aerodinamika Pert 2 PRINSIP DASAR Ketika aliran udara

aerodinamika Pert. 2

PRINSIP DASAR Ketika aliran udara melewati circular silinder, yang mana tegak lurus dengan aliran. p. Usaran udara dibentuk dibelakang silinder dimana terdapat faktor jumlah frekuensi. Yaitu, ukuran silinder, kecepatan aliran

Permasalahan diatas jumlah frekuensi pusaran udara (n), akan tergantung pada: 1. ukuran silinder (d) 2. kecepatan aliran (v) 3. massa jenis fluida (p kecepatan fluida dapat menggunakan simbol µ atau v

Gravitational effects are also excluded. Then and, assuming that this function (. . . ) may be put in the form where C is a constant and a, b, e and f are some unknown indices in dimensional form leads to where each factor has been replaced by its dimensions. Now the dimensions of both sides must be the same and therefore the indices of M, L and T on the two sides of the equation may be equated as follows: Mass(M) 0 =e Length (L) 0 =a+b-3 e+2 f Time (T) -1 = -b-f

Here are three equations in four unknowns. One unknown must therefore be left undetermined: f, the index of u, is selected for this role and the equations are solved for a, b and e in terms off. The solution is, therefore,

where g represents some function which, as it includes the undetermined constant C and index f, is unknown from the present analysis. Although it may not appear so at first ight, Eqn (1. 38) is extremely valuable, as it shows that the values of nd/V should epend only on the corresponding value of Vd/v, regardless of the actual values of the original variables. This means that if, for each observation, the values of nd/V and Vd/v are alculated and plotted as a graph, all the results should lie on a single curve, this curve representing the unknown function g. A person wishing to estimate the eddy frequency for some given cylinder, fluid and speed need only calculate the value of Vd/v, read from the curve the corresponding value of nd/V and convert this to eddy frequency n. Thus the results of the series of observations are now in a usable form.

Consider for a moment the two compound variables derived above: (b) Vd/v. The dimensions of this are given by

Dimensional analysis applied to aerodynamic force Assume, then, that the aerodynamic force, or one of its components, is denoted by F and when fully immersed depends on the following quantities: fluid density p, fluid kinematic viscosity v, stream speed V, and fluid bulk elasticity K. The force and moment will also depend on the shape and size of the body, and its orientation to the stream. If, however, attention is confined to geometrically similar bodies, e. g. spheres, or models of a given aeroplane to different scales, the effects of shape as such will be eliminated, and the size of the body can be represented by a single typical dimension; e. g. the sphere diameter, or the wing span of the model aeroplane, denoted by D. Then, following the method above

The Eqns (1. 40) may then be solved for a, b and c in terms of d and e giving

Kecepatan suara and V/a is the Mach number, M, of the free stream. Therefore equation may be written as : where g(VD/v) and h(M) are undetermined functions of the stated compound variables. Thus it can be concluded that the aerodynamic forces acting on a family of geometrically similar bodies (the similarity including the orientation to the stream), obey the law

Example 1. 1 An aircraft and some scale models of it are tested under various conditions, given below. Which cases are dynamically similar to the aircraft in flight, given as case (A)? Case (A) represents the full-size aircraft at 6000 m. The other cases represent models under test in various types of wind-tunnel. Cases (C), (E) and (F), where the relative density is greater than unity, represent a special type of tunnel, the compressed-air tunnel, which may be operated at static pressures in excess of atmospheric. From the figures given above, the Reynolds number VDp/p may be calculated for each case. These are found to be

From the figures given above, the Reynolds number VDp/p may be calculated for each case. These are found to be It is seen that the values of Re for cases (C) and (E) are very close to that for the full-size aircraft. Cases (A), (C) and (E) are therefore dynamically similar, and the flow patterns in these three cases will be geometrically similar. In addition, the ratios of the local velocity to the free stream velocity at any point on the three bodies will be the same for these three cases. Hence, from Bernoulli's equation, the pressure coeficients will similarly be the same in these three cases, and thus the forces on the bodies will be simply and directly related. Cases (B) and D) have Reynolds numbers considerably less than (A), and are, therefore, said to represent a 'smaller aerodynamic scale'. The flows around these models, and the forces acting on them, will not be simply or directly related to the force or flow pattern on the full-size aircraft. In case (F) the value of Re is larger than that of any other case, and it has the largest aerodynamic scale of the six.

Example 1. 2 An aeroplane approaches to land at a speed of 40 m s-l at sea level. A 1/5 th scale model is tested under dynamically similar conditions in a Compressed Air Tunnel (CAT) working at 10 atmospheres pressure and 15°C. It is found that the load on the tailplane is subject to impulsive fluctuations at a frequency of 20 cycles per second, owing to eddies being shed from the wing-fuselage junction. If the natural frequency of flexural vibration of the tailplane is 8. 5 cycles per second, could this represent a dangerous condition? For dynamic similarity, the Reynolds numbers must be equal. Since the temperature of the atmosphere equals that in the tunnel, 15°C, the value of p is the same in both model and full-scale cases. Thus, for similarity

This is very close to the given natural frequency of the tailplane, and there is thus a considerable danger that the eddies might excite sympathetic vibration of the tailplane, possibly leading to structural failure of that component. Thus the shedding of eddies at this frequency is very dangerous to the aircraft.

Example 1. 3 An aircraft flies at a Mach number of 0. 85 at 18300 m where the pressure is 7160 Nm-2 and the temperature is -56. 5 "C. A model of l/l. Oth scale is to be tested in a highspeed wind-tunnel. Calculate the total pressure of the tunnel stream necessary to give dynamic similarity, if the total temperature is 50 "C. It may be assumed that the dynamic viscosity is related to the temperature as follows:

If the total pressure available in the tunnel is less than this value, it is not possible to achieve equality of both the Mach and Reynolds numbers. Either the Mach number may be achieved at a lower value of Re or, alternatively, Re may be made equal at a lower Mach number. In such a case it is normally preferable to make the Mach number correct since, provided the Reynolds number in the tunnel is not too low, the effects of compressibility are more important than the effects of aerodynamic scale at Mach numbers of this order. Moreover, techniques are available which can alleviate the errors due to unequal aerodynamic scales.