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NASA NTRS1944

The "limiting line" in mixed subsonic and supersonic flow of compressible fluids

It is well known that the vorticity for any fluid element is constant if the fluid is non-viscous and the change of state of the fluid is isentropic. When a solid body is placed in a uniform stream, the flow far ahead of the body is irrotational. Then if the flow is further assumed to be isentropic, the vorticity will be zero over the whole filed of flow. In other words, the flow is irrotational. For such flow over a solid body, it is shown by Theodorsen that the solid body experiences no resistance. If the fluid has a small viscosity, its effect will be limited in the boundary layer over the solid body and the body will have a drag due to the skin friction. This type of essentially isentropic irrotational flow is generally observed for a streamlined body placed in a uniform stream, if the velocity of the stream is kept below the so-called "critical speed." At the critical speed or rather at a certain value of the ratio of the velocity of the undisturbed flow and the corresponding velocity of sound, shock waves appear. This phenomenon is called the "compressibility bubble." Along a shock wave, the change of state of the fluid is no longer isentropic, although still adiabatic. This results in an increase in entropy of the fluid and generally introduces vorticity in an originally irrotational flow. The increase in entropy of the fluid is, of course, the consequence of changing part of the mechanical energy into heat energy. In other words, the part of fluid affected by the shock wave has a reduced mechanical energy. Therefore, with the appearance of shock waves, the wake of the streamline body is very much widened, and the drag increases drastically. Furthermore, the accompanying change in the pressure distribution over the body changes the aerodynamic moment acting on it and in the case of an airfoil decreases the lift force. All these consequences of the breakdown of isentropic irrotational flow are generally undesirable in applied aerodynamics. Its occurrence should be delayed as much as possible by modifying the shape or contour of the body. However, such endeavor will be very much facilitated if the cause or the criterion for the breakdown can be found first.

MACH NUMBER↗

NASA NTRS2003

Technical Evaluation Report, Part A - Vortex Flow and High Angle of Attack

A symposium entitled Vortex Flow and High Angle of Attack was held in Loen, Norway, from May 7 through May 11, 2001. The Applied Vehicle Technology (AVT) panel, under the auspices of the Research and Technology Organization (RTO), sponsored this symposium. Forty-eight papers, organized into nine sessions, addressed computational and experimental studies of vortex flows pertinent to both aircraft and maritime applications. The studies also ranged from fundamental fluids investigations to flight test results, and significant results were contributed from a broad range of countries. The principal emphasis of this symposium was on "the understanding and prediction of separation-induced vortex flows and their effects on military vehicle performance, stability, control, and structural design loads." It was further observed by the program committee that "separation- induced vortex flows are an important part of the design and off-design performance of conventional fighter aircraft and new conventional or unconventional manned or unmanned advanced vehicle designs (UAVs, manned aircraft, missiles, space planes, ground-based vehicles, and ships)." The nine sessions addressed the following topics: vortical flows on wings and bodies, experimental techniques for vortical flows, numerical simulations of vortical flows, vortex stability and breakdown, vortex flows in maritime applications, vortex interactions and control, vortex dynamics, flight testing, and vehicle design. The purpose of this paper is to provide brief reviews of these papers along with some synthesizing perspectives toward future vortex flow research opportunities. The paper includes the symposium program. (15 refs.)

VORTEX BREAKDOWN↗

NASA NTRS1999

The value of assessing pulmonary venous flow velocity for predicting severity of mitral regurgitation: A quantitative assessment integrating left ventricular function

Although alteration in pulmonary venous flow has been reported to relate to mitral regurgitant severity, it is also known to vary with left ventricular (LV) systolic and diastolic dysfunction. There are few data relating pulmonary venous flow to quantitative indexes of mitral regurgitation (MR). The object of this study was to assess quantitatively the accuracy of pulmonary venous flow for predicting MR severity by using transesophageal echocardiographic measurement in patients with variable LV dysfunction. This study consisted of 73 patients undergoing heart surgery with mild to severe MR. Regurgitant orifice area (ROA), regurgitant stroke volume (RSV), and regurgitant fraction (RF) were obtained by quantitative transesophageal echocardiography and proximal isovelocity surface area. Both left and right upper pulmonary venous flow velocities were recorded and their patterns classified by the ratio of systolic to diastolic velocity: normal (>/=1), blunted (<1), and systolic reversal (<0). Twenty-three percent of patients had discordant patterns between the left and right veins. When the most abnormal patterns either in the left or right vein were used for analysis, the ratio of peak systolic to diastolic flow velocity was negatively correlated with ROA (r = -0.74, P <.001), RSV (r = -0.70, P <.001), and RF (r = -0.66, P <.001) calculated by the Doppler thermodilution method; values were r = -0.70, r = -0.67, and r = -0.57, respectively (all P <.001), for indexes calculated by the proximal isovelocity surface area method. The sensitivity, specificity, and predictive values of the reversed pulmonary venous flow pattern for detecting a large ROA (>0.3 cm(2)) were 69%, 98%, and 97%, respectively. The sensitivity, specificity, and predictive values of the normal pulmonary venous flow pattern for detecting a small ROA (<0.3 cm(2)) were 60%, 96%, and 94%, respectively. However, the blunted pattern had low sensitivity (22%), specificity (61%), and predictive values (30%) for detecting ROA of greater than 0.3 cm(2) with significant overlap with the reversed and normal patterns. Among patients with the blunted pattern, the correlation between the systolic to diastolic velocity ratio was worse in those with LV dysfunction (ejection fraction <50%, r = 0.23, P >.05) than in those with normal LV function (r = -0.57, P <.05). Stepwise linear regression analysis showed that the peak systolic to diastolic velocity ratio was independently correlated with RF (P <.001) and effective stroke volume (P <.01), with a multiple correlation coefficient of 0.71 (P <.001). In conclusion, reversed pulmonary venous flow in systole is a highly specific and reliable marker of moderately severe or severe MR with an ROA greater than 0.3 cm(2), whereas the normal pattern accurately predicts mild to moderate MR. Blunted pulmonary venous flow can be seen in all grades of MR with low predictive value for severity of MR, especially in the presence of LV dysfunction. The blunted pulmonary venous flow pattern must therefore be interpreted cautiously in clinical practice as a marker for severity of MR.

Non-NASA Center↗

NASA NTRS1972

Distribution and directional fabric of ash-flow sheets in the northwestern Mogollon Plateau, New Mexico.

Individual ash-flow sheets distributed over wide areas in the Mogollon-Datil volcanic province can be delineated and related by flow direction techniques to specific source cauldrons. Two major mid-Tertiary ash flows in the Mogollon Plateau have measurable microscopic directional fabric indicative of primary flow direction imprinted in the ash-flow sheets during late-stage laminar flow. Regional stratigraphic relationships and flow patterns of the ash-flow sheets indicate a late Tertiary origin of the Mogollon Plateau depression. They also show that Basin-Range faulting in southwestern New Mexico was not initiated until after emplacement of the younger ash flow (23 m.y. B.P.). Directional fabric is an inherent property of many calc-alkalic ash-flow sheets and measurement of preferred orientation provides a powerful tool in unravelling the geologic history of complex volcanic terrane.

Rhodes, R. C.↗

NASA NTRS1982

Some observations of separated flow on finite wings

Wind tunnel test results for aspects of flow over airfoils exhibiting single and multiple trailing edge stall 'mushroom' cells are reported. Rectangular wings with aspect ratios of 4.0 and 9.0 were tested at Reynolds numbers of 480,000 and 257,000, respectively. Surface flow patterns were visualized by means of a fluorescent oil flow technique, separated flow was observed with a tuft wand and a water probe, spanwise flow was studied with hot-wire anemometry, smoke flow and an Ar laser illuminated the centerplane flow, and photographs were made of the oil flow patterns. Swirl patterns on partially and fully stalled wings suggested vortex flow attachments in those regions, and a saddle point on the fully stalled AR=4.0 wing indicated a secondary vortex flow at the forward region of the separation bubble. The separation wake decayed downstream, while the tip vortex interacted with the separation bubble on the fully stalled wing. Three mushroom cells were observed on the AR=9.0 wing.

Winkelmann, A. E.↗

NASA NTRS1983

Visualization studies of turbulent transition flows in a porous medium

Results are reported for flow-visualization studies of the flow regimes of water passing through a porous medium consisting of cylindrical glass and plexiglas rods arranged in a complex and fixed three-dimensional geometry. The Reynolds number (Re) varied from 50 to 700; the flow was visualized by injecting a 5% potassium permanganate dye solution into the pores and photographing the resulting dye streaklines with both a still camera and a movie camera. The results indicate that four distinct flow regimes exist in the porous medium: (1) Darcy or creeping flow up to Re = 3; (2) steady inertia-dominated laminar flow for Re = 3-150; (3) unsteady transitional laminar flow for Re = 150-250; and (4) fully turbulent flow for Re greater than 250. It is concluded that a laminar wake instability mechanism typical of the external flow about bluff bodies may be responsible for the overall transition from laminar to turbulent flow in porous media.

Bilardo, V. J.↗

NASA NTRS1983

Progress toward the analysis of supersonic inlet flows

A zonal flow analysis procedure was developed to predict the flow through the supersonic diffuser of an axisymmetric mixed compression inlet at angle-of-attack. In this analysis, the inlet flow is divided into three types of regions, each with different dominant flow phenomena. These are the inviscid supersonic core, boundary layer, and shock/boundary layer interaction flows. An appropriate analysis was selected or developed for the three-dimensional flow in each type of region. Procedures were developed to interface these analyses for the overall inlet flow analysis. This analysis was applied to an inlet operating at M = 2.58 at several angle-of-attack conditions. Comparisons are presented between computed and measured flow properties for the inlet and for the component analysis flows. Extensions of the present procedure to include the terminal shock and subsonic diffuser flows are recommended. Desirable experiments for evaluation of the inlet analysis procedure or the component analyses and to support improved modeling or extension of the inlet analysis are defined and recommended.

Paynter, G. C.↗

NASA NTRS1984

Physical aspects of computing the flow of a viscous fluid

One of the main themes in fluid dynamics at present and in the future is going to be computational fluid dynamics with the primary focus on the determination of drag, flow separation, vortex flows, and unsteady flows. A computation of the flow of a viscous fluid requires an understanding and consideration of the physical aspects of the flow. This is done by identifying the flow regimes and the scales of fluid motion, and the sources of vorticity. Discussions of flow regimes deal with conditions of incompressibility, transitional and turbulent flows, Navier-Stokes and non-Navier-Stokes regimes, shock waves, and strain fields. Discussions of the scales of fluid motion consider transitional and turbulent flows, thin- and slender-shear layers, triple- and four-deck regions, viscous-inviscid interactions, shock waves, strain rates, and temporal scales. In addition, the significance and generation of vorticity are discussed. These physical aspects mainly guide computations of the flow of a viscous fluid.

Mehta, U. B.↗

NASA NTRS1984

A theoretical study of resin flows for thermosetting materials during prepreg processing

A flow model which describes the process of resin consolidation during prepreg lamination was developed. The salient features of model predictions were explored. It is assumed that resin flows in all directions originate from squeezing action between two approaching adjacent fiber/fabric layers. In the horizontal direction, a squeezing flow between two nonporous parallel plates is analyzed, while in the vertical direction a poiseuille type pressure flow through porous media is assumed. Proper force and mass balance was established for the whole system which is composed of these two types of flow. A flow parameter, CF, shows to be a measure of processibility for the curing resin. For a given external load-F the responses of resin flow during prepreg lamination, as measured by CF, are categorized into three regions: (1) the low CF region where resin flows are inhibited by the high chemoviscosity during initial curing stages; (2) the median CF region where resin flows are properly controllable; and (3) the high CF region where resin flows are ceased due to fiber/fabric compression effects. Resin losses in both directions are calculated. Potential uses of this model and quality control of incoming prepreg material are discussed.

Hou, T. H.↗

NASA NTRS1985

Geomorphology and Geology of the Southwestern Margaritifer Sinus and Argyre Regions of Mars. Part 4: Flow Ejecta Crater Distribution

Flow ejecta craters - craters surrounded by lobate ejecta blankets - are found throughout the study area. The ratio of the crater's diameter to that of the flow ejecta in this region is approximately 40 to 45%. Flow ejecta craters are dominantly sharply defined craters, with slightly degraded craters being somewhat less common. This is probably indicative of the ejecta's relatively low resistence to weathering and susceptibility to burial. Flow ejecta craters here seem to occur within a narrow range of crater sizes - the smallest being about 4km in diameter and the largest being about 27km in diameter. Ejecta blankets of craters at 4km are easily seen and those of smaller craters are simply not seen even in images with better than average resolution for the region. This may be due to the depth of excavation of small impacting bodies being insufficient to reach volatile-rich material. Flow ejecta craters above 24km are rare, and those craters above 27km do not display flow ejecta blankets. This may be a result of an excavation depth so great that the volatile content of the ejecta is insufficient to form a fluid ejecta blanket. The geomorphic/geologic unit appears also to play an important role in the formation of flow ejecta craters. Given the typical size range for the occurrence of flow ejecta craters for most units, it can be seen that the percentage of flow ejecta craters to the total number of craters within this size range varies significantly from one unit to the next. The wide variance in flow ejecta crater density over this relatively small geographical area argues strongly for a lithologic control of their distribution.

Parker, T. J.↗

NASA NTRS1985

Experimental and numerical investigation of supersonic flow through a square duct

Steady, developing, adiabatic supersonic flow in a square duct is investigated for an inlet Mach number of 3.91 and a unit Reynolds number of 1.8 x 10 to the 6th/m. The numerical results for laminar flow show that two secondary flow cells develop in the near vicinity of the corner which are centered about the corner bisector and distort the primary flow in this region. For turbulent flow, the experimental results indicate that two secondary flow cells also develop about the corner bisector, but are directed in an opposite sense to that observed for the laminar case. Numerical results based on the Baldwin-Lomax model show that this model is incapable of predicting turbulence-generated secondary flow cells. For a suitable choice of constants, the Gessner-Emery model is able to predict the strength of these cells, but is deficient with respect to predicting their positions in the flow and their distorting influence on the primary flow. These observations are based on comparisons made in this paper between predicted and measured total pressure contours, cross flow velocity profiles, and local wall shear stress distributions.

Davis, D. O.↗

NASA NTRS1985

Symposium on Numerical and Physical Aspects of Aerodynamic Flows, 3rd, California State University, Long Beach, CA, January 21-24, 1985, Proceedings

Among the topics discussed are hydrodynamic stability and turbulent transition, separated flow simulations employing finite difference methods, a quasi-simultaneous finite difference approach for strongly interacting flow, the Newton solution of coupled Euler and boundary layer equations, multielement airfoil aerodynamics, vorticity dynamics, the significance of the thin layer Navier-Stokes approximation, a comparison of interactive and Navier-Stokes calculations of separating boundary layer flows, and a Navier-Stokes analysis for the mechanism of shock wave/boundary layer interactions. Also discussed are transonic interactions of unsteady vortical flows, boundary layers on oscillating airfoils, a laser-interferometer skin friction meter, flow over surface-mounted semibluff bodies, computations for spinning and spin-stabilized supersonic projectiles, transition calculations in three-dimensional flows, the effect of projectile boattailing in transonic flow, flow characteristics of a body of revolution at incidence, the influence of the boundary layer on the leading edge flow of a swept wing, and an interactive scheme for three-dimensional transonic flows.

Source record↗

NASA NTRS1986

Flow in out-of-plane double S-bonds

Developing flows in two out-of-plane double S-bend configurations have been measured by laser-Doppler anemometry. The first duct had a rectangular cross-section 40mmx40mm at the inlet and consisted of a uniform area 22.5 deg. - 22.5 deg. S-duct upstream with a 22.5 deg.- 22.5 deg. S- diffuser downstream. The second duct had a circular cross-section and consisted of a 45 deg. - 45 deg. uniform area S-duct upstream with a 22.5 deg. -22.5 deg. S-diffuser downstream. In both configurations the ratio of the mean radius of curvature to the inlet hydraulic diameter was 7.0, the exit-to-inlet area ratio of the diffusers was 1.5 and the ducts were connected so that the centerline of the S-duct lay in a plane normal to that of the S-diffuser. Streamwise and cross-stream velocity components were measured in laminar flow for the rectangular duct and in turbulent flow for both configurations; measurements of the turbulence levels, cross-correlations and wall static pressures were also made in the turbulent flow cases. Secondary flows of the first kind are present in the first S-duct and they are complemented or counteracted by the secondary flows generated by the area expansion and by the curvature of the S-diffusers downstream. Cross-stream velocities with magnitudes up to 0.19 and 0.11 of the bulk velocity were measured in the laminar and turbulent flows respectively in the rectangular duct and six cross-flow vortices were evident at the exit of the duct in both flow cases. The turbulent flow in the circular duct was qualitatively similar to that in the rectangular configuration, but the cross-stream velocities measured at the exit plane were smaller in the circular geometry. The results are presented in sufficient detail and accuracy for the assessment of numerical calculation methods and are listed in tabular form for this purpose.

Schmidt, M. C.↗

NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1987

Further experiments on supersonic turbulent flow development in a square duct

The mean-flow structure of supersonic, turbulent, adiabatic-wall flow in a square duct is investigated experimentally over a development length x/D = 0-50 for a uniform flow, Mach 3.9 condition at the duct inlet. The results show that a secondary flow cell structure develops which is similar to that for the incompressible case. Development of the primary flow is influenced by the combined effects of the secondary flow and the streamwise adverse pressure gradient. Total pressure, axial mean velocity, and Mach number profiles are presented which show that the outer flow is sensitive primarily to the streamwise pressure gradient, while flow in the near-wall region is dominated by the secondary flow. Axial mean-velocity profiles plotted in terms of van Driest-scaled variables show that a well-defined log-law region exists in the near-wall layer. This region exists in the presence of a secondary flow which continuously modifies spanwise wall shear stress behavior along the length of the duct.

Davis, D. O.↗

NASA NTRS1988

Unsteady three-dimensional flow separation

A concise mathematical framework is constructed to study the topology of steady 3-D separated flows of an incompressible, or a compressible viscous fluid. Flow separation is defined by the existence of a stream surface which intersects with the body surface. The line of separation is itself a skin-friction line. Flow separation is classified as being either regular or singular, depending respectively on whether the line of separation contains only a finite number of singular points or is a singular line of the skin-friction field. The special cases of 2-D and axisymmetric flow separation are shown to be of singular type. In regular separation it is shown that a line of separation originates from a saddle point of separation of the skin-friction field and ends at nodal points of separation. Unsteady flow separation is defined relative to a coordinate system fixed to the body surface. It is shown that separation of an unsteady 3-D incompressible viscous flow at time t, when viewed from such a frame of reference, is topologically the same as that of the fictitious steady flow obtained by freezing the unsteady flow at the instant t. Examples are given showing effects of various forms of flow unsteadiness on flow separation.

Hui, W. H.↗

NASA NTRS1989

Numerical investigation of an internal layer in turbulent flow over a curved hill

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulence field of the boundary layer flow over the curved hill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of the strongly curved surface on the turbulence field. The turbulent flow equations are solved by a control-volume based finite difference method. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. Computational results for the mean flow field (pressure distributions on the walls, wall shearing stresses and mean velocity profiles), the turbulence structure (Reynolds stress and turbulent kinetic energy profiles), and the integral parameters (displacement and momentum thicknesses) compared favorably with the measured data. Computational results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. Development of the internal layer was more obviously observed in the Reynolds stress profiles and in the turbulent kinetic energy profiles than in the mean velocity profiles. In this regard, the internal layers is significantly different from wall-bounded simple shear layers in which the mean velocity profile characterizes the boundary layer most distinguishably. Development of such an internal layer, characterized by an intense turbulence field, is attributed to the enormous mean flow strain rate caused by the streamline curvature and the strong pressure gradient. In the turbulent flow over the curved hill, the internal layer begin to form near the forward corner of the hill, merges with the external boundary layer, and develops into a new fully turbulent boundary layer as the fluid flows in the downstream direction. For the flow over the symmetric airfoil, the boundary layer began to form from almost the same location as that of the curved hill, grew in its strength, and formed a fully turbulent boundary layer from mid-part of the airfoil and in the downstream region. Computational results also show that the detailed turbulence structure in the region very close to the wall of the curved hill is almost the same as that of the airfoil in most of the curved regions except near the leading edge. Thus the internal layer of the curved hill and the boundary layer of the airfoil were also almost the same. Development of the wall shearing stress and separation of the boundary layer at the rear end of the curved hill mostly depends on the internal layer and is only slightly influenced by the external boundary layer flow.

Kim, S-W.↗

NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

Hall, Kenneth C.↗