載貨汽車氣壓制動系統(tǒng)設計,載貨汽車氣壓制動系統(tǒng)設計,載貨,汽車,氣壓,制動,系統(tǒng),設計 附錄B Problem Formulation In this paper, the realization of an aerodynamic brake integrated in a rear wing of a formula car has been consi- dered. The first step consists in the choice of an appropriate aerodynamic appendix. In particular, it was decided to study an Italian Formula 4 race car [1], being a category in the first stages of development. Also, the regula- tion of this championship is easy to find and the car is characterized by uniformity of the mechanics and the air- foils. Therefore, taken note of the technical regulation on FIA website, it was decided to study the upper airfoil, of which was shown a dimensioned drawing (Figure 1). It is an aluminum alloy wing, with a chord line of 237.9 mm and a height of 54.2 mm. Formula 4 championship will provide the use of a 4T heat engine (Otto/Beau de Rochas cycle): it can be na- turally aspirated or turbocharged, with maximum power in the order of 120 kW (160 HP). Considering the weight of the car and the race tracks of the championship, it is predicted a maximum speed of 230 km/h (64 m/s). Regarding the operating conditions, an air temperature of 300K was assumed at atmospheric pressure. Briefing Description of Airfoil Behavior Considering an airfoil, there are several elements that have a specific nomenclature: Mean camber line: locus of points halfway between the upper and lower surface as measured perpendicular to the mean chamber line itself; Leading edge: the most forward point of the mean camber line; Trailing edge: the rearmost point of the mean camber line; Chord: the straight line joining the leading edge with the trailing edge; Upper surface: the upper boundary of the profile; Lower surface: the lower boundary of the profile; Thickness: the distance between the lower surface and the upper surface. The different airfoil shapes are marked by a logical numbering system which was introduced by the U.S. fed- eral agency NACA. This system consists of four digits which have a definite meaning: the first digit indicates the maximum camber in hundredths of chord; the second digit represents the location of maximum camber along the chord from leading edge in tenths of chord; the third and fourth give the maximum thickness in hundredths of chord. When an airfoil is moving relative to the air, it generates an aerodynamic force, in a rearward direction at an angle with the direction of relative motion. This aerodynamic force is commonly resolved into two components: lift and drag. Lift is the force component perpendicular to the direction of relative motion while Drag is the force component parallel to the direction of relative motion. These forces are studied at different angles of attack which is the angle at whices smoothly over the airfoil and is attached to the back of the wing. As soon as α increases, the flow tends to separate from the surface of the airfoil, creating a region of “dead air” behind the profile. A briefing flow analysis of the physical phenomenon in question in order to understand better what is happening in the latter case is reported. It is clear from Figure 2 that the speed at the trailing edge tends to in- crease, with a strong reduction of the pressure, while in the stagnation point the speed tends to be zero and pres- sure rises sharply. It creates an adverse pressure gradient, thus particles of fluid move from the trailing edge to the stagnation point, and then it has a rapid separation of the boundary layer below. Stagnation point does not have a stable position in these conditions because there is not pressure recovery. The recirculation generated . Figure 1. Dimensioned Drawing of a F4 rear wing (in mm). the detachment of the boundary layer creates first vortex that causes a wake vortex. It is necessary to study the turbulent behavior of the fluid that meets the wing, through the Navier-Stokes equations in order to consider the stall of the wing:where u(x, t) is the instantaneous velocity, ρ the medium density, μ the viscosity and f the applied force. This system of equations is a system of partial differential equations that describe the behavior of a Stokesian fluid: the fluid can be considered to be continuous. There is an analytical solution only in simplified cases, while solutions in the other cases can be obtained using simplified methods of numerical analysis. The most straight- forward method for the numerical simulation of turbulent flows is direct numerical simulation DNS which dis- cretizes the Navier-Stokes equations. It resolves the entire range of turbulent length scales thus the description of the flow is so detailed that the validity of the simulation is similar to an experiment. The computational cost is proportional to Re3, thus it is necessary to use a different solution studying turbulent flows at high Reynolds, because the computational resources required by a DNS would exceed the capacity of the most powerful com- puter currently available. In practical applications, the knowledge of the average quantities is enough to solve the problem of a turbulent flow; the basic idea of the technique RANS (Reynolds Averaged Navier-Stokes Equ- ations) is to derive only the average parameters (mediated in time) from Navier-Stokes equations, reducing the enormous computational cost required by DNS. In practice, the turbulent motion consists of a mean motion and fluctuation over time. Using the decomposition of Reynolds:The K-ε model is one of the most common models of turbulence, even if it is not appropriate in the case of strong adverse pressure gradients. It is a model with two equations: it includes two additional transport equations to represent properties of the turbulent flow and effects such as convection and diffusion of turbulent energy. The first variable transported is the turbulent kinetic energy, k. The second variable transported is the turbulent dissipation, ε; the second variable determines the scale of turbulence, while the first variable k determines the energy in the turbulence. There are two formulations of the K-ε models: the standard k-epsilon model and the RNG k-epsilon model. In the standard k-epsilon model, eddy viscosity is determined by single length scale turbulence, so the turbu- lent diffusion is calculated only through a specified scale, whereas in reality all scales of motion will contribute to turbulent diffusion. The approach RNG (Re-Normalisation Group), a mathematical technique that can be used to obtain a model similar to the k-epsilon turbulence, presents a modified equation ε, which attempts to explain the different scales of turbulence through changes at the term of production of turbulence. Project Description The purpose of this project is to improve the race performance, reducing the breaking distance and increasing the bending speed. So, we decided to intervene on the drag generated by the wing during the breaking, and also on the grip provided by downforce, function of velocity. To explain the lift, and then the downforce, reference may be made to the wing of an airplane, observing its section. The latter is asymmetric, the top has a profile longer than the bottom: when the wing moves, it separates the relative flow in two parts, so the air layers scroll faster in the top. The outflow over the wing undergoes a boost and then is aerodynamic brake for formula cars accelerated towards the tail at a higher velocity than the air under the wing, which follows a shorter path. So the two currents are reunited in the tail after a same time interval, without creating imbalances. This is not just the facts, but as a first approximation, we can refer to this model. In reference to the Bernoulli trinomial law, since in the lower flow velocity is lower than in the upper, the pressure under the wing has to be greater than that above the wing. Therefore, the difference between the two pressures generates a resultant directed upwards, that is the lift, which holds the aircraft in the air. In detail, lift can be expressed as: The overall resistance opposed by a fluid medium to the object forward movement is given, in first approxi- mation, by the sum of the frictional resistance, the wake resistance and the induced resistance of lift. In particu- lar, for a tapered body, the flow resistance is given by friction (laminar and/or turbulent), that is the rubbing of the surface against the medium. For this purpose we introduce the concept of boundary layer: it’s the dynamic range, laminar or turbulent, in which internal current speed is subject to strong gradients (continuous changes), due to the viscosity of the fluid. The thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which surrounds it. In a turbulent boundary layer, the viscous stresses are added also the stresses, due to the exchange of transverse momentum; these actions increase with the fluid density. The chaos of the turbulent fluid motions implies higher thermal dissipation, so the braking opposing force, in turbulent flow con- ditions, is greater than that of the laminar regime. The resistance generated, in this way, is affected by the sur- face roughness: moreover, the rougher surfaces ignite earlier and more easily the turbulent condition in the flow, and then, determine higher resistances. Wing Design The first phase of the design is to draw the profile of the wing with a CAD software. In this way, it is possible to make a CFD simulation, to evaluate the aerodynamic performance of the wing, in terms of downforce and drag, and estimate the useful angles of attack before stall phenomenon occurs [3]. In fluid dynamics the stall is a re- duction of the lift coefficient due to an increase of the angle of attack or due to the incident velocity decrease on an aerodynamic profile, such as an airfoil, a propeller blade or a turbomachinery rotor. The minimum value of the angle of attack for which the stall occurs is called critical angle of attack. This value which corresponds to the maximum lift coefficient, changes significantly, depending on the particular profile or on the considered Reynolds number [4]. Similarly, the profile of the active cavities has been reported, and appropriate simulations were performed. In this way it was possible to estimate the sizes and configurations to achieve the project target. Based on the data collected, the application of these cavities on the wing is studied, evaluating the performance on the different possible arrangements of these cavities. At this moment only 2D simulations have been per- formed, and a 3D series is considered as future improvement of the project. The models, the different configura- tions and the results obtained from all the cases mentioned above, will be shown in detail in the following para- graphs. Geometry Modeling To this pur- pose, a sizeable set of data was created by means of sufficiently accurate numerical simulations, to derive initial values. The simulations were performed on 3-D models in kinematic similarity using a commercial CFD simula- tion code, ANSYS/Fluent. The turbulence model was the k-ε realizable, with second order accuracy. Each model was meshed to ensure a y+max ~ 5, a necessary condition for adopting the enhanced wall treatment, since the quality of the grid has a relevant importance on the accuracy and stability of the numerical simulation. Figure 2. Boundary layer. Regarding to the active cavity, the geometry is illustrated in Figure 4(b). The space surrounding the geometry of the aerodynamic and the cavities was discretized using a special dedicated software available as ANSYS package. Furthermore, to observe the progress of the boundary layer, it was built on a reference mesh of 5 layers, with growth factor 1.1, starting from the adjacent profiles of height 0.18 mm (Figure 5). To this pur- pose, a sizeable set of data was created by means of sufficiently accurate numerical simulations, to derive initial values. The simulations were performed on 3-D models in kinematic similarity using a commercial CFD simula- tion code, ANSYS/Fluent. The turbulence model was the k-ε realizable, with second order accuracy. Each model was meshed to ensure a y+max ~ 5, a necessary condition for adopting the enhanced wall treatment, since the quality of the grid has a relevant importance on the accuracy and stability of the numerical simulation. Commercial software allows the “plastering” of cell layers to the critical boundaries of the control volume, which are obviously, in this case, the wall surfaces of the hub, casing and blades. In these zones the usual practice is that of creating a completely structured boundary layer, specifying whenever possible both the height of the first row of cells and the “growth ratio”, i.e. the rate that determines the height of the successive cells. In this process, the height of the first row of cells is usually determined via an empirical formula that gives the value of a wall-based local Reynolds number, denoted by y+ (y+ = u*·y/v where u* = (τwall/ρ)1/2, with τwall being the wall shear stress). For the wing analysis control volume was split in several smaller sub-volumes, to achieve a more con- sistent set of faces and to better exploit the possibility of creating a locally more refined grid. The choice of the boundary conditions was made as follows: it was performed heuristically, starting from the preliminary sizing data, calibrating them by means of a first simulation, adjusting the values by iteratively resetting the outlet static pressure on the near-wake radial area downstream of the trailing edge. Through subsequent simulations the values of the inlet total pressure and temperature were refined as well in order to ensure conservation. Simulation Results Wing Performance In this paragraph, the performance of the wing has been analyzed. The results obtained by using CFD simulation (see Figures 6-8), were used as the reference model for the subsequent tests [5]. Since, the following figure shows the results for a 0? angle of attack. In particular, for a hypothetical unitary extension wing (1 m), it is obtained:The thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which surrounds it. In a turbulent boundary layer, the viscous stresses are added also the stresses, due to the exchange of transverse momentum; these actions increase with the fluid density. The chaos of the turbulent fluid motions implies higher thermal dissipation, so the braking opposing force, in turbulent flow con- ditions, is greater than that of the laminar regime. The resistance generated, in this way, is affected by the sur- face roughness: moreover, the rougher surfaces ignite earlier and more easily the turbulentThe thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which surrounds it. In a turbulent boundary layer, the viscous stresses are added also the stresses, due to the exchange of transverse momentum; these actions increase with the fluid density. The chaos of the turbulent fluid motions implies higher thermal dissipation, so the braking opposing force, in turbulent flow con- ditions, is greater than that of the laminar regime. The resistance generated, in this way, is affected by the sur- face roughness: moreover, the rougher surfaces ignite earlier and more easily the turbulentThe thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which surrounds it. In a turbulent boundary layer, the viscous stresses are added also the stresses, due to the exchange of transverse momentum; these actions increase with the fluid density. The chaos of the turbulent fluid motions implies higher thermal dissipation, so the braking opposing force, in turbulent flow con- ditions, is greater than that of the laminar regime. The resistance generated, in this way, is affected by the sur- face roughness: moreover, the rougher surfaces ignite earlier and more easily the turbulentThe thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which surrounds it. In a turbulent boundary layer, the viscous stresses are added also the stresses, due to the exchange of transverse momentum; these actions increase with the fluid density. The chaos of the turbulent fluid motions implies higher thermal dissipation, so the braking opposing force, in turbulent flow con- ditions, is greater than that of the laminar regime. The resistance generated, in this way, is affected by the sur- face roughness: moreover, the rougher surfaces ignite earlier and more easily the turbulent.The thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which surrounds it. In a turbulent boundary layer, the viscous stresses are added also the stresses, due to the exchange of transverse momentum; these actions increase with the fluid density. The chaos of the turbulent fluid motions implies higher thermal dissipation, so the braking opposing force, in turbulent flow con- ditions, is greater than that of the laminar regime. The resistance generated, in this way, is affected by the sur- face roughness: moreover, the rougher surfaces ignite earlier and more easily the turbulentThe thickness of the boundary layer is very small, and it is of one order of magnitude lower than the overall dimensions of the object, that generates the viscose perturbation. Then, inside the boundary layer, the tangential shear stress is “dense”. For this reason in the layer is exerted an intense dissipative braking action, converting part of the movement in thermal agitation. The dissipative action limits the relative velocity between the object and the fluid, which su