Dominik Rupprecht

Rainer Blum

Birgit Bomsdorf

User Centered Inclusive Design for People with Dyslexia: Experiences from a Project on Accessibility

Keywords: User Centered Design, Inclusive Design, Accessibility, User Participation, Methods and Techniques, Dyslexia

User participation is a key element in user centered design of interactive systems. However, applying established methods is not straightforward while realizing a system for people with cognitive impairment due to their specific, heterogeneous needs and abilities. This paper presents experiences from conducting a user centered inclusive design process within an ongoing project. It aims at the development of a web application for people with dyslexia caused by cognitive impairment. A distinctive feature is the intended use of the application: It must support the counseling interviews for planning the real life inclusion of the target group. In addition, it must enable cognitively impaired as well as nonimpaired people using it cooperatively. One of the most challenging issues was how and when to involve cognitively impaired users.

Introduction

In user centered design (UCD) the focus throughout the development process is on the users' needs and (dis-)abilities. Applying traditional methods, however, is not straightforward while realizing a system for people with cognitive impairment. For example, most of the well-known methods of user participation, a key element in UCD, rely on face-to-face meetings that are not easily applicable, because of a lack of knowledge of the diverse, heterogeneous characteristics of the user group. Furthermore cognitively impaired may be unable to concentrate on a topic or to utter a want. All in all, designing interactive systems for and with people with disabilities and their involved personal supporters (caregivers, relatives) is highly complex because of the resulting multi-faceted interplay of needs, abilities, and objectives. Involving people with disabilities in the design process, even though challenging, is important to increase the understanding about these complexities and enables to create more meaningful and useful systems for them. We adapted in a current project, similar to Newell et al. [START_REF] Newell | User-Sensitive Inclusive Design[END_REF], traditional UCD methods aiming at a user centered inclusive design process. This con-tribution presents lessons learned, particularly in facing the challenge of involving people with cognitive impairmentand additional stakeholders. As the focus is on UCD methods, usability problems are only mentioned but not reported in detail.

In the remaining part of this section the project background is introduced and related work is reported. Section 2 shows the involvement of the clients throughout the project. The third section outlines the usage of guidelines for the target application. The final section gives a summarization and a short outlook on ongoing work.

Background of the Project

The main objective of the project referenced in this paper is the investigation of how interactive web forms can be accessible for people with dyslexia caused by cognitive impairment. The proof-of-concept example is a specific form intended to discuss and plan central aspects of the daily life of individuals with impairments. This form is used once a year in collaboration with the concerned persons to perform counseling interviews. The aim is to determine required help and integration services. In these interviews information on the current situation, impairments and wishes of the impaired people are collected. This builds the basis for granting vital support activities in the areas of self-care, living and working for the next months. The currently used form is a PDF document of eight pages crowded with arrays of questions. During the interviews it is used by assistants not only to collect the needed data, but to keep track of the whole process.

Three different stakeholders are involved in the project: The first user group in focus are people with dyslexia attributable to cognitive impairments, in the following referred to as "clients". The second group comprises caregivers and relatives of the clients guiding the counseling interviews, referred to as "assistants". The last group consists of the marketer of the form (the current PDF form and the upcoming web application), a small-sized enterprise with years of experience in providing trainings for using the form.

Related Work

McCarthy and Swierenga [START_REF] Mccarthy | What we know about dyslexia and Web accessibility: a research review[END_REF] give an overview of the literature considering dyslexia and accessibility produced until 2010. The authors highlight that much work has been done in the topics of dyslexia and web accessibility separately. But there is only a small amount of work addressing both aspects at once. They also report that most efforts are focused on how to support users that are blind or have low vision. De Santana et al. [START_REF] De Santana | Web Accessibility and People with Dyslexia: A Survey on Techniques and Guidelines[END_REF] give a good and comprehensive overview over existing guidelines regarding people with dyslexia. They present 41 guidelines to support three website stakeholders: Developers, designers and content producers. These guidelines were gathered on websites discussing dyslexia and accessibility and are based on available sets of guidelines like the Web Content Accessibility Guidelines (WCAG) [START_REF]Web Content Accessibility Guildlines (WCAG) 2.0, W3C Recommendation[END_REF]. The authors divided the guidelines in the following groups: navigation, colors, text presentation, writing, layout, images and charts, end user customization, markup, and videos and audios. One conclusion the authors draw is that end user customization is an important step to achieve accessibility considering dyslexia. But they identified only two guidelines and recommended a deeper study on end user customization.

The Web Accessibility Initiative (WAI) [START_REF]Web Accessibility Initiative (WAI[END_REF] of the W3C proposes an analysis procedure when working with guidelines containing three phases: evaluation by experts, automatically or manual conformity assessment and user evaluation. For the conformity assessment the WebAIM [START_REF]WebAIMweb accessibility in mind[END_REF] project created a checklist (Cognitive Web Accessibility Checklist) and the self-acting evaluation tool WAVE [START_REF]WebAIM: WAVEweb accessibility evaluation tool[END_REF] based on the WCAG guidelines.

Newell at al. [START_REF] Newell | User-Sensitive Inclusive Design[END_REF], [START_REF] Newell | User sensitive inclusive design"in search of a new paradigm[END_REF] point out the need for a shift of paradigm towards a "User Sensitive Inclusive Design" extending the methodologies of the UCD. The authors show challenges when working with people with disabilities and point out differences to the UCD. Challenges we identified also in our project are:  Users may not be able to communicate their thoughts,  Users may not be the purchaser of the final product,  Users with disabilities may have specialized and little known requirements and  Different user groups may provide very conflicting requirements for a product.

Differences we also identified in our project are:

 Much greater variety of user characteristics  Difficulty of finding and recruiting "representative users"  Conflicts between accessibility and ease of use for less disabled people  Possible conflicts of interest between accessibility for people with different types of disabilities

Existing methods and approaches are a good starting point to support the work with disabled users. Newell et al. [START_REF] Newell | User-Sensitive Inclusive Design[END_REF] points out that the designer should develop an "empathetic relationship" with disabled users, rather than rely on standards and guidelines. Thus, following the idea of participatory design, the authors underline the importance of the involvement of the impaired users from the beginning. Furthermore, they suggest to begin the design process with only a narrow list of features to get products that are usable by the target user group and to avoid function-overloaded products the users cannot work with. They also argue for the use of personas in the early project phases. Personas are descriptions of hypothetical archetypes of actual user groups and are developed based on identified user profiles. Zhang et al. [START_REF] Zhang | Social Reader: a Cognitive Stimulation Approach towards Helping Dyslexics[END_REF] make use of personas in the early design and also in the evaluation phases. In their methods, called "persona self-guided evaluation method" and "persona think-aloud method", experts act from the perspective of the persona. These methods cannot fully replace user testing, but enable designers to create a better product when the target user population is not accessible. Working with personas can be helpful to avoid ethical and legislative barriers in working with impaired people. Another approach to this is proposed by Newell et al. [START_REF] Newell | User-Sensitive Inclusive Design[END_REF]: Instead of asking experts to adopt the roles of personas they had well-briefed professional actors working to a well-crafted script in the phase of design. The actors provided a personification of the target user and throughout improvisation interacted with the designers or the users. The authors showed that this method can be a powerful tool of communication between designers and users of technology and in raising the designers' awareness of the challenges when working with disabled people.

There are some projects working with people with dyslexia or cognitive impairments, too. For example Sutcliff et al. [START_REF] Sutcliffe | Investigating the usability of assistive user interfaces[END_REF] investigated an e-mail system for users with cognitive impairments (e.g. attention span problems, working memory limitations, mild problem-solving and language disorders). They showed that with cognitively impaired people, often, training is no solution when there are problems with the user interface. Or Hagelkruys et al. [START_REF] Hagelkruys | Including Dyslexic Users in the Early Design of the LITERACY Portal[END_REF] who are working on the ongoing LITERACY web portal to improve social inclusion of youth and adults with dyslexia. They use additional tools like screen reader to support people with dyslexia. The usage of those tools is not part of this paper, but is considered in our development.

Involvement of Clients

At the beginning of the project all members of the project consortium assumed that substantial contributions of the clients for the analysis could not be expected due to their cognitive and verbal impairments (compare to [START_REF] Newell | User sensitive inclusive design"in search of a new paradigm[END_REF]). Within the early phase of gathering requirements only assistants and the marketer were involved but no clients. However, members of the development team visited six clients in their daily environment like the foster homes they are living in to get a better understanding of the target group (compare to [START_REF] Newell | User-Sensitive Inclusive Design[END_REF]). Out of their observations and statements of the caregivers different client profiles were built containing information about their computer skills like Internet usage, their form of dyslexia and additional physical impairments. This was the basis for building personas to be used at least in the first development and evaluation steps.

During the process the importance to get information from both the clients and the caregivers was underlined and increased. On the one hand, more skills of the clients were observed than the caregivers knew of. On the other hand, the evaluation recordings were analyzed together with caregivers, because the clients have learned to pretend and fake social interaction skillsthus some of their impairments were not visible at first glance.

Early on in the first four months of the project it became clear that the clients could be involved more often. So the project consortium decided to shorten the planned development cycles and to include the clients directly in the process instead of the personas ahead of the original schedule.

To get a greater user base in order to prevent the need of redesign in later phases of the project the initial group of six clients was extended over the course of the project up to eleven clients. With each extension the range of client profiles grew based on the additional information and the existing personas had to be altered and additional ones had to be created. For example, all clients from the beginning were familiar to the web and to browsers. Subsequently, clients without these abilities joined in, resulting in a very heterogeneous group of clients. With each addition more assistants joined in, too.

All of the clients were familiar to the counseling interviews and the original PDF form. Not only in the meetings with only the assistants and the marketer but in general each of them favored a different group of clients. Hence it was harder to come up with coherent solutions, and from time to time the focus was on a subgroup but mostly the design considered the whole group. It is still challenging to specify priorities of user profiles or of impairments to lead the design processes.

Prototypes of different fidelity and type were utilized throughout the development process. As also suggested by Zhang et al. [START_REF] Zhang | Social Reader: a Cognitive Stimulation Approach towards Helping Dyslexics[END_REF] we started with sketches and paper prototypes to come up with a number of different ideas. Based on selected solutions simple HTML pages were created including only parts of the intended system. Later on we used interactive prototypes using the wireframe and rapid prototyping tool Pidoco [START_REF]Pidoco -The Rapid Prototyping Tool[END_REF]. It enabled us to realize interactive low-fidelity prototypes very fast to get feedback on them and to evaluate those involving assistants and the marketer.

Even the first evaluations were conducted with the clients and not by using personas as projected before. This decision resulted from the positive experiences. The evaluations with the clients were conducted as field tests taking place in their familiar surroundings. They were performed in form of a user test combined with further standard usability methods like questionnaires and scenario-based tasks the user were asked to perform as well as audio and video recording. The recordings were analyzed together with the caregivers and assistants so that they could individually interpret the reactions and statements of the clients.

For the different client groups nearly identical scenario-based tasks and test settings were implemented. We started with the first HTML prototype with only limited functionality to check the hierarchy, navigation structure and simple input fields. The clients understood that the prototype did not represent the whole PDF form they are familiar with and no problems with this artificiality of the system were observable. Whether or not the clients realized the artificial situation became not clear, but this was not a problem, too. But quickly we realized that the process of filling out the PDF form is really essential to the life of the clients. The clients were enthusiastic being part of the test and started to work on their participation in life. For example, they were not in favor to fill in "only" test data but wanted to have their actual data filled in. Therefore, a person of the evaluation team had to assist them by instructing them how to type single words. In subsequent evaluations we considered bigger parts of the counseling interviews and followed the known counseling procedure.

With each of the conducted four iterations the range of functions and the level of detail of the implementation grew resulting in an evolutionary prototyping with a fully functional demonstrator version of our application at the end.

Other variations from the original procedure based on the PDF form were that the clients wandered from one topic to another and didn't focus on the given task. Sometimes the clients only wanted to show what they could do with the computer, regardless if it was on subject or not.

As mentioned above clients are used to hide their impairments and have strategies to avoid attracting attention. This made it difficult to get information from the clients about their opinions of the tested prototypes. Most of the time it seemed that the clients had two strategies: providing answers that they assumed the observers wanted to get or providing answers by which they hoped to avoid follow-up questions. When they were asked to mention positive and negative points about the application, almost all answers were that everything is all rightalthough problems were observed. Particularly in the first two prototypes clients were not aware of most of the interactive elements and navigation possibilities. However they were not pointed to the problems (afterwards) not to unsettle them and to keep up their motivation to participate.

Guidelines

Another part of our approach was consulting existing accessibility guidelines. The summary of de Santana et al. [START_REF] De Santana | Web Accessibility and People with Dyslexia: A Survey on Techniques and Guidelines[END_REF] was a good starting point. Typical guidelines like avoiding scrolling, recommended text size or the use of short, simple and direct sentences were considered throughout the design phases. We also used the mentioned WAVE tool [START_REF]WebAIM: WAVEweb accessibility evaluation tool[END_REF] to automatically check against the common accessibility guidelines.

Additionally the project consortium committed to advance guidelines. It was discussed which (minimal) mental model of the application the users should be required to build and what the clients are capable of. We wanted to use as few different concepts as possible (compare to [START_REF] Newell | User-Sensitive Inclusive Design[END_REF]) that have to be understood by the clients (easy-of-use), because training of using the interface was not possible (see [START_REF] Sutcliffe | Investigating the usability of assistive user interfaces[END_REF]).

It was not possible to show the entire hierarchy and structure of the eight-page PDF form at once. The form was therefore split up resulting in a hierarchical structure. According to the assistants' and marketer's previous knowledge about the clients the number of layers of the hierarchy was reduced to four (more width, less depth), each layer containing a set of elements that could be shown only partially. The main question at this point was how to support the clients to move through the hierarchy even if they are unable to build a mental model of it. This could be split up into:  How to show that there is more to find in lower levels?  How to show that there is more on the same level?

We re-formulated such questions from the client perspective using simple language (e.g. if at a current subordinate node of the hierarchy a set of elements exists that could not be presented at a time: "How to show, that there is more?" "How to show, that there is a sub-layer?"). This helped us in different ways: Fist it supported the developers to empathize with the clients and to get the perspective of the clients. Second it helped in communicating with the assistants, because this communication can be difficult as they come from different backgrounds and have different jargons (compare to [START_REF] Newell | User sensitive inclusive design"in search of a new paradigm[END_REF]). Further guidelines refer to the visual design of the interface, e.g.:

 No use of 3D elements: A use of three-dimensional elements in the interface was not possible, because this representation would demand too much cognitive resources of the clients to understand and work with it.

Other examples of guidelines and conflicts between them are:

 Prevent distractions: Each webpage should contain only one input field. The attention of the clients should be targeted only at one information unit at a time to prevent distraction. At the same time, however, every option should be visible. Following "out of sight, out of mind" an invisible option will most likely be forgotten.

In the current prototype some pages contain more than one input field to preserve information. Additionally, each webpage contains as many visual clues as possible to navigate to the remaining input fields.

 Control: No use of a wizard to guide the users. Some of the assistants and the marketer wanted that the clients are enabled to have free control over the dialog and navigation. The clients should be able to visit the pages in an arbitrary order not to force a specific sequence in filling out the form. Later on assistants and marketer agreed with the developers that software assistants such as a wizard are needed.  Always save automatically: The clients do not have to save their inputs explicitly, e.g., by a "Save"-UI-Element. The behavior of the application should be like filling out a paper based form, where you do not need to save the inputs separately. This was in conflict to the assistants' expectation, who were missing the explicit and familiar saving function when working with the application.

General applicability of these guidelines is still under investigation. Nevertheless, these guidelines often served us within the project to find a common sense. Every time an additional feature was under discussion, it was counter-checked to the guidelines. For example, based on their own "prevent distraction" guideline the assistants and the marketer were convinced not to demand too much additional functionality per page.

Conclusion and Future Work

In this paper we presented experiences from adapting UCD for a user centered inclusive design process within a project aiming at the inclusion of people with dyslexia caused by cognitive impairments (clients). The proof-of concept application was taken from the domain of digital forms the clients have to understand and interact with. One finding is that real clients could be involved much earlier than assumed before. Their contribution to the analysis and evaluation is essential even if this contribution is more difficult to achieve due to the cognitive and verbal impairments. In our project the clients were highly encouraged to work with us. They were proud to take part and working with us was a welcome distraction of their daily life. All in all, they asked to be more involved. For the developers this was a very positive experience, too, and they are willing to expand client participation even though it is more challenging and time consuming. Statements and behavior of the clients have to be analyzed very carefully since the clients are used to "fake", i.e. they develop strategies to hide their impairments. Not only because of this but in general, working with the assistants and caregivers is very important due to their specific knowledge and expertise about their clients.

Throughout the project the use of rapid prototyping and of the developed guidelines proved to be valuable to find solutions. The prototypes essentially supported communicating design ideas within the project team (assistants, marketer, and developers). New features were easily counter-checked against the guidelines. The impact on the whole system of features to be implemented was rapidly checked by new prototype versions.

One challenge for the developers was to implement "simple" solutions, e.g. "no use of 3D elements" (see above). However, reactions of the stakeholders to the current system were positive. One of our next step is to evaluate, if the developed application can improve the counseling interviews and thus the inclusion of impaired people.

Acknowledgement

This project (HA project no. 310/11-55) is funded in the framework of Hessen Mod-ellProjekte, financed with funds of LOEWE -Landes-Offensive zur Entwicklung Wissenschaftlich-ökonomischer Exzellenz, Förderlinie 3: KMU-Verbundvorhaben (State Offensive for the Development of Scientific and Economic Excellence).


Nikolai V Kozlov
email: kozlov.n@icmm.ru

Dominique Pareau

Andrei O Ivantsov

Moncef Stambouli

Steady flow instability in annulus with deflectors at rotational vibration

Keywords: Mixing, Mass Transport, Annulus, Rotational Vibration

Experimental study and direct numerical simulation of dynamics of an isothermal low-viscosity fluid are done in a coaxial gap of a cylindrical container making rotational vibrations relative to its axis. On the inner surface of the outer wall of the container, semicircular deflectors are placed regularly, playing the role of flow activators. As a result of vibrations, the activators oscillate tangentially. In the simulation a two-dimensional configuration is considered, excluding the end-wall effects. In the experiment a container with large aspect ratio is used. Steady streaming is generated in the viscous boundary layers on the activators. On each of the latter, beyond the viscous domain, a symmetric vortices pair is formed. The steady streaming in the annulus has an azimuthal periodicity. With an increase in the vibration intensity, a competition between the vortices occurs, as a result of which one of the vortices (let us call it even) approaches the activator and the other one (odd) rolls away and couples with the vortices from the neighbouring pairs. Streamlines of the odd vortices close on each other, forming a flow of a cog-wheel shape that encircles the inner wall. Comparison of the experiment and the simulation reveals an agreement at moderate vibration intensity.

Introduction

Vibration is an efficient instrument for control of mechanical systems [START_REF] Blechman | Vibrational Mechanics[END_REF] and it brings multiple advantages and new solutions to technological processes. A remarkable effect due to vibration in fluid systems is the steady streaming, which found its application in diverse areas [START_REF] Riley | Steady Streaming[END_REF].

A problem of mixing and homogenization of solutions in chemical and biological reactors is vital for efficient mass transfer. For instance, traditionally a rotating stirrer is used for agitating a liquid solution. This technique can be very efficient in terms of homogenization at high rotation rates. But it has some drawbacks, for example high energy consumption. In the case of multiple phases, one of the disadvantages is interface destabilization, which creates difficulties in controlling the chemical reaction rate. And in biological systems it is high shear stress, which is harmful for living organisms like microalgae. An approach to deal with agitation in a reactor is based on the use of vibration-induced streaming. For instance, introducing vibrating activators in a chemical cell with constant interface has demonstrated promising results based on a heat transfer study [START_REF] Ivanova | Heat Transfer in a Closed Cavity under Conditions of Forced Vibrational Convection[END_REF].

The study of transport of sub-micron sized particles in the acinar region of the lung revealed that the steady streaming is at the origin of kinematic mixing in the alveolus [START_REF] Kumar | Steady streaming: A key mixing mechanism in low-Reynolds-number acinar flows[END_REF]. Steady streaming may also be used for enhancement of the separation process, in which it allows the reduction of membrane fouling. So, [START_REF] Kola | Application of low frequency transverse vibration on fouling limitation in submerged hollow fibre membranes[END_REF] successfully applied the transversal vibrations to a system with cylindrical hollow-fibre membrane.

The flow around an oscillating cylinder has been an object of interest for many researchers. [START_REF] Schlichting | Berechnung ebener periodischer Grenzschichtströmungen[END_REF] studied theoretically and experimentally the flow around a circular cylinder oscillating along its diameter. He found that a steady streaming is generated in the Stokes layers on the surface of the cylinder and that a secondary steady streaming is excited outside these viscous boundary layers. [START_REF] Stuart | Double boundary layers in oscillatory viscous flow[END_REF] theoretically showed that at a large characteristic Reynolds number, an outer boundary layer appears within which the steady-streaming velocity decays to zero. [START_REF] Honji | Streaked flow around an oscillating circular cylinder[END_REF] experimentally found a three-dimensional streaked flow around an oscillating cylinder developing due to an instability. A systematic experimental study of different flow regimes around an oscillating cylinder was performed by [START_REF] Tatsuno | A visual study of the flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers and low Stokes numbers[END_REF] in a quite large range of Keulegan-Carpenter numbers.

The use of rotational vibrations brings an advantage in controlling the shear stress, since the flow is mainly tangential to the container walls and eventual deflectors. Another advantage is the possibility of producing homogeneous mixing of the solution by the means of shaping the container walls according to some regular pattern.

Vibrational flows can be highly disturbed and the study of their stability is an important problem for optimization of operational regimes of vibratory devices. In the present work an experimental and numerical study is done of the fluid flow in an annulus with deflectors regularly situated on the outer wall. The considered apparatus represents a conception of liquid mixing via rotational vibrations.

Experimental setup

The working volume is formed by two coaxial cylinders. The inner and outer radii of the annulus are, respectively, R i = 30.0 mm and R o = 50.0 mm (Fig. 1a). The interior height of the cell equals 200.0 mm. On the interior surface of the outer cylindrical wall, six deflectors with the shape of half-cylinders of diameter d = 16.0 mm are placed equidistantially. They serve as flow activators.

A photo of the experimental setup is shown in Fig. 1b and a scheme of the vibrator is presented in Fig. 1c. The transparent cylindrical container 1 with an annular cavity is fixed on the vibrating platform 2 and filled with a working liquid. The stepper motor McLennan 34HSX-208 3 transmits rotation to the crank 4 via a belt drive 5 . The motor is controlled by the drive MSE570-2. The connecting rod 6 transforms rotation of the crank into rotational oscillations of the platform and the cavity. The vibration frequency f varies from 0 to 20 Hz. The DC alimentation of the motor is done with the help of a power supply Isotech IPS 303DD. When a higher intensity of vibration is needed, two power supplies are connected in a series. The clock signal for the motor is provided by a sound generator Hameg HM8150. The angular amplitude of vibration is set by positioning a crank pin 7 and varies in the range ϕ 0 = 0.05 -0.2 rad. The vibration amplitude is measured optically; for this, a laser 8 is fixed on the vibrating platform. The laser beam is projected on a screen 9 and the length of the laser track is measured. In the studied range of parameters f and ϕ 0 the motion of the vibrating platform remains sinusoidal.

The working fluid was water, into which a small amount of tracer particles Rilsan D40 (with the diameter of 40 µm) was added. Laser light sheet was used for particles illumination. The images were captured using a Dantec CCD camera FlowSense 2M and processed for PIV (Particle Image Velocimetry) with PIVlab software [START_REF] Thielicke | PIVlab -Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB[END_REF]. PIV technique was adapted for studying a steady streaming: the images were taken with the frequency of vibration. Consequently, they were all in the same phase. The time step for each image pair was taken equal to the period of vibration. For higher precision, velocity field obtained through PIV was averaged over 50 image pairs. Each image pair was processed in three consecutive passes with gradual decrease in the size of interrogation area: 64×64, 32×32, 16×16 pixels.

Numerical method

Direct numerical simulation (DNS) of the flow was done in a software package ANSYS Fluent. A two-dimensional transient-time formulation was used. Pressure and velocity were coupled. The spatial descretization was done using the model PRESTO! for pressure and the third-order MUSCL scheme for momentum. For temporal discretization a second order implicit formulation was chosen. Rotational vibrations and time averaging of solution were done through the user defined functions (UDF). The time step was equal to 1 100 of the oscillation period, τ = T /100. The frame rotation at a constant rate was imposed. These parameters correspond to the following Navier-Stokes equation:

∂v ∂t + ∇ (v r v) + Ω r × v = -∇p + ν∆v
Here, p stands for pressure, ν is the fluid kinematic viscosity. v r is the fluid velocity in the rotating reference frame: The angular rotation rate Ω r was substituted through the UDF by a harmonic function

v r = v -Ω r × r. R i R o d 0 sinΩt a b
Ω r = kϕ 0 cos Ωt.
Here, k is the axial unit vector, and Ω = 2πf .

The fluid velocity was averaged over a period of oscillations, i.e. each 100 time steps.

For the working fluid, the properties of water were used. The laminar viscous model was chosen. Since the fluid is low-viscosity, viscous interaction takes place in thin Stokes boundary layers of the thickness δ = 2ν/Ω near the solid walls. In order to have an appropriate resolution of the boundary layers, an adaptive mesh was used (Fig. 2). The regions near the walls (viscous domain) were meshed with quasi-rectangular cells of constant azimuthal dimension and with progressively increasing radial thickness. The thickness of the first cell was calculated as δ/25, the increment factor was 1.1, the number of cells in the boundary zone was taken such as to cover the thickness of 3 20 of the annulus width (R o -R i ). The azimuthal size of the cells on the wall was taken as 1 50 of the activator circumferential length. The region outside the boundary zone (non-viscous domain) was meshed with triangular cells with the average size equal to 1 40 of the annulus width.

The numerical method was tested with finer boundary zone meshing, with the thickness of the first cell δ/40. The time-averaged flow velocity discrepancy was only 0.07%. This allows us to consider that the thickness of the first cell equal to δ/25 is sufficient.

Steady streaming

Rotational vibration creates tangential oscillations of the cavity wall relative to the fluid. Part of the fluid is displaced by oscillating activators, which move together with the cavity wall. Since the width of the annulus is not constant, narrower at activators, the azimuthal gradient of the pulsation velocity amplitude appears. In these conditions, fluid oscillations lead to the generation of average flows in the thin oscillating boundary layers near the walls [START_REF] Schlichting | Boundary-layer Theory[END_REF]). This mechanism is known as steady streaming [START_REF] Batchelor | An Introduction to Fluid Dynamics[END_REF]. The average mass force acting in the boundary layers involves fluid in the whole layer in a steady motion of vibrational nature.

Experimental results

At vibration, on the background of oscillatory motion, a steady streaming is generated, and a periodic average vortex pattern is formed in the annulus (Fig. 3). Each vortex is in contact with an activator and washes its surface in the outward direction (with respect to the container axis). At equal distance from two neighbouring activators the vortices come into contact and are directed inward. The spatial period of vortex pattern is equal to the period of activators positioning. On a single activator two vortices are counter-rotating (Fig. 3a,1 ). Besides, a pair of minor vortices is generated on the opposite side, near the inner wall (Fig. 3a,2 ). Another pair of minor vortices is formed on the outer wall between the activators (Fig. 3a,3 ).

The most intensive flow is found in the corners, where the cylindrical surface of an activator comes in contact with the outer wall of the container (Fig. 3a). The flow velocity between the activators is rather weak, and a characteristic time for a fluid particle to cross the annular layer would be an order of a minute, i.e. a few tens to hundreds of oscillation periods. Vibrational convection produces a sufficiently homogeneous velocity distribution across the layer, with little stagnant zones.

By displacing the laser light sheet along the container axis it was shown that the flow pattern and fluid velocity are invariant along the z-axis. The vortices of the steady streaming are elongated parallel to the rotation axis and form regular rolls. Hence, the flow structure can be considered two-dimensional and the results obtained for one annulus cross section can be taken as representative of the whole volume.

v τ = - 3 4Ω V 0 ∂V 0 ∂x τ . (1)
Here, V 0 is the amplitude of pulsation velocity, x τ is the coordinate tangential to the activator surface. In Fig. 5 outside the boundary layer the flow is directed opposite the gradient ∂V 0 /∂x τ , which is in agreement with the expression (1).

Instability

With an increase in vibration intensity, in a threshold way the flow symmetry with respect to an activator is broken (Fig. 6). Let us call the vortices on Fig. 3, which are rotating clockwise, "even" and those rotating counter-clockwise "odd". At a critical value of vibration acceleration, R o ϕ 0 Ω 2 , either "even" or "odd" vortices expand beyond the activators and form a large-scale vortex encircling the inner wall in the form of a cog-wheel, let us denote it as vortex A. All of the grouped vortices have the same rotation direction, and it determines the direction of the vortex A. Meanwhile the other half of the vortices are oppressed and localized in close proximity of the activators, these vortices will be denoted as B (Fig. 6b).

The choice between "even" and "odd" vortices is random. For example at equal parameters, f = 4.0 Hz and ϕ 0 = 0.061 rad, in experiment (Fig. 7) and computation (Fig. 8) the opposite direction of the supercritical flow is found. The fluid velocity, excluding from consideration the viscous domain, found in the numerical simulation is in agreement with that from the experiment. Despite the opposite direction, the magnitude is the same. This means that the described bifurcation may be considered as instability of the nonviscous, secondary steady flow. The vortices grow in size with Re p as can be seen from comparison of Figures 9 and10. This creates a tendency of a vortex to invade the space of its neighbouring vortex, which rotates in the opposite direction. Such situation is prone for the growth of small perturbations. And, as will be shown in Section 6, this leads to the soft onset of instability at the critical values of Re p and ω.

Analysis

The flow stability has been studied systematically for the range of frequencies from 1 to 10 Hz, which corresponds to ω = 402 -4021. The bifurcation diagrams are presented in Fig. 12. They split according to the value of vibration frequency. The stability threshold depends on the vibration acceleration, and with the frequency increase the critical value of the amplitude ϕ 0 decreases (Fig. 13). The series of points in Fig. 12 are shifted along the axis ϕ 0 likewise. The stability threshold and the dependence of supercritical dynamics on the vibration amplitude is determined by the dimensionless frequency. This is demonstrated by a comparison of computation results for the containers of different size: R o = 50 mm (points 3 ) and R o = 100 mm (6 ), meanwhile the geometrical similarity was preserved. Since the characteristic length for the points 6 was doubled, at the frequency f = 1.0 Hz the dimensionless frequency in this case is equal to the case of the four times higher frequency. The flow rates are equal for points 3 and 6, as well as the threshold values of ϕ 0 . Quantitative results of the experiment and the numerical simulation are in good agreement at the pulsation Reynolds number up to about 200, which corresponds to the symmetrical regime and to the moderate supercriticality. Conventionally, one can determine the latter as a condition when the average flow rate through the radial crosssection between an activator and the wall is greater than the flow rate in the threshold by about an order of magnitude. Experimental points 4 in Fig. 12 have a slight discrepancy with respect to the numerical points 3 at ϕ ≤ 0.06 rad, but at ϕ ≥ 0.07 rad the dependence Q a (ϕ 0 ) found in experiment is completely different. PIV analysis of the flow revealed that in experiment a secondary instability occurs, at which the structure of the cog-wheel vortex is broken (Fig. 14b). This instability is not found in the numerical simulation, despite the wide range of parameters was studied. This means that at ω = 1608, the used two-dimensional numerical model is valid for description of the flow in the container of large aspect ratio in the range Re p < 267 ± 41. In order to compare the results at different values of the dimensionless frequency ω, we introduce a dimensionless flow rate (Q a /ν) ω. The points series split according to the dimensionless frequency, and it is possible to follow the evolution of the dependency with ω increase (Fig. 15). At ω = 402 (points 1 ) the dimensionless flow rate grows with Re p by a logarithmic law. At ω = 4021 (points 5 ) this dependence is very close to linear. The curves interpolating the series at ω = 804 (points 2 ) and at ω = 1608 (points 3 -6 ) have a transient shape. If now we consider the threshold of symmetric flow stability, the studied range of ω lies between two asymptotic limits, in which Re p does not depend on ω (Fig. 16). This explains that the transition of the dependence of (Q a /ν) ω on Re p from logarithmic to linear is associated with the transition between two limiting cases.

The instability of secondary steady flow in the limit of high ω was reported by [START_REF] Ivanova | Vibrational Convection in a Nontranslationally Oscillating Cavity (Isothermal Case)[END_REF]. They experimentally studied the dynamics of fluid flow in a rotationally vibrating cylinder of the square cross-section. In this case a steady streaming in the form of eight vortices is generated. In each corner of the square crosssection, a pair of vortices with opposite circulation are located. With an increase in Re p , a half of vortices with the same rotation direction are united in one large-scale vortex, Stability threshold on the plane of dimensionless parameters (ω, Re p ) , 1 -DNS, 2 -experiment. At extremities of the studied range of ω the points approach two asymptotic values of Re p while the other four vortices are pushed towards the container walls. At ω > 5000 the flow is self-similar with respect to the frequency; here ω is calculated from the half of the lateral size of the square a/2 as the length scale. In this limiting case the subcrical and supercritical flow velocity, as well as the symmetry break threshold, are determined uniquely by the pulsation Reynolds number. In the work by [START_REF] Ivanova | Vibrational Convection in a Nontranslationally Oscillating Cavity (Isothermal Case)[END_REF] the rotation rate of the large-scale vortex is proportional to Re p . This qualitatively agrees with the results of the present research for high ω (Fig. 15, points 5 ).

Conclusion

The flow excited by rotational vibrations in an annulus with deflectors has been studied experimentally and numerically. Tangential oscillations of the deflectors lead to the generation of the steady streaming in the Stokes boundary layers. The secondary steady flow establishes in the whole volume of the annulus. The flow pattern is a regular system of two-dimensional vortices with alternating rotation direction, each pair of vortices being symmetric with respect to an activator.

With an increase in the vibration intensity the secondary steady flow undergoes an instability, and the vortices with the same rotation direction merge in one large-scale cog-wheel vortex, while their opposites are reduced in size and pushed closer to the activators. Thus, the activator-wise symmetry is broken. The instability occurs because at the higher forcing acceleration the neighbouring vortices become too big and invade the space of their respective neighbours.

The results obtained in experiment and in DNS are in good agreement below the symmetry-break threshold, and above it if the forcing is not high. Above a certain value of the pulsation Reynolds number (Re p = 267 ± 41 at ω = 1608), in the experiment a secondary instability is observed, which has not been found in the numerical simulation. This regime of higher supercriticality remains an open topic for study.

Stability threshold is governed by two parameters: the dimensionless frequency ω and the pulsation Reynolds number Re p . With increase in ω the critical value of Re p decreases. At the extremities of the studied range of frequencies the dependency Re p (ω) tends to become asymptotic.

In the limiting case of high frequencies, a qualitative agreement is found with an earlier research done by other authors for rotationally oscillating container with the square cross-section. The law, by which the rotation rate of the cog-wheel vortex grows with Re p , tends to become linear at the highest ω.

Figure 1 .

 1 Figure 1. Experimental setup. a -Photograph of the annulus through the upper lid, along the axis of rotation; the dimensions are depicted in the plane of the laser light sheet. b -Experimental cell mounted on the vibrator. c -Scheme of the vibrator: 1 -cell with annulus, 2 -vibrating platform, 3 -stepper motor, 4 -crank, 5 -belt drive, 6 -connecting rod, 7 -crank pin, 8 -laser, 9 -screen

Figure 2 .

 2 Figure 2. Annulus with deflectors with the grid meshed for the frequency 4 Hz (a); R i -inner radius, R o -outer radius, d -activator diameter. The figure (b) is zoomed: adaptive mesh is seen in the boundary zone on the walls

Figure 3 .Figure 5 .

 35 Figure 3. Experimental results for f = 4.0 Hz and ϕ 0 = 0.050 rad. A vector plot of the average velocity field (a) is obtained from PIV; a colour map shows the average velocity magnitude; the streamlines on the right-hand side of the figure (a) are drawn automatically as tangents to the vectors . A vorticity plot (b) is derived from the velocity field.

Figure 6 .

 6 Figure 6. The vector plot of the average velocity (a) and the vorticity plot (b) obtained in experiment at f = 5.0 Hz, ϕ 0 = 0.050 rad. The "odd" vortices have formed a cog-wheel vortex rotating counter-clockwise, its center coincides with the container axis

  Figure 12. Bifurcation diagrams: transversal flow rate vs. amplitude. f = 1 Hz (1, 6 ), 2 Hz (2 ), 4 Hz (3, 4 ), 10 Hz (5 ). Points 4 are obtained in experiment; points 6 are calculated for R o = 100 mm

Figure 14 .

 14 Figure 14. Streamlines traced based on PIV data for f = 4.0 Hz, ϕ 0 = 0.06 rad (a) and 0.09 rad (b). The cog-wheel vortex is regular in figure (a), at the higher amplitude it undergoes an instability (b)

  Figure 15. Bifurcation diagrams on the plane of dimensionless parameters. Notations correspond to Fig. 12

  Figure16.Stability threshold on the plane of dimensionless parameters (ω, Re p ) , 1 -DNS, 2 -experiment. At extremities of the studied range of ω the points approach two asymptotic values of Re p

Acknowledgments

The work was supported by the Ministry of Education of Permskii Krai (project С-26/625) and by the Ministry of Education of Russian Federation (task 2014/372, project 2176).