Laminar-turbulent boundary layer transition

Underlying Flow Regime 3-04 © copyright ERCOFTAC 2004

Description

Preface

Laminar-turbulent transition in boundary layers influences performance of many technical devices. The location of the onset and the extension of transition are of major importance since they determine drag and lift forces and heat fluxes that are crucial for an overall efficiency and performance of a variety of machinery and devices. One the most common examples of the machinery where the laminar-turbulent transition is of particular importance is turbomachinery and gas and aero-engine turbines in particular. Despite a technical maturity of gas turbines the research, optimisation and development of this technology still continues, as increasing the engines performance by a fraction of a percent or improving the turbine cooling in face of ever-increasing turbine inlet temperature provides enormous economic benefits. Hence the understanding of the laminar-turbulent transition in gas turbine cascades plays very important role in their optimisation (Mayle,1991).

In general there are three important transition regimes. The first is called natural transition. This transition regime can appear in practice only if free stream turbulence is very low that happens only occasionally in technical applications. Such a mode of transition begins with a weak instability in the laminar boundary layer as described first by Tollmien and Schlichting (see Schlichting, 1979) and proceeds through various stages of amplified instability to fully turbulent flow. The linear stability theory plays an important role in research and understanding of this transition regime.

The second mode, frequently called bypass transition following Morkovin (1969), is caused by interaction of the vortex structures in the free stream and the boundary layer and completely bypasses the Tollmien-Schlichting waves. This is a common mode of transition in the case of turbomachinery flows.

The third mode, called separated-flow transition following Mayle (1991), occurs in a separated boundary layer and may or may not involve the mechanism of Tollmien-Schlichting waves. This mode of transition appears in the boundary layers with strong adverse pressure gradient particularly in the compressors and low-pressure turbines (Howell and Hodson, 2001). The pressure gradient, apart from turbulence intensity, is one of the most important parameters influencing laminar-turbulent transition. The influence of the pressure gradient on the transition is presented among others by Abu-Ghannam & Shaw (1980) and Gostelow et al. (1994). Experimental study of the transition under favourable pressure gradient was in turn showed by Volino & Simon (1995, 1997).

In technical applications due to high turbulence level of the incoming flow the bypass transition is the dominant mode and hence its modelling is crucial for practice.

The LES and DNS developing rapidly during last decade still cannot be applied in practical industrial cases due to limited computer resources. However, the LES and DNS is already widely used to generate test cases in simpler geometry to verify and validate transition models. As it was already mentioned the linear methods cannot be applied to bypass transition hence the RANS methods with appropriately modelled transitional boundary layer remain the only presently applicable engineering tool to study the transitional flows. Existing turbulence models for laminar-turbulent transition boundary layer, as reviewed by Savill (1993,1996) and recently by Menter et al. (2002) are highly empirical and require experimental data for the proper calibration. Following the results of the TRANSPRETURB European Network on transition prediction the two following approaches to model bypass transition in the industrial applications can be pointed out: low-Reynolds number turbulence models (Jones & Launder, 1972, Priddin, 1975, Rodi & Scheuerer 1984, Hadzic 1999) and experimental correlations that relate the free stream turbulence intensity to the transition Reynolds number (Mayle, 1991, Abu-Ghannam & Shaw, 1980). According to Menter et al. (2002) the ability of a low-Reynolds turbulence model to predict transition seems to be coincidental, as the calibration of the damping functions is based on the viscous sublayer behaviour and not on transition from laminar to turbulent flow. Industry favours to use experimental correlations which are usually linked with a two-equation turbulence models by modification of the turbulent production term based on an intermittency equation (Suzen & Huang, 2000) or by the more complex conditioned equations (Steelant & Dick, 1996). However, Menter et al. (2002) mentioned some significant numerical stability problems related to the experimental correlation approach and proposed a new method which is based on the transport equation for the intermittency model which can be used to trigger transition locally.

Most of experimental and numerical works on the laminar-turbulent transition done in the past concerned the so called steady transition which is understood as a steadiness of the mean parameters of the free stream. However, in turbomachinery applications due to rotor-stator interaction an unsteady transition is of the fundamental importance in which the transition is governed by unsteady periodic or large scale vortex structures passing in the free stream. The review of fundamental studies of the laminar-turbulent transition induced by periodically passing wakes was presented by Alfredsson & Matsubara (1996). Direct numerical simulation (DNS) of the unsteady transition induced by the wake of periodically passing cylinders was performed by Wu et al. (1999) and compared with the experimental work of Liu & Rodi (1991). This study showed that the concept of puffs is relevant in passing wake-induced bypass transition. The puffs generated at the inlet have tendency to elongate and decay but due to an interaction with certain types of free-stream vortices these structures can be amplified and evolve into turbulent spots. Visualizations from the numerical study have been compared to liquid crystal experiments of Zhong et al. (1998) showing good agreement of geometrical characteristics of the simulated and measured puffs prior to breakdown as well as the matured turbulent spots.

The present document is focused on the steady and unsteady bypass transition on the turbine blade profile N3-60. The work was performed within the TRANSPRETURB Thematic Network on Transition (EC Contract ERBICT 20-CT98-005) and the research grant funded by Polish State Committee for Scientific Research No. 7T07A007-15. The experimental data concerning steady transition as well as wake induced transition are available in the data base on the website of the TRANSPRETURB Thematic Network http://tajfun.imc.pcz.czest.pl/transpret/. The numerical simulations of the steady transition will be described and compared with experimental results in the present document. The unsteady transition induced by passing cylinders is also currently studied numerically and will be available soon.

Introduction

There exist three general scenarios according to which flow goes from laminar to turbulent state. The first one is natural transition, which begins from weak instability in the laminar boundary layer that is two-dimensional Tollmien-Schlichting (TS) waves. As the two-dimensional disturbances convect downstream they grow in an increasingly nonlinear manner, then they develop unstable three-dimensional waves, which form into hairpin vortices. The vortices break down and develop into turbulent spots, which grow and convect downstream until they coalesce into fully developed turbulent boundary layer. This path of transition, is however restricted to rather low free-stream turbulence intensity under say 1% which is not very common in turbomachinery flows. Under the free-stream turbulence intensity higher than 1% it is observed that transition occurs rapidly, bypassing the Tollmien-Schlichting mode of instability and turbulent spots form immediately in the laminar boundary layer. This type of transition called bypass transition after Morkovin (1969) is the most common scenario in turbomachinery flows. The third mode is separated flow transition (Mayle, 1991), which is especially common in an overspeed regions near an airfoil leading edge and in the strong adverse pressure gradient just downstream of the point of minimum pressure on the suction side of the profile.

Most of the experimental and numerical works on the laminar-turbulent transition done in the past concerned natural transition, so the physics of this mode is nowadays well understood (Volino, Simon, 1997). Now it is available also a sizable body of literature on fundamental studies of by-pass transition but still are many doubts about physics of this mechanism and the conditions, under which it occurs are not well defined. As it was said this complex phenomenon depends mainly on the free-stream turbulence intensity, but also on the pressure gradient (Volino, Simon, 1997) and structure of turbulence that is length scale (Jonas et al., 2000).

One of the first explanations of bypass mechanism was proposed by Johnson (1993) who stated that the transition could be inferred from laminar fluctuations of near wall velocity induced by freestream turbulence. He argued that turbulent bursts were directly attributed to the spanwise vorticity produced through unsteadiness, which induced transient separation of the boundary layer flow. He assumed that the effect of the pressure field close to the wall is restricted to two dimensions and there is negligible phase shift across the boundary layer. According to his next simplification the mean velocity as well as instantaneous velocity is proportional to y (normal direction). When the flow is perturbed by a local reduction in pressure the fluid will accelerate and move closer to the wall, while the pressure increases, the streamline move away from the surface. Excessive value of pressure increase results in strong outward deflection of streamline what leads to development of boundary layer instability.

According to his opinion when near wall velocity drops below half the mean local velocity the near wall flow stalls and separates instantaneously that creates hairpin vortices which are known to precede breakdown. Analysis of the spot spreading parameters and the influence of pressure gradient analysis was performed with the use of linear perturbation model assuming inviscid and parallel time mean flow with Pohlhausen velocity profile. The theoretical analysis was confirmed by the experimental work of Johnson and Dris (2000).

Another path for turbulence generation is the mechanism through which disturbances are introduced into a boundary layer, which is usually denoted as receptivity mechanisms (Reshotko, 1976). The small scales from the freestream are prevented to perturb the boundary layer by the mean shear (it is known as sheltering mechanism). It has been observed that freestream turbulence can, however induce at least two types of boundary layer disturbances: randomly occurring TS-wave packets and large amplitude low frequency fluctuations in streamwise velocity component (Westin at al 1998). Usually, the latter one is observed only in boundary layer subjected to higher freestream turbulence, but it is believed that also the TS-wave packets can exist and amplify in such a case, but they are very difficult to detect. The low-frequency fluctuations mainly caused by irregular motion of long structures with narrow spanwise scales (greater usually than 15-20 times the boundary layer thickness) inside the boundary layer are denoted by Kendall (1985) as Klebanoff mode. The maximum of this disturbances is found approximately in the middle of the boundary layer and it is growing downstream in linear proportion to the displacement thickness. The formation of long and narrow streaky structures inside laminar and transitional boundary layers were observed experimentally by Greek et al. in 1985 and termed as puffs. In his experiment he generated localized disturbances from the freestream through short duration jets ejected from a pipe located upstream of the leading edge of a flat plate. Similar observation have been made by Westin at all. (1998) and lately by Alfredson and Matsubara (1996), who found that the maximum disturbance level in the boundary layer grows in linear proportion to the laminar boundary layer thickness. In fact the Klebanoff mode is ensemble-averaged view of streaky structures observed in different experimental works.

Input for the understanding of bypass transition physics was given by Jacobs and Durbin (2001), who performed DNS simulation of such a type of flow. Long streaks of streamwise velocity perturbation described above are initiated by low-frequency modes from the freestream. Despite the broad inlet spectrum, energy within boundary layer due to shear amplification, or essentially by vertical displacement of mean momentum, focuses only onto low-wave number frequencies. It is also worth to note that initially emerging spanwise waves decays due to viscous dissipation in boundary layer, according to hypothesis of Butler and Farrell (1992) and Anderson et al (1999). The near-wall streaks called by Jacobs and Durbin (2001) backward jets do not undergo instability as they only remain in the vicinity to the wall. Intense negative jets are compensated by broader positive jets. These jets however, produced possibly by blocked by the wall downward flow, are present only close to the wall.

Backward jets are lifted from near the wall region upwards due to large scale freestream eddies and close to the boundary layer edge have increasingly negative velocity relative to the ambient mean velocity. The substantial role of upward velocity in an early stage of bypass transition was confirmed in LES simulation by Young and Voke (1995) and in DNS simulation by Berlin and Henningson(1999). As the backward jets are close to the edge of boundary layer they are disturbed by small-scale eddies from freestream and irregularities similar to Kelvin-Helmholtz instability are triggered and develop into turbulent spots. It could be stated then that external disturbances do not penetrate the boundary layer, rather backward jets rises to the edge of boundary layer where they break down. Jacobs and Durbin (2001) claimed, however that not all backward jets results in turbulent spots and that the reason for this is not yet clear. They only suggest that most unstable situation which could provoke breakdown is when the negative jet are of sufficient amplitude and are overlaying the positive jet.

Once formed turbulent spots spread laterally and intensively as they propagate downstream the flow. As a result, spots originating from different locations merge to form a completely turbulent boundary layer. Spots originating at the edge of boundary layer are different in shape than classical Emmons spots (Emmons, 1951). The spots of Emmons, which have been generated by forcing at the wall have well known triangular pointing-down shape defined as a top-down shape, while spots developed at the outer edge have bottom-up shape. Confirmation of this phenomenon could be deduced from visualization of wake-induced transition by Zhong at al (1999).

Growth and merging of spots are crucial features of the bypass mechanism. One of the basic hypothesis was Narasimhas concentrated breakdown hypothesis (Narasimha, 1957), stating that spot production rate could be represented by Dirac delta function. This is because upstream of the start of transition, spots are unable to form while downstream of the start, the formation of spots is inhibited by calmed regions following spots which were formed earlier (Ramesh and Hodson, 1999). The transition onset, length of transition zone and spot formation rate are the information which are necessary for modeling of boundary layer. Lack of clear explanation of bypass phenomenon results in various experimental correlations, which are used to help in identification of transition zone.

The above analysis concerns steady flows, but for turbomachinery applications unsteady transition is even more important. Transition in unsteady conditions develops in two coupled paths. There exists a wake-induced strip under the convecting wake and transition between wakes developed according to ways described above. The high complexity of such a flow causes that it is difficult to isolate the physical mechanism. Realizing such a complexity a number of investigators have considered simpler geometries, where unsteady blade rows interaction was simulated by passing a row of wake-generating cylinders. The first detailed investigation concerning the role of wakes in transition process was performed by Pfeil et al (1983), who proposed a basic model of an unsteady transition process, in the form of distance-time diagrams, which still fits well to the latest results. The very detailed analysis concerning the mechanism of transition due to wake turbulence has been presented by Mayle (1991), Liu and Rodi (1991), Hodson at al (1992) and lately by Chakka and Schobeiri (1999). Furthermore, a substantial number of papers done by Gostelow and his co-workers (1994) indicated additional parameters, which should be considered apart of wakes, e.g. the inlet turbulence intensity and pressure gradient.

The troublesome problem is the presence of periodically varying flow field and varying instantaneous turbulent intensity produced by the incoming upstream wake. Usually, at the first part of the blade surface, after the leading edge, the boundary layer is resistant to the presence of the wake as the turbulence level within the wake is not generally sufficient to create the transition and this case is called disturbed laminar boundary layer. As the turbulent level in the centre of wake is very high, up to 13% the physical mechanism of wake induced transition should be the same as in the case of bypass transition. The confirmation of this suggestion was given in the paper of Wu et al. (1999) who performed DNS analysis on the wake interaction with boundary layer on the flat plate. Inlet wake disturbances inside the boundary layer evolve rapidly into longitudinal puffs during an initial receptivity phase. In the absence of strong forcing from freestreem vortices these structures exhibit streamwise elongation with gradual decay in the amplitude. Small scales freestream vortices interact with boundary layer edge (longitudinal streaks) through a local Kelvin-Helmholtz instability. When it happens, negative streamwise fluctuations associated with the inflectional profiles evolve into strong forward eddying motions, producing young spots. Wu et al. (1999) argue that these spots have an arrowhead pointing upstream (bottom-up spots) what could be also concluded from the experiment of Zong et al (1998).

These spots form so called turbulent strip which is developing downstream and at certain distance from the leading edge, the turbulent regions coming from consecutive wakes merge together creating uniform turbulent boundary layer. Such phenomenon is well described in many papers and usually presented at a distance-space diagrams. Behind the turbulent patch the so-called becalmed region develops. It is characterised by low value of fluctuations and initially high shear stresses, which then decrease to the value characteristic for laminar boundary layer. The second important feature of becalmed region is its insusceptibility to external disturbances, what means that in this region spot production is to some extent inhibited. These and other features of becalmed region were well described by Schulte and Hodson (1998).

Description presented above of the various stages of the bypass transition process shows that accurate physical modeling is required to obtain a reliable prediction method for modeling of such a type of transition. This should include not only the formation of the incipient spots and their growth and coalescence into fully developed turbulent boundary layer, but also formation and growth of a streaky structures and the development of secondary instabilities.

Review of UFR studies and choice of test case

The prediction of the onset location and extention of transition is of the main importance to correctly design the turbine blading. It is clear today that using point transition with an assumed transition location is not sufficient to improve the design of modern turbomachinery. However, early works of Jones & Launder (1972) showed that low Reynolds number turbulence models can predict bypass transitional flows. The first comparison of a variety of closure models for predicting bypass transition, from the simplest correlation methods to DNS approach, was conducted as a part of the 1^st ERCOFTAC Workshop in Laussane in 1990 (see Pironneau et al., 1992). The results showed that specific turbulent models can predict flow development through transition more accurately than industrial correlations and led to establishing the ERCOFTAC Special Interest Group on Transition. The results of activities of the Transition SIG was reviewed by Savill (1993,1996). A variety of low Reynolds number models were tested and it was showed that only some models were able to predict transition effects correctly. However, according to Menter et al. (2002) the ability of the low-Re turbulence models to predict transition seems to be coincidental as the calibration of the damping functions is based on the viscous sublayer and not on the transition region. The physical mechanism of low turbulence intensity in the sublayer and in the transition layer are entirely different and it is unrealistic to expect a consistent transition model.

An alternative approach to low-Re models are the models which use the experimental correlations concerning the intermittency factor. A review of such transition models was delivered by Menter (2002) and Savill (2001). In this type of the transition models an assumption is adopted that the transition process can be modeled as a superposition of laminar and turbulent flows. The intermittency method for transition was first introduced by Emmons (1951) who observed that turbulent spots form randomly in time and space through the transition region. The experimental data of Schubauer & Klebanoff (1955) showed that the assumptions introduced by Emmons cannot describe correctly the transition zone. However, the necessary agreement between experiment and numerical results was provided by Narashima (1957) who introduced a concentrated breakdown hypothesis based on the observations that spots were formed only in narrow band. Narashima assumed that the spot production rate can be represented by a Dirac delta function showing (Dhawan & Narashima, 1958) that this hypothesis leads to correctly predicted all mean flow properties in the transition zone. Although the concentrated breakdown hypothesis provided necessary agreement with experimental data no explanation for its success was provided for almost 40 years. Schulte and Hodson (1998) introduced a corrected spot production rate model that took into account the effects of existing spots on the production of new spots in calmed regions. An improved version of the concept invented by Schulte and Hodson (1998) was introduced by Ramesh and Hodson (1999) who presented a closed form solution for the corrected spot production rate in a zero pressure gradient flow. By approximating the calmed region behind each spot by a rectangular shape they showed excellent agreement with the intermittency factor of Narashima. The suppression of spot formation by existing turbulent spots was previously documented by Johnson and Fashifar (1994) who performed measurements in a transitional boundary layer on a flat plate with zero pressure gradient. They calculated the statistics of the burst length, gap length and spacing between turbulent events and found that new turbulent spots were not formed randomly but were suppressed within a recovery period adjacent to existing turbulent spot. In order to apply the intermittency model one needs a knowledge on the spot production rate as well the onset location of transition as a function of main transition governing parameters namely the streamwise pressure gradient and free stream turbulence. An extensive experimental study on transition in turbomachinery was performed by Abu-Ghannam and Shaw (1980). They provided a correlation for transition onset as a function of turbulence level and pressure gradient. It was observed that the pressure gradient has less significant effect on transition onset at higher turbulence levels. Mayle (1991) correlates transition onset with turbulence level in zero pressure gradient flows. Based on the assumption that the turbulence level dominates the effect of pressure gradient in gas turbine environment, Mayle (1991) proposed his zero pressure gradient correlation for transition onset as sufficient for all conditions with the turbulence level above 3%.

The correlations for the transition onset and the turbulent spot production rate can be verified recently by the DNS approach. The direct numerical simulations of bypass transition was performed by Jacobs and Durbin (2001) showing that better understanding of the mechanism leading to the turbulent spot production is needed.

As it was already mentioned the transition in turbomachinery is influenced by unsteady phenomena due to rotor-stator interactions. The DNS calculations of the wake induced transition performed by Wu et al. (1999) were already mentioned. These simulations showed very good agreement with the experimental data of Liu & Rodi (1991) and with visualization experiments of Zhong et al. (1999).

An extensive experimental work on transition on turbine blade profile N3-60 was performed at the Institute of Thermal Machinery, TU Czestochowa in steady state conditions as well as in the case of the transition induced by periodically passing wakes (http://tajfun.imc.pcz.czest.pl/transpret/). The analysed case concerns a medium loaded blade and low Mach number flows. The experimental set-up and major results will be described in the following chapters of this document. The numerical calculations of this test case were performed using the unsteady UNNEWT+PUIM solver developed at CFD Laboratory of Cambridge University (Vilmin et al., 2002). The most important feature of this code is capability of determining the intermittency distribution as a multiplier of the eddy viscosity on planes normal to the stream direction. The intermittency was determined with the use of the subroutine PUIM developed at Whittle Laboratory Cambridge University (Schulte and Hodson, 1998). The numerical results for the steady case will be shown in the following chapter while the use of the procedure in the unsteady wake induced transition is currently investigated.

Contributors: Andrzej Boguslawski - Technical University of Czestochowa