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.

Relevance of zero lift drag coefficient and lift coefficient to Mach number for large aspect ratio winged rigid body

Synthetic analysis is conducted to the wind tunnel experiment results of zero lift drag coefficient and lift coefficient for large aspect ratio winged rigid body.By means of wind tunnel experiment data,the dynamics model of the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body is amended.The research indicates that the change trends of zero lift drag coefficient and lift coefficient to Mach number are similar.The calculation result and wind tunnel experiment data all verify the validity of the amended dynamics model by which to estimate the zero lift drag coefficient and lift coefficient for the large aspect ratio winged rigid body,and thus providing some technical reference to aerodynamics character analysis of the same types of winged rigid body.

Analysis of Flow Structure and Calculation of Drag Coefficient for Concurrent-up Gas-Solid Flow

This study investigates the heterogeneous structure and its influence on drag coefficient for concurrent-up gas-solid flow. The energy-minimization multi-scale (EMMS) model is modified to simulate the variation of structure parameters with solids concentration, showing the tendency for particles to aggregate to form clusters and for fluid to pass around clusters. The global drag coefficient is resolved into that for the dense phase, for the dilute phase and for the so-called inter-phase, all of which can be obtained from their respective phase-specific structure parameters. The computational results show that the drag coefficients of the different phases are quite different, and the global drag coefficient calculated from the EMMS approach is much lower than that from the correlation of Wen and Yu. The simulation results demonstrate that the EMMS approach can well describe the heterogeneous flow structure, and is very promising for incorporation into the two-fluid model or the discrete particle model as the closure law for drag coefficient.

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.

Assessment of surface drag coefficient parametrizations based on observations and simulations using the Weather Research and Forecasting model

The drag coefficient is important in meteorological studies of the boundary layer because it describes the air-sea momentum flux. Eight drag coefficient schemes were assessed. These parametrizations were compared taking into account data from in situ and laboratory observations.The drag coefficients determined using three schemes were consistent with the level-off phenomenon, supported by the results of laboratory studies. The drag coefficient determined using one scheme decreased at wind speeds higher than approximately 30 m s-1, in agreement with indirect measurements under typhoon conditions. In contrast, the drag coefficients determined using the other four schemes increased with wind speed, even under high wind regimes. Sensitivity tests were performed using simulations of two super typhoons in the Weather Research and Forecasting model. While the typhoon tracks were negligibly sensitive to the parametrization used, the typhoon intensities （the maximum lO-m wind speed and the minimum sea level pressure）, sizes, and structure, were very sensitive to it.

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.

The Influence of Wave State and Sea Spray on Drag Coefficient from Low to High Wind Speeds

Ocean waves alter the roughness of sea surface,and sea spray droplets redistribute the momentum flux at the air-sea interface.Hence,both wave state and sea spray influence sea surface drag coefficient.Based on the new sea spray generation function which depends on sea surface wave,a wave-dependent sea spray stress is obtained.According to the relationship between sea spray stress and the total wind stress on the sea surface,a new formula of drag coefficient at high wind speed is acquired.With the analysis of the new drag coefficient,it is shown that the drag coefficient reduces at high wind speed,indicating that the sea spray droplets can limit the increase of drag coefficient.However,the value of high wind speed corresponding to the initial reduced drag coefficient is not fixed,and it depends on the wave state,which means the influence of wave cannot be ignored.Comparisons between the theoretical and measured sea surface drag coefficients in field and laboratory show that under different wave ages,the theoretical result of drag coefficient could include the measured data,and it means that the new drag coefficient can be used properly from low to high wind speeds under any wave state condition.

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.

Numerical study on the spatially varying drag coefficient in simulation of storm surges employing the adjoint method

From the simulation of storm surges resulting from Typhoons 7203 and 8509 in the Bohai Sea, Yellow Sea and East China Sea, water level data at tide stations are assimilated into a two-dimensional storm surge model, to study the spatially varying drag coefficient (DC) by employing the adjoint method. In this study, the DC at some grid points is uniformly selected as the independent DC, while the DC at other grid points is obtained through linear interpolation of the independent DC. The DC at independent points is optimized by employing the adjoint assimilation method, and global optimization is achieved by optimizing the independent DC. To demonstrate the method's performance, three comparative experiments are carried out. In the first experiment, the DC is treated as a constant. In the second and third experiments, the DC is derived using an empirical formula. Comparing the experimental results, it is found that the simulation accuracy for both Typhoons 7203 and 8509 increases greatly when optimizing the independent DC. However, the number of independent points makes no great difference to the precision of simulation. Moreover, the DC inverted from Typhoons 7203 and 8509 differs in some sea areas because of the different typhoon tracks. However, the spatial distribution of the inverted DC, for both Typhoons 7203 and 8509, demonstrates a clear effect of the DC on the storm surge modeling near the coastal areas where the DC is highest or lowest.

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.

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.

Impacts of Wave and Current on Drag Coefficient and Wind Stress over the Tropical and Northern Pacific

By taking into consideration the effects of ocean surface wave-induced Stokes drift velocity Un, and current velocity Uc on the drag coefficient, the spatial distributions of drag coefficient and wind stress in 2004 are computed over the tropical and northern Pacific using an empirical drag coefficient parameterization formula based on wave steepness and wind speed. The global ocean current field is generated from the Hybrid Coordinate Ocean Model （HYCOM） and the wave data are generated from Wavewatch Ill （WW3）. The spatial variability of the drag coefficient and wind stress is analyzed. Preliminary results indicate that the ocean surface Stokes drift velocity and current velocity exert an important influence on the wind stress. The results also show that consideration of the effects of the ocean surface Stokes drift velocity and current velocity on the wind stress can significantly improve the modeling of ocean circulation and air-sea interaction processes.

General formulas for drag coefficient and settling velocity of sphere based on theoretical law

The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number （Re） range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data （Re 〈 2 × 10^5）. The results show that the 2nd approximation of a rational function containing only one parameter can describe Co-Re relationship accurately over the whole Re range of 0-2× 10^5. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based Co-Re formulas giving the lowest sum of squared relative errors Qover the whole Re range （Re 〈 2 × 10^5）, a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.

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.