Prediction of static aerodynamic characteristics for slender bodies alone and with lifting surfaces to very high angles of attack
01 Sep 1977-
TL;DR: In this paper, an engineering-type method was presented for computing normal-force and pitching-moment coefficients for slender bodies of circular and noncircular cross section alone and with lifting surfaces.
Abstract: An engineering-type method is presented for computing normal-force and pitching-moment coefficients for slender bodies of circular and noncircular cross section alone and with lifting surfaces. In this method, a semi-empirical term representing viscous-separation crossflow is added to a term representing potential-theory crossflow. For many bodies of revolution, computed aerodynamic characteristics are shown to agree with measured results for investigated free-stream Mach numbers from 0.6 to 2.9. The angles of attack extend from 0 deg to 180 deg for M = 2.9 from 0 deg to 60 deg for M = 0.6 to 2.0. For several bodies of elliptic cross section, measured results are also predicted reasonably well over the investigated Mach number range from 0.6 to 2.0 and at angles of attack from 0 deg to 60 deg. As for the bodies of revolution, the predictions are best for supersonic Mach numbers. For body-wing and body-wing-tail configurations with wings of aspect ratios 3 and 4, measured normal-force coefficients and centers are predicted reasonably well at the upper test Mach number of 2.0. Vapor-screen and oil-flow pictures are shown for many body, body-wing and body-wing-tail configurations. When spearation and vortex patterns are asymmetric, undesirable side forces are measured for the models even at zero sideslip angle. Generally, the side-force coefficients decrease or vanish with the following: increase in Mach number, decrease in nose fineness ratio, change from sharp to blunt nose, and flattening of body cross section (particularly the body nose).
Citations
More filters
TL;DR: In this article, the authors used the Reynolds number to estimate the pitch rate of the nose tip roll rate of a single forebody vortice, which is based on dmax and freestream conditions; usually Re = Rd Reynolds number, Rd = U^d/v^ reference area.
Abstract: body length forebody length forward of rotation center (Fig. 8) nose length = rolling moment, coefficient C, = £/ (p* U^ /2)Sb vortex wake wave length Mach number pitching moment, coefficient Cm=Mp/(PooUl/2)Sc yawing moment, coefficient Cn=n/(p00 U00/2)Sc = normal force, coefficient CN=N/ (p^ C/i/2)S = nose tip roll rate = pitch rate Reynolds number based on dmax and freestream conditions; usually Re = Rd Reynolds number, Rd = U^d/v^ reference area, S = ird /4 reference area ( = projected wing area) time velocity axial body-fixed coordinate (distance from apex) side force, coefficient CY=Y/(PooUx /2)S angle of attack da/df, C^ = d C m / d j > ' l 0 / U ( X ) sideslip angle rotation of plane of symmetry of forebody vortices (Fig. 8) cone half-angle 6A = apex half-angle p = air density = roll angle 5 = three-dimensional separation angle (Fig. 15) a' = total angle of inclination (Fig. 8) v — kinematic viscosity oj = angular rate
99 citations
TL;DR: In this paper, a comparative study of computational fluid dynamics (CFD) and analytical and semi-empirical (ASE) methods applied to the prediction of the normal force and moment coefficients of an AUV is presented.
Abstract: This paper presents a comparative study of computational fluid dynamics (CFD) and analytical and semiempirical (ASE) methods applied to the prediction of the normal force and moment coefficients of an autonomous underwater vehicle (AUV). Both methods are applied to the bare hull of the vehicle and to the body-hydroplane combination. The results are validated through experiments in a towing tank. It is shown that the CFD approach allows for a good prediction of the coefficients over the range of angles of attack considered. In contrast with the traditional ASE formulations used in naval and aircraft fields, an improved methodology is introduced that takes advantage of the qualitative information obtained from CFD flow visualizations.
71 citations
Cites background or methods from "Prediction of static aerodynamic ch..."
...This parameter is a function of the fineness ratio [21], [27], where is the body length and is the body maximum diameter....
[...]
...This result has been adopted by the missile community even for the subsonic flow [27], [29]....
[...]
...The formulas used in this paper originated in the aircraft and missile related literature [27] but were properly modified to include the results of research work in the marine field, namely, in what regards the study of rudder influence on ship maneuverability [28]....
[...]
...In the “PNA model” (Principles of Naval Architecture [27]), the interference between the fin and the bare hull is considered through the effective aspect ratio, which is different from the geometric aspect ratio....
[...]
01 Jan 1986
TL;DR: Schlieren et al. as discussed by the authors investigated the effect of angle of attack, Reynolds number, and Mach number on the occurrence of vortices, the position of vortex shedding, the principal surfaceflow-separation patterns, the magnitude of surface-flow angles, and the extent of laminar and turbulent flow for symmetric, asymmetric, and wake-like flow separation regimes.
Abstract: Flow-visualization studies of ogival, parabolic, and conical forebodies were made in a comprehensive investigation of the various types of flow patterns. Schlieren, vapor-screen, oil-flow, and sublimation flow-visualization tests were conducted over an angle-of-attack range from 0 deg. to 88 deg., over a Reynolds-number range from 0.3X10(6) to 2.0X10(6) (based on base diameter), and over a Mach number range from 0.1 to 2. The principal effects of angle of attack, Reynolds number, and Mach number on the occurrence of vortices, the position of vortex shedding, the principal surface-flow-separation patterns, the magnitude of surface-flow angles, and the extent of laminar and turbulent flow for symmetric, asymmetric, and wake-like flow-separation regimes are presented. It was found that the two-dimensional cylinder analogy was helpful in a qualitative sense in analyzing both the surface-flow patterns and the external flow field. The oil-flow studies showed three types of primary separation patterns at the higher Reynolds numbers owing to the influence of boundary-layer transition. The effect of angle of attack and Reynolds number is to change the axial location of the onset and extent of the primary transitional and turbulent separation regions. Crossflow inflectional-instability vortices were observed on the windward surface at angles of attack from 5 deg. to 55 deg. Their effect is to promote early transition. At low angles of attack, near 10 deg., an unexpected laminar-separation bubble occurs over the forward half of the forebody. At high angles of attack, at which vortex asymmetry occurs, the results support the proposition that the principal cause of vortex asymmetry is the hydrodynamic instability of the inviscid flow field. On the other hand, boundary-layer asymmetries also occur, especially at transitional Reynolds numbers. The position of asymmetric vortex shedding moves forward with increasing angle of attack and with increasing Reynolds number, and moves rearward with increasing Mach number.
60 citations
14 Jan 1980
59 citations
TL;DR: In this paper, the authors used analytical and semi-empirical methods to estimate the hydrodynamic derivatives of a popular class of AUVs and compared the results with the results obtained by using computational fluid dynamics to evaluate the bare hull lift force distribution around a fully submerged body.
49 citations
References
More filters
TL;DR: In this article, Schlieren photographs of the wake have been analyzed by means of the impulse flow analogy and also by considering the vortices to be part of a yawed infinite vortex street.
Abstract: Extensive schlieren studies and yawmeter traverses of the wake behind slender cone-cylinders at large angles of incidence have shown that the flow pattern is generally steady. Under certain flow conditions, however, the wake exhibits an instability which is not understood. For cross-flow Reynolds numbers in the subcritical region the wake can be described in terms of a cross-flow Strouhal number which has a constant value of 0·2 for cross-flow Mach number components (Mc) up to 0·7 and then increases steadily to a value of 0·6 at Mc = 1·6. The strength of the wake vortices varies substantially with Mc, increasing to a maximum at Mc ≈ 0·7 and then decreasing rapidly for higher values of Mc. Schlieren photographs of the wake have been analysed by means of the impulse flow analogy and also by considering the vortices to be part of a yawed infinite vortex street. The impulse flow analogy is shown to be of use in determining the cross-flow Strouhal number but estimates of vortex strength are too high. The Karman vortex street theory combined with the sweepback principle leads to reliable estimates of vortex strength up to Mc = 1·0.Information is given on the spacing, path and strength of the vortices shed from the body for flow conditions varying from incompressible speeds up to Mc = 1·0. Finally this information is used to determine the vortex drag of a two-dimensional circular cylinder below Mc = 1·0.
192 citations
185 citations
01 Mar 1922
TL;DR: In this paper, it was shown that the drag depends on the absolute dimensions of the body and the velocity and viscosity of the fluid in a much more complex manner than has heretofore been supposed.
Abstract: Thus far, all attempts at the quantitative determination of drag, on the basis of the theory of viscous fluids, have met with but slight success. For this reason, whenever a more accurate knowledge of the drag is desirable, it must be determined by experiment. Here, a few experimental results are given on the drag of a cylinder exposed to a stream of air at right angles to its axis. It is shown that the drag depends on the absolute dimensions of the body and the velocity and viscosity of the fluid in a much more complex manner than has heretofore been supposed.
146 citations
TL;DR: In this paper, the cross-flow drag and normal force coefficients are determined experimentally as a function of the relative displacement of fluid in time-dependent two-dimensional flow, and the evolution with time of the body-wake characteristics are determined from high-speed motion pictures.
Abstract: The analogy between the impulsive flow over circular cylinders and flat plates and the separated flow about slender bodies moving at high angles of attack in the subsonic to moderately supersonic-velocity range is discussed. The cross-flow drag and normal force coefficients are determined experimentally as a function of the relative displacement of fluid in time-dependent two-dimensional flow. The evolution with time of the body-wake characteristics are determined from high-speed motion pictures. The results show that during the growth of symmetrical vortices, the laminar flow drag coefficients of the test bodies reach a value about 25% higher than their corresponding steady flow values. In the supercritical range, records for the drag show considerable disagreement, except that the drag coefficient lies between 0.25 and 0.40.
120 citations