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NASA NTRS2003

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

Mavriplis, Dimitri J.↗

NASA NTRS1991

Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave break-down. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the 2-D test problem. This discrepancy is attributed to far-field boundary- condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.

Joslin, R. D.↗

NASA NTRS1986

Semiempirical methods for computing turbulent flows

Two semiempirical theories which provide a basis for determining the turbulent friction and heat exchange near a wall are presented: (1) the Prandtl-Karman theory, and (2) the theory utilizing an equation for the energy of turbulent pulsations. A comparison is made between exact numerical methods and approximate integral methods for computing the turbulent boundary layers in the presence of pressure, blowing, or suction gradients. Using the turbulent flow around a plate as an example, it is shown that, when computing turbulent flows with external turbulence, it is preferable to construct a turbulence model based on the equation for energy of turbulent pulsations.

Belov, I. A.↗

NASA NTRS1971

Laminar or turbulent boundary-layer flows of perfect gases or reacting gas mixtures in chemical equilibrium

Turbulent boundary layer flows of non-reacting gases are predicted for both interal (nozzle) and external flows. Effects of favorable pressure gradients on two eddy viscosity models were studied in rocket and hypervelocity wind tunnel flows. Nozzle flows of equilibrium air with stagnation temperatures up to 10,000 K were computed. Predictions of equilibrium nitrogen flows through hypervelocity nozzles were compared with experimental data. A slender spherically blunted cone was studied at 70,000 ft altitude and 19,000 ft/sec. in the earth's atmosphere. Comparisons with available experimental data showed good agreement. A computer program was developed and fully documented during this investigation for use by interested individuals.

Anderson, E. C.↗

NASA NTRS1973

Non-reacting and equilibrium chemically reacting turbulent boundary-layer flows.

Turbulent boundary-layer flows of nonreacting gases are predicted for both internal (nozzle) and external flows. Effects of favorable pressure gradients on two eddy viscosity models were studied in rocket and hypervelocity wind tunnel flows. Nozzle flows of equilibrium air with stagnation temperatures up to 10,000 K were computed. Predictions of equilibrium nitrogen flows through hypervelocity nozzles were compared with experimental data. A slender spherically blunted cone was studied at 70,000 ft altitude and 19,000 ft/sec in the earth's atmosphere. Comparisons with available experimental data showed good agreement. A computer program was developed and fully documented during this investigation for use by interested individuals.

Anderson, E. C.↗

NASA NTRS2021

Raman Temperature and Density Measurements in Supersonic Jets

Prediction of flow-field properties in supersonic jets using computational fluid dynamics (CFD) code predictions has become routine; however, obtaining accurate solutions becomes more challenging when there is a significant temperature difference between the jet core and the ambient air and/or compressibility effects are significant. Benchmark sets of flow field property data are required in order to assess current CFD capabilities and develop better modeling approaches for these turbulent flow fields where accurate calculation of temperatures and turbulent heat flux is important. Particle Image Velocimetry (PIV), spontaneous rotational Raman scattering (SRS) spectroscopy and Background Oriented Schlieren (BOS) have been previously used to acquire measurements of the mean and root mean square (rms) velocities, the mean and rms gas temperatures and density gradients in subsonic jet flows and film cooling flows. In this work, the ability to measure density is added to the list of measurands available using the acquired Raman spectra. The suite of measurement techniques are now applied to supersonic jet flows. The computation of the local gas pressure in the potential core of an over-expanded jet is demonstrated using the Raman measured gas temperature and density. Additionally, a unique density feature in temperature matched, perfectly expanded jet flow shear layers identified using BOS was verified using the Raman measurement technique. These non-intrusive flow measurements are compared against RANS predictions of the supersonic jet flow properties as a means of assessing their prediction accuracy.

Raman Spectroscopy↗

NASA NTRS1990

Scattered-light scanner measurements of cryogenic liquid-jet breakup

The effect of highly turbulent Mach 1 gas flow and high thermal gradients on drop size measurements was investigated with a scattered light scanner. The instrument, developed at NASA-Lewis, was used to measure characteristic drop diameters or cyrogenic liquid sprays. By correcting for gas turbulence and thermal gradient affects, it was possible to obtain good reproducible data with the scattered light scanner. Tests were conducted primarily in the aerodynamic-stripping regime of liquid atomization and it was found that the loss of small droplets due to vaporization and dispersion had a marketed effect on drop size measurements. The nitrogen gas flow rate exponent of 1.33 is the same as that predicted by atomization theory for liquid jet breakup in high velocity gas flow. However, when the sprays were sampled farther downstream of the atomizer, at axial distances of 2.5 and 4.5 cm, the exponent for W sub n decreased 1.2 and 0.9, respectively. This was attributed to the loss of small droplets due to vaporization when values of downstream axial distances exceeded 1.3 cm.

Ingebo, Robert D.↗

NASA NTRS2004

Bubble Eliminator Based on Centrifugal Flow

The fluid bubble eliminator (FBE) is a device that removes gas bubbles from a flowing liquid. The FBE contains no moving parts and does not require any power input beyond that needed to pump the liquid. In the FBE, the buoyant force for separating the gas from the liquid is provided by a radial pressure gradient associated with a centrifugal flow of the liquid and any entrained bubbles. A device based on a similar principle is described in Centrifugal Adsorption Cartridge System (MSC- 22863), which appears on page 48 of this issue. The FBE was originally intended for use in filtering bubbles out of a liquid flowing relatively slowly in a bioreactor system in microgravity. Versions that operate in normal Earth gravitation at greater flow speeds may also be feasible. The FBE (see figure) is constructed as a cartridge that includes two concentric cylinders with flanges at the ends. The outer cylinder is an impermeable housing; the inner cylinder comprises a gas-permeable, liquid-impermeable membrane covering a perforated inner tube. Multiple spiral disks that collectively constitute a spiral ramp are mounted in the space between the inner and outer cylinders. The liquid enters the FBE through an end flange, flows in the annular space between the cylinders, and leaves through the opposite end flange. The spiral disks channel the liquid into a spiral flow, the circumferential component of which gives rise to the desired centrifugal effect. The resulting radial pressure gradient forces the bubbles radially inward; that is, toward the inner cylinder. At the inner cylinder, the gas-permeable, liquid-impermeable membrane allows the bubbles to enter the perforated inner tube while keeping the liquid in the space between the inner and outer cylinders. The gas thus collected can be vented via an endflange connection to the inner tube. The centripetal acceleration (and thus the radial pressure gradient) is approximately proportional to the square of the flow speed and approximately inversely proportional to an effective radius of the annular space. For a given FBE geometry, one could increase the maximum rate at which gas could be removed by increasing the rate of flow to obtain more centripetal acceleration. In experiments and calculations oriented toward the original microgravitational application, centripetal accelerations between 0.001 and 0.012 g [where g normal Earth gravitation (.9.8 m/s2)] were considered. For operation in normal Earth gravitation, it would likely be necessary to choose the FBE geometry and the rate of flow to obtain centripetal acceleration comparable to or greater than g.

Gonda, Steve R.↗

NASA NTRS1982

Velocity gradient method for calulating velocities in an axisymmetric annular duct

The velocity distribution along an arbitrary line between the inner and outer walls of an annular duct with axisymmetric swirling flow is calculated. The velocity gradient equation is used with an assumed variation of meridional streamline curvature. Upstream flow conditions can vary between the inner and outer walls, and an assumed total pressure distribution can be specified.

Katsanis, T.↗

NASA NTRS1990

Numerical investigations in three-dimensional internal flows

The flow in the transonic test facility was investigated using the three dimensional computational fluid dynamics techniques. The application of the full Navier-Stokes three dimensional code to the flow qualities in the contraction section of transonic wind tunnel is discussed. Initially, two dimensional solutions indicated the possibility for large secondary flow to exist as a result of the asymmetries involved in the contraction section as it is constructed. The results of a full three dimensional solution indicate that only minor pressure variations actually occur in the contraction section within any given cross flow plane. Further analysis of the three dimensional solution indicated that these slight lateral pressure gradients lead to negligible secondary flows, except within a small region in the corners within the boundary layer. On the basis of present solution, it would not be expected that any flow asymmetries and/or secondary flow present within contraction section are associated with the methods by which the contraction is implemented in its present configuration.

Rose, William C.↗

NASA NTRS1992

An Implementation Of The Solution-Adaptive-Grid Method

NASA technical memorandum discusses solution-adaptive-grid method and Self Adaptive Grid Evolution (SAGE) computer code, which implements method. Provides for redistribution of points in grids used to compute flows, especially supersonic and hypersonic flows containing shocks, and other strong gradient regions, discontinuities, and sheer layers. Performed on basis of flow solution obtained on initial grid, then flow recomputed on adapted grid.

Davies, Carol B.↗

NASA NTRS1994

A vorticity dynamics based model for the turbulent dissipation: Model development and validation

A new model dissipation rate equation is proposed based on the dynamic equation of the mean-square vorticity fluctuation for large Reynolds number turbulence. The advantage of working with the vorticity fluctuation equation is that the physical meanings of the terms in this equation are more clear than those in the dissipation rate equation. Hence, the model development based on the vorticity fluctuation equation is more straightforward. The resulting form of the model equation is consistent with the spectral energy cascade analysis introduced by Lumley. The proposed model dissipation rate equation is numerically well behaved and can be applied to any level of turbulence modeling. It is applied to a realizable eddy viscosity model. Flows that are examined include: rotating homogeneous shear flows; free shear flows; a channel flow and flat plate boundary layers with and without pressure gradients; and backward facing step separated flows. In most cases, the present model predictions show considerable improvement over the standard kappa-epsilon model.

Shih, Tsan-Hsing↗

NASA NTRS2002

Review of Research on Low-Profile Vortex Generators to Control Boundary-Layer Separation

An in-depth review of boundary-layer flow-separation control by a passive method using low-profile vortex generators is presented. The generators are defined as those with a device height between 10% and 50% of the boundary layer thickness. Key results are presented for several research efforts, all of which were performed within the past decade and a half where the majority of these works emphasize experimentation with some recent efforts on numerical simulations. Topics of discussion consist of both basic fluid dynamics and applied aerodynamics research. The fluid dynamics research includes comparative studies on separation control effectiveness as well as device-induced vortex characterization and correlation. The comparative studies cover the controlling of low-speed separated flows in adverse pressure gradient and supersonic shock-induced separation. The aerodynamics research includes several applications for aircraft performance enhancement and covers a wide range of speeds. Significant performance improvements are achieved through increased lift and/or reduced drag for various airfoils-low-Reynolds number, high-lift, and transonic-as well as highly swept wings. Performance enhancements for non-airfoil applications include aircraft interior noise reduction, inlet flow distortion alleviation inside compact ducts, and a more efficient overwing fairing. The low-profile vortex generators are best for being applied to applications where flow-separation locations are relatively fixed and the generators can be placed reasonably close upstream of the separation. Using the approach of minimal near-wall proturbances through substantially reduced device height, these devices can produce streamwise vortices just strong enough to overcome the separation without unnecessarily persisting within the boundary layer once the flow-control objective is achieved. Practical advantages of low-profile vortex generators, such as their inherent simplicity and low device drag, are demonstrated to be critically important for many applications as well.

Lin, John C.↗

NASA NTRS2000

A Study of Wake Development and Structure in Constant Pressure Gradients

Motivated by the application to high-lift aerodynamics for commercial transport aircraft, a systematic investigation into the response of symmetric/asymmetric planar turbulent wake development to constant adverse, zero, and favorable pressure gradients has been conducted. The experiments are performed at a Reynolds number of 2.4 million based on the chord of the wake generator. A unique feature of this wake study is that the pressure gradients imposed on the wake flow field are held constant. The experimental measurements involve both conventional LDV and hot wire flow field surveys of mean and turbulent quantities including the turbulent kinetic energy budget. In addition, similarity analysis and numerical simulation have also been conducted for this wake study. A focus of the research has been to isolate the effects of both pressure gradient and initial wake asymmetry on the wake development. Experimental results reveal that the pressure gradient has a tremendous influence on the wake development, despite the relatively modest pressure gradients imposed. For a given pressure gradient, the development of an initially asymmetric wake is different from the initially symmetric wake. An explicit similarity solution for the shape parameters of the symmetric wake is obtained and agrees with the experimental results. The turbulent kinetic energy budget measurements of the symmetric wake demonstrate that except for the convection term, the imposed pressure gradient does not change the fundamental flow physics of turbulent kinetic energy transport. Based on the turbulent kinetic energy budget measurements, an approach to correct the bias error associated with the notoriously difficult dissipation estimate is proposed and validated through the comparison of the experimental estimate with a direct numerical simulation result.

Thomas, Flint O.↗

NASA NTRS1992

Glomerular hemodynamic alterations during acute hyperinsulinemia in normal and diabetic rats

Treatment of insulin dependent diabetes invariably requires exogenous insulin to control blood glucose. Insulin treatment, independent of other factors associated with insulin dependent diabetes, may induce changes that affect glomerular function. Due to exogenous delivery of insulin in insulin dependent diabetes entering systemic circulation prior to the portal vein, plasma levels of insulin are often in excess of that observed in non-diabetics. The specific effects of hyperinsulinemia on glomerular hemodynamics have not been previously examined. Micropuncture studies were performed in control (non-diabetic), untreated diabetic and insulin-treated diabetic rats 7 to 10 days after administration of 65 mg/kg body weight streptozotocin. After the first period micropuncture measurements were obtained, 5 U of regular insulin (Humulin-R) was infused i.v., and glucose clamped at euglycemic values (80 to 120 mg/dl). Blood glucose concentration in non-diabetic controls was 99 +/- 6 mg/dl. In control rats, insulin infusion and glucose clamp increased nephron filtration rate due to decreases in both afferent and efferent arteriolar resistance (afferent greater than efferent) resulting in increased plasma flow and increased glomerular hydrostatic pressure gradient. However, insulin infusion and glucose clamp produced the opposite effect in both untreated and insulin-treated diabetic rats with afferent arteriolar vasoconstriction resulting in decreases in plasma flow, glomerular hydrostatic pressure gradient and nephron filtration rate. Thromboxane A2 (TX) synthetase inhibition partially decreased the vasoconstrictive response due to acute insulin infusion in diabetic rats preventing the decrease in nephron filtration rate.(ABSTRACT TRUNCATED AT 250 WORDS).

NASA Discipline Cardiopulmonary↗

NASA NTRS1984

Theoretical analysis of aircraft afterbody flow

The strongly interactive flow field about aircraft afterbodies is investigated using computational techniques by which the thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved. A time-dependent implicit numerical algorithm is used to obtain solutions for a variety of afterbody and nozzle geometries, within the class of bodies of revolution, for both subsonic and supersonic external flow, and for sonic and supersonic underexpanded jets. Only centered nozzles with either a sharp lip or a blunt base are considered. In all cases, computed results are compared with experimental data taken at flight Reynolds numbers for like-flow conditions. Turbulence closure is realized using algebraic eddy-viscosity concepts. A new and unique adaptive-grid technique is used to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computational scheme. Special singular point boundary conditions are used for similar purposes, and are especially effective for highly under-expanded jets. For all cases considered, except one with a very large base-to-nozzle-exit-diameter ratio, the agreement with experimental measurements is excellent. For geometries with large base regions, enhancements in the turbulence transport model are necessary to support improvements in the flow-field simulation.

Deiwert, G. S.↗

NASA NTRS1976

The partially aligned gradient instability in the ionosphere

Ionization irregularities which are almost but not exactly aligned along the magnetic field may grow much more rapidly than purely aligned irregularities in the presence of a background gradient of ionization and current flow. The stability of these irregularities is considered, taking into account the finite thickness of the gradient and shear in the ion motion. It is shown in particular that the normal E region of the ionosphere is usually stable, whereas sporadic E is often unstable, and this may limit the compression of metallic ions to form such layers. The F region may sometimes be unstable. Temperate zone conditions are considered throughout.

Whitehead, J. D.↗

NASA NTRS1982

Steady thermocapillary flows in two-dimensional slots

Liquid in a slot flows owing to a temperature gradient applied along its free surface. The thermal variation of surface tension induces a steady viscous flow directed on the surface from hot to cold, and recirculating below. For small aspect ratios A, giving flow in thin, two-dimensional slots, an asymptotic theory valid for A yields to 0 is used to obtain the fluid and thermal fields as well as the interfacial shapes. Solutions are obtained for both fixed lines and fixed angles at the contact between the interface and the solid side walls.

Sen, A. K.↗