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A computer program developed for determining the subsonic pressure, force, and moment coefficients for a fuselage-type body using slender body theory is described. The program is suitable for determining the angle of attack and sideslipping characteristics of such bodies in the linear range where viscous effects are not predominant. Procedures developed which are capable of treating cross sections with corners or regions of large curvature are outlined.
A computationally efficient body analysis designed to couple with a comprehensive helicopter analysis is developed in order to calculate the body-induced aerodynamic effects on rotor performance and loads. A modified slender body theory is used as the body model. With the objective of demonstrating the accuracy, efficiency, and application of the method, the analysis at this stage is restricted to axisymmetric bodies at zero angle of attack. By comparing with results from an exact analysis for simple body shapes, it is found that the modified slender body theory provides an accurate potential flow solution for moderately thick bodies, with only a 10%-20% increase in computational effort over that of an isolated rotor analysis. The computational ease of this method provides a means for routine assessment of body-induced effects on a rotor. Results are given for several configurations that typify those being used in the Ames 40- by 80-Foot Wind Tunnel and in the rotor-body aerodynamic interference tests being conducted at Ames. A rotor-hybrid airship configuration is also analyzed.
A modified slender body theory was used in modelling the flowfield around an axisymmetric body at zero angle of attack. The model was defined in an attempt to characterize body-induced effects on helicopter rotor performance and loading using efficient computation methods. The streamfunction for an axial source distribution was applied in the body model, which was then adapted to the helicopter analysis code (CAMRAD). The body-induced velocities were calculated for separate locations on the rotor disk. Three different rotor models in nonuniform inflow with a free wake geometry were considered. Comparison of predictions with data on ellipsoidal and axisymmetric bodies showed good agreement for moderately thick ellipsoidal bodies. Oscillatory blade bending moments were increased by the presence of the body, but overall performance impact was negligible. Computational efficiency was 10-20 percent better than with a potential flow panel code.
Linearized slender-body theory is applied to the computation of aerodynamic forces on an oscillating, or deforming, body in supersonic flow. The undeformed body is a body of revolution and the deformed body is represented by movement of a line through the centers of the cross sections which are assumed to remain circular. The time dependence is based on sinusoidal motion. For a body of vanishing thickness the slender-body theory yields the apparent mass approximation as it is obtained for incompressible crossflow around a cylinder. Both linearized slender-body theory and the apparent mass approximation are used to calculate the pitching-moment coefficients on a rigid slender body with a parabolic arc nose cone, and these coefficients are compared with some experimental results.
Hypersonic flow past slender bodies, discussing inviscid flows, outer edge singularity of boundary layer and three dimensional interaction on needle- like bodies
The Sychev (1960) analysis for inviscid hypersonic flow past slender bodies at large angle of attack is shown to be applicable to all slender-body flows whose crossflow Mach numbers are greater than sonic; it is therefore not restricted to flows with hypersonic crossflow Mach number values, as indicated elsewhere in the literature. It is also noted that the Sychev similarity applies to a number of slender-body flows with subsonic crossflow Mach numbers, including incompressible flow.
The basic ideas of the slender-body approximation have been applied to the nonlinear transonic-flow equation for the velocity potential in order to obtain some of the essential features of slender-body theory at transonic speeds. The results of the investigation are presented from a unified point of view which demonstrates the similarity of slender-body solutions in the various Mach number ranges. The transonic area rule and some conditions concerning its validity follow from the analysis. (author)
The basic ideas of the slender-body approximation have been applied to the nonlinear transonic-flow equation for the velocity potential in order to obtain some of the essential features of slender-body theory at transonic speeds. The results of the investigation are presented from a unified point of view which demonstrates the similarity of slender-body solutions in the various Mach number ranges. The transonic area rule and some conditions concerning its validity follow from the analysis.
This work presents a slender-body approach to evaluate the second-order wave loads acting on a floating structure in the frequency domain. The approach is in the same spirit as the common use of Morison’s equation to approximate the wave loads without solving the radiation/diffraction problem. To do so, we employ Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear effects. We introduce modifications to Rainey’s formulation in order to evaluate wave kinematics at the mean body position instead of the original approach of considering instantaneous displacements. We also propose a simple approximation to partially account for wave scattering effects on the second-order loads based on the analytical solution of a surface-piercing bottom-mounted vertical circular cylinder. Though limited to structures composed of cylinders, this slender-body approach is orders of magnitude faster than computing second-order wave coefficients with a radiation/diffraction code. We implemented this approach for difference-frequency (slow drift) loads in an open-source frequency-domain floating wind turbine model. We present comparisons against results obtained with radiation/diffraction theory for three reference floating wind turbine designs: the OC3-Hywind spar, the OC4-DeepCwind semisubmersible, and the VolturnUS-S semisubmersible. In general, the results show that the proposed slender-body approach with the correction to approximate wave scattering effects provides useful estimations of the difference-frequency wave loads and the resulting motions of the floater.
Quasi-slender body theory for slowly oscillating bodies of revolution in supersonic flow
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The Advanced Supersonic Parachute Inflation Research and Experiments (ASPIRE) project will investigate the supersonic deployment, inflation, and aerodynamics of Disk- Gap-Band (DGB) parachutes in the wake of a slender body. The parachutes will be full-scale versions of the DGBs used by the Mars Science Laboratory in 2012 and planned for NASA’s Mars 2020 project and will be delivered to targeted deployment conditions representative of flight at Mars by sounding rockets launched out of NASA’s Wallops Flight Facility. The parachutes will be tested in the wake of a slender payload whose diameter is approximately a sixth that of entry capsules used for Mars missions. Models of the deployment, inflation, and aerodynamic performance of the parachutes are necessary to design key aspects of the experiment, including: determining the expected loads and applicable margins on the parachute and payload; guiding sensor selection and placement; evaluating the vehicle trajectory for targeting, range safety, and recovery operations. In addition, knowledge of the differences in the behavior of the parachutes in the wake of slender and blunt bodies is required in order to interpret the results of the sounding rocket experiment and determine how they relate to expected performance behind blunt bodies at Mars. However, modeling the performance of a supersonic DGB in the wake of a slender body is challenging due to the scarcity of historical test data and modeling precedents. This paper describes the models of the aerodynamic performance of DGBs in supersonic slender-body wakes being developed for the ASPIRE sounding rocket test campaign. Development of these models is based on the four available flight tests of DGBs deployed in supersonic slender-body wakes as well as on data from past flight and wind-tunnel experiments of DGBs deployed in the wake of blunt bodies, on the reconstructed at-Mars DGB performance during past missions, and on computational fluid dynamics simulations. Simulations of the wakes of blunt and slender bodies in supersonic flow have been conducted in order to investigate the differences in the flowfields encountered by parachutes deployed in both wake types. The simulations have allowed the project to investigate the fundamental differences between the sounding rocket tests and the flight of a DGB during a Mars mission and to assess the limitations of the sounding rocket test architecture for evaluating flight performance at Mars.
Quasi-slender body theory for oscillating low aspect ratio wings and bodies of revolution in supersonic flow
Slender-body theory for subsonic and supersonic flow past bodies of revolution is extended to a second approximation, Methods are developed for handling the difficulties that arise at round ends, Comparison is made with experiment and with other theories for several simple shapes.
Previous studies have demonstrated that the use of counterflowing jets can greatly reduce the drag and heat loads on blunt-body geometries, especially when the long penetration mode jet condition can be established. Previously, the authors had done some preliminary numerical studies to determine the ability to establish long penetration mode jets on a typical Mach 1.6 slender configuration, and study its impact on the boom signature. The results indicated that a jet with a longer penetration length was required to achieve any impact on the boom signature of a typical Mach 1.6 slender configuration. This paper focuses on an in-depth parametric study, done using the space-time conservation element solution element Navier-Stokes flow solver, for investigating the effect of various counterflowing jet conditions/configurations on two supersonic slender-body models (cone-cylinder and quartic body of revolution). The study is aimed at gaining a better understanding of the relationship between the shock penetration length and reduction of drag and boom signature for these two supersonic slender-body configurations. Different jet flow rates, Mach numbers, nozzle jet exit diameters and jet-to-base diameter ratios were examined. The results show the characteristics of a short-to-long-to-short penetration-mode pattern with the increase of jet mass flow rates, observed across various counterflowing jet nozzle configurations. Though the optimal shock penetration length for potential boom-signature mitigation is tied to the long penetration mode, it often results in a very unsteady flow and leads to large oscillations of surface pressure and drag. Furthermore, depending on the geometry of the slender body, longer jet penetration did not always result in maximum drag reduction. For the quartic geometry, the maximum drag reduction corresponds well to the longest shock penetration length, while this was not the case for the cone-cylinder-as the geometry was already optimized for drag. Numerical results and assessments obtained from this parametric study along with the recommendation for future implementation of counterflowing jets as a means for drag and noise reduction are detailed in this paper.
The similarity parameters deduced by Sychev for inviscid hypersonic flow over slender bodies are reviewed and used to correlate flowfield, surface-pressure, normal-force and center-of-pressure data for supersonic flow over thin slender wings and smooth slender bodies at low-to-high angles of attack. Although Sychev expected similarity to hold only for hypersonic freestream and cross flows, it is demonstrated empirically that similarity holds for any value of cross-flow Mach number if the axial flow component is supersonic. It is also shown for thin wings that similarity holds for much larger values of aspect ratio than Sychev supposed. A one-term power-law expression is found to fit all of the normal-force correlations which suggests that it may be possible to develop a simple semi-empirical method for estimating the aerodynamic characteristics of arbitrary slender airframes.
The problems of asymmetric flow around slender bodies and its control are formulated using the unsteady, compressible, thin-layer or full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. The problem is numerically simulated for both locally-conical and three-dimensional flows. The numerical applications include studies of the effects of relative incidence, Mach number and Reynolds number on the flow asymmetry. For the control of flow asymmetry, the numerical simulation cover passive and active control methods. For the passive control, the effectiveness of vertical fins placed in the leeward plane of geometric symmetry and side strakes with different orientations is studied. For the active control, the effectiveness of normal and tangential flow injection and surface heating and a combination of these methods is studied.