Prediction Of Boundary Layer Transition Research Articles

Amplification factor transport equation modelling of Mack mode disturbances in hypersonic boundary layers

In the hypersonic boundary layer, the streamwise instability modes are mainly the Mack first mode and the Mack second mode. After the Mach number exceeds 4.0, the Mack second mode becomes the dominant instability mode for boundary layer transition. Currently, there is no complete analytical method to establish an amplification factor transport equation for the second mode. In order to improve the application of the amplification factor transport (AFT) model in hypersonic boundary layer transition prediction, this paper employs boundary layer similarity solutions to conduct stability analysis on the second mode and introduces a function to calculate the growth rate of disturbances. Additionally, a transport equation for the amplification factor of the second mode is formulated. For the non-local variables appearing in the equation, a local calculation method is provided. Combined with the intermittency factor transport equation, a transition prediction model for the second mode is formed. Hypersonic flat plate, wedge, and flared wedge are selected for model validation. The computed results show good agreement with standard stability analysis or experimental results, demonstrating the rationality of the transition model and its high prediction accuracy and reliability.

Gas Kinetic Scheme Coupled with High-Speed Modifications for Hypersonic Transition Flow Simulations.

The issue of hypersonic boundary layer transition prediction is a critical aerodynamic concern that must be addressed during the aerodynamic design process of high-speed vehicles. In this context, we propose an advanced mesoscopic method that couples the gas kinetic scheme (GKS) with the Langtry-Menter transition model, including its three high-speed modification methods, tailored for accurate predictions of high-speed transition flows. The new method incorporates the turbulent kinetic energy term into the Maxwellian velocity distribution function, and it couples the effects of high-speed modifications on turbulent kinetic energy within the computational framework of the GKS solver. This integration elevates both the transition model and its high-speed enhancements to the mesoscopic level, enhancing the method's predictive capability. The GKS-coupled mesoscopic method is validated through a series of test cases, including supersonic flat plate simulation, multiple hypersonic cone cases, the Hypersonic International Flight Research Experimentation (HIFiRE)-1 flight test, and the HIFiRE-5 case. The computational results obtained from these cases exhibit favorable agreement with experimental data. In comparison with the conventional Godunov method, the new approach encompasses a broader range of physical mechanisms, yielding computational results that closely align with the true physical phenomena and marking a notable elevation in computational fidelity and accuracy. This innovative method potentially satisfies the compelling demand for developing a precise and rapid method for predicting hypersonic boundary layer transition, which can be readily used in engineering applications.

Improvements in the Prediction of Steady and Unsteady Transition and Mixing in Low-Pressure Turbines by Means of Machine-Learnt Closures

Abstract In this article, novel machine-learnt transition and turbulence models are applied to the prediction of boundary-layer transition and wake mixing in a low-pressure turbine (LPT) cascade, including unsteady inflow cases with incoming wakes. A laminar kinetic energy (LKE) transport approach is employed as baseline transition framework. The application of the machine-learnt explicit algebraic Reynolds stress models (EARSMs) takes advantage of a zonal strategy based on a newly developed sensing function that allows automated wake demarcation. This work compares the performance of several approaches that are based on the application of improved transition models without machine learnt EARSMs, baseline transition model with EARSMs trained for improved wake mixing, and new transition and turbulence closures that are simultaneously developed in a fully coupled way and aimed at improving both transition and wake mixing predictions in LPTs. The investigation is carried out on a cascade of industrial footprint, representative of modern LPT bladings. First, the various modeling frameworks are evaluated, without bar wakes (steady conditions), over a wide range of Reynolds number values. Unsteady Reynolds-averaged Navier–Stokes (URANS) analyses have also been carried out to investigate the predictive capabilities of machine-learnt closures in the presence of incoming bar wakes. Reynolds-averaged Navier–Stokes (RANS)/URANS results are scrutinized against large eddy simulation (LES) calculations and experimental data. It will be demonstrated that machine-learnt EARSMs are capable of producing realistic wake mixing when simply applied on top of the baseline transition models. However, the most accurate predictions will be shown to be provided by fully integrated machine-learnt transition/turbulence closures.

Improved Amplification Factor Transport Transition Model for Transonic Boundary Layers

Linear-stability-theory-based method plays an important role in boundary-layer transition prediction of aeronautical flows. Based on the simplification of linear stability theory (Drela and Giles, AIAA J, 1987), the amplification factor transport (AFT) equation for Tollmien–Schlichting waves using local variables was first proposed in 2013 (Coder and Maughmer, AIAA J, 2014). However, in transonic high-Reynolds-number flows, the AFT model seriously overestimates the value of . To fix this problem, we have conducted many linear stability analyses to rebuild the formulations of AFT model. Compressibility effect, which has a significant impact on the prediction of value, has been considered in the improved version. Coupled with the model for crossflow instabilities (Xu et al., CJA, 2020), the improved AFT model is established for transonic boundary layers. Several classic test cases are successfully employed to validate present AFT model, including a flat plate, an airfoil, an infinite swept wing, a sickled-shape wing, a 6:1 inclined prolate spheroid, the NASA Common Research Model, and ARA Transonic Swept Wing. Our prediction results show that both Tollmien–Schlichting instabilities and stationary crossflow instabilities can be captured and predicted well by the improved model in subsonic and transonic boundary layers.

Improvement of transition prediction model in hypersonic boundary layer based on field inversion and machine learning framework

The classical four-equation γ−Reθ transition model has presented excellent accuracy in low-speed boundary layer transition prediction. However, once the incoming flow reaches hypersonic speed, the original model is no longer applicable due to the compressibility problem and the appearance of multiple instability modes. Recently, there has been widespread interest in data-driven modeling for quantifying uncertainty or improving model prediction accuracy. In this paper, a data-driven framework based on field inversion and machine learning is performed to extend the prediction capability of the original γ−Reθ transition model for the hypersonic boundary layer transition. First, the iterative regularized ensemble Kalman filter method is applied to obtain the spatial distribution of the perturbation correction term β for the switching function Fonset1, and the effectiveness of this method is initially verified in the hypersonic flat plate case. Then, the random forest algorithm is adopted to construct a mapping from the average flow features to β. The generalizability of the well-trained learning model is fully validated in the blunt cone cases with different unit Reynolds numbers, free-stream flow temperature, and bluntness. The simulation results indicate that the performance of the original γ−Reθ transition model in the hypersonic boundary layer transition prediction is significantly improved, and the boundary layer transition onset location and the length of transition zone can be correctly obtained. In addition, the machine learning model investigates the importance of the input features and confirms that the effective length scale plays a significant role in the numerical simulation of the hypersonic boundary layer transition.

A three-equation transition model with mechanical considerations

A three-equation transition model based on the transition V-model is proposed for subsonic flows in this study. Considering the mechanical approximation of the generation process of the pre-transitional vorticities, the value of laminar Reynolds shear stress related to the mean shear deformation was calculated in the original transition V-model. Then a new transition model, named V-SA model, was proposed, which considered the phenomenological process of transition and presented great results for flows with and without pressure gradient. It is well-known that the baseline Shear Stress Transport (SST) turbulence model shows excellent performance of accuracy and robustness in plentiful flow cases, but it is important to predict boundary layer transition. The current model (V-SST) successfully couples the V-model to the SST turbulence model by introducing the effective turbulent viscosity and additional correction terms into the transport equations. A thorough evaluation of its ability to predict transition features is performed versus the well-documented flat plate of ERCOFTAC, including T3A and T3B without pressure gradient, T3L2 and T3L3 with semi-circular leading edge, the three-dimensional 6:1 prolate-spheroid under two angles of attack, and the NLR-7301 airfoil under different Mach numbers. Numerical results show that the current model has an attractive and superior performance in the simulation of boundary layer transition processes

Physics-based model for boundary layer transition prediction in a wide speed range

A new physics-based model employing three transport equations is developed for the simulation of boundary layer transitions in a wide speed range. The laminar kinetic energy is used to represent pretransitional streamwise velocity fluctuations, taking account of different instability modes. The fluctuation velocity components normal to the streamwise direction are modeled by another transport equation. Transition is triggered automatically with the development of the pretransitional velocity fluctuations. In the fully turbulent region, the model reverts to the k-ω turbulence model. Different test cases, including subsonic, supersonic and hypersonic flows around flat plates, airfoils and straight cones, are numerically simulated to validate the performance of the model. The results demonstrate the excellent predictive capabilities of the model in different paths of transition. The model can serve as a basis for the extension of additional transition mechanisms, such as rotation and curvature effects, roughness-induced transition and crossflow-induced transition.

Influence of the gas model on the boundary layer characteristic parameters and transition prediction for the Mars entry capsule

<p indent="0mm">Turbulent transition is an important factor affecting the thermal environment of spacecraft. A boundary layer transition prediction method was developed for both smooth and rough thermal protection system surfaces of a large-scale entry capsule in the process of entering the Martian atmosphere. The effects of the gas model and wall temperature constraints on the boundary layer characteristic parameters and transition features were analyzed. The results indicate that the dissociation reaction of carbon dioxide and its thermodynamic non-equilibrium effect will lead to increases in the momentum thickness Reynolds number and the roughness-height-based Reynolds number of the boundary layer. The radiative-equilibrium wall temperature constraint also results in a higher momentum thickness Reynolds number and roughness-height-based Reynolds number compared to those of the cold wall conditions. Therefore, the thermochemical non-equilibrium and radiative-equilibrium wall temperature boundary condition should be included in the analysis model to obtain the actual transition features.

Numerical Investigation of Unsteady Boundary Layer Transition on a Dynamically Pitching Rotor

Predictions of unsteady boundary layer transition are performed on a four-bladed rotor in axial inflow using a computational fluid dynamics approach. The configuration is based on experiments performed at the German Aerospace Center (DLR) in the 1.6-m × 3.4-m wind tunnel in the rotor test facility (RTG). Simulations are performed using the NASA OVERFLOW 2.3 solver with hybrid RANS/LES and laminar turbulent transition modeling. Solutions are based on a hover tip Mach number of 0.143 with prescribed cyclic pitching conditions. Computational methods and grid generation are described. The rotor flow field is analyzed, and the effect of transition modeling on unsteady boundary layer transition prediction is assessed. Laminar-turbulent transition predictions and rotor performance are compared to experimental measurements obtained at the DLR RTG. A study of sensitivity was performed on freestream turbulence intensity to investigate its effect on predicted rotor transition.

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.

Toward a Practical Method for Hypersonic Transition Prediction Based on Stability Correlations

An accurate boundary-layer transition prediction method integrated with computational fluid dynamics (CFD) solvers is pursued for hypersonic boundary-layer flows over slender hypersonic vehicles at flight conditions. The geometry and flow conditions are selected to match relevant trajectory locations from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7 deg half-angle cone with 2.5 mm nose radius, freestream Mach numbers in the range of 3.8–5.5, and freestream unit Reynolds numbers in the range of . Earlier research had shown that the onset of transition during the Hypersonic International Flight Research Experimentation 1 (HIFiRE-1) flight experiment correlated with an amplification factor of for the planar Mack modes. However, to incorporate the -factor correlations into a CFD code, we investigate surrogate models for disturbance amplification that avoids the direct computation of stability characteristics. The results demonstrate that the application of the commonly used approach, which is based on a database of stability characteristics for locally similar profiles, leads to large, unacceptable errors in the predictions of amplification factors. We propose and demonstrate an alternate approach that employs the stability computations for a canonical set of blunt cone configurations to train a convolutional neural network model that is shown to provide substantially improved transition predictions. The excellent performance of the neural network model is also confirmed for cone configurations with nose radius and half-angle values outside of those used to build the database. Finally, the convolutional neural network model is found to outperform the linear stability calculations for underresolved basic states.

Impact of Vibrational Nonequilibrium on the Supersonic Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic boundary layers has recently been shown to achieve a larger peak growth rate than the traditional second mode in particular circumstances relevant to free flight. In this environment, high levels of aerodynamic heating are encountered such that incorporation of chemical and vibrational nonequilibrium effects can become critical. The impact of thermal nonequilibrium (TNE) on the supersonic mode in particular has not been thoroughly and systematically investigated. This work uses thermochemical nonequilibrium (TCNE) direct numerical simulation (DNS) and TCNE linear stability theory (LST) to obtain a more complete investigation of the supersonic mode using both nonequilibrium and frozen gas models. The simulation is Mach 5 flow over a 1-mm-nose-radius axisymmetric cone 1 m in length, representative of experimental conditions in ground test facilities. Both LST and DNS results indicate that TNE effects are destabilizing compared with frozen flow and can lead to an -factor difference of approximately at the end of the cone. LST results also indicate that TNE effects are stabilizing to the second and supersonic modes in comparison with thermal equilibrium. The supersonic mode appeared to be slightly more affected by TNE than the second mode. Collectively, the findings in this work suggest that even in ground test facilities where TCNE effects are relatively small compared with free flight, incorporating nonequilibrium models in both the mean flow and stability solvers can have a practical effect on hypersonic boundary-layer transition prediction analyses.

Predicting crossflow induced transition with laminar kinetic energy transition model

The hypersonic laminar kinetic energy transition model is developed to be appropriate for crossflow induced boundary layer transition prediction. A crossflow timescale is constructed and incorporated in the kT-kL-ω transition model to reflect crossflow effect during three-dimensional boundary layer transition. The stream-wise vorticity is selected as the indicator of crossflow strength. Regarding the inviscid unstable characteristic of crossflow instability, the crossflow timescale is constructed by reference to the second mode timescale. To eliminate inappropriate development of the crossflow timescale where the effective length scale is large enough while the crossflow strength remains at a quite low level, a crossflow velocity limit function is proposed. The revised kT-kL-ω transition model has been applied to HIFiRE-5 and blunt cone with 1°angle of attack test cases. Results show good correspondence with the experimental data and DNS data, which demonstrates that the constructed crossflow timescale makes the revised transition model capable of reproducing crossflow induced transition behavior with a reasonable degree of accuracy.

Study of hydrofoil boundary layer transition using different turbulence models

Boundary layer transition is one of the key factors affecting the hydrodynamic characteristics of hydrofoil. In order to explore the capability of a transition model coupled to different turbulence models in the prediction of hydrofoil boundary layer transition, the flow field around the NACA0009 blunt-edge hydrofoil at 0°angle of attack was calculated using γ-Reθt transition model coupled with SST, SST-DES, SST-SAS, SST-DDES turbulence models. The characteristics of the hydrofoil boundary layer at ReL=2*106 are analysed. The experimental data and numerical calculation results are compared. The results show that the four turbulence models differ quite a bit in simulating hydrofoil boundary layer transition at the same calculation conditions. The flow parameters of the hydrofoil boundary layer calculated by the transition model coupled with SST-DDES are closer to the experimental results.

A FEniCS-based model for prediction of boundary layer transition in low-speed aerodynamic flows

In the paper, a finite element model is developed that predicts boundary layer transition in low-speed aerodynamic flows. The model is based on a Reynolds-averaged Navier-Stokes approach, where the incompressible form of the Navier-Stokes equations is solved together with a three-equation eddy-viscosity model utilizing the FEniCS framework. A least-square stabilized Galerkin method is employed in order to prevent numerical oscillations that can arise from dominant advection terms. The proposed FEniCS model is ideal for applications with complex geometries and is tested on high performance computing platforms for parallel processing. The FEniCS model is validated by comparing the skin friction coefficient as well as profiles of velocity and total fluctuation kinetic energy with the benchmark experimental data for transitional boundary layers on a flat plate. The validity of the solver is further examined using experimental measurements reported for a NLF(1)-0416 natural laminar flow airfoil at different angles of attack. The airfoil results are also compared with those obtained using XFOIL, a well-known tool for the design of two-dimensional airfoils. These comparisons suggest that the proposed FEniCS-based model can effectively simulate aerodynamic flow fields that involve laminar-to-turbulent transition.

Predicting Boundary Layer Transition on X-51A Forebody with kT-kL-(omega) Transition Model

Boundary layer transition is of significance to the hypersonic aircrafts. In this paper, boundary layer transition on X-51A forebody is predicted with the kT-kL-(omega) transition model. An overview of the transition zone is depicted and the transition onset on the leeward is compared with the experiment result. The comparison demonstrates that for the complex hypersonic aircraft X-51A forebody, the kT-kL-(omega) transition model can reflect the effect of freestream Reynolds number on boundary layer transition, but under certain condition, there is still room to improve the accuracy of boundary layer transition onset prediction.

Study on Oil-Film Interferometry Measurement Technique of Hypersonic Boundary Layer Transition

Prediction of boundary layer transition is important for the design of hypersonic aircrafts. The study of boundary layer transition of hypersonic flow around a flat plate using oil-film interferometry was investigated at Φ500mm traditional hypersonic wind tunnel. In order to measure the skin friction fast and precisely on the hypersonic wind tunnel, the traditional oil-film interferometry technique is improved. A high-speed camera is used to capture the images of fringes and the viscosity of the silicon oil is modified according to the wall temperature measured by thermocouples during the test. The skin frictions of smooth surface and the surface with single square roughness element were measured. For the smooth surface, the boundary layer is laminar. However, the boundary layer transition is promoted by wake vortices induced by the roughness element. Both the results of skin friction with and without the roughness element are in good agreement with the simulation results correspondingly, indicating high accuracy of the oil film interferometry technique.

Characterization of Freestream Disturbances in Conventional Hypersonic Wind Tunnels

Although low-disturbance (“quiet”) hypersonic wind tunnels are believed to provide more reliable extrapolation of boundary-layer transition behavior from ground to flight, the presently available quiet facilities are limited to Mach 6, moderate Reynolds numbers, low freestream enthalpy, and subscale models. As a result, only conventional (“noisy”) wind tunnels can reproduce both Reynolds numbers and enthalpies of hypersonic flight configurations and must therefore be used for flight vehicle test and evaluation involving high Mach number, high enthalpy, and larger models. This paper outlines the recent progress and achievements in the characterization of tunnel noise that have resulted from the coordinated effort within the AVT-240 specialists group on hypersonic boundary-layer transition prediction. The new experimental measurements cover a range of conventional wind tunnels with different sizes and Mach numbers from 6 to 14 and extend the database of freestream fluctuations within the spectral range of boundary-layer instability waves over commonly tested models. New direct numerical simulation datasets elucidate the physics of noise generation inside the turbulent nozzle wall boundary layer, characterize the spatiotemporal structure of the freestream noise, and account for the propagation and transfer of the freestream disturbances to a Pitot-mounted sensor.

Boundary-Layer Transition Prediction over Cavities and Its Morphing Skin Design Application

Flow over cavities can behave in one of three different modes, namely, the wake mode, the shear-layer mode, and the no-oscillations mode. In this study, the unsteady Reynolds-averaged Navier–Stokes equations ae used to numerically solve the flow over two-dimensional deep cavities with upstream laminar boundary layers. The numerical model successfully captures the three flow modes, and the results are validated against experimental data and semiempirical solutions. It is observed that, in some cases, the boundary layer maintains its laminar state while travelling over the cavity and, in other cases, the boundary layer experiences a transition over the cavity vicinity. To investigate the cavity parameters that influence the transition of the boundary layer, a parametric study is performed over a wide range of flow conditions and cavity dimensions. It is found that the boundary layer bypasses the cavity and maintains its laminar state when , where is the cavity length, is the momentum thickness of the boundary layer, and is the Reynolds momentum thickness at the cavity leading edge. Some aerodynamic applications of this finding are presented, with an emphasis on morphing wings and morphing skins design.

Hypersonic Crossflow Instability

Under the auspices of NATO STO AVT-240: “Hypersonic Boundary-Layer Transition Prediction”, this paper describes the results of close collaborations among the authors toward the fundamental understanding and modeling of the instabilities associated with three-dimensional boundary layers in hypersonic flight. Specifically, the focus is directed toward the crossflow instability. A common straight circular cone geometry is analyzed for and from both a computational and experimental perspective using methods that are unique to each facility and methodology. Disturbance wavelength and trajectory, surface roughness, and the use of quiet wind tunnels are just a few items found to be key factors in the investigation of the crossflow instability. Quiet tunnels allow experiments to be performed in a disturbance environment comparable to that expected from flight, and the combination of different facilities and computations displays a comprehensive analysis that would be unobtainable from any individual approach alone.