Numerical Investigation of Unsteady Transitional Flows in Turbomachinery Components Based on a RANS Approach

This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications. The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation. The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number, amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence of main flow unsteadiness. This revised version was published online in July 2006 with corrections to the Cover Date.     

DNS and LES of some engineering flows

In this paper, direct numerical simulations (DNS) and large eddy simulations (LES) of three engineering flows carried out in the author's research group are presented. The first example, simulated both with DNS and LES, is the flow in a low-pressure turbine cascade with wakes passing periodically through the cascade channel. In this situation, the laminar–turbulent transition of the boundary layers on the blade surfaces, which is strongly influenced by the passing wakes, is of special interest. Next, LES of the flow past the Ahmed body is presented, which is a car model with slant back. In spite of the fairly simple geometry, the flow around the model has many features of the complex, fully 3D flow around real cars. The third example, for which LES is presented, is the flow past a surface mounted circular cylinder of height-to-diameter ratio of 2.5. In this case also complex 3D flow develops with interaction of various vortices behind the cylinder. By means of these examples, the paper shows that complex turbulent flows of engineering relevance can be predicted realistically by DNS and LES, albeit at large cost. The methods are particularly suited and superior to RANS methods for situations where unsteadiness like shedding and large-scale structures dominate the flow, and DNS has evolved into an important tool for studying transition mechanisms.     

Distributed Roughness Effects on Transitional and Turbulent Boundary Layers

A numerical investigation is carried out to study the transition of a subsonic boundary layer on a flat plate with roughness elements distributed over the entire surface. Post-transition, the effect of surface roughness on a spatially developing turbulent boundary layer (TBL) is explored. In the transitional regime, the onset of flow transition predicted by the current simulations is in agreement with the experimentally based correlations proposed in the literature. Transition mechanisms are shown to change significantly with the increasing roughness height. Roughness elements that are inside the boundary layer create an elevated shear layer and alternating high and low speed streaks near the wall. Secondary sinuous instabilities on the streaks destabilize the shear layer promoting transition to turbulence. For the roughness topology considered, it is observed that the instability wavelengths are governed by the streamwise and spanwise spacing between the roughness elements. In contrast, the roughness elements that are higher than the boundary layer create turbulent wakes in their lee. The scale of instability is much shorter and transition occurs due to the shedding from the obstacles. Post-transition, in the spatially developing TBL, the velocity defect profiles for both the smooth and rough walls collapsed when non dimensionalized in the outer units. However, when compared to the smooth wall, deviation in the Reynolds stresses are observable in the outer layer; the deviation being higher for the larger roughness elements.     

Numerical investigation of secondary flows in a high-lift low pressure turbine

In turbomachines, secondary flows (or endwall flows) typically originate at the junction between endwalls and the blade surface. Within the blade passage, the strength of the secondary flows is amplified by the crossflow from the pressure to the suction surface of the blade. The enhanced mixing due to secondary flows induce additional losses into the system. This decreases the overall work output and also changes the flow incidence onto the downstream blade rows. Using a series of high-fidelity eddy resolving simulations, the current study attempts to provide an improved understanding for the complex flow physics over the endwalls of a high-lift Low Pressure Turbine (LPT) blade. The effect of three different inflow conditions has been studied. These include a laminar boundary layer (LBL), a turbulent boundary layer (TBL) and wakes with secondary flow (W&S) from an upstream blade row. For the simulations with TBL and W&S, precursor eddy resolving simulations were used to prescribe realistic inflows. The loss generation mechanisms were subsequently studied both at the endwall and the midspan, which includes evaluating the mass-averaged total pressure loss coefficient (Y_p) and the loss generation rate.When compared to LBL, additional disturbances from an incoming TBL and wakes with secondary flows enhanced the mixing within the blade passage resulting in a substantial increase in the total pressure loss. Prior to flow transition, incoming wakes with secondary flows increased the local loss generation rate at both the endwall and the midspan in the front portion of the blade passage (x/C_x < 0.84). In contrast, in the aft portion of the passage (x/C_x > 0.8), the incoming wakes effectively suppressed the separation bubble at the midspan thereby decreasing the local loss generation rate. It is also demonstrated that the wakes shed from the trailing edge at the mid-span mix out rapidly when compared to the passage vortex at the endwall.     

Direct Computations of Boundary Layers Distorted by Migrating Wakes in a Linear Compressor Cascade

A Direct Numerical Simulation (DNS) of flow in the V103 Low-Pressure (LP) compressor cascade with incoming wakes was performed. The computational geometry was chosen largely in accordance with the setup of the experiments performed by Hilgenfeld and Pfitzner (J Turbomach 126:493–500, 2004) at the University of the Armed Forces in Munich. The computations were carried out on the NEC-SX8 in Stuttgart using 64 processors and 85 million grid points. The incoming wakes stemmed from a separate DNS of incompressible flow around a circular cylinder with a Reynolds number of Re _d  = 3300 (based on mean inflow velocity and cylinder diameter). The boundary layer along the suction surface of the blade was found to separate and roll up due to a Kelvin–Helmholtz instability triggered by the periodically passing wakes. Inside the rolls further transition to turbulence was found to occur. The boundary-layer flow along the pressure surface did not separate, instead it underwent by-pass transition.     

DNS of heat transfer in transitional, accelerated boundary layer flow over a flat plate affected by free-stream fluctuations

Direct numerical simulations (DNS) of flow over and heat transfer from a flat plate affected by free-stream fluctuations were performed. A contoured upper wall was employed to generate a favourable streamwise pressure gradient along a large portion of the flat plate. The free-stream fluctuations originated from a separate LES of isotropic turbulence in a box. In the laminar portions of the accelerating boundary layer flow the formation of streaks was observed to induce an increase in heat transfer by the exchange of hot fluid near the surface of the plate and cold fluid from the free-stream. In the regions where the streamwise pressure gradient was only mildly favourable, intermittent turbulent spots were detected which relaminarised downstream as the streamwise pressure gradient became stronger. The relaminarisation of the turbulent spots was reflected by a slight decrease in the friction coefficient, which converged to its laminar value in the region where the streamwise pressure gradient was strongest.     

Statistical modeling of the turbulent transition in the boundary layer

A method of statistical modeling the flow in the boundary-layer transition region is proposed on the basis of experimental data on kinematics and dynamics of turbulent spots (Emmons spots) on a flat plate in an incompressible fluid. This method allows one to determine the intermittency with allowance for overlapping of the spots, the forces on the plate surface, and the flow field in the vicinity of the transition region if the field of the streamwise component of the mean velocity in the developed turbulent boundary layer is known as a function of the Reynolds number. In contrast to multi-parameter models of the transition, this approach makes it possible to avoid the use of physically meaningless parameter values.     

Surface flow visualization using the thermal wakes of small heated spots

 This note describes a surface flow visualization technique which uses the thermal wakes of an array of small heated spots to infer the local flow direction. The thermal wake is made visible using wide band thermochromic liquid crystals. The technique is illustrated using the endwall flow under a horseshoe vortex at the base of a right circular cylinder in a turbulent boundary layer. Comparisons to results generated using the oil of wintergreen technique were in good agreement. In addition to surface flow direction, the technique has the potential to be used to measure the heat transfer coefficient at each spot. Data are presented in terms of photographs of the actual visualization surface. The techniques is suitable for low speed flows. Received: 11 November 1996 / Accepted: 12 December 1997     

Experimental study of boundary-layer transition on an airfoil induced by periodically passing wake

 Hot-wire measurements are performed in boundary-layer flows developing on a NACA 0012 airfoil over which wakes pass periodically. The periodic wakes are generated by rotating circular cylinders clockwise or counterclockwise around the airfoil. The time- and phase-averaged mean streamwise velocities and turbulence fluctuations are measured to investigate the phenomena of wake-induced transition. Especially, the phase-averaged wall shear stresses are evaluated using a computational Preston tube method. The passing wakes significantly change the pressure distribution on the airfoil, which has influence on the transition process of the boundary layer. The orientation of the passing wake alters the pressure distribution in a different manner. Due to the passing wake, the turbulent patches are generated inside the laminar boundary layer on the airfoil, and the boundary layer becomes temporarily transitional. The patches propagate downstream at a speed smaller than the free-stream velocity and merge together further downstream. Relatively high values of phase-averaged turbulence fluctuations in the outer part of the boundary layer indicate the possibility that breakdown occurs in the outer layer away from the wall. It is confirmed that the phase-averaged mean velocity profile has two dips in the outer region of the transitional boundary layer for each passing cycle. Received: 12 February 2001 / Accepted: 6 July 2001 Published online: 23 November 2001     

Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects

Laminar separation and transition processes of the boundary layer developing under a strong adverse pressure gradient, typical of Ultra-High-Lift turbine profiles, have been experimentally investigated for a low Reynolds number case. The boundary layer development has been surveyed for different conditions: with steady inflow, with incoming wakes and with the synchronized forcing effects due to both incoming wakes and synthetic jet (zero net mass flow rate jet). In this latter case, the jet Strouhal number has been set equal to half the wake-reduced frequency to synchronize the unsteady forcing effects on the boundary layer. Measurements have been taken by means of a single-sensor hot-wire anemometer. For the steady inflow case, particle image velocimetry has been employed to visualize the large-scale vortical structures shed as a consequence of the Kelvin?CHelmholtz instability mechanism. For the unsteady inflow cases, a phase-locked ensemble averaging technique, synchronized with the wake and the synthetic jet frequencies, has been adopted to reconstruct the boundary layer space-time evolution. Results have been represented as color plots, for several time instants of the forcing effect period, in order to provide an overall view of the time-dependent transition and separation processes in terms of ensemble-averaged velocity and unresolved unsteadiness distributions. The phase-locked distributions of the unresolved unsteadiness allowed the identification of the instability mechanisms driving transition as well as the Kelvin?CHelmholtz structures that grow within the separated shear layer during the incoming wake interval and the synthetic jet operating period. Incoming wakes and synthetic jet effects in reducing and/or suppressing flow separation are investigated in depth.     

Direct Numerical Simulation of an Accelerating Channel Flow

Direct Numerical Simulation of a linearly accelerating channel flow starting from an initially statistically steady turbulent flow has been performed. It is shown that the response of the accelerating flow is fundamentally the same as that of the step-change transient flow described in He and Seddighi (J Fluid Mech 715:60–102, 2013). The flow structure again behaves like a boundary layer bypass transition undergoing three distinct phases, namely, (i) initially (pre-transition), the flow is laminar-like and the pre-existing turbulent structures are modulated resulting in elongated streaks leading to a strong and continuous increase in the streamwise fluctuating velocity but little changes in the other two components; (ii) it then undergoes transition when isolated turbulent spots are generated which spread and merge with each other, and (iii) they eventually cover the entire surface of the wall when the flow is fully turbulent. The similarity between the turbulence responses in the two flows is significant noting the contrasting features of the two types of mean flow unsteadiness: in the step-change flow, a sharp boundary layer is resulted in nearly instantly on the wall which closely resembles the spatially developing boundary layer, whereas the linear flow acceleration causes a continuing change of velocity gradient adjacent to the wall which propagates into the flow field with time, resulting in a gradually-developing boundary layer. There are, however, quantitative differences in the detailed behavior of the two flows and especially the transition is much delayed in the accelerating flow. It is also shown that the late pre-transition and early transition stages in both flows are characterised by significantly increased inwards sweep events in the wall region and ejection events in the outer layer. The flatness of the wall-normal velocity increases markedly near the wall around the time of onset of transition as a consequence of the huge intermittency of the velocity fluctuations. That is, there are long periods of quiescent flow coupled with occasional turbulent bursts.     

DNS of a Laminar Separation Bubble in the Presence of Oscillating External Flow

A three-dimensional Direct Numerical Simulation (DNS) of a laminar separation bubble in the presence of oscillating flow is performed. The oscillating flow induces a streamwise pressure gradient varying in time. The special shape of the upper boundary of the computational domain, together with the oscillating pressure gradient causes the boundary layer flow to alternately separate and re-attach. When the inflow decelerates, the shear layer starts to separate and rolls up. Simultaneously the flow becomes 3D. After a transient period, the phase-averaged reverse flow inside the separation bubble reaches speeds ranging from 20 up to 150% of the free-stream velocity. During these phases, the flow is absolutely unstable and self-sustained turbulence can exist. When the inflow starts to accelerate, a spanwise roll of turbulent flow is shed from the shear layer. Shortly after this, the remainder of the separation bubble moves downstream and rejoins with the shed turbulent roll. During the flow-acceleration phase, a patch of laminar boundary layer flow is obtained. Along the flat plate, a series of turbulent patches of flow travelling downstream, separated by laminar flow can be observed, reminiscent of boundary layer flow in a turbine cascade with periodically appearing free-stream disturbances.     

Flow stability analysis and excitation using pulsating jets

Classical flow stability applied to transition from laminar to turbulent flow may also describe the behavior of vorticity fluctuations created by a pulsating jet placed along a solid boundary. A numerical laminar flow experiment involving a pulsating jet placed along the surface of a duct with flow separation downstream, resulted in eliminating most part of the separated flow region. Applying the same approach to a turbulent flow, it was possible to develop a turbulent stability flow formulation and apply successfully turbulent pulsating jet flow separation control. To cite this article: D. Skamnakis, K. Papailiou, C. R. Mecanique 333 (2005).     

LES-based Study of the Roughness Effects on the Wake of a Circular Cylinder from Subcritical to Transcritical Reynolds Numbers

This paper investigates the effects of surface roughness on the flow past a circular cylinder at subcritical to transcritical Reynolds numbers. Large eddy simulations of the flow for sand grain roughness of size k/D = 0.02 are performed (D is the cylinder diameter). Results show that surface roughness triggers the transition to turbulence in the boundary layer at all Reynolds numbers, thus leading to an early separation caused by the increased momentum deficit, especially at transcritical Reynolds numbers. Even at subcritical Reynolds numbers, boundary layer instabilities are triggered in the roughness sublayer and eventually lead to the transition to turbulence. The early separation at transcritical Reynolds numbers leads to a wake topology similar to that of the subcritical regime, resulting in an increased drag coefficient and lower Strouhal number. Turbulent statistics in the wake are also affected by roughness; the Reynolds stresses are larger due to the increased turbulent kinetic energy production in the boundary layer and separated shear layers close to the cylinder shoulders.     

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a ‘high-lift’ and an ‘ultra high-lift’ turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in ‘ultra high-lift’ design when compared to the ‘high-lift’ design. Stronger ‘Klebanoff streaks’ are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The ‘part-span’ Kelvin–Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging.     

An experimental investigation of unsteady turbulent-wake/boundary-layer interaction

An experimental investigation of unsteady-wake/boundary-layer interaction, similar to that occurring in turbomachinery, has been conducted in a specially modified wind tunnel. Unsteadiness in a turbomachine is periodic in nature, due to the relative motion of rotor and stator blades, resulting in travelling-wave disturbances that affect the blade boundary layers. In the experimental rig, travelling-wave disturbances were generated by a moving airfoil apparatus installed upstream of a flat plate to provide a two-dimensional model of a turbomachine stage. The boundary layer on the flat plate was tripped near the leading edge to generate a turbulent flow prior to interaction with the wakes, and measurements of velocity throughout the boundary layer were taken with a hot-wire probe. The Reynolds number, based on distance along the plate, ranged from 0.144×10⁵ to 1.44×10⁵, and all data were reduced through a process of ensemble averaging. Due to the nonlinear interactions with the boundary layer, the travelling discrete frequency wakes were found to decrease the shape factor of the velocity profile and to increase the level of turbulent fluctuations. Unlike the phase advance found with stationary-wave external disturbances, velocity profiles subject to the travelling wake fluctuations exhibited increasingly negative phase shifts from the free-stream towards the wall.     

Direct numerical simulation of the transition to turbulence in a supersonic boundary layer on smooth and rough surfaces

Direct numerical simulations of instability development and transition to turbulence in a supersonic boundary layer on a flat plate are performed. The computations are carried out for moderate supersonic (free-stream Mach number M = 2) and hypersonic (M = 6) velocities. The boundary layer development is simulated, which includes the stages of linear growth of disturbances, their nonlinear interaction, stochastization, and turbulent flow formation. A laminar–turbulent transition initiated by distributed roughness of the plate surface at the Mach number M = 2 is also considered.     

Analysis of DNS and LES of Flow in a Low Pressure Turbine Cascade with Incoming Wakes and Comparison with Experiments

The flow around a low-pressure turbine rotor blade with incoming periodic wakes is computed by means of DNS and LES. The latter adopts a dynamic sub-grid-scale model. The computed results are compared with time-averaged and instantaneous measured quantities. The simulation sreveal the presence of elongated flow structures, stemming from the incoming wake vorticity, which interact with the pressure side boundary layer. As the wake approaches the upstream half of the suction side, its vortical structures are stretched and align with the main flow, resulting in an impingement at virtually zero angle of attack. Periodically, in the absence of impinging wakes, the laminar suction side boundary layer separates in the adverse pressure gradient region. Flow in the laminar separation bubble is found to undergo transition via a Kelvin–Helmholtz instability. Subsequent impingement of the wake inhibits separation and thus promotes boundary layer reattachment. LES provides a fair reproduction of the DNS results both in terms of instantaneous, phase-averaged, and time-averaged flow fields with a considerable reduction in computational effort. This revised version was published online in July 2006 with corrections to the Cover Date.     

Visualizing supersonic inlet duct unstart using planar laser Rayleigh scattering

Planar laser Rayleigh scattering (PLRS) from condensed CO₂ particles is used to visualize flow structure in a Mach 5 wind tunnel undergoing unstart. Detailed flow features such as laminar/turbulent boundary layers and shockwaves are readily illustrated by the technique. A downstream transverse air jet, inducing flow unchoking downstream of the jet, is injected into the free stream flow of the tunnel, resulting in tunnel unstart. Time sequential PLRS images reveal that the boundary layer growth/separation on a surface with a thick turbulent boundary layer, initiated by the jet injection, propagates upstream and produces an oblique unstart shock. The tunnel unstarts upon the arrival of the shock at the inlet. In contrast, earlier flow separation on the opposite surface, initially supporting a thin laminar boundary layer, is observed when a jet induced bow shock strikes that surface. The resulting disturbance to this boundary layer also propagates upstream and precedes the formation of an unstart shock.