power law over the inertial subrange of the turbulence kinetic energy spectrum is one of the most well-known concepts in fluid physics. Obukhov and Corrsin extended the original hypothesis to a passive tracer, leading to the concept of an inertial-convective subrange. These postulates have been empirically validated in the atmospheric turbulence over land but have not been comprehensively studied in the marine air flow. During a recent oceanic campaign, the platform FLIP was deployed with an array of sensors to measure the perturbation wind velocity, temperature, and water vapor. Using these data, a previous study found that Kolmogorov's hypothesized −5/3 was not universally valid over the ocean. Here, we continue that work to analyze the spectrum of temperature and water vapor to empirically evaluate the theoretical extension by Obukhov-Corrsin. For temperature, the observed spectra were too noisy for thorough analysis; our conjecture for the source of noise and its implications for near-surface observations of atmospheric turbulence are discussed. For water vapor, we found strong agreement with the previous analysis of the kinetic energy spectrum. These findings corroborate (1) the theoretical notion of the scalar energy dissipation subrange driven by the inertial motions in the marine boundary layer and (2) evidence for non-Kolmogorov turbulence in the high Reynolds flow immediately above ocean waves. Our analysis shows a strong relationship with distance from the wavy surface; using linear extrapolation, we find that divergence from −5/3 persists in the lowest 25 m of the atmosphere.

Spatial Distribution of Pressure Using Fluid Physics for the Vanadium Redox Flow Battery and Minimizing Fluid Crossover Between the Battery Electrodes

Our focus in this treatment is a relatively novel approach to minimizing the fluid transfer imbalance between the negative and positive electrodes of a vanadium redox flow battery (VRFB) through the membrane, and determination of the horizontal/lateral change in pressure across each electrode, as well as the vertical pressure distributions. Underpinnings of the fluid transfer are the Darcy continuum equation. Here we develop analytical equations from the field equations affecting the fluid flow in the VRFB, which are very useful for controlling settings in battery stacks consisting of several cells.

The Effect of Creative Problem-Solving Model to Enhance Scientific Creativity: Study in Static Fluid Physics Learning

The purpose of this study is to ascertain how applying the Creative Problem-Solving model in physics classes affects students' scientific creativity when studying static fluids and how applying the model can improve students' scientific creativity. This study employed a quasi-experimental method, with the population of focus being 11th-grade science students at SMAN 4 South Tangerang, totaling 200 students. The sample in this study involves 78 students selected through the purposive sampling technique and divided into two groups (experimental and control), each comprising 39 students. Both groups were assessed for their skills through pretests and post-tests. The instruments used in this research consisted of 5 structured essay questions referring to three indicators of scientific creativity dimensions developed by Hu and Adey. The result of this study shows that the data generated, based on the Mann-Whitney U test, indicates a significant difference between the post-test scores of the two groups, with a Sig. Value of 0.000, which is below 0.05. The N-gain results also showed a gain of 0.56 in the experimental group and 0.43 in the control group. In conclusion, the Creative Problem-Solving model influenced students' scientific creativity, and it effectively improved students' scientific creativity. The research implications suggest that teachers should implement this teaching method to improve students' scientific creativity skills, enabling them to actively and skillfully address various complex problems in everyday life.

Editorial: Multi-scale fluid physics in oceanic flows: new insights from laboratory experiments and numerical simulations

Editorial: Multi-scale fluid physics in oceanic flows: new insights from laboratory experiments and numerical simulations

ON PARAMETRIC STUDY OF FLUID LEAVES AND FLUID PINEAPPLE

Liquid chain is a commonly known phenomenon, and it is found to be formed under free fall or due to impact of liquid on surface. Usually, these liquid chains have rim and lamina, which are explained by instabilities. In this article, we examined a variant of liquid chain and carried a parametric study experimentally. Since this phenomenon is reason for the shape of leaves in a plant, we call them fluid leaves or liquid leaves. Another fluid phenomenon called fluid pineapple (FP), which is actually the result of an interaction of multiple laminar jets, is the reason for the shape of the pineapple. From the abovementioned fluid phenomena and, it is evident the shape of the living organism is based on fluid physics. Experimental study and the results are provided in detail. All living organisms follows the Fibonacci series and fractal formation. This article shows that the property of fluids to store its molecules in a series is the reason behind the series and fractals' formation in the entire universe. A unified theory is provided to explain the universal presence of leaf shapes and details about the FP in this work.

Advances in CUDA for computational physics

Advances in the graphics processing unit (GPU) development led to the opportunity for software developers to increase the execution speed for their programs by massive parallelization of the algorithms using GPU programming. NVIDIA company developed an arhitecture for parallel computing named Compute Unified Device Architecture (CUDA) which includes a set of CUDA instructions and the hardware for parallel computing. Computational Physics is an interdisciplinary field which is in continuous progress and which studies, develops and optimizes numerical algorithms and computational techniques for their application in solving various physics problems. Computational Physics has applicability in all sub-branches of physics and related fields such as: biophysics, astrophysics, plasma physics, biomechanics, fluid physics, etc. Moreover, with the evolution of technology in the last few decades, this relatively new field has helped to quickly obtain results in these fields, facilitating the connection between theoretical and experimental physics. In this paper, some of the latest researches and results obtained in computational physics by using GPU computing with CUDA architecture are reviewed.

Applications of fluid dynamics and mechanics of continua in forensics

Here, an overview is given of a collection of works published by Physics of Fluids under an umbrella-title Flow and Forensics. These works span the two fields, which currently coexist without too much interaction, namely, fluid mechanics and forensic science. Nevertheless, both fields reveal mutual interest for quite some time. The present work demonstrates that not only a tangential interaction, but a wide mutual polymer-like reptation might be beneficial for both fields. The present set of works already demonstrates that sub-fields of fluid mechanics, such as multi-phase flows, gas dynamics, and rheology, fluid mechanical topics, such as drops and vortices, and tools, such as de Laval nozzle, are not alien at all to forensic science subjects and could be beneficial for them. In its turn, forensic science can enrich fluid mechanics by such subjects as blood pattern analysis, blood and brain spatter analysis, prediction of the blood spatter origin, and delineation of a staged suicide (a homicide) from a real one.

Preface: 1st International Conference on Fluid Mechanics, Computational Mathematics and Physics (FMCMP 2023)

The 1st International Conference on Fluid Mechanics, Computational Mathematics and Physics (FMCMP 2023) was held in Xi'an City, China during November 18-19, 2023, it included original and peer-reviewed research papers.&#x0D; FMCMP is an annual international conference devoted to the discussion of original work on theoretical, computational, and experimental aspects of the mechanics of fluids, with special regards to the Navier-Stokes equations. FMCMP conference covers the field of Fluid Mechanics, Computational and Applied Mathematics, and Physics.&#x0D; FMCMP aims to provide a knowledge exchange and sharing platform of fluid mechanics, computational mathematics and physics for the aviation and aerospace industry, automobile industry, shipbuilding industry, etc. We welcome experts in fields related to fluid mechanics, computational mathematics and physics to join us.&#x0D; We would like to thank all the author submitted papers to this FMCMP 2023 and thank all the reviewers for their time and effort in reviewing articles. Especially we would like to thank the organizing committee for their valuable advices in the organization and helpful peer review of the papers.&#x0D; Organizing Committee of FMCMP 2023&#x0D; Xi'an City, China

On the multi-objective perspective of discrete topology optimization in fluid-structure interaction problems

Fluid-structure interaction is a challenging topic that addresses fluid and solid physics, as well as the stress coupling between them. Traditional topology optimization methods are performed with coupling load interpolation schemes in order to have some information on fluid flow sensitivity analysis and improve compliance minimization into design-dependent problems. In this paper, we propose a strategy to design fluid-structure systems by combining solid and fluid objectives without the need for the coupling load interpolation scheme. Therefore, we investigate topology optimization applied to fluid-structure interaction problems via a multi-objective formulation. We combine structural compliance with some fluid flow objective functions (energy dissipation, downforce, and drag) subject to a volume constraint. We assume linear elasticity for the solid and the steady incompressible Navier-Stokes equations for the fluid. The optimization problem is solved by using sequential integer linear programming via the TOBS (Topology Optimization of Binary Structures) method with a geometry trimming (GT) technique. It is a gradient-based method that produces explicit (discrete) boundaries that are convenient for coupled physics problems. Numerical results are presented for two and three-dimensional problems considering low to moderate Reynolds numbers. We demonstrate that the proposed multi-objective approach yields physically meaningful designs with improved performance, highlighting that the incorporation of coupling load interpolation into fluid-structure interaction optimization is redundant.

Time-averaged flow field reconstruction based on a multifidelity model using physics-informed neural network (PINN) and nonlinear information fusion

PurposeCurrent methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods.Design/methodology/approachA multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data.FindingsTwo experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction.Originality/valueIn this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.

Development of Two-Phase Frictional Pressure Gradient Correlation for Saturated Cryogenic Flow Boiling in Uniformly Heated Tubes

Experiments to determine two-phase frictional pressure drop for saturated cryogenic flow boiling in uniformly heated round tubes have been performed throughout the globe during the past sixty years for a variety of cryogens. However, the experimental data are scarce and either rarely published or published only for a few cryogens, with majority of the data remaining in the archives of authors, or in obscure technical reports of an organization or other inaccessible sources. In the present study, the Purdue University-Boiling and Two-Phase Flow Laboratory (PU-BTPFL) Cryogenic Total Pressure Drop Database is consolidated both for saturated adiabatic liquid-vapor and saturated flow boiling for cryogens from world literature dating back to 1964. With 474 total pressure drop data points for LHe, LH2, LNe, and LN2, it represents the largest total pressure drop database for cryogenic saturated two-phase flow assembled to date. Using this database, predictive accuracy of seminal frictional pressure gradient correlations employing both the Homogenous Equilibrium Model (HEM) and the Separated Flow Model (SFM) are assessed. The distinct fluid physics unique to cryogens is studied further using the database and new dimensionless criteria are developed to demarcate a dispersed flow dominant data subset from the separated flow dominant data subset, which are better represented using HEM and SFM, respectively. These criteria are subsequently used to develop a hybrid HEM-SEM frictional pressure gradient correlation for saturated cryogenic flow for the two distinct data subsets. The new hybrid correlation performs the best of all seminal correlations and provides excellent predictive agreement with the database, evidenced by a Mean Absolute Error (MAE) of 14.7 %.

Development of the on-orbit maintenance and manipulation workbench (MMW) for the Chinese space station

The logistic supply for Space Station is very expensive and difficult compared with any other human natural exploration activities due to launch costs and challenges, and the logistic problems of establishing bases on the Moon and Mars in the future will be more prominent. Especially for emergencies, the losses caused by ground support delay will be immeasurable. Considering the successful maintenance of the Hubble Telescope and operations on the ISS, one of the most effective methods to solve the logistic supply problem is to enhance the capability of self-maintenance and support of the facilities. Through the participation of astronauts and a series of tools and technical support, the capability of self-maintenance and support of the facilities can be effectively improved. For this purpose, the on-orbit Maintenance and Manipulation Workbench (MMW) has been developed and installed on the Mengtian Lab Module (MLM) of the Chinese Space Station (CSS) to provide an enclosed working area for on-orbit fault diagnosis, maintenance, and manual or mechanical operations for the payload. This paper introduces the development and functions of the MMW on the MLM. In the limited rack space and limited resources, the MMW provides a 380-L work volume, 1000-W DC power with a versatile supply interface (100, 28, and 12 Vdc), 800-W cooling capability, video and data recording and real-time downlink capabilities, ground commanding capability, wastes (waste gases and waste particles) treatment capabilities. With these capabilities, the MMW is an ideal platform to support the operation and test verification of fine mechanical operations, structural and electronic assembly of scientific experiments and technical experiments in the cabin, and to support the development of space robots and telescience technology experiments. Areas of research that will benefit from investigations in the MMW include fluid physics, materials science, combustion science, on-orbit maintenance and manipulation, and advanced life support technologies. The mechanical, electrical and thermal control subsystems are discussed separately. Special tests for the treatment of wastes have been carried out to verify the capabilities. The development of the MMW will surely enhance the space research in the forthcoming long-term activities of CSS.

Innovative multiphysics approach for designing high-performance thermo-responsive shape memory polymer microvalve

Shape memory polymers (SMPs), classified as smart materials, have emerged as promising candidates for microfluidic devices due to their significant potential. In this study, we present the design and analysis of an SMP microvalve. The thermomechanical response of the SMP microvalve is studied using a recently introduced nonlinear constitutive model that incorporates nonlinear hyperelasticity and viscoelasticity for SMPs. This model is coupled with the fluid field and accounts for heat transfer in both fluid and solid physics. The governing equations for the multiphysics behavior are discussed. Then an overview of the finite element model is provided. The most important characteristics of the SMP valve, such as SMP thickness, flow rate, contact pressure, and pressure distribution, are examined numerically. The results expound upon the significance of employing fluid-solid interaction conjugated heat transfer analysis as a crucial factor in the proficient development of microvalves for diverse applications, with the primary objective being the prevention of overheating and the mitigation of potential failures.

Experimental characterization of pressure and friction factor in an interior subchannel of a 61-pin wire-wrapped rod bundle with a porous blockage

Comprehending and counteracting accident conditions presented by impedances of flow in diminutive subchannels of a Liquid Metal Fast Reactor (LMFR) hexagonal rod bundle are imperative toward their development and safety. Scarce experimental research currently exists in the literature to characterize the pressure and friction factor for partial blockages in LMFR assemblies. Experimental pressure measurements were conducted in a 61-pin prototypical LMFR fuel assembly using specialized instrumented wire-wrapped rods with a three-dimensional printed porous blockage installed. The pressure drop was measured for one helical pitch at four distinct interior subchannel locations: two in the blocked subchannel and two unblocked adjacent locations (near-center and near-wall of the assembly). A wide range of Reynolds numbers between 140 and 24 000 were studied to evaluate the blocked subchannel friction factor and to determine the flow regime boundaries for laminar-to-transition and transition-to-turbulent flows. Power spectral density analysis of the pressure fluctuations for three distinct locations (one upstream and two downstream of the porous blockage) revealed the mechanisms of coherent structure formations and transport, and dominant location-dependent Strouhal numbers. One-dimensional continuous wavelet transforms of the pressure fluctuations demarcated temporal instances of flow events with their frequency content. Temporal cross correlation quantified the temporal delay between the blocked subchannel pressure fluctuations in the blockage vicinity. The presented research provides first-of-its-kind datasets and fluid physics based-analyses for the interior LMFR subchannel in the presence of a porous blockage and provides a benchmark for the validation of computational flow models and predictive correlations for the safety enhancement of LMFR rod bundles.