Location Of Transition Research Articles

Experimental study of the laminar-turbulent transition on models of wings with subsonic and supersonic leading edge at M = 2

The paper is devoted to an experimental study of laminar-turbulent transition in supersonic boundary layers on swept wings at Mach 2. The experiments were fulfilled in the low nose supersonic wind tunnel T-325 of Khristianovich Institute of Theoretical and Applied Mechanics on the models with supersonic or subsonic leading edges. The transition location was determined using a constant temperature hot-wire anemometer. while experiments for the case of a supersonic leading edge are a continuation of previous studies, then for the case of a subsonic leading edge, the first data have been obtained that show the possibility of carrying out studies on the development of unstable perturbations. It was obtained that transition take place parallel to the leading edge for both models. The destabilizing effect of the surface curvature of the model on the position of the laminar-turbulent transition for the case of a supersonic leading edge was confirmed. This experimental data is the room for further investigation.

New models for generating hard random boolean formulas and disjunctive logic programs

We propose two models of random quantified boolean formulas and their natural random disjunctive logic program counterparts. The models extend the standard models of random k-CNF formulas and the Chen-Interian model of random 2QBFs. The first model controls the generation of programs and QSAT formulas by imposing a specific structure on rules and clauses, respectively. The second model is based on a family of QSAT formulas in a non-clausal form. We provide theoretical bounds for the phase transition region in our models, and show experimentally the presence of the easy-hard-easy pattern and its alignment with the location of the phase transition. We show that boolean formulas and logic programs from our models are significantly harder than those obtained from the standard k-CNF and Chen-Interian models, and that their combination yields formulas and programs that are “super-hard” to evaluate. We also provide evidence suggesting that formulas from one of our models are well suited for assessing solvers tuned to real-world instances. Finally, it is noteworthy that, to the best of our knowledge, our models and results on random disjunctive logic programs are the first of their kind.

Estimation and Analysis of Hybrid Laminar Flow Control on a Transonic Experiment

This paper investigates the method for predicting the laminar-to-turbulent transition in the context of hybrid laminar flow control. Transonic wind tunnel experiments are used to support our study. The relation between the discrete hole velocity in wind tunnel tests and the continuous surface velocity used in the simulation is established. With the calibrated relation, the method, consisting of a boundary-layer code and linear stability theory framework, has successfully predicted the transition location at various conditions, within 4% chord error compared with the experimental results. Additionally, the simulation profile drag by the integration of momentum loss method matches the results of the experimental wake rake, and the difference is within 1.85 counts. The simulation results show that the microsized wall suctioning reduces the amplitude of cross-flow velocity and lowers the inflection point in the boundary layer, hence suppressing the cross-flow vortices. Hence, the laminar-to-turbulent transition is pushed aft significantly. Meanwhile, the experimental and simulation results show that the wall blowing degrades the HLFC benefit, and it needs to be avoided in applications. This paper concludes that the method can be applied in the hybrid laminar flow control transition prediction with the given perforated panel properties.

Advanced infrared thermography data analysis for unsteady boundary layer transition detection

Advanced data processing methods for detecting unsteady boundary layer transition in periodic aerodynamic processes by means of infrared thermography measurements are presented. The thermal radiation emitted from the heated suction surface of a pitching airfoil model in subsonic flow is measured with an infrared camera. The unsteady boundary layer transition location is detected by analyzing the difference in the infrared radiation signal over short periods of time with differential infrared thermography (DIT). The DIT method is optimized and automated in the present study, which facilitates the extension of the part of the motion period where valid DIT transition measurements are produced. Additionally, a new infrared thermography data processing method is introduced in this study. The extraction of the extrema of the measured radiation signal at fixed locations on the model surface yields instants of the motion period that relate to the occurrence of boundary layer transition. The local infrared thermography (LIT) approach can be extended to measuring the two-dimensional unsteady boundary layer transition front.

Friction-Induced Vibration in a Bi-Stable Compliant Mechanism

This paper investigates friction-induced self-excited vibration in a bi-stable compliant mechanism. A single-degree-of-freedom oscillator, hanged vertically, vibrates on a belt moving horizontally with a constant velocity. The oscillator is excited through the frictional input provided by the belt. The friction coefficient is defined as an exponentially decaying function of the sliding velocity. Due to the specific configuration of spring and damper, the normal contact force is variable. Therefore, the friction force is a function of the system states, namely, slider velocity and position. Employing eigenvalue analysis gives an overview of the local stability of the linearized system in the vicinity of each equilibrium point. It is shown that the normal force, spring pre-compression and belt velocity are bifurcation parameters. Since the system is highly nonlinear, a local analysis does not provide enough information about the steady-state response. Therefore, the oscillating system is studied numerically to attain a global qualitative picture of the steady-state response. The possibility of the mass-belt detachment and overshoot are studied. It is shown that one equilibrium point is always dominant. In addition, three main questions, i.e., possible mass-belt separation, location of stick-slip transition and overshoot are answered. It is proven that the occurrence of overshoot is impossible.

Probing the many-body localization phase transition with superconducting circuits

Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we study the bosonic many-body localization phase transition using the methods of exact diagonalization as well as matrix product state dynamics. We estimate the location of transition separating the ergodic and the many-body localized phases as a function of the disorder strength and the many-body on-site interaction strength. The main difference between the bosonic model realized by superconducting circuits and similar fermionic model is that the effect of the on-site interaction is stronger due to the possibility of multiple excitations occupying the same site. The phase transition is found to be robust upon including longer-range hopping and interaction terms present in the experiments. Furthermore, we calculate experimentally relevant local observables and show that their temporal fluctuations can be used to distinguish between the dynamics of Anderson insulator, many-body localization, and delocalized phases. While we consider unitary dynamics, neglecting the effects of dissipation, decoherence and measurement back action, the timescales on which the dynamics is unitary are sufficient for observation of characteristic dynamics in the many-body localized phase. Moreover, the experimentally available disorder strength and interactions allow for tuning the many-body localization phase transition, thus making the arrays of superconducting circuit devices a promising platform for exploring localization physics and phase transition.

Study on flow separation and transition of the airfoil in low Reynolds number

As typical flow characteristics in a low Reynolds number, laminar separation bubbles (LSBs) and transition to turbulence over airfoils have been extensively studied in recent years. In order to analyze their flow mechanism, numerical investigation using the finite volume method to solve the Reynolds averaged Navier-Stokes equations with a transition Shear Stress Transport (SST) four-equation transition model is performed in this work, combined with the experimental study facilitated by the oil film interferometry technique. Specifically, the transition SST four-equation transition model is solved to simulate the separation location and LSB structure at low Reynolds numbers on a Wortmann FX63-137 airfoil. Good agreement is obtained between the numerical simulation and experimental measurements regarding the separation, transition and reattachment location, aerodynamic coefficients, and overall flow structures. At higher Reynolds numbers of 200 000 and 300 000, similar bubble structures on the airfoil surface are observed, and the location of the bubble moves toward the leading edge of the airfoil by increasing the angle of attack. However, in Reynolds numbers ranging from 300 000 to 500 000, significant changes of the laminar flow separation structures emerge. The flow structure changes from the classical laminar separation bubble to the nonclassical separation flow structure that is composed of a major vortex 1(V1) and a minor vortex 2(V2). Due to the small distance between V1 and V2, it is difficult to distinguish the delicate structure of the two separation bubbles from the classical laminar separation bubble by the experimental method.

Magnetic nozzle efficiency in a low power inductive plasma source

The nozzle efficiency and performance of a magnetic nozzle operating at low power (<200 W) are experimentally and analytically characterized. A suite of diagnostics including Langmuir probes, emissive probes, Faraday probes, and laser induced fluorescence are employed to map the spatial distribution of the plasma properties in the near-field of a nozzle operated with xenon and peak magnetic field strengths ranging from 100 to 600 G. The nozzle efficiency is found to be <10% with plasma thrust contributions <120 μN and specific impulse <35 s. These performance measurements are compared with predictions from quasi-1D idealized nozzle theory and found to be 50%–70% of the model predictions. It is shown that the reason for this discrepancy stems from the fact that the underlying assumption of the idealized model—that ions are sonic at the throat of the nozzle—is violated at low power operation. By correcting for the shifting location of the sonic transition point, the model and experiment are made to agree. The physical mechanism by which the sonic line moves with respect to the nozzle geometry is attributed to non-ideal behavior at low power. In particular, it is posited that the low ionization fraction at these low operational powers gives rise to neutral-collisional effects in the near-field of the device that can impede ion acceleration. The roles of ionization, enhanced electron resistivity, and charge exchange collisions are all examined. It is found that the ion sonic transition location is most correlated with the ratio of the charge exchange mean free path to the characteristic electrostatic acceleration length giving rise to an effective drag term on the ions.

Allowance for Gas Compressibility in the γ-Model of the Laminar–Turbulent Transition

The formulation and applicability range of the $$\gamma $$ -model of laminar–turbulent transition are analyzed. Its implementation in the EWT-TsAGI application package and verification results for the problem of computing a transitional boundary layer on a plate are described. The cases of zero and adverse pressure gradients are considered. A modification of the $$\gamma $$ -model that takes into account the effect of compressibility on the laminar–turbulent transition location is proposed. Two problems are considered to calibrate and test the correction term: the flow over the LV6 laminar-flow airfoil and the flow over the nacelle of a bypass turbojet engine. It is shown that, with the used of the proposed correction, the laminar–turbulent transition location can be correctly predicted in transonic flow regimes.

Parallel Large-Eddy Simulation of Subsonic and Transonic Flows with Transition in Compressor Cascade

Laminar–turbulent transition plays a critical role in the aerodynamic performance of compressors and is sensitive to flow conditions and external disturbances. In the present work, a parallel large-eddy-simulation solver is developed and applied to investigate the effects of free-stream turbulence on the mode and location of transition on the blade suction surface of a compressor cascade under subsonic and transonic conditions. Both the parallel accuracy and efficiency of the solver are demonstrated. The transition location is observed to shift upstream as the free-stream turbulence level increases at both the subsonic and transonic conditions. Moreover, increasing the free-stream turbulence level from 0 to 4% causes the transition mode to change from Kelvin–Helmholtz instability-induced transition to bypass transition in the case of subsonic flow, whereas transition occurs in a Kelvin–Helmholtz instability-induced mode even at a high free-stream turbulence level of up to 7% in the case of transonic flow. The work demonstrates the ability of the parallel large-eddy-simulation method to capture the transitional-flow structures in compressor cascades and its potential application to the analysis and design of advanced compressor.

Lattice theory for binding of linear polymers to a solid substrate from polymer melts: I. Influence of chain connectivity on molecular binding and adsorption.

Most theories of the binding of molecules to surfaces or for the association between molecules treat the binding species as structureless entities and neglect their rigidity and the changes in their stiffness induced by the binding process. The binding species are also taken to be "ideal," meaning that the existence of van der Waals interactions and changes in these interactions upon molecular binding are also neglected. An understanding of the thermodynamics of these multifunctional molecular binding processes has recently come into focus in the context of the molecular binding of complex molecules, such as dendrimers and DNA grafted nanoparticles, to surfaces where the degree of binding cooperativity and selectivity, as well as the location of the binding transition, are found to be sensitive to the number of binding units constrained to a larger scale polymeric scaffold. We address the fundamental problem of molecular binding by extending classical Langmuir theory to describe the particular example of the reversible binding of semiflexible polymer chains to a solid substrate under melt conditions. The polymer chains are assumed to have a variable number N of binding units (segments) and to exhibit variable bending energies and van der Waals interactions in the bulk and on the surface, in addition to strong directional interactions with the surface. The resulting generalized Langmuir theory is applied to the examination of the influence of the chain connectivity of ideal polymers on the surface coverage Θ, transition binding temperature T1/2 at which Θ = 1/2, and on the derivative |dΘ/dT|T=T1/2 and the constant volume specific heat of binding, Cv bind, measures of the cooperativity and "sharpness" of the binding transition, respectively. Paper II is devoted to the impact of the van der Waals attractive interactions and chain stiffness on the reversible binding of nonideal polymer chains to a solid surface, including the enthalpy-entropy compensation phenomenon observed experimentally in many molecular and particle binding processes.

Statistical analysis of the Chern number in the interacting Haldane-Hubbard model

In the context of many-body interacting systems described by a topological Hamiltonian, we investigate the robustness of the Chern number with respect to different sources of error in the self-energy. In particular, we analyze the importance of non-local (momentum dependent) vs. local contributions to the self-energy and show that the local self-energy provides a qualitative description of the topological phase diagrams of many-body interacting systems, whereas the explicit momentum-dependence constitutes a correction to the exact location of the phase transition. For the latter, we propose a statistical analysis, on the basis of which we develop a stochastic upper bound for the uncertainty of the Chern number as a function of the amount of momentum-dependence of the self-energy. We apply this analysis to the Haldane-Hubbard model and discuss the implications of our results for a general class of many-body interacting systems.

Determination of the laminar-turbulent transition location in numerical simulations of subsonic and transonic flows past a flat plate

The study is aimed at determining the position of the laminar-turbulent transition in subsonic and transonic two-dimensional boundary layers with the use of a novel software package LOTRAN 2.0 developed by the authors. The package is based on the eN-method and employs numerical data of numerical simulations of the laminar flow performed by standard gas-dynamic software systems based on the Reynolds-averaged Navier-Stokes equations. As an example, the flow past a flat plate is considered. The good agreement of the computed and experimental data on the laminar-turbulent transition location is demonstrated. New data on the laminar-turbulent transition in the boundary layer on a flat plate for transonic flow regimes are obtained.

Nonmodal Growth of Traveling Waves on Blunt Cones at Hypersonic Speeds

The existing database of transition measurements in hypersonic ground facilities has established that, as the nose-tip bluntness is increased, the onset of boundary-layer transition over a circular cone at zero angle of attack shifts downstream. However, this downstream movement in transition slows down and eventually reverses at sufficiently large values of the nose Reynolds number. Because modal amplification is too weak to initiate the measured frustum transition at moderate to large bluntness values, nonmodal growth is investigated as the potential basis for a physics-based model. The present analysis investigates the nonmodal growth of traveling disturbances initiated within the nose-tip vicinity. Results show that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for successively higher disturbance frequencies as the nose bluntness is increased. For relatively small bluntness values, the initial nonmodal growth is followed by a partial decay that is 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 waves still undergo a significant amount of nonmodal growth. These findings do not provide a definitive link between optimal growth and the onset of frustum transition on moderately blunt cones, but they are qualitatively consistent with the experimental observations of an initial peak near the nose tip followed by a decay and growth in disturbance energy, as well as the appearance of inclined structures above the boundary-layer edge.

First-mode-induced nonlinear breakdown in a hypersonic boundary layer

The mechanisms underlying transition of a Mach 6 flat plate boundary layer with adiabatic wall conditions are explored with Direct Numerical Simulations (DNS) using a high-order hybrid upwind-centered method. The forcing employed is obtained from linear stability theory (LST), which is used to identify Tollmien–Schlichting (T-S) or first-mode instability in the hypersonic boundary layer (HBL). At small amplitudes, the DNS displays linear growth, and matches those obtained from LST, including the spanwise structure of the most amplified oblique wave in the first-mode as well as the spreading angle of the turbulent wedge induced by the oblique wave under transitional scenarios. The main emphasis of the paper is on the nonlinear breakdown process, obtained by forcing the DNS at a higher amplitude so that the linear amplification region yields to nonlinear saturation and breakdown of the first-mode. The oblique waves are seen to first evolve into lambda-vortices with peak perturbation amplitudes around the generalized inflection point (GIP) of the HBL. The fundamental forcing frequency gives rise to progressive superharmonics: These first appear within the foot region of the lambda-vortices, and spread in the spanwise direction into the ring-shaped vortices that develop along the symmetry plane of the oblique waves. Transition and loss of symmetry is initiated upon saturation of the fundamental and harmonics. A modal analysis used to extract each frequency component yields further insight into streak-formation in these modes, resulting in localized regions of peak skin friction near the transition location. The near-wall boundary layer in the transitional zone displays coherent spanwise structures, which represent compressed regions of fluid and induce high gradients over the surface. Towards the end of the breakdown region, the flow displays a broadband spectrum, and the anticipated inertial sub-range appears inside the boundary layer, as a prelude to self-similar turbulent boundary layer evolution.

Laminar‐turbulent transition detection on airfoils by high‐frequency microphone measurements

AbstractIn the present work, various data processing methods for laminar to turbulent transition detection on airfoils are assessed based on experimental data. For this purpose, NACA 63‐418 airfoil profile with surface microphones flush mounted both on the suction and the pressure side is used in the wind tunnel experiments. Reynolds numbers are changed in the range from 1.6·106 to 6·106 for various angles of attack. In this way, the transition behaviour of the airfoil is characterized. Time signals and spectrogram of the data, chordwise pressure level changes, and first moments are investigated. Standard deviations of pressure are observed to exhibit a peak at transition and slightly decreases for the fully turbulent flow staying always higher than the laminar flow. The most robust method to detect the transition location is found to be the characteristic frequency approach by spectral moments provided that the inflow turbulence is low. The numerical results are in agreement with experimental results on the pressure side where natural transition occurs. However, the transition due to surface irregularity and microphone placement occurs on the suction side. This cannot be predicted by the numerical tools. The Tollmien‐Schlichting wave frequencies and neutral curve points are determined from the experiments. The analysis shows that the most common curve length of the transition process is around 15% to 20%, and it can vary between 0% to 30 % of the chord. Increasing the Reynolds number leads to an earlier transition position closer to leading edge at both upper and lower surfaces.

Bipartitioning of directed and mixed random graphs

We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the relative size of the giant OUT component reaching 1/2. Moreover, when counting undirected links as two directed ones, the partition cost, and cluster properties, as well as location of the replica symmetry breaking transition for these random graphs depend primarily on the total number of directed links and not on their specific distribution.

Nonlinearly most dangerous disturbance for high-speed boundary-layer transition

Laminar-to-turbulent transition in a zero-pressure-gradient boundary layer at Mach 4.5 is studied using direct numerical simulations. For a given level of total disturbance energy, the inflow spectrum was designed to correspond to the nonlinearly most dangerous condition that leads to the earliest possible transition Reynolds number. The synthesis of the inlet disturbance is formulated as a constrained optimization, where the control vector is comprised of the amplitudes and relative phases of the inlet modes; the constraints are the prescribed total energy and that the flow evolution satisfies the full nonlinear compressible Navier–Stokes equations; the cost function is defined in terms of the mean skin-friction coefficient and, once maximized, ensures the earliest possible transition location. An ensemble-variational (EnVar) technique is developed to solve the optimization problem. Starting from an initial guess, here a broadband disturbance, EnVar updates the estimate of the control vector at the end of each iteration using the gradient of the cost function, which is evaluated from the outcomes of an ensemble of possible solutions. Two inflow conditions are computed, each corresponding to a different level of energy, and their spectra are contrasted: the lower-energy case includes two normal acoustic waves and one oblique vorticity perturbation, whereas the higher-energy condition consists of oblique acoustic and vorticity waves. The focus is placed on the former case because it cannot be categorized as any of the classical breakdown scenarios (fundamental, subharmonic or oblique), while the higher-energy condition undergoes a second-mode oblique transition. At the lower energy level, the instability wave that initiates the rapid breakdown to turbulence is not present at the inlet plane. Instead, it appears at a downstream location after a series of nonlinear interactions that spur the fastest onset of turbulence. The results from the nonlinearly most potent inflow condition are also compared to other inlet disturbances that are selected solely based on linear theory, and which all yield relatively delayed transition onset.

Prediction of Separation-Induced Transition on the SD7003 Airfoil Using Algebraic Transition Triggering

The paper investigates the performance of a recently developed laminar separation transition triggering approach (criteria-based) that controls the transitional turbulence source terms. Computational results are compared with available experimental and large-eddy simulation data for low-Reynolds-number quasi-incompressible flow over the SD7003 airfoil. The influence of the angle of attack, the chord-based Reynolds number, and the turbulence intensity at transition onset is satisfactory, provided that the correct transition location is returned by the correlations. The results highlight the importance of correctly modeling the rapid growth of turbulence kinetic energy immediately downstream of transition onset.

Investigation of stationary-crossflow-instability induced transition with the temperature-sensitive paint method

The Temperature-Sensitive Paint (TSP) method is used for surface-based flow visualizations on a swept-wing wind-tunnel model with a generic natural laminar-flow airfoil. Within the investigated parameter range the stationary crossflow instability is the dominating instability mechanism. Based on the TSP results the location of the laminar-turbulent transition and the most amplified wavenumber of the stationary crossflow instability are determined. The test is performed with three different conditions of the leading-edge surface: highly polished, unpolished, and highly polished with discrete roughness elements applied. The Temperature-Sensitive Paint method has proven to have sufficient spatial resolution and temperature sensitivity to resolve skin friction variations to detect the footprint of stationary crossflow vortices even inside of turbulent wedges. With the discrete roughness elements, i.e. cylindrical elements with micron-sized height, the transition could be delayed successfully for certain conditions. Local low-frequency movement of the beginning of turbulent wedges was detected for some data points with an unpolished leading edge.