Correlation of Two Experimental Methods of Determining the Rolling Characteristics of Unswept Wings
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Maclachlan, Robert↗
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A method for determining the aerodynamic characteristics of two-and three-dimensional shapes at hypersonic speeds
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FLOW - BODIES, ROTATING↗
An Analysis of the Applicability of the Hypersonic Similarity Law to the Study of Flow About Bodies of Revolution at Zero Angle of Attack
The hypersonic similarity law as derived by Tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of Mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of Mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of Mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream Mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of Mach number and fineness ratio within defined limits.
PRESSURE DISTRIBUTION - BODIES OF REVOLUTION↗
Practical Calculation of Second-order Supersonic Flow past Nonlifting Bodies of Revolution
Calculation of second-order supersonic flow past bodies of revolution at zero angle of attack is described in detail, and reduced to routine computation. Use of an approximate tangency condition is shown to increase the accuracy for bodies with corners. Tables of basic functions and standard computing forms are presented. The procedure is summarized so that one can apply it without necessarily understanding the details of the theory. A sample calculation is given, and several examples are compared with solutions calculated by the method of characteristics.
Van Dyke, Milton D↗
The Aerodynamic Design and Calibration of an Asymmetric Variable Mach Number Nozzle with a Sliding Block for the Mach Number Range 1.27 to 2.75
A method of designing as asymmetric, fixed geometry, variable Mach number nozzle has been developed by using the method of characteristics. A small nozzle conforming to the analytically determined ordinates was constructed and calibrated over a range of Mach numbers extending from 1.27 to 2.75. The results show the variation in Mach number to be plus or minus 0.01 or less and in the flow direction to be plus or minus 0.2 degrees within the test section. The range of Mach numbers from 1.27 to 2.75 was obtained by translating the lower block in a straight line parallel to the test-section center line for a distance of 2.17 test-section heights.
NOZZLES↗
Investigation at Mach Number 1.91 of Side and Base Pressure Distributions over Conical Boattails Without and with Jet Flow Issuing from Base
Experimental side and bade pressure distributions over a series of conical boattails without and with jet flow from the base are presented at a Mach number of 1.91. For the case of no jet flow the methods of characteristics and linearized theory are shown to overpredict the side pressure drag. A semi-empirical theory is presented to predict the effect of boattail angle on base pressure. With the boattail extending to a sharp edge at the nozzle exit, the over-pressure jet is shown to decrease the side pressure drag. Presence of an annular base may eliminate the effect of the jet on the side pressure drag, but the jet effect on the base pressure drag may greatly increase or decrease the total boattail drag.
FLOW, JET MIXING↗
Two-dimensional Cascade Investigation of the Maximum Exit Tangential Velocity Component and Other Flow Conditions at the Exit of Several Turbine Blade Designs at Supercritical Pressure Ratios
The nature of the flow at the exit of a row of turbine blades for the range of conditions represented by four different blade configurations was evaluated by the conservation-of-momentum principle using static-pressure surveys and by analysis of Schlieren photographs of the flow. It was found that for blades of the type investigated, the maximum exit tangential-velocity component is a function of the blade geometry only and can be accurately predicted by the method of characteristics. A maximum value of exit velocity coefficient is obtained at a pressure ratio immediately below that required for maximum blade loading followed by a sharp drop after maximum blade loading occurs.
TURBINES - AXIAL FLOW↗
Loitering and range performance of turbojet-powered aircraft determined by off-design engine cycle analysis
The loitering and range performance of airplanes equipped with several different turbojet engines was analytically investigated by applying the results of off-design cycle analyses to specific airplane characteristics. The method of off-design cycle analysis is presented herein and is verified by a check with experimental data. For all engines considered, the loitering and the range fuel flows obtained with rated tail-pipe nozzle area, variable engine speed operations were within 2 or 3 percent of the optimum fuel flow obtainable with any method of engines operation. The optimum loitering altitude generally occurred between approximately 25,000 and 35,000 feet with corresponding optimum flight Mach numbers of 0.4 to 0.65. In general, the optimum range fuel flows occurred at 3000 to 5000 feet higher altitude and at approximately 0.15 higher flight Mach numbers than the optimum loitering fuel flow.
Koutz, Stanley L↗
A method for determining turbine design characteristics for rocket turbodrive applications
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Stewart, Warner L↗
Loiter performance of turbojet-powered aircraft performance determined by off-design cycle analysis
Loitering performance of airplanes equipped with various turbojet engines was analytically investigated. The engines used in this analysis were selected to show the effects of various engine design variables. Engine performance was determined by means of an off-design cycle analysismaking use of experimentally determined component characteristics. The method of off-design cycle analysis is presented herein and is verified by a check with experimental data.
Koutz, Stanley L↗
Guidance law development for aeroassisted transfer vehicles using matched asymptotic expansions
This report addresses and clarifies a number of issues related to the Matched Asymptotic Expansion (MAE) analysis of skip trajectories, or any class of problems that give rise to inner layers that are not associated directly with satisfying boundary conditions. The procedure for matching inner and outer solutions, and using the composite solution to satisfy boundary conditions is developed and rigorously followed to obtain a set of algebraic equations for the problem of inclination change with minimum energy loss. A detailed evaluation of the zeroth order guidance algorithm for aeroassisted orbit transfer is performed. It is shown that by exploiting the structure of the MAE solution procedure, the original problem, which requires the solution of a set of 20 implicit algebraic equations, can be reduced to a problem of 6 implicit equations in 6 unknowns. A solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle, has been obtained. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the zeroth order MAE problem to obtain the feedback controls. Finally, a general procedure is developed for constructing a MAE solution up to first order, of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is valid for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is shown to be inappropriate since it is not valid over a narrow range of the independent variable. That is, it is not uniformly valid. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished-one where the left boundary condition coincides with, or lies to the right of, the singular region, and another one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure where the obtained solution is uniformly valid to O(Epsilon(exp 2)). The potential application of this procedure to aeroassisted plane change is also described and partially evaluated.
Calise, Anthony J.↗
Shock-free supersonic elliptic nozzles and method of forming same
A method of forming a shock-free supersonic elliptic nozzle, in which the nozzle to be designed is divided into three sections, a circular-to-elliptic section which begins at a circular nozzle inlet, an elliptic subsonic section downstream from the circular-to-elliptic section, and a supersonic section downstream from the elliptic subsonic section is described. The maximum and minimum radii for each axial point in the circular-to-elliptic section and the elliptic subsonic section are then separately determined, the maximum and minimum radii being the radii for the widest part of an elliptic cross-section and the narrowest part of the elliptic cross-section, respectively. The maximum and minimum radii for each axial point in the supersonic section are determined based on the Method of Characteristics. Then, each of the three sections are based on the maximum and minimum radii for each axial point in the section. The resulting nozzle is acoustically superior.
Seiner, John M.↗
Supersonic minimum length nozzle design for dense gases
Recently, dense gases have been investigated for many engineering applications such as for turbomachinery and wind tunnels. Supersonic nozzle design for these gases is complicated by their nonclassical behavior in the transonic flow regime. In this paper a method of characteristics (MOC) is developed for two-dimensional (planar) and, primarily, axisymmetric flow of a van der Waals gas. Using a straight aortic line assumption, a centered expansion is used to generate an inviscid wall contour of minimum length. The van der Waals results are compared to previous perfect gas results to show the real gas effects on the flow properties and inviscid wall contours.
Aldo, Andrew C.↗
High temperature resistant jet fuels
The thermal stability of aviation fuels is evaluated according to the ASTM D 2341 method. This characteristic is linked to the presence of generators of instability, mainly diolephins and N and S derivates. The objectives of the present work are as follows: to obtain, in the laboratory, kerosene which is thermally stable; the isolation and identification of generators of instability; and the regeneration of thermally unstable kerosenes.
Luis M. Peloche↗
Optimized design of a hypersonic nozzle
Conventional procedures for designing nozzles involve the design of an inviscid contour (using the method of characteristics) that is corrected with a displacement thickness calculated from boundary-layer theory. However, nozzles designed using this classical procedure have been shown to exhibit poor flow quality at Mach numbers characteristic of hypersonic applications. The nozzle to be designed will be a part of the NASA HYPULSE facility which is being used for hypervelocity flight research. Thus, the flow quality of the nozzle is a critical question that needs to be addressed. Design of nozzles for hypersonic applications requires a proper assessment of the effects of the thick boundary layer on the inviscid flowfield. Since the flow field is largely supersonic, the parabolized form of the Navier-Stokes (PNS) equations can be used. The requirement of a uniform flow at the exit plane of the nozzle can be used to define an objective function as part of an optimization procedure. The design procedure used in this study involves the coupling of a nonlinear (least-squares) optimization algorithm with an efficient, explicit PNS solver. The thick boundary layers growing on the walls of the nozzle limit the extent of the usable core region (region with uniform flow) for testing models (especially rectangular). In order to maximize the region of uniform flow, it was decided to have the exit plane of this nozzle to be (nearly) rectangular. Thus, an additional constraint on the nozzle shape resulted, namely the nozzle will have a shape transitioning from a circular one at the inlet to that of a rectangle at the exit. In order to provide for a smooth shape transition, the cross sectional contour of the nozzle is defined by a superellipse. The nozzle is taken to be a meter in length. The axial variations of the major and minor radii of the superellipse are governed by cubic splines. The design parameters are the coefficients of the splines associated with the local nozzle wall slopes. Extensive calculations have been made (with a three-dimensional Euler code) to understand the effects of various parameters such as location of the knot points of the spline function, different ways of characterizing the uniformity of the flow in the exit plane, as well as the effect of constraining the area of the nozzle to be invariant. Turbulent flow (measurements indicate that the flow at the nozzle inlet is turbulent) calculations are now being performed (with the inviscidly designed nozzle contours) to assess the flow quality.
Krishnamurthy, Ramesh↗
Sensitivity of engine-integrated waverider performance to static margin constraint
The performance of an engine-integrated wedge caret-wing waverider is optimized with respect to a set of geometric and flight attitude variables with constraints for steady state flight and static margin. The optimization is done with different values for the constraint on the static margin, and the resulting performances and geometries compared. This comparison is done for three performance parameters: L/D ratio, range coefficient, and a parameter that measures energy height gain per unit weight of fuel. The vehicle model incorporates a one-dimensional calculation on the forebody, inlet and wings. Fuel injection is done prior to the combustor entrance and flow properties are calculated with a one-dimensional model using a correlation for the shock shape in front of a transverse jet. The combustor is modeled as a shock-induced-combustion scramjet, and the nozzle flow field is calculated using the method of characteristics.
Tarpley, C.↗
Predictions of thermal buckling strengths of hypersonic aircraft sandwich panels using minimum potential energy and finite element methods
Thermal buckling characteristics of hypersonic aircraft sandwich panels of various aspect ratios were investigated. The panel is fastened at its four edges to the substructures under four different edge conditions and is subjected to uniform temperature loading. Minimum potential energy theory and finite element methods were used to calculate the panel buckling temperatures. The two methods gave fairly close buckling temperatures. However, the finite element method gave slightly lower buckling temperatures than those given by the minimum potential energy theory. The reasons for this slight discrepancy in eigensolutions are discussed in detail. In addition, the effect of eigenshifting on the eigenvalue convergence rate is discussed.
Ko, William L.↗
A Parametric Study of a Plug Nozzle, Using the Liquid Propellant Program (LPP) Code
The Liquid Propellant Program (LPP) computer code is a super-set of the industry standard Two Dimensional Kinetics (TDK) computer code. The TDK code uses a two dimensional method of characteristics solution with fully coupled finite rate kinetics for axially symmetric nozzles. The chemical reactions are modeled with a generalized reaction package that include three dimensional body efficiencies and four reaction rate forms. The code performs optional solutions for frozen or equilibrium flow. TDK evaluates discrete shocks, both attached or induced. The Transonic module models variable mixture ratio profiles from the combustion chamber injector. The Mass Addition Boundary Layer module (MABL) calculates the boundary parameters with the same chemistry options, and includes transpiration or tangential slot injection of gas at the wall. The LPP upgrades include: planar nozzle, scarfed nozzles, plug nozzles, and scramjet nozzle configurations. The code evaluates both upper and lower wall flow simulation, and includes the interaction with the external flow. The MABL module evaluates equilibrium radiation heat transfer for both upper and lower walls. In addition, LPP code models combustion effects due to injector inefficiencies with the Spray Combustion Analysis Program (SCAP) module. The LPP package provides extensive post plotting capabilities for flow visualization. The LPP is sufficiently fast and robust to provide performance predictions for extensive parametric studies and sufficiently accurate to provide flow field and performance solutions for detailed studies.
Dunn, Stuart S.↗