Minimum Drag Coefficient Research Articles

Experimental Evaluation of a Self-Contained Circulation-Control Wing

A low-speed experimental investigation detailing the design and evaluation of a self-contained circulation-control wing is presented. A moderate aspect-ratio wing (3.34) utilizing a low-Reynolds-number S8036 profile was tested at . The trailing-edge jet was produced using two internal impellers drawing air off the wing tips. The effect of trailing-edge bluntness was examined as was the jet’s quiescent characteristics. Achievable jet-momentum coefficients were low, limiting circulation control to the boundary-layer control regime. Force-balance testing indicated that the circulation-control system could achieve a moderate zero-lift angle-of-attack shift; however, the primary effect of the jet was flow control at high incidence, in which stall was delayed significantly. The blunt trailing edge (Coanda surface) caused a significant increase in the minimum drag coefficient, reducing both the range and endurance parameters.

Drag reduction on grooved cylinders in the critical Reynolds number regime

Experiments show that significant drag reductions may be realized for circular cylinders in cross-flow by using grooves, even at very shallow relative groove depths. It is demonstrated that the total groove area has a significant effect on reducing the critical Reynolds number, whether the area is increased through changing the groove shape, width, or depth. A strong correspondence to the minimum drag coefficient is also observed.

The Optimum Design of a Cavitator for High-Speed Axisymmetric Bodies in Partially Cavitating Flows

In this paper, the partially cavitating flow over an axisymmetric projectile is studied in order to obtain the optimum cavitator such that, at a given cavitation number, the total drag coefficient of the projectile is minimum. For this purpose, the boundary element method and numerical simulations are used. A large number of cavitator profiles are produced using a parabolic expression with three geometric parameters. The potential flow around these cavitators is then solved using the boundary element method. In order to examine the optimization results, several cavitators with a total drag coefficient close to that of the optimum cavitators are also numerically simulated. Eventually, the optimum cavitator is selected using both the boundary element method and numerical simulations. The effects of the body radius and the length of the conical section of the projectile on the shape of the optimized cavitator are also investigated. The results show that for all cavitation numbers, the cavitator that creates a cavity covering the entire conical section of the projectile with a minimum total drag coefficient is optimal. It can be seen that increasing the cavitation number causes the optimum cavitator to approach the disk cavitator. The results also show that at a fixed cavitation number, the increase in both the radius and length of the conical section causes the cavitator shape to approach that of the disk cavitator.

Testing of fabrics for use in alpine ski competition suits

This paper describes the process of testing fabrics for use in alpine ski competition suits for the Norwegian national team. The main goal of the project was to indentify the aerodynamically best currently available fabric for use in Slalom, Giant Slalom and Super G/Downhill suits for the 2011/2012 competition season. A selection of fabrics were selected and tested in a wind tunnel on cylinder models of varying diameters and on an airfoil model. Additional measurements were performed with increased stretching in order to identify how this would alter the performance of the fabrics. The fabrics tested showed a large spread in critical velocity, minimum drag coefficient (CD) and supercritical drag characteristics, clearly illustrating the need to individualize fabrics for each of the alpine competition disciplines according to average race speeds. Full race suits were made from three of the fabrics and tested on athletes. These measurements confirmed the trend from the model measurements, although the variability in these measurements was too large to make a reliable estimate of actual drag reduction.

Oil Streak Visualisation of Fluid Flow Over Single D-Type Cylinder

An experimental study on the effect of cut angle on circular cylinders to the drag force is performed. Six cylinders were cut at different angles and the air flow impinges perpendicular to the cut surface of the cylinder. The cut angles applied include: 0°, 30°, 45°, 53°, 55°, and 75°. The shear layer visualisation on the surface of cylinder was conducted as well. Drag force was measured using a wind tunnel force balance and the wind speed was set so that a corresponding Rey-nolds number of 5.3 × 104 was achieved. Visualisation was carried out by covering the cylinder with paper wetted by mixture of oil and titanium dioxide powder. Experimental results show that drag force has similar trend to that of previous experiment results. The minimum drag coefficient is attained at the cut angle of 53°. From oil streak visualisation the streamlines pattern of the flow over the cylinder could be reconstructed.

Aerodynamics of airfoil sections and their influence on wind turbine design and performance

The primary goal of this work is to reflect the effectiveness of the aerodynamic characteristics of blade airfoil-sections on the design and overall performance predictions of the horizontal-axis wind turbines. A post-stall model has been introduced and used throughout the work to secure reliable data in a wide range of angles of attack. It has been found that the general performance requirement of such airfoils is to exhibit a maximum lift-coefficient which is relatively insensitive to roughness effects and to have a low minimum drag coefficient and/or a high lift/drag ratio. The contribution of these parameters at the blade-tip region is very high and almost equal to the contributions of the mid and root regions together. Consequently, the airfoil section should be designed/selected according to its location along the blade to ensure its highest contribution to the overall performance of the rotor.

A quasi-static investigation of the effect of leg position on cyclist aerodynamic drag

The aerodynamic drag of a cyclist mannequin is measured in a ¾ open jet wind tunnel. The mannequin leg position is systematically varied over a complete crank cycle and aerodynamic drag measurements are taken every 15 degrees. The results show that rider aerodynamic drag is strongly affected by leg position with a difference between the maximum and minimum drag coefficients measured over a pedal cycle being approximately 15%. A small variation in cyclist frontal area is apparent over the pedal stroke, however the change in aerodynamic drag coefficient is identified as the dominant mechanism affecting cyclist drag. A series of flow visualization studies have been used to demonstrate the large effect that the position of the legs has on the flow around the entire body of the mannequin. It is observed that the flow regime is symmetrical for the low drag case and asymmetrical for the high drag case. This work highlights that the flow regime changes significantly throughout the pedal stroke of a cyclist, and consequently drag varies. This has implications in terms of analyzing cyclist aerodynamic performance as it highlights that multiple flow regimes should be considered.

Drag performance of divergent tubular-truncated cones: a shape optimization study

The use of more efficient energy consuming devices, which are closely associated with reduction of environmental pollution, has gained significant interest in the recent decades. The reduction of drag coefficient also improves safety and durability of environmental structures subjected to high-velocity fluid flow, and causes the noise and vibration to decrease as well. This paper describes the efficiency improvement in energy management by means of reducing drag coefficient in a practical divergent tubular-truncated cone. Extensive numerical simulations with emphasis on the shape optimization study were performed in order to find minimum drag coefficient for both laminar and turbulent flows (9.41 × 102 ≤ Re ≤ 1.882 × 107) around the mentioned cone. The numerical results were validated with experimental data, obtained by performing tests in an open circuit wind tunnel. The results showed that the minimum drag coefficient of optimum model within the shape modification process, comparable to the value for the primary model in turbulent flow decreased by 69.8% (the maximum discrepancy) at the highest considered Reynolds number of 1.882 × 107. Furthermore, the study of streamwise velocity profile led to more useful result. In this regard, the velocity magnitude inside the inlet span of the primary model, close to the entrance was approximately 1.6 times as great as the free upstream velocity. This is a noticeable result for the use of efficiency important structures in industrial applications.

Aerodynamic behaviour of stretchable sports fabrics

The variable surface characteristics of sports fabrics can affect the aerodynamics of athletes. In speed sports, most sports garments are worn with reasonable stretches that alter the fabrics' surface morphology. However, no correlation between the stretches and aerodynamic parameters is reported in the open literature. Therefore, the primary objective of this paper is to measure the aerodynamic properties of three commercially available sports fabrics over a range of Reynolds numbers and stretch conditions. Aerodynamic parameters of each fabric under a range of applied stretches were measured experimentally. The findings indicate that the surface morphology of the fabric under tension changes significantly and also affects the aerodynamic behaviour of the fabric. Less stretched knitted fabrics can provide an aerodynamic advantage by reducing drag at higher speeds, while more stretched knitted fabrics can provide an aerodynamic advantage by reducing drag at lower speeds. As the surface roughness increases, the critical Reynolds number (Recrit ) decreases and the minimum drag coefficient (C Dmin) value increases. Using same fabric under different tensions, the aerodynamic drag can be reduced up to 40% compared to a smooth-surface fabric.

Numerical and Experimental Study on Aerodynamic Characteristics of Basic Airfoils at Low Reynolds Numbers

The aerodynamic characteristics of airfoils have been researched in higher Reynolds-number ranges more than 106, in a historic context closely related with the developments of airplanes and fluid machineries in the last century. However, our knowledge is not enough at low and middle Reynolds-number ranges. So, in the present study, we investigate such basic airfoils as a NACA0015, a flat plate and the flat plates with modified fore-face and after-face geometries at Reynolds number Re < 1.0×105, using two- and three-dimensional computations together with wind-tunnel and water-tank experiments. As a result, we have revealed the effect of the Reynolds number Re upon the minimum drag coefficient CDmin. Besides, we have shown the effects of attack angle α upon various aerodynamic characteristics such as the lift coefficient CL, the drag coefficient CD and the lift-to-drag ratio CL/CD at Re = 1.0×102, discussing those effects on the basis of both near-flow-field information and surface-pressure profiles. Such results suggest the importance of sharp leading edges, which implies the possibility of an inversed NACA0015. Furthermore, concerning the flat-plate airfoil, we investigate the influences of fore-face and after-face geometries upon such effects.

An Experimental Study on Heat Transfer Around Two Side-by-Side Closely Arranged Circular Cylinders

The present paper describes heat transfer around two side-by-side closely arranged circular cylinders. The flows around two circular cylinders in a side-by-side arrangement can be classified into three flow patterns according to the gap between the two cylinders. The heat transfer characteristics of the cylinders in each flow regime were experimentally investigated. The diameter of the circular cylinders was 40 mm and the gap between the two cylinders varied from 4 mm to 40 mm. The free stream velocity ranged from 4 m/s to 24 m/s, resulting in Reynolds nos. ranging from 1.1×104 to 6.2×104. The local heat transfer coefficient of both cylinders was measured. The overall Nusselt no. of the two cylinders was found to be minimum at G/D(=gap/diameter)=0.4, which is the minimum drag coefficient condition of the two cylinders, too.

Study on aerodynamic force acting on a sphere with and without boundary layer trips around the critical Reynolds number with a magnetic suspension and balance system

Aerodynamic force acting on a sphere for five kinds of boundary layer trips around the critical Reynolds number, together with the force on a smooth sphere, was successfully measured. This was achieved using JAXA’s 60-cm Magnetic Suspension and Balance System after performing detailed simulations and adjusting the sphere mass and its control parameters. The minimum drag coefficient of a smooth sphere was evaluated around 0.19 in the support-interference-free condition. No hysteresis was observed for the drag coefficient in the critical range for tested sphere with boundary layer trips. Using three serially connected 2nd-order Butterworth low-pass filters, an inertia force oscillating at less than 15 Hz was evaluated from the measured model position, and the unsteady aerodynamic force acting on the sphere was also evaluated with reasonable accuracy. Two kinds of oscillatory aerodynamic forces appeared in the critical range depending on the sphere surface condition: a force rotating around an axis parallel to the uniform flow for both a smooth sphere and a sphere with axially symmetric 0.17-mm-high backward step, and an oscillating force in the plane including the axis parallel to the flow for a sphere with axially symmetric step implemented with 0.35–mm-thick tape with wrinkles acting as small vortex generators. There was also observed a force irregularly rotating through less than 180° in the range about a sphere axis parallel to the flow for a smooth sphere in the supercritical range.

Experimental Investigation of Double-Hinged Vortex Flap Configurations

D ELTA wings are poor lift generators. An often-employed design approach to ameliorate the low lift production is to sharpen thewing’s leading edge. A consequence of the enforced flow separation is the formation of leading-edge vortices. The vortices induce high surface velocities over the wing and may significantly augment lift, especially as the delta becomes more slender [1]. Leading-edge flaps (formed by downward rotation of a segment of the wing’s leading edge) may be used to lessen the performance loss by recovering thrust from the vortices by positioning them over wing elements with a forward-facing area: so-called leading-edge vortex flaps (LEVFs) [2]. Studies of vortex flaps (VFs) have shown the concept to be effective [2,3]; however, their performance is constrained by the characteristics of the leading-edge vortices with incidence. The vortices expand in size and migrate inboard off the flap. As a result, the flaps lose effectiveness. A study by Rinoie and Stollery [3] showed that the maximum lift-to-drag ratio L=D for the 60 and 70 deg delta wings they tested with vortex flaps coincided with smooth flow onto the flap with no separation. As a result, increasing wing incidence requires larger flap deflections to maintain maximized L=D values. Deflecting the flap reduces lift for a given geometric angle of attack as the vortex strength is reduced, as well as to a lesser extent, the attached flow lift [4]. An additional byproduct of flap deflection is a moderate increase in the minimum-drag coefficient. As a result, the initialL=D is attenuated, butmay increase significantly beyond that of the sharp planar delta for moderate to high lift coefficients. An attempt to reduce the drag penalty as well as limit the expansion of thevortex off theflapswas documented byRao [5]. Various flap configurations were investigated, variants including constant length and segmented configurations. The segmented flaps generated two smaller distinct leading-edge vortices so as to minimize vortex spillage. Rao’s results suggested that generating multiple leading-edge vortices was effective in delaying vortex spillage and thus suction loss from the flap. Generally, experimental observation has indicated that the leading-edge vortices on a planar delta lie along a trajectory of approximately 70% of the local semispan [6]. It may be feasible to design a vortex flap that is located further inboard, such that the flap hingeline runs along a ray of approximately 65% semispan. To limit the flap size, a tab may be employed, where the outer wing surface is inclined so as to be parallel to the inner wing section (see Fig. 1). A small tab was evaluated by Hoffler and Rao [7]; some of their designs resulted in the tab having a rearward inclination such that vortex formation over the tab would contribute additional drag. Other tabbed configurations that were tested were not deemed as successful [7]. In this paper, so-called double-hinged vortex flaps (HVF) are evaluated, where the configuration consists of a planar inboard portion, a vortex flap and a planar outboard panel. HVFs may reduce vortex loss with incidence (as its hingeline orientation is closer to the natural vortex trajectory, i.e., the flap is located further inboard), the minimum-drag penalty and structural complication. The undeflected outboard panel of the HVF may also augment the strength of the primary vortex compared with a conventional LEVF, where the effective leading-edge incidence is diminished. The proposed design would mitigate against a movable flap; thewing configuration would be fixed. The basis of comparison of the flaps in this study is different from that of Hoffler and Rao [7]. In the present study the flap area is conserved for a given flap area ratio, and does not include the area of the outboard panel (or tab). The configuration and size of the outboard panels are also conceptually different from those in [7], where the tabs were approximately constant chord and were not an integral part of the wing design, but an add-on. A low-speed windtunnel investigation was conducted to evaluate the concept, characterized through force-balance, pressure measurement, surface flow visualization, and vortex burst trajectories.

Maximum range of flying discs

Since the original 1963 Frisbee flying discs have evolved, becoming ubiquitous and far-ranging. Effects of drag, lift, pitching moment and spin on range are analysed. With lift, ranges significantly exceed the drag-free ballistic range. An upper limit wings level case, optimized for range, is compared with the realistic free case of a spinning, banking disc. For 30 m/s launch and 0.033 minimum drag coefficient the wings level range is 186 m, but the free range only 157 m. Tests report ranges between 77–170 m. The procedure is a powerful tool for designing superior discs.

Shape optimization of the airfoil comprising a cross flow fan

PurposeFanwing airfoil is a new lift‐generating section invented in 1997 by Patrick Peebles. The early shape of the airfoil has not changed until now. So far, no research has been done to change or modify the airfoil shape in order to improve its aerodynamic performance. In this paper, possibility of changing the airfoil shape to improve its aerodynamic performance is studied. For this purpose, six different geometric shapes of the airfoil are investigated numerically to determine the best airfoil on the basis of lift and drag coefficients. Flow over the airfoil is solved by developing a computational fluid dynamics (CFD) code. The purpose of this paper is to find a more efficient configuration for the Fanwing airfoil with lower power consumption and better performance.Design/methodology/approachFlow over the airfoil is investigated by CFD. At the airfoil solid walls, the no slip condition is applied. Re‐Normalization Group k‐ε model is used for turbulence modeling. The pressure‐velocity coupling is calculated by the SIMPLEC algorithm. Second‐order upwind discretization is considered for the convection terms. Finite volume method with rectangular computational cells is used for the entire solution domain.FindingsIt is observed that the airfoil with curved bottom wall and a slot in upper wall has the maximum lift coefficient. Also, the airfoil with curved bottom wall and no slot has the minimum drag or maximum thrust (negative drag) coefficient. Therefore, instead of increasing the airfoil lift or decreasing its drag by enhancing driving motor speed with larger energy consumption, this can be done only by changing the airfoil shape. It is perceived that the airfoil lift coefficient can be augmented at least 10 percent and its drag can be reduced more than 2.8 percent only by changing its shape and no excessive power consumption. Since the airfoil shape is modified, these advantages are permanent and its benefits are cumulative through time. Eccentric vortex inside the cross flow fan that is reported earlier in the research paper is found in this airfoil, too. In addition, velocity vectors, contours of static pressure and distribution of the static pressure over the airfoils surfaces are illustrated for better understanding of the flow details.Research limitations/implicationsSince the airfoil shape is very complicated for numerical study, two‐dimensional simulation has been carried out. Also, flow over the airfoil is considered steady‐state and incompressible.Practical implicationsIn this paper, some modifications for the Fanwing airfoil are suggested in order to improve its aerodynamic performance. This is the first research for changing the configuration of the Fanwing airfoil and can be very helpful for the researchers involved in this topic as well as aerospace industries.Originality/valueThis paper is valuable for researchers in the new and up to date concept of the Fanwing airfoil. This work is original.

Aerodynamic/Stealthy/Structural Multidisciplinary Design Optimization of Unmanned Combat Air Vehicle

An optimization strategy is proposed to deal with the aerodynamic/stealthy/structural multidisciplinary design optimization (MDO) issue of unmanned combat air vehicle (UCAV). In applying the strategy, the MDO process is divided into two levels, i.e. system level optimization and subsystem level optimization. The system level optimization is to achieve optimized system objective (or multi-objective) through the adjustment of global external configuration design variables. The subsystem level optimization consists of the aerodynamic/stealthy integrated design and the structural optimization. The aerodynamic/stealthy integrated design aims at achieving the minimum aerodynamic drag coefficient under the constraint of stealthy requirement through the adjustment of local external configuration design variables. The structural optimization is to minimize the structural weight by adjusting the dimensions of structural components. A flowchart to implement this strategy is presented. The MDO for a flying-wing configuration of UCAV is employed to illustrate the detailed process of the optimization. The results indicate that the overall process of the surrogate-based two-level optimization strategy can be implemented automatically, and quite reasonable results are obtained.

Plasma Flaps and Slats: An Application of Weakly Ionized Plasma Actuators

The experimental validation of an application of weakly-ionized plasma actuators for improved aerodynamic performance of multi-element wings and wings with movable control surfaces is presented. Two spanwise arrays of plasma actuators, configured to produce a wall-jet effect, were applied on the suction surface of a two-dimensional NACA 0015 wing model, one at the leading edge and the other near the trailing edge to mimic the effects of a wing leading-edge slat and a trailing-edge flap, respectively. Flow control tests were conducted at chord Reynolds numbers, corrected for blockage, of 0.217 x 10 6 and 0.307 x 10 6 in a low-speed wind tunnel at the University of Notre Dame. The leading-edge-separation control resulted in an increase in both the maximum lift coefficient and the stall angle of attack and a lift-to-drag improvement of as much as 340%. An optimum frequency was found to exist for unsteady excitation of the leading-edge separation. Under this condition, the power to the actuator was estimated to be only 2 W. The trailing-edge actuator was found to produce the same effect as a plain trailing-edge flap. This included a uniform shift at all angles of attack of the lift coefficient and a shift toward higher lift coefficients of the drag bucket. In addition, there was a slight decrease in the minimum drag coefficient. The obvious advantages of this approach are its simplicity, as there are no moving parts, and its lack of hinge gaps, which add drag. An example of their use as ailerons for roll control produces a comparable roll moment coefficient to a sample general aviation aircraft.

Effects of Gurney Flaps on an Annular Wing

F OR a constrained wing span, nonplanar wings exhibit significant aerodynamic benefits. These are generally indicated through increased lift curve slopes and reduced drag due to lift. These benefits are accrued through thewing capturing a larger volume of air to generate the lift impulse, and consequently the downwash at a point is reduced [1]. A simple biplane is a clear embodiment of nonplanarity. As the spacing between the upper and lower wings tends to infinity, the lift curve slope of the biplanewing tends to twice that of the equivalent monoplane, and the lift dependent drag tends to half that of the monoplane. Naturally, an infinitely spaced biplane or even that with a significant gap is not a practical design solution. As the gap between the biplanewings reduces, mutual wing interference effects reduce the nonplanar benefits. An annular (or ring) wing achieves the same aerodynamic benefits as an infinitely spaced biplane but with a maximum vertical wing spacing of the diameter of the ring. However, annular wings are hindered by their significant minimum drag coefficient that is largely due to their wetted area, which is 1.57 times greater than an equivalent projected span biplane of equal aspect ratio. Annular wings also suffer from pitch-up at stall due to dissimilar stall characteristics between the upper and lower wing halves [2]. Consequently, an active design space for annular wings is where flight operations at low speed (high loading) for extended duration are a design driver, as may be required for a small reconnaissance unmanned air vehicle [3]. Gurneyflaps have received considerable attention of late as simple devices capable of augmenting the lift of a wing or airfoil [4–7]. The flap itself is usually composed of a small metal tab, typically nomore then 1–2% of the chord attached perpendicular to the trailing edge on the pressure side (generally within the pressure side’s boundary layer). The flaps essentially work by violating the Kutta condition at the trailing edge; thus greater loading is carried over the aft section as final pressure recovery occurs in thewake. This also has the benefit of reduced pressure recovery demands on the upper surface boundary layer [5]. The flaps have also been observed to increase base suction; beneficial in delaying stall but also causing a drag increase. Flap inclination has been indicated to be favorable in reducing drag, and placement at the trailing edge is generally indicated as being themost advantageous [5]. Segmented flaps have been studied as a means to attenuate the drag penalty of the flaps by introducing instabilities into the wake, which culminate in the breakdown of the two-dimensional vortex street that has been observed aft of theflap [6]. Liftmodulation of an annular wing can be complicated due to the wing’s geometric shape; flaps or ailerons may require large end gaps for clearance. Consequently, a Gurney flap may prove an effective device for force andmomentmodulation on an annular wing. Lift augmentation of an annular wing usingGurney flaps is apparently not documented in the literature. Consequently, a study has been undertaken to elucidate the effects of various Gurney flap configurations and layouts on the aerodynamic characteristics of an annular wing.

Experimental Investigation of Annular Wing Aerodynamics

A low-speed wind-tunnel investigation was conducted to explore the behavior of annular (ring) wings. Effects of aspect ratio as well as gap were investigated. Ring wings using a low Reynolds number Eppler section and a NACA 0012 profile were manufactured and tested. Measurements were recorded using a six-component sting balance. Experimental and theoretical trend comparisons were effected using a vortex-lattice code. The experimental results indicate wing efficiency factors well above 1 are achievable. The effect of gap was to increase the wing lift-curve slope as well as efficiency. The large increases in aerodynamic efficiency were generally mitigated by the significant minimum drag coefficient. Pitching moment characteristics were unfavorable and were dominated by dissimilar stall behavior between the upper and lower wing sections.

Hydrodynamic abilities of riverine fish: a functional link between morphology and velocity use

To better understand the effects of perturbations (e.g. global change) or habitat restorations on fish popu- lation dynamics, it is crucial to improve the knowledge about strategies of habitat use (especially in terms of velocity use) by fish. Many recent studies accurately describe kinematics or energetic budgets of swimming activities, which are often species-specific and hardly transferable to other species. The main goal of the present study was to revive more general ecomorphological relationships between body shape and strategies of velocity use by highlighting a functional aspect of fish morphology: the hydrodynamic potential. For this purpose, potential relationships between minimum drag coefficients (Cdmin, constant at high Reynolds numbers), velocity use, fish morphology and drag in given flow con- ditions were investigated. To assess these relationships, dead drag values (i.e. drag values measured on dead, straight individuals) of 27 riverine species (108 individuals in total) common in France were experimentally measured under various flow conditions. These values served to estimate theCdmin of fish. For pelagic species, Cdmin values were related to both preferred and near-maximum flow velocity used by the fish in nature. Explaining 61% of its variability, Cdmin was described using six morphological variables, which demonstrates the functional link between fish morphology and velocity use. For all studied species, a model explained 94% of drag variability using the Reynolds number of fish and three morphological variables. The link between morphology and drag force at given velocity conditions provides sim- ple elements for modelling fish energetics in the context of physical habitat use. Moreover, the relationships between fish velocity use and their Cdmin open many applied perspectives, such as assessing the species abilities to withstand discharge modulations.