Adverse Pressure Gradient Flows Research Articles

Hot-wire spatial resolution issues in adverse pressure gradient turbulent boundary layers

The effect of a finite length of hot-wire probe sensor length on the measured streamwise velocity fluctuations is well understood in canonical wall-bounded flow, where the small-scale energy has been found to be universal and invariant with Reynolds number. A straightforward application of that assumption to non-canonical flows such as strong adverse pressure gradient (APG) flows has, however, been hampered since the effect of Re and APG could not conclusively be studied separately due to the lack of data with a clear scale separation. The present experimental investigation at Reτ≈4000 in weak, moderate and strong APGs with different wire length shows that spatial averaging effects are not only limited to the inner layer. A note of caution is hence warranted for measurements that seemingly try to take the bias effect of spatial attenuation into account by performing measurements with albeit long but fixed viscous-scaled wire length.

An innovative modification to the Menter shear-stress transport turbulence model employing the symbolic regression approach

Drawing from the non-equilibrium link between the production Pk and dissipation ε of turbulent kinetic energy (TKE), we advocate for the introduction of a limiter to modulate the TKE production term within the Menter shear-stress transport (SST) model. The original SST model is made more sensitive to the adverse pressure gradient (APG) by Bradshaw's assumption. Bradshaw's assumption introduces the equilibrium condition Pk/ε = 1 in most regions of the turbulent boundary layer. In the APG flows with Pk≫ε, the equilibrium condition suppresses the magnitude of TKE (k) within the boundary layer, resulting in an early separation problem. To address this issue, we employ the symbolic regression (SR) to scrutinize the physical correlation between Pk/ε and local turbulence parameters, obtaining an approximate function FSR that encapsulates the relationship between Pk/ε, Sk/ε, and y+ in the APG flow. Following its incorporation into the original SST model in the form of a limiter, the FSR evolves into the SST-Symbolic Regression Evolution model. The SST-SRE is then applied to four cases with APGs. The modification leads to an increase in the skin-friction coefficient Cf in the APGs region and causes a downstream shift in the separation location, improving the consistency with high-accuracy data and experimental results. It is demonstrated that this correction can improve the early separation problem in the Menter SST turbulence model.

A modification of production term for the shear stress transport turbulence model based on a new wall-law for adverse pressure gradient

This paper presents an attempt to improve the predictive accuracy of the Menter shear stress transport (SST) turbulence model for adverse pressure gradient (APG) flows. The foundation of this work lies in the newly modified law of the wall and turbulent kinetic energy (TKE) transport equation within the APG turbulent boundary layer. The modification of the law of the wall is achieved through a newly proposed variable λ, which is derived theoretically and calibrated using direct numerical simulation data. Based on the new law of the wall, we analyze the TKE transport equation of the SST model at APG and demonstrate that the analytical solution satisfying the law of the wall cannot achieve equilibrium in the current SST model. Further theoretical analysis reveals that this imbalance is caused by the TKE production term Pk, and the decomposition of the wall friction coefficient Cf indicates that Pk directly affects the prediction of flow separation. Based on the analysis and the new law of the wall, an additional term for Pk is suggested to correct Pk and improve the model's predictive accuracy for APG flows. Numerical validation results show that the correction leads to an increase in Pk within the APG turbulent boundary layer, resulting in more accurate predictions of Cf and the mean velocity profile in the inner layer of the turbulent boundary layer.

Aerodynamic and Aeroacoustic Effects of Different Transition Mechanisms on an Airfoil

The paper delves into the detailed sound generation and propagation mechanisms associated with tripping-induced flow perturbations and trailing-edge scattering using wall-resolved large-eddy simulations. Two distinct boundary-layer tripping techniques, namely a geometrically resolved stair strip and an artificially modeled trip using suction and blowing, are investigated. To facilitate comparison, the natural boundary-layer transition is also simulated as a baseline scenario. The analysis takes into account a Reynolds number of 4×105, a Mach number of 0.058, and a nonzero angle of attack of 6.25° over a NACA 0012 airfoil configuration. The mechanisms for sound generation and propagation related to trailing-edge noise remain consistent across the three transition scenarios. However, boundary-layer tripping notably leads to intricate, scenario-specific noise generation: there is an interaction between the laminar separation bubble and tripping for the stair strip case, whereas laminar boundary-layer instability is evident for the suction and blowing scenario. Aerodynamic flowfields involving acoustic noise sources, their propagating natures near the wall, and far-field acoustics are cross-examined in detail. The comprehensive analysis of observed phenomena provides valuable insights for understanding nonlinear flow and acoustic interactions relevant to airfoil noise and designing new types of trips under adverse pressure gradient flows.

Convection velocity in turbulent boundary layers under adverse pressure gradient

The convection velocity (UC) of turbulent structures has been studied in adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) for a wide range of Reynolds numbers Reτ≈1400−4000. The study is based on estimation of the convection velocity using decomposed streamwise skewness factor introduced in (Dróżdż A., Elsner W., Int. J. of Heat and Fluid Flow. 63 (2017) 67-74) and verified by means of two-point correlation method. It was shown that in the overlapping region of APG flows, the convection velocity profiles (when scaled in viscous units) reassemble the universal logarithmic law characteristic for the ZPG flows up to Clauser-Rotta pressure gradient parameter β≲19 for the considered range of Reynolds number, what means that in the inner region of TBL the friction velocity in APG is not proportional to U (as in ZPG) but to UC instead. The physical mechanism that explains the impact of increased convection velocity on the mean flow is proposed. The difference between UC and U increases as a function of APG, which causes the stronger sweeping that enhances momentum transfer to the wall and compensates the weaker mean shear profile that is created by low vorticity near the wall. This effect is a result of an enhancement of amplitude modulation of the small scales by large-scale motion. The process becomes more pronounced as eddy density grows, so with increasing Re. The proposed model addresses a number of literature observations found in adverse pressure gradient flows which have been so far left without a well-founded explanation.

Investigation of the unsteady flow in a transonic axial compressor adopted in the compressed air energy storage system

During operation, compressed air energy storage systems should respond rapidly to variations in power network demand, requiring that the compression system should always be in changeable off-design conditions. Compression systems with low flow rates confront difficulties such as diminished aerodynamic performance and increased flow losses. Given that the emergence of compressor instability is a process of the accumulation and intensification of flow unsteadiness. In this study, a numerical simulation was conducted for a transonic compressor to investigate the unsteady evolution characteristics of the tip leakage flow field, and it focused on the flow field of a condition where the flow unsteadiness was stimulated and further investigated the origin of flow unsteadiness, which was supposed to provide insights in developing flow control strategies and enable the application in a compressed air energy storage system under low mass flow rate conditions. The Fourier fast transformation (FFT) signal analysis showed that characteristic frequency of the unsteady tip flow field was 1863.3 Hz. Unsteady disturbances were predominantly distributed in the following three regions: the leakage vortex region of the blade suction surface, the location of the epitaxially detached shock wave at the entrance of passage, and the 5 %–30 % chord of the blade pressure surface. The high disturbance region of leakage vortex was generated by the periodic shift in leakage vortex intensity over time, the interaction between the main flow and various types of secondary flow due to leakage vortex breaking processes was the primary cause for the disturbance region of the epitaxially detached shock wave at the entrance of passage, and the high disturbance region of blade pressure surface was caused by the adverse pressure gradient effect and flow direction deflection of the airflow in the passage, as well as the impacted on the pressure surface of the adjacent blade. It was speculated that leakage vortex breakdown due to vortex wave interference was the key factor to induce the unsteadiness of the flow field. A new vortex structure was formed at the leading edge of adjacent blades after leakage vortex breakdown, which was defined as a “leading edge vortex”, and its series of evolutionary processes occurring timely were the main reasons for the unsteady flow in the tip flow field. This study laid a theoretical foundation for the research of the flow field control strategy of axial compressor operating in off-design conditions in a large-scale compressed-air energy storage system.

Experimental study of laminar-to-turbulent transition in an adverse pressure gradient flow

Experimental results on laminar-to-turbulent transition in a separated laminar boundary layer formed over a flat plate in an adverse pressure gradient are provided. Experiments have been performed for a range of Reynolds numbers (1.4 − 2.4 · 105) and for two freestream turbulence levels (Tu =3.6 and 5.3%). The measurements of mean and fluctuating velocity profiles have been carried out at inlet to the test section using Constant Temperature Anemometry (CTA). The data might be useful for validation and development of transition models. In order to characterize the dynamics leading to the transition process in the separated boundary layer on the plate surface, the Particle Image Velocimetry (PIV) measurements have been performed. The results show that the transition process in the separated boundary layer is influenced by breakdown of the Klebanoff streaks.

Curvature-Sensitive Transition Model Application to Flow Around a Smooth Circular Cylinder

Abstract Transition modeling in complex flow situations including adverse pressure gradient, streamline curvature, and massive flow separation represents one of the key challenges in computational fluid dynamics that greatly affects the flow characteristics in many thermal and fluid sciences applications. Here, we report a comparative study that helps investigate the capability of the curvature-sensitive kT−kL−ω−v2 transition model against the original kT−kL−ω algorithm in predicting the flow behavior surrounding a smooth circular cylinder subjected to Reynolds numbers in the range from 3.9×103 to 3.6×106. A C-program that fully accounts for the model's four transport equations is particularly developed and coupled with the transient solver of ansysfluent. The present simulation enables accurate prediction of the distributions of skin-friction and pressure coefficients along with careful specification of the corresponding drag coefficients and angles of separation and transition. The simulation reveals insignificant variations in the bulk flow behaviors using either model in both sub- and critical flow regimes while a remarkable improvement in the supercritical drag result is achieved using the curvature-sensitive model.

Semi-empirical wall pressure spectral modeling for zero and favorable pressure gradient flows.

Semi-empirical models are used to predict the power spectral density of wall pressure fluctuations in the turbulent boundary layer. Current advancements in power spectral density wall pressure fluctuation prediction have focused on expanding the range of experiments that can be predicted to include adverse pressure gradient flows; however, favorable pressure gradient flows have not received much attention. An experiment was performed to capture the effects of the favorable pressure gradient on the power spectral density. A model was then created to improve upon some of the limitations of existing models. The proposed model improves upon the prediction of the high-frequency roll-off location, incorporates improvements made by past models, and captures the effects of favorable pressure gradients.

Galilean-Invariant Stability-Based Transition Transport Modeling Framework

A new stability-based transition transport modeling framework for unstructured computational fluid dynamics is introduced. Based on a four-equation model published recently by the authors of this paper, new model formulations are derived being Galilean invariant and fully local. Moreover, the complexity of the four-equation model is reduced, yielding a one-equation model that is based on a local pressure-gradient parameter and a three-equation model that is based on an averaged pressure-gradient parameter considering convection (history) effects. Since the model versions are identical except the pressure-gradient parameter, the implementation effort is reduced. To be able to compute test cases in adverse pressure gradient flow regions at low Reynolds numbers, a method was developed to accelerate the turbulence production (downstream of the point of transition onset) that can also be used inside laminar separation bubbles. The models were implemented into the DLR TAU code, the unstructured compressible finite-volume flow solver of the German Aerospace Center (DLR) for external flows. For verification and validation purposes different test cases are shown capturing a wide range of parameters and flow conditions. This includes a test case verifying that the model yields identical results with and without uniform motion (Galilean invariance). Additionally, industrially relevant three-dimensional test cases were computed. This includes a helicopter rotor in vertical flight.

Coherence of wall pressure fluctuations in zero and adverse pressure gradients

The wall pressure fluctuations induced by turbulent boundary layers on a flat plate model were measured with an L-shaped array of Kulite miniature pressure sensors. By installing a NACA airfoil above the plate with an adjustable angle of attack, different adverse pressure gradients were produced on the plate. The streamwise and spanwise coherence and coherence lengths of the wall pressure fluctuations are calculated for zero and adverse pressure gradient flows. The effect of the pressure gradient on the coherence and coherence lengths in both streamwise and spanwise directions is quantified. Based on the results of the present test cases and selected published datasets in zero pressure gradients, covering the range of Reynolds numbers based on the momentum thickness between 3300 and 42000, the Reynolds number dependence of the streamwise wall pressure coherence is discussed and mathematically expressed. A coherence length model for zero pressure gradient boundary layers, taking into account the Reynolds number effect, is proposed based on scaled spectra of the coherence lengths. In comparison with the other published models, the present model achieves a considerable improvement of the prediction accuracy for boundary layer flows, covering a large range of Reynolds numbers. Furthermore, an evaluation of the Corcos model and the Smol’yakov and Tkachenko model for prediction of the off-axis coherence of the fluctuating wall pressure field is made.

Application of the diagnostic plot in estimation of the skin friction in turbulent boundary layer under an adverse pressure gradient

The paper concerns the problem of determining friction velocity in wallbounded flows affected by an adverse pressure gradient (APG). In the work of Niegodajew et al. [22] the corrected Clauser chart method (CCCM) for such flow conditions was proposed. This approach utilises the mean velocity profiles and turbulence intensity profiles to accurately estimate the friction velocity. In another work, Drozdz et al. [27] presented a modified version of the diagnostic-plot scaling (DPS) which allows for direct reconstruction of turbulence intensity profiles based on the local mean velocity profile, even when the flow is affected by a strong pressure gradient. This paper is aimed at verifying whether, when combining both of these methods (i.e. DPS and CCCM), the friction velocity can be accurately determined for APG flow conditions and one can possibly take advantage from both methods. The analysis revealed that the new approach is able to predict the friction velocity with uncertainty less than 5% for all the considered cases for the Clauser–Rotta parameter β < 17. Lastly, DPS-CCCM was also confronted with two empirical approaches (from available literature) allowing for estimation of the friction velocity under APG conditions. The performance of DPS-CCCM was found to be better than the ones of two other empirical approaches.

Boundary Layer Flashback Model for Hydrogen Flames in Confined Geometries Including the Effect of Adverse Pressure Gradient

Abstract The combustion properties of hydrogen make premixed hydrogen-air flames very prone to boundary layer flashback. This paper describes the improvement and extension of a boundary layer flashback model from Hoferichter et al. (2017, “Prediction of Confined Flame Flashback Limits Using Boundary Layer Separation Theory,” ASME J. Eng. Gas Turbines Power, 139(2), p. 021505) for flames confined in burner ducts. The original model did not perform well at higher preheat temperatures and overpredicted the backpressure of the flame at flashback by 4–5×. By simplifying the Lewis number-dependent flame speed computation and by applying a generalized version of Stratford's flow separation criterion (Stratford, 1959, “The Prediction of Separation of the Turbulent Boundary Layer,” J. Fluid Mech., 5(1), p. 1), the prediction accuracy is improved significantly. The effect of adverse pressure gradient flow on the flashback limits in 2 deg and 4 deg diffusers is also captured adequately by coupling the model to flow simulations and taking into account the increased flow separation tendency in diffuser flow. Future research will focus on further experimental validation and direct numerical simulations to gain better insight into the role of the quenching distance and turbulence statistics.

Assessment of anisotropic minimum-dissipation (AMD) subgrid-scale model: Gently-curved backward-facing step flow

The impetus of this study is to evaluate the performance of the anisotropic minimum-dissipation (AMD) subgrid-scale model (SGS) for flow over a gently-curved backward-facing step (BFS) at a Reynolds number of 13 700. Minimum-dissipation sub-grid models were developed as simple alternatives to the dynamic eddy-viscosity SGS models. AMD model is a static type of eddy-viscosity SGS model incorporating anisotropic SGS effects into numerical predictions through the large-eddy simulation (LES) approach. The open-source CFD package of OpenFOAM was used to implement the AMD model. Before focusing on the BFS flow, we investigated the impact of the AMD model coefficient magnitude on the numerical predictions of the decaying isotropic turbulence flow. In the next step, numerical solutions were obtained for the curved backward-facing step using the AMD model and Dynamic Smagorinsky model (DSM). The curved backward-facing step was considered here for the evaluation of the SGS model predictions due to its weak adverse pressure gradient and high sensitive flow mechanism. The rescaling/recycling method was employed as a turbulent inflow generation technique. The AMD model results were compared with the prediction of the DSM and Vreman model. Moreover, AMD model predictions were compared with the reported solutions obtained using different turbulent inflow generation methods. The assessments revealed the high capability of the AMD model to capture decaying turbulence and predict velocity profiles and resolved flow statistics turbulent parameters in the gently-curved backward step flow.

An improved prediction model for corner stall in axial compressors with dihedral effect

Corner stall predictions are important and difficult in axial compressors. However, all of the prediction models have proved to be ineffective for advanced compressor blades, which tend to use the combined sweep and dihedral. As for the prediction parameter DL, although it effectively modeled the effects of the adverse pressure gradient and secondary flow, it failed to predict the corner stall of curved blades because the model failed to consider the intersection of the boundary layer at the corner region. In this paper, the shape factor gradient Ψ of the boundary layer at the corner region was investigated by numerically studying specially shaped expansion pipes under different adverse pressure gradients. The improved prediction parameter DJ was presented based on the model of Ψ and the circumferential pressure gradient ξ. A comparison of the critical range of the prediction parameters DL and DJ was investigated using the NACA65 cascade database, which was established by a numerical method. Then, the stall criterion was validated according to the experimental results of various test facilities with different blade geometries and experimental conditions. The results show that the improved prediction parameter is able to predict the corner separation/stall flows and is in good agreement with the experimental results for axial compressors with three-dimensional designed blades.

Skin Friction Measurements of Transition in High Reynolds Number, Adverse Pressure Gradient Flow

Abstract A combined experimental and analytical modeling effort has been carried out to measure the skin friction response of the boundary layer in high Reynolds number adverse pressure gradient flow. The experiment was conducted in the United Technologies Research Center (UTRC) Acoustic Research Tunnel, an ultra-low freestream turbulence facility capable of laminar boundary layer research. Boundary layer computational fluid dynamics and stability modeling were used to provide pre-test predictions, as well as to aid in interpretation of measured results. Measurements were carried out at chord Reynolds numbers 2–3 × 106, with the model set at multiple incidence angles to establish a range of relevant leading edge pressure gradients. The combination of pressure gradient and flight Reynolds number testing on a thin airfoil has produced a unique data set relevant to propulsion system turbomachinery.

Developing code-friendly variant of V2F turbulence model

Relevant modifications to the code-friendly variant of v¯2−f turbulence model is proposed that accounts for the distinct effects of low-Reynolds number and near-wall turbulence. It incorporates compatible formulations for inter-dependent coefficients Cϵ(1,2) and σ(k,ϵ) to amplify the level of dissipation in non-equilibrium flow regions, thus reducing the turbulent kinetic energy and time/length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. A non-linear eddy-viscosity coefficient with a realizable eddy-viscosity bound that may enhance the predicted accuracy for complex flows, is introduced with the present model. Coefficients of the elliptic-relaxation equation are constructed such as to preserve the anisotropic characteristics of turbulence, encountered in rotational and irrotational flows. Fully-developed turbulent channel and flat-plate flows are computed to validate the model ability in replicating the near-wall turbulence. An asymmetric plane diffuser flow is simulated to verify the model accuracy in capturing non-equilibrium flows with separation and reattachment. The Computation of flow over a three-dimensional (3D) axisymmetric hill is presented, rectifying the model competency in predicting an adverse-pressure-gradient flow with 3D turbulent separation. Model predictions are compared with the widely used SST (shear stress transport) k−ω model; a good correlation is obtained between the current model and DNS/experimental data.

Turbulent flow and noise sources on a circular cylinder in the critical regime

The flow around a circular cylinder with long spanwise length has been investigated in the critical regime using a compressible wall-resolved Large Eddy Simulation (LES) for the first time. The flow at such a critical Reynolds number combines complex features: large favorable and adverse pressure gradient, separation and turbulence transition and flow reattachment. The results of the present simulation agree well with previous experimental and incompressible LES data, for the distribution of the mean wall-pressure coefficient that dominates the drag coefficient, and the skin-friction coefficient that illustrates the flow separation and reattachment behaviors. A weak reattachment is observed from the quasi-zero skin-friction in the reattachment region. A detailed study of the boundary-layer and shear-layer development around the cylinder with profiles of mean velocity and turbulence intensities confirms the transition, separation and reattachment behaviors shown by the skin-friction coefficient. The maximum tangential velocity and its location above the wall have also proven to be adequate measures of the edge velocity and associated boundary layer thickness. The Kelvin-Helmholtz instabilities have been observed in the shear layer and the ratio of the frequency of these instabilities and the fundamental vortex shedding frequency matches well with the existing scaling based on experimental data. The far-field noise obtained by both direct computation and acoustic analogy shows a dominant vortex shedding tone, but with additional broadband sources in the cylinder wake. These sound sources are evaluated from maps of filtered pressure signals and cross-correlation analysis of the pressure fluctuations around the cylinder and in the far-field.

Assessment of viscosity models that incorporate lag parameter scaling

Elliptic blending lag models combine a ‘stress-strain misalignment’ parameter with conventional k−ω or k−ε based linear eddy viscosity models. The lag parameter is effective in scaling the behavior of the eddy viscosity, particularly in the near wall region. This proves to be critical for prediction of non-equilibrium flows. Flow configurations demonstrating such regimes are evaluated with the new class of lag models and their performances are compared with frequently used RANS formulations (k−ωSST,k−ω-2006). A two-dimensional bump geometry that creates different pressure gradient regimes in the flow field was chosen as the first test case as RANS models often perform poorly in adverse pressure gradient flows. A swept configuration of similar bump geometry was also chosen to assess the performance of models for flows with transverse pressure gradients. Separation inside a 3D diffuser of varying inlet aspect ratios expanding in both wall-normal and spanwise directions was studied. Such a configuration incorporates the effect of multi-directional pressure gradient on a flow and usually proves challenging for linear eddy viscosity models. Finally, the models were tested on a complex 3D test case with a variation of NACA 0020 airfoil attached to a plate. This junction flow has been widely examined both experimentally and numerically in the past with emphasis being on the prediction of flow around the junction and subsequent downstream development. The lag models were observed to be successful in reproducing the mean flow quantities when compared to high fidelity/experimental solutions for the 2D and 3D flows.

Turbulence modeling effects on the aerodynamic characterizations of a NASCAR Generation 6 racecar subject to yaw and pitch changes

The characterization of a racecar’s aerodynamic behavior at various yaw and pitch configurations has always been an integral part of its on-track performance evaluation in terms of lap time predictions. Although computational fluid dynamics has emerged as the ubiquitous tool in motorsports industry, a clarity is still lacking about the prediction veracity dependence on the choice of turbulence models, which is central to the prediction variability and unreliability for the Reynolds Averaged Navier–Stokes simulations, which is by far the most widely used computational fluid dynamics methodology in this industry. Subsequently, this paper presents a comprehensive assessment of three commonly used eddy viscosity turbulence models, namely, the realizable [Formula: see text] (RKE), Abe–Kondoh–Nagano [Formula: see text], and shear stress transport [Formula: see text], in predicting the aerodynamic characteristics of a full-scale NASCAR Monster Energy Cup racecar under various yaw and pitch configurations, which was never been explored before. The simulations are conducted using the steady Reynolds Averaged Navier–Stokes approach with unstructured trimmer cells. The tested yaw and pitch configurations were chosen in consultation with the race teams such that they reflect true representations of the racecar orientations during cornering, braking, and accelerating scenarios. The study reiterated that the prediction discrepancies between the turbulence models are mainly due to the differences in the predictions of flow recirculation and separation, caused by the individual model’s effectiveness in capturing the evolution of adverse pressure gradient flows, and predicting the onset of separation and subsequent reattachment (if there be any). This paper showed that the prediction discrepancies are linked to the computation of the turbulent eddy viscosity in the separated flow region, and using flow-visualizations identified the areas on the car body which are critical to this analysis. In terms of racecar aerodynamic performance parameter predictions, it can be reasonably argued that, excluding the prediction of the %Front prediction, shear stress transport is the best choice between the three tested models for stock-car type racecar Reynolds Averaged Navier–Stokes computational fluid dynamics simulations as it is the only model that predicted directionally correct changes of all aerodynamic parameters as the racecar is either yawed from the 0° to 3° or pitched from a high splitter-ground clearance to a low one. Furthermore, the magnitude of the shear stress transport predicted delta force coefficients also agreed reasonably well with test results.