Unsteady Transition Research Articles

Computational Fluid Dynamics Study of Wake-Induced Transition on a Compressor-Like Flat Plate

Recent experimental work has documented the importance of wake passing on the behavior of transitional boundary layers on the suction surface of axial compressor blades. This paper documents computational fluid dynamics (CFD) simulations using a commercially available general-purpose CFD solver, performed on a representative case with unsteady transitional behavior. The study implements an advanced version of a three-equation eddy-viscosity model previously developed and documented by the authors, which is capable of resolving boundary layer transition. It is applied to the test cases of steady and unsteady boundary layer transition on a two-dimensional flat plate geometry with a freestream velocity distribution representative of the suction side of a compressor airfoil. The CFD results are analyzed and compared to a similar experimental test case from the open literature. Results with the model show a dramatic improvement over more typical Reynolds-averaged Navier–Stokes (RANS)-based modeling approaches, and highlight the importance of resolving transition in both steady and unsteady compressor aerosimulations.

Unsteady RANS modelling of wake–blade interaction: computational requirements and limitations

An investigation is presented of the ability of the unsteady RANS approach to represent, from a numerical point of view, the characteristics and evolution of moving wakes as they interact with the flow around a turbine blade and in a related variable-passage configuration. The context of the study is wake-induced transition in unsteady turbomachine flows. Its emphasis is on numerical and computational issues, with physical aspects of predicting unsteady transition in the boundary layer of a turbine blade being covered in a companion paper. Issues addressed include: resolution and time-step requirements––especially in relation to the convective transport of scalar-wake properties, the sensitivity of the solution to the numerical scheme, and the relative merits and limitations of either including the wake-generating moving devices––in the present case an array of circular bars––as part of the computational process, or of prescribing the moving wakes as part of the flow-inlet conditions upstream of the blade passage. In relation to the latter option, the viability of extracting the wake conditions from a precursor RANS computation for an isolated wake-generating body is examined. In total, results for 21 test conditions are reported in an effort to derive some general conclusions and recommendations. The investigation demonstrates that (i) extremely high resolution is needed to ensure that numerical issues do not obscure physical phenomena and turbulence-model capabilities; (ii) the inclusion of the wake-generating device in the computation poses serious problems associated with vortex shedding; and (iii) the results of precursor calculations for the wake can be seriously flawed because of inherent limitations in the RANS approach.

Simulation of heat transfer and melt flow in Czochralski growth of Si 1− xGe x crystals

Using numerical simulation, we have studied the Si 1− x Ge x Czochralski (CZ) growth with 3 at% initial melt Ge content. Global heat transfer computations in the entire CZ system and 2D or 3D computations of melt turbulent convection in the crystallization zone have been made. The computed crystallization front shape is compared with respective experimental data obtained by X-ray topography. Unsteady transitions of the melt flow are studied to analyze the stability of the crystallization process.

A Correlation-Based Transition Model Using Local Variables—Part II: Test Cases and Industrial Applications

A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) methods using unstructured grids and massive parallel execution. The model is based on two transport equations, one for the intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models), but form a framework for the implementation of correlation-based models into general-purpose CFD methods. Part I of this paper (Menter, F. R., Langtry, R. B., Likki, S. R., Suzen, Y. B., Huang, P. G., and Völker, S., 2006, ASME J. Turbomach., 128(3), pp. 413–422) gives a detailed description of the mathematical formulation of the model and some of the basic test cases used for model validation. Part II (this part) details a significant number of test cases that have been used to validate the transition model for turbomachinery and aerodynamic applications, including the drag crisis of a cylinder, separation-induced transition on a circular leading edge, and natural transition on a wind turbine airfoil. Turbomachinery test cases include a highly loaded compressor cascade, a low-pressure turbine blade, a transonic turbine guide vane, a 3D annular compressor cascade, and unsteady transition due to wake impingement. In addition, predictions are shown for an actual industrial application, namely, a GE low-pressure turbine vane. In all cases, good agreement with the experiments could be achieved and the authors believe that the current model is a significant step forward in engineering transition modeling.

From spheres to circular cylinders: the stability and flow structures of bluff ring wakes

The low-Reynolds-number wake dynamics and stability of the flow past toroids placed normal to the flow direction are studied numerically. This bluff body has the attractive feature of behaving like the sphere at small aspect ratios, and locally like the straight circular cylinder at large aspect ratios. Importantly, the geometry of the ring is described by a single parameter, the aspect ratio (, the initial asymmetric transition is structurally analogous to the mode A transition for the circular cylinder, with a discontinuity present in the Strouhal–Reynolds-number profile. The present numerical study reveals a shedding-frequency decrease with decreasing aspect ratio for ring wakes, and an increase in the critical Reynolds numbers for flow separation and the unsteady flow transition. A Floquet stability analysis has revealed the existence of three modes of asymmetric vortex shedding in the wake of larger rings. Two of these modes are analogous to mode A and mode B of the circular cylinder wake, and the third mode, mode C, is analogous to the intermediate wavelength mode found in the wake of square section cylinders and circular cylinder wakes perturbed by a tripwire. Furthermore, three distinct asymmetric transition modes have been identified in the wake of small aspect ratio bluff rings. Fully developed asymmetric simulations have verified the unsteady transition for rings that exhibit a steady asymmetric wake.

Advances in Unsteady Boundary Layer Transition Research, Part I: Theory and Modeling

This two‐part article presents recent advances in boundary layer research that deal with the unsteady boundary layer transition modeling and its validation. A new unsteady boundary layer transition model was developed based on a universal unsteady intermittency function. It accounts for the effects of periodic unsteady wake flow on the boundary layer transition. To establish the transition model, an inductive approach was implemented; the approach was based on the results of comprehensive experimental and theoretical studies of unsteady wake flow and unsteady boundary layer flow. The experiments were performed on a curved plate at a zero streamwise pressure gradient under a periodic unsteady wake flow, where the frequency of the periodic unsteady flow was varied. To validate the model, systematic experimental investigations were performed on the suction and pressure surfaces of turbine blades integrated into a high‐subsonic cascade test facility, which was designed for unsteady boundary layer investigations. The analysis of the experiment′s results and comparison with the model′s prediction confirm the validity of the model and its ability to predict accurately the unsteady boundary layer transition.

Advances in Unsteady Boundary Layer Transition Research, Part II: Experimental Verification

This two‐part article presents recent advances in boundary layer research into the unsteady boundary layer transition modeling and its validation. This, Part II, deals with the results of an inductive approach based on comprehensive experimental and theoretical studies of unsteady wake flow and unsteady boundary layer flow. The experiments were performed on a curved plate at a zero streamwise pressure gradient under periodic unsteady wake flow, in which the frequency of the periodic unsteady flow was varied. To validate the model, systematic experimental investigations were performed on the suction and pressure surfaces of turbine blades integrated into a high‐subsonic cascade test facility, which was designed for unsteady boundary layer investigations. The analysis of the experiment′s results and comparison with the model′s prediction confirm the validity of the model and its ability to predict accurately the unsteady boundary layer transition.

Numerical and experimental investigation of unsteady flow interaction in a low-pressure multistage turbine

The paper presents results of unsteady viscous flow calculations and corresponding cold flow experiments on a three-stage low-pressure turbine. The investigation emphasizes the study of unsteady flow interaction. A time-accurate, Reynolds-averaged Navier-Stokes solver is applied for the computations. Turbulence is modelled using the Spalart-Allmaras one-equation turbulence model. The influence of modern transition models on the unsteady flow predictions is investigated. Integration of the governing equations in time is performed with a four-stage Runge-Kutta scheme, which is accelerated by a two-grid method in the viscous boundary layer around the blades. At the inlet and outlet, non-reflecting boundary conditions are used. The quasi-three-dimensional calculations are conducted on a stream surface around mid-span, allowing a varying stream tube thickness. A three-stage, low-pressure turbine rig of a modern commercial jet engine is used for a study of the unsteady flow interaction. The numerical method is able to capture important unsteady effects found in the experiments, i.e. unsteady transition as well as the bladerow interaction. In particular, the flowfield with respect to time-averaged and unsteady quantities such as surface pressure, vorticity and turbulence intensity is compared with the experiments conducted in the cold airflow test rig.

Structure of mixed convective longitudinal vortex air flow driven by a heated circular plate embedded in the bottom of a horizontal flat duct

In this study experimental flow visualization combined with transient temperature measurement are conducted to investigate the structure of the buoyancy driven longitudinal vortex rolls in low Reynolds number mixed convective air flow through a horizontal flat duct with an isothermally heated circular disk embedded in the bottom plate of the duct for the Reynolds number ranging from 15.1 to 99.2 and Rayleigh number from 3506 to 29,493. How the circular geometry of the heated surface affects the longitudinal vortex flow characteristics is investigated in detail. The results indicate that the longitudinal vortex rolls (L-rolls) in the duct core are induced at more upstream locations than those near the duct sides, which is completely opposite to those induced in a duct with a uniformly heated bottom. Besides, the thermals driven by the circular heated surface are not evenly spaced in the spanwise direction and are slightly asymmetric. It is of interest to note that at a given Rayleigh number Ra the thermals are unstable at high Reynolds numbers, suggesting the existence of the inertia driven instability. Thus the L-rolls evolved from these thermals are also unstable with the presence of nonperiodic generation and disappearance of new L-rolls. But at slightly lower Re the thermals and L-rolls are steady and regular. The vortex flow becomes unstable and irregular for a further reduction in the Reynolds number, which obviously results from the buoyancy driven instability. The simultaneous presence of these two instability mechanisms explains the appearance of the reverse steady–unsteady transition in the vortex flow. Based on the present data, a flow regime map is given to delineate various L-roll patterns driven by the circular heated plate. In addition, the boundaries separating these patterns are empirically correlated. Empirical correlations for the onset points of the L-rolls are also provided.

Size and shape effects on two-phase flow patterns in microchannel forced convection boiling

An integrated microchannel heat sink consisting of shallow, nearly rectangular microchannels has been fabricated using standard micromachining techniques to highlight the effects of the micrometer sized channel shape on the evolving flow patterns and, consequently, on the thermal performance of the microsystem. An integrated heater serves as a local heat source, while an array of micro thermistors is used for temperature distribution measurements. The working fluid, DI water, is pressurized through the microchannels for forced convection heat transfer studies. Boiling curves for different flow rates have been recorded and analyzed based on the visualized flow patterns. Local nucleation, including bubble formation and bubble dynamics, is documented and found to be negligible. Although detected, in contrast with triangular microchannels, annular flow is observed to be unstable. Instead, the dominant flow pattern is an unsteady transition region connecting an upstream vapor zone to a downstream liquid zone with an average location depending on the input power. A physical mechanism based on the force balance across the vapor–liquid interface, and the development of a restoring force, is proposed to explain the flow visualization results.

PCR in a Rayleigh-Bénard convection cell.

PCR in a Rayleigh-Bénard convection cell.

The Russian Financial System's Unsteady Transition

The financial crisis that began on 17 August 1998 confirmed any fears that we might have had as to the robustness of the Russian banking system and more generally its financial system. It also pointed up the organic link between the confidence essential to the working of the banking system and the State's ability to guarantee the legality of it. Although improvements have been seen since then, the fundamental issue remains.

Experimental Investigation of Turbulence Influence of Wake Passing on the Boundary Layer Development of Highly Loaded Turbine Cascade Blades

Experimental investigations regarding the effects of wake passing on boundary layer development were performed on a highly loaded low pressure (LP) turbine cascade blade. Data was obtained for various flow conditions and is intended to be used for the validation of numerical models dealing with periodic unsteady transition. A phase shift between turbulence and velocity fluctuations in the wake path was observed in the near-wall boundary layer, which might have considerable impact on the use of integral-type transition criteria. The experimental data set is already publicly available for download on the web page of the institute. A moving bar type wake generator was employed to simulate the upstream blade row. Tests were performed at turbomachinery-like Mach and Reynolds number conditions in the High-Speed Cascade Wind Tunnel for different bar speeds, bar spacings and background turbulence levels. This paper focuses on the exemplary description of flow phenomena characteristic for unsteady flow for a single exit Reynolds number of Re2th = 200,000. Conventional measurement techniques like static pressure tappings on the suction and pressure side as well as five hole probe traverses were complemented with fast-response pressure transducers embedded into and hot film sensors glued onto the suction surface to study the time-resolved boundary layer development in detail. Additional studies using single hot wire traverses in the suction side boundary layer and triple hot wire probes upstream of the cascade inlet plane were deployed to complete the data sets. The results indicate that for the LP turbine the transition point moves periodically when subjected to wake passing, which greatly affects the loss generation in the suction side boundary layer. Laminar separation is suppressed or reduced whenever the wake is present.

Prediction of turbine blade heat transfer and aerodynamics using a new unsteady boundary layer transition model

The effects of periodic unsteady flow on heat transfer and aerodynamic characteristics, particularly on the boundary layer transition along the suction and the pressure surfaces of a typical gas turbine blade, are experimentally and theoretically investigated. Comprehensive aerodynamic and heat transfer experimental data are collected for different unsteady passing frequencies that are typical of gas turbines. To predict the effect of the impinging periodic unsteady flow on the heat transfer and the aerodynamics of turbine blades, a new unsteady boundary layer transition model is developed. The model is based on a universal unsteady intermittency function and utilizes an inductive approach that implements the results of comprehensive experimental and theoretical studies of unsteady wake development and the boundary layer flow. Three distinct quantities are identified as primarily responsible for the transition of an unsteady boundary layer: (1) the universal relative intermittency function, (2) maximum intermittency, and (3) minimum intermittency. The analysis of the experimental results and the comparison with the model prediction confirm the validity of the model and its capability to accurately predict the unsteady boundary layer transition.

Unsteady heat transfer in subsonic boundary layers

Unsteady boundary layer transition experiments are performed in a modified Ludwieg tube setup. The transition is initiated by means of a moving bar mechanism which translates cylinders in front of a test plate. The intensity of the wakes shed by the cylinders is so large that transition starts at the leading edge. In streamwise direction the wake-induced transition area grows and keeps its initial shape. Also experiments are performed in which the moving cylinders are combined with a static grid. In the time between two wakes, individual turbulent spots develop which grow in streamwise direction. These spots merge with the wake-induced transition until a completely turbulent boundary layer is obtained. When the experimental results are transformed in intermittency distributions based on the turbulent-to-laminar time fraction, the superposition principle proofs to be applicable. However, the intermittency distribution based on the mean heat flux cannot be determined unequivocally. This is due to the fact that there does not exist a unique turbulent heat flux. This flux appears to be dependent on the origin of the transition.

Numerical simulation of wake velocity and wake turbulence effects on unsteady boundary layer transition

Linear and non-linear low Reynolds number k-ɛ eddy viscosity models are applied to the simulation of unsteady transitional flows pertinent to axial turbomachine aerodynamics. Adequate test cases are selected to allow an individual investigation of wake velocity and wake turbulence effects on unsteady transition induced by separation bubbles and wake passing respectively. Separation bubbles under steady main flow conditions are calculated first, demonstrating the applicability of the numerical scheme and the selected turbulence models. Unsteady simulations show that essential features of the experimental investigation can be reproduced, although oscillation characteristics of the separation bubble, such as phase shifts, can only be partly reproduced. Predictions of wake-induced transition on a flat plate agree with the underlying direct numerical simulation study in many important aspects. However, simulation results show deficiencies with respect to the time-averaged transition length and the spatio-temporal evolution of turbulent flow regions.

Numerical and Experimental Investigation of Unsteady Flow Interaction in a Low-Pressure Multistage Turbine

This paper presents results of unsteady viscous flow calculations and corresponding cold flow experiments of a three-stage low-pressure turbine. The investigation emphasizes the study of unsteady flow interaction. A time-accurate Reynolds-averaged Navier–Stokes solver is applied for the computations. Turbulence is modeled using the Spalart–Allmaras one-equation turbulence model and the influence of modern transition models on the unsteady flow predictions is investigated. The integration of the governing equations in time is performed with a four-stage Runge–Kutta scheme, which is accelerated by a two-grid method in the viscous boundary layer around the blades. At the inlet and outlet, nonreflecting boundary conditions are used. The quasi-three-dimensional calculations are conducted on a stream surface around midspan, allowing a varying stream tube thickness. In order to study the unsteady flow interaction, a three-stage low-pressure turbine rig of a modern commercial jet engine is built up. In addition to the design point, the Reynolds number, the wheel speed, and the pressure ratio are also varied in the tests. The numerical method is able to capture important unsteady effects found in the experiments, i.e., unsteady transition as well as the blade row interaction. In particular, the flow field with respect to time-averaged and unsteady quantities such as surface pressure, entropy, and skin friction is compared with the experiments conducted in the cold air flow test rig. [S0889-504X(00)02004-3]

Taylor Vortex Flow at Very Small Aspect Ratio. Mode Formation and Bifurcation in Time-Developing Dynamic System.

Mode formation and bifurcation in Taylor vortices are interesting physical phenomena which are typical of those in nonlinear dynamics. In this study, we investigate the system with aspect ratios (column height/gap width) of order of unity and present the numerical results of flows in various modes and unsteady transitions between modes. The appearance of the normal two-cell mode, anomalous one-cell mode, twin-cell mode and unsteady mode is predicted. When the flow starts from rest, the flow in an anomalous mode or twin-cell mode is established after the sudden breakdown of symmetric two-cell mode. In the flow of unsteady mode, the values of physical properties vary periodically. When the rotation speed of the inner cylinder decelerates, the mode transition between normal two-cell mode and anomalous one-cell mode and the transition from twin-cell mode to anomalous one-cell mode are found.

Periodic Unsteady Flow Aerodynamics and Heat Transfer: Studies on a Curved Surface, Combined Part I and II

Aerodynamic and heat transfer investigations were done on a constant curvature curved plate in a subsonic wind tunnel facility for various wake passing frequencies and zero pressure gradient conditions. Steady and unsteady boundary layer transition measurements were taken on the concave surface of the curved plate at different wake passing frequencies where a rotating squirrel‐cage generated the unsteady wake flow. The data were analyzed using timeaveraged and ensemble‐averaged techniques to provide insight into the growth of the boundary layer and transition. Ensemble‐averaged turbulence intensity contours in the temporal spatial domain showed that transition was induced for increasing wake passing frequency and structure. The local heat transfer coefficient distribution for the concave and convex surface was determined at those wake passing frequencies using a liquid crystal heat transfer measurement technique. Detailed aerodynamic and heat transfer investigations showed that higher wake passing frequency caused transition to occur earlier on the concave surface. Local Stanton numbers were also calculated on the concave surface and compared with Stanton numbers predicted using a differential boundary layer and heat transfer calculation method. On the convex side, no effect of wake passing frequency on heat transfer was observed due to a separation bubble that induced transition.

Periodic Transition on an Axial Compressor Stator: Incidence and Clocking Effects: Part I—Experimental Data

Periodic wake-induced transition on the outlet stator of a 1.5-stage axial compressor is examined using hot-film arrays on both the suction and pressure surfaces. The time-mean surface pressure distribution is varied by changing the blade incidence, while the free-stream disturbance field is altered by clocking of the stator relative to an inlet guide vane row. Ensemble-averaged plots of turbulent intermittency and relaxation factor (extent of calmed flow following the passage of a turbulent spot) are presented. These show the strength of periodic wake-induced transition phenomena to be significantly influenced by both incidence and clocking effects. The nature and extent of transition by other modes (natural, bypass, and separated flow transition) are altered accordingly. Leading edge and midchord separation bubbles are affected in a characteristically different manner by changing free-stream periodicity. There are noticeable differences between suction and pressure surface transition behavior, particularly as regards the strength and extent of calming. In Part II of this paper, the transition onset observations from the compressor stator are used to evaluate the quasi-steady application of conventional transition correlations to predict unsteady transition onset on the blading of an embedded axial compressor stage.