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Boundary-layer linear stability theory

Most fluid flows are turbulent rather than laminar and the reason for this was studied. One of the earliest explanations was that laminar flow is unstable, and the linear instability theory was first developed to explore this possibility. A series of early papers by Rayleigh produced many notable results concerning the instability of inviscid flows, such as the discovery of inflectional instability. Viscosity was commonly thought to act only to stabilize the flow, and flows with convex velocity profiles appeared to be stable. The investigations that led to a viscous theory of boundary layer instability was reported. The earliest application of linear stability theory to transition prediction calculated the amplitude ratio of the most amplified frequency as a function of Reynolds number for a Blasius boundary layer, and found that this quantity had values between five and nine at the observed Ret. The experiment of Schubauer and Skramstad (1947) completely reversed the prevailing option and fully vindicated the Gottingen proponents of the theory. This experiment demonstrated the existence of instability waves in a boundary layer, their connection with transition, and the quantitative description of their behavior by the theory of Tollmien and Schlichting. It is generally accepted that flow parameters such as pressure gradient, suction and heat transfer qualitatively affect transition in the manner predicted by the linear theory, and in particular that a flow predicted to be stable by the theory should remain laminar. The linear theory, in the form of the e9, or N-factor is today in routine use in engineering studies of laminar flow. The stability theory to boundary layers with pressure gradients and suction was applied. The only large body of numerical results for exact boundary layer solutions before the advent of the computer age by calculating the stability characteristics of the Falkner-Skan family of velocity profiles are given. When the digital computer reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.

Leslie M Mack↗

Boundary layer transition studies

A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated holes in the impervious test plate that used to establish the Blasius base flow. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance, for conditions corresponding to strong suction and without suction. The technique was enhanced by using up to nine multiple probes to reduce the experimental run-time. In both cases, 3D contour surfaces in the vicinity of the hole show highly 3D TS waves which fan out in the spanwise direction forming bow-shaped waves downstream. The case without suction has proved useful for evaluating calculation methods. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the TS waves in the far field are similar to the case without suction. Downstream, the contour surfaces of the TS waves develop spanwise irregularities which eventually form into clumps. The spanwise clumping is evidence of a secondary instability that could be associated with suction vortices. Designers of porous surfaces use Goldsmith's Criterion to minimize cross-stream interactions. It is shown that partial TS wave cancellation is possible, depending on the hole spacing, disturbance frequency and free-stream velocity. New high-performance Constant Temperature Hot-Wire Anemometers were designed and built, based on a linear system theory analysis that can be extended to arbitrary order. The motivation was to achieve the highest possible frequency reponse while ensuring overall system stability. The performance is equal to or superior to commercially available instruments at about 10% of the cost. Details, such as fabrication drawings and a parts list, have been published to enable the instrument to be construced by others.

Watmuff, Jonathan H.↗

Simulations of bypass transition for spatially evolving disturbances

The spatial evolution of disturbances in plane Poiseuille flow and zero pressure gradient boundary layer flow is considered. For disturbances governed by the linearized equations, potential for significant transient growth of the amplitude is demonstrated. The maximum amplification occurs for disturbances with zero or near zero frequencies. Spatial numerical simulations of the transition scenario involving a pair of oblique waves has been conducted for both flows. A fully spectral solver using a simple but efficient fringe region technique allowed the flows to be computed with high resolution into the fully turbulent domain. A modal decomposition of the simulation results indicates that non-linear excitation of the transient growth is responsible for the rapid emergence of low-frequency structures. Physically, this corresponds to streaky flow structures, as seen from the results of a numerical amplitude expansion. Thus, this spatial transition scenario has been found to be similar to the corresponding temporal one. In the boundary layer simulations the streaks are seen to break down from what appears to be a secondary instability.

Lundbladh, A.↗

Boundary-Layer Code For Supersonic Combustion

HUD is integral computer code based on Spaulding-Chi method for predicting development of boundary layers in laminar, transitional, and turbulent regions of flows on two-dimensional or axisymmetric bodies. Approximates nonequilibrium velocity profiles as well as local surface friction in presence of pressure gradient. Predicts transfer of heat in turbulent boundary layer in presence of high axial presure gradient. Provides for pressure gradients both normal and lateral to surfaces. Also used to estimate requirements for cooling scramjet engines. Because of this capability, HUD program incorporated into several scramjet-cycle-performance-analysis codes, including SCRAM (ARC-12338) and SRGULL (LEW-15093). Written in FORTRAN 77.

Pinckney, S. Z.↗

Computational design of natural laminar flow wings for transonic transport application

Two research programs are described which directly relate to the application of natural laminar flow (NLF) technology to transonic transport-type wind planforms. Each involved using state-of-the-art computational methods to design three-dimensional wing contours which generate significant runs of favorable pressure gradients. The first program supported the Variable Sweep Transition Flight Experiment and involves design of a full-span glove which extends from the leading edge to the spoiler hinge line on the upper surface of an F-14 outer wing panel. Boundary-layer and static-pressure data will be measured on this design during the supporting wind-tunnel and flight tests. These data will then be analyzed and used to infer the relationship between crossflow and Tollmein-Schlichting disturbances on laminar boundary-layer transition. A wing was designed computationally for a corporate transport aircraft in the second program. The resulting wing design generated favorable pressure gradients from the leading edge aft to the mid-chord on both upper and lower surfaces at the cruise design point. Detailed descriptions of the computational design approach are presented along with the various constraints imposed on each of the designs. Wing surface pressure distributions, which support the design objective and were derived from transonic three-dimensional analyses codes, are also presented. Current status of each of the research programs is included in the summary.

Waggoner, Edgar G.↗

Skin friction measurement in complex flows using thin oil film techniques

The NASA Grant NAG2-261 was initiated to support a program of research to study complex flows that occur in flight and laboratory experiments by building, testing and optimizing an on-board technique for direct measurement of surface shear stress using thin oil film techniques. The program of research has proceeded under the supervision of the NASA Ames Research Center and with further cooperation from the NASA Ames-Dryden and NASA Langley Research Centers. In accordance with the original statement of work, the following research milestones were accomplished: (1) design and testing of an internally mounted one-directional skin friction meter to demonstrate the feasibility of the concept; (2) design and construction of a compact instrument capable of measuring skin friction in two directions; (3) study of transitional and fully turbulent boundary layers over a flat plate with and without longitudinal pressure gradients utilizing the compact two-directional skin friction meter; (4) study of the interaction between a turbulent boundary layer and a shock wave generated by a compression corner using the two-directional meter; and (5) flight qualification of the compact meter and accompanying electronic and pneumatic systems, preliminary installation into flight test fixture.

Source record↗

Transition control of instability waves over a flexible surface in the presence of an acoustic field

Experimental results are presented which demonstrate the coupling of a laminar boundary layer flow with a typical flexible aircraft panel. It is shown that the boundary layer induces plate oscillations which, in turn, perturb the flow at the same frequencies. This feedback mechanism is an inherent property of laminar boundary layer flow passing over a flexible plate. As a result, the flexibility of the plate becomes a source of early transition. The laminar boundary layer at the leading edge of the plate reacts to small, upstream, unsteady disturbances due to a streamwise pressure gradient. The experiments demonstrate that a nominal sound pressure incident at the leading edge triggers early transition. It is shown that transition can be delayed by activating a heat source at the leading edge of the plate which results in downstream cooling.

Maestrello, L.↗

Modelling the transitional boundary layer

Recent developments in the modelling of the transition zone in the boundary layer are reviewed (the zone being defined as extending from the station where intermittency begins to depart from zero to that where it is nearly unity). The value of using a new non-dimensional spot formation rate parameter, and the importance of allowing for so-called subtransitions within the transition zone, are both stressed. Models do reasonably well in constant pressure 2-dimensional flows, but in the presence of strong pressure gradients further improvements are needed. The linear combination approach works surprisingly well in most cases, but would not be so successful in situations where a purely laminar boundary layer would separate but a transitional one would not. Intermittency-weighted eddy viscosity methods do not predict peak surface parameters well without the introduction of an overshooting transition function whose connection with the spot theory of transition is obscure. Suggestions are made for further work that now appears necessary for developing improved models of the transition zone.

Narasimha, R.↗

Modeling of the heat transfer in bypass transitional boundary-layer flows

A low Reynolds number k-epsilon turbulence model and conditioned momentum, energy and turbulence equations were used to predict bypass transition heat transfer on a flat plate in a high-disturbance environment with zero pressure gradient. The use of conditioned equations was demonstrated to be an improvement over the use of the global-time-averaged equations for the calculation of velocity profiles and turbulence intensity profiles in the transition region of a boundary layer. The approach of conditioned equations is extended to include heat transfer and a modeling of transition events is used to predict transition onset and the extent of transition on a flat plate. The events, which describe the boundary layer at the leading edge, result in boundary-layer regions consisting of: (1) the laminar, (2) pseudolaminar, (3) transitional, and (4) turbulent boundary layers. The modeled transition events were incorporated into the TEXSTAN 2-D boundary-layer code which is used to numerically predict the heat transfer. The numerical predictions in general compared well with the experimental data and revealed areas where additional experimental information is needed.

Simon, Frederick F.↗

Potential flow calculations and preliminary wing design in support of an NLF variable sweep transition flight experiment

NASA Langley and NASA Ames-Dryden have defined a variable-sweep transition-flight experiment utilizing the F-14 aircraft to enhance understanding of the interaction of crossflow and Tollmien-Schlichting instabilities on a laminar-boundary-layer transition. The F-14 wing outer panel will be modified to generate favorable pressure gradients on the upper wing surface over a wide range of flight conditions. Extensive computations have been performed using two-dimensional and three-dimensional transonic analysis codes. Flight-test and computational data are compared and shown to validate the applicability of the three-dimensional codes (WBPPW and TAWFIVE). In addition, results from two preliminary glove designs derived from two different approaches to the design problem are presented. Advantages and disadvantages of each approach are identified, and it is concluded that coupling an analysis code with an automated design procedure yields a powerful code with distinct advantages over a 'cut-and-dry' approach.

Waggoner, E. G.↗

Computational wing design in support of an NLF variable sweep transition flight experiment

A natural laminar flow outer panel wing glove has been designed for a variable sweep fighter aircraft using state-of-the-art computational techniques. Testing of the design will yield wing pressure and boundary-layer data under actual flight conditions and environment. These data will be used to enhance the understanding of the interaction between crossflow and Tollmien-Schlichting disturbances on boundary-layer transition. The outer wing panel was contoured such that a wide range of favorable pressure gradients could be obtained on the wing upper surface. Extensive computations were performed to support the design effort which relied on two- and three-dimensional transonic design and analysis techniques. A detailed description of the design procedure that evolved during this study is presented. Results on intermediate designs at various stages in the design process demonstrate how the various physical and aerodynamic constraints were integrated into the design. Final results of the glove design analyzed as part of the complete aircraft configuration with a full-potential wing/body analysis code indicate that the aerodynamic design objectives were met.

Waggoner, E. G.↗

A Review of Hypersonic Boundary Layer Stability Experiments in a Quiet Mach 6 Wind Tunnel

Three recent experimental studies of transition on cones with adverse pressure gradient produced by a flared afterbody and with the additive stability modifiers of wall cooling, angle of attack and bluntness are reviewed. All tests were conducted in a quiet Mach 6 wind tunnel. The dominant instability was found to be the second mode. For the cases examined with linear stability theory, the N factors at mode saturation were in the range of 8.5 to 11. Evidence of a combined second-mode/Gortler transition process was found. Mean, rms and spectral freestream data for the quiet facility is presented and the role of low frequency freestream noise is discussed.

Wilkinson, Stephen P.↗

Analytical and Experimental Evaluation of the Heat Transfer Distribution over the Surfaces of Turbine Vanes

Three airfoil data sets were selected for use in evaluating currently available analytical models for predicting airfoil surface heat transfer distributions in a 2-D flow field. Two additional airfoils, representative of highly loaded, low solidity airfoils currently being designed, were selected for cascade testing at simulated engine conditions. Some 2-D analytical methods were examined and a version of the STAN5 boundary layer code was chosen for modification. The final form of the method utilized a time dependent, transonic inviscid cascade code coupled to a modified version of the STAN5 boundary layer code featuring zero order turbulence modeling. The boundary layer code is structured to accommodate a full spectrum of empirical correlations addressing the coupled influences of pressure gradient, airfoil curvature, and free-stream turbulence on airfoil surface heat transfer distribution and boundary layer transitional behavior. Comparison of pedictions made with the model to the data base indicates a significant improvement in predictive capability.

Hylton, L. D.↗

Metafusion: A breakthrough in metallurgy

The Metafuse Process is a patented development in the field of thin film coatings utilizing cold fusion which results in a true inter-dispersion of dissimilar materials along a gradual transition gradient through a boundary of several hundred atomic layers. The process is performed at ambient temperatures and pressures requiring relatively little energy and creating little or no heat. The process permits a remarkable range of material combinations and joining of materials which are normally incompatible. Initial applications include titanium carbide into and onto the copper resistance welding electrodes and tungsten carbide onto the cutting edges of tool steel blades. The process is achieved through application of an RF signal of low power and is based on the theory of vacancy fusion.

Joseph, Adrian A.↗

Numerical simulation of transition in a decelerating boundary layer

Transition in a decelerating flat-plate boundary layer is numerically simulated up to the beginning of three-dimensional breakdown, and the results are compared with an experiment. The adverse pressure gradient induced by deceleration increases the growth rate of disturbances and allows transition at lower Reynolds numbers. The primary instability is characterized by a wave packet, which undergoes three-dimensional distortion. Lambda vortices are locally observed, but they are not aligned with respect to the flow direction.

Yang, Kyung Soo↗

Experimental study of boundary layer transition with elevated freestream turbulence on a heated flat plate

A detailed investigation to document momentum and thermal development of boundary layers undergoing natural transition on a heated flat plate was performed. Experimental results of both overall and conditionally sampled characteristics of laminar, transitional, and low Reynolds number turbulent boundary layers are presented. Measurements were acquired in a low-speed, closed-loop wind tunnel with a freestream velocity of 100 ft/s and zero pressure gradient over a range of freestream turbulence intensities (TI) from 0.4 to 6 percent. The distributions of skin friction, heat transfer rate and Reynolds shear stress were all consistent with previously published data. Reynolds analogy factors for R(sub theta) is less than 2300 were found to be well predicted by laminar and turbulent correlations which accounted for an unheated starting length. The measured laminar value of Reynolds analogy factor was as much as 53 percent higher than the Pr(sup -2/3). A small dependence of turbulent results on TI was observed. Conditional sampling performed in the transitional boundary layer indicated the existence of a near-wall drop in intermittency, pronounced at certain low intermittencies, which is consistent with the cross-sectional shape of turbulent spots observed by others. Non-turbulent intervals were observed to possess large magnitudes of near-wall unsteadiness and turbulent intervals had peak values as much as 50 percent higher than were measured at fully turbulent stations. Non-turbulent and turbulent profiles in transitional boundary layers cannot be simply treated as Blasius and fully turbulent profiles, respectively. The boundary layer spectra indicate predicted selective amplification of T-S waves for TI is approximately 0.4 percent. However, for TI is approximately 0.8 and 1.1 percent, T-S waves are localized very near the wall and do not play a dominant role in transition process.

Sohn, Ki-Hyeon↗

A low-Reynolds-number two-equation turbulence model for predicting heat transfer on turbine blades

A modified form of the Lam-Bremhorst low-Reynolds number kappa-epsilon turbulence model was developed for predicting transitional boundary layer flows under conditions characteristic of gas turbine blades. The application of the model to flows with pressure gradients is described. Tests against a number of turbine blade cascade data sets are included. Some additional refinements of the model that were made in recent months are explained.

Patankar, Suhas V.↗

Data correlation and analysis of arc tunnel and wind tunnel tests of RSI joints and gaps, phase 2. Volume 1: Technical report

Heat transfer data measured in gaps representative of those being employed for joints in the space shuttle reusable surface insulation (RSI) thermal protection systems (TPS) were assimilated, analyzed, and correlated. Several types of gap were investigated with emphasis on simple butt joints. Gap widths ranged from 0.0 to 0.76 cm and depths ranged from 1 to 6 cm. Laminar, transitional, and turbulent boundary layer flows over the gap opening were investigated. The angle between gap axis and external flow was varied between 0 and pi/2 radians. The contoured cross section gap performed significantly better than all other wide gaps and slightly better than all other narrow gap geometries. Three dimensional heating variations were observed within gaps in the absence of external flow pressure gradients. Interactions between heating within gaps and heating of adjacent top tile surfaces were observed. Gaps aligned with the flow were observed to promote boundary layer transition. Heat transfer correlation equations were obtained for many of the tests. The TPS thickness requirements with and without gaps were computed for a current shuttle entry trajectory. Experimental data employed in the study are summarized. A description of each test facility, run schedule and test conditions, model descriptive information, and heat flux data are included.

Cristensen, H. E.↗