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A family of high aspect ratio nozzles were designed to provide a parametric database of canonical embedded propulsion concepts. Nozzle throat geometries with aspect ratios of 2:1, 4:1, and 8:1 were chosen, all with convergent nozzle areas. The transition from the typical round duct to the rectangular nozzle was designed very carefully to produce a flow at the nozzle exit that was uniform and free from swirl. Once the basic rectangular nozzles were designed, external features common to embedded propulsion systems were added: extended lower lip (a.k.a. bevel, aft deck), differing sidewalls, and chevrons. For the latter detailed Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) simulations were made to predict the thrust performance and to optimize parameters such as bevel length, and chevron penetration and azimuthal curvature. Seventeen of these nozzles were fabricated at a scale providing a 2.13 inch diameter equivalent area throat." ! The seventeen nozzles were tested for far-field noise and a few data were presented here on the effect of aspect ratio, bevel length, and chevron count and penetration. The sound field of the 2:1 aspect ratio rectangular jet was very nearly axisymmetric, but the 4:1 and 8:1 were not, the noise on their minor axes being louder than the major axes. Adding bevel length increased the noise of these nozzles, especially on their minor axes, both toward the long and short sides of the beveled nozzle. Chevrons were only added to the 2:1 rectangular jet. Adding 4 chevrons per wide side produced some decrease at aft angles, but increased the high frequency noise at right angles to the jet flow. This trend increased with increasing chevron penetration. Doubling the number of chevrons while maintaining their penetration decreased these effects. Empirical models of the parametric effect of these nozzles were constructed and quantify the trends stated above." Because it is the objective of the Supersonics Project that future design work be done more by physics-based computations and less by experiments, several codes under development were evaluated against these test cases. Preliminary results show that the RANS-based code JeNo predicts the spectral directivity of the low aspect ratio jets well, but has no capability to predict the non-axisymmetry. An effort to address this limitations, used in the RANS-based code of Leib and Goldstein, overpredicted the impact of aspect ratio. The broadband shock noise code RISN, also limited to axisymmetric assumptions, did a good job of predicting the spectral directivity of underexpanded 2:1 cold jet case but was not as successful on high aspect ratio jets, particularly when they are hot. All results are preliminary because the underlying CFD has not been validated yet. An effort using a Large Eddy Simulation code by Stanford University predicted noise that agreed with experiments to within a few dB.
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Low aspect ratio plates flutter analysis for subsonic and supersonic models
Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.
The effect of increased wing aspect ratio of subsonic aircraft on configurations with and without strut bracing. Results indicate that an optimum cantilever configuration, with a wing aspect ratio of approximately 26, has a 19% improvement in cruise range when compared to a baseline concept with a wing aspect ratio of approximately 10. An optimum strut braced configuration, with a wing aspect ratio of approximately 28, has a 31% improvment in cruise range when compared to the same baseline concept. This improvement is mainly due to the estimated reduction in wing weight resulting from use of lifting struts. All configurations assume the same mission payload and fuel. The drag characteristics of the wings are enhanced with the use of laminar flow airfoils. A method for determining the extent of attainable natural laminar flow, and methods for preliminary structural design and for aerodynamic analysis of wings lifting struts are presented.
High-aspect-ratio aircraft include most transport aircraft such as commercial and military transports, business aircraft, and cargo aircraft. Generally, these types of aircraft are designed to cruise over a narrow range of lift coefficients and Mach numbers in the performance of their mission. Emphasis is therefore placed on the cruise performance of transport aircraft and every effort is made to obtain accurate wind-tunnel data to use as a basis for prediction of full-scale cruise performance. However, off-cruise performance is also important and methods were developed for extrapolating wind-tunnel data on buffet and flutter at transonic speed. Transport-type aircraft were tested extensively in various wind tunnels around the world and many different test techniques were developed to simulate higher Reynolds numbers. Methods developed for one tunnel may not be applicable to another tunnel because of differences in size, Reynolds number capability, running time, and test objectives. Many of the methods of boundary-layer control developed in two-dimensional airfoil testing can be applied in tests of transport configurations, but sometimes the three-dimensional flow fields that develop on tranpsort aircraft can make application of the two-dimensional methods difficult or impossible. The discussion is intended to be a representative, but not exhaustive, survey of the various methods of high Reynolds number simulation in the testing of high-aspect-ratio aircraft.
Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.
Two rocket-propelled missiles have been test flown by the Langley Pilotless Aircraft Research Division in order to study the stability characteristics of a body with six rectangular fins of very low aspect ratio. The fins, which had exposed aspect ratios of approximately o.o4 and 0.02 per fin, were mounted on bodies of fineness ratios of 12 and 18, respectively. Each body had a nose with a fineness ratio of 3.5 and a cylindrical afterbody. The body and the fin chord of the model having a fineness ratio of 12 were extended the length of 6 body diameters to produce the model with a fineness ratio of 18. The missiles were disturbed in flight by pulse rockets in order to obtain the stability data. The tests were performed over a Mach number range of 1.4 to 3.2 and a Reynolds number range of 2 x 10(exp 6) to 21 x l0(exp 6). The results of these tests indicate that these configurations with the long rectangular fins of very low aspect ratio showed little induced roll" with the missile of highest fineness ratio and longest fin chord exhibiting the least amount. Extending the body and fin chord of the shorter missile six body diameters and thereby increasing the fin area approximately 115 percent increased the lift-curve slope based on body cross-sectional area approximately 40 to 55 percent, increased the dynamic stability by a substantial amount, and increased the drag from 14 to 33 percent throughout the comparable Mach number range. The center-of-pressure location of both missiles remained constant over the Mach number range.
A series of electrically heated tube experiments was performed to investigate the effect of high aspect ratio on curvature heat transfer enhancement in uniformly heated rectangular cooling passages. Three hardware geometries were tested: a baseline straight aspect ratio 10 tube, an aspect ratio 1 (square) tube with a 45 deg. curve, and an aspect ratio 10 tube with a 45 deg. curve. Gaseous nitrogen with the following properties was used as the coolant: ambient inlet temperature, pressures to 8.3 MPa, wall-to-bulk temperature ratios less than two, and Reynolds numbers based on hydraulic diameter ranging from 250,000 to 1,600,000. The measured curvature enhancement factors were compared to values predicted by three previously published models which had been developed for low aspect ratio tubes. The models were shown to be valid for the high aspect ratio tube as well the low aspect ratio tube, indicating that aspect ratio had little impact on the curvature heat transfer enhancement in these tests.
The effect of stator and rotor aspect ratio on transonic-turbine performance was experimentally investigated. The stator aspect ratios covered were 1.6. 0.8, and 0.4, while the rotor aspect ratios investigated were 1.46 and 0.73. It was found that the observed variation in turbine design-point efficiency was negligible. Thus, within the range of aspect ratio investigated, these results verify for turbines operating in the transonic flow range the finding of a reference report, which showed analytically that, if blade shape and solidity are held constant, the aspect ratio may be varied over a wide range without appreciable change in turbine efficiency.
An experimental investigation was conducted to evaluate the effectiveness of using high-aspect-ratio cooling passenges to improve the life and reduce the colant pressure drop in high-pressure rocket thrust chambers. A plug-nozzle rocket-engine test apparatus was used to test two cylindrical chambers with low-aspect-ratio cooling passages and one with high-aspect-ratio cooling passages. The chambers were cyclically tested and data were taken over a wide range of coolant mass flows. The results showed that for the same coolant pressure drop, the hot-gas-side wall temperature of the high-aspect-ratio chamber was 30 percent lower than the baseline low-aspect-ratio chamber, resulting in no fatigue damage to the wall. The coolant pressure drop for the high-aspect-ratio chamber was reduced in increments to one-half that of the baseline chamber, by reducing the coolant mass flow, and still resulted in a reduction in the hot-gas-side wall temperature when compared to the low-aspect-ratio chambers.
An experimental investigation was conducted to evaluate the effectiveness of using high-aspect-ratio cooling passages to improve the life and reduce the coolant pressure drop in high-pressure rocket thrust chambers. A plug-nozzle rocket-engine test apparatus was used to test two cylindrical chambers with low-aspect-ratio cooling passages and one with high-aspect-ratio cooling passages. The chambers were cyclically tested and data were taken over a wide range of coolant mass flows. The results showed that for the same coolant pressure drop, the hot-gas-side wall temperature of the high-aspect-ratio chamber was 30 percent lower than the baseline low-aspect-ratio chamber, resulting in no fatigue damage to the wall. The coolant pressure drop for the high-aspect-ratio chamber was reduced in increments to one-half that of the baseline chamber, by reducing the coolant mass flow, and still resulted in a reduction in the hot-gas-side wall temperature when compared to the low-aspect-ratio chambers.
Experimental investigation of small aspect ratio rectangular wings mounted on a free-to-roll sting balance indicated that self-induced roll oscillations are possible when the aspect ratio of such wings is less than 0.5. The oscillations are probably driven by the periodic changes in the location and strength of the side edge vortices, as it has been shown for the 'wing rock' motion of delta wings, where similar changes in the leading edge vortex strength and position cause the roll oscillations. During the roll oscillation cycle the roll angle, normal force, and the side force were recorded and presented for three wings with aspect ratios of 0.25, 0.35, and 0.47. This data indicates that the lift loss during roll oscillations of rectangular wings is less than what was measured for similar delta wings. Also, the flow field of such slender rectangular wings at high angles of attack is more complicated due to the additional leading edge vortex, when compared with the flow field over slender delta wings.