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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Flow friction of the turbulent coolant flow in cryogenic porous cables

Considered are cryogenic power transmission cables with porous cores. Calculations of the turbulent coolant flow with injection or suction through the porous wall are presented within the framework of a two-layer model. Universal velocity profiles were obtained for the viscous sublayer and flow core. Integrating the velocity profile, the law of flow friction in the pipe with injection has been derived for the case when there is a tangential injection velocity component. The effect of tangential velocity on the relative law of flow friction is analyzed. The applicability of the Prandtl model to the problem under study is discussed. It is shown that the error due to the acceptance of the model increases with the injection parameter and at lower Reynolds numbers; under these circumstances, the influence of convective terms in the turbulent energy equation on the mechanism of turbulent transport should be taken into account.

Hendricks, R. C.↗
NASA NTRS1952

On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

Kaplan, Carl↗
NASA NTRS1990

A Detailed Investigation of Staged Normal Injection into a Mach 2 Flow

A study of the staged injection of two jets of air behind a rearward facing step into a Mach 2 flow was performed using the SPARK 3-D Navier-Stokes code. Calculated mole fraction distributions were compared with an extensive set of planar mole fraction measurements made with a laser induced iodine fluorescence technique. A statistical measure, the standard deviation, was used to help assess agreement between calculation and experiment. Overall, good agreement was found between calculated and measured values. Generally, agreement was better in the far field of the injectors. The effect of grid resolution was investigated by calculating solutions on grids of 60,000, 200,000, and 450,000 points. Differences in the solutions on the two finer grids were small. However, the mole fraction distributions were distinguishable. The effect of turbulence modeling was investigated by employing three different algebraic models for the jet turbulence: the Baldwin-Lomax model, the Prandtl mixing length model, and the Eggers mixing length model. Overall, the Eggers mixing length model was found to be superior for this case. Finally, the effect of the jet exit conditions was examined. A recently proposed Mach number distribution at the jet exit was found to slightly improve agreement between measurement and calculation.

Eklund, Dean R.↗
NASA NTRS1952

A Correlation by Means of the Transonic Similarity Rules of the Experimentally Determined Characteristics of 22 Rectangular Wings of Symmetrical Profile

The transonic similarity rules have been applied to the correlation of experimental data for a series of 22 rectangular wings having symmetrical NACA 63A-series sections, aspect ratios from 1/2 to 6, and thicknesses from 2 to 10 percent. The data were obtained by use of the transonic bump technique over a Mach number range from 0.40 to 1.10, corresponding to a Reynolds number range from 1.25 to 2.05 million. The results show that it is possible to correlate experimental data throughout the subsonic, transonic, and moderate supersonic regimes by using the transonic similarity parameters in forms which are consistent with the Prandtl-Glauert rule of linearized theory. The multiple families of basic data curves for the various aspect ratios and thickness ratios have been summarized in single presentations involving only one geometric variable - the product of the aspect ratio and the l/3 power of the thickness ratio.

Mcdevitt, John B↗
NASA NTRS1992

Development of an efficient analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is described. It uses an inviscid/viscid interaction approach, wherein the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation. The viscous-layer solution is obtained using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and the wake streamline. A semiinverse global iteration procedure permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for two cascades where a range of inlet flow conditions was considered for one of them including conditions leading to large-scale flow separation.

Barnett, M.↗
NASA NTRS1986

Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

Warfield, M. J.↗
NASA NTRS1944

On the flow of a compressible fluid by the hodograph method I : unification and extension of present-day results

Elementary basic solutions of the equations of motion of a compressible fluid in the hodograph variables are developed and used to provide a basis for comparison, in the form of velocity correction formulas, of corresponding compressible and incompressible flows. The known approximate results of Chaplygin, Von Karman and Tsien, Temple and Yarwood, and Prandtl and Glauert are unified by means of the analysis of the present paper. Two new types of approximations, obtained from the basic solutions, are introduced; they possess certain desirable features of the other approximations and appear preferable as a basis for extrapolation into the range of high stream Mach numbers and large disturbances to the main stream. Tables and figures giving velocity and pressure-coefficient correction factors are included in order to facilitate the practical application of the results.

Garrick, I E↗
NASA NTRS1943

The flow of a compressible fluid past a curved surface

An iteration method is employed to obtain the flow of a compressible fluid past a curved surface. The first approximation which leads to the Prandtl-Glauert rule, is based on the assumption that the flow differs but little from a pure translation. The iteration process then consists in improving this first approximation in order that it will apply to a flow differing from pure translatory motion to a greater degree. The method fails when the Mach number of the undisturbed stream reaches unity but permits a transition from subsonic to supersonic conditions without the appearance of a compression shock. The limiting value at which potential flow no longer exits is indicated by the apparent divergence of the power series representing the velocity of the fluid at the surface of the solid boundary.

Kaplan, Carl↗
NASA NTRS1939

Airfoil Theory at Supersonic Speed

A theory is developed for the airfoil of finite span at supersonic speed analogous to the Prandtl airfoil theory of 1918-1919 for incompressible flow. In addition to the profile and induced drags, account must be taken at supersonic flow of still another drag, namely, the wave drag, which is independent of the wing aspect ratio. Both wave and induced drags are proportional to the square of the lift and depend on the Mach number, that is, the ratio of flight to sound speed. In general, in the case of supersonic flow, the drag-lift ratio is considerably less favorable than is the case for incompressible flow. Among others the following examples are considered: 1) lifting line with constant lift distribution (horseshoe vortex); 2) computation of wave and induced drag and the twist of a trapezoidal wing of constant lift density; 3) computation of the lift distribution and drag of an untwisted rectangular wing.

Schlichting, H↗
NASA NTRS1993

An analysis for high Reynolds number inviscid/viscid interactions in cascades

An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.

Barnett, Mark↗
NASA NTRS1980

Calculation of oblique-shock-wave laminar-boundary-layer interaction on a flat plate

A finite difference solution to the problem of the interaction between an impinging oblique shock wave and the laminar boundary layer on a flat plate is presented. The boundary layer equations coupled with the Prandtl-Meyer relation for the external flow are used to calculate the flow field. A method for the calculation of the separated flow region is presented and discussed. Comparisons between this theory and the experimental results of other investigators show fairly good agreement. Results are presented for the case of a cooled wall with an oncoming flow at Mach number 2.0 without and with suction. The results show that a small amount of suction greatly reduces the extent of the separated region in the vicinity of the shock impingement location.

Goldberg, U.↗
NASA NTRS1987

Investigation of turbulent flow in highly curved ducts with application to turbomachinery components

Numerical predictions were performed using a semi-elliptic calculation procedure for the case of turbulent flow in passage through a 90 deg bend of square cross section. Two versions of the isotropic turbulent viscosity two equation k-epsilon model were used. The first, the wall function model (WFM), employs the logarithmic law-of-the-wall relation and the notion of equilibrium flow to set all the necessary boundary conditions at the first grid point adjacent to a solid wall. The second model, the Van Driest model (VDM), employs Prandtl's original mixing length formulation, in conjunction with Van Driest's semi-empirical relation for the mixing length, to calculate the turbulent viscosity in the near wall regions of the flow. In this case, boundary conditions for k and epsilon, required to calculate these quantities in the core of the flow, are obtained by matching the mixing length and Reynolds number model formulations in an overlapping region of the flow near the walls. In both cases the results obtained show an improvement over earlier calculations using an elliptic numerical procedure. This is attributed to the finer grids possible in the present work. Of the two models, the VDM formulation shows better overall conformity with the mean flow measurements. Neither model reproduces well the details of the stress distribution as a result of the implied isotropic turbulent viscosity.

Humphrey, J. A. C.↗
NASA NTRS1993

A Grid-resolved Analysis of Base Flowfield for a Four-Engine Clustered Nozzle Configuration

The objective of this study is to propose a computational methodology that can effectively anchor the base flowfield of a four-engine clustered nozzle configuration. This computational methodology is based on a three-dimensional, viscous flow, pressure-based computational fluid dynamics (CFD) formulation. For efficient CFD calculation, a Prandtl-Meyer solution treatment is applied to the algebraic grid lines for initial plume expansion resolution. As the solution evolves, the computational grid is adapted to the pertinent flow gradients. The CFD model employs an upwind scheme in which second- and fourth-order central differencing schemes with artificial dissipation are used. The computed quantitative base flow properties such as the radial base pressure distributions, model centerline static pressure, Mach number and impact pressure variations, and base pressure characteristic curve agreed reasonably well with those of the measurement.

Wang, Ten-See↗
NASA NTRS1920

Gottingen Wind Tunnel for Testing Aircraft Models

Given here is a brief description of the Gottingen Wind Tunnel for the testing of aircraft models, preceded by a history of its development. Included are a number of diagrams illustrating, among other things, a sectional elevation of the wind tunnel, the pressure regulator, the entrance cone and method of supporting a model for simple drag tests, a three-component balance, and a propeller testing device, all of which are discussed in the text.

Prandtl, L↗
NASA NTRS2004

Induced Power of the Helicopter Rotor

A simplified rotor model was used to explore fundamental behavior of lifting rotor induced power at moderate and high advance ratios. Several rotor inflow theories, including dynamic inflow theory and prescribed-wake vortex theory, together with idealized notional airfoil stall models were employed. A number of unusual results were encountered at high advance ratios including trim control reversal and multiple trim solutions. Significant increases in rotor induced power (torque) above the ideal minimum were observed for moderately high advance ratio. Very high induced power was observed near and above unity advance ratio. The results were sensitive to the stall characteristics of the airfoil models used. An equivalent wing analysis was developed to determine induced power from Prandtl lifting line theory and help interpret the rotor induced power behavior in terms of the spanwise airload distribution. The equivalent wing approach was successful in capturing the principal variations of induced power for different configurations and operating conditions. The effects blade root cutout were found to have a significant effect on rotor trim and induced power at high advance ratios.

Ormiston, Robert A.↗
DOE OSTI2022

Challenge Problem 1: Preliminary Model Development and Assessment of Flexible Heat Transfer Modeling Approaches

This report presents the modeling progress of a university consortium studying flexible modeling for turbulent heat transfer. In the context of advanced nuclear reactor design, where challenges include non-unity Prandtl fluids, free and mixed convection, and transitional flow, computational fluid dynamics methods are underutilized due to low confidence in modeling approaches and high computational cost. This report evaluates the performance of engineering CFD models in diabatic, buoyant turbulent flow. It finds that all turbulence models including several variants of the k-ε and k-ω models struggle to predict accurate turbulent momentum and heat transfer in such flows. The Nusselt numbers have been compared between the models and the DNS data, where calculations have been performed for each case and trends have shown a good agreement between DNS estimated Nusselt numbers and available correlations as well as experimental data. A novel DNS correlation for high Pr cases as they are transitioning from mixed convection to natural convection has been proposed. While Nusselt number errors relative to DNS range from 20% to 50%, the models capture similar trends to DNS with respect to Nusselt suppression and amplification under varying levels of buoyancy effect. This report also highlights model form error as a significant contributor to CFD predictions and proposes a framework for quantifying model error and improving confidence in CFD calculations. To improve the predictive capability of engineering CFD models, data-driven approaches for turbulence models are investigated. Theoretical frameworks based on the invariant tensor / vector basis neural networks for prediction of Reynolds stresses and turbulent heat fluxes are employed. The models are developed using direct numerical simulations data for forced convection flows of different fluids in vertical planar channel domain. The framework is implemented in spectral element solvers Nek5000 / nekRS and has shown a potential for future development and consideration of mixed convection flows.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1972

Thermal elastoplastic structural analysis of non-metallic thermal protection systems

An incremental theory and numerical procedure to analyze a three-dimensional thermoelastoplastic structure subjected to high temperature, surface heat flux, and volume heat supply as well as mechanical loadings are presented. Heat conduction equations and equilibrium equations are derived by assuming a specific form of incremental free energy, entropy, stresses and heat flux together with the first and second laws of thermodynamics, von Mises yield criteria and Prandtl-Reuss flow rule. The finite element discretization using the linear isotropic three-dimensional element for the space domain and a difference operator corresponding to a linear variation of temperature within a small time increment for the time domain lead to systematic solutions of temperature distribution and displacement and stress fields. Various boundary conditions such as insulated surfaces and convection through uninsulated surface can be easily treated. To demonstrate effectiveness of the present formulation a number of example problems are presented.

Chung, T. J.↗
NASA NTRS1976

Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

Baldwin, B. S.↗