Search NASA⌕ Search

SEARCH · Search NASA

Results for “Two-dimensional analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Effect of Mach Number on the Flow and Application of Compressibility Corrections in a Two-Dimensional Subsonic-Transonic Compressor Cascade Having Varied Porous-Wall Suction at the Blade Tips

A cascade of 65-(12)10 compressor blades was tested at one geometric setting over a range of inlet Mach number from 0.12 to 0.89. Two groups of data are presented and compared: the first from the cascade operating conventionally with no boundary-layer control, and the second with the boundary layer controlled by a combination of upstream slot suction and porous-wall suction at the blade tips. A criterion for two-dimensionality was used to specify the degree of boundary-layer control by suction to be applied. The data are presented and an analysis is made to show the effect of Mach number on turning angle, blade wake, pressure distribution about the blade profile and static-pressure rise. The influence of boundary-layer control on these parameters as well as on the secondary losses is illustrated. A system of correlating the measured static-pressure rise through the cascade with the theoretical isentropic values is presented which gives good agreement with the data. The pressure distribution about the blade profile for an inlet Mach number of 0.21 is corrected with the Prandtl-Glauert, Karman-Tsien, and vector-mean velocity - contraction coefficient compressibility correction factors to inlet Mach numbers of 0.6 and 0.7. The resulting curves are compared with the experimental pressure distributions for inlet Mach numbers of 0.6 and 0.7 so that the validity of applying the three corrections can be evaluated.

Briggs, William B.↗

Turbulent Friction in the Boundary Layer of a Flat Plate in a Two-Dimensional Compressible Flow at High Speeds

In the present report an investigation is made on a flat plate in a two-dimensional compressible flow of the effect of compressibility and heating on the turbulent frictional drag coefficient in the boundary layer of an airfoil or wing radiator. The analysis is based on the Prandtl-Karman theory of the turbulent boundary later and the Stodola-Crocco, theorem on the linear relation between the total energy of the flow and its velocity. Formulas are obtained for the velocity distribution and the frictional drag law in a turbulent boundary later with the compressibility effect and heat transfer taken into account. It is found that with increase of compressibility and temperature at full retardation of the flow (the temperature when the velocity of the flow at a given point is reduced to zero in case of an adiabatic process in the gas) at a constant R (sub x), the frictional drag coefficient C (sub f) decreased, both of these factors acting in the same sense.

Frankl, F.↗

Experimental investigation of the effect of aspect ratio and Mach number on the flutter of cantilever wings

The results of some wind-tunnel experiments to investigate the effects of aspect ratio and Mach number on the flutter of uniform, unswept, cantilever wings are reported. Models having aspect ratios ranging from 2 to 13 were tested at Mach numbers up to 0.92. No general attempt is made to correlate the data with three-dimensional-flow theory, but an examination of the data is made on the basis of reference theoretical values obtained from the two-dimensional incompressible-flow theory. On this basis a reduction in aspect ratio, in general, increased the ratio of the experimental flutter speed to the calculated flutter speed. The analysis also indicated that for a given aspect ratio, this ratio decreased slightly as the Mach number is increased.

Widmayer, E , Jr↗

Two-and three-dimensional unsteady lift problems in high-speed flight

The problem of transient lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchoff's formula is applied so that the analysis is reduced, just as in the steady state, to an investigation of sources and doublets. The applications include the evaluation of indicial lift and pitching-moment curves for two-dimensional sinking and pitching wings flying at Mach numbers equal to 0, 0.8, 1.0, 1.2 and 2.0. Results for the sinking case are also given for a Mach number of 0.5. In addition, the indicial functions for supersonic-edged triangular wings in both forward and reverse flow are presented and compared with the two-dimensional values.

Lomax, Harvard↗

Analytical Investigation of Flow Through High-speed Mixed-flow Turbine

An analysis was made of the flow trough a high-speed mixed-flow turbine based on axially symmetric conditions. The calculated weight flow was lower than that used in the two-dimensional design. The rotor could be redesigned to increase the weight flow and a flow and alleviate undesirable pressure gradients at the expense of increased rotor blade stresses.

TURBINES - MIXED FLOW↗

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↗

Velocity distributions on two-dimensional wing-duct inlets by conformal mapping

The conformal-mapping method of the Cartesian mapping function is applied to the determination of the velocity distribution on arbitrary two-dimensional duct-inlet shapes such as are used in wing installations. An idealized form of the actual wing-duct inlet is analyzed. The effects of leading edge stagger, inlet-velocity ratio, and section lift coefficients on the velocity distribution are included in the analysis. Numerical examples are given and, in part, compared with experimental data.

Perl, W↗

Theoretical Prediction of Pressure Distributions on Nonlifting Airfoils at High Subsonic Speeds

Theoretical pressure distributions on nonlifting circular-arc airfoils in two-dimensional flows with high subsonic free-stream velocity are found by determining approximate solutions, through an iteration process, of an integral equation for transonic flow proposed by Oswatitsch. The integral equation stems directly from the small-disturbance theory for transonic flow. This method of analysis possesses the advantage of remaining in the physical, rather than the hodograph, variable and can be applied in airfoils having curved surfaces. After discussion of the derivation of the integral equation and qualitative aspects of the solution, results of calculations carried out for circular-arc airfoils in flows with free-stream Mach numbers up to unity are described. These results indicate most of the principal phenomena observed in experimental studies.

Spreiter, John R↗

Aerodynamic Design of Axial-flow Compressors. VI - Experimental Flow in Two-Dimensional Cascades

Available experimental two-dimensional cascade data for conventional compressor blade sections are correlated at a reference incidence angle in the region of minimum loss. Variations of reference incidence angle, total-pressure loss, and deviation angle with cascade geometry, inlet Mach number, and Reynolds number are investigated. From the analysis and the correlations of the available data, rules and relations are evolved for the prediction of blade-profile performance. These relations are developed in simplified forms readily applicable to compressor design procedures.

Lieblein, Seymour↗

Theoretical and Experimental Investigation of the Effect of Tunnel Walls on the Forces on an Oscillating Airfoil in Two-Dimensional Subsonic Compressible Flow

This report presents a theoretical and experimental investigation of the effect of wind-tunnel walls on the air forces on an oscillating wing in two-dimensional subsonic compressible flow. A method of solving an integral equation which relates the downwash on a wing to the unknown loading is given, and some comparisons are made between the theoretical results and the experimental results. A resonance condition, which was predicted by theory in a previous report (NACA report 1150), is shown experimentally to exist. In addition, application of the analysis is made to a number of examples in order to illustrate the influence of walls due to variations in frequency of oscillation, Mach number , and ratio of tunnel height to wing semichord.

Runyan, Harry L↗

Aerodynamic Design of Axial-flow Compressors

Available experimental two-dimensional-cascade data for conventional compressor blade sections are correlated. The two-dimensional cascade and some of the principal aerodynamic factors involved in its operation are first briefly described. Then the data are analyzed by examining the variation of cascade performance at a reference incidence angle in the region of minimum loss. Variations of reference incidence angle, total-pressure loss, and deviation angle with cascade geometry, inlet Mach number, and Reynolds number are investigated. From the analysis and the correlations of the available data, rules and relations are evolved for the prediction of the magnitude of the reference total-pressure loss and the reference deviation and incidence angles for conventional blade profiles. These relations are developed in simplified forms readily applicable to compressor design procedures.

Source record↗

Analytical study of blockage- and lift-interference corrections for slotted tunnels obtained by the substitution of an equivalent homogeneous boundary for the discrete slots

The solid-blockage interference for a doublet on the tunnel axis and the boundary interference for lifting wings in circular, rectangular, and two-dimensional slotted tunnels have been calculated by substituting an equivalent homogeneous boundary for the physical boundary of discrete slots. In the case of small wings, the interference calculated with the assumption of homogeneity has been found to be consistent with that calculated for the discrete slots for as few as four slots in a circular tunnel. Furthermore, available experimental results for blockage interference are consistent with the results of the present analysis. As a consequence of the assumption of homogeneity it is possible to express the interference of multislotted tunnels as a function of a single parameter which combines the effects of two physical variables: the ratio of open to total slotted wall perimeter and the number of slots. A curve is presented which permits the rapid evaluation of this parameter and numerical results for lift and blockage interference are plotted against the parameter.

Davis, Don D , Jr↗

Summary of Airfoil Data

Recent airfoil data for both flight and wind-tunnel tests have been collected and correlated insofar as possible. The flight data consist largely of drag measurements made by the wake-survey method. Most of the data on airfoil section characteristics were obtained in the Langley two-dimensional low-turbulence pressure tunnel. Detail data necessary for the application of NACA 6-serles airfoils to wing design are presented in supplementary figures, together with recent data for the NACA 24-, 44-, and 230-series airfoils. The general methods used to derive the basic thickness forms for NACA 6- and 7-series airfoils and their corresponding pressure distributions are presented. Data and methods are given for rapidly obtaining the approximate pressure distributions for NACA four-digit, five-digit, 6-, and 7-series airfoils. The report includes an analysis of the lift, drag, pitching-moment, and critical-speed characteristics of the airfoils, together with a discussion of the effects of surface conditions. Available data on high-lift devices are presented. Problems associated with lateral-control devices, leading-edge air intakes, and interference are briefly discussed. The data indicate that the effects of surface condition on the lift and drag characteristics are at least as large as the effects of the airfoil shape and must be considered in airfoil selection and the prediction of wing characteristics. Airfoils permitting extensive laminar flow, such as the NACA 6-series airfoils, have much lower drag coefficients at high speed and cruising lift coefficients than earlier types-of airfoils if, and only if, the wing surfaces are sufficiently smooth and fair. The NACA 6-series airfoils also have favorable critical-speed characteristics and do not appear to present unusual problems associated with the application of high-lift and lateral-control devices. Much of the data given in the NACA Advance Confidential Report entitled "Preliminary Low-Drag-Airfoil and Flap Data from Tests at Large Reynolds Number and Low Turbulence," by Eastman N. Jacobs, Ira R. Abbott, and Milton Davidson, March 1942 has been corrected and included in the present paper, which supersedes the previously published paper.

LOW-DRAG↗

An Overview of Experiments and Modeling of Polysiloxane-Coated Thermal Protection Systems for Missions to Mars, Titan, and Beyond.

Phenolic Impregnated Carbon Ablator (PICA) gained heritage during the historic Stardust mission, where it successfully returned samples from a comet’s tail and has since been instrumental in delivering payloads to the surface of Mars [1-3]. Most recently, PICA enabled the safe return of samples collected from asteroid Bennu as part of the OSIRIS-REx mission. This rich legacy underscores PICA’s critical role in allowing NASA’s most ambitious exploration missions. However, the friable nature of its phenolic phase presents challenges during handling and pre-launch activities. To mitigate this issue, PICA is coated with a polysiloxane resin system, which serves to suppress particulate dispersion and thereby safeguard spacecraft components. A comprehensive understanding of the polysiloxane resin’s behavior is imperative, as it profoundly shapes the material response of PICA during atmospheric entry by influencing its thermal and oxidative stability. This influence extends to thermocouple plugs embedded within thermal protection systems. These plugs have demonstrated their significance in missions such as Mars Science Laboratory (MSL) and Mars 2020, where the MEDLI and MEDLI2 instrumentation suites delivered in-valuable insights into the performance of thermal protection systems during entry into the Martian atmosphere [4]. Looking ahead, missions such as Dragonfly, set to descend into Titan’s dense atmosphere, aim to leverage advanced sensor technologies to further refine our understanding of thermal protection response [5]. Moreover, thermocouple plugs play an essential role in validating cutting-edge material response models, such as those pioneered under NASA’s Entry Systems Modeling Project (ESM), designed, in-part, to predict the operational integrity of thermal protection systems under the extreme stresses of atmospheric entry. To achieve these modeling goals, ground-based experiments are crucial to provide the foundational data necessary for developing and refining these predictive tools. To this end, an extensive test campaign was conducted at the Hypersonic Materials Environmental Test System (HyMETS) to investigate the high-temperature behavior of the polysiloxane resin in an air environment [6]. These experiments revealed critical phenomena, including the formation of a silicon oxycarbide layer that enhances oxidation resistance, moderates surface temperatures, and alters in-depth thermal response. Building on these findings, subsequent tests were designed to simulate atmospheric entry conditions in reactive gases, such as CO2 and N2, to mimic the environments of Mars and Titan, respectively, as well as non-reactive gases representing the atmospheres of the Ice Giants (Neptune and Uranus). A heating rate dependent decomposition mechanism has been identified for the polysiloxane resin under oxidizing conditions (Fig. 1). In the initial stage, the resin and the underlying thermal protection system undergo pyrolysis, rapidly generating a thin amorphous silicon oxycarbide interwoven with carbonaceous char and residual fibers from PICA. During the second stage, the nascent oxide layer establishes a robust, oxidation-resistant thermal barrier coating, which significantly impedes heat transfer to the underlying carbonaceous char, resulting in a stagnation of the surface temperature. A key factor contributing to this thermal resistance is the low recombination efficiency of atomic oxygen (γ), which further diminishes the heat load on the material’s interior layers [7]. Moreover, as the surface temperature stagnates, the silicon oxycarbide phase separates into distinct regions of silica and free graphite. Ultimately, when the heat flux reaches a critical threshold, a third stage is triggered, leading to the breakdown of the coating through carbothermal reduction, exposing the underlying char layer. This exposure leads to a dramatic surface temperature spike, driven by highly exothermic reactions between atomic oxygen and the char layer, further accelerating material degradation. A detailed mass and heat transfer model of PICA coated with polysiloxane resin was implemented in the Porous material Analysis Toolbox based on OpenFOAM, PATO [8]. The initial stage was considered negligible in this model because the resin decomposition occurs rapidly within a thin surface layer. Instead, the coating was directly considered as an oxygen-resistant thermal barrier coating. For the second stage, the thin amorphous silicon oxycarbide was treated as a pure silica surface to simplify the thermochemical behavior. The model ac-counts for surface equilibrium processes using representative elements of the coating-environment system. For the third stage, specific boundary conditions were developed to estimate the onset and progression of the coating removal. Two-dimensional material response simulations were conducted to compare uncoated and coated PICA using boundary conditions calibrated with HyMETS data. Fig. 2 illustrates that the simulations closely align with experimental data, successfully reproducing measured temperature profiles. This work will include the latest advancements in the coating model, including the calibration of recombination of atomic oxygen at the surface during the second phase. These simulated results will be further validated against additional CO2 data points from HyMETS, reinforcing the models’ predictive capabilities. These mechanisms and their effects on thermal protection systems, including thermochemical behavior and thermocouple probe performance in extreme environments, provide crucial insights for optimizing spacecraft designs that safeguard scientific payload and ensure mission success in future planetary exploration endeavors.

Active Oxidation↗

Full-scale-wind-tunnel Tests of a 35 Degree Sweptback Wing Airplane with High-velocity Blowing over the Training-edge Flaps

A wind-tunnel investigation was made to determine the effects of ejecting high-velocity air near the leading edge of plain trailing-edge flaps on a 35 degree sweptback wing. The tests were made with flap deflections from 45 degrees to 85 degrees and with pressure ratios across the flap nozzles from sub-critical up to 2.9. A limited study of the effects of nozzle location and configuration on the efficiency of the flap was made. Measurements of the lift, drag, and pitching moment were made for Reynolds numbers from 5.8 to 10.1x10(6). Measurements were also made of the weight rate of flow, pressure, and temperature of the air supplied to the flap nozzles.The results show that blowing on the deflected flap produced large flap lift increments. The amount of air required to prevent flow separation on the flap was significantly less than that estimated from published two-dimensional data. When the amount of air ejected over the flap was just sufficient to prevent flow separation, the lift increment obtained agreed well with linear inviscid fluid theory up to flap deflections of 60 degrees. The flap lift increment at 85 degrees flap deflection was about 80 percent of that predicted theoretically.With larger amounts of air blown over the flap, these lift increments could be significantly increased. It was found that the performance of the flap was relatively insensitive to the location of the flap nozzle, to spacers in the nozzle, and to flow disturbances such as those caused by leading-edge slats or discontinuities on the wing or flap surfaces. Analysis of the results indicated that installation of this system on an F-86 airplane is feasible.

Kelley, Mark W↗

Approximate Turbulent Boundary-Layer Development in Plane Compressible Flow Along Thermally Insulated Surfaces with Application to Supersonic-Tunnel Contour Correction

Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.

BOUNDARY LAYER - WIND TUNNEL WALLS↗

Two-dimensional compressible flow in centrifugal compressors with straight blades

Six numerical examples are presented for steady, two-dimensional, compressible, nonviscous flow in centrifugal compressors with thin straight blades, the center lines of which generate the surface of a right circular cone when rotated about the axis of the compressor. A seventh example is presented for incompressible flow. The solutions were obtained in a region of the compressors, including the impeller tip, that was considered to be unaffected by the diffuser vanes or by the impeller-inlet configuration. Each solution applies to radial and mixed flow compressors with various cone angles but with the same angle between blades on the conic flow surface. The solution also apply to radial and mixed flow turbines with the rotation and the flow direction reversed. The effects of variations in the following parameters were investigated: (1) flow rate, (2) impeller-tip speed, (3) variation of passage height with radius, and (4) angle between blades on conic flow surface. The numerical results are presented in plots of the streamlines and constant Mach number lines. Correlation equations are developed whereby the flow conditions in any impeller with straight blades can be determined (in the region investigated by this analysis) for all operating conditions.

Stanitz, John D↗

Flow through cascades in tandem

An exact treatment of the problem of finding the incompressible, inviscid two-dimensional flow around two cascades in tandem is presented. The analysis includes solutions of both the direct and the inverse problems. These problems are solved by conformally mapping the tandem cascade onto the region between two concentric circles in which region there are suitably placed flow singularities. Formulas for the velocity and the potential in the annular region are presented in a closed form by means of elliptic functions. The equations are presented in a form suitable for computation.

Spraglin, William E↗