Results Of Computational Fluid Dynamics Model Research Articles

Advanced 2D Computational Fluid Dynamics Model of an External Gear Pump Considering Relief Grooves

The article presents an advanced two-dimensional (2D) computational fluid dynamics (CFD) model of an external gear pump which considers relief grooves. Relief grooves are limiting design features for the flow process of this type of pump, and their influence in existing studies is considered by a three-dimensional (3D) model only. The structural modification proposed by the authors is beyond the possibilities of real implementation, but it gives the possibility to precisely model the pump’s design features. In contrast to the existing studies (using 3D CFD), the proposed advanced 2D model requires significantly fewer computing resources. Numerical experiments were carried out using the 2D model at different pump operating modes depending on the rotation frequency (950–1450 min−1) and pressure load (5–150 bar). The numerical results were validated by a real-world experiment for the same pump operating modes using an existing laboratory experimental setup. An analysis of the CFD model and real experiment results was carried out by determining a quantitative index of match (FIT), which varies in the range of 97.93–99.82%. This proves the performance of the proposed CFD model, which can be further used as a part of more complex hydraulic systems models.

Optimisation of the performance of a new vertical roller mill by computational fluid dynamics simulations

The performance of two new Vertical Roller Mills (VRM) has been analysed using Computational Fluid Dynamics (CFD). The results show notable air ingress from the bottom of the mill, due to moving components in the mill. This is detrimental to mill performance as the milled powder gets recirculated back into the milling region and reduces the overall milling efficiency. Optimisation of the mill design has been carried out based on CFD modelling results. Proposed reconfigurations produce a positive pressure upstream, suppressing air ingress. Design modifications were implemented in a pilot-scale mill, resolving the air ingress problem. Additionally, erosion patterns were computed for the mill geometry and qualitatively confirmed by visual inspection of the mill.

RESEARCH OF THE SIDE VENTILATION SYSTEM IN THE POULTRY HOUSE USING CFD

Maintaining a standardized microclimate in the poultry house is one of the main factors. The quality of the output ultimately depends on the quality indicators of the air parameters. Keeping a bird requires great efforts and technological solutions. In connection with this study, there is an improvement of the microclimate system in the air environment of the poultry house due to the inclusion of exhaust fans on the rear end wall in an unconventional way. Computational Fluid Dynamics (CFD) using ANSYS Fluent is a powerful tool for predicting the microclimate system in the poultry house as an alternative to experimental studies. The CFD model was performed on the Navier-Stokes equations for convective flows. The calculations use the Discrete Ordinates radiation model and the Spalart-Allmaras turbulence model.
 The calculations were made with an air consumption of 21.5 kg/s. The temperature of the outside air is assumed equal to +3 ºС and the thermal radiation parameter is entered. For air removal, Munters EM50 1.5 HP exhaust fans are used in a total number of 4 pcs. Inflow valves Wlotpowietrza 3000-VFG with a total number of 80 pcs., which are placed at a height of 0.21 m from the ceiling (1-8 valves) and 0.81 m for 9-40 valves.
 According to the results of CFD modeling of hydrodynamics and heat and mass exchange processes, it was concluded that changing the angle of the spoiler by 73o allows air to be supplied to the center of the poultry house. The upper air layers near the ceiling and near the side wall have a slightly higher temperature. This is accompanied by radiation from the sun and ranges from +21.5 to +24.5 ℃. Since the bird is a source of heat, and in combination with radiation, the air in the room is partially heated. In the center of the room along the entire height, the temperature reaches +15-16 ℃. At the same time, the pressure drop of the inlet valves is 70 Pa, which allows the exhaust fan to be fully supplied. The air velocity at the inlet of the inflow valves is 11.54 m/s. The average air speed at a height of 0.7 m from the floor level is 0.5 m/s, the temperature is 16.55 ℃.
 Thus, the presented scientific research can be used in the future to develop new ventilation systems for poultry houses.

Exploring decentralized ammonia synthesis for hydrogen storage and transport: A comprehensive CFD investigation with experimental validation and parametric study

Hydrogen energy plays a vital role in the transition towards a carbon-neutral society but faces challenges in storage and transport, as well as in production due to fluctuations in renewable electricity generation. Ammonia (NH3), as a carbon-neutral hydrogen carrier, offers a promising solution to the energy storage and transport problem. To realize its potential and support the development of a hydrogen economy, exploring NH3 synthesis in a decentralized form that integrates with distributed hydrogen production systems is highly needed. In this study, a computational fluid dynamics (CFD) model for the Ruthenium (Ru) catalysts-based Haber–Bosch reactor is developed. First, a state-of-the-art kinetic model comprehensively describing the complex catalytic reaction is assessed for its sensitivity and applicability to temperature, pressure and conversion. Then, the kinetic model is integrated into the CFD model, and its accuracy is verified through comparison with experimental data obtained from different Ru-based catalysts and operation conditions. Detailed CFD results for a given case are presented, offering a visual understanding of thermal gradients and species distributions inside the reactor. Finally, a CFD-based parametric study is performed to reveal the impacts of key operation parameters and optimize the NH3 synthesis reactor. The results show that the NH3 production rate is predominantly influenced by temperature, with a two-fold difference observed for every 30 °C variation, while pressure primarily affects the equilibrium. Additionally, the affecting mechanism of space velocity is thoroughly discussed and the best value for efficient NH3 synthesis is found to be 180,000 h−1. In conclusion, the CFD model and simulation results provide valuable insights for the design and control of decentralized NH3 synthesis reactor and operation, contributing to the advancement of sustainable energy technologies.

Computational Fluid Dynamics (CFD) modeling of static maceration in view to optimize continuous flow extractions of robinetin and dihydrorobinetin from Robinia pseudoacacia wood

Computational Fluid Dynamics (CFD) modeling was used to study solid-liquid extraction applied to Robinia pseudoacacia. Experimental and simulation studies on maceration and continuous flow extractions were performed at various solid-solvent ratios and flow rates. To validate the CFD modeling results, parameters such as diffusivity or diffusion coefficient and kinetic parameter of the extracts were estimated from experimental kinetic data. A good agreement was found between the CFD model and the experimental data. The mass diffusivity of the extracts in the liquid phase was 1.7 × 10−7 m2/s (R2=0.985) and 1.8 × 10−7 m2/s (R2=0.992) for dihydrorobinetin (DHR) and robinetin (Rob). Moreover, the phase change coefficient was 1.2 × 10−4 and 1.6 × 10−4 1/s for DHR and Rob, respectively. In addition, static maceration was combined with continuous flow extraction. The optimal condition was 213 min of static maceration followed by a flow of 1 mL/min for 465 min to obtain yields of 45.18 and 6.64 mg/g DHR and Rob, respectively.

Development of foam-breaking measures after removing liquid contamination from wells and flowlines by using surface-active substances

The purpose is to consider the complications that arise during the operation of gas condensate wells, in particular, the accumulation of liquid contamination. Development of new approaches to improve the efficiency of the separation equipment performance of gas gathering and treatment systems when a multiphase flow enters. Development of a foam breaking method in a gas-liquid flow after removal of liquid contaminants from wells and flowlines using surfactants. An analysis was made of the complications that may arise when removing liquid contaminants from wells and flowlines using surfactants. Measures have been developed that will make it possible to timely prevent the ingress of foam into the separation equipment of gas gathering and treatment systems. Using computational fluid dynamics (CFD) modelling, an effective foam-breaking device was developed by supplying stable hydrocarbon condensate. A method to minimize the negative impact of foam on the operation of separation equipment after fluid removal from wells and gas condensate field flowlines using a surfactant solution was elaborated. A method for its breaking was proposed to prevent the flow of foam into the gas processing unit. This method foresees the application of the technological scheme layout for supplying a stable hydrocarbon condensate to a gas-liquid flow entering the separators of the first of separation, both the main line and the measuring line. CFD modelling was used to study the process of foam breaking by feeding hydrocarbon condensate into it. The influence of the hydrocarbon condensate supplying method on gas-dynamic processes (distribution of pressure, velocity, volumetric particles of phases), and the efficiency of foam breaking was estimated. It was established that the supply of hydrocarbon condensate from one branch pipe to the pipeline through which the foam moved did not ensure its complete breaking. To increase the efficiency of foam breaking, a device with designed four nozzles for supplying hydrocarbon condensate was developed. CFD modelling made it possible to substantiate that in this case, a pressure reduction zone appeared at the place of condensate supply. Because of a sharp change in pressure, a strong improvement in the effect of foam breaking occurred. The understanding of the regularities of foam breaking processes by hydrocarbon condensate was obtained, and the design of a device for the complete foam breaking was developed. The obtained results of laboratory studies have shown that a sharp decrease in the stability of the foam occurs under the condition of an increase in the volume of stable hydrocarbon condensate added to the studied model of mineralized formation water. Based on the results of CFD modeling, a device for breaking foam by stable hydrocarbon condensate has been worked out, the effectiveness of which will be confirmed experimentally and in field conditions. The results of the performed laboratory studies and CFD modelling allow a more reasonable approach to using various available methods and measures to prevent the ingress of foam with a gas-liquid flow into the separation equipment of gas gathering and treatment systems. This approach makes it possible to develop new effective ways and measures to prevent this complication. Based on CFD modelling, it was found that when a stable hydrocarbon condensate is supplied into a gas-liquid flow, foam breaks. A method for breaking foam in a gas-liquid flow has been developed, which is original and can be introduced in practice.

An improved computational fluid dynamics (CFD) model for predicting hydrate deposition rate and wall shear stress in offshore gas-dominated pipeline

Gas hydrates in pipelines is still a flow assurance problem in the oil and gas industry and requires a proactive hydrate plugging risk predicting model. As an active area of research, this work has developed a 3D 10 m length by 0.0204 m diameter horizontal pipe CFD model based on the eulerian-eulerian multiphase modelling framework to predict hydrate deposition rate in gas-dominated pipeline. The proposed model simulates the conditions for hydrate formation with user defined functions (UDFs) for both energy and mass sources implemented in ANSYS Fluent, a commercial CFD software. The empirical hydrate deposition rates predicted by this model at varying subcooling temperatures and gas velocities are consistent with experimental results within ±10% uncertainty bound. At lower gas velocity of 4.7 m/s, the model overpredicted the hydrate deposition rates of the experimental results in Aman et al. (2016) by 9–25.7%, whereas the analytical model of Di Lorenzo et al. (2018) underpredicted the same experimental results by a range of 27–33%. Consequently, the CFD model can enhance proactive hydrate plugging risk predictions earlier than the analytical model, especially at low gas productivity. Similarly, at a velocity of 8.8 m/s and subcooling temperatures of 2.5 K, 7.1 K and 8.0 K, the CFD model underpredicted the hydrate deposition rates of the regressed experimental results in Di Lorenzo et al. (2014a) by 14%, 6% and 4% respectively, and overpredicted the results by 1% at a subcooling temperature of 4.3 K. From the CFD model results, we also suggest that hydrate sloughing shear stress is relatively constant, and the wall shedding shear stress by hydrate vary during deposition. Finally, the CFD model also predicted the phase change during hydrate formation, agglomeration, and deposition.

Multi-objective optimization of helical baffles in the shell-and-tube heat exchanger by computational fluid dynamics and genetic algorithm

Baffles are significant components to control shell-side flow distribution and enhance heat transfer in the shell-and-tube heat exchangers (STHXs). The helical baffles have become popular as a suitable alternative to segmental baffles The thermal-hydraulic performance in the shell and tube heat exchanger with helical baffles was modeled by the computational fluid dynamics (CFD) technique. The effects of the two main geometrical parameters including baffle pitch and baffle angle on heat transfer coefficient and pressure drop were studied. The CFD modeling results were validated with experimental data. The validated data were employed to develop predictive correlations. Finally, the optimum geometries of the investigated helical baffles were suggested using multi-objective genetic algorithm (MOGA) optimization. The optimum results presented a trade-off between heat transfer coefficient and pressure drop in the heat exchangers.

A new combination approach for optimal design of sedimentation tanks based on hydrodynamic simulation model and machine learning algorithms

The current study aims to propose a novel approach to design rectangular primary sedimentation tanks using computational fluid dynamics (CFD) and artificial intelligence. Hybrid adaptive neuro-fuzzy inference system and particle swarm optimization algorithm (ANFIS-PSO) is trained using CFD model's results. ANFIS-PSO is coupled with two multi-objective algorithms to optimize two objectives: Mean velocity and baffles' configurations. For the single-baffle tank, the optimal baffle position regarding flow velocity was approximately at 0.13 of the basin length, with the height ratio (ratio of baffle height to weir height) of 0.21, but the most cost-effective design was obtained when the single baffle was placed at about 0.06 of total length, with the height ratio of 0.17. Using two baffles could enhance the tank's hydraulic performance, especially when the first and second baffles were at 0.11 and 0.25 of the tank's length, respectively, with the height ratio of 0.33 and 0.22, respectively.

Investigation of the lateral ventilation system in a poultry house using CFD

Maintaining a normalised microclimate in a poultry house is one of the main factors. It is the quality indicators of air parameters that ultimately determine the quality of product output. Keeping poultry requires considerable efforts and technological solutions. In this regard, the purpose of the study is to improve the microclimate system in the poultry house by installing ventilation equipment on the side wall. A powerful tool for predicting the air flow pattern in a poultry house is Computational Fluid Dynamics (CFD) modelling using ANSYS Fluent. This is an alternative to experimental research. CFD modelling results have shown that the valves operate most efficiently at 330 mm from the ceiling. The pressure drop of the supply valves is 45.85 Pa. The air velocity at the inlet of the supply valves is 9.17 m/s. The air velocity at a height of 0.7 m from the floor level varies within 0.57 m/s, the temperature – 9.91°C

Numerical Study of Vortex Flow in a Classifier with Coaxial Tubes

Centrifugal air classifiers are one of the most used separation devices in particle technology. The study aims to obtain a detailed description of the bulk material classification mechanism in the developed centrifugal classifier. The classifier design and the mechanism of the stable vortex structure formation in the inter-tube space of the device are described. Velocities within and between the vortices are studied to identify regions with inverse flows, which serve as transport channels for particles. The computational fluid dynamics modeling results indicate three channels with negative or near-zero axial velocities: between the vortices, near the outer wall of the internal tube, and the inner wall of the external tube. The selectivity of the device decreases when transport channels are disrupted due to flow mixing, which is caused by the height shifting of the vortex centers.

Electromagnetic induction-assisted pyrolysis of pre-treated MSW: Modelling and experimental analysis

The paper presents an innovative method for the energetic valorisation of municipal solid waste (MSW) through pyrolysis with electromagnetic induction technology. The MSW fraction treated is retained during the sieving pretreatment operation to separate the organic fraction intended for the anaerobic digestion producing advanced biofuel. Pyrolysis is a technology that could be a valuable option for the treatment of municipal solid waste. It is considered a valid alternative to waste incineration since it allows the production of chemicals and biofuels with low SOx and NOx emissions and, therefore, a low environmental impact.The heating system based on induction technology avoids traditional burners, improving the process energy efficiency and optimising the thermal distribution inside the reactor. The study is conducted by computational fluid dynamic (CFD) simulations, which allowed to optimise the geometry, to analyse the heat distribution within the reactor, guaranteeing more flexibility in the high variability of input material to be treated. Experiments on a laboratory scale reactor were carried out to validate the CFD model results. The proposed model correctly predicts the experimental outputs at the operative conditions tested.

Phenol degradation of waste and stormwater on a flat plate photocatalytic reactor with TiO2 on glass slide: An experimental and modelling investigation

Heterogeneous photocatalytic oxidation process using TiO2 (titanium dioxide) and UV light is a promising method to degrade a wide variety of recalcitrant organic substances such as phenol, pesticides, herbicides, etc. from waste and stormwater. Due to lack of suitable computational fluid dynamics (CFD) model, the industrial-scale application of this technique poses a few challenges indicating the need to clearly understand the hydrodynamic behaviour of the photocatalytic system and investigate the ways of improving their performance. Inadequate mixing and turbulence in a fixed photocatalytic reactor limit the performance of the reactor in terms of pollutant mass transport to the catalyst surface and pollutant degradation. In this study, a 3D flat plate photocatalytic reactor was designed and developed, and numerically analysed using CFD code FLUENT to investigate the performance of the reactor. The CFD modelling results were validated against the experimental data at various flow conditions. The CFD results including velocity and phenol concentration was found in strong agreement with the experimental results with R2 value of 0.998. The experimental results shows that the phenol degradation was 85.5% when the irradiation was 70.6 Wm−2 and initial concentration of phenol was 20 PPM The experimental results also show that the phenol degradation increases with the increase of irradiation but decreases with the increase of initial concentration. The results show that phenol degradation of the reactor decreases with the increase in flow rate as expected. The CFD model can accurately predict the velocity and the concentration of phenol at different flow rates.

FBR for Polyolefin Production in Gas Phase: Validation of a Two‐Phase Compartmentalized Model by Comparison with CFD

AbstractTwo different modeling approaches are applied in this work to the simulation of fluidized bed reactors containing solid particles of Geldart A‐B type and operated at typical conditions for polyolefins production. On one side, a fully detailed computational fluid‐dynamics (CFD) model is developed, considering a 2D planar geometry and a multi‐fluid description with kinetic theory of granular flows. On the other, a conventional three‐phase, 1D compartmentalized model (SCM) is also developed, implementing the fluid dynamic description based on popular, semi‐empirical relationships available in the literature. Given the huge difference of computational effort associated with the corresponding numerical solutions, our aim is to confirm the reliability of the simplified model by comparison with the results of the detailed CFD model. The results show that the oversimplified compartmentalized approach is capable to predict the solid mixing features established inside the reactor operated in bubbling fluidization regime with good reliability for non‐reactive polyethylene particles. Average solid volume fractions are particularly close to the values predicted by the CFD model when monodisperse particles are considered inside the examined range of gas velocity values. A generally good agreement is also found when solids with broad size distribution are analyzed.

A hybrid analytical-numerical model for predicting the performance of the Horizontal Ground Heat Exchangers

Horizontal Ground Heat Exchangers (HGHE) as a means of exploiting geothermal energy has come to the fore for a few decades. Various analytical and Computational Fluid Dynamics (CFD) methods have been proposed to predict the performance of the HGHEs. The available analytical approaches are fast; however, they are based on various simplifications and assumptions, affecting their accuracy. On the other hand, CFD methods are more accurate, but their computational cost is a burden. Therefore there is an acute need for an accurate and fast method for predicting the long-term performance of HGHEs. To this aim, this study puts forward a novel hybrid analytical-numerical model for predicting the performance of HGHEs. The proposed approach is based on Duhamel's theorem, modified infinite line source method, and superposition principles that allow fast and straightforward simulation. The thermal interference between adjacent pipes is also considered via the superposition method. The computational time and performance of the proposed approach are evaluated via several benchmark cases and are compared with the results of a three-dimensional CFD model. The results depicted that the present model can predict well the transient performance of linear HGHEs with various pipe arrangements. Moreover, according to the obtained results, the proposed semi-analytical method is up to 50 times faster than the CFD approach.

Efficient Prediction of Proppant Placement along a Horizontal Fracturing Stage for Perforation Design Optimization

Summary Multistage plug and perforation (plug-n-perf) fracturing is commonly used for horizontal well completion in unconventional reservoirs. Uniform distribution of proppant across all clusters in each stage has proved to be challenging with low viscosity slickwater owing to its limited transport capability. Computational fluid dynamics (CFD) has been used to model proppant transport in wellbore to improve perforation and fracturing design for achieving uniform proppant placement. However, traditional CFD modeling of a full-scale stage is computationally expensive, which limits its applicability in the completion design optimization. A new approach was developed in this paper to efficiently predict proppant placement along a multicluster stage based on a machine learning (ML) model trained with extensive CFD modeling results. Its high computational efficiency permits quick sensitivity analyses to optimize perforation and fracturing designs. The new approach was validated against full-stage CFD modeling results as well as post-treatment field diagnostics. Sensitivity analyses show that proppant inertia effect is a key factor affecting proppant placement in heel clusters with higher slurry flow rates, allowing more proppant carried to the toe owing to its higher density in comparison with fluid. Proppant settling allows bottom perforations to accept more proppant than top perforations. This gravitational effect is not negligible near the heel at high flow rates and becomes more dominant near toe clusters where the flow rate is reduced. Near-uniform proppant placement is achievable via perforation design optimization by taking advantage of these two key mechanisms controlling proppant transport in horizontal wellbores. It is demonstrated that in-line perforating designs with all perforations having the same orientation in each cluster or the entire stage, especially with perforations at the bottom or on the side of the wellbore, improve the proppant placement uniformity. However, it is recommended that the optimum perforation design should be identified case by case depending on specific input parameters. The ML-based model developed in this study has overcome some of the limitations from existing models in the literature and is able to provide quick and yet reliable solutions to proppant placement prediction and design optimization.

Experimental and numerical study of Zuppinger water wheel model

The Zuppinger water wheel, developed in the 1850s, is one of the most efficient water wheels and is commonly used for low-head hydropower generation. The high efficiencies of the wheel over a wide operating range, its simplicity in design and slow rotational speed offer a low-cost and environmentally friendly low-head hydropower solution. A physical and numerical model study of a wheel is presented in this paper. Three-dimensional numerical simulations were performed using the computational fluid dynamics (CFD) code Flow-3D. The influence of grid size on the results of the numerical model was assessed using a systematic grid refinement study. Grid convergence indices (GCIs) were calculated for two grid sets each, with three different grid sizes, using a constant grid refinement ratio. The GCIs were reduced to levels below 5% for the selected quantities of interest. The CFD model results were compared with physical model results at different operating points of the wheel. The maximum differences in power output and efficiency between the physical and numerical model results were 2.5% and 8%, respectively.

A study on droplets dispersion and deposition characteristics under supersonic spray flow for nanomaterial coating applications

Supersonic spray coating of nanomaterials, owing to high impact velocity of particles, offers significant potential to improve the physical and mechanical properties of target surfaces. Rather than handling individual light nano-scale particles directly with a number of limitations, aqueous nanomaterial colloids and suspensions can be supersonically deposited onto surfaces by converting these complex liquid mixtures into the form of atomized micro-scale droplets. Dispersion and deposition characteristics of these droplets play a vital role in the quality and efficacy of the resultant nanomaterial coating. In the present study, comprising numerical modeling and experimental validation, we investigate details of the dispersion and deposition characteristics of droplets under supersonic flow conditions. In the numerical study, a two-way coupled discrete phase modeling is used to track the discrete phase (i.e., droplets) and to investigate the interaction of droplets with the continuous gas phase (i.e., high-velocity driving gas) in regard to their properties and conditions. The results through computational fluid dynamics (CFD) show that driving gas properties (i.e., temperature, pressure, gas type) and droplet size play a prominent role in droplets dispersion and deposition phenomena. In particular, smaller droplets (≤2 μm) are observed to be more susceptible to turbulent dispersion and evaporation. In the experimental study, an atomization-based supersonic spray system is developed for model validation and a case example of nano-coating applications. The CFD modeling results are validated by particle image velocimetry (PIV) measurements. A case study of titanium dioxide (TiO2) nanomaterial coating on a polymer substrate (ITO/PET film) is performed to demonstrate the suitability of the present spray deposition system, which also addresses the current challenges of TiO2 coating onto ITO/PET surface.

Hydrodynamics of a novel 3D printed structured packing–SpiroPak

Hydrodynamic performance of an ultra low-pressure drop and high surface area, 3D printed structured packing (SpiroPak) was investigated in this study. Computational fluid dynamics (CFD) modelling combined with single-phase (dry) and irrigated (multiphase) experiments were carried out to validate the CFD modelling results. Experiments were conducted to measure the dry and wet pressure drop at a range of liquid load (0–38.2 m3/m2∙h) and F-factor (0–1.2 Pa0.5). Liquid distribution was measured using Wire Mesh Sensor (WMS) for SpiroPak and compared with a commercial and 3D printed replica of Mellpak 250X and Montzpak B1–500. The topology of the packing was analysed to calculate the specific surface area that could be available for mass transfer. It was found that the SpiroPak can have up to 50~200% more surface area per unit volume when compared with commercial packing. Experimental and modelling results showed that SpiroPak could reduce the dry pressure drop by approximately 50%. Parametric study found that reducing corrugation size to increase surface area and increasing the gap size to reduce the pressure drop were key design parameters of SpiroPak. Finally, scale-up and scale-out (tessellation) techniques were compared to determine the optimum element size for the application of SpiroPak on a large scale.

A novel approach to calculating induced drag from computational fluid dynamics

Early aerodynamic mathematical methods rely on potential flow concepts that formally isolate aerodynamic drag into a profile and an induced drag component. The more recent evolution of Navier–Stokes-based Computational Fluid Dynamics (CFD) methods typically directly computes aerodynamic forces. It does so using surface integration of pressure and viscous forces, which does not readily enable conventional separation of profile and induced drag. Isolating induced drag from aerodynamic drag is not well developed using CFD, leading to the present effort that derives a mathematical framework to extract induced drag from CFD model results. The present approach builds on mass, momentum, and energy equation control volume analysis performed within the CFD results. We find that the energy equation provides the necessary means for the closure of quantifying induced drag within the context of minor assumptions. In addition, the results indicate an interesting character in the development of energy losses in the context of induced drag associated with flow reorganization into a tip vortex. The results from the approach indicate accuracy in the method as displayed with good correlation to predictions from analytical and potential flow methods for a variety of wing planforms. Results indicate a novel and efficient method to extract induced drag from CFD models.