Fluid mechanics

Experiments on stability, transition and turbulence in boundary layer flows

Researchers: Henrik Alfredsson, Per Elofsson, John Matsson, Masuhara Matsubara, Nils Tillmark, Johan Westin

Sponsors: NUTEK, TFR, KVA

The transition between laminar and turbulent flow is an important aspect of the design of e.g. turbo-machinery or vehicles, and effects for instance heat exchange and friction loss. From a technical point of view, it is therefore important to be able to predict the transition region and if possible also to control it. Fluid dynamic research has led to a fairly good understanding of laminar-turbulent transition in the absence of ambient disturbances and resulted in reliable transition prediction methods for flow on for instance aircraft wings where external (atmospheric) disturbances are small. Under less ideal conditions encountered for other technical applications, ambient disturbances or effects of body forces may cause earlier transition. However, in this case, the prediction of the transition relies so far upon uncertain empirical correlations, since the transition mechanisms are presently unknown.

The receptivity of the laminar boundary layer to free stream turbulence is investigated through detailed velocity measurements in the MTL wind tunnel, where free stream turbulence is generated by different grids. It has been shown that the interaction with the boundary layer gives rise to elongated structures of high and low velocity which seem to be susceptible to secondary instabilities and subsequent breakdown. The role of Tollmien-Schlichting waves in this type of transition is presently studied. This research is carried out partly in cooperation with scientists from the Institute of Applied and Theoretical Mechanics, Novosibirsk.

Formation of elongated structures may also occur through the interaction between two finite-amplitude oblique waves. This is experimentally investigated by introducing two oblique TS-waves in an air flow channel by means of vibrating ribbons (one at each channel wall). Measurements were carried out at Reynolds numbers of about one third of the critical one, and at an initial streamwise disturbance level of the order of 1-4 %. With only one ribbon excited the oblique wave decayed downstream in accordance with linear theory, but with the excitation of both ribbons dramatic changes of the flow field occurred. A strong mean flow distortion in the form of a spanwise peak-valley structure and a strong growth of higher harmonics prior to breakdown were observed.

In cases where body forces affect boundary layer flows different other types of instability may be dominating. For instance a boundary layer flow along a wall in a rotating system will be affected by a Coriolis force which can give rise to instabilities in the form of longitudinal vortices. Similar vortices can develop along concave walls due to centrifugal effects. Flows with both system rotation and curvature are important in many technical applications, such as pumps, fans, turbines etc. These instabilities may arise at much lower Reynolds numbers than the traditional TS-wave instability. A project which studies such effects experimentally consists both of flow visualization and detailed velocity measurements of the flow field with hot-wire anemometry in a curved air channel with and without system rotation.

Turbulent plane Couette flow is one of the canonical flow cases and among its interesting and distinguishing (as compared to pressure driven flows) features are the monotonous velocity profile, the constant shear stress distribution and the finite production rate of turbulent energy at all positions across the channel. Recent numerical simulations have shown persistent counter-rotating streamwise vortices of infinite length contributing to a large fraction of the turbulent energy. This has given experimenters a new incentive to investigate whether it is an effect of streamwise periodic boundary conditions in the numerical simulation or an inherent feature of the flow. The present apparatus uses an "infinite" plastic band moving along vertical glass surfaces in water, with spanwise and streamwise aspect ratios of the channel larger than 30 and 150, respectively. By using a transparent plastic band it is possible to use Laser-Doppler-Velocimetry for non-intrusive measurements and of special interest is two-point correlations of the streamwise velocity. In comparison to other wall bounded shear flows the distance over which streamwise correlation is found is exceptionally long (larger than where is the half-channel width). There is also a regular periodic structure in the spanwise direction with a wavelength of about . This indicates that there exist large scale structures in turbulent plane Couette flow that do not have a counterpart in for instance plane Poiseuille flow and that this probably leads to large difficulties in trying to simulate this flow. A cooperation with researchers from NTH-Trondheim and prof. Johansson's group carrying out DNS for this flow is on-going.

Publications: 9,10,12,32,40,41,42,62,63,67

Hypersonic stability and transition

Researchers: Henrik Alfredsson, Anders Dahlkild, Ardeshir Hanifi, Dan Henningson

Sponsors: Swedish National Space Board, Aeronautic Research Institute of Sweden (FFA), KTH "Rörlig resurs"

Hypersonic transition research is carried out within the Swedish participation of the "SÄNGER"-project. As an important model problem the stability of the hypersonic boundary layer on a yawed pointed cone have been chosen. As a first step a code has been developed which uses the -method to theoretically predict the locations of transition. The computations have been focused to the windward and leeward meridians of the cone for which an efficient method to calculate the basic laminar boundary layer flow has been developed. Effects of transverse curvature and body divergence are included in the linear stability equations as well as in the non-similar boundary layer equations of the flow. As compared to existing experimental results in the literature the relative movement of the transition point as the yaw angle is changed was predicted fairly well with the present method. An approximate method to obtain the basic flow at any meridian, just from the knowledge of the exact solution at the leeward and windward meridians of the cone, were used for calculations of growth rates also at the sides of the cone. It was found that even a very small cross flow component may give a substantial increase of the growth rate of the perturbations. The second step of the project is a new transition prediction tool which is being developed in cooperation with DLR in Göttingen. The code uses the parabolized stability equations and is so far based on the linearized equations. It has been carefully checked against existing solutions and will now be extended to handle non-linear interactions between wave components.

Publications: 85

Modelling of microstructure formation in solidification

Researchers: Gustav Amberg, Robert Tönhardt

Sponsors: TFR

This project is concerned with mathematical models for solidification in processes such as welding and near net shape casting. The aim is to develop mathematical models that predict microstructure, i.e. the crystal structure and the size, geometry and orientation of crystals. In particular the effect of liquid flow on microstructure will be investigated. The figure above shows a close-up photograph of a solidifying model substance (from Chen & Chen, JFM v 227, p 567), and may give an idea of the complexity of the microstructure. The models developed within the project are to be incorporated in available codes for simulating the macroscopic convection heat and mass transfer during solidification. Development of mathematical models will require simulations of individual dendrites. Models and predictions will be continuously tested against experiments (collaboration with Hasse Fredriksson, KTH).

Evolution and stability of mushy zones in solidifying melts

Researchers: Gustav Amberg

Sponsors: 'Rörlig resurs, KTH'

During solidification, mushy zones consisting of dendritic crystals often form. The figure above (from Chen & Chen, JFM 227, p 567, 1991) shows a photograph of the edge of a mushy zone in a binary liquid, with a growing mesh of dendritic crystals. The properties of for example a finished casting, is often strongly affected by convective heat and mass transfer through this mushy zone. Code to simulate mushy zones, predicting macrosegregations and the evolution of the solid fraction of the mush has been developed in 2D. Using a similar model of the mush, the convective instability leading to freckles (or chimneys or A-segregates) in mushy layers solidified from below has been studied theoretically. The picture above actually shows the top of one such chimney, resembling a volcano, through which light liquid rises. Further work on this problem is intended.

Publications: 2,3,20,105

Convective heat and mass transfer during floating zone crystal growth

Researchers: Gustav Amberg, Mårten Levenstam

Sponsors: TFR, BRITE/EURAM.

Thermocapillary convection in float zones are simulated numerically. As the Marangoni number is increased, the flow is traced past several bifurcations, until it becomes unsteady. This transition to unsteady flow is technologically important in the float zone crystal growth process. The flow in a float zone is a generic thermocapillary flow, and is of interest also as fundamental fluid mechanics. Comparisons are made with actual float zone experiments in space and on earth (cooperation with Torbjörn Carlberg, Sundsvall). Other thermocapillary flows are also studied (button melting, and possibly in the future, weld pools).

Publications: 36

Convection in electrochemical systems

Researchers: Fritz Bark, Rolf Karlsson, Yurij Kharkats*, Daniel Simonsson**, Rikard Eriksson**, Artjom Sokirko*, Lars-Göran Sundström, Fredrik Wallgren

Sponsors: KVA, NUTEK, TFR

In many electrochemical systems, transport of ionic species takes place due to migration in the electric field, diffusion due to concentration gradients and advection by a moving liquid electrolyte. Examples of such systems are lead acid batteries and cells for refining of metals. The purpose of the present project, which involves both theoretical modeling and experimental studies, is to provide the electrochemical industry with theoretical design tools and experimental methods for validation. The theoretical modeling involves approximate analytic methods and numerical analysis. In the experimental studies, concentration and velocity fields are measured by using laser holography and laser Doppler velocimetry, respectively. Attention is focussed on the nonlinear coupling between the electrode kinetics and the aforementioned transport mechanisms. Also the formation of dendrites and some fundamental electrokinetic phenomena are investigated theoretically. The studies have so far been restricted to continuous phases. In a longer perspective, however, effects of gas bubbles in the electrolyte will be considered. This project is a joint venture with the Department of Chemical Engineering and Technology, KTH and the A.N. Frumkin Institute of Electrochemistry.
* Affiliated with the A.N. Frumkin Institute of Electrochemistry of the Russian Acad. of Sciences. ** Affiliated with the Department of Chemical Engineering and Technology, KTH.

Publications: 8,31,52,53,54,107,128

Fluid mechanics of twin wire paper machines

Researchers: Fritz Bark, Rolf Karlsson, Bengt-Joel Andersson, Bo Norman*, Mats Nigam, Sima Zahrai

Sponsors: NUTEK, Bo Rydin Foundation, Swedish Forestry Research Foundation, Swedish Pulp and Paper Research Institute (STFI)

In modern paper machines, the wood fibre suspension is de-watered through two permeable webs. These webs, which are called wires, are highly prestressed. A significant part of the water content is removed by having the pair of wires run over a permeable roll. After the passage over the roll, the direction of motion of the wires is deflected slightly a number of times (in alternating directions) by moving the wires over a set of sharp blades. The motion over the blades sets up a straining field in the suspension, which probably causes break up of fibre flocs. This is a highly desirable process as the paper quality is improved. The wire deflection also leads to some further de-watering. The purpose of the project is to provide the paper industry with a quantitative model of the procceses taking place during the passage of the wires over the blades. Preliminary, in the sense that all relevant quantities have not yet been measured, experiments have been carried out at STFI. Therefore, theoretical predicitons are so far only in qualitative agreement with measured data.
* Affiliated with the Department of paper and pulp technology, KTH.

Models for turbulent ignition

Researchers: Elna Holmberg, Anthony Burden

Sponsors: NUTEK

In this project computational models have been developed for the mean influence of turbulence on small flame kernels, such as in spark-ignition combustion engines. The basic idea is to carefully distinguish between large eddies, which merely impart a random walk to the kernel, and small to moderately sized eddies which affect the internal structure of the kernel and may even quench the flame. During the year attention has been focused on to the concept of flame-front surface-area density. The numerical calculations are based on adaptive discretization and extrapolation in time. The basic modelling approach of the project is being implemented in the joint computer code for Otto-cycle combustion engines of six European car manufacturers.

Theoretical studies of the wave-number spectra of turbulence

Researchers: Erik Lindborg, Anthony Burden

Sponsors: TFR

This activity consisits of theoretical and numerical analysis of the statistical formulation of turbulence in wave-number space. Careful study of the invariants of the 2nd-order velocity correlation of axisymmetric, reflectionally symmetric, turbulence has demonstrated the feasability of evaluating the 2nd-order spectrum from measurements of only two velocity components along a single line orthogonal to the axis of symmetry. In principle, the pressure-strain-rate correletation and anisotropic dissipation rate can also be evaluated. Erik Lindborg has also considered the effects of system rotation, in particular on the -equation. An ongoing project is the study of the equilibrium range of wave numbers and in particular the Eddy-Damped Quasi-Normal closure procedure. The theoretical analysis is supported by direct simulation of Navier-Stokes turbulence at low Reynolds numbers as well as by numerical calculations using shell models at high Reynolds numbers.

Sedimenting two-phase flow

Researchers: Anders Dahlkild

Sponsors: 'Rörlig resurs', KTH

Problems of centrifugal and gravitational sedimentation of small particles suspended in a fluid is studied theoretically. One objective has been to complement the indeed very few analytical studies on continuous, rotating separation processes and also to verify the computational results of a numerical scheme for such processes. This verification is of particular need for two-phase flow fields since quantitative measurements on centrifugal problems are rare. A fundamental problem in separation processes is also the removal of accumulated material of settled particles on the container walls. The models of shear induced resuspension of particles has been complemented to account also for Brownian diffusion of particles. In particular, the accumulation and flow of particles down an incline are studied. With Brownian diffusion included steady solutions are found in parameter regimes which otherwise would lead to a continuous packing of a very dense sediment. Additional extensions of the model may include a yield stress due to interparticle friction appearing at elevated concentrations. Continued work will also investigate these models for a sediment in a rotating environment for which novel effects can be expected. There are also plans to extend the existing numerical scheme for a monodisperse suspension to a scheme for a bidisperse suspension, which is largely an unexplored area for rotating systems.

Publications: 13,77

Hypersonic Afterbody flow fields

Researchers: Tor-Arne Grönland, Anders Dahlkild Sponsors: ESA

This work is part of a research project performed external to KTH by the team FFA and DASA. The aim of the study is to make a thorough and basic investigation of the importance of different physical and geometrical effects which influence the efficiency and versatility of a hypersonic afterbody design. The complete propulsion system is an integrated part of the airframe of a hypersonic airbreathing vehicle. The vehicle body will act as expansion surface, yielding an unsymmetric expansion of the engine exhaust gases to the surrounding pressure. In the design of such an afterbody there are a number of critical issues of which one needs a thorough knowledge.

Modelling of IC-engine flows

Researchers: Magnus Eriksson, Laszlo Fuchs

Sponsor: NUTEK

Turbulent flows in IC-engine configurations are computed by solving the Reynolds averaged Navier-Stokes equation, with k- turbulence model, on a system of overlapping, possibly moving grids. Until now only non-reacting isothermal situations have been considered. The technique has been applied for analyzing the flow prior to ignition, for different piston geometries. Currently, we study the application of a "dynamic" LES model for accounting for turbulence in the engine. These calculations utilize heavily the variable resolution offered by locally refined grids.

Publications: 65

Flow and heat-transfer in ventilated rooms

Researchers: Y. Li, Laszlo Fuchs, M.Sc. student

Sponsor: BFR

Ventilation quality, air-change efficiency and the effects of radiative heat-transfer are the main issues in this work. The problem has been studied both by numerical simulations and full-scale measurements. Numerical simulation can now provide quantititative data for designing and optimizing ventilation systems. Similar techniques can be used for analyzing the stability of stratified layers that are found under certain ventilation conditions.

Publications: 37,38,98

Large Eddy Simulation of swirling jets

Researchers: Magnus Olsson, Laszlo Fuchs

Sponsor: NUTEK, TFR

"Dynamic" Large-Eddy-Simulations (D-LES) have the advantage that the model is paramter free. It also offers the possibility of treating transitional flows as the model "shuts" itself "down" in laminar regions. One of the main issues that is addressed here is the way of determining the validity of the basic assumption that the model has reached an "asymptotic" behaviour. Furthermore, one has to be able to distinguish between the truncation errors and the generalized moments (which may contain numerical errors due to the way the double spatial filtering is carried out!). The technique is tested/applied to spatially developing jets and to the mixing (of passive scalar) in annular swirling jets. The computations are compared to measured data (from LTH).

Publications: 101,102,103

Reacting flow modelling

Researchers: Xue-Song Bai, Laszlo Fuchs

Sponsor: NUTEK

Models for the interaction between turbulence and chemical reactions are studied and analyzed. These models include EDC (Eddy-Dissipation Concept), PDF and flamelet models. The models include some adaptivity in terms of determining which chemical reactions (of a reduced set of reactions) have to be computed together with the flow solver and which reactions are slow (low Damköhler number) and thus can be computed as part of a "post-processing". The sensitivity of different models to the numerical value of model paramters has been studied. These type of studies indicate when and for what purposes, one may use a particular model. Simulation of reacting flows in furnaces and gasturbine combustion chambers have been carried out. The combined models have also been used for geometrical optimization of a specific furnace. In these calculations even radiative heat-transfer was taken into account.

Publications: 6,7,70,71,72,73,74,75,76

Numerical methods for compressible flows

Researchers: Henri Joona, Pär Ekstrand

Sponsor: NUTEK, SAAB, CEC (BRITE-EURAM)

For efficiently solving 3-D transonic flows, a Multi-grid based, Finite-volume Multi-block/overlapping-grid code has been developed. One may solve the Reynolds averaged equations using algebraic turbulence models, or a combined Euler/boundary-layer (SOBOL) solver. The latter technique has been extended to include flows where shock induce boundary-layer separation occurs. The separated flow region is computed iteratively by using the boundary-layer approximation as a "booster". Thus, the combined methods offers an industrially attractive alternative for full Navier-Stokes solvers. In addition, we have extended the basic hyperbolic solver to handle flows from the incompressible limit up to high, supersonic speeds. Currently, we implement "dynamic" LES techniques for handling transitional wing flows. Within the BRITE-EURAM project we are developing methods for generating adaptive grids to be used in conjunction with fast Multi-grid solvers, in low and high Mach numbers flows.

Publications: 88,89

Direct numerical simulations of transition in 3D boundary layers

Researchers: Anders Lundbladh, Dan Henningson

Sponsors: NUTEK, FFA

The project involves DNS of transition to turbulence in three-dimensional boundary layers. Spatial development of disturbances in Falkner-Skan-Cooke boundary layers are under consideration. These flows are important models of aeronautically related flows, such as those over swept wings. A new direction in this research is the consideration of transition to turbulence in flows with separation bubbles, of high importance for aircraft in high-lift situations.

Publications: 122

Bypass transition

Researchers: Stellan Berlin, Anders Lundbladh, Dan Henningson

Sponsors: TFR

This project involves reserach to determine the maximum growh possible of disturbances evolving according to linear theory, as well as to investigate the importance of this growth when non-linearity comes into play. Several shear flow types have been considered. The results show that non-modal growth, i.e. growth not associated with a individual eigenmodes but inherrently dependent on their superposition, can cause large transient amplification. This growth is mainly associated with streaky structures in the streamwise direction. Detailed investigation of the non-linear energy transfer between Fourier components in plane Poiseuille flow shows that energy supplied to smaller scales during transition mainly originates from the non-modal transient growth. Non-linear calculations have shown that when the optimal disturbances from linear theory are used as initial conditions, the threshold amplitudes required for transition to turbulence is lower than for general disturbances.

Another part of the project involves direct numerical simulations (DNS) of transition to turbulence where these tranisent growth mechanisms play a major role. This bypass of the traditional Tollmien-Schlichting instability waves is involved in many shear flow transition scenarios. Previously transition associated with localized disturbances have been investigated, and at present two other bypass scenarios are under consideration. First, the transition in boundary layers starting with a pair of oblique waves is investigated. These waves generate elongated structures in the streamwise velocity which rapidly grow due to the non-modal mechanism, see figure. The resulting streaks break down to turbulence due to a secondary instability. Second, investigations of transition in boundary layers due to turbulence in the free-stream is just starting. Experiments have shown that free-stream turbulence generate streaky structures that grow algebraically, indicating that a similar non-modal instability is operating as in the breakdown of oblique waves. Transition due to turbulence in the free-stream is important in many technological applications, e.g. in turbines and jet engines.

Publications: 11,23,24,25,26,27,33,45,46,47,50,51,117,121,123,124,125

Measurement, modelling and simulation of turbulence

Researchers: A.V. Johansson, M. Hallbäck, T. Sjögren, P. Wikström

Sponsors: TFR, NUTEK

The aim of the project is to develop and critically evaluate models for statistical description of turbulent flows. The main methods used for gaining knowledge of the physics involved are experimental studies and direct numerical simulations of turbulent flows. These methods are complemented by the so called rapid distortion analysis and to some extent also by spectral theories. The models so far investigated belong to the realm of one-point closures for the turbulent stresses, with the main emphasis on closures based on the transport equations for these stresses. Particularly, our efforts have been focused on the modeling problems of flows exhibiting strongly anisotropic turbulence. A number of terms responsible for intercomponent energy redistribution have been scrutinized and models for the individual terms have been proposed. The models are cast in continuum mechanics type of tensor formulations and satisfy basic principles such as realizability of the solutions.

Models for terms in the Reynolds stress evolution equations have been proposed in the limit of homogeneous turbulence. Investigation of near-wall and other inhomogeneity effects have been initiated and some preliminary results from direct simulations of a so called free (stress-less) surface flow have been obtained. The most important result is that the pressure transport is an important term in the near wall anisotropic region.

Detailed measurements using arrangements of double X hot-wires have been performed of the individual components of the Reynolds stress tensor and the two-point second and third order velocity correlations. From these measurements information have been extracted concering the intercomponent energy transfer terms. The results agree well with earlier numerical simulation results and a proposed model for the Re-dependence of the slow pressure-strain correlation (figure ). Also, work on turbulence in a rotating system focusing on the energy cascade mechanism has been pursued and will be concluded in the near future.

During the last year research on turbulence modelling for passive scalars have been started. The approach is analogous to that of the turbulent stress modelling research. So far the main effort has been directed to experimental work, among other things involving development of constant currect anemometry probes for fluctuating scalar derivative measurements.

  
Figure: Large-scale wind-tunnel experiment and direct numerical simulation data in comparison with a proposed model for the so called `Rotta parameter' of the slow pressure-strain rate model.

21,28,29,83,84,114,118,126

Researchers: Arne Johansson, Jukka Komminaho, Anders Lundbladh (FFA)

Sponsors: NUTEK

Fully developed turbulence in plane Couette flow is studied by means of direct numerical simulation. Experience has shown that this is a particularly difficult case to study because of a tendency to develop extremely long vortical structures aligned in the streamwise direction. For a numerical simulation study an extremely long (and also rather wide) box is needed, almost 90 half-heights long in the present case (see figure below). The computations were carried out on a massively parallel computer (CM200) at KTH where the calculations amounted to a total of almost one CPU-month. Accurate statistics have been acquired and the long structures have been studied in detail. It was also shown that a weak (spanwise) rotation has a drastic effect on the long structures. Comparisons with experimental results of Tillmark and Alfredsson are under way.

  
Figure: A greyscale coding of the streamwise velocity component in the midplane between the two walls moving in opposite directions. The turbulence in this Couette flow exhibits extremely elongated structures. Horizontal dimensions of the field shown are

Turbulent boundary layers at high Reynolds numbers

Researchers: Arne Johansson, Jens Österlund

Sponsors: NUTEK

For turbulent boundary layers typical Reynolds numbers are in most applications very high, whereas most laboratory experiments have been carried out at low to moderate Re. In the present project boundary layer measurements are carried out in the MTL wind tunnel at KTH, on a 7 m long boundary layer plate and with free-stream velocities up to 50 m/s. This gives Reynolds numbers based on momentum loss thickness of up to 20000 or roughly 20 million based on , which is realistic for practical applications. Hot-wire anemometry is used with X-probes with box sides down to 0.10 mm. However, severe restrictions in the method have been identified that are coupled to interaction of the thermal wakes from the wires (occurring at low Peclet numbers). Also new types of probe geometries are tested. The thermal wake interactions have been studied in detail by means (2-D) numerical computations of heat transfer from two point sources subjected to a fluctuating velocity field. Several conclusions have been reached from the numerical results regarding the problems in different parameter regimes and on criteria for suitable design of two-wire probes.

Publications: 134

Development of 3 - D LDV measurement techniques with applications to wall bounded shear flows

Researchers:Rolf Karlsson, Jan Eriksson

Sponsors:NUTEK, Vattenfall Utveckling AB

The aim of the project is to develop a practically useful methodology for making simultaneous 3 - D LDV measurements with high spatial and temporal resolution, and to apply this technique to obtain detailed 3 - D turbulence data in the plane turbulent wall jet. In a longer perspective, such data will be used to improve near - wall Reynolds stress turbulence modelling.

One of the main advantages of the LDV technique is that the measuring volume can be made very small, which is very important for turbulence measurements when large gradients are present, e.g. near walls. For measurements of the turbulent shear stress, the LDV measuring volume can be an order of magnitude smaller than that for the hot - wire.

The first phase of the project was to develop and verify the measurement technique. This part of the work has now been successfully completed, and measurements in an enclosed circular jet with a measuring volume as small as have been made.

The intention is now to supplement an earlier (2 - D) investigation of the turbulent wall jet with simultaneous 3 - D measurements of the total velocity vector. In particular, attention will be focussed on the equation for the turbulent kinetic energy and on the limiting behaviour of the Reynolds stresses near the wall.

Publications: 91,92,106,111,119