Prediction Of Friction Factor Research Articles

Optimizing thermal performance in internal passage cooling with extended rib: Applying response surface method with artificial neural networks

Efficient cooling technology is crucial for high-temperature gas turbines which are significant applications in thermal processes particularly in industries such as power generation aerospace and marine propulsion. Enhancing cooling efficiency in these systems not only improves energy utilization but also plays a critical role in reducing fuel consumption increasing operational reliability and minimizing environmental impacts. This research focuses on optimizing the thermal performance of internal passage cooling channels with extended ribs using a combination of the response surface method and artificial neural networks. By varying the extended rib length and rib width the study aims to enhance heat transfer and minimize flow loss leading to improvements in overall system efficiency. Latin Hypercube Sampling is employed to strategically select variables and automated numerical simulations are conducted to perform a thorough parametric analysis. A steady-state k-ω shear stress transport turbulence model is applied in the simulations and the numerical results are validated against experimental data ensuring accuracy. The combined response surface method–artificial neural network approach integrated with TensorFlow-based modeling allows for the prediction of heat transfer and friction factor ultimately generating a comprehensive response surface to identify the optimal design point. Applying the optimized design leads to a 23.99 % improvement in the thermal performance factor compared to the reference case. The findings of this study highlight a significant enhancement in the thermal performance of the cooling channel structure particularly in high heat flux environments. This research provides valuable insights into the design of more efficient thermal management systems for gas turbines and has broader implications for other high-temperature thermal processes. The proposed optimization methodology offers a reliable approach for improving cooling technologies contributing to the development of the next generation of energy-efficient high-performance gas turbines and other industrial applications where effective thermal management is essential.

Advanced intelligence model for prediction of sediment transport rate and friction factor in alluvial channel

Advanced intelligence model for prediction of sediment transport rate and friction factor in alluvial channel

Turbulent pipe flow with spherical particles: Drag as a function of particle size and volume fraction

Suspensions of finite-size solid particles in a turbulent pipe flow are found in many industrial and technical flows. Due to the ample parameter space consisting of particle size, concentration, density and Reynolds number, a complete picture of the particle–fluid interaction is still lacking. Pressure drop predictions are often made using viscosity models only considering the bulk solid volume fraction. For the case of turbulent pipe flow laden with neutrally buoyant spherical particles, we investigate the pressure drop and overall drag (friction factor), fluid velocity and particle distribution in the pipe. We use a combination of experimental (MRV) and numerical (DNS) techniques and a continuum flow model. We find that the particle size and the bulk flow rate influence the mean fluid velocity, velocity fluctuations and the particle distribution in the pipe for low flow rates. However, the effects of the added solid particles diminish as the flow rate increases. We created a master curve for drag change compared to single-phase flow for the particle-laden cases. This curve can be used to achieve more accurate friction factor predictions than the traditional modified viscosity approach that does not account for particle size.

Heat transfer enhancement characteristics of sinusoidal corrugated tubes fabricated via laser powder bed fusion

Laser powder bed fusion (LPBF) has emerged as a powerful tool to develop heat transfer devices with higher efficiency. Corrugated tubes are commonly used components to achieve enhanced heat transfer in these devices. However, there still lacks a comprehensive study on the thermal-hydraulic performance of LPBF-fabricated corrugated tubes. In this work, we investigated the heat transfer enhancement characteristics of sinusoidal corrugated tubes (SCTs) fabricated via LPBF. SCTs with different amplitude-to-diameter ratios (A/D ratio) and wavelength-to-diameter ratios (S/D ratio) were designed and fabricated. The geometrical morphologies and surface roughness of LPBF-fabricated SCTs were characterized. Numerical simulations were performed to investigate the effects of A/D ratio and S/D ratio on the flow patterns and flow dynamics. A test system was developed to measure the pressure loss and thermal performance. Performance Evaluation Criterion were calculated to characterize the heat transfer enhancement. A/D ratio was found to have more significant impacts on the friction factor and Nusselt numbers than S/D ratio. Correlation models were developed to predict friction factors and Nusselt numbers based on the least square method. Mean prediction errors of ±3.3 % and ±5.3 % and maximum prediction errors of ±11.6 % and ±18.1 % were achieved for Nusselt numbers and friction factor, respectively.

Flow Regime Classification in Hexagonal Wire-Wrapped Fuel Assembly Using Advanced Machine Learning Models

This study presents a new approach to flow regime classification specifically tailored for typical wire-wrapped fuel assemblies in sodium fast reactors. Historically, the definition and understanding of flow regime boundaries have been extensively researched. However, many of these models suffer inaccuracy due to a lack of comprehensive data. In particular, the limited data, with only 36 data points for the laminar-to-transition boundary and 145 data points for the transition-to-turbulent boundary, often result in suboptimal models. Recognizing the critical data gap, this study classified flow regimes based on a robust data set of over 5000 data points. A diverse range of algorithms was used to find the optimal classification model. These included logistic regression, artificial neural networks, support vector classifiers, Naïve Bayes, Gaussian Naïve Bayes, K-Nearest Neighbors, random forest, AdaBoost, GradientBoost, and XGBoost. A comparative analysis of these algorithms provides valuable insights. This study presents a comprehensive set of machine learning algorithms to improve the accuracy and reliability of flow regime classification, which is a critical step in predicting friction factors and the efficient operation of sodium fast reactors.

Improving the prediction of turbulent kinetic energy for drag reduction in turbulent viscoelastic pipe flow

Reducing turbulence in pipe flows using polymer additives is crucial for industrial applications like crude oil, water, and sewage transportation. While previous research has accurately predicted friction factor and velocity profiles, none has fully understood turbulent kinetic energy (TKE) behavior in such fluids. Authors are now focusing on exploring turbulence models to better understand the TKE behavior. In this research, we have introduced a model to improve the behavior of TKE in a modified generalized Newtonian fluid (GNF). The developed model aims to simulate the viscoelastic effects of fluids that result in drag reduction in turbulent pipe flow. The work is noteworthy as it integrates turbulence and viscoelastic components, offering a comprehensive understanding of the phenomenon. By incorporating the rheological properties of viscoelastic fluids and replacing the damping function with a non-Newtonian alternative proposed by Cruz and Pinho, the Launder–Sharma k–ε turbulence model is now suitable for simulating dilute non-Newtonian viscoelastic fluids. The viscoelastic aspect of the model employs the modified GNF model. The developed model has been subjected to simulations using the computational fluid dynamics software. The results obtained for fluid TKE demonstrate a significant improvement in comparison to our previous research and the findings of other researchers. Furthermore, the model's prediction for the Darcy friction factor has been enhanced, resulting in an average error of only 3.71% in this section. It is noteworthy that the model consistently maintains a high level of accuracy in predicting other essential flow parameters such as mean axial velocity and Reynolds stresses. The provided model advances our understanding of viscoelastic fluid behavior in turbulent pipe flow by applying the modified GNF model.

Performance Analysis of a Compact Offset Strip Fin Heat Exchanger for Lubrication System in Aero Engine

Abstract As a typical fuel-oil heat exchanger, an offset strip fin heat exchanger (OSFHX) can ensure the efficient and stable operation of the aero engine lubrication system. The paper establishes 20 kinds of numerical models of OSFHX that are verified by experiments. The effects of different structural parameters on the performance of lubricating oil in OSFHX were systematically studied. Based on dimensional analysis, the prediction model which can describe the overall performance of the OSFHX is obtained. The results show that with the decrease of fin distance (s), fin length (l), fin height (h), fin thickness (t), and fin shape angle (α), the heat transfer performance of the OSFHX is enhanced and the resistance is increased. With the decrease of s and h, and the increase of t and α, the comprehensive performance of the OSFHX is enhanced. The OSFHX exhibits the optimal performance when l = 4 mm. α has the most significant effect on the comprehensive performance of the OSFHX, successively followed by h, s, t, and l. The average error of Colburn factor (j) and friction factor (f) prediction models is 4.09% and 5.31%, respectively, which can realize the theoretical calculation of the performance of the OSFHX for aviation.

Improving flow efficiency in micro and mini-channels with offset strip fins: A stacking ensemble technique for Accurate friction factor prediction in steady periodically developed flow

A novel machine-learning model for micro and mini-channel friction factor prediction is presented in this article. In recent years, periodic array offset strip fins in micro and mini channels have gained attention due to their compactness and aid in heat transfer in chemical processing and electronic cooling devices. The research uses fin length-to-height ratios below one, and Reynolds numbers between one and six hundred contain 2765 geometrically dimensioned. The friction factor, the most significant barrier to heat transfer channel use, must be accurately estimated to design efficient systems. The Krylov subspace method is implemented using the finite element method using the FEniCS software. Additionally, three machine learning algorithms, Catboost, XGboost, and Random Forest regressors, are implemented to predict the friction factor for periodic steady flow through channels with offset strip fin arrays, and the corresponding prediction performance is analysed. A stacking ensemble model is proposed to enhance the precision of friction factor forecasts. The results demonstrate that the proposed method outperforms empirical correlations in predicting friction factor values for specific performance evaluation metrics with an absolute error of 0.403%, indicating that the model accurately represents the complexity of the data.

Unified ANN model for heat transfer factor (j) and friction factor (f) prediction in offset strip and wavy fin PFHEs

Accurate prediction of the dimensionless heat transfer (j factor) and friction factor (f factor) is crucial for optimizing plate-fin heat exchanger (PFHE) performance. However, current models, including existing ANN models, have difficulty predicting these factors for complex fin geometries such as offset strip fins and wavy fins. To address this challenge, this research proposes a novel, unified artificial neural network (ANN) model, specifically a multilayer perceptron (MLP), capable of accurately predicting both factors across various fin types, including offset strip fins and wavy fins. The ANN was trained and validated using a comprehensive dataset that encompasses a wide range of fin configurations and Reynolds numbers, from 300 to 10,000, covering both laminar and turbulent flow conditions. Advanced learning techniques, like Bayesian regularization (BR), were employed to enhance the model's performance. The proposed model surpasses existing models, achieving a predictive accuracy with a deviation of just 1–2% from actual values, compared to the typical ±20 % seen in previous models. This significant improvement implies the new ANN model could enhance PFHE performance, energy efficiency, and cost-effectiveness across diverse applications. Introducing a unified ANN model, the research underscores machine learning's potential in thermal engineering and paves the way for future advancements.

A comprehensive study of various regressions and deep learning approaches for the prediction of friction factor in mobile bed channels

Abstract A fundamental issue in the hydraulics of movable bed channels is the measurement of friction factor (λ), which represents the head loss because of hydraulic resistance. The execution of experiments in the laboratory hinders the predictability of λ over a short period of time. The major challenges that arise with traditional forecasting approaches are due to their subjective nature and reliance on various assumptions. Therefore, advanced machine learning (ML) and artificial intelligence approaches can be utilized to overcome this tedious task. Here, eight different ML techniques have been employed to predict the λ using eight different input features. To compare the performance of models, various error metrics have been assessed and compared. The graphical inferences from heatmap data visualization, Taylor diagram, sensitivity analysis, and parametric analysis with different input scenarios (ISs) have been carried out. Based on the outcome of the study, it has been observed that K Star in the IS1 with correlation coefficient (R2) value equal to 0.9716 followed by M5 Prime (0.9712) and Random Forest (0.9603) in IS2 and IS4, respectively, have provided better results as compared to the other ML models to predict λ in terms of least errors.

Numerical simulation of a toroidal single-phase natural circulation loop with a k-kL-ω transitional turbulence model

The wall friction correlations of oscillatory natural circulation loops are highly loop-specific, making it difficult to perform 1-D system simulations before obtaining specific experimental data. To better predict the friction characteristics, the nonlinear dynamics of a toroidal single-phase natural circulation loop were numerically investigated, and the transition effect was considered. The k-kL-ω transitional turbulence and k-ω SST turbulence models were used to compute the flow characteristics of the loop under different heating powers varying from 0.48 to 1.0 W/cm2, and the results of both models were compared with previous experiments. The mass flow rates and friction factors predicted by the k-kL-ω model showed a better agreement with the experimental data than the results of the k-ω SST model. The oscillation frequencies calculated using both models agreed well with the experimental data. The k-kL-ω transitional turbulence model provided better friction-factor predictions in oscillatory natural circulation loops because it can reproduce the temporal and spatial variation of the wall shear stress more accurately by capturing the movement of laminar, transition turbulent zones inside unstable natural circulation loops. This study shows that transition effects are a possible explanation for the highly loop-specific friction correlations observed in various oscillatory natural circulation loops.

Experimental study on flow split and pressure drop characteristics in a 3 × 3 dual-cooled annular rod bundle

In this paper, flow split and pressure loss experiments were performed in a 3 × 3 dual-cooled annular rod bundle. A novel experimental methodology was developed to obtain the flow split between the internal and external channels. The flow split ratio was close to the flow area ratio of the internal channel to the external channel but didn’t change significantly with the increase of flow rate and inlet temperature. An approximate mathematical expression was proposed to analyze the flow split mechanism. The overall and local pressure drops were also measured. The friction factor in bare rod bundle and pressure loss coefficient at the spacer grid were examined. An assessment of existing correlations for predicting the friction factor and the pressure loss coefficient at the spacer grid was carried out against the experimental data. Correlations for predicting friction factor and spacer loss coefficient were developed, which agreed well with the experimental results.

Thermo-Hydraulic Performance of Spring Tape Inserts in a Circular Channel in Transitional Flow Regime

In this work, forced convection experiments were carried out to investigate the variation of heat transfer and pressure drop inside a uniformly heated circular duct fitted with full-length spring tape inserts of varying spring ratios in a transition flow regime. Air was used as the working fluid medium, and experiments were conducted for three constant heat fluxes of 2, 3, and 4 kW-m−2 with Reynolds numbers varied from 502 to 10936 to cover all three flow regimes. For a plain channel heated with 2 kW/m2 of heat flux, the transition begins at a Reynolds number of 2897 and terminates at a Reynolds number of 3783 which brings the transition Reynolds number width of 886. For the same heat flux, a channel with spring tape having a spring ratio of 3, the transition begins at Reynolds number 661 and ends at 1734 while for the case of spring ratio 5, the transition begins at 1305 and ends at 2226. For constant heat flux conditions, a decrease in the spring ratio results in the early onset of transition and which in turn increased the transition length. Predictive Nusselt number and friction factor correlations for different flow regimes have also been presented.

Prediction of Friction Factor and Heat Transfer Coefficient for Single-Phase Forced Convection Inside Microfin Tubes

Microfin tubes are widely used to enhance heat transfer in heat exchangers in order to reduce volumes, costs and refrigerant charge. Much experimental work has been published for the flow of liquids, while some experimental work is available for the flow of gases for the chemical, refrigeration and air conditioning industry. This work reviews the literature and presents new experimental friction factors for the flow of the superheated vapor of R1234ze(E) in a 5 mm outside diameter microfin tube. The authors have also collected an extensive data bank of heat transfer coefficients (around 648 points from different research laboratories) and friction factors (around 536 points), covering 45 different geometries of inner finned tubes. After comparing the predictions from available correlations with experimental data, the present paper suggests the best performing equations for the calculation of the friction factor and of the Nusselt number during forced convection flow of liquids and gases. The suggested model for friction factor estimates the experimental values with a relative and absolute deviation of −0.3% and 7.9%, respectively, whereas the suggested model for the heat transfer coefficient predicts the experimental data bank with a relative and absolute deviation of −3.3% and 13.9%, respectively. The validity range of the two correlations is extremely wide, covering microfin tubes with diameters from 2.6 mm to 24.4 mm, and Reynolds number from about approximately 1000 to 300,000 for the friction factor, and from 3000 to 1,000,000 for the heat transfer coefficient.

Demonstration of RANS models with wall functions in the spectral element code Nek5000

The spectral element based computational fluid dynamics (CFD) code Nek5000 has been traditionally used for high-fidelity applications, such as direct numerical simulation (DNS) and large eddy simulation (LES). These techniques require very fine numerical resolution to accurately capture turbulent fluctuations which can be prohibitively expensive for users without access to leadership class computing facilities. For broader application and adoption, significant effort has been invested to develop Reynolds-averaged Navier–Stokes (RANS) capabilities in Nek5000.This work presents details of the implementation and demonstration of the standard wall functions for the k – τ model in Nek5000. Results using the wall-modeled approach are compared to a wall-resolved approach for cases with negligible pressure gradient, viz., channel flow, pipe flow and flow in a reactor subchannel. Results show reasonably good agreement between the two approaches for friction factor and Nusselt number. Some expected differences are identified near the wall. These cases demonstrate the potential for significant computational savings by using much coarser meshes for the wall-modeled approach, with only minor differences between the predicted result. Additionally, several Reynolds numbers up to 1,000,000 are demonstrated for pipe flow and predicted friction factors and Nusselt numbers compared well to available correlations, with the worst below 10%. As the Reynolds number is increased, better agreement is observed between the correlations and the wall-modeled approach. In addition, flow in a molten salt fast reactor (MSFR) core is considered which features an adverse pressure gradient and flow separation. It showcases the inability of standard wall functions to accurately predict flows with adverse pressure gradients. The results, however, match reasonably well in trend in regions of the flow where the boundary layer is attached. Ongoing research is dedicated to include a pressure gradient correction to wall functions to improve the accuracy of flows with separation or reattachment and adverse or favorable pressure gradients.

Plot investigation on rill flow resistance due to path tortuosity

The path tortuosity t is an indicator of rill morphology accounting for the deviation of the thalweg from a straight alignment. The effect of t on flow resistance has been little investigated for rills. This paper reports the results of a plot investigation aimed to establish the suitable accuracy of the rill thalweg measurement to determine the tortuosity parameter and to test the reliability of a theoretical flow resistance law. Four rills were incised in clay soil (CS) and clay-loam soil (LS) and shaped by a clear flow discharge. The three-dimensional Digital Terrain Models were created by the Structure from Motion technique. For rills on LS, an approximate thalweg was tracked by photo-interpretation, and a specific calculation routine was applied to identify the cross sections with a constant spacing d. The actual rill thalweg was obtained as the line joining the lowest points of these cross-sections. Among the different tested d values, d = 0.075 m was chosen to determine t. For both CS and LS, the Darcy-Weisbach friction factor f featured a non-monotonic relation with t, which was explained as the result of three additive components due to bed roughness, sediment transport, and localized energy losses due to curves. The effect of the former two components on f contrasts that of the third, resulting in a linearly decreasing f-t relationship and constant flow velocity for the three lowest tortuosity values, and an increased friction factor and reduced flow velocity for the highest tortuosity value. The flow resistance law was positively tested, and the predicted friction factor was dependent on t.

Utilizing artificial neural networks to predict the thermal performance of conical tubes with pulsating flow

A novel model of an artificial neural network is presented to predict friction factor and Nusselt number for pulsating flow in conically coiled tubes. The tubes are manufactured with coil torsions ranging between 0.02 and 0.052 and are subjected to a uniform heat flux. Experiments using pulsating flow with a pulsating frequency of 4 to 10Hz and a Reynolds number between 4836 and 12,562 were expanded. In terms of overall heat transfer improvement, the pulsing flow with a frequency of 4 Hz performs the best within the investigated range. Results demonstrated that the Nusselt number and thermal performance index increased when the Reynolds number and coil torsion decreased. The results predicted by a Feed-forward neural network were compared to the actual experimental data. A comparison showed that a feed-forward neural network could predict the Nusselt number and friction factor. The average root mean square error for the predicted Nusselt number was 4.6025. There is a good agreement between the predicted values and the experimental values. At the same Reynolds number and with a frequency of 4 Hz, reducing coil torsion from 0.052 to 0.02 improves Nusselt number by 23 % and 10 %, experimentally and in a feed-forward neural network, respectively.

Design of an Additively Manufactured Recuperator With 800 °C Inlet Temperature for sCO2 Power Cycle Application

Abstract Recuperators with design temperatures at and above 800 °C can further increase the thermal efficiency of supercritical CO2 power cycles by enabling higher turbine exhaust temperatures. Mar-M247 is a well-suited nickel-based superalloy for high temperature service due to its high creep strength that prevents excessive material thickness being required for pressure containment. Additive manufacturing using a high-speed laser-directed energy deposition (L-DED) process presents a promising solution, with build trials demonstrating the ability to produce nonconventional flow channels for enhanced heat transfer. A design process is presented that includes aerothermal and mechanical evaluation to maximize performance within the constraints of the manufacturing process. A 2-D heat transfer network and pressure drop code allows prediction of flow distribution and its effect on overall thermal performance. Established literature correlations, along with CFD simulation, inform the prediction of heat transfer coefficients and friction factors for the flowpaths and enhancement features in the heat exchanger core. Mechanical evaluation using finite element analysis (FEA) modeling with the intent of the ASME Boiler & Pressure Vessel Code (BPVC) Section VIII, Div. 2 assesses the operational safety of the design. The detailed design features annular finned passages that take advantage of helical flow paths to distribute the flow from separated headers to shared heat transfer surfaces. Performance predictions for the recuperator at a 50 kW scale provide insights into the feasibility of the additively manufactured (AM) process to produce recuperators on a commercial scale that extend existing operating envelopes.

Computational fluid dynamics simulations to improve performance characteristics of a manifold having a central inlet and outlet

In the present work, performance/flow characteristics (namely, the effect of operating parameters like pressure on flow patterns, pressure drop, and the extent of flow uniformity) and transport phenomena of a manifold (header tube assembly) having an inlet and outlet at the center are carried out on a macroscale geometry using CFD simulations. In this study, an existing design available in the published literature (with high flow non-uniformity) was considered and an optimized design (with minimum flow non-uniformity) was developed. The optimization is performed by incorporating a perforated plate (distributor) inside the top header of the manifold. First, CFD simulations for different configurations of the existing design with the perforated plate have been performed for a pressure of 10 bar with steam as a working fluid, and an optimized configuration having a minimum flow non-uniformity of less than 3% is obtained. CFD simulations for both the existing design and optimized design are then performed for a pressure range (10 ≤ p ≤ 70 bar) and the corresponding Reynolds number (Re) range (2.82E+05 ≤ Re ≤ 2.82E+06) with steam as the working fluid. The extent of non-uniformity (ENU) and pressure drop for the existing design (without a distributor) and optimized design (with a distributor) have been analyzed and compared. The optimized design gives the near uniform flow (∼1–4%) for all pressures and Reynolds numbers considered. An empirical correlation relating the friction factor (as per the Chilton–Colburn analogy) and Re has been developed for both designs (with and without a distributor). The predicted friction factors are compared with the present CFD predictions, and experimental data of the shell and tube heat exchanger are available in the published literature. A good agreement within a 10–15% deviation has been observed. Based on the Chilton–Colburn analogy, a correlation for the Nusselt number is obtained from the friction factor correlations for both with and without distributor cases. The correlations for friction factors were found to be valid under any operating conditions for a pressure drop range within 0.05 < ∆p < 1.8 bar irrespective of the design of the distributor, assuming that the manifold is able to withstand the pressure drops in the given range.

Machine-learning-aided design optimization of internal flow channel cross-sections

• Artificial neural network-based models are developed for prediction of nusselt number and friction factor. • The predictions apply for fully developed laminar flow in constant cross-section ducts of different cross section shapes. • The machine learning (ML) model predictions are validated and compared against numerical simulations. • Use of ML models in shape optimization of channel cross section for different objective functions is demonstrated. • Guidelines for usage of the developed ML models are discussed. The design optimization of various thermal management components such as cold plates, heat sinks, and heat exchangers relies on accurate prediction of flow heat transfer and pressure drop. During the iterative design process, the heat transfer and pressure drop is typically either computed numerically or obtained using geometry-specific correlations for Nusselt number and friction factor. Numerical approaches are accurate for evaluation of a single design but become computationally expensive if many design iterations are required (such as during formal optimization processes). Correlation-based approaches restrict the design space to a specific set of geometries for which correlations are available. Surrogate models for the Nusselt number and friction factor, which are more universally applicable to all geometries than traditional correlations, would enable flexible and computationally inexpensive design optimization. The current work develops machine-learning-based surrogate models for predicting the Nusselt number and friction factor under fully developed internal flow in channels of arbitrary cross section and demonstrates use of these models for optimization of the cross-sectional channel shape. The predictive performance and generality of the machine learning surrogate models is first verified on various shapes outside the training dataset, and then the models are used in the design optimization of flow cross sections based on performance metrics that weigh both heat transfer and pressure drop. The optimization process leads to novel shapes outside the training data, and so numerical simulations are carried out on these optimized shapes to compare with the surrogate model predictions and show their performance is at least as good as that of shapes with known correlations available. A three-lobed shape was found to reduce friction factor, whereas a pentagon with rounded corners and an ice cream cone-shaped duct, both found using different performance metrics. Although the ML model predictions lose accuracy outside the training set for these novel shapes, the predictions follow the correct trends with parametric variations of the shape and therefore successfully direct the search toward optimized shapes.