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At least 109 records · Page 6

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NASA NTRS1992

Combined forced and free convection in a curved duct

The purpose of this study is to investigate the flow and heat transfer characteristics of a combined forced and free convection flow in a curved duct. Solutions are obtained by solving the low Mach number model of the Navier-Stokes equation using a control volume method. The finite-volume method was developed with the use of a predictor-corrector numerical scheme and some new variations of the classical projection method. Solutions indicated that the existence of a buoyancy force has changed the entire flow structure inside a curved duct. Reversed flow at both inner and outer bend is observed. For moderate Reynolds number, the upstream section of the duct was significantly influenced by the free convection processes. In general, heat transfer is strong at the inner bend of the beginning of the heated section and at the outer bend on the last half of the heated section. The maximum velocity location is strongly influenced by the combined effects of buoyancy and centrifugal forces. A strong buoyancy force can reduce the strength of the secondary flow where it plays an important role in mixing.

Yam, Clement G.↗

NASA NTRS1978

Turbulent boundary layers with large streamline curvature effects

It has been shown that turbulent flows are greatly affected by streamline curvature. In spite of this and the fact that curved shear flows are frequently encountered in engineering applications, the predictions of such flows are relatively less developed than the predictions of two-dimensional plane flows. Recently, various attempts were made by different investigators; however, their methods are only successful when the product of the boundary layer thickness to the local surface curvature is approximately 0.05. The present paper investigates the more general case where this product is in the range from 0.1 to 0.5. Results show that the calculated boundary-layer characteristics for arbitrary free stream conditions are in good agreement with measurements.

So, R. M. C.↗

NASA NTRS1985

Instability of time-periodic flows

The instabilities of some spatially and/or time-periodic flows are discussed, in particular, flows with curved streamlines which can support Taylor-Gortler vortices are described in detail. The simplest flow where this type of instability can occur is that due to the torsional oscillations of an infinitely long circular cylinder. For more complicated spatially varying time-periodic flows, a similar type of instability can occur and is spatially localized near the most unstable positions. When nonlinear effects are considered it is found that the instability modifies the steady streaming boundary layer induced by the oscillatory motion. It is shown that a rapidly rotating cylinder in a uniform flow is susceptible to a related type of instability; the appropriate stability equations are shown to be identical to those which govern the instability of a boussinesq fluid of Prandtl number unity heated time periodically from below.

Hall, P.↗

NASA NTRS1987

Instability of time-periodic flows

The instabilities of some spatially and/or time-periodic flows are discussed, in particular, flows with curved streamlines which can support Taylor-Gortler vortices are described in detail. The simplest flow where this type of instability can occur is that due to the torsional oscillations of an infinitely long circular cylinder. For more complicated spatially varying time-periodic flows, a similar type of instability can occur and is spatially localized near the most unstable positions. When nonlinear effects are considered it is found that the instability modifies the steady streaming boundary layer induced by the oscillatory motion. It is shown that a rapidly rotating cylinder in a uniform flow is susceptible to a related type of instability; the appropriate stability equations are shown to be identical to those which govern the instability of a Boussinesq fluid of Prandtl number unity heated time periodically from below.

Hall, Philip↗

NASA NTRSDate not supplied

The Effects of Freestream Turbulence on Wing-Gust Interactions

There is a growing interest in the experimental study of discrete vertical gusts motivated by the proliferation of small Uncrewed Air Systems. However, gusts are not the only unsteady flow disturbances that these vehicles are expected to encounter. Freestream turbulence is also a serious consideration. Previous work has indicated that freestream turbulence has significant effects on the flow around airfoils, so this work investigates the interaction of these two unsteady flow disturbances. Airfoils are pitched to mimic the flow angle change caused by a gust at different levels of incoming freestream turbulence. The lift generated during the gust encounters with elevated incoming freestream turbulence show that the effects on the performance of the airfoil are dependent on the turbulence intensity. Low turbulence intensity has beneficial effects, delaying stall and increasing the maximum lift, whereas higher freestream turbulence intensity delays stall without a corresponding increase in the maximum lift. A preliminary investigation of 15-trial ensemble-averaged flow fields suggests that freestream turbulence dominates the flow, but the flow features associated with the dynamic lift seen in the "clean" case are still somewhat present. However, lift curves and flow fields from individual trials indicates that the turbulence increases the unsteadiness in the interaction, but the general trends are dominated by the gust interaction. Further work is still needed to better determine the flow physics of these interactions and the interplay between repeatable and stochastic flow phenomena.

Unsteady Aerodynamics↗

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 NTRS1979

Calculation of three-dimensional turbulent subsonic flows in transition ducts

A method for computing three-dimensional turbulent subsonic flow in curved ducts is being developed. A set of tube-like surface oriented coordinates is employed for a general class of geometries applicable to subsonic diffusers with offset bends. The geometric formulation is complex and no previous treatment of this class of viscous flow problems is known to the authors. The duct centerline is a space curve specified by piecewise polynomials. A Frenet frame is located on the centerline at each axial location. The cross sections are described by superellipses imbedded in the Frenet frame. Duct surfaces are also coordinate surfaces, which greatly simplifies the boundary conditions. The resulting coordinates are nonorthogonal. An approximate set of governing equations is employed for viscous flows having strong flow in a primary flow direction. The derivation is coordinate invariant and the resulting equations are expressed in tensor form. These equations are solved by an efficient alternating direction implicit (ADI) method. This numerical method is generally stable and permits solution in difficult geometries using the general tensor formulation.

Levy, R.↗

NASA NTRS1989

Unsteady density-current equations for highly curved terrain

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

Sivakumaran, N. S.↗

NASA NTRS1989

Siphon flows in isolated magnetic flux tubes. 3: The equilibrium path of the flux tube arch

The arched equilibrium path of a thin magnetic flux tube in a plane-stratified, nonmagnetic atmosphere is calculated for cases in which the flux tube contains a steady siphon flow. The large scale mechanical equilibrium of the flux tube involves a balance among the magnetic buoyancy force, the net magnetic tension force due to the curvature of the flux tube axis, and the inertial (centrifugal) force due to the siphon flow along curved streamlines. The ends of the flux tube are assumed to be pinned down by some other external force. Both isothermal and adiabatic siphon flows are considered for flux tubes in an isothermal external atmosphere. For the isothermal case, in the absence of a siphon flow the equilibrium path reduces to the static arch calculated by Parker (1975, 1979). The presence of a siphon flow causes the flux tube arch to bend more sharply, so that magnetic tension can overcome the additional straightening effect of the inertial force, and reduces the maximum width of the arch. The curvature of the arch increases as the siphon flow speed increases. For a critical siphon flow, with supercritical flow in the downstream leg, the arch is asymmetric, with greater curvature in the downstream leg of the arch. Adiabatic flow have qualitatively similar effects, except that adiabatic cooling reduces the buoyancy of the flux tube and thus leads to significantly wider arches. In some cases the cooling is strong enough to create negative buoyancy along sections of the flux tube, requiring upward curvature of the flux tube path along these sections and sometimes leading to unusual equilibrium paths of periodic, sinusoidal form.

Thomas, John H.↗

NASA NTRS1993

On the Accuracy of CFD-Based Pressure Drop Predictions for Right-Angle Ducts

The predictive capability of computational fluid dynamics (CFD) codes for turbulent flow through curved ducts is of significant importance to the design and performance analysis of modern rocket engine flowpaths. Code calibration and validation studies for this class of flow are desireable to estimate the performance margin and operating range of components designed using Navier-Stokes methods. Parametric experimental studies such as that of Weske (NACA ARR W-39) provided a wealth of performance data for the design of single- and compound elbow configurations with various cross-sections, curvature and aspect ratios at varying Reynolds numbers. In that work, the majority of data is presented in the form of loss coefficients, characterizing pressure losses due to duct curvature, and including losses due to wall friction. Using measured friction coefficients, losses of equivalent straight lengths of duct are subtracted, resulting in performance curves useful for design computations. These data are currently used in a CFD-based parametric study covering a broad range of operating conditions. Of particular interest for the accuracy of CFD predictions are the effects on pressure loss due to inlet boundary layer thickness (dependent on upstream development length), and the wall treatment for the turbulence equations (conventional wall functions vs. wall integration using a two-layer model). The experimental data are reassessed in the form of an error analysis, and are compared with CFD predictions for 18 computational cases. Grid-independence, grid spacing, and convergence requirements of the cases are discussed. Conclusions regarding the relative importance of the parametric variables will be presented.

Brankovic, Andreja↗

NASA NTRS1991

Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

A Navier-Stokes equations solver based on a pressure correction method with a pressure-staggered mesh and calculations of separated three-dimensional flows are presented. It is shown that the velocity pressure decoupling, which occurs when various pressure correction algorithms are used for pressure-staggered meshes, is caused by the ill-conditioned discrete pressure correction equation. The use of a partial differential equation for the incremental pressure eliminates the velocity pressure decoupling mechanism by itself and yields accurate numerical results. Example flows considered are a three-dimensional lid driven cavity flow and a laminar flow through a 90 degree bend square duct. For the lid driven cavity flow, the present numerical results compare more favorably with the measured data than those obtained using a formally third order accurate quadratic upwind interpolation scheme. For the curved duct flow, the present numerical method yields a grid independent solution with a very small number of grid points. The calculated velocity profiles are in good agreement with the measured data.

Kim, S.-W.↗

NASA NTRS1991

Calculations of separated 3-D flows with a pressure-staggered Navier-Stokes equations solver

Kim, S.-W.↗

NASA NTRS1993

Computation of flows in a turn-around duct and a turbine cascade using advanced turbulence models

Numerical investigation has been carried out to evaluate the capability of the Algebraic Reynolds Stress Model (ARSM) and the Nonlinear Stress Model (NLSM) to predict strongly curved turbulent flow in a turn-around duct (TAD). The ARSM includes the near-wall damping term of pressure-strain correlation phi(sub ij,w), which enables accurate prediction of individual Reynolds stress components in wall flows. The TAD mean flow quantities are reasonably well predicted by various turbulence models. The ARSM yields better predictions for both the mean flow and the turbulence quantities than the NLSM and the k-epsilon (k = turbulent kinetic energy, epsilon = dissipation rate of k) model. The NLSM also shows slight improvement over the k-epsilon model. However, all the models fail to capture the recovery of the flow from strong curvature effects. The formulation for phi(sub ij,w) appears to be incorrect near the concave surface. The hybrid k-epsilon/ARSM, Chien's k-epsilon model, and Coakley's q-omega (q = the square root of k, omega = epsilon/k) model have also been employed to compute the aerodynamics and heat transfer of a transonic turbine cascade. The surface pressure distributions and the wake profiles are predicted well by all the models. The k-epsilon model and the k-epsilon/ARSM model provide better predictions of heat transfer than the q-omega model. The k-epsilon/ARSM solutions show significant differences in the predicted skin friction coefficients, heat transfer rates and the cascade performance parameters, as compared to the k-epsilon model. The k-epsilon/ARSM model appears to capture, qualitatively, the anisotropy associated with by-pass transition.

Lakshminarayana, B.↗

NASA NTRS1959

Heat Transfer from Cylinders in Transition From Slip Flow to Free-Molecule Flow

Over 600 measured heat-transfer coefficients in the transition from slip to free-molecule flow have been correlated by using the Nusselt number Nu as a function of the Knudsen Kn and Reynolds Re (or Mach M) numbers. The experimental range for these heat-transfer data from transverse cylinders in air corresponds to the following dimensionless groups: M, 0.10 to 0.90; Re, 0.03 to 11.5; Kn, 0.10 to 5.0. The total air temperature T(sub t) was maintained constant at 80 F, but wire temperature was Varied from 150 to 580 F. At Kn=0.10, Nu extrapolates smoothly into slip-flow empirical curves that show Nu as a function of Re and M or Kn. The correlation gradually changes from the square root of Re(sub t) dependence characteristic of continuum flow to first-power Re dependence as Kn increases (decreasing Re). At the experimental limit Kn ft 5.0, the Nu data correlate with a mean fractional error of 413 percent by the prediction of free-molecule-flow theory. In comparing experimental results with theory, an accommodation coefficient of 0.57+/-0.07 was inferred from the heat-transfer data, which were obtained with etched tungsten wire in air. The wire recovery temperature T(sub e) was measured and compared with existing data and theory in terms of a ratio eta(equivalent to T(sub e)/T(sub t). The results can be divided into three groups by Kn criteria: For Kn less than 2.01, eta is independent of Kn, and eta decreases from 1.0 to 0.97 as M increases from 0 to 0.90; for 2.0 less than Kn less than 5.0, eta is a function of both Kn and M in this transition region to fully developed free-molecule flow; and for Kn greater than 5.0, eta predicted by free-molecule-flow theory is observed and increases from 1.0 to 1.08 as M increases from 0 to 0.90, again independent of Kn. Therefore, these T(sub e) data provide a guide to the boundary of fully developed free-molecule flow, which is.inferred from this research to exist for Kn greater than 5.0. This boundary criterion is substantiated by other published data on T(sub e) at supersonic speeds.

Cybulski, Ronald J.↗

NASA NTRS1994

Inducer analysis/pump model development

Current design of high performance turbopumps for rocket engines requires effective and robust analytical tools to provide design information in a productive manner. The main goal of this study was to develop a robust and effective computational fluid dynamics (CFD) pump model for general turbopump design and analysis applications. A finite difference Navier-Stokes flow solver, FDNS, which includes an extended k-epsilon turbulence model and appropriate moving zonal interface boundary conditions, was developed to analyze turbulent flows in turbomachinery devices. In the present study, three key components of the turbopump, the inducer, impeller, and diffuser, were investigated by the proposed pump model, and the numerical results were benchmarked by the experimental data provided by Rocketdyne. For the numerical calculation of inducer flows with tip clearance, the turbulence model and grid spacing are very important. Meanwhile, the development of the cross-stream secondary flow, generated by curved blade passage and the flow through tip leakage, has a strong effect on the inducer flow. Hence, the prediction of the inducer performance critically depends on whether the numerical scheme of the pump model can simulate the secondary flow pattern accurately or not. The impeller and diffuser, however, are dominated by pressure-driven flows such that the effects of turbulence model and grid spacing (except near leading and trailing edges of blades) are less sensitive. The present CFD pump model has been proved to be an efficient and robust analytical tool for pump design due to its very compact numerical structure (requiring small memory), fast turnaround computing time, and versatility for different geometries.

Cheng, Gary C.↗

NASA NTRS1991

On the nonlinear development of the most unstable Goertler vortex mode

The nonlinear development of the most unstable Gortler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Gortler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Gortler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Gortler equations valid for O(1) Gortler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗

NASA NTRS1993

On the nonlinear development of the most unstable Goertler vortex mode TLSP - Final report

The nonlinear development of the most unstable Goertler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Goertler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Goertler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Goertler equations valid for O(1) Goertler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Denier, James P.↗

NASA NTRS1998

An Assessment of Artificial Compressibility and Pressure Projection Methods for Incompressible Flow Simulations

Performance of the two commonly used numerical procedures, one based on artificial compressibility method and the other pressure projection method, are compared. These formulations are selected primarily because they are designed for three-dimensional applications. The computational procedures are compared by obtaining steady state solutions of a wake vortex and unsteady solutions of a curved duct flow. For steady computations, artificial compressibility was very efficient in terms of computing time and robustness. For an unsteady flow which requires small physical time step, pressure projection method was found to be computationally more efficient than an artificial compressibility method. This comparison is intended to give some basis for selecting a method or a flow solution code for large three-dimensional applications where computing resources become a critical issue.

Kwak, Dochan↗