Drag coefficients with applications to satellite orbits

In the last twenty or so years the results of theory and experiment have produced much information on the characteristics of gas-surface interactions relevant to a satellite in hyperthermal free-molecular flow. This thesis contains reviews of the rarefied gas dynamics applicable to satellites and has attempted to compare existing models of gas-surface interaction with contemporary knowledge of such systems. It is shown that a more natural approach would be to characterise the gas-surface interaction using the normal and tangential momentum accommodation coefficients, igma' and igma respectively, specifically in the form igma = constant , igma' = igma'0 -igma'1sec i where i is the angle subtended between the incident flow and the surface normal and igma,igma'0 and igma'1 are constants. Adopting these relationships, the effects of atmospheric lift on inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS-1 (1974-70A) show that the observed perturbation in i can be ascribed primarily to non-zero igma'1 whilst perturbations in a and e produce constraint equations between the three parameters. The numerical results seem to imply that a good theoretical orbit is achieved despite a much lower drag coefficient than anticipated by earlier theories.

Minimum drag profiles in infinite cavity flows

The problem considered is that of minimizing the drag of a symmetric plate in infinite cavity flow under the constraints of fixed arclength and fixed chord. The flow is assumed to be steady, irrotational, and incompressible. The effects of gravity and viscosity are ignored.

Using complex variables, expressions for the drag, arclength, and chord, are derived in terms of two hodograph variables, Γ (the logarithm of the speed) and β (the flow angle), and two real parameters, a magnification factor and a parameter which determines how much of the plate is a free-streamline.

Two methods are employed for optimization:

(1) The parameter method. Γ and β are expanded in finite orthogonal series of N terms. Optimization is performed with respect to the N coefficients in these series and the magnification and free-streamline parameters. This method is carried out for the case N = 1 and minimum drag profiles and drag coefficients are found for all values of the ratio of arclength to chord.

(2) The variational method. A variational calculus method for minimizing integral functionals of a function and its finite Hilbert transform is introduced, This method is applied to functionals of quadratic form and a necessary condition for the existence of a minimum solution is derived. The variational method is applied to the minimum drag problem and a nonlinear integral equation is derived but not solved.

How to parametrize urban-canopy drag to reproduce wind-direction effects within the canopy

The mean wind direction within an urban canopy changes with height when the incoming flow is not orthogonal to obstacle faces. This wind-turning effect is induced by complex processes and its modelling in urban-canopy (UC) parametrizations is difficult. Here we focus on the analysis of the spatially-averaged flow properties over an aligned array of cubes and their variation with incoming wind direction. For this purpose, Reynolds-averaged Navier–Stokes simulations previously compared, for a reduced number of incident wind directions, against direct numerical simulation results are used. The drag formulation of a UCparametrization ismodified and different drag coefficients are tested in order to reproduce the wind-turning effect within the canopy for oblique wind directions. The simulations carried out for a UC parametrization in one-dimensional mode indicate that a height-dependent drag coefficient is needed to capture this effect.

The effect of a new drag-law parameterization on ice shelf water plume dynamics

A drag law accounting for Ekman rotation adjacent to a flat, horizontal bou ndary is proposed for use in a plume model that is written in terms of the depth-mean velocity. The drag l aw contains a variable turning angle between the mean velocity and the drag imposed by the turbulent bound ary layer. The effect of the variable turning angle in the drag law is studied for a plume of ice shelf wat er (ISW) ascending and turning beneath an Antarctic ice shelf with draft decreasing away from the groundi ng line. As the ISW plume ascends the sloping ice shelf–ocean boundary, it can melt the ice shelf, wh ich alters the buoyancy forcing driving the plume motion. Under these conditions, the typical turning ang le is of order 10° over most of the plume area for a range of drag coefficients (the minus sign arises for th e Southern Hemisphere). The rotation of the drag with respect to the mean velocity is found to be signifi cant if the drag coefficient exceeds 0.003; in this case the plume body propagates farther along and across the b ase of the ice shelf than a plume with the standard quadratic drag law with no turning angle.

Impact of variable atmospheric and oceanic form drag on simulations of Arctic sea ice

Over Arctic sea ice, pressure ridges and floe andmelt pond edges all introduce discrete obstructions to the flow of air or water past the ice and are a source of form drag. In current climate models form drag is only accounted for by tuning the air–ice and ice–ocean drag coefficients, that is, by effectively altering the roughness length in a surface drag parameterization. The existing approach of the skin drag parameter tuning is poorly constrained by observations and fails to describe correctly the physics associated with the air–ice and ocean–ice drag. Here, the authors combine recent theoretical developments to deduce the total neutral form drag coefficients from properties of the ice cover such as ice concentration, vertical extent and area of the ridges, freeboard and floe draft, and the size of floes and melt ponds. The drag coefficients are incorporated into the Los Alamos Sea Ice Model (CICE) and show the influence of the new drag parameterization on the motion and state of the ice cover, with the most noticeable being a depletion of sea ice over the west boundary of the Arctic Ocean and over the Beaufort Sea. The new parameterization allows the drag coefficients to be coupled to the sea ice state and therefore to evolve spatially and temporally. It is found that the range of values predicted for the drag coefficients agree with the range of values measured in several regions of the Arctic. Finally, the implications of the new form drag formulation for the spinup or spindown of the Arctic Ocean are discussed.

Wingbeat frequency and the body drag anomaly: wind-tunnel observations on a thrush nightingale (Luscinia Luscinia) and a teal (Anas crecca)

A teal (Anas crecca) and a thrush nightingale (Luscinia luscinia) were trained to fly in the Lund wind tunnel for periods of up to 3 and 16 h respectively. Both birds flew in steady flapping flight, with such regularity that their wingbeat frequencies could be determined by viewing them through a shutter stroboscope. When flying at a constant air speed, the teal's wingbeat frequency varied with the 0.364 power of the body mass and the thrush nightingale's varied with the 0.430 power. Both exponents differed from zero, but neither differed from the predicted value (0.5) at the 1 % level of significance. The teal continued to flap steadily as the tunnel tilt angle was varied from -1° (climb) to +6° (descent), while the wingbeat frequency declined progressively by about 11%. In both birds, the plot of wingbeat frequency against air speed in level flight was U-shaped, with small but statistically significant curvature. We identified the minima of these curves with the minimum power speed (Vmp) and found that the values predicted for Vmp, using previously published default values for the required variables, were only about two-thirds of the observed minimum-frequency speeds. The discrepancy could be resolved if the body drag coefficients (CDb) of both birds were near 0.08, rather than near 0.40 as previously assumed. The previously published high values for body drag coefficients were derived from wind-tunnel measurements on frozen bird bodies, from which the wings had been removed, and had long been regarded as anomalous, as values below 0.01 are given in the engineering literature for streamlined bodies. We suggest that birds of any size that have well-streamlined bodies can achieve minimum body drag coefficients of around 0.05 if the feet can be fully retracted under the flank feathers. In such birds, field observations of flight speeds may need to be reinterpreted in the light of higher estimates of Vmp. Estimates of the effective lift:drag ratio and range can also be revised upwards. Birds that have large feet or trailing legs may have higher body drag coefficients. The original estimates of around CDb=0.4 could be correct for species, such as pelicans and large herons, that also have prominent heads. We see no evidence for any progressive reduction of body drag coefficient in the Reynolds number range covered by our experiments, that is 21600-215 000 on the basis of body cross-sectional diameter.

Experimental Investigation of the Hydrodynamic Coefficients of a Remotely Operated Vehicle Using a Planar Motion Mechanism

The determination of hydrodynamic coefficients of full scale underwater vehicles using system identification (SI) is an extremely powerful technique. The procedure is based on experimental runs and on the analysis of on-board sensors and thrusters signals. The technique is cost effective and it has high repeatability; however, for open-frame underwater vehicles, it lacks accuracy due to the sensors' noise and the poor modeling of thruster-hull and thruster-thruster interaction effects. In this work, forced oscillation tests were undertaken with a full scale open-frame underwater vehicle. These conducted tests are unique in the sense that there are not many examples in the literature taking advantage of a PMM installation for testing a prototype and; consequently, allowing the comparison between the experimental results and the ones estimated by parameter identification. The Morison's equation inertia and drag coefficients were estimated with two parameter identification methods, that is, the weighted and the ordinary least-squares procedures. It was verified that the in-line force estimated from Morison's equation agrees well with the measured one except in the region around the motion inversion points. On the other hand, the error analysis showed that the ordinary least-squares provided better accuracy and, therefore, was used to evaluate the ratio between inertia and drag forces for a range of Keulegan-Carpenter and Reynolds numbers. It was concluded that, although both experimental and estimation techniques proved to be powerful tools for evaluation of an open-frame underwater vehicle's hydrodynamic coefficients, the research provided a rich amount of reference data for comparison with reduced models as well as for dynamic motion simulation of ROVs. [DOI: 10.1115/1.4004952]

Discrete Vortex Method-Based Model for Ground-Effect Studies

A discrete vortex method-based model has been proposed for two-dimensional/three-dimensional ground-effect prediction. The model merely requires two-dimensional sectional aerodynamics in free flight. This free-flight data can be obtained either from experiments or a high-fidelity computational fluid dynamics solver. The first step of this two-step model involves a constrained optimization procedure that modifies the vortex distribution on the camber line as obtained from a discrete vortex method to match the free-flight data from experiments/computational fluid dynamics. In the second step, the vortex distribution thus obtained is further modified to account for the presence of the ground plane within a discrete vortex method-based framework. Whereas the predictability of the lift appears as a natural extension, the drag predictability within a potential flow framework is achieved through the introduction of what are referred to as drag panels. The need for the use of the generalized Kutta-Joukowski theorem is emphasized. The extension of the model to three dimensions is by the way of using the numerical lifting-line theory that allows for wing sweep. The model is extensively validated for both two-dimensional and three-dimensional ground-effect studies. The work also demonstrates the ability of the model to predict lift and drag coefficients of a high-lift wing in ground effect to about 2 and 8% accuracy, respectively, as compared to the results obtained using a Reynolds-averaged Navier-Stokes solver involving grids with several million volumes. The model shows a lot of promise in design, particularly during the early phase.

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

On the effects of turbulence modelling in design optimisation for high-lift devices

Aerodynamic shape optimisation is being increasingly utilised as a design tool in the aerospace industry. In order to provide accurate results, design optimisation methods rely on the accuracy of the underlying CFD methods applied to obtain aerodynamic forces for a given configuration. Previous studies of the authors have highlighted that the variation of the order of accuracy of the CFD solver with a fixed turbulence model affects the resulting optimised airfoil shape for a single element airfoil. The accuracy of the underlying CFD model is even more relevant in the context of high-lift configurations where an accurate prediction of flow is challenging due to the complex flow physics involving transition and flow separation phenomena. This paper explores the effect of the fidelity of CFD results for a range of turbulence models within the context of the computational design of aircraft configurations. The NLR7301 multi-element airfoil (main wing and flap) is selected as the baseline configuration, because of the wealth of experimental an computational results available for this configuration. An initial validation study is conducted in order to establish optimal mesh parameters. A bi-objective shape optimisation problem is then formulated, by trying to reveal the trade-off between lift and drag coefficients at high angles of attack. Optimisation of the airfoil shape is performed with Spalart-Allmaras, k - ω SST and k - o realisable models. The results indicate that there is consistent and complementary impact to the optimum level achieved from all the three different turbulence models considered in the presented case study. Without identifying particular superiority of any of the turbu- lence models, we can say though that each of them expressed favourable influence towards different optimality routes. These observations lead to the exploration of new avenues for future research. © 2012 AIAA.

On the effects of turbulence modelling in design optimisation for high-lift devices

Aerodynamic shape optimisation is being increasingly utilised as a design tool in the aerospace industry. In order to provide accurate results, design optimisation methods rely on the accuracy of the underlying CFD methods applied to obtain aerodynamic forces for a given configuration. Previous studies of the authors have highlighted that the variation of the order of accuracy of the CFD solver with a fixed turbulence model affects the resulting optimised airfoil shape for a single element airfoil. The accuracy of the underlying CFD model is even more relevant in the context of high-lift configurations where an accurate prediction of flow is challenging due to the complex flow physics involving transition and flow separation phenomena. This paper explores the effect of the fidelity of CFD results for a range of turbulence models within the context of the computational design of aircraft configurations. The NLR7301 multi-element airfoil (main wing and flap) is selected as the baseline configuration, because of the wealth of experimental an computational results available for this configuration. An initial validation study is conducted in order to establish optimal mesh parameters. A bi-objective shape optimisation problem is then formulated, by trying to reveal the trade-off between lift and drag coefficients at high angles of attack. Optimisation of the airfoil shape is performed with Spalart-Allmaras, k - ω SST and k - ε realisable models. The results indicate that there is consistent and complementary impact to the optimum level achieved from all the three different turbulence models considered in the presented case study. Without identifying particular superiority of any of the turbu- lence models, we can say though that each of them expressed favourable influence towards different optimality routes. These observations lead to the exploration of new avenues for future research. © 2012 by the authors.

The impact of variable sea ice roughness on changes in Arctic Ocean surface stress: a model study

The Arctic sea ice cover is thinning and retreating, causing changes in surface roughness that in turn modify the momentum flux from the atmosphere through the ice into the ocean. New model simulations comprising variable sea ice drag coefficients for both the air and water interface demonstrate that the heterogeneity in sea ice surface roughness significantly impacts the spatial distribution and trends of ocean surface stress during the last decades. Simulations with constant sea ice drag coefficients as used in most climate models show an increase in annual mean ocean surface stress (0.003 N/m2 per decade, 4.6%) due to the reduction of ice thickness leading to a weakening of the ice and accelerated ice drift. In contrast, with variable drag coefficients our simulations show annual mean ocean surface stress is declining at a rate of -0.002 N/m2 per decade (3.1%) over the period 1980-2013 because of a significant reduction in surface roughness associated with an increasingly thinner and younger sea ice cover. The effectiveness of sea ice in transferring momentum does not only depend on its resistive strength against the wind forcing but is also set by its top and bottom surface roughness varying with ice types and ice conditions. This reveals the need to account for sea ice surface roughness variations in climate simulations in order to correctly represent the implications of sea ice loss under global warming.

Modelling yarn balloon motion in ring spinning

Air-drag on a ballooning yarn and balloon shape affect the yarn tension and ends-down (yarn breakage), which in turn affects energy consumption and yarn productivity in ring spinning. In this article, a mathematical model of yarn ballooning motion in ring spinning is established. The model can be used to generate balloon shape and predict tension in the ballooning yarn under given spinning conditions. Yarn tension was measured using a computer data acquisition system and the balloon shapes were captured using a digital camera with video capability during the experiments using cotton and wool yarns at various balloon-heights and with varying yarn-length in the balloon. The air-drag coefficients on ballooning cotton and wool yarns in ring spinning were estimated by making a “best fit” between the theoretical and experimental turning points. The theoretical results were verified with experimental data. The effects of air-drag and balloon shape on yarn tension are discussed.

Desenvolvimento de perfis aerodinâmicos a partir de suas características utilizando redes neurais artificiais

One of the current major concerns in engineering is the development of aircrafts that have low power consumption and high performance. So, airfoils that have a high value of Lift Coefficient and a low value for the Drag Coefficient, generating a High-Efficiency airfoil are studied and designed. When the value of the Efficiency increases, the aircraft s fuel consumption decreases, thus improving its performance. Therefore, this work aims to develop a tool for designing of airfoils from desired characteristics, as Lift and Drag coefficients and the maximum Efficiency, using an algorithm based on an Artificial Neural Network (ANN). For this, it was initially collected an aerodynamic characteristics database, with a total of 300 airfoils, from the software XFoil. Then, through the software MATLAB, several network architectures were trained, between modular and hierarchical, using the Back-propagation algorithm and the Momentum rule. For data analysis, was used the technique of cross- validation, evaluating the network that has the lowest value of Root Mean Square (RMS). In this case, the best result was obtained for a hierarchical architecture with two modules and one layer of hidden neurons. The airfoils developed for that network, in the regions of lower RMS, were compared with the same airfoils imported into the software XFoil

Cálculo de coeficientes de arrasto para satélites artificiais

Pós-graduação em Física - FEG