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NASA NTRS2018

Transition Delay via Vortex Generators in a Hypersonic Boundary Layer at Flight Conditions

The potential of realizable, stationary streaks undergoing non-modal growth to stabilize a hypersonic boundary-layer flow and, subsequently, delay the laminar-turbulent transition onset, is studied via numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7-degree half-angle cone with 2.5 mm nose radius, freestream Mach number of 5.30, freestream unit Reynolds number equal to 13.42 x 10(exp 6)/m, and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the test article. This paper investigates flow modifications induced by wall-mounted vortex generators (VGs), followed by an analysis of the modal instability of the perturbed, streaky boundary-layer flow. Results are presented both for a single array of VGs that was designed on the basis of optimal growth theory and for a VG configuration involving two separate arrays with opposite orientations that ware designed to provide staged control of flow instabilities while simultaneously reducing the amplification of streak instabilities resulting from the control devices. Earlier research had shown that the onset of transition during the HIFiRE-1 flight experiment, which did not include any control devices, correlated with an amplification factor of N = 14.7 for the planar Mack modes. If one assumes that the transition N -factor is not affected by the introduction of the VGs, then the control configurations based on a single array of VGs and two separate arrays would result in a transition delay of 17% and 40%, respectively. These findings suggest a passive flow control s to induce streaks that would delay transition in hypersonic boundary dominated by Mack-mode instabilities.

Incompressible boundary layer↗

NASA NTRS2019

Nonmodal Growth of TravelingWaves on Blunt Cones at Hypersonic Speeds

The existing database of transition measurements in hypersonic ground facilities has established that, as the nosetip bluntness is increased, the onset of boundary layer transition over a circular cone at zero angle of attack shifts downstream. However, this trend is reversed at sufficiently large values of the nose Reynolds number, so that the transition onset location eventually moves upstream with a further increase in nose-tip bluntness. Because modal amplification is too weak to initiate transition at moderate-to-large bluntness values, nonmodal growth has been investigated as the potential basis for a physics-based model for the frustum transition. The present analysis investigates the nonmodal growth of traveling disturbances initiated within the nose-tip vicinity that peak within the entropy layer. Results show that, with increasing nose bluntness, both planar and oblique traveling disturbances experience appreciable energy amplification up to successively higher frequencies. For moderately blunt cones, the initial nonmmodal growth is followed by a partial decay that is more than overcome by an eventual, modal growth as Mack-mode waves. For larger bluntness values, the Mack-mode waves are not amplified anywhere upstream of the experimentally measured transition location, but the traveling modes still undergo a significant amount of nonmodal growth. This finding does not provide a definitive link between optimal growth and the onset of transition, but it is qualitatively consistent with the experimental observations that frustum transition in the absence of sufficient Mack-mode amplification implies a double peak in disturbance amplification and the appearance of transitional events above the boundary-layer edge.

Hypersonic speed↗

NASA NTRS2019

Effect of 3D Roughness Patch on Instability Amplification in a Supersonic Boundary Layer

Surface roughness is known to have a substantial impact on the aerothermodynamic loading of high-speed vehicles, particularly via its influence on the laminar-turbulent transition process within the boundary layer. Numerical simulations are performed to investigate the effects of a distributed region of densely packed, sinusoidal shape roughness elements on a Mach 3.5 flat plate boundary layer for flow conditions corresponding to the planned conditions of an upcoming experiment in the Mach 3.5 Supersonic Low Disturbance Tunnel at the NASA Langley Research Center. Analysis of convective instabilities in the wake of the roughness patch was reported in a previous paper and the current work extends that analysis to instability amplification across the length of the roughness patch. Quasi-parallel stability analysis of the modified boundary layer flow over the patch indicates two dominant families of unstable disturbances, namely, a group of high frequency modes that amplify in localized regions along the roughness patch and another group of low frequency modes that have smaller peak amplification rates but amplify steadily both above the roughness patch and in the wake region behind it. The results suggest that the amplification factors associated with the high-frequency modes are sufficiently low, at least for the roughness patches considered in this paper, so that these modes are unlikely to have a major influence on the transition process. The amplification of the low-frequency modes within the region of the roughness patch is further quantified via direct numerical simulations. Results confirm the strongly destabilizing influence of the roughness patch on the first mode instabilities, yielding an N-factor increment of ΔN ≈ 3.6 for a roughness patch length of eight wavelengths.

Laminar turbulent transition↗

NASA NTRS2020

Streak Instability Analysis for BOLT Configuration

The BOLT configuration designed for an upcoming flight experiment exemplifies the complexities of hypersonic boundary layer transition in the presence of multiple and potentially interacting instability mechanisms. A numerical study of the boundary layer instabilities over this configuration has been performed with the goal of applying state-of-the-art tools in multidimensional stability analysis that complement the other ongoing research related to the BOLT flight campaign. Specifically, the paper outlines modal instability characteristics of the boundary layer streaks adjacent to the minor-axis symmetry plane of a 1/3 rd scale BOLT configuration that was tested in the low-disturbance hypersonic wind tunnel at Purdue University and both quiet and conventional tunnels at Texas A&M University (TAMU). The basic state computations agree well with the heat flux measurements in the Purdue quiet tunnel as well as with the off-body velocity field described in a previous DNS study at the University of Minnesota. The encouraging agreement between the predicted frequency spectra of the streak instability in the region of increased boundary layer thickness and the surface pressure spectra measured during the TAMU experiments suggests that these streak instabilities may play an important role during the transition process near the symmetry plane. The modest value of the predicted peak N-factor (N max ≈ 5) for the streak instabilities provides a potential explanation for why transition is not observed under quiet flow conditions, but may occur in a noisy wind tunnel. Similar instability analyses are performed for the flight configuration at two selected flow conditions from the ascent portion of the planned flight trajectory. The predicted values of the peak N-factor suggest that transition onset in the vicinity of the center plane is possible at the ascent time of t = 26.98 seconds (N max ≈ 12.5 at X/L = 0.77), but the streak instabilities weaken sufficiently at the later time of t = 28.88 seconds (N max ≈ 11.5 at X/L ≈ 1.00) and are less likely to cause transition at that time.

Laminar turbulent transition↗

NASA NTRS2021

A Computational Analysis of Boundary Layer Instability over the BOLT Configuration

Boundary layer transition↗

NASA NTRS2021

A Computational Analysis of Boundary Layer Instability over the BOLT Configuration

The complex boundary layer flow over the BOLT flight configuration is known to exhibit multiple and potentially interacting instability mechanisms. This paper represents a continuation of our numerical investigation of the flow instabilities over the main test surface of the BOLT configuration by using state-of-the-art tools in multidimensional instability analysis. Specifically, the paper extends our previous computations by considering the separate effects of a nonzero angle of attack and a nonzero yaw on the modal instability characteristics of the boundary layer streaks adjacent to the minor-axis symmetry plane, specifically near both ends of the azimuthal region of a thick boundary layer in the middle, where this region rapidly changes to a thinner boundary layer on either side. At the t = 28.8767 s condition from the ascent part of the anticipated flight trajectory with a flight Mach number of M ∞ = 5.53 and unit Reynolds number of 4.25 x 10 6 /m, either type of departure from the design condition is shown to have a considerable impact on the structure of the basic state rollup within the region of interest and, hence, also on the amplification characteristics of instability waves within the resulting streaks. Yet, for a yaw angle of β = 4 degrees, the computations indicate only a slight reduction with respect to the peak N-factor of nearly 11 at the design condition of zero degrees yaw and zero degrees angle of attack. In contrast, an angle of attack equal to α = 4 degrees, the peak N-factor decreases to nearly 6 on the leeward side and increases above 16 on the windward side, making the onset of transition highly likely on the windward side. Computations also highlight the role of streak instabilities that originate as Mack mode disturbances and also demonstrate the potential pitfalls in using surface pressure sensors alone to gauge the magnitude of instability amplification.

Boundary layer transition↗

NASA NTRS2021

Hypersonic Boundary-Layer Transition on Blunted Cones at Angle of Attack

Experimental studies of cones at several high-speed facilities have demonstrated that, for small nosetip bluntness, transition onset over a circular cone moves upstream along the leeward side and downstream along the windward side, but this trend may be reversed at large bluntness values, where transition onset moves downstream along the leeward side and upstream along the windward side. A theoretical and numerical investigation is performed to characterize the effects of nose bluntness on disturbance amplification over the circular cone for several angles of attack, with the goal of understanding the potential physical mechanisms behind the experimental observations. The three-dimensional laminar basic states over a 1.5 m long, 7-degree half-angle cone with 9.525 mm nosetip radius are computed for selected angles of attack values and freestream conditions that are selected to match the Mach 10 experiments conducted within the Hypervelocity Wind Tunnel 9 at the Arnold Engineering Development Complex (AEDC). The solutions at a freestream unit Reynolds number of 17.1 million per meter are used to perform detailed instability analyses for angles of attack equal to 0, 1, 3, and 5 degrees. Results indicate that the linear amplification of stationary crossflow waves along inflection lines may begin to influence transition along the acreage of the cone for angles of attack equal to or larger than 5 degrees. The measured trend in transition front with respect to increasing angle of attack is found to be consistent with the predicted increase in the amplification factors for Mack mode disturbances along the streamline trajectories. The increase in Mack mode amplification along the windward ray for higher angles of attack is shown to be the result of a progressively earlier entropy-layer swallowing. Computations also indicate that the transition amplification factor along the windward ray is not constant and increases with the angle of attack and that the transition #-factors along the leeward ray are rather small. The nonmodal analysis for zero degrees angle of attack shows that entropy-layer disturbances with appreciably strong energy growth can coexist with Mack mode instabilities at the measured transition location.

Boundary Layer Transition↗

NASA NTRS2021

Transition Analysis for Isolated Trips on BOLT-II Wind-Tunnel and Flight Configuration

The BOLT-II configuration designed for an upcoming flight experiment exemplifies the complexities of hypersonic boundary layer transition in the presence of multiple and potentially interacting instability mechanisms. The present paper is related to the NASA-led roughness experiment on the secondary side of the BOLT-II configuration. First, computations are performed to aid mean-flow based correlations for the transition measurements acquired during an experimental campaign in the Ludwieg Tube facility at the United States Air Force Academy. To that end, both laminar and turbulent flow computations are performed for selected conditions of the experiment with a 1:3 scale model of the slightly shorter BOLT configuration. The variation in well-known correlation parameters for transition due to isolated roughness elements with respect to element position, height, and flow Reynolds number is delineated. Furthermore, the wake instability theory is used to examine the amplification of unstable disturbances behind the centerline trip at the design conditions of the BOLT-II flight experiment and for its dynamically scaled version on the 1:3 scale model of the wind tunnel experiment. To our knowledge, this study represents the first analysis of the wake instabilities in the presence of a prominent entropy layer outside the boundary layer. At the nominal flight design condition of Re ∞ ) = 5.44 and Re ∞ = 2.5 x 10 6 /m, a diamond planform (“pizza-box”) trip with k/δ = 0.70 and planform-halfwidth-to-height ratio of b/k = 3.0 at X/L = 0.254 induces a strong distortion of the boundary-layer flow in the vicinity of the symmetry plane, such that the wake structure includes a centerline streak produced by the flow retardation behind the trip along with multiple additional, prominent vorticity structures representing the necklace vortex system. Stability results reveal that each of these streaks can support a strong amplification of wake instabilities within a frequency band of 95 kHz–255 kHz, with a peak N-factor of greater than 15 beyond X/L ≈ 0.42. The dynamically scaled wind tunnel configuration with Re ∞ = 20.25 x 10 6 /m is also found to support N > 15 at similar axial stations.

BOLT↗

NASA NTRS2021

Wake Instability Behind Isolated Trip Near the Leading Edge of the BOLT-II Configuration

The BOLT-II (Holden Mission) configuration is an extended version of the BOLT flight article and depicts hypersonic boundary-layer transition in the presence of multiple and potentially interacting instability mechanisms. Several numerical studies of the boundary-layer instabilities over these configurations have been reported in the recent literature, including our previous studies of the modal instability characteristics of boundary-layer streaks adjacent to the minor-axis symmetry plane of the BOLT configuration and the wake instabilities behind a diamond planform (“pizza-box”) trip along the symmetry plane on the secondary side of the BOLT-II configuration. The present work extends the latter study to a scaled version of the same trip that is located in the region of nonzero crossflow in the vicinity of the leading edge at X/L = 0.5. Collectively, the trips along the symmetry plane and near the leading edge are the focus of the NASA roughness experiment on the secondary side of the BOLT-II configuration. The laminar basic state computation at the nominal flight design condition of Re ∞ = 5.44 x 10 6 /m and Re ∞ = 2.5 x 10 6 /m shows that the leading-edge trip with k/δ ≈ 0.70 and planform-side-length-to-height ratio of b/k = 3.0 induces multiple asymmetric, longitudinal streaks within the trip wake. The most prominent streak among these resembles a finite amplitude crossflow vortex, and it supports the amplification of multiple families of unstable modes. The application of multi-dimensional instability analysis to the wake flow reveals that the most amplified unstable mode can achieve a peak N-factor of up to 20 by X/L = 0.80, indicating that the onset of transition is more than likely to occur within eighty percent of the model length. To the best of our knowledge, the present study represents the first analysis including nonparallel and curvature effects on hypersonic tripwake instabilities in the presence of boundary-layer crossflow over a three-dimensional configuration.

Boundary layer transition↗

NASA NTRS2021

Hypersonic Boundary-Layer Instabilities over Ogive-Cylinder Models

Computational investigations of an ogive-cylinder geometry with varying nosetips at zero degrees angle of attack are presented. The model geometry and conditions are selected to match experiments conducted in the Air Force Research Laboratory (AFRL) Mach 6 Ludwieg Tube. Five nosetips of interest were selected for the computational studies herein: two sharp ogives, two blunt ogives, and one hemispherical nosetip. Computations are performed at a freestream Reynolds number of 7.01 × 10 6 m -1 . Each sharp and blunt tip ogives had a 14 and 28 degree version for the tip angles. A cylindrical section follows the nosetip, resulting in a meter long model such as in the experiments. The laminar flow solutions are analyzed. The boundary-layer-edge properties and the velocity and temperature profiles are compared across streamwise locations aft of the ogive-cylinder junction. The blunt nosetips induce an entropy layer that envelopes the boundary-layer profiles. Modal stability analysis identifies most amplified frequencies corresponding to Mack’s second modes that agree with experimental results for the sharp tips. Similar to the experimental measurements based on wall-mounted pressure sensors, no unstable modes are found for the blunt models. Nonmodal analysis revealed a broadband set of disturbances present for the blunter tips, in agreement with experimental observations. Flow perturbation contours of most amplified planar and oblique disturbances are shown to qualitatively match wind tunnel Schlieren images, with a switch from rope-like to elongated structures, i.e., from high frequency Mack’s second modes to low frequency Mack’s first modes, as the nosetip angle is increased for the sharp tip, and from boundary-layer to entropy-layer disturbances as the bluntness is increased.

Boundary layer transition↗

NASA NTRS2022

Linear Disturbance Amplification Over Blunted Flat Plates in High-Speed Flows

Modal and nonmodal instability characteristics of cylindrically blunted flat plates with varying leading edge radii are described for Mach 4 and Mach 6 freestream conditions. The selection of leading edge radii and freestream parameters is informed by experimental conditions. The investigation of this 2D problem provides a slow entropy layer swallowing which allows for an isolated development of perturbations seeded upstream within different wall-normal regions of the flow. At both Mach numbers, a decrease in modal instability amplification was seen as the leading edge radius was increased. Nonmodal analysis reveals amplifying perturbations in the boundary layer as well as in the entropy layer. The medium bluntness regime exhibits the strongest amplification of nonmodal disturbances that is nonmonotonic in character. Small amplitude boundary forcing at the plate surface or volumetric forcing at various wall-normal heights was used to account for receptivity effects. While wall forcing effectively induced modal instabilities, only an actuation above the boundary layer captured disturbances that amplify within the entropy layer. The optimal nonmodal theory’s entropy-layer disturbance evolution exhibited outstanding agreement with controlled forcing, including receptivity effects. The evolution of entropy-layer disturbances from the optimal nonmodal theory showed excellent agreement with the results of receptivity to controlled forcing. Therefore, the nonmodal optimal growth analysis may provide a useful as well as efficient technique to identify the complete disturbance spectrum in blunt hypersonic configurations, where both modal and nonmodal disturbances can amplify in the boundary-layer and entropy-layer regions.

Boundary layer transition↗

NASA NTRS2023

CFD Integrated Transition Modeling for High-Speed Flows via Coupled OVERFLOW-LASTRAC Analysis

This work details ongoing efforts at the NASA Langley Research Center to develop and validate a general-use CFD tool that includes built-in predictions of boundary-layer transition in high-speed flows. Existing tools for the coupling of the NASA OVERFLOW structured overset RANS solver and LASTRAC stability analysis code have been extended to capture boundary-layer transition in high-speed flows driven by either Mack’s first-mode or secondmode instabilities and/or crossflow instabilities. The efficacy of this coupled approach has been demonstrated by examining a variety of supersonic and hypersonic test cases for which experimental validation data is available. The intermittency prescription parameters inherited from prior low-speed applications are found to be suitable for some, but not all high-speed flow scenarios. The method is found to be robust for straight cone configurations and improvements necessary to accurately capture transition on geometries with spatially complex amplification factor envelopes with intermediate regions of slow N-factor variation are examined. The automated, coupled analysis is demonstrated for a 3d supersonic test case and found to perform well within the limits of the linear stability analysis on which it relies. Finally, a preliminary investigation of the method’s robustness to non-ideal CFD meshes is conducted.

High-speed flow↗

NASA NTRS1973

A stability analysis for a semilinear parabolic partial differential equation

The parabolic partial differential equation considered is u sub t = u sub xx + f(u), where minus infinity x plus infinity and o t plus infinity. Under suitable hypotheses pertaining to f, a class of initial data is exhibited: phi(x), minus infinity x plus infinity, for which the corresponding solutions u(x,t) appraoch zero as t approaches the limit of plus infinity. This convergence is uniform with respect to x on any compact subinterval of the real axis.

Chafee, N.↗

NASA NTRS1979

Explicit numerical formulas of improved stability and accuracy for the solution of parabolic equations

A class of explicit numerical formulas which involve next nearest neighbor as well as nearest neighbor points are explored in this paper. These formulas are formal approximations to the linear parabolic partial-differential equation of first order in time and second order in distance. It was found that some of these formulas can employ time steps as much as four times that for the conventional explicit technique without becoming unstable. Others showed improved accuracy for a given time step and spatial grid spacing. One formula achieved a steady-state solution of specified accuracy for an example problem in less than 4 percent of the total computational time required by the conventional explicit technique.

Olstad, W. B.↗

NASA NTRS1993

Summation by parts, projections, and stability

We have derived stability results for high-order finite difference approximations of mixed hyperbolic-parabolic initial-boundary value problems (IBVP). The results are obtained using summation by parts and a new way of representing general linear boundary conditions as an orthogonal projection. By slightly rearranging the analytic equations, we can prove strict stability for hyperbolic-parabolic IBVP. Furthermore, we generalize our technique so as to yield strict stability on curvilinear non-smooth domains in two space dimensions. Finally, we show how to incorporate inhomogeneous boundary data while retaining strict stability. Using the same procedure one can prove strict stability in higher dimensions as well.

Olsson, Pelle↗

NASA NTRS1993

A model of concurrent flow flame spread over a thin solid fuel

A numerical model is developed to examine laminar flame spread and extinction over a thin solid fuel in lowspeed concurrent flows. The model provides a more precise fluid-mechanical description of the flame by incorporating an elliptic treatment of the upstream flame stabilization zone near the fuel burnout point. Parabolic equations are used to treat the downstream flame, which has a higher flow Reynolds number. The parabolic and elliptic regions are coupled smoothly by an appropriate matching of boundary conditions. The solid phase consists of an energy equation with surface radiative loss and a surface pyrolysis relation. Steady spread with constant flame and pyrolysis lengths is found possible for thin fuels and this facilitates the adoption of a moving coordinate system attached to the flame with the flame spread rate being an eigen value. Calculations are performed in purely forced flow in a range of velocities which are lower than those induced in a normal gravity buoyant environment. Both quenching and blowoff extinction are observed. The results show that as flow velocity or oxygen percentage is reduced, the flame spread rate, the pyrolysis length, and the flame length all decrease, as expected. The flame standoff distance from the solid and the reaction zone thickness, however, first increase with decreasing flow velocity, but eventually decrease very near the quenching extinction limit. The short, diffuse flames observed at low flow velocities and oxygen levels are consistent with available experimental data. The maximum flame temperature decreases slowly at first as flow velocity is reduced, then falls more steeply close to the quenching extinction limit. Low velocity quenching occurs as a result of heat loss. At low velocities, surface radiative loss becomes a significant fraction of the total combustion heat release. In addition, the shorter flame length causes an increase in the fraction of conduction downstream compared to conduction to the fuel. These heat losses lead to lower flame temperatures, and ultimately, extinction. This extinction mechanism differs from that of blowoff, where the flame is unable to be stabilized due to the high flow velocity.

Ferkul, Paul V.↗

NASA NTRS1977

Finite element analysis of low speed viscous and inviscid aerodynamic flows

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Baker, A. J.↗

NASA NTRS1978

An interaction solution algorithm for viscous aerodynamic performance prediction

A weak-interaction solution algorithm is established for aerodynamic flow field prediction about an isolated airfoil. It requires numerical solution of differential equations governing potential flow, viscous and turbulent boundary layer flow, and the turbulent wake flow downstream of a trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. These in turn alter the viscous flow through imposed pressure gradients. Closure for turbulence is accomplished using a second order model. Numerical evaluations assess factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems as solved using a finite element algorithm.

Baker, A. J.↗