Laminar-turbulent Transition Process Research Articles

Numerical Simulation of the Interaction between Weak Shock Waves and Supersonic Boundary Layer on a Flat Plate with the Blunt Leading Edge

The interaction of weak shock waves in form of an N-wave with the supersonic laminar boundary layer on a flat plate with blunt leading edge at the free-stream Mach number M = 2.5 is numerically studied. The numerical results are compared with known experimental data. The combined influence of the N-wave and the leading edge bluntness on the laminar-turbulent transition process is discussed.

Constrained large-eddy simulation of laminar-turbulent transition in compressible channel flows

An improved approach for constrained large-eddy simulations (CLES) of wall-bounded compressible transitional flows is proposed by introducing an intermittency factor. The improved model is tested and validated with compressible channel flows at various Mach numbers and Reynolds numbers that are transitioning from laminar to turbulent states. The improved model is compared against traditional dynamic Smagorinsky model (DSM) and Direct Numerical Simulations (DNS), where the improved model is in better agreement with DNS results than traditional DSM model, in terms of mean velocity profiles, total Reynolds stress and total heat flux. Therefore, the proposed method can be used to accurately predict the temporal laminar-turbulent transition process of compressible wall-bounded flows.

Extension of the KDO turbulence/transition model to account for roughness

Wall roughness significantly influences both laminar-turbulent transition process and fully developed turbulence. A wall roughness extension for the KDO turbulence/transition model is developed. The roughness effect is introduced via the modification of the k and νt boundary conditions. The wall is considered to be lifted to a higher position. The difference between the original position and the higher position, named as equivalent roughness height, is linked to the actual roughness height. The ratio between the two heights is determined by reasoning. With such a roughness extension, the predictions of the KDO RANS model agree well with the measurements of turbulent boundary layer with a sand grain surface, while the KDO transition model yields accurate cross-flow transition predictions of flow past a 6:1 spheroid.

Laminar-Turbulent Transition Process in Later Stage of an Inlet Region in a Circular Pipe by the Jet Disturbance

Laminar-Turbulent Transition Process in Later Stage of an Inlet Region in a Circular Pipe by the Jet Disturbance

Permutation Entropy Analysis of Relaminarizing Turbulent Boundary Layer

An information analysis using permutation entropy of was applied to a relaminarizing sink flow turbulent boundary layer. The turbulent boundary layer was relaminarized by an acceleration because of the contraction of the flow area. It has been shown by the present authors that laminar-turbulent transition processes in the free-shear flow, the permutation entropy was effective for a measure of the transition progress. Velocity fluctuations were measured by a hot-wire anemometer. From the time series of the fluctuations, the permutation pattern of the data increase or decrease was discriminated, then the entropy based on the probability of the pattern was obtained. The permutation entropy did not decrease with the progress of the relaminarization. Therefore, it is hard to be an appropriate measure of the progress. It increased at the outer edge of the boundary layer. The two factors contributed it. One was an increase of number of permutation patterns, the other was an equalization of the permutation pattern probabilities. Both factors were affected by the intermittent fluctuations there. When the number of extracted data matched the Kolmogorov timescale, the permutation entropy took a large constant value near the wall in the boundary layer because of extremely large number of the extracted data.

Numerical Investigation of Nonlinear Boundary-Layer Transition for Cones at Mach 6

Direct numerical simulations were carried out for a straight and a flared cone at Mach 6 and zero angle of attack to investigate the effects of geometry on the linear and nonlinear stages of the laminar–turbulent transition process. The cone geometries and the flow conditions of the simulations are chosen to closely match those of the experiments conducted at the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. In the linear (primary) instability regime the flared cone resulted in larger integrated growth rates ( factors) and a higher dominant second mode frequency. Investigations of the secondary instability regime revealed that the flared cone also leads to a stronger fundamental resonance, characterized by larger integrated growth rates of the secondary instability waves after resonance onset. For both cases, the so-called controlled fundamental breakdown simulations were carried out, which showed the development of similar patterns of streamwise hot streaks on the surface of the cones. Streamwise streaks were also observed in the Purdue experiments (for the flared cone only) using temperature-sensitive paint. A detailed comparison of the results obtained for both geometries indicated that the streak development is caused by the same nonlinear mechanisms.

A dual-eddy EMMS-based turbulence model for laminar–turbulent transition prediction

Turbulence is a century-old physics problem, and the prediction of laminar–turbulent transition remains a major challenge in computational fluid dynamics (CFD). This paper proposes a new conceptual multiscale-structure flow system consisting of a nonturbulent part and two types of turbulent eddies with different properties. The stability criterion for turbulent transition flows, based on the principle of compromise-in-competition between viscosity and inertia, is used to obtain model closure. The multiscale-structure concept and stability criterion are the characteristics of the dual-eddy energy-minimization multiscale (EMMS)-based turbulence model. The solved heterogeneous structure parameters and energy dissipation rate are analyzed, which reveal the laminar–turbulent transition process. To validate the dual-eddy EMMS-based turbulence model, three benchmark problems, namely, the transitional flows over the flat plate boundary layer with zero pressure gradient, NACA0012, and Aerospatiale-A airfoils, were simulated. The simulation was performed by combining the optimized results from the proposed model with the equations of the well-known k−ω shear stress transfer (SST) turbulence model. The numerical results show that the dual-eddy EMMS-based turbulence model improves the prediction in the laminar–turbulent transition process. This demonstrates the soundness of using the multiscale-structure concept in turbulent flows to establish the turbulence transition model by considering the principle of compromise-in-competition between viscosity and inertia.

A high-throughput hybrid task and data parallel Poisson solver for large-scale simulations of incompressible turbulent flows on distributed GPUs

The solution of the pressure Poisson equation arising in the numerical solution of incompressible Navier–Stokes equations (INSE) is by far the most expensive part of the computational procedure, and often the major restricting factor for parallel implementations. Improvements in iterative linear solvers, e.g. deploying Krylov-based techniques and multigrid preconditioners, have been successfully applied for solving the INSE on CPU-based parallel computers. These numerical schemes, however, do not necessarily perform well on GPUs, mainly due to differences in the hardware architecture. Our previous work using many P100 GPUs of a flagship supercomputer showed that porting a highly optimized MPI-parallel CPU-based INSE solver to GPUs, accelerates significantly the underlying numerical algorithms, while the overall acceleration remains limited (Zolfaghari et al. [3]). The performance loss was mainly due to the Poisson solver, particularly the V-cycle geometric multigrid preconditioner. We also observed that the pure compute time for the GPU kernels remained nearly constant as grid size was increased. Motivated by these observations, we present herein an algebraically simpler, yet more advanced parallel implementation for the solution of the Poisson problem on large numbers of distributed GPUs. Data parallelism is achieved by using the classical Jacobi method with successive over-relaxation and an optimized iterative driver routine. Task parallelism is enhanced via minimizing GPU-GPU data exchanges as iterations proceed to reduce the communication overhead. The hybrid parallelism results in nearly 300 times less time-to-solution and thus computational cost (measured in node-hours) for the Poisson problem, compared to our best-case scenario CPU-based parallel implementation which uses a preconditioned BiCGstab method. The Poisson solver is then embedded in a flow solver with explicit third-order Runge-Kutta scheme for time-integration, which has been previously ported to GPUs. The flow solver is validated and computationally benchmarked for the transition and decay of the Taylor-Green Vortex at Re=1600 and the flow around a solid sphere at ReD=3700. Good strong scaling is demonstrated for both benchmarks. Further, nearly 70% lower electrical energy consumption than the CPU implementation is reported for Taylor-Green vortex case. We finally deploy the solver for DNS of systolic flow in a bileaflet mechanical heart valve, and present new insight into the complex laminar-turbulent transition process in this prosthesis.

Numerical Method for Particulate-Induced High-Speed Boundary-Layer Transition Simulations

A new numerical method to efficiently simulate particulate interactions with high-speed transitional boundary-layer flows is presented. A particulate solver, employing Crowe’s correlation, is used to calculate the particulate trajectory. The solver is fully coupled via a particulate–flow interaction source term to a nonlinear disturbance flow solver based on the compressible Navier–Stokes equations. To efficiently simulate the particulate–flow interactions, an adaptive mesh refinement approach is used to capture the wide range of temporal and spatial scales present in the laminar–turbulent transition process. The particulate impingement simulations for a flow over a 14 deg wedge and two different particulate impingement locations employing the newly developed numerical approach are compared against simulations using a conventional static-mesh approach. For the flow conditions considered, oblique first-mode instability waves dominate the early stage of the transition process. In the second part of this paper, the differences between pulse and particulate impingement simulations are investigated in two and three dimensions for a flat-plate boundary-layer flow where two-dimensional second-mode instability waves are most amplified in the primary instability regime.

Laminar-Turbulent Transition Process in a Circular Pipe in an Inlet Region by the Jet Disturbance

Laminar-Turbulent Transition Process in a Circular Pipe in an Inlet Region by the Jet Disturbance

Numerical investigation into the cavitating jet inside water poppet valves with varied valve seat structures

Owing to the strong three-dimensionality and transient evolution, the flow dynamics of a cavitating jet inside a water poppet valve is poorly understood, leading to insufficient basis for exploring the governing mechanism of cavitation effects. In this paper, a three-dimensional simulation considering the compressibility of each constituent phase is performed, to clarify the governing mechanisms under the cavitating flow inside two water poppet valves. The cavitation structures inside the poppet valves are primarily located at three regions and triggered by different mechanisms. The vortex cavitation, mainly confined within the free shearing layer, is due to vortex dynamics, while the attached cavitation at the poppet trailing edge and within the chamfered groove arises from flow separation. The fast laminar–turbulent transition process contributes to the three-dimensionality within the free shearing layer and the rear part of the chamfered groove. The flow separation due to the chamfered groove leads to increased velocity of the central potential core, contributing to a different flow discharge performance from that of the poppet valves with a sharp seat. In addition, the periodic variation in cavitation reveals the significant interaction between the shed cavitating vortex and attached cavitation at the poppet trailing edge. In conclusion, the change in velocity distribution due to different poppet valve seat structures leads to variation in flow discharge performance, and the vortex dynamics makes sense for all three kinds of cavitation occurring inside poppet valves.

On the classification of the laminar-turbulent transition process using the methods of nonlinear dynamics: general analysis and the future

The definition of a turbulent flow is still not mathematically defined. Different methods exists that provide different definitions resulting in different approaches and classifications of the laminar-turbulent transition as well as the fully developed turbulent flows. The paper includes the analysis of different stages of turbulence development, specific methods that are used in each stage and possible methods of unification of these methods based on the nonlinear-dynamical approach. Results are demonstrated for some characteristic fluid dynamics problems. Future highlights on the path to possible unification are discussed.

Effects of streamwise wall curvature variation on the nonlinear evolution of different Görtler vortices wavelengths

In this paper, a high-order, pseudo-spectral numerical code (HOPe) is used to investigate the influence of curvature variations on the nonlinear evolution of different Gortler vortices wavelengths. The mechanism by which Gortler instability selects the wavelength of the vortex when considering boundary layer over variable curvature surface is not clearly understood. In order to investigate the influence of the wall curvature and the effects of the spanwise wavelength on the laminar–turbulent transition process, three spanwise wavelengths and four different streamwise wall curvature distributions were analyzed: constant, concave–convex, concave-flat, and periodic curvature wall. The results show concave–convex wall distribution is the most stable case. With the change from concave to convex curvature, the centrifugal effects were turned off and this tends to eliminate the inflection points from the spanwise and normal profiles of the streamwise velocity. Thus, there is evidence that the convex curvature can be useful for laminar flow control. Furthermore, the numerical results indicate that the spanwise wavelength of stationary disturbance has a significant effect on the instability phenomenon, where the largest spanwise wavelength is the most unstable case when the curvature distribution is changed.

Effects of Reynolds number and loading distribution on the aerodynamic performance of a high subsonic compressor airfoil

The laminar-turbulent transition process on the compressor blade surface is often induced by the laminar separation flow at low Reynolds number ( Re). In the present study, numerical simulations were conducted to investigate the structure of the laminar separation bubble and its effects on the profile loss of a high subsonic compressor airfoil under different Re conditions, and the mechanism for the performance deterioration of compressor airfoil at low Re was clarified. Besides, the airfoil was redesigned to obtain a series of airfoils with different loading distributions, and the aerodynamic performance of these airfoils was compared and analyzed in detail. According to the simulation results, the laminar separation bubble mainly determined the loss generation process of a compressor airfoil. When Re decreased from 12 × 105 to 1.5 × 105, the laminar separation bubble on the suction surface grew thicker and the length was increased by 11.2% of the axial chord. As such, the reversed flow inside the laminar separation bubble became more obvious and the turbulence level downstream of the maximum thickness of laminar separation bubble was increased. Also, the growth in the turbulent boundary layer was enhanced, causing more serious flow blockage and wake mixing. According to the Denton's profile loss model, the larger trailing edge loss caused by the stronger displacement effect of laminar separation bubble was supposed to be the main reason for the performance deterioration of compressor airfoil under low Re conditions. The ultra-front loading distribution for airfoil has the possibility to suppress or even eliminate the negative effect of laminar separation bubble, and the profile loss was decreased by 26.7% at Re = 1.5 × 105; however, the less significant performance improvement was observed at some higher Re. Moreover, the ultra-front loaded airfoil was less sensitive to the inlet turbulence level and the superiority still holds even at some supercritical conditions.

Various information and complexity measures for analyzing the laminar-turbulent transition process in mixing layer (Analysis of fluctuating vorticity and turbulent energy dissipation rate)

In this paper, the laminar-turbulent transition process of a mixing layer downstream of a two-dimensional nozzle exit was analyzed based on various information and complexity measures. Shannon entropy, permutation entropy, and approximated Kolmogorov complexity were also obtained. To obtain the Shannon entropy, the temporal probability distribution of the hot-wire output voltage data was determined and analyzed. In addition to the fluctuating velocity, its time derivative and the square of this derivative were analyzed. The Shannon entropy of the time derivative and its square slightly decreased downstream, in accordance with the increase in the time scale of the turbulence. When the length of the extracted data was constant, the permutation entropy of the time derivative and its square increased around the peripheral region of the mixing layer, in accordance with the intermittent nature of the velocity signals. The region is at the 3-4 times farther from the jet centerline than the region where the fluctuating velocity becomes maximum. When the length of the extracted data was varied in accordance with the integral time scale of turbulence, the permutation entropy initially decreased in the potential core and subsequently increased after the disappearance of the potential core, as the transition progressed. The approximated Kolmogorov complexity of the time derivative and its square were smaller than that of the fluctuating velocity. Owing to the simplification of the data, they slowly increased after the disappearance of the potential core and then quickly decreased after the development of turbulence.

Control of Laminar-Turbulent Transition Process of Plate Boundary Layer by DBD plasma actuator

Control of Laminar-Turbulent Transition Process of Plate Boundary Layer by DBD plasma actuator

Spanwise resolution requirements for the simulation of high-Reynolds-number flows past a square cylinder

In the past, the coarse spanwise resolution was widely used for high-Reynolds-number flow simulations of a two-dimensional bluff body with the purpose of reducing the computational resources. The effects and requirements of spanwise resolution (dz/D, where D is the width of the cylinder) remain unclear for direct numerical simulation (DNS) or large-eddy simulation (LES). This numerical study, without any explicit subgrid-scale model, focuses on the typical flow around a square cylinder at the Reynolds number of 22,000. dz/D varies between 0.08 and 0.013. The requirement is recommended based on the systematical examination of aerodynamic pressure forces, vortex shedding in the wake, and flow structures in the separating shear layers. dz/D ≈ 0.04 is suggested sufficient for the prediction of mean and r.m.s aerodynamic pressures acting on the cylinder, mean and r.m.s velocity fields and small-scale turbulent motions in the wake. The coarser dz/D causes longer vortex formation length behind the cylinder and smaller fluctuating velocities around the cylinder (except the spanwise component). However, a stricter dz/D ≤ 0.02 is suggested necessary for accurately predicting the shear layer behaviors. Only if this requirement is satisfied, the subharmonic and harmonic of the Kelvin-Helmholtz instability can be captured, together with the process of laminar-turbulent transition in the shear layer. The shear layer when dz/D ≤ 0.02 is composed of interconnected small-scale spanwise and streamwise vortices. The shear layer has greater integrity along the spanwise direction and flaps as a whole at the same pace with vortex shedding. However, the shear-layer spanwise vortices are discrete when dz/D>0.02 as the streamwise vortices are not sufficiently reproduced.

Three-dimensional Тurbulent Supersonic Flow over a Plate

The process of laminar-turbulent transition in a boundary layer is studied in terms of vortex evolution, from the growth of weak external disturbances to the formation of intense waves resulting in the development of a turbulent flow having internal scales of the problem. The self-sustained turbulence is obtained and the flow patterns on the plate surface and inside the turbulent boundary layer with fluid plumes propagating from the plate surface in the form of “bursting” are investigated. The basic flow parameters are calculated, such as the frequency and intensity of gas velocity fluctuations in turbulent spots. The validity of a local turbulence similarity law is confirmed. The study is performed on the basis of direct numerical simulation of a flow over a plate with Mach number M = 2 using unsteady Navier-Stokes equations without any closure model of turbulence.

Experimental and theoretical study of swept-wing boundary-layer instabilities. Unsteady crossflow instability

Extensive combined experimental and theoretical investigations of the linear evolution of unsteady (in general) Cross-Flow (CF) and three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. CF-instability characteristics are investigated in detail at an angle of attack of −5° when this kind of instability dominates in the laminar-turbulent transition process, while the 3D TS-instability characteristics are studied at an angle of attack of +1.5° when this kind of instability is predominant in the transition process. All experimental results are deeply processed and compared with results of calculations based on several theoretical approaches. For the first time, very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved both for unsteady CF- and 3D TS-instability modes for the case of a boundary layer developing on a real swept airfoil. The first part of the present study (this paper) is devoted to the description of the case of CF-dominated transition, while the TS-dominated case will be described in detail in a subsequent second part of this investigation.

Nonlinear Theories for Shear Flow Instabilities: Physical Insights and Practical Implications

This article reviews the nonlinear stability theories that have been developed to explain laminar–turbulent transition processes in boundary and free shear layers. For such spatially developing shear flows, a high–Reynolds number approach is necessary to account for, in a systematic and self-consistent manner, multiple competing physical factors, such as nonlinearity, nonparallelism, nonequilibrium, and viscosity. While the basic ideas and fundamental mechanisms are rooted in the classical weakly nonlinear theory, which was formulated primarily for exactly parallel flows and on the basis of finite Reynolds number, the high–Reynolds number formulations lead to low-dimensional evolution systems, which differ significantly from the finite–Reynolds number counterparts and better describe the observations. Owing to efforts in the past 30 years or so, nonlinear evolution systems have been derived for inviscid Rayleigh modes, viscous Tollmien–Schlichting waves, (first and second) Mack modes, and cross-flow vortices. Theories have also been developed for nonlinear intermodal interactions, including oblique mode interaction, subharmonic resonance, phase-locked interactions, and fundamental resonance; these underpin many intriguing behaviors in the three-dimensional stages of transition. These theories and results explain several key nonlinear features observed and should play a useful role in guiding future experimental and numerical investigations.