The Influence of Sea Sprays on Drag Coefficient at High Wind Speed

Field and laboratory observations indicate that the variation of drag coefficient with wind speed at high winds is different from that under low-to-moderate winds.By taking the effects of wave development and sea spray into account,a new parameterization of drag coefficient applicable from low to extreme winds is proposed.It is shown that,under low-to-moderate wind conditions so that the sea spray effects could be neglected,the nondimensional aerodynamic roughness first increases and then decreases with the increasing wave age;whereas under high wind conditions,the drag coefficient decreases with the increasing wind speed due to the modification of the logarithmic wind profile by the effect of sea spray droplets produced by bursting bubbles or wind tearing breaking wave crests.The drag coefficients and sea surface aerodynamic roughnesses reach their maximum values vary under different wave developments.Correspondingly,the reduction of drag coefficient under high winds reduces the increasing rate of friction velocity with increasing wind speed.

Drag Coefficient of a Non-Convex Polygonal Plate during Free Fall

Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.

Dependence of sea surface drag coefficient on wind-wave parameters

The relationships between sea surface roughness z 0 and wind-wave parameters are analyzed,and spurious self-correlations are found in all of the parameterization schemes.Sea surface drag coefficient C D is fitted by four wind-wave parameters that are wave age,wave steepness,windsea Reynolds number R B and R H ,and the analyzed data are divided into laboratory,field and combined data sets respectively.Comparison and analysis of dependence of C D on wind-wave parameters show that R B can fit the C D most appropriately.Wave age and wave steepness are not suitable to fit C D with a narrow range data set.When the value of wave age has a board range,R H is not suitable to fit C D either.Three relationships between C D and R B are integrated into the bulk algorithm COARE to calculate the observational friction velocity,and the results show that the relationship between C D and R B which is fitted with field data set can describe the momentum transfer in the open ocean,under low-moderate wind speed condition,most appropriately.

Introduction of parameterized sea ice drag coefficients into ice free-drift modeling

Many interesting characteristics of sea ice drift depend on the atmospheric drag coefficient （Ca） and oceanic drag coefficient （Cw）. Parameterizations of drag coefficients rather than constant values provide us a way to look insight into the dependence of these characteristics on sea ice conditions. In the present study, the parameterized ice drag coefficients are included into a free-drift sea ice dynamic model, and the wind factor a and the deflection angle θ between sea ice drift and wind velocity as well as the ratio of Ca to Cw are studied to investigate their dependence on the impact factors such as local drag coefficients, floe and ridge geometry. The results reveal that in an idealized steady ocean, Ca/Cw increases obviously with the increasing ice concentration for small ice floes in the marginal ice zone, while it remains at a steady level （0.2-0.25） for large floes in the central ice zone. The wind factor a increases rapidly at first and approaches a steady level of 0.018 when A is greater than 20%. And the deflection angle ~ drops rapidly from an initial value of approximate 80° and decreases slowly as A is greater than 20% without a steady level like a. The values of these parameters agree well with the previously reported observations in Arctic. The ridging intensity is an important parameter to determine the dominant contribution of the ratio of skin friction drag coefficient （Cs＇/Cs） and the ratio of ridge form drag coefficient （Cr＇/Cr） to the value of Ca/Cw, a, and 8, because of the dominance of ridge form drag for large ridging intensity and skin friction for small ridging intensity among the total drag forces. Parameterization of sea ice drag coefficients has the potential to be embedded into ice dynamic models to better account for the variability of sea ice in the transient Arctic Ocean.

On the parameterization of drag coefficient over sea surface

Six parameterization schemes of roughness or drag coefficient are evaluated on the basis of the data from six experiments. They present great consistency with measurement when friction velocity u＊〈0.5 m/s （ap- proximately corresponding to 10 m wind speed U10〈 12 m/s） and large deviation from measurement when u＊≥0.5 m/s （approximately U10 ≥ 12 m/s）. In order to improve the deviation, a new parameterization of drag coefficient is derived on the basis of the similarity theory, Charnock relationship and Toba 3/2 power law. Wave steepness and wind-sea Reynolds number are considered in the new parameterization. Then it is test- ed on the basis of the measurements and shows significant improvement when u＊≥0.5 m/s. Its standard errors are much smaller than the ones of the other six parameterizations. However, the new parameteriza- tion still needs more tests especially for high winds.

A rapid assessment method for calculating the drag coefficient in wave attenuation by vegetation

Vegetation in wetlands is a large-scale nature-based resource that can provide multiple benefits to human beings and the environment,such as wave attenuation in coastal zones.Traditionally,there are two main calibration approaches to calculate the attenuation of wave driven by vegetation.The first method is a straightforward one based on the exponential attenuation of wave height in the direction of wave transmission,which,however,overlooks the crucial drag coefficient(CD).The other method is in accordance with more complicate equations for predicting the damping factor,which is regarded as a function of CD.In this study,a new relation,combining these above two conventional approaches,is proposed to predict the CD in an operative approach.Results show that values yielded by the new assessment method perform a strong linear relationship with a collection of historical observations,with a promising R2 value of 0.90.Besides,the linear regression derives a new predictive equation for the bulk drag coefficient.Additionally,a calibrated value of 4 for the empirical plant drag coefficient(CP)is revealed.Overall,this new equation,with the superiority of the convenient exponential regression,is expected to be a rapid assessment method for calculating wave attenuation by vegetation and predicting the drag coefficient.

Determination of the Drag Coefficient over the Tibetan Plateau

In this paper,a preliminary study is given on the drag (i.e.bulk transfer for momentum) coefficient,on the basis of data from four sets of AWS in Tibet during the first observational year from July 1993 to July 1994 according to China Japan Asian Monsoon Cooperative Research Program.The results show that the drag coefficient over the Tibetan Plateau is 3.3 to 4.4×103.In addition,monthly and diurnal variations of drag coefficient and the relationship among the drag coefficients and the bulk Richardson number,surface roughness length and wind speed at 10 m height are discussed in detail.

Wind speed scaling and the drag coefficient

Wind speed scaling in similarity law in wind-generated waves and the drag coefficient are studied. In analyzing the data in the wind wave channel, it is found that the u＊ scaling greatly reduces the scatter in the U10 scaling. The u＊ scaling has much less scatter than the scaling using other wind speeds. The friction velocity seems to play a distinctive role in wave growth. The result is important in the applications of the similarity law and in wave modeling. In theory it gives an insight into the mechanism of wind wave interaction. It is found that wave steepness is important in influencing the drag coefficient. The variability of the coefficients in the currently widely used drag form can be explained by the differences in wave steepness in the observations. A drag coefficient model with wind speed and wave steepness as parameters is proposed. An explanation for Kahma＇s result that the u, scaling does not reduce the scatter in the U10 scaling is given.

Simulation on hydrodynamics of non-spherical particulate system using a drag coefficient correlation based on artificial neural network

Fluidization of non-spherical particles is very common in petroleum engineering.Understanding the complex phenomenon of non-spherical particle flow is of great significance.In this paper,coupled with two-fluid model,the drag coefficient correlation based on artificial neural network was applied in the simulations of a bubbling fluidized bed filled with non-spherical particles.The simulation results were compared with the experimental data from the literature.Good agreement between the experimental data and the simulation results reveals that the modified drag model can accurately capture the interaction between the gas phase and solid phase.Then,several cases of different particles,including tetrahedron,cube,and sphere,together with the nylon beads used in the model validation,were employed in the simulations to study the effect of particle shape on the flow behaviors in the bubbling fluidized bed.Particle shape affects the hydrodynamics of non-spherical particles mainly on microscale.This work can be a basis and reference for the utilization of artificial neural network in the investigation of drag coefficient correlation in the dense gas-solid two-phase flow.Moreover,the proposed drag coefficient correlation provides one more option when investigating the hydrodynamics of non-spherical particles in the gas-solid fluidized bed.

Numerical Analysis of Turbulent Fluid Flow and Drag Coefficient for Optimizing the AUV Hull Design

Autonomous Underwater Vehicles (AUVs) are robots able to perform tasks without human intervention (remote operators). Research and development of this class of vehicles has growing, due to the excellent characteristics of the AUVs to operate in different situations. Therefore, this study aims to analyze turbulent single fluid flow over different geometric configurations of an AUV hull, in order to obtain test geometry that generates lower drag force, which reduces the energy consumption of the vehicle, thereby increasing their autonomy during operation. In the numerical analysis was used ANSYS-CFX&#174 11.0 software, which is a powerful tool for solving problems involving fluid mechanics. Results of the velocity (vectors and streamlines), pressure distribution and drag coefficient are showed and analyzed. Optimum hull geometry was found. Lastly, a relationship between the geometric parameters analyzed and the drag coefficient was obtained.

Numerical Study on the Drag Coefficients of Sphere and Double Spheres

Winds on the earth are commonly strong enough to erode transport and deposit sediment. The modes of sand transport by the wind are greatly different from those by water flow. On the other hand wind-blown sands are of a material circulation process of the earth surface. They affect wind-sand transport flux and sand ejection of a flux, the damage of grains formed cannot be neglected in engineering. Because of the complexity of windblown sand flux system, the understanding of its basic mechanics is not yet clear. The key forces in sand salutation mainly includes： the valid gravity, air drag force ＇Magnus force＇ Saffman force ＇Basset force＇ additional quality force and scatter force among grains. The most important force in sand salutation is the air drag force. Computation of the single sphere drag coefficient and double spheres drag coefficient is presented for the distance between two spheres being smaller than twelve times of the sphere diameter and the spheres being at different angular positions. The flow interference of two spheres was investigated for the distance s = 0.08 d to 12d, angular position 0 = 0 to 360 and Reynolds number 15≤Re≤1000.

EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities. We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient, respectively, for small driving force and for large driving force. In the case of small driving force, the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential. The effective drag coefficient is increased by approximately the same factor. As a result, the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small. For moderately large driving force, both the effective diffusion and the effective drag coefficient are increased from their Brownian values, and the Einstein relation breaks down. In the limit of very large driving force, both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.

A novel predictive model of drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids

In oil and gas well drilling operations,it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings in non-Newtonian drilling fluids.In this paper,the free-falling of 172 groups of spheres and 522 groups of irregular-shaped sand particles in Newtonian/non-Newtonian fluids were investigated experimentally.It was found that the drag coefficient calculated based on Newtonian correlations can result in a significant error when the particle settles in the non-Newtonian fluid.Therefore,predictive models of drag coefficient were established respectively for different types of fluids.The validity of the proposed drag coefficient model of spheres was verified by comparing it with the previous works.On this basis,the drag coefficient model of irregular-shaped sand particles was established by introducing a shape factor.The models do not use the shape factor that requires detailed threedimensional shape and size information.Instead,two-dimensional geometric information(circularity)is obtained via image analysis techniques.The present new models predict the settling velocity of sand particles in the power-law fluid and Herschel-Bulkley fluid accurately with a mean relative error of5.03%and 6.74%,respectively,which verifies the accuracy of the model.

Effects of Drag Coefficients on Surface Heat Flux during Typhoon Kalmaegi (2014)

The lack of in situ observations and the uncertainties of the drag coefficient at high wind speeds result in limited understanding of heat flux through the air-sea interface and thus inaccurate estimation of typhoon intensity in numerical models.In this study,buoy observations and numerical simulations from an air-sea coupled model are used to assess the surface heat flux changes and impacts of the drag coefficient parameterization schemes on its simulations during the passage of Typhoon Kalmaegi(2014).Three drag coefficient schemes,which make the drag coefficient increase,level off,and decrease,respectively,are considered.The air-sea coupled model captured both trajectory and intensity changes better than the atmosphere-only model,though with relatively weaker sea surface cooling(SSC)compared to that captured by buoy observations,which led to relatively higher heat flux and thus a stronger typhoon.Different from previous studies,for a moderate typhoon,the coupled simulation with the increasing drag coefficient scheme outputted an intensity most consistent with the observation because of the strongest SSC,reasonable ratio of latent and sensible heat exchange coefficients,and an obvious reduction in the overestimated surface heat flux among all experiments.Results from sensitivity experiments showed that surface heat flux was significantly determined by the drag coefficient-induced SSC rather than the resulting wind speed changes.Only when SSC differs indistinctively(<0.4°C)between the coupled simulations,heat flux showed a weak positive correlation with the drag coefficient-impacted 10-m wind speed.The drag coefficient also played an important role in decreasing heat flux even a long time after the passage of Kalmaegi because of the continuous upwelling from deeper ocean layers driven by the impacted momentum flux through the air-sea interface.

Periodic Variations of Drag Coefficient for the ANDE Spherical Satellites During its Lifetime

A drag coefficient(C_d) inversion method is introduced to study the variations of the drag coefficient for orbital satellites with spherical geometry.Drag coefficients of the four micro satellites in the Atmospheric Neutral Density Experiment(ANDE) are compiled out with this new method. The Lomb-Scargle Periodgram(LSP) analysis of the four ANDE satellites' C__d series has shown that there are obvious 5,7,9,and 27 days' period in those data.Interesting results are found through comparing the LSP analysis with series of the daily solar radio flux at 10.7cm(F_(10.7) index),the Ap index,and the daily averaged solar wind speed at 1AU.All series in the same time interval have an obvious period of about 27 days,which has already been explained as the association with the 27 days' solar rotation.The oscillating periods less than 27 days are found in series of C_D,Ap and solar wind speed at 1 AU,e.g.,the 5,7,9 days period.However,these short periods disappeared in the time series of F_(10.7) index.The same periodicities of 5,7,9 days in Ap and solar wind are presented at the same time interval during the declining phase of solar cycle 23.While in the ascending phase of solar cycle 24,these short oscillations are not so obvious as that in the declining phase of solar cycle 23.These results provide definite evidence that the C_d variations with period of 5,7 and 9 days are produced by a combination of space weather effects caused by the solar wind and geomagnetic activity.

Characteristics of Drag Coefficient in Different Coastal Regions of the South China Sea Under Tropical Cyclones-An Observational Study

To investigate the values of 10-m drag coefficient(CD ) in different coastal areas under the influence of tropical cyclones, the present study used the observational data from four towers in different coastal areas of the South China Sea(SCS) during six tropical cyclone(TC) passages, and employed the eddy covariance method and the flux profile method.The analysis of footprint showed that the fluxes at Zhizai Island(ZZI), Sanjiao Island(SJI) and Donghai Island(DHI)were influenced basically by the ocean, and the flux at Shangyang Town(SYT) was influenced mainly by the land. The results showed that the dependence relationships of CD on 10-m wind speed(U10) in four different coastal areas under the influence of TCs were different. CD at ZZI and SJI initially increased and then decreased as U10 increased, similar to the pattern over the ocean. CD at ZZI and SJI represented the values over shallow water with seawater depths of ~7 m and ~2 m, respectively. Moreover, the critical wind speed at which CD peaked gradually decreased as the seawater depth became shallower in the coastal areas. CD at DHI and SYT decreased monotonously as U10 increased, similar to the pattern over the land. CD at DHI represented the value over the transition zone from shallow water to coastal land, and CD at SYT represented the value over the coastal land. Meanwhile, the eddy covariance method and the flux profile method were compared at ZZI and SYT during TC passages. It was found that their CD values obtained by the two methods were close. Finally, the parameterizations of observed u*and CD as a function of U10 over four different coastal areas were given under the influence of high winds. These parameterizations of observed CD may be used in high-resolution numerical models for landfalling TC forecast.

A STUDY OF DRAG COEFFICIENT RELATED WITH VEGETATION BASED ON THE FLUME EXPERIMENT

This study is focused on the effects of ecological factors （diameter and flexibility） and vegetation community composition on the drag coefficient related with vegetation. The single leafy shrub and three mixed communities （including shrub-grass, shrub-reed and reed-grass community） were studied. The flow velocity and water level were measured and used to calculate the drag coefficient based on the Bernoulli＇s equation, Darcy drag formula and the expression for the drag coefficient related with Darcy drag factor. The trend of the drag coefficient in the vertical direction was analyzed against flow depth, diameter, diameter P（eynolds number, flow depth Reynolds number and relative roughness height in different discharges. The results show that beside the dense leafy shrubs community, the vertical trend of the drag coefficient among other cases against flow depth, diameter, diameter Reynolds number, flow depth Reynolds number and relative roughness height can be approximately expressed by power law functions under different flow discharges. Moreover, in a mixed community with two plants with distinctly different ecological factors, the one with the most distinct variations of ecological factors determines the vertical trend of the drag coefficient; the other one only affects the magnitude of the drag coefficient. Furthermore, if the ecological factors of the vegetation in the vertical direction are kept almost not changed, the drag coefficient can be approximately regarded as a constant.

CFD modeling of pressure drop and drag coefficient in fixed beds:Wall effects

Simulations of fixed beds having column to particle diameter ratio （D/dp） of 3, 5 and 10 were performed in the creeping, transition and turbulent flow regimes, where Reynolds number （dpVLρL/μL） was varied from 0.1 to 10,000. The deviations from Ergun＇s equation due to the wall effects, which are important in D/dp 〈 15 beds were well explained by the CFD simulations. Thus, an increase in the pressure drop was observed due to the wall friction in the creeping flow, whereas, in turbulent regime a decrease in the pressure drop was observed due to the channeling near the wall. It was observed that, with an increase in the D/dp ratio, the effect of wall on drag coefficient decreases and drag coefficient nearly approaches to Ergun＇s equation. The predicted drag coefficient values were in agreement with the experimental results reported in the literature, in creeping flow regime, whereas in turbulent flow the difference was within 10-15%.

Instability analysis and drag coefficient prediction on a swept RAE2822 wing with constant lift coefficient

Swept wing is widely used in civil aircraft,whose airfoil is chosen,designed and optimized to increase the cruise speed and decrease the drag coefficient.The parameters of swept wing,such as sweep angle and angle of attack,are determined according to the cruise lift coefficient requirement,and the drag coefficient is expected to be predicted accurately,which involves the instability characteristics and transition position of the flow.The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically,and then the mean flow is calculated by solving the boundary layer（BL） equation with spectral method.The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory（LST）,and the transition position is predicted by eNmethod.The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator.A simple approach to calculate the lift coefficient of swept wing is proposed.It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant;when the angle of attack is small,the flow on the leeward of the wing is stable.when the angle of attack is larger than 3°,the flow becomes unstable quickly;with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable,leading to the moving forward of the transition position to the leading edge of the wing;the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward;the optimal range of sweep angle for civil aircraft is suggested.

Prediction of interphase drag coefficient and bed expansion using a variational model for fluidization of small spherical particles

In this study,we applied the variational model to fluidization of small spherical particles.Fluidization experiments were carried out for spherical particles with 13 diameters between dp=0.13 and 5.00 mm.We propose a generalized form of our variational model to predict the superficial velocity U and interphase drag coefficientβby introducing an exponent n to describe the different dependences of the drag force Fd on fluid velocity for different particle sizes(different flow regimes).By comparing the predictions with the experimental results,we conclude that n=1 should be used for small particles(dp<1 mm)and n=2 for larger particles(dp>1 mm).This conclusion is generalized by proposing n=1 for particles with Ret<160 and n=2 for particles with Ret>160.The average mean absolute error was 5.49%in calculating superficial velocity for different bed voidages using the modified variational model for all of the particles examined.The calculated values ofβwere compared with values of literature models for particles with dp<1.0 mm.The average mean absolute error of the modified variational model was 8.02%in calculatingβfor different bed voidages for all of the particles examined.