Adverse Pressure Gradient Research Articles

Analysis of the effect of vortex reduction structures on submarine tonal noise via frequency-domain method employing thickness noise source

In this study, the acoustic effect of unfavorable flow, such as horseshoe vortex (HSV) generated around the appendages, on propeller radiated noise was analyzed. To analyze this, a frequency-domain noise model is developed, which can predict the noise of an underwater propeller placed in a non-uniform wake. To clearly analyze the acoustic effects of HSV around appendages, vortex reduction structures (VRS) are installed at the junctions of a submarine where HSV is generated intensively, and the acoustic effects before and after the installation of the VRS are compared. In a hydrodynamic analysis of submarines, adverse pressure gradients are resolved and the HSV is suppressed after installing the VRS. In a hydroacoustic analysis, directivity and contribution analysis by radius and order are performed. In the directivity analysis, when the VRS are installed, the first blade-passing frequency (BPF) is reduced by 5∼12 dB, while the second BPF is reduced by up to 20 dB. Through the contribution analysis involving radius, it was found that installing VRS on the rudder is effective in reducing the first BPF noise. By contrast, in the second BPF, the VRS installed on the sail was more effective in noise reduction than that on the rudder.

Active Flow Control of Helicopter Rotor Based on Coflow Jet

When a helicopter rotor undergoes flow separation, the drag of the rotor increases substantially, as does the power demand, which seriously affects the aerodynamic performance and flight safety of the helicopter. Therefore, it is crucial to research how to suppress the flow separation of rotor blades. An active control technique based on a coflow jet (CFJ) at the rotor blade tip was employed in this study to suppress the flow separation over the rotor. The mechanisms and behavior were investigated. The rotor flow field was numerically simulated by solving the Reynolds-averaged Navier–Stokes equations with the finite volume method. The turbulence model was k − ω SST, and the rotor motion was simulated using the overset mesh technique. After applying CFJ control, the airflow from the injection slot at the leading edge of the rotor increased the energy of the mainstream in the near-wall area, which enhanced its ability to resist the adverse pressure gradient. A flow separation was effectively suppressed, both on the advancing and retreating sides, which improved the aerodynamic performance of the rotor. During the whole rotation period, the thrust coefficient of the rotor increased by up to 5.6%, the moment coefficient decreased by as much as 26.8%, and the equivalent lift-to-drag ratio increased by up to 44.0%. Moreover, the effects of the CFJ parameters on the flow separation suppression of the rotor are researched. These results may provide a foundation for the development of aerodynamic performance improvement for helicopter rotor based on a CFJ.

Aerodynamic performance characterization of bio-inspired wings with leading edge tubercles at low Reynolds number

On the observation of biomimetic Humpback Whale (HW) flippers, the airfoil aerodynamic performance characteristics are explored. The Leading Edge (LE) tubercle geometry was inspired by the flipper of HW that has rounded LE protuberances and tapered trailing edge configurations. The tubercles have excellent flow control characteristics at the post-stall region. Aerodynamic characteristics of airfoils such as NACA0015 and NACA4415 with LE tubercles are experimentally and numerically investigated at the low Reynolds number about Re = 1.83 × 105. The bio-inspired modified airfoils (HUMP 0015 and 4415) are designed with the amplitude to wavelength ratio [Formula: see text] of 0.05. The numerical simulation over the modified airfoils shows that, at higher Angle of Attack the flow separation is delayed in the peak region whereas the early flow separation is observed in the trough region adjacent to the LE. The boundary layer flow separation analysis is done extensively through numerical simulations and the velocity vector profiles are captured at different chordwise positions. The stall delay phenomenon is observed through the outcome of this research that specifically insists at the peak region of tubercles. Computation of Coefficient of pressure [Formula: see text] distribution is also done by both numerical and wind tunnel experiments. Analysis of [Formula: see text] distribution allows the identification of critical regions that initiate the adverse pressure gradient and region of flow separation. It is a novel effort to predict the Coefficients of Lift [Formula: see text] and Drag [Formula: see text] concerning the bio-inspired airfoils through [Formula: see text] distribution such that the influence of flow separation and vortex distribution are characterized for the modified and baseline airfoils. Comparison of [Formula: see text], [Formula: see text], and [Formula: see text] between the baseline and modified airfoils reveal the enhanced momentum transfer characteristics of bio-inspired tubercles.

Design of Curved Annular Diffusers II: Using Splitter Blades

Abstract The use of splitter blade as a passive flow control mechanism in the design of separation free aggressive annular diffuser is explored through computational fluid dynamics simulations. The fundamental working principle of a splitter blade in case of a two-dimensional rectangular diffuser and an annular diffuser is discussed. The effects of splitter blade configuration on the end-wall adverse pressure gradients are discussed. An aggressive diffuser design space is identified with ducts of maximum slope of 50 deg and maximum divergence angle between the outer and inner walls of 10 deg for axial-length to inlet height ratio ranging from 1.25 to 2.5. One or more splitter blades are employed in the duct to eliminate flow separation for all the ducts in the aggressive design space considered. Requirement of number of splitter blades in the aggressive design space is demarcated. Performance charts for the ducts in this aggressive design space are also established.

Interaction of a shock train with inherent isentropic waves in a curved isolator

Shock-train transitions in simplified curved isolators are carefully studied by simulation. The results show the shock-train behavior is subject to the complex pressure field created by the duct deflection, eventually presenting five modes during a backpressure-varying process. Of them, the most special one is the abrupt shock-train leap. It appears as the leading shocks interact with an adverse pressure gradient and follows a different path after a reversal of the direction the backpressure takes, which causes a shock-train hysteresis. If the curvature increases, the leap phenomenon, together with the related hysteresis, grows in number and intensity. Analysis indicates the background pressure gradients stem from the inherent left-running expansion waves and right-running compression waves. They control alternately the near-wall flow state, provoking the cyclic changes in the pressure gradient sign. Unlike the former, the latter can enhance separation through a positive feedback mechanism, rendering the shock train highly sensitive to backpressure. This is why the leap occurs. Comparing with the previously reported shock-induced leap indicates that there is a marked similarity in their behaviors, suggesting the irrelevance of the occurrence of a leap to the category of incident waves. Nevertheless, a delay in the onset usually follows a compression-wave-typed leap, which reflects that there is a triggering threshold for an incident wave. Given the fact that no local separation is provoked by the compression waves, it is speculated that the threshold should lie below the criterion for causing a separation, as opposed to the impression from the previous research.

Numerical Simulation of the Turbulent Boundary Layer with an Adverse Pressure Gradient

Numerical Simulation of the Turbulent Boundary Layer with an Adverse Pressure Gradient

Sensor-size-related attenuation correction of wall pressure spectra measurements

A correction model is presented for sensor-size-related high-frequency attenuation when measuring the wall pressure fluctuations beneath turbulent boundary layers. The model is developed based on the wall pressure spectra measured on a flat plate model using sensors of different sizes and types. The measurement covers the range of Reynolds numbers, Reθ, based on the momentum thickness between 1500 and 11 400, including flows with adverse and favorable pressure gradients, which were produced by a National Advisory Committee for Aeronautics (NACA) 0012 airfoil installed above the flat plate. The present model follows the principle of the Corcos correction and is expressed with a simple mathematical form. Major improvements compared with the Corcos correction are made with regard to determining the effective sensing area and the convection velocity for a specific sensor. With the help of convection velocity modeling, the present correction model can be applied to flows in pressure gradients with high accuracy. To assess the generality of the assumptions, the model is used to correct the wall pressure spectra measured at different test facilities with different sensor types, covering a large range of Reynolds numbers, 1.6×103<Reθ<1.19×105.

Transient nature of secondary vortices in an axial compressor stage with a tandem rotor

An efficient and compact design of a compressor continues to be a challenging area of research. The unavoidable streamwise adverse pressure gradient together with passage transverse pressure gradient restricts the maximum allowable blade turning. Tandem blading is an interesting concept for increasing the pressure rise by permitting a higher blade turning angle. The energized flow through the tandem blade nozzle gap helps to minimize the possibility of flow separation over the suction surface of the aft blade. However, a coherent transient analysis of a tandem rotor stage in an axial compressor is yet to be well explored. In the present paper, the complex flow field over a tandem rotor and the succeeding stator passage is analyzed in detail. Although the tandem rotor increases the flow turning and diffusion effect, the presence of separate trailing edge wakes and hub corner vortex causes early onset of flow separation over the stator suction. The flow structures developed within the rotor and the stator passages at different time instances are highlighted with the help of limiting streamlines and iso-surface Q-criterion superimposed with entropy contours. The results indicate that within the rotor passage, transient flow features are observed near the hub corner region close to the aft blade trailing edge rather than the tip region. When the rotor passes the stator leading edge, the rotor trailing edge leakage flow at the hub is entrained into the stator leading edge reverse flow region. This is then further circumferentially dragged into the mid-passage region. The interference of multiple rotor wakes with the stator leading edge leads to the formation of longitudinal and arch like separation vortices at the stator-hub and the stator-casing regions, respectively. These separation vortices grow in size while being convected downstream. Eventually, as time progresses, the vortices split and shed periodically from the stator surface. The present investigation highlights the requirement of a new stator design in a tandem rotor–conventional stator configuration. Such designs could further magnify the significant aerodynamic performance obtained using a tandem configuration.

The pulsatile 3D-Hemodynamics in a doubly afflicted human descending abdominal artery with iliac branching

The study of patient-specific human arterial flow dynamics is well known to face challenges like a) apt geometric modelling, b) bifurcation zone meshing, and c) capturing the hemodynamic prone to variations with multiple disease complications. Due to aneurysms and stenosis in the same arterial network, the blood flow dynamics get affected, which needs to be explored. This study develops a new protocol for accurate geometric modelling, bifurcation zone meshing and numerically investigates the arterial network with abdominal aortic aneurysms (AAA) and right internal iliac stenosis (RIIAS). A realistic arterial model is reconstructed from the computed tomography (CT) data of a human subject. To understand the combined effect of the aneurysm and aortoiliac occlusive diseases in a patient, an arterial network with AAA, RIIAS, multiple branches tapering, and curvature has been considered. Clinically significant pulsatile blood flow simulations have been carried out to trace the alteration in the flow dynamics with multiple pathological complications under consideration. The transient blood flow dynamics are investigated via wall shear stress, wall pressure, velocity contour, streamlines, vorticity, and swirling strength. During the systolic deceleration phase, the rhythmic nested rapid secondary oscillatory WSS, adverse pressure gradients, high WSS, and high WP bands are noticed. Also, the above studies will help researchers, clinicians, and doctors understand the influence of morphological changes on hemodynamics in cardiovascular studies.

Turbulent flow over a cylinder confined in a channel at Re = 3,900

This paper presents data from numerical simulation of the flow over a cylinder confined in a channel at Reynolds number of 3,900. Direct numerical simulation (DNS) of the flow field from blockage ratio of 0 (i.e. the canonical flow over an unconfined cylinder) up to blockage ratio of 0.7 have been performed. At large blockage ratios, an adverse pressure gradient develops and the boundary layer on the channel walls separates and interacts with the cylinder wake. It is observed that the interaction gives rise to complex flow dynamics, affecting the size of the wake, making the wake asymmetric and also resulting in a decrease in the intensity of the turbulent fluctuations in the shear layer. Analysis of the spectra of the turbulent near wake shows an increase of the shedding frequency of the Kármán vortices as blockage ratio is increased. This occurs up to around blockage ratio of 0.7 where it is observed that the formation and shedding of coherent Kármán vortices no longer occur. For all except the blockage ratio of 0.5 case, the frequency of the shear layer is well approximated by the natural frequency of the shear layer instabilities obtained from linear stability theory. In all of these cases, there is a peak of energy associated with subharmonics of the shear layer frequency indicating pairing of the Kelvin–Helmholtz vortices in the shear layer.

Effect of turbulence intensity on aerodynamic characteristics of extended trailing edge airfoil

PurposeThis paper aims to study the extended trailing edge airfoil for a range of angle of attack at different intensities of turbulence.Design/methodology/approachIn this paper, an experimental study on NACA 0020 airfoil with thin extended trailing edge modification of amplitude of h = 0.1c, 0.2c and 0.3c at the Reynolds number of 2.14 × 105 are tested. The research was carried out for an angle of attack ranging from 0° = α = 35° for the turbulence intensity of 0.3%, 3%, 5%, 7% and 12%. From the experimental readings, the surface pressures are scanned using a Scanivalve (MPS2464) pressure scanner for a sampling frequency of 700 Hz. The scanned pressures are converted to aerodynamic force coefficient and the results are combined and discussed.FindingsThe airfoil with the extended trailing edge will convert the adverse pressure gradient to a plateau pressure zone, indicating the delayed flow separation. The CL value at higher turbulence intensity (TI = 12%) for the extended trailing edge over perform the base airfoil at the post-stall region. The maintenance of flow stability is observed from the spectral graph.Practical implicationsA thin elongated trailing edge attached to the conventional airfoil serves as a flow control device by delaying the stall and improving the lift characteristics. Additionally, extending the airfoil's trailing edge helps to manage the performance of the airfoil even at a high level of turbulence.Originality/valueDistinct from existing studies, the presented results reveals how the extended trailing edge attached to the airfoil performs in the turbulence zone ranging from 0.3% to 12% of TI. The displayed pressure distribution explains the need for increasing trailing edge amplitude (h) and its impact on flow behaviour. The observation is that extended trailing edge airfoil bears to maintain the performance even at higher turbulence region.

A driving mechanism of near-wall turbulence subject to adverse pressure gradient in a plane Couette flow

The effect of adverse pressure gradient (APG) on near-wall turbulence is studied, with a particular attention to the turbulence production mechanism. A plane turbulent Couette flow is considered for several values of constant APG in the lower wall region. A direct numerical simulation (DNS) in a large computational domain shows that turbulence near the lower wall continues to exist even at sufficiently large APGs. On increasing the APG, the cross-streamwise turbulence intensities increase, and the near-wall streaks gradually disappear. A linear analysis using the optimal transient growth indicates that the APG inhibits the generation of near-wall streaks due to the significant reduction of the mean shear in the region near the lower wall. The turbulent fluctuation dynamics beyond the linear regime is studied with a DNS in a minimal flow unit. The near-wall self-sustaining process involving streaks is significantly weakened or destroyed as APG increases, while the turbulent fluctuations become more isotropic and localised. Using a conditional averaging analysis, a new mechanism of near-wall turbulence production under strong APG is uncovered. This mechanism is initiated by the wall-normal nonlinear transport of an outer wall-normal velocity fluctuation to the near-wall region. The transported wall-normal velocity fluctuation is subsequently amplified via the Orr mechanism, resulting in the non-zero turbulence production involving spatially localised vortical structures. This mechanism is also confirmed by DNS of the flow in a large computational domain, where strong correlation between the wall-normal nonlinear transport and turbulence production is observed.

Experimental and Numerical Investigation of Stall Mechanism in Centrifugal Pump Impeller

Stall is a complex flow phenomenon in centrifugal pumps at part load conditions. However, there is no clear description of the stall evolution process and mechanism, which is critical for stall control. Based on a high-frequency Particle Image Velocimetry (PIV) system (10k Hz) and a non-refraction experimental bench, emphasis is laid on the flow structures near the initial stall conditions. The results show that as the flow rate decreased, the flow separation occurred at the middle of the blade suction side and then evolved into a stall vortex which moved to the impeller’s inlet direction and kept growing. Subsequently, it broken into two vortexes when reaching the location where the impeller cross-sectional area is the smallest. One stall vortex continued its motion toward the passage inlet direction, while the other vortex separates to the impeller outlet. As the stall vortex’s size at the impeller inlet enlarged, the flow incident direction at the impeller inlet was directed to the blade suction side, which caused the stall vortex on the suction side to disappear. The stall mechanism is explained in detail using both experiments and numerical simulations. Meanwhile, the Scale Adaptive Simulation-Shear Stress Transport (SAS-SST) hybrid model is used to simulate several flow rate conditions near the stall initial stage. The findings indicate that the increasing adverse pressure gradient and the high-pressure zone move along the suction blade towards the impeller inlet as the flow rate is reduced; however, the relative velocity is constantly decreasing. When the fluid can’t provide enough kinetic energy to maintain its continuous flow along the suction surface, flow separation occurs. The stall vortex, which results from flow separation, blocks the passage impeller. The increasing adverse pressure from the impeller outlet to the inlet is the main cause of flow separation; and the adverse pressure gradient is a major manifestation of the stall vortex.

Genesis of Antibiotic Resistance (AR) LXXXI: Turbulence Modeling of Simplified Severe Sepsis Protocol‐2 (SSSP‐2), NCT01663701: ERP Induced Fluid Volume Expansion Confer Transition from Laminar to Turbulence by Discontinuity

NCT01663701(PMID:28973227) observed that a primary outcome of in‐hospital mortality (ihm) occurred in 51 of 106 patients (48.1%) in the sepsis protocol group vs 34 of 103 patients (33.0%) in the usual care group while the vital status after hospital discharge at day 28 reported for 97 patients in each study group; 28‐day mortality was 67.0% with the sepsis protocol vs 45.3% with usual care. Hypothesis: Based on the data on risk of ihm by subgroup for patients treated with the sepsis protocol vs usual care (Fig3), compared to elements of sepsis resuscitation (Table 2), and baseline characteristics of the patients (Table 1), we hypothesize that the discontinuity in fluid volume due to ERP is the pivotal determining factor for an exacerbated mortality rate in NCT0166370. Relevance of Central Venous Pressure(CVP) or Jugular Venous Pressure (JVP) for the Determination of Fluid Overload(PMID: 23774337, PMID: 24132054):NCT01663701, p1237, Table 1: The JVP data indicate that the baseline: by proximity to the sternal angle, ≥4cm below: sepsis protocol cohort: 32.1% vs usual care: 40.8%; 1‐3cm below:sepsis protocol cohort: 28.3% vs usual care 21.4%; At the sternal angle, 20.8% vs 27.2%; ≥1 cm above: sepsis protocol 20.8% vsusual care 10.7%. Cause(s) of elevated CVP or JVP:A plausible cause would be RV failure (pulmonary edema!) due to fluid volume overload by excessive fluid administration. Geometry, Governing Eq. & Analysis: The mass continuity eq: 2.17, (p14‐ISBN‐13:978‐0521598866); where V1= fluid velocity, ρ1= fluid density, at terminal arteriole (cross‐sectional area) = A1and tis time interval dt, prior to ERP, length dl1=V1dt mass that enters the A1in the time interval is: dm1=ρ1dV1= ρ1A1dl1=ρ1A1v1dt. After the ERP, the expanded fluid volume passing through metarteriole (cross‐sectional area) =A2and length dl2=V2dt in the time interval dt is=dm2=ρ2dV2=ρ2A2dl2=ρ2A2v2dt. As per the mass continuity equation, (flow at any given point in a closed hydraulic system will be equal to flow at any other points) an equal amount of mass that enters the area A1in the time interval dt, must pass through area A2,therefore, dm1=dm2or ρ1A1v1dt=ρ2A2v2dt.Dividing by dt, will result ρ1A1v1=ρ2A2v2for a steady flow pattern referred to as mass continuity equation for steady flow. Our simulation analysis implicates that for the ERP induced fluid volume overload fluid flow is A1v1≠A2v2 . The rationale is that, the laminar fluid flow is in streamlines with equal space but ERP induced will not be in streamline but widely spaced, ⬆viscosity, ⬆ rate of LPE aggregation and ⬇velocity, ⬆torque & drag with an unknown angular momentum, on endothelial layer in terminal arteriole. Prospects: It is suggested that the total mass of expanded fluid vol. within 6 hrs, entering/exiting the terminal arteriole (Cerebral BBB) elicit CCP rupturing the pre‐capillary vessels due to an adverse pressure gradient (APG). Differential shear stress due to APG, induce temporal regulation of ARGR expression in clinical persisters in vivo w/ orw/o vasoplegia may have been the cause for an exacerbated mortality in NCT01663701.

K-kL TÜRBÜLANS MODELİNİN UYGULAMASI, DOĞRULAMASI VE GiRDAP YAKALAMA YETENEKLERİNİN DEĞERLENDİRİLMESİ

This study presents the first results of a new turbulence model implementation in our compressible finite volume CFD solver. The k - kL turbulence model is one of the newest two-equation models, and it is based on the ideas of Rotta’s two-equation model. Various research groups progressively develop the model, and it is maturing rapidly. Reports suggest that the k - kL turbulence model provides superior results compared to the other two-equation turbulence models in specific problems. The improved solutions are observed mainly for the flows with high adverse pressure gradients, the blunt-body wakes and jet interactions. We have implemented the k - kL model (with the standard designation of k-kL-MEAH2015) in our solver, and we are testing it rigorously. This paper presents our results on standard turbulence test cases: subsonic flat plate and subsonic wall-mounted bump. The results compare well with the reference study previously presented and published by model developers. The design of the k - kL model prevents excessive production of turbulence and dissipation; hence it preserves vortices significantly better than the other two-equation models. The implemented model is also tested with a transonic fin trailing vortex case to support this statement. Results show that the k-kL model yields considerably better results than the SST turbulence model in cases including vortices.

The structure of near-wall re-entrant flow and its influence on cloud cavitation instability

The so-called ‘re-entrant jet’ is fundamental to periodic cloud shedding in partial cavitation. However, the exact physical mechanism governing this phenomenon remains ambiguous. The complicated topology of the re-entrant flow renders whole-field, detailed measurement of the re-entrant flow cumbersome. Hence, most studies in the past have derived a physical understanding of this phenomenon from qualitative analyses of the re-entrant jet. Thus, quantitative studies are scarce in the literature. In this work, we present a methodology to experimentally measure the re-entrant flow below the vapour cavity in an axisymmetric venturi. The axisymmetry of the flow geometry is exploited to image tracer particles in the near-wall re-entrant flow. The main objective of employing tomographic imaging and subsequent velocimetry is to resolve the thickness and the velocity of the re-entrant flow. Additionally, phase-averaging conditioned on cavity length sheds light on the temporal evolution of re-entrant flow in a shedding cycle. The measured re-entrant film is as thick as sim 1.2 mm for a maximum cavity length of sim 0.9 D_{t}, where D_{t} is the venturi throat diameter. However, the re-entrant film thickness at higher cavitation number is measured to be about 0.5 mm. Further, the re-entrant flow is seen to attain a maximum velocity up to half the throat velocity as the vapour cavity grows in time and the re-entrant flow thickens. We observe that a complex spatio-temporal evolution of re-entrant flow is involved in the cavity detachment and periodic cloud shedding. Finally, we apply the demonstrated methodology to study the evolution of the near-wall liquid flow, below the vapour cavity in different cavity shedding flow regimes. The role of two main mechanisms responsible for cloud shedding, i.e. (i) the adverse-pressure gradient driven re-entrant jet, and (ii) the bubbly shock wave emanating from the cloud collapse are quantitatively assessed. We observe that the thickness of the re-entrant liquid film with respect to the cavity thickness can influence the cavity shedding behaviour. Further, we show that both the mechanisms could be operating at a given flow condition, with one of them dominating to dictate the cloud shedding behaviour.Graphical abstract

Numerical investigation of centrifugal compressor stability enhancement using vaned diffuser endwall contouring technology

To improve the stable operating range of centrifugal compressor stage, endwall contouring technology is introduced on the hub-side wall of the vaned diffuser for NASA CC3 centrifugal compressor as a promising technique to redistribute the flow field near the endwall in this paper. The main contents of this paper are listed as follows. First, a specific parameterized endwall contouring guideline is developed based on sinusoidal function and Bézier curve, and three factors are considered, namely, peak height, peak radial position, and frequency coefficient. Then, centrifugal compressor stages with baseline diffuser and contoured endwall diffusers are numerically investigated to reveal the influence of endwall contouring on the stable operating range. Results show that endwall contouring is an effective method to achieve stability enhancement with no evident reduction in stage performance on the design point. CEW13-12 has the most successful combination of endwall contouring parameters, and stall margin is increased by up to 40% for CEW13-12. Finally, the influence mechanism of endwall contouring on the stable operating range is discussed. At the near stall condition, the contouring endwall forces the fluid within the semi vaneless space to deflect toward the suction side to increase the momentum of low-energy fluid in the suction surface boundary layer and reduce the adverse pressure gradient on the suction side, which delay the development of flow separation on the vane leading edge near the shroud side to suppress the onset of rotating stall. At the near choke condition, the contouring endwall has more potential to increase the throat area, resulting in a decrease of throat blockage to improve choke margin. The results show that the endwall contouring technology is a reliable method to achieve stability enhancement of centrifugal compressor stage.

Adaptive Determination of the Optimal Exchange Location in Wall-Modeled Large-Eddy Simulation

Wall-modeled large-eddy simulation introduces a modeling interface (or exchange location) separating the wall-modeled layer from the rest of the domain. The current state-of-the-art is to rely on user expertise when choosing where to place this modeling interface, whether this choice is tied to the grid or not. This paper presents a postprocessing algorithm that determines the exchange location systematically. The algorithm is based on a model for the error in the predicted wall shear stress and a model for the computational cost, and then finds the exchange location that minimizes a combination of the two. The algorithm is tested both a priori and a posteriori using an equilibrium wall model for the flow over a wall-mounted hump, a boundary layer in an adverse pressure gradient, and a shock/boundary-layer interaction. The algorithm produces exchange locations that mostly agree with what an experienced user would suggest, with thinner wall-modeled layers in nonequilibrium flow regions and thicker wall-modeled layers where the boundary layer is closer to equilibrium. This suggests that the algorithm should be useful in simulations of realistic and highly complex geometries.

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.

An adverse-pressure-gradient turbulent boundary layer with nearly constant up to

In this study, a new well-resolved large-eddy simulation of an incompressible near-equilibrium adverse-pressure-gradient (APG) turbulent boundary layer (TBL) over a flat plate is presented. In this simulation, we have established a near-equilibrium APG over a wide Reynolds-number range. In this so-called region of interest, the Rotta–Clauser pressure-gradient parameter $\beta$ exhibits an approximately constant value of around 1.4, and the Reynolds number based on momentum thickness reaches ${\textit {Re}}_{\theta }=8700$ . To the best of the authors’ knowledge, this is to date the highest ${\textit {Re}}_{\theta }$ achieved for a near-equilibrium APG TBL under an approximately constant moderate APG. We evaluated the self-similarity of the outer region using two scalings, namely the Zagarola–Smits and an alternative scaling based on edge velocity and displacement thickness. Our results reveal that outer-layer similarity is achieved, and the viscous scaling collapses the near-wall region of the mean flow in agreement with classical theory. Spectral analysis reveals that the APG displaces some small-scale energy from the near-wall to the outer region, an effect observed for all the components of the Reynolds-stress tensor, which becomes more evident at higher Reynolds numbers. In general, the effects of the APG are more noticeable at lower Reynolds numbers. For instance, the outer peak of turbulent-kinetic-energy (TKE) production is less prominent at higher $Re$ . Although the scale separation increases with ${\textit {Re}}$ in zero-pressure-gradient TBLs, this effect becomes accentuated by the APG. Despite the reduction of the outer TKE production at higher Reynolds numbers, the mechanisms of energisation of large scales are still present.