Drag Force Model Research Articles

Drag Force Modeling of Surface Wave Dissipation by a Vegetation Field

In this paper, we explore the use of coastal vegetation as a natural barrier to defend our shoreline from hazards caused by large wind waves, storm surges, and tsunamis. A numerical model based on XBeach is employed to evaluate the wave damping by vegetation. An explicit formula for the required drag coefficient used to help describe the additional force imposed by the vegetation is developed through a series of numerical experiments. Overall, our predictions agree reasonably with available laboratory data in the literature for various incident wave conditions and vegetation configurations. Our analysis suggests that a small unvegetated open space in the middle of a vegetation strip does not have a significant impact on the amount of wave height attenuation at the exit of the vegetated bed.

A drag force formula for heterogeneous granular flow systems based on finite average statistical method

The existing drag models are mostly based on the assumption of homogenous fluidization. However, the use of a homogeneous drag model to predict a heterogeneous granular flow system will cause a deviation. In this study, we developed a drag force model based on the assumption of heterogeneous fluidization. To prevent weakening of the heterogeneous characteristics in the drag force formula, we propose a finite average statistical method to filter the information of the heterogeneous granular cluster. The filtered information was used to fit the modified drag formula, which can reflect the heterogeneity of the granular cluster considering different configurations. A comparison shows that the new proposed drag formula filtered by the finite average statistical method fits well with energy minimization multi-scale simulation results.

A continuum model of drag and lift forces for inclined planes dragged through granular beds

Both drag and lift forces impact an inclined plane when it is dragged through a granular bed. In this paper, the following results have been obtained: the drag and lift forces grow with the velocity of motion; when the immersion depth is constant, the inclination angle has no effect on drag force, however, the lift force increases linearly with this inclination angle. In order to describe this physical process macroscopically, a continuum wedge model based on the Coulomb model is established to predict drag and lift forces. Particularly, the dynamic friction angle in the assumed shear band is predicted as a function of both inclined angle and moving velocity.

Pacific Lamprey drag force modeling to optimize fishway design

Typically, fish passage design is informed by a critical velocity model whereby fish are assumed to fail passage if the water velocity is higher than the critical swim speed, an assumption that may not be met when locomoting fish are partially submerged. We applied a drag force model (DFM) approach for use in design of Pacific Lamprey (Entosphenus tridentatus) Passage Structures (LPS) where lamprey may be partially or fully submerged. Our investigation assessed the dead-drag forces at four levels of static submergence: fully submerged (120 mm), equally submerged (40 mm), partially submerged (15 mm), and skin-flow (5 mm) for a Pacific Lamprey physical model by varying simulated LPS slope and discharge conditions. We then used the results to establish drag force thresholds corresponding to the known critical velocity thresholds of Pacific Lamprey to predict passage success under partial and full submergence conditions. Consideration of drag force in fish passage could be used to improve or create species-specific design recommendations for fishways, or to inform the design of barriers to prevent invasive species passage. The results suggest consideration of drag force in addition to velocity is beneficial to predict Pacific Lamprey passage success under partial submergence conditions.

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

AbstractThe present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.

Identification and Modeling of the Airbrake of an Experimental Unmanned Aircraft

This paper presents the modeling, system identification, simulation and flight testing of the airbrake of an unmanned experimental aircraft in frame of the FLEXOP H2020 EU project. As the aircraft is equipped with a jet engine with slow response an airbrake is required to increase deceleration after speeding up the aircraft for flutter testing in order to remain inside the limited airspace granted by authorities for flight testing. The airbrake consists of a servo motor, an opening mechanism and the airbrake control surface itself. After briefly introducing the demonstrator aircraft, the airbrake design and the experimental test benches the article gives in depth description of the modeling and system identification referencing also previous work. System identification consists of the determination of the highly nonlinear (saturated and load dependent) servo actuator dynamics and the nonlinear aerodynamic and mechanical characteristics including stiffness and inertia effects. New contributions relative to the previous work are a unified servo angular velocity limit model considering opening against the load or closing with it, the detailed construction and evaluation of airbrake normal and drag force models considering the whole deflection and aircraft airspeed range, the presentation of a unified aerodynamic - mechanic nonlinearity model giving direct relation between airbrake angle, dynamic pressure and servo torque and the transfer function-based modeling of stiffness and inertial effects in the mechanism. The identified servo dynamical model includes system delay, inner saturation, the aforementioned load dependent angular velocity limit model and a transfer function model. The servo model was verified based-on test bench measurements considering the whole opening angle and dynamic load range of the airbrake. New, unpublished measurements with gradually increasing servo load as the servo moves are also considered to verify the model in more realistic circumstances. Then the full airbrake model is constructed and tested in simulation to check realistic behavior. In the next step the airbrake model integrated into the nonlinear simulation model of the FLEXOP aircraft is tested by flying simulated test trajectories with the baseline controller of the aircraft in software-in-the-loop (SIL) Matlab simulation. First, the standalone airbrake simulation is compared to the SIL results to verify flawless integration of airbrake model into the nonlinear aircraft simulation. Then deceleration times with and without airbrake are compared underlining the usefulness of the airbrake in the test mission. Finally, real flight data is used to verify and update the airbrake model and show the effectiveness of the airbrake.

Multi-fluid modelling of hydrodynamics in a dual circulating fluidized bed

In this work, a multi-fluid model based on the Eulerian-Eulerian framework is used to study the gas-solid hydrodynamics, such as solid distribution, particle motion and solid velocity, in a three-dimensional (3D) dual circulating fluidized bed (DCFB). The influence of four different drag force models, including two classic models, i.e. Gidaspow, EMMS drag model and two recent drag models, i.e. Rong and Tang drag model, on hydrodynamics in DCFB are assessed. Numerical results show that the characteristics of solid distribution and velocity in different sections are distinct. For qualitative analysis, all the drag models can predict a reasonable radial solid distribution and pressure distribution, but only the EMMS, Rong and Tang drag model can capture the phenomenon of dense solid concentration in the low part. For quantitative analysis, the solid circulating rate predicted by the EMMS drag model is the closest to the experimental value while the Gidaspow drag model shows the most significant deviation. The overall assessments confirm that the drag model selection has a significant influence on the simulations of gas-solid flow in DCFBs. This study sheds lights on the design and optimization of fluidized bed apparatuses.

Expansion dynamics of atmospheric pressure helium plasma jet in ambient air

In this work, the expansion dynamics of a helium plasma jet in ambient air is examined. By using a fast imaging technique, the expansion of plasma jet from glass nozzle to air is captured which is in the form of plasma bullet propagating into the air. To understand the plasma bullet travel path from glass nozzle to plasma jet tip a drag force model is used. Moreover, the spatial variation of plasma density along the plasma jet length is estimated using drift velocity, plasma jet current and the cross-sectional area of the plasma jet. It is observed that the slight increase in plasma density is due to the combined effect of reduction of drift velocity, plasma jet current, and jet cross-sectional area. The obtained plasma density from glass nozzle to jet tip is in the range of (0.069-5.96) × 1012 cm−3. The above parameters can be of the essence in biological and industrial applications.

Thin interface limit of the double-sided phase-field model with convection.

The thin interface limit of the phase-field model is extended to include transport via melt convection. A double-sided model (equal diffusivity in liquid and solid phases) is considered for the present analysis. For the coupling between phase-field and Navier-Stokes equations, two commonly used schemes are investigated using a matched asymptotic analysis: (i) variable viscosity and (ii) drag force model. While for the variable viscosity model, the existence of a thin interface limit can be shown up to the second order in the expansion parameter, difficulties arise in satisfying no-slip boundary condition at this order for the drag force model. Nevertheless, detailed numerical simulations in two dimensions show practically no difference in dendritic growth profiles in the presence of forced melt flow obtained for the two coupling schemes. This suggests that both approaches can be used for the purpose of numerical simulations. Simulation results are also compared to analytic theory, showing excellent agreement for weak flow. Deviations at higher fluid velocities are discussed in terms of the underlying theoretical assumptions. This article is part of the theme issue 'Patterns in soft and biological matters'.

Computational fluid dynamic simulations of thermochemical conversion of pulverized biomass in a dilute flow using spheroidal approximation

A drag force model for spheroids, referred as the spheroid model, was implemented in OpenFOAM, in order to better predict the thermochemical conversion of pulverized biomass. Our previous work has found that the spheroid model predicts more dispersed results in terms of particle velocities and local concentrations comparing to other conventional particle models under non-reactive conditions. This work takes the spheroid model one step further, by validating against experiments performed under reactive conditions with a newly implemented heat transfer model for spheroids as well as updated devolatilization kinetic parameters. In addition, simulations were conducted in a configuration similar to a pilot-scale entrained flow gasifier for more realistic scenarios. Particle mass and axial velocity development were compared accordingly using four different modelling approaches with increasing complexity. When compared with models of spheroidal shape assumptions, the sphere and simplified non-sphere model predict 61% and 43% longer residence times, respectively. The combination of the spheroid shape assumption with the heat transfer model for spheroids tends to promote drying and devolatilization. On the other hand, the traditional spherical approach leads to longer particle residence times. These opposing effects are believed to be a major contributing factor to the fact that no significant differences among modelling approaches were found in terms of syngas production at the outlet. Furthermore, particle orientation information was reported in both experiments and simulations under reactive conditions. Its dependency on gas velocity gradient under reactive conditions is similar to what was reported under non-reactive conditions.

A Dynamic Coarse Grain Discrete Element Method for Gas-Solid Fluidized Beds by Considering Particle-Group Crushing and Polymerization

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is used extensively for the numerical simulation of gas-solid fluidized beds. In order to improve the efficiency of this approach, a coarse grain model of the DEM was proposed in the literature. In this model, a group of original particles are treated as a large-sized particle based on the initial particle distribution, and during the whole simulation process the number and components of these particle-groups remain unchanged. However, collisions between particles can lead to frequent crushing and polymerization of particle-groups. This fact has typically been ignored, so the purpose of this paper is to rationalize the coarse grain DEM-CFD model by considering the dynamic particle-group crushing and polymerization. In particular, the effective size of each particle-group is measured by a quantity called equivalent particle-group diameter, whose definition references the equivalent cluster diameter used by the energy-minimization multi-scale (EMMS) model. Then a particle-group crushing criterion is presented based on the mismatch between the equivalent diameter and actual diameter of a particle-group. As to the polymerization of two colliding particle-groups, their velocity difference after collision is chosen as a criterion. Moreover, considering the flow heterogeneity induced by the particle cluster formation, the EMMS drag force model is adopted in this work. Simulations are carried out by using a finite volume method (FVM) with non-staggered grids. For decoupling the Navier-Stokes equations, the semi-implicit method for pressure linked equations revised (SIMPLER) algorithm is used. The simulation results show that the proposed dynamic coarse grain DEM-CFD method has better performance than the original one.

Assessment of new thermospheric mass density model using NRLMSISE-00 model, GRACE, Swarm-C, and APOD observations

Thermospheric mass density estimates from in-situ observations along satellite orbits are difficult to validate due to their inherent spatiotemporal sparse nature, and difficulties related to drag-force modeling and estimation of actual mass density state. Current upper atmospheric models are unable to accurately represent the actual thermospheric variability, and in-situ observations are far to fulfill the minimum requirements in practical applications. In this manuscript, the new Thermospheric Mass Density Model (TMDM) is based on the fit of solar flux, annual, Local Solar Time (LST), and magnetospheric proxies into the Principal Component Analysis (PCA) of 13 years of accelerometer-based mass density estimates derived from the GRACE (Gravity Recovery and Climate Experiment) mission. We employ the NRLMSISE-00 model and estimates from APOD (Atmospheric density detection and Precise Orbit Determination), Swarm-C, and GRACE satellites, and assess the new model, including statistical analyses, and a Precise Orbit Determination (POD) scheme. We compare 2 years of APOD and Swarm-C estimates, and study the dynamic orbit propagation of the 3 missions under different mass density input schemes and different magnetospheric activity conditions. The results with TMDM show similar differences in the dynamically propagated orbits from NRLMSISE-00 and in-situ observations. The statistical analyses show that NRLMSISE-00 overestimates about 20%, and TMDM underestimates about 20%, the in-situ observations.

A Partially Orthogonal EnKF approach to atmospheric density estimation using orbital debris

A key requirement for accurate trajectory prediction and space situational awareness is knowledge of how non-conservative forces affect space object motion. These forces vary temporally and spatially, and are driven by the underlying behavior of space weather particularly in Low Earth Orbit (LEO). Existing trajectory prediction algorithms adjust space weather models based on calibration satellite observations. However, lack of sufficient data and mismodeling of non-conservative forces cause inaccuracies in space object motion prediction, especially for uncontrolled debris objects. The uncontrolled nature of debris objects makes them particularly sensitive to the variations in space weather. Our research takes advantage of this behavior by utilizing observations of debris objects to infer the space environment parameters influencing their motion.The hypothesis of this research is that it is possible to utilize debris objects as passive, indirect sensors of the space environment. We focus on estimating atmospheric density and its spatial variability to allow for more precise prediction of LEO object motion. The estimated density is parameterized as a grid of values, distributed by latitude and local sidereal time over a spherical shell encompassing Earth at a fixed altitude of 400 km. The position and velocity of each debris object are also estimated. A Partially Orthogonal Ensemble Kalman Filter (POEnKF) is used for assimilation of space object measurements to estimate density.For performance comparison, the scenario characteristics (number of objects, measurement cadence, etc.) are based on a sensor tasking campaign executed for the High Accuracy Satellite Drag Model project. The POEnKF analysis details spatial comparisons between the true and estimated density fields, and quantifies the improved accuracy in debris object motion predictions due to more accurate drag force models from density estimates. It is shown that there is an advantage to utilizing multiple debris objects instead of just one object. Although the work presented here explores the POEnKF performance when using information from only 16 debris objects, the research vision is to utilize information from all routinely observed debris objects. Overall, the filter demonstrates the ability to estimate density to within a threshold of accuracy dependent on measurement/sensor error. In the case of a geomagnetic storm, the filter is able to track the storm and provide more accurate density estimates than would be achieved using a simple exponential atmospheric density model or MSIS Atmospheric Model (when calm conditions are assumed).

Numerical investigation on vibration-induced two-phase distribution in a vertical annular channel

Earthquake vibrations have great impacts on two-phase flow in the reactor core. In this paper, numerical simulations were conducted to identify the air-water two-phase distribution in a vertical upward annular channel under horizontal vibration condition. The inner and outer diameter of the annular channel are 19.1 mm and 38.1 mm. The simulations were performed based on the two-fluid Euler-Euler modeling framework. Benchmark simulations for bubbly flow under stationary condition were firstly conducted to validate the up-to-date interfacial force models. Applicability of the interfacial force models were evaluated and a set of Ishii-Zuber drag force model, Tomiyama lift force model, Frank wall lubrication force model and Burns turbulent dispersion force model was found to provide the best agreement with experimental results. Based on this work, two-phase flow distributions under vibration condition were studied. Horizontal vibration of the annular channel was simulated by introducing simple harmonic motion. The vibration frequency and vibration amplitude were set to 1.97 Hz and 9.5 mm, respectively. Additional interfacial force caused by inertial effect was imposed on disperse bubbles under vibration condition, which promoted the lateral migration of bubbles. The numerical results showed that the distributions of local interfacial parameters varied periodically along the vibration direction. A maximum increase of about 32% was observed in the peak void fraction compared to that under stationary condition for case 3. But the distribution of local flow parameters remained unchanged in the direction perpendicular to the vibration. A good consistency between the simulation results and the experimental data was found. The comparison results indicate that the present modeling method is able to predict the two-phase distribution of bubbly flow under vibration condition. But an inhomogeneous model considering bubble interactions and grouping is suggested for two-phase flow beyond bubbly regime.

Effect of interfacial drag force model on code prediction for upward adiabatic two-phase bubbly flow in vertical channels

Accurate modeling of the interfacial drag force is one of the keys to predicting thermo-fluid parameters using one-dimensional nuclear thermal-hydraulic system analysis code architected through the two-fluid model. The interfacial drag force appears in the interfacial momentum transfer term and governs the velocity slip or the relative velocity between gas and liquid phases. The most straightforward method to model the interfacial drag force is to model the force through the drag law (drag law approach). A drag coefficient and interfacial area concentration should be given to close the interfacial drag force model. Among them, the modeling of the interfacial area concentration has been one of the weakest links in the interfacial drag force modeling due to the lack of reliable data covering a wide test condition including prototypic nuclear reactor conditions and lack of physically sound interfacial area model. To avoid a considerable uncertainty in the prediction of the interfacial area concentration, Andersen and Chu (1982) proposed the interfacial drag force model using the drift-flux parameters (Andersen approach). The Andersen approach is practical for the simulation of a slow transient flow and a steady flow. Major system analysis codes such as USNRC TRACE have adopted the Andersen approach in the interfacial drag force modeling. Some attempts to improve the code performance have been considered using the drag law approach with the interfacial area transport equation. The dynamic modeling of the interfacial area concentration has the potential to improve the prediction accuracy of the interfacial area concentration in a transient flow and developing flow. Due to the importance of the improved interfacial drag force modeling, the implementation and evaluation of the interfacial area transport equation in USNRC TRACE code has been performed by Talley et al. (2011, 2013). The study claimed that the introduction of the interfacial area transport equation into the TRACE code improved the code performance in an adiabatic bubbly flow analysis significantly. The present study assessed the code calculation made by Talley et al. (2011) and identified several issues in the code calculation results. The present study analytically demonstrated that the drag law approach became identical with the Andersen approach for the distorted particle regime (or a major bubble shape regime in bubbly flow) due to the balancing-out of the interfacial area concentration (or bubble size) in the numerator and denominator of the interfacial drag force formulation. The code calculation using TRAC code endorsed the analytical assessment of the insignificant or no merit of the interfacial area transport equation in the code performance of the adiabatic bubbly flow analysis. The present study also pointed out the inconsistency of the code calculation made by Talley et al. (2011).

A wake oscillator model with nonlinear coupling for the vortex-induced vibration of a rigid cylinder constrained to vibrate in the cross-flow direction

In this paper, a new wake oscillator model with nonlinear coupling is proposed for the modelling of vortex-induced vibration. The purpose is to develop a model that is capable of reproducing both free and forced vibration experiments. To achieve this goal, an existing van der Pol wake oscillator model is first reviewed. The limitations of the model are discussed and the influence of different drag force models on the dynamic characteristics of the fluctuating lift force that matches the forced vibration experiments are studied. Based on this model, nonlinear coupling terms are introduced to improve its predictive capabilities. The tuning of this improved model to the forced vibration shows a good agreement with experiments in terms of the added damping. However, the model failed to capture the negative added mass at high reduced velocities. As a result, the new model underpredicts both the range and frequency of lock-in in free vibration tests. To eliminate this discrepancy, the model is further enhanced by introducing frequency dependent nonlinear couplings, which are achieved in the time domain by means of convolution integrals. A single set of frequency dependent, complex-valued functions – which are the Laplace transforms of corresponding convolution kernels – that reproduce the forced vibration experiments is determined over a limited range of frequencies. However, no analytical extension of these functions to the infinite frequency domain was found such that the causality principle and the energy conservation would be satisfied. The latter is a major challenge for all existing wake oscillator models that aim at reproducing the forced vibration experiments.

Numerical simulation of fluidization for application in oxyfuel combustion

<p style='text-indent:20px;'>This paper is concerned with the simulation of multiphase flow hydrodynamics in an experimental oxyfuel fluidized bed combustor designed for biomass fuels. The aim is to perform cross-validation between several models and solvers that differ in the description of some phenomena in question. We focus on the influence of turbulence modeling, inter-phase drag force models, the presence of biomass in the mixture. Also the possibility to simplify the full 3D description to a quasi-1D model is tested. However, the results indicate that such simplification is not suitable for chaotic phenomena in considered scenarios. The models were developed using ANSYS Fluent and OpenFOAM CFD software packages as well as our in-house CFD code CFBSim. The quantities relevant for comparison (the densities of the dispersed solid phases and the phase velocities) are presented in the form of cross-section averaged vertical profiles.

Evaluation of the Performance of the Drag Force Model in Predicting Droplet Evaporation for R134a Single Droplet and Spray Characteristics for R134a Flashing Spray

Drag force plays an important role in determining the momentum, heat and mass transfer of droplets in a flashing spray. This paper conducts a comparative study to examine the performance of drag force models in predicting the evolution of droplet evaporation for R134a single droplet and spray characteristics for its flashing spray. The study starts from single moving R134a droplet vaporizing in atomispheric environment, to a fully turbulent, flashing spray caused by an accidental release of high-pressure R134a liquid in the form of a straight-tube nozzle, using in-house developed code and a modified sprayFoam solver in OpenFOAM, respectively. The effect of the nozzle diameter on the spray characteristics of R134a two-phase flashing spray is also examined. The results indicate that most of the drag force models have little effect on droplet evporation in both single isolated droplet modelling and fully two-phase flashing spray simulation. However, the Khan–Richardson model contributes to different results. In particular, it predicts a much different profile of the droplet diameter distribution and a much lower droplet temperature in the radial distance. The nozzle diameter has a significant impact on the flashing spray. A smaller diameter nozzle leads to more internse explosive atomization, shorter penetration distance, lower droplet diameter and velocity, and a faster temperature decrease.

Simulation on the effect of particle on flow hydrodynamics in a slurry bed

A combined Computational Fluid Dynamics and Population Balance Model (CFD-PBM) was developed to study the flow hydrodynamics of the slurry bed. The CFD-PBM applied a modified drag force model by considering the reduced drag force between gas and liquid phases at the presence of particle. Results show that the CFD-PBM with the modified drag force model can reasonably predict the flow hydrodynamics compared with the experimental data. It was predicted that the increased particle loading can enhance bubble coalescence to form larger bubbles, which can flow faster and reduce the gas holdup in the slurry bed. In addition, simulation results indicate that the particle flow becomes more non-uniform with much faster upward flow in the center and downward flow near the wall with the increase of superficial velocity. Particle back-mixing can be enhanced at higher superficial gas velocity, which can be beneficial for the reaction system with limited decrease in catalyst particle's reaction activity and unbeneficial for the reaction system with almost fully deactivation of catalyst.

Validation of the STEG code using PGV experiments on hydrodynamics of horizontal steam generator

The results of the validation of the STEG code using the experiments on the PGV test facility are presented. The PGV test facility (Electrogorsk, Russia) is a slice of the upper part of the horizontal steam generator for Russian type VVER reactors. The main aim of the tests is to investigate the influence of submerged perforated sheets (SPSs) with uniform and non-uniform perforation degrees on the hydrodynamics of two-phase water-steam flows. The brief description of the STEG code based on the 3D two-fluid model is presented. The crucial constitutive laws that allow an accurate simulation of the PGV tests are the correlation for SPS pressure drop and the interfacial drag force model. The SPS pressure drop is calculated with empirical correlation obtained at the PGV experimental data. It is demonstrated that three different models of interfacial drag force are necessary in different regions of the test facility (above the SPS, below the SPS and zone between the tube bundle and the SPS). The formulations of the models are presented. All experiments are analyzed using the STEG code. The peculiarities of the spatial two-phase flows have been established, and a quantitative comparison with experimental data (SPS pressure drops and void fractions) has been performed. It can be argued that the results generally indicate the relatively good predictive ability of the STEG code.