Contribution Of Drag Research Articles

Numerical study of heat transfer and fluid flow in the offset strip-fin heat exchanger: A fin-by-fin analysis

Heat transfer and fluid flow in the offset strip-fin heat exchanger are studied numerically, fin by fin. The impact of the offset strip-fin geometry on j/f performance is also evaluated. The mathematical model is validated against j- and f-factor correlations from the literature. The numerical analysis revealed that the offset strip-fin heat exchanger achieves best j/f performance in the laminar flow region (Redh < 700). At higher Reynolds numbers, the j/f factor deteriorates under the impact of flow recirculations, oscillatory wakes and the contribution of form drag. Compared to the continuous rectangular fin, the offset strip-fin increases the air-side heat transfer coefficient by 50% at Redh = 100 and by 120% at Redh = 4000 while the pressure drop increases by a factor of 3–5. Generally, the offset strip-fin achieves j/f performance between 0.20 and 0.30, with maximum values found in the laminar flow region (Redh 〈1000). Offset strip-fin geometries with reduced fin space and increased wall thickness strongly affect the form drag, which reduces the j/f performance, especially for Redh > 1000. The fin height weakly influences the performance, and the j/f factor is between 0.22 and 0.23 for a wide range of fin heights.

The Impact of Surface Drag on the Structure and Evolution of Surface Boundaries Associated with Tornadogenesis in Simulated Supercells

Abstract Surface boundaries in supercells have been suspected of being important in the arrangement and concentration of vorticity for the development and intensification of tornadoes, but there has been little attention given to the effects of the underlying surface roughness on their behavior. This study investigates the impact of surface drag on the structure and evolution of these boundaries, their associated distribution of near-surface vorticity, and tornadogenesis and maintenance. Comparisons between idealized simulations without and with drag introduced in the mature stage of the storm prior to tornadogenesis reveal that the inclusion of surface drag substantially alters the low-level structure, particularly with respect to the number, location, and intensity of surface convergence boundaries. Substantial drag-generated horizontal vorticity induces rotor structures near the surface associated with the convergence boundaries in both the forward and rear flanks of the storm. Stretching of horizontal vorticity and subsequent tilting into the vertical along the convergence boundaries lead to elongated positive vertical vorticity sheets on the ascending branch of the rotors and the opposite on the descending branch. The larger near-surface pressure deficit associated with the faster development of the near-surface cyclone when drag is active creates a downward dynamic vertical pressure gradient force that suppresses vertical growth, leading to a weaker and wider tornado detached from the surrounding convergence boundaries. A conceptual model of the low-level structure of the tornadic supercell is presented that focuses on the contribution of surface drag, with the aim of adding more insight and complexity to previous conceptual models. Significance Statement Tornado development is sensitive to near-surface processes, including those associated with front-like boundaries between regions of airflow within the parent storm. However, observations and theory are insufficient to understand these phenomena, and numerical simulation remains vital. In our simulations, we find that a change in a parameter that controls how much the near-surface winds are reduced by friction (or drag) can substantially alter the storm behavior and tornado potential. We investigate how surface drag affects the low-level storm structure, the distribution of regions of near-surface rotation, and the development of tornadoes within the simulation. Our results provide insight into the role of surface drag and lead to an improved conceptual model of the near-surface structure of a tornadic storm.

Breakdown of Near-Surface Sea Current from High-Frequency Radar Data

Abstract To assess the contribution of wind drag and Stokes drift on the near-surface circulation, a methodology to isolate the geostrophic surface current from high-frequency radar data is developed. The methodology performs a joint analysis utilizing wind field and in situ surface currents along with an unsupervised neuronal network. The isolation method seems robust in the light of comparisons with satellite altimeter data, presenting a similar time variability and providing more spatial detail of the currents in the coastal region. Results show that the wind-induced current is around 2.1% the wind speed and deflected from the wind direction in the range [18°, 23°], whereas classical literature suggests higher values. The wave-induced currents can represent more than 13% of the ageostrophic current component as function of the wind speed, suggesting that the Stokes drift needs to be analyzed as an independent term when studying surface sea currents in the coastal zones. The methodology and results presented here could be extended worldwide, as complementary information to improve satellite-derived surface currents in the coastal regions by including the local physical processes recorded by high-frequency radar systems. The assessment of the wave and wind-induced currents have important applications on Lagrangian transport studies.

Impact of spanwise effective slope upon rough-wall turbulent channel flow

Whereas streamwise effective slope ( $ES_{x}$ ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( $ES_{y}$ ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of $ES_{y}$ is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height $k^{+}\approx 65.8$ (where $k$ is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified $ES_{y}$ for three different values of $ES_{x}$ . All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying $ES_{y}$ , since roughness amplitude, skewness and $ES_{x}$ can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that $ES_{y}$ can strongly affect the roughness drag penalty – particularly for low- $ES_{x}$ surfaces. A secondary observation is that particular low- $ES_{y}$ surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall.

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in theliterature.

Transient analysis of H-type Vertical Axis Wind Turbines using CFD

In this study, the effect of various parameters on the start-up and transient behavior of Darrieus straight-bladed Vertical Axis Wind Turbine (VAWT) was analyzed. Airfoil profile, angle-of-attack, and chord length were varied, yielding two optimal turbines, one for transient and another for steady performance. This optimization revealed that the chord length (solidity) has the most significant impact on the performance of the turbine undergoing both transient and steady operations. An examination of the contribution of drag and lift forces to the startup of these two optimized turbines shows that the drag has a positive contribution to the performance of the transient optimized turbine especially at high TSRs. The performance of the optimized turbines when subject to four different wind profiles: a real wind profile, and three distinct sinusoidal profiles was also assessed. At low average wind speeds, a high frequency of the incoming wind is favorable for allowing both optimized turbines to produce more power. The rotor behavior under dynamic loads was also investigated, demonstrating that the transient optimized turbine is more responsive and therefore easier to control. In addition, minimizing the inertia of the steady-optimized turbine significantly improves its startup characteristics, making it superior to its steady-optimized counterpart.

Amplitude and wavelength scaling of sinusoidal roughness effects in turbulent channel flow at fixed

Direct numerical simulations are performed for incompressible, turbulent channel flow over a smooth wall and different sinusoidal wall roughness configurations at a constant$Re_\tau = 720$. Sinusoidal walls are used to study the effects of well-defined geometric features of roughness-amplitude,$a$, and wavelength,$\lambda$, on the flow. The flow in the near-wall region is strongly influenced by both$a$and$\lambda$. Establishing appropriate scaling laws will aid in understanding the effects of roughness and identifying the relevant physical mechanisms. Using inner variables and the roughness function to scale the flow quantities provides support for Townsend's hypothesis, but inner scaling is unable to capture the flow physics in the near-wall region. We provide modified scaling relations considering the dynamics of the shear layer and its interaction with the roughness. Although not a particularly surprising observation, this study provides clear evidence of the dependence of flow features on both$a$and$\lambda$. With these relations, we are able to collapse and/or align peaks for some flow quantities and, thus, capture the effects of surface roughness on turbulent flows even in the near-wall region. The shear-layer scaling supports the hypothesis that the physical mechanisms responsible for turbulent kinetic energy production in turbulent flows over rough walls are greatly influenced by the shear layer and its interaction with the roughness elements. Finally, a semiempirical model is developed to predict the contribution of pressure and skin friction drag on the roughness element based purely on its geometric parameters and the corresponding shear-layer velocity scale.

Effect of paramagnon drag on thermoelectric transport properties: Linear response theory

It has been proposed that paramagnetic materials exhibit a unique thermoelectric effect near the ferromagnetic transition point due to spin fluctuations. This phenomenon is often referred to as paramagnon drag. We calculate the contribution of this paramagnon drag to the Seebeck coefficient microscopically on the basis of the linear response theory. This leed to a general formula for the contribution to the Seebeck coefficient due to the paramagnon drag, and we clarify the conditions in which the Seebeck coefficient enhances near the ferromagnetic transition point for a single-band and isotropic system. Moreover, we calculate the Seebeck coefficients for a band $\varepsilon \propto k^n$ and a mixture of free-electron-like and flat bands.

Numerical investigation of three-dimensional asymmetric hovering flapping flight

Direct numerical simulations are performed to assess the aerodynamic performance of three-dimensional wings undergoing asymmetric hovering flapping flight. A large number of flapping kinematics is investigated, varying the pitch rate and the upstroke and downstroke angles of attack. We show that, for all cases, time-averaged performance is driven, to leading order, by the mean angle of attack over a flapping period despite the increased contribution of drag to vertical force with increased stroke plane angle. We hence suggest that asymmetric hovering is not intrinsically more efficient than normal hovering, conversely to what has been previously reported in the literature. This may explain the under-representation of this flight mode in nature.

Analytic quasi-steady evolution of marginally unstable kinetic plasma instabilities in the presence of drag and scattering

The 1D bump-on-tail problem is studied in order to determine the influence of drag on quasi-steady solutions near marginal stability (1−γd/γL≪1) when effective collisions are much larger than the instability growth rate (ν≫γ). In this common tokamak regime, it is rigorously shown that the paradigmatic Berk–Breizman cubic equation for the nonlinear mode evolution reduces to a much simpler differential equation, dubbed the time-local cubic equation, which can be solved directly. It is found that in addition to increasing the saturation amplitude, drag introduces a shift in the apparent oscillation frequency by modulating the saturated wave envelope. Excellent agreement is found between the analytic solution for the mode evolution and both the numerically integrated Berk–Breizman cubic equation and fully nonlinear 1D Vlasov simulations. Experimentally isolating the contribution of drag to the saturated mode amplitude for verification purposes is explored but complicated by the reality that the amount of drag cannot be varied independently of other key parameters in realistic scenarios. While the influence of drag is modest when the ratio of effective drag to effective scattering α/ν is very small, it can become substantial when α/ν≳0.5, suggesting that drag should be accounted for in quantitative models of fast-ion-driven instabilities in fusion plasmas.

Investigation of Reduction in Base Drag using Experiment and CFD at Subsonic Speed Regimes

Base drag, arising from flow separation at the blunt base of a body can be a sizeable fraction of total drag in the context of projectiles, missiles and after bodies of fighter aircrafts. The base drag is the major contribution of total drag for low speed regimes, flight tests have shown that the base drag may account for up to 50% of the total drag. Computational and experimental investigation for a hemispherical flight vehicle body of length 500mm and diameter 50mm was conducted for the purpose of investigating the base drag. Three case studies were conducted to investigate the properties of the flow field around the flight vehicle at different flow velocities of 20m/s, 30m/s and 50m/s at zero angle of attack (AoA). The three cases were (i) a flight vehicle with flat base configuration, (ii) a flight vehicle with a nozzle at the base and (iii) a flight vehicle configuration with a boat tail, Fig 1. Also, the three configurations were investigated at different AoA of -2ï‚°, 0ï‚° and +2ï‚°. The base drags for three configurations are calculated and the experimental results are compared with the CFD results.

Computational Analysis of Base Drag Reduction for a Subsonic Missile Projectile at Different Flow Velocity Conditions

Base drag is arising from flow separation at blunt base of a body. It can be a sizeable fraction of total drag in context of projectiles, missiles and after bodies of fighter aircrafts. The base drag is the major contribution of total drag for low speed regimes, flight tests have shown that the base drag may account for up to 50% of total drag. In this paper an experimental investigation for simple semi-circular flight vehicle body of length 500mm and diameter 50mm was conducted for the purpose of investigating base drag. The base drags for three configurations are calculated and the results are compared with CFD data. The three configurations used for testing are flat base configuration, closed nozzle configuration and boat tail configuration. The evaluation of base drag for three different flow velocities such as (i) 20m/s, (ii) 35m/s and (iii) 50m/s at different angle of attack such as -2ï‚°, 0ï‚° and 2ï‚° are experimented and compared.

Experimental and numerical analysis of thermal flow in open-cell porous metal during Darcy-Forchheimer transition regime

A numerical analysis of pressure drop and heat transfer for open-cell porous media is performed using a three-dimensional conjugate heat transfer model. Porous metal with a pore density of 20 pores per inch (PPI) and porosity of 95.7% is used in the present numerical simulation. Real microstructure of the open-cell porous metal is constructed using stacked images obtained by X-ray computed tomography method. Computed thermal-fluid characteristics are compared directly with the experimental pressure drop and unit overall thermal resistance values. The flow through porous metal can be divided into the Darcy regime and the Forchheimer regime. The thermo-fluidic characteristics in the Darcy regime and the Forchheimer regime are investigated numerically. The flow separation is not observed in the Darcy regime, but the wake region occurs in the Forchheimer regime because of the flow separation on the ligament surface. The contribution of the total drag acting on the walls (top & bottom) is very small, namely, less than 5% compared to the total drag on ligaments. The total drag force coefficient of ligaments tends to converge at high Reynolds number. This is because the pressure drag force is dominant due to the wake effect in the Forchheimer regime. Local Nusselt number is large near the upstream side of the ligament and very low in the wake region. Average Nusselt number increases with Reynolds number. In the Forchheimer regime, wakes developed behind ligaments increase the pressure loss and decrease the heat transfer performance.

Forward flight and sideslip manoeuvre of a model hawkmoth

This paper presents a computational study on the free forward flight and sideslip manoeuvre of an insect-like flapping-wing flyer modelled after the hummingbird hawkmoth (Macroglossum stellatarum), with Reynolds number . The numerical model integrated a Navier–Stokes fluid solver with the Newtonian free-body dynamics of the flyer. A generic proportional–integral–derivative (PID)-based wing kinematics controller was used to achieve stable controlled flight. State-equation analyses of flight dynamics were helpful in identifying the roles of kinematic wing actions and for establishing control coefficients for stable flight. Forward flights up to a speed of were simulated, which show that the wingbeat frequency decreased below the hovering frequency for cruising flight in the low- and medium-speed range, and higher frequency was only needed for high-speed flight. Similarly, the aerodynamic power consumption was also lower than that for hovering flight over the simulated speed range, due to the contribution of wing drag to overall lift. In addition, flight with higher speed tends to be more efficient in terms of energy consumption for the same distance travelled. In a complete sideslip manoeuvre, the model hawkmoth took approximately 20 wing cycles to translate laterally 4.5 wing lengths to its right and another 30 wing cycles to stabilize hovering at the new location. Slightly higher wingbeat frequency and power were required during the sideslipping phase to adjust for drop in lift due to body roll. The evolution of the vortical wakes reflects quite well the major mechanisms of force generation that were at play at key stages in these flights.

Accurate decomposition method and identification technology of drag

Aiming at accurate decomposition and identification of drag, the drag prediction technology based on the mid/far-field integral method is developed. The method decomposes the far-field drag into entropy drag and induced drag according to its physical mechanism, and introduces an appropriate entropy correction to eliminate the numerical dissipation by analyzing the influence of the trailing integral section position on the entropy drag calculation. Based on the analysis of thermodynamic reversible processes and irreversible processes, the drag is refined into viscous drag, shock wave drag, induced drag and pseudo-drag. The mid-field integral method is used to calculate the separate contribution of viscous drag, shock wave drag and induced drag by calculating the limited integral domain. Numerical results show that the developed method is feasible in accurately reflecting the physical mechanism and predicting the drag ratio. Thus, it provides a reliable tool for drag reduction of large passenger aircraft.

Numerical study on flow past a confined half cylinder in two bluff arrangements

Two-dimensional flow past a half cylinder in the two bluff arrangements confined by parallel walls is studied for the range of Reynolds number as 1 ≤ Re ≤ 160 at a blockage ratio of β = 0.2. A direct comparison is made of all results obtained for the two half-cylinder arrangements and the full cylinder. Critical Reynolds numbers signifying the onset of flow separation (Rec1) and vortex shedding (Rec2) have been identified for both bluff arrangements, the values of which are lower than that for the full cylinder of the same blockage ratio. The value of Rec2 reported in the literature [Kumar et al 2016 Int. J. Heat Mass Transfer 102 417–425] for a confined half cylinder at β = 0.25 has also been evaluated and clarified. The mean value of the coefficient of drag CD increases with Re in the vortex shedding regime for the half cylinder, which is well-known to manifest opposite trends with Re from the full cylinder. A possible explanation for this difference is provided. In addition, the pressure and friction (viscous) components are analyzed for all instances studied in both the steady and vortex shedding regimes, and provide an understanding of the competition between the forces due to pressure and friction acting on the cylinder with increasing Reynolds number. In particular, a very high percentage contribution (nearly 99%) of pressure drag to total drag is found at Re = 160 for the half cylinder with its flat surface facing upstream. Finally, flow features are detailed to further illustrate the fluid-structure interaction for the half cylinder.

Experimental constraints on subglacial rock friction

AbstractSubglacial rock friction is an important control on the sliding dynamics and erosive potential of hard-bedded glaciers, yet it remains largely unconstrained. To explore the relative influence of basal melt rate, effective stress and ice temperature on frictional resistance, we conducted abrasion experiments in which limestone beds were slid beneath a fixed slab of ice laden with granitic rock fragments. Shear stress scales linearly with melt rate and cryostatic stress, confirming that both viscous drag and effective stress are first-order controls on the contact force in drained conditions. Furthermore, temperature gradients in the ice increase the contribution of viscous drag on basal shear stress. In all experiments, the relationship between melt rate and shear stress is best explained by a model that accounts for the effects of regelation and viscous creep on the bed-normal drag force. We interpret this to mean fluid flow around entrained clasts contributed to basal drag even at subfreezing temperatures. Incorporating premelting dynamics into the Watts/Hallet model for subglacial rock friction, we find that the predicted debris-bed drag decreases by approximately an order of magnitude, with a corresponding ~3.5 × increase in the transition radius. This is lower than we observe for ice slightly below the pressure melting point.

New Nature-Inspired Cycloidal Propeller for Low-Reynolds-Number Hovering Flight

A new type of pivoting-blade cycloidal propeller, which can equip aircraft with vertical take-off and landing capability, is presented in this paper. This propeller has the appearance of damselfly wings and the advantage of low mass compared with other types developed to date. The operating mode shows similarities with the movement of these insects’ wings to generate upward vertical thrust. To cover the range of Reynolds number from 2250 to 25,000, propellers with 70 and 200 mm blades were constructed. Using the blade element theory, a simplified two-dimensional mathematical model was developed to predict thrust, power, and hovering efficiency. Experiments were performed to validate that model for the case of hovering flight. Quantitatively, the results of the experiments match the prediction produced by the two-dimensional mathematical model very well. The theoretical analysis proves that both lift and drag contribute to the net vertical force, and the contribution of drag is at least 50%. This way of generating vectored thrust is emerging as an alternative solution to other types of propulsion in low-Reynolds-number regimes with a blade tip Mach number not greater than 0.2.

Particle dispersion in turbulent, square open duct flows of high Reynolds number

Large eddy simulation is used to study particle dispersion in fully-developed, square open duct flow at Reynolds numbers of 83 k,250 k based on the bulk velocity and duct width. Particle motion is governed by drag, lift, added mass force, pressure gradient force, buoyancy and gravity, with particle size in the range St = 0.032–2415.42. The results show that in the open duct cross-section, secondary flow dominates small particles' dispersion. For larger particles (St > 3.23), gravity plays a significant role in dominating their distribution and deposition rate, which increased with particle size. They tend to disperse better in the spanwise direction than vertical direction. Particles with St = 3.23–96.62 tend to accumulate in the corners, while those with St > 323 in Re = 83 k flow are prone to concentrate in the central regions of duct floor. It is observed that the Reynolds number could enhance particle dispersion in the whole cross-sectional plane. Near the bottom wall, particles with St = 12.93 are found to be also preferentially concentrated by near-wall turbulence, with particle size for this kind of accumulation increasing with Reynolds number. In addition, particles are found to be less dispersed in open duct flow in comparison with closed duct flow. Such trend increases with particle size and dimensionless time. A dynamic force analysis shows that the contribution of pressure drag and lift force gradually increases with particle size. Pressure drag can inhibit particle dispersion, whereas lift force has the opposite effect. The mechanism of particle dispersion in turbulent, open square duct flows is eventually elucidated.

The influence of the rim depth to the aerodynamic performances of a wheel: a numerical study

Summary  The aerodynamic drag and side force of five different wheels are evaluated by means of Computational Fluid Dynamics (CFD). The wheels are identical with the exception of the depth of the rim, which varies from 20 to 100 mm (Figure 1a).  Introduction  Aerodynamic drag is responsible for about 90 % of the total resistance of a cyclist travelling at racing speeds (Kyle & Burke, 1984). The bike contribution to the total drag ranges from 28% to 36% of the total drag depending on his or her position (Defraeye et al., 2010a). Earlier research has shown that the wheels’ contribution to the total drag is within 10% i€­ 15% and that an overall reduction in aerodynamic drag of 2-3% is possible solely by optimizing the wheels (Greenwell et al. 1995).  Therefore, a correct selection of the wheel can make a difference in the final result of a cycling race. In this paper the aerodynamics of spoked wheels as the most commonly used wheels in cycling races are investigated. The aerodynamic performances of spoked wheels are mainly affected by three factors: i) spoke count; ii) spoke shape and iii) rim depth. The first two parameters are kept fixed in this study while the rim depth is varied in order to better understand its effect on the aerodynamic forces generated on the wheel. To do so, an elliptical rim shape is adopted for all wheels.  Methods 3D steady Reynolds-Averaged Navier-Stokes (RANS) CFD simulations are performed to investigate the aerodynamic forces acting on five wheels with different rim depth at different yaw angles. The evaluation is based on validation with wind-tunnel measurements of Zipp Speed Weaponry, Indiana, USA, as presented in Godo et al., 2010.  The wheel considered for the validation study is the Zipp 404. Detailed characteristics of the wheel are provided in Godo et al. (2010). Subsequently, five wheels are created with elliptical rim shape of different depth.  The fluid domain is split in three regions. The first zone is built around the hub, the spokes and the internal part of the rim, and is later modelled as a moving reference frame (Figure 1b). The second zone is built externally to the wheel and has a cylindrical shape, which can be rotated to obtain different yaw angles for the wheel. The third zone is a parallelepiped representing the far-field domain.  The wheels are first drawn using the Computer-Aided Design (CAD) program PTC-Creo. The computational grid is then built using ANSYS/Fluent Meshing (Figure 1c). The volume grids consist of prismatic cells in the boundary layer region near the wheel and the ground while tetrahedral cells are employed nearby the wheel. Moreover, hexahedral cells are used in the far-field. The rotation of the wheel is imposed using a moving reference frame in the volume zone near the spokes. In the rest of the wheel, a rotational moving wall boundary condition is applied. The wheel-ground contact is modelled extruding the wheel’s footprint for 7mm. The k-I‰ SST turbulence model is used. Note that the good performance of this turbulence model for cyclist aerodynamics has been shown in several occasions in the past, e.g. Defraeye et al., 2010b. Results Earlier research results (Godo et al. 2010), have shown that for spoked wheels a decrease occurs in the drag coefficient, C D , when the yaw angle is increased up to 10 degrees. For larger yaw angles, C D increases. The expected effect of increasing the rim depth is to decrease the aerodynamic drag of the wheel, but an increase of the side force for large yaw angles is also expect. Â