Transitional Boundary Layer Flows Research Articles

Skin-friction measurements using oil-film interferometry in hypersonic transitional boundary layer flows

Skin-friction measurements in hypersonic transitional boundary layer (HTBL) flows on a flared cone at Mach 6 at zero angle of attack are obtained using oil-film interferometry (OFI). In addition, the amplitude evolution of instability waves is investigated using fast-response pressure sensors and Rayleigh-scattering flow visualization (RSFV). The connection between the skin-friction coefficient and near-wall dynamics during the whole transition process is illustrative and the underlying mechanism of the generation of the wall skin friction is revealed. There exist two peaks of skin-friction rise along the streamwise direction of the model. The first one is at the transitional region (denoted as FS) which is caused by the second-mode instability. The second one is at the region where the transition is completed (denoted as FT). The drastic growth of skin friction near the end of transition is mainly attributed to the rapid boundary-layer breakdown into small scales. It is found that the strong shear in the near-wall region in the quiet zone where dominant hairpin-shaped vortices evolved from the second modes can also cause a local skin-friction rise (denoted as FQ). Further investigations show that in the region between FS and FQ, there is a slight increase in the skin friction, which is associated with the growing low-frequency waves. The skin friction coefficient value decreases slowly after FT but does not reach the expected turbulent theoretical value by the end of the test domain, indicating that the development towards the completely turbulent boundary layer appears to be a gradual process.

Vortex dynamics and boundary layer transition in flow around a rectangular cylinder with different aspect ratios at medium Reynolds number

The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios ( $L/D=5$ , $10$ , $15$ ) at a Reynolds number of $1000$ . The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at $L/D=5$ , three KH vortices merge into a single LE vortex. However, at $L/D=10$ and $15$ , two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at $L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for $L/D=10$ and $15$ , but not for $L/D=5$ . The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.

Natural laminar flow airfoil design via adjoint-based transition onset delay

This work is focused on the aerodynamic shape optimization (ASO) of airfoils with the aim of attaining natural laminar flow (NLF) designs. The two-equation Amplification Factor Transport (AFT) model is utilized for an accurate prediction of the transitional boundary layer flows. The NLF designs are achieved by utilizing two different objective functions. In the first approach, the conventional drag minimization problem is solved with a target lift coefficient. In addition, a second approach is proposed in this work that directly aims at delaying the transition onset on both the pressure and suction sides, thus expanding the natural laminar flow region around the airfoil. It is shown that by utilizing a sigmoid fitting of the turbulence index profile, the transition onset locations can be accurately predicted in a differentiable and smooth fashion, which is essential to the adjoint-based sensitivity analysis of the RANS solver. The efficacy of the proposed technique for NLF design has been tested for NACA 0012 and RAE 2822 airfoils at moderate lift coefficients. Results have shown that a significantly lower drag count can be achieved by delaying the transition onset locations compared to the case where only a drag minimization is sought. Additionally, the transition onset locations on both sides of the airfoil are delayed using our proposed technique which results in a significant expansion of the natural laminar flow region.

Characterization of the transitional boundary layer flow on a marine propeller blade through Under-resolved Direct Numerical Simulation

In this paper, the full boundary layer flow on a C-series marine propeller is investigated through Under-resolved Direct Numerical Simulation (U-DNS). The simulated Reynolds number of 600,000 corresponds to experimental conditions for which a lab-scale propeller was designed and tested at MARIN’s towing tank in the late 1970s. The operating conditions of the simulations are set by matching the experimental advance ratio of 0.73. The simulation uses the high-order spectral element code Nek5000 to solve the boundary layer flow accurately. A specific computational domain is set to simulate the flow in the near-wall region of one of the propeller blades. The results are validated using experimental data on the propeller’s performances and the boundary layer regimes obtained from previous paint test measurements. The detailed boundary layer flow analysis provides new insights into understanding the transition mechanisms on both sides of the blade. Results suggest that centrifugal instabilities occur at the blade’s surface, inducing laminar-to-turbulent transition. A new flow map of the boundary layer regime is then discussed. The laminar cross-flow vortice inception and breakdown are studied in detail to characterize the transition dynamics.

The spatial stability and transition of boundary layer flow over the skin made of micro floating raft arrays

The spatial stability and transition of boundary layer flow over the skin made of micro floating raft arrays

Aerofoil Design and Boundary Layer Transition Flow Studies at Subsonic Speeds for a Typical Transport Aircraft

Reliable computational aerodynamic prediction of airfoil drag, maximum lift and the effect of Reynolds number continue to be a challenge to aerodynamicists, using large computer programs and memory resources even today. Design of an aerofoil for an efficient wing is presented here for the typical transport aircraft which is being developed. Flow around five digit NACA23015 aerofoil was investigated at three distinct Reynolds numbers viz, 2 x 106, 10 x 106 and 20 x 106 typical to small and medium size transport aircrafts for various angle of incidences up to stall. This paper provides insights into the geometry shape design of an aerofoil taking into consideration the effect of Reynolds number on overall efficiency i.e. the lift to drag ratio of an aerofoil. Further the paper provides some aspects of prediction and comparison of the movement of transition point for free transition flow at specific Reynolds numbers. Extensive use is made here of the open source XFOIL. With its analysis and excellent interactive inverse design capabilities for low speed single element aerofoil, the design of the aerofoil has been studied with respect to lifting characteristics, drag characteristics and pitching moment. The results are compared with those of the classical NACA 23015 aerofoil and another NASA Natural Laminar Flow (NLF) aerofoil. The comparative numerical studies using the XFOIL has shown some promising results of the modified aerofoil for use on the aircraft under design.

Quantifying How Turbulence Enhances Boundary Layer Skin Friction and Surface Heat Transfer

Transitional and turbulent boundary layer (BL) flows possess dramatically larger wall-shear stresses and surface heat fluxes than their laminar counterparts. Locally, this can be explained by appealing to the presence of spatiotemporally coherent velocity and temperature regions that enhance the momentum and thermal transport across the BL. However, these coherent structures are seldom present alone, but usually influenced by other physical phenomena, such as the streamwise growth of BLs or freestream pressure gradients. A moment of enthalpy integral equation is introduced to quantify how turbulence and other flow phenomena enhance surface heat flux. Results from a direct numerical simulation of a transitional and turbulent BL are used to demonstrate the proposed analysis method and to form a quantitative assessment of the BL physics. The integral analysis demonstrated in this paper for canonical turbulent flows provides an interpretable analysis tool for unlocking key BL physics, including future extensions to compressible BLs, freestream pressure gradients, and the evaluation of flow control schemes.

Multi-fidelity approach for transitional boundary layer

A multi-fidelity computational approach is proposed for transitional boundary layer flow in order to obtain both high fidelity and high efficiency in flow simulation. Because we can categorize the transitional flow into three regions, i.e., laminar region with instabilities, transition region, and turbulent region, three models are judiciously selected. A boundary layer stability method, here nonlinear parabolized stability equations (NPSE), is chosen for the laminar region incorporating nonlinear interactions between instabilities. Large-eddy simulation (LES) is applied for the transition region including the beginning of the turbulent flow. Reynolds-averaged Navier–Stokes (RANS) simulation is used for the downstream turbulent flow. Since the NPSE-coupled LES method has been validated for transitional boundary layers including both incompressible (Kim et al., 2018, 2019, 2020, 2021) and compressible (Lim et al., 2021) flows, appropriate treatments for the interface between LES and RANS are mainly investigated in this study. The current multi-fidelity approach is tested for a transitional boundary layer on a flat plate. Computational fidelity and cost are compared with previous high-fidelity computations. We successfully demonstrate that the proposed multi-fidelity approach provides both high fidelity and high efficiency in transitional flow computations.

Stable, entropy-pressure compatible subsonic Riemann boundary condition for embedded DG compressible flow simulations

One approach to reducing the computational cost of simulating transitional compressible boundary layer flow is to adopt a near body reduced domain with boundary conditions enforced to be compatible with a computationally cheaper three-dimensional RANS simulation. In such an approach it is desirable to enforce a consistent pressure distribution which is not typically the case when using the standard Riemann inflow boundary conditions. We therefore revisit the Riemann problem adopted in many DG based high fidelity formulations.Through analysis of the one-dimensional linearized Euler equations it is demonstrated that maintaining entropy compatibility with the RANS simulation is important for a stable solution. It is also necessary to maintain the invariant for the Riemann outflow boundary condition in a subsonic flow leaving one condition that can be imposed at the inflow boundary. Therefore the entropy-pressure enforcement is the only stable boundary condition to enforce a known pressure distribution. We further demonstrate that all the entropy compatible inflow Riemann boundary conditions are stable providing the invariant compatible Riemann outflow boundary condition is also respected.Although the entropy-pressure compatible Riemann inflow boundary condition is stable from the one-dimensional analysis, two-dimensional tests highlight divergence in the inviscid problem and neutrally stable wiggles in the velocity fields in viscous simulations around the stagnation point. A two-dimensional analysis about a non-uniform baseflow assumption provides insight into this stability issue (ill-posedness) and motivates the use of a mix of inflow boundary conditions in this region of the flow.As a validation we apply the proposed boundary conditions to a reduced domain of a wing section normal to the leading-edge of the CRM-NLF model taken out of a full three-dimensional RANS simulation at Mach 0.86 and a Reynolds number of 8.5 million. The results show that the entropy-pressure compatible Riemann inflow boundary condition leads to a good agreement in pressure distribution.

Quantification of Reynolds-averaged-Navier–Stokes model-form uncertainty in transitional boundary layer and airfoil flows

It is well known that the Boussinesq turbulent-viscosity hypothesis can introduce uncertainty in predictions for complex flow features such as separation, reattachment, and laminar-turbulent transition. This study adopts a recent physics-based uncertainty quantification (UQ) approach to address such model-form uncertainty in Reynolds-averaged Naiver–Stokes (RANS) simulations. Thus far, almost all UQ studies have focused on quantifying the model-form uncertainty in turbulent flow scenarios. The focus of the study is to advance our understanding of the performance of the UQ approach on two different transitional flow scenarios: a flat plate and a SD7003 airfoil, to close this gap. For the T3A (flat-plate) flow, most of the model-form uncertainty is concentrated in the laminar-turbulent transition region. For the SD7003 airfoil flow, the eigenvalue perturbations reveal a decrease as well as an increase in the length of the separation bubble. As a consequence, the uncertainty bounds successfully encompass the reattachment point. Likewise, the region of reverse flow that appears in the separation bubble is either suppressed or bolstered by the eigenvalue perturbations. This is the first successful RANS UQ study for transitional flows.

Wavelet analysis of high-speed transition and turbulence over a flat surface

This paper presents a study of high speed boundary layers using the wavelet method. We analyze direct numerical simulation data for high-speed, compressible transitional, and turbulent boundary layer flows using orthogonal anisotropic wavelets. The wavelet-based method of extraction of coherent structures is applied to the flow vorticity field, decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. We show that the coherent parts of the flow, enstrophy spectra, are close to the statistics of the total flow, and the energy of the incoherent, noise-like background flow is equidistributed. Furthermore, we investigate the distribution of the incoherent vorticity in the transition and turbulent regions and examine the correlation with the near-wall pressure fluctuations. The results of our analysis suggest that the incoherent vorticity part is not a random “noise” and correlates with the actual noise emanating from inside the boundary layer. This could have implications regarding our understanding of the physics of compressible boundary layers and the development of engineering models.

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.

Liutex core line and POD analysis on hairpin vortex formation in natural flow transition

In this study, the new method of the vortex core line based on Liutex definition, also known as Liutex core line, is applied to support the hypothesis that the vortex ring is not a part of the Λ - vortex and the formation of the ring-like vortex is formed separately from the Λ - vortex. The proper orthogonal decomposition (POD) is also applied to analyze the Kelvin-VHelmholtz (K-H) instability happening in hairpin ring areas of the flow transition on the flat plate to understand the mechanism of the ring-like vortex formation. The new vortex identification method named modified Liutex-Omega method is efficiently used to visualize and observe the shapes of vortex structures in 3-D. The streamwise vortex structure characteristics can be found in POD mode one as the mean flow. The other POD modes are in stremwise and spanwise structures and have the fluctuation motions, which are induced by K-H instability. Moreover, the result shows that POD modes are in pairs and share the same characteristics such as amplitudes, mode shapes, and time evolutions. The vortex core and POD results confirm that the Λ - vortex is not self-deformed to a hairpin vortex, but the hairpin vortex is formed by the K-H instability during the development of Lambda vortex to hairpin vortex in the boundary layer flow transition.

An Extended Version of an Algebraic Intermittency Model for Prediction of Separation-Induced Transition at Elevated Free-Stream Turbulence Level

An algebraic intermittency model for boundary layer flow transition from laminar to turbulent state, is extended using an experimental data base on boundary layer flows with various transition types and results by large eddy simulation of transition in a separated boundary layer. The originating algebraic transition model functions well for bypass transition in an attached boundary layer under a moderately high or elevated free-stream turbulence level, and for transition by Kelvin–Helmholtz instability in a separated boundary layer under a low free-stream turbulence level. It also functions well for transition in a separated layer, caused by a very strong adverse pressure gradient under a moderately high or elevated free-stream turbulence level. It is not accurate for transition in a separated layer under a moderately strong adverse pressure gradient, in the presence of a moderately high or elevated free-stream turbulence level. The extension repairs this deficiency. Therefore, a sensor function for detection of the front part of a separated boundary layer activates two terms that express the effect of free-stream turbulence on the breakdown of a separated layer, without changing the functioning of the model in other flow regions. The sensor and the breakdown terms use only local variables.

Assessment of turbulence models for the boundary layer transition flow simulation around a hydrofoil

Boundary layer transition is a typical phenomenon in flows around hydrofoils and has a large influence on the hydrodynamic characteristics such as lift & drag, and vortex shedding. The purpose of this paper is to assess the predictive capability of different turbulence models in computational fluid dynamics (CFD) on boundary layer transition along a hydrofoil. Two typical sub-grid scale (SGS) stress models (LES WALE and LES Smagorinsky), as well as DDES γ-Reθt, DDES, SSTCC γ-Reθt, SST γ-Reθt, and SST k−ω are selected. The boundary layer and wake flow calculated by different models are analyzed in detail and compared with the experimental data. The results show that large eddy simulation is more accurate than other models in terms of boundary layer velocity distribution, vortex shedding and wake structure prediction at the same grid conditions. The transition model considering curvature correction influences the predictive capability in the near-wall region compared with SST γ-Reθt. The flow fields calculated by different curvature correction coefficients are quite different. In this paper, the prediction in the front of the transition end point (0.85L) has achieved good results as scaling coefficient is equal to 75 or 100. The transition model considering curvature modification improves the prediction of boundary layer transition by decreasing the turbulence intensity and increasing the pressure gradient of the aft part of the curvature hydrofoil leading. It is found that the LES model is the first choice in the case of enough computing resources. However, for engineering problems, it is highly efficient to adopt SSTCC γ-Reθt model by adjusting the curvature correction coefficient.

Direct numerical simulation of transitional boundary layers on a horizontal axis wind turbine blade

In boundary layer flow around rotating machines, a radial (or cross-flow) velocity exists due to Coriolis and centrifugal forces. This velocity component can be of great importance for laminar-turbulent transition. A series of direct numerical simulations (DNS) are performed to study the boundary layer flow transition on a rotating Horizontal Axis Wind Turbine blade. To quantify the effect of blade rotation, results are compared with that from airfoil DNS, where the section is taken from 3D blades and does not rotate. It is shown that the rotation gives rise to a small radial velocity and slightly modifies the shape of unstable waves. However, the transition location and mechanism of 3D blade boundary layer flow resemble 2D flow for the investigated case.

Assessment of the wall-adapting local eddy-viscosity model in transitional boundary layer

The main idea of this manuscript is to assess the wall-adapting local eddy-viscosity (WALE) model, which is designed for large-eddy simulation (LES) of turbulent boundary layer, in transitional flow. In contrast to many other sub-grid-scale (SGS) models, the WALE model demonstrates the asymptotic decay of the eddy viscosity in the vicinity of a solid wall in turbulent boundary layer without relying on a dynamic procedure on the SGS model coefficient. Furthermore, the WALE model yields zero eddy viscosity in pure shear flow. Such features are attractive for LES of laminar-to-turbulent transition, yet the WALE model has not been thoroughly investigated in transitional boundary layer flow. Well-resolved LES is conducted for canonical boundary layer transition triggered by sub-harmonic resonance. The model formulation is thoroughly analyzed in the transition process. The asymptotic behavior of the two major tensors, i.e., the strain rate tensor and the traceless tensor of the velocity gradient squared, are confirmed in the current well-resolved LES. The cubic decay of the eddy viscosity in the wall distance is confirmed from the asymptotic analysis on the transitional flow. The presence of the strain rate in the model formulation generates practically zero eddy viscosity in the pre-transition region, allowing interactions of small-amplitude instabilities. The traceless tensor of the velocity gradient squared escalates if small-scale eddies appear, leading to sizable eddy viscosity particularly in the log-law layer in turbulent flow. The response of the WALE model to grid resolution is also discussed. The performance of the WALE model is compared to two other SGS models, Smagorinsky and Vreman models with a constant coefficient, in the current transitional wall-bounded flow.

Assessment of two-parameter mixed models for large eddy simulations of transitional and turbulent flows

In the present study, improved two-parameter mixed models for large eddy simulations are proposed based on previous two-parameter mixed models of Salvetti and Banerjee [1] and Horiuti [2]. The subgrid-scale (SGS) stress in our models is decomposed into the modified Leonard stress, modified cross stress and modified SGS Reynolds stress terms. Although the modified Leonard stress term is explicitly calculated based on the scale-similarity, the modified cross stress term is built using an extension of the filtered Bardina model proposed by Horiuti [3] for better predictions of the interaction between resolved and unresolved scales (i.e., energy exchange). The modified SGS Reynolds stress is modeled by the dynamic Smagorinsky model or by a dynamic global model, leading to two unknown model coefficients for the modified cross stress and the modified SGS Reynolds stress terms. In order to demonstrate the reliability of the proposed SGS models, large eddy simulations of two types of flows (i.e., a fully developed turbulent channel flow and a transitional boundary layer flow) are performed. It is shown that the modified cross stress term makes an important contribution to the accurate predictions of such flows because the emergence of negative SGS dissipation (backward scatter) by the modified cross stress term decreases the excessive positive SGS dissipation (forward scatter). A direct comparison of the turbulent statistics with those from previous SGS models shows that the proposed SGS models result in better prediction performance both in transitional and turbulent flows.

Boundary-layer transition of advanced fighter wings at high-speed cruise conditions

The achievement of laminar flow in the boundary layer at high-speed cruise conditions may further, in addition to shock-wave control, reduce the drag and extend the range of military fighter aircraft. To this end, a further investigation on transitional boundary-layer flow of fighter wings is needed due to different configurations from the wings used on conventional transport aircraft. In this paper, wind tunnel experiments and numerical simulations were conducted on three-dimensional transition of thin diamond-shaped wings used on advanced fighter aircraft at tran/supersonic design points. A newly proposed correlation of crossflow transition which includes the effect of surface roughness was introduced into the γ-Reθt transition model. Predicted results were in good agreement with flow visualizations. Results showed that the strength of the crossflow component grew rapidly around the leading edge because of the severe flow acceleration, just as the same as wings with a large aspect ratio. However, there seemed no regular pattern of instability-dominance variation in span-wise for a diamond configuration. The dominance of different instability mechanisms strongly depended on the local pressure distribution. Hereby, the research recommended a “roof-like” shape of pressure distribution to suppress both crossflow and Tollmien-Schlichting (T-S) instabilities. Besides, a sharp suction peak with a serious pressure rise should be cut off to avoid stronger instabilities. Further discussions also revealed an independence of the unit Reynolds number when transition was triggered by T-S instabilities. Aerodynamic force comparisons indicated that further benefit on drag reduction could be expected by including the three-dimensional transition effect into a wing design process.

Bypass Boundary Layer Transition on Flat Plate by Adverse Pressure Gradient

Bypass boundary layer transition in flows on flat plate by adverse pressure gradient was investigated experimentally. It was measuered cases with combination of adverse pressure gradient by different free stream turbulence intenzity. Hot wire anemometry technique was used. Measuerement were made on flat plate in closed wind tunnel. Adverse pressure gradient was set by diffuser in tested section of wind tunnel. Grid turbulence of free stream was controlled by screen. Hot wire anemometry technique was used, intermitency factor was evaluated. Results were compared wih cases with simpliest conditions.