28 Wind Tunnels and Experimental Fluid Dynamics Research 0 2 Wire Robot Suspension Systems for Wind Tunnels Tobias Bruckmann, Christian Sturm and Wildan Lalo Chair of Mechatronics, University of Duisburg-Essen Germany 1 Introduction In the past decade, the main focus in ship hydrodynamic simulation was the computation of the viscous flow around a ship at constant speed and parallel inflow to the ship longitudinal axis Meanwhile, the numerical methods developed by extensive research allow to simulate the viscous flow around a maneuvering vessel Having these methods at hand, experimental data are required for the validation of the applied simulation models These data can be obtained e.g by wind tunnel experiments Here, particularly the velocity distribution around the body and forces of the flow during a predefined motion are of interest The motion of the ship model can be realized by a superposition of longitudinal motion simulated through the inflow in the wind tunnel and a transverse or rotational motion of the ship realized by a suspension mechanism Mechanisms for guiding a ship model along a predefined trajectory are known e.g from towing tank applications However, the design criteria for these mechanisms are totally different from a wind tunnel suspension system In the towing tank, the weight of the studied vessel is compensated by the buoyancy force On the other hand, the required forces to move the model along a trajectory are much higher due to the higher density and mass of the water in comparison with air In the wind tunnel application, the mass of the model leads to gravity and inertia forces which have to be compensated by the suspension system This chapter describes the development of a suspension system based on wire robot technology Wire robots use wires for the suspension of their end effectors In this application, this is very advantageous since wires have a relatively small aerodynamical footprint and allow for high loads The system described within this chapter is installed at the Technical University Hamburg-Harburg, where ship models must be moved on defined trajectories within the wind tunnel, as described above (Sturm & Schramm, 2010) The application requires the motion of heavyweight payloads up to 100kg with a frequency of up to 0.5Hz for the translational degrees-of-freedom and up to 2.5Hz for the rotational degrees-of-freedom Within this chapter, at first a short historical review of the very active wire robot research within the last years is given in section 2 Afterwards, an appropriate design of the wire robot system is discussed in section 3 Due to the adaptability of the wire robot concept, different geometries are possible Based upon the mechatronic development process according to VDI (2004), two designs are investigated in section 3 Therefore, virtual prototypes using mathematical models and numerical simulation are developed in sections 3.1 and 3.2 Based on the simulation results, the two designs are compared in section 3.3 Using numerical 30 2 Wind Tunnels and Experimental Fluid Dynamics Research Will-be-set-by-IN-TECH optimization approaches, the chosen design is adapted to the specific task, see section 4 In section 5, the mechatronic system design is described Finally, conclusions and future steps are discussed 2 History and state of the art Wires are widely used to suspend models in wind tunnels (Alexeevich et al., 1977; Griffin, 1988) Usually, these wires are fixed and therefore, the model is installed at a statical pose The idea of using a wire robot suspension system adds the capability for performing dynamic and repeatable maneuvers during the experiment This concept was already proposed by Lafourcade (Lafourcade, 2004; Lafourcade et al., October 3-4, 2002) The SACSO (S USPENSION AC TIVE POUR SO UFFLERIE ) robot made at CERT-ONERA is an active wire suspension for dynamic wind tunnel applications Recently, results are presented by chinese researchers (Yangwen et al., 2010; Zheng, 2006; Zheng et al., 2007; 2010), e.g covering the aspects of load precalculation The WDPSS (W IRE - DRIVEN P ARALLEL S USPENSION S YSTEM ) (Zheng et al., 2007) was optimized for large attack angles Note, that in these approaches, the mass of the prototypes was much less than in the application described here which defines new challenges and requirements as described above From a kinematical point of view, the wire robot suspension system described here belongs to the parallel kinematic machines Generally, parallel kinematic machines have major advantages compared to serial manipulators in terms of precision, load distribution and stiffness Contrary, classical parallel kinematic machines have a relatively small workspace compared to serial systems In 1985, Landsberger (Landsberger & Sheridan, 1985) presented the concept of a parallel wire driven robot, also known as tendon-based parallel manipulator or parallel cable robot These robots – in the following denoted as wire robots – share the basic concepts of classical parallel robots, but overcome some of their typical drawbacks: • Flexible wires can be coiled on winches which allow larger strokes in the kinematical chain Therefore, larger workspaces can be realized • No complicated joints are required Instead, winches and deflection pulleys are used • Simple and fast actuators can be used Ideally, winches integrating drives and sensors for the coiled wire length and the force acting onto each wire, respectively, are applied Wires can only transmit tension forces, thus at least m = n + 1 wires are needed to tense a system having n degrees-of-freedom (Ming & Higuchi, 1994a;b) From a kinematical point of view, this leads to redundancy Taking into consideration that the wire robot must always be a fully tensed system to be stiff, the solution space of the wire force distribution has dimension m − n Thus, for each pose of the platform within the workspace, there exists an unlimited number of wire force distributions which balance the load acting onto the platform Contrarily, the wire forces are limited by lower and upper bounds to prevent slackness and wire breaks, respectively From a control point of view, the force distributions must also be continuous while following a continuous trajectory through the workspace This makes the force computation a complicated task, especially when the computation has to be performed in realtime, i.e when a cyclic control system offers only a predefined time slot for all computations during run time Wire robots are subject to extensive research At the University of Duisburg-Essen, the projects S EGESTA (S EILGETRIEBENE S TEWART-P LATTFORMEN IN T HEORIE UND A NWENDUNG , supported by the Germany Research Counsil DFG under HI 370/18, and A RTIST Wire Robot Suspension Systems for Wind Tunnels for Wind Tunnels Wire Robot Suspension Systems 31 3 (A RBEITSRAUMSYNTHESE SEILGETRIEBENER PARALLELKINEMATIKSTRUKTUREN , supported by the Germany Research Counsil DFG under HI370/24-1 and SCHR1176/1-2, focused on aspects of workspace calculation, design optimization and wire force calculation as well as on the realization of the S EGESTA testbed Due to its acceleration capabilities, this testbed was successfully applied e.g for the evaluation of inclinometers used within automotive electronic control units (ECU) (Bruckmann, Mikelsons, Brandt, Hiller & Schramm, 2008a;b; Fang, 2005; Hiller et al., 2005; Verhoeven, 2004) Besides the acceleration potential, the large workspace of wire robots is advantageous which was addressed e.g in the R OBO C RANE project (Albus et al., 1992; Bostelman et al., 2000) at the National Institute of Standards and Technology (NIST), USA The CABLEV (CAB LE LEV ITATION ) prototype at the University of Rostock, Germany (Woernle, 2000) was realized to investigate problems of control and oscillation cancellation (Heyden, 2006; Heyden et al., 2002; Maier, 2004) At the Institut national de recherche en informatique et en automatique (INRIA), Merlet achieved advances in workspace analysis of wire robots e.g by applying interval analysis (Merlet, 1994a; 2004) Aspects of practical application and control are investigated in his project MARIONET which is referenced in section 3 Tadokoro developed the wire robot WARP (W IREPULLER -ARM - DRIVEN R EDUNDANT P ARALLEL M ANIPULATOR ) for highly dynamical motions (Maeda et al., 1999; Tadokoro et al., 2002) and as a rescue system after earthquakes (Tadokoro & Kobayashi, 2002; Tadokoro et al., 1999; Takemura et al., 2006) The acceleration potential was also exploited in the project FALCON (FAST L OAD C ONVEYANCE ) by Kawamura (Kawamura et al., 1995; 2000) At the Fraunhofer Institute for Manufacturing Engineering and Automation (IPA) in Stuttgart (Germany), Pott focuses on the application of wire robots e.g for handling of solar panels (Pott et al., 2009; 2010) and developed the prototypes IPA NEMA and IPA NEMA 2 On the theoretical side, algorithms for fast workspace analysis are developed (Pott, 2008) Several research groups investigate on the application of wire robots for the positioning of reflectors above a telescope (Su et al., 2001; Taghirad & Nahon, 2007a;b) which is challenging in terms of stiffness and kinematics At the Eidgenössische Technische Hochschule (ETH) in Zurich (Switzerland), the interaction of wire robots and humans is adressed This includes e.g a rowing simulator (Duschau-Wicke et al., 2010; von Zitzewitz et al., 2009; 2008) and haptical displays e.g for tennis simulation Additionally, sleep research has been investigated by using the S OMNOMAT setup Nowadays, the wire robot S KY C AM ® by Winnercomm, Inc (USA), is well known from sports television The patent "‘Suspension system for supporting and conveying equipment, such as a camera"’ Brown (1987) was already applied in 1987 In Europe the system became very popular with the soccer championship UEFA EURO 2008™ Wire robots using elastic springs instead of active drives were investigated by Ottaviano and Thomas Ottaviano & Ceccarelli (2006); Ottaviano et al (April 18-22 2005); Thomas et al (September 14-19, 2003) They propose passive wire robots for pose measurements of moving objects In this case the forward kinematics problem has to be solved 3 Topological design Using the suspension system, a wide range of motions should be possible to realize arbitrary maneuvers Two requirements have to be covered: 1 Generally, the maneuvers to be performed are not known a priori (which is contrary to robots and manipulators in many applications) Therefore, a generally large volume of the workspace is demanded to allow for a wide range of motion paths 32 4 Wind Tunnels and Experimental Fluid Dynamics Research Will-be-set-by-IN-TECH 2 The system has to offer a wide range of motion dynamics Again, generally the trajectories are not known which makes it hard to specify the power demands and force or torque requirements, respectively, for the drives and winches and to choose a geometry As a design criterion, one example trajectory was chosen which is described later This leads to the problem of finding an adequate geometry design Due to architectural limitations, the geometry of the supporting frame is fixed and forms a cuboid (see Fig 1 and Tab 1) A similar limitation holds for the moving end effector of the wire robot which is the ship model to be moved Since a wire robot is used and a cuboid platform has to be moved within a cuboid frame on symmetrical paths, an intuitive decision in the topological design step is to use eight wires Two different design concepts are developed and evaluated in the Fig 1 Principle of application following sections: • The first approach uses a rail-based system with wires of constant length The configuration of this mechanism is shown in Fig 1 The wires are used as links of constant length, driven by a skid-rail system Although each two skids share a common rail, every skid is separately operated by a DC motor via a drive belt This equates to a linear drive Linear drives for wire robots were introduced by Merlet (Merlet, 2008) who proposed this concept due to its enormous dynamic potential when coupled with pulley blocks Application examples of the MARIONET robot can be found in Merlet (2010) • The second concept – called winch-based system in the following – is based on classical wire robot approach using motorized winches This principle used e.g at the S EGESTA prototype of the University Duisburg-Essen in Duisburg, Germany (Fang, 2005), or at the IPA NEMA prototypes of the Fraunhofer Institute for Manufacturing Engineering and Automation (IPA) in Stuttgart, Germany (Pott et al., 2009; 2010) In the following, both design approaches are compared to each other using mathematical models and simulation environments This allows to evaluate the performance of the designs at a virtual stage and eliminates the need for expensive real prototypes 33 5 Wire Robot Suspension Systems for Wind Tunnels for Wind Tunnels Wire Robot Suspension Systems 3.1 Kinematical and dynamical modeling of the rail-based system 3.1.1 Kinematics As a base for referencing all fixed points, an inertial frame 6 is introduced which may be B located at an arbitrary point (see Fig 2) Note, that it makes sense to choose a point which can be easily found on the real system, e.g for the positioning of the deflection units or rails A similar approach is used for the definition of points which are attached to the end effector, P i.e which are measured with respect to the moving ship model Therefore, a frame 6 is introduced Now the relation – or, in terms of kinematical analysis – the kinematical transformation B P between the coordinate systems 6 and 6 can be described: The vector r p defines the position of 6 with respect to the inertial frame The orientation of the end effector with respect to the P inertial system is described by "roll-pitch-yaw" angles which are very common in nautical research The local rotation around the x-axis is given by angle ψ, around the y-axis by angle θ and around the z-axis by angle ϕ The end effector pose is therefore described by T B P X = x y z ψ θ ϕ To represent the rotation between 6 and 6, the rotation matrix R is introduced This simple kinematic foundation can already be used to calculate the inverse kinematics which allows to compute the required linear drive positions for a predefined end effector pose (Sturm et al., 2011) Note, that this description is purely kinematic – thus, elastic effects which may have a major influence in wire robots are not taken into account As for most parallel kinematic machines, the inverse kinematics calculation is simple Given an end effector pose X, the inverse kinematics for each driving unit of this robot can be calculated by an intersection between a sphere – representing the wire – and a straight line (see Fig 2) which represents the rail The sphere is described by (bi − rc i )2 − li2 = 0, 1 ≤ i ≤ 8, (1) where the vector bi denotes the current position of the i th skid and li is the constant length of the ith wire Now B rc i = B r p + R P p i (2) describes the position of the i th wire connection point pi on the end effector, referred in the inertial frame 6 B The line can be described by b i = r Si + q i n R i , 1≤i≤8 (3) where rSi is a known point on the ith fixed rail axis, q i the actuator degree of freedom – i.e translation along the rail – and n Ri a unit vector in direction of the length of the rail In case of the proposed robot, n Ri is equal to ey for i = 1 ≤ i ≤ 8 The substitution of equation (1) into equation (3) leads to the equation q i = − ci n R i ± (ci n Ri )2 − c2 + li2 , i (4) where ci = rSi − rc i Analytically, there exist two possible solutions for each actuator due to the quadratic equations On the other hand, from a technical point of view, there are two skids 34 Wind Tunnels and Experimental Fluid Dynamics Research Will-be-set-by-IN-TECH 6 per rail that cannot intersect each other Thus, it is easy to derive a unique solution In the case of the wire robot under consideration, it is assumed that the equation q i = −ci n Ri + (−1)i (ci nRi )2 − c2 + li2 i (5) shall hold for the actuator i As already mentioned, these considerations only describe the 6 P pi l i +1 rp r ci li S i +1 6 B bi rsi hi Si qi nRi Fig 2 Kinematic model motion of the system without the influences of forces or torques Therefore, also elastic effects are not covered by this model Additionally, it is not possible to derive information regarding the required drive performance The base for these calculations is the introduction of a dynamic model in the next section, describing the behaviour of the system under the influence of loads, forces and torques 3.1.2 Dynamics The dynamical equations of motion of the end effector can be described by mpE 0 0 I Mp ¨ r 0 f + − E τE ω ˙ ω × (Iω) gC ¨ x −w gE = AT f (6) 357 Wire Robot Suspension Systems for Wind Tunnels for Wind Tunnels Wire Robot Suspension Systems with mass matrix of end effector, Mp cartesian space vector of coriolis and centrifugal forces and torques, gC vector of generalized applied forces and torques gE Here AT denotes the so-called structure matrix This matrix describes the influence of the wire forces f acting onto the end effector (Ming & Higuchi, 1994a; Verhoeven, 2004) The structure matrix can be derived by ⎡ vm v1 p1 × v1 pm × vm ⎤ f1 ⎢ ⎥ T ⎣ ⎦ = A f = −w, fm (7) where li = li vi , i.e vi is the unit vector along the wires As already introduced in section 2, a wire robot has a redundant structure Thus, for a body – in this case, the ship model – that moves freely in three translational and three rotational degrees of freedom at least seven wires are required Due to symmetry and architectural considerations, in this application eight wires are applied Accordingly, the robot is even twofold redundant This is also reflected by the structure matrix A T which is element of R6×8 Accordingly, eq 7 represents an under-determined system of linear equations Therefore, the calculation of the wire force distribution is not straightforward and rather complicated On the other hand, this offers a potential for optimizations Considering that in this application fast motions of the heavy-weight end effector are desired, it is reasonable to reduce the motor power consumption and the applied load on the mechanical components Additionally, the unilateral properties of the wires have to be taken into account as introduced in section 2: On the one hand, wires have a limited breaking load, on the other hand, the wires need a defined minimum tension to avoid slackness Accordingly, the force distribution f can be formulated as a constrained nonlinear optimization problem (Bruckmann, Mikelsons, Brandt, Hiller & Schramm, 2008a) with minimize f 2 = m 2 ∑ f i2 i =1 s.t fmin ≤ f ≤ fmax ∧ AT f + w = 0 (8) In this paper the function lsqlin from the MATLAB® Optimization Toolbox® has been used to solve the problem Note, that this implementation cannot be used for realtime control since the worst-case run-time in each control cycle cannot be guaranteed a priori Several approaches are known to handle this problem (Borgstrom et al., 2009; Bruckmann, Mikelsons, Brandt, Hiller & Schramm, 2008a;b; Bruckmann et al., 2007b; Bruckmann, Pott, Franitza & Hiller, 2006; Bruckmann, Pott & Hiller, 2006; Ebert-Uphoff & Voglewede, 2004; Fattah & Agrawal, 2005; Oh & Agrawal, 2005; Verhoeven, 2004) In this application, a force minimizing algorithm for realtime force distribution will be implemented, using a geometric approach (Bruckmann, 2010; Bruckmann et al., 2009; Mikelsons et al., 2008) Each wire is driven by a combination of a skid and a DC motor The dynamics of the skid subsystems can be modeled as ¨ ˙ (9) Ms q + D s q + f y = f s 36 Wind Tunnels and Experimental Fluid Dynamics Research Will-be-set-by-IN-TECH 8 with mass matrix of the skids Ms diagonal matrix of coulomb friction between skids and rails, Ds vector of wire force component in direction of skid movement fy skid driving force vector fs Motor and skid are connected by a gear belt, providing a linear drive The elasticity of these belts – as well as the elasticity of the wires as already mentioned – are not taken into account The dynamical equations of the DC motors can be described by ¨ ˙ Mm Θ + Dm Θ + ηfs = u with Mm Dm η Θ u (10) inertia matrix of the drive units including crown gear and motor, diagonal matrix of coulomb friction at the crown gear bearing, radius of the crown gear, vector of motor shaft angles, electromechanical driving torque vector f f si , qi Fig 3 Skid dynamics 3.2 Kinematical and dynamical modeling of the winch-based system 3.2.1 Kinematics Wire driven parallel kinematic systems that use winches instead of rails are well studied as introduced in section 2 Therefore, only a very short description of the kinematics and dynamics is given here The end effector properties are considered to be identical for both systems By the use of fixed eyelets as exit points for the wires, the inverse kinematics approach can be calculated by l w i = b w i − rc i 2, i = 1 ≤ i ≤ 8 (11) In this case the vector bwi denotes the fixed position of the exit point of the i th wire, while equation (2) is used for the transformation of the vectors pi into the inertial coordinate system Here, lwi describes the current length of the i th wire 3.2.2 Dynamics The end effector dynamics, the structure matrix AT and the minimum force distribution are calculated in the same way as presented in section 3.1.2 The significant difference between the rail-based and the winch-based system lies in the actuator dynamics The winch dynamics including the motor can be modeled as ¨ ˙ Jw Θ w + Dw Θ w + μft = uw (12) 52 Wind Tunnels and Experimental Fluid Dynamics Research meaningful in a particular wind flow environment, however they vary depending on the properties of the particulates and the flow conditions and generally do not correspond to well-defined size categories On Earth, in a typical natural environment, dust grains are typically less than 10µm as they are on Mars 2.2 Particle size concept Particles used in wind tunnel experiments are normally single grain particles if they are of sand size But will often aggregate during transport if they are of silt and clay size If the particles were all spheres, no special difficulty would arise in defining and determining their size The diameter would be a well defined parameter However, natural particles are of irregular shape, and generally more irregular the smaller the particles are Measurements of the particle diameters are commonly made though the irregular shape causes difficulties A particle could be regarded as a matchbox 50x35x15 mm or a triaxial ellipsoid and it is obvious that the 3-dimensional form is not easily described by one unique number The term diameter varies widely in meaning with respect to the way in which it is measured All methods of measurements end up with regarding the particles as spheres, or that the measurements made can be expressed as diameter of equivalent spheres However, as sand, silt and clay particles from nature are not spheres the reported sizes are incorrect or inaccurate In the laboratory we have different methods of measuring particle sizes Sieves are commonly used to separate and measure particles of loose single grain materials But sieves do not measure size alone Long cigar shaped particles may pass a sieve and be weighed with particles of a smaller volume but a more regular shape Thus sieves classify particles on the basis of their smallest cross section The holes in sieves have a certain size distribution and laboratory experiments show that the longer sieving times the bigger particles get through the sieves (pers com Dalsgaard, K.) They find the bigger holes Sedimentation after Stoke’s law is another way of sorting particles This is a classic statement of settling velocity of spherical particles Under standard conditions, constant temperature, a given fluid, and a known specific gravity of the spheres v = Cr2, where v is the velocity in cm pr second, r is the radius of the sphere in cm, and C is a constant equal to (2/9) (d1- d2) g/η d1 and d2 are the densities of the sphere and the fluid, respectively, g is gravity acceleration, and η is the viscosity Stokes law has been shown to hold for particles of silt size and smaller down to where Brownian movement influences the settling velocities Sedimentation of the silt and clay size fractions for particle size determination is often done in sedimentation cylinders (Andreasen pipettes) However, if we look at particles collected in dunes of wind blown sand we can see that the equivalent diameter is a debatable expression Figure 1, 2, 3 and 4 are from dune sand samples (Nørnberg 2002) An assumed density of 2.65 g/cm (quartz) is often used for natural particles, but talking about a nominal diameter as we do in Stokes law can be far away from realities, and when it comes to sedimentation in media that do not have a homogenous density like planet atmospheres this have to be taken into account In wind tunnel experiments glass spheres can be used to overcome problems with irregular particle shape If we look at a single sand grain like Figure 5 it is obvious that there are a number of different answers to giving the size 53 Wind Tunnels for the Study of Particle Transport Fig 1 Sand fraction 250-125 µm Fig 2 Silt 63-20 µm Fig 3 Silt 20-2 µm Fig 4 Clay < 2 µm 54 Wind Tunnels and Experimental Fluid Dynamics Research Fig 5 A 100 µm sand grain It could be 1) a sphere of the same maximum length, 2) a sphere with the same minimum length, 3) a sphere with the same weight, 4) a sphere with the same sedimentation rate, 5) a sphere passing the same sieve aperture, 6) a sphere with the same surface area, or 7) a sphere with the same volume This also tells us that particle size standards for e.g sand grains are defined by the technique used for the determination Sieves are often used to split up sand fractions and sedimentation used for silt and clay size fractionation This is however, two very different techniques if used for particle size distribution measurements, and it is often difficult to inter calibrate the two methods An alternative method widely used in industry production and research laboratories is the laser diffraction method This method is based on Low Angle Laser Light Scattering (LALLS) A laser source of coherent light like a He-Ne gas laser with a wavelength of 633 nm is the most commonly used in laser diffraction (LD) instruments A parallel beam of light is sent through a cuvette with suspended particles, either in water or air and a Fourier Transform Lens focuses the light scattered by the particles on a ring formed multi element detector The advantage of using this method is that the whole particle range from < 2 µm to > 3.5 mm can be measured by the same technique The laser diffraction system generates a volume distribution of the sample which is directly equal to the weight distribution if the density is constant The volume is calculated to an equivalent sphere with a certain diameter Data determined by LD is not directly comparable with sieving or pipette methods However, the LD method based on volume is a valid, reproducible method that is very little time consuming (Eshel et al 2004 and Beuselinck et al 1998) 55 Wind Tunnels for the Study of Particle Transport Examples on sand size materials used in the terrestrial wind tunnels, and silt size (dust) used in experiments in the low pressure Mars wind tunnels is seen in Table 1 (all LD determinations) Sample >500 µm 500250 µm 250125 µm 12563 µm 6332 µm 3216 µm 16-8 µm 8-4 µm 4-2 µm 99% of the sand is quartz This material resembles dune sand in Denmark which has also very high quartz content The dust materials used in wind tunnel experiments under Mars conditions are chosen for mechanical physical properties reasons like particle size, magnetic properties, colour These are properties which can be close to Mars dust conditions, while the chemistry is in most cases different from the chemical properties of the Martian dust As seen in table 2 the chemical composition of JSC-1 described by Morris et al (2001) and Moroz et al (2009) and Salten Skov I (Nørnberg et al 2004, Nørnberg et al 2009) are very different, and as we have at present no quantitative chemical analyses of the dust on Mars the samples can not be compared with Mars samples A number of other Mars analogue dust samples used World wide in experiments are described by Marlow et al (2008) The magnetic properties of the atmospheric dust on Mars is estimated to have a saturation magnetization Js of 2.5 Am2/kg (Morris et al 2001), which is not far from the Js of dust captured by Morris at al (2001) on the Mauna Kea volcano, Hawaii which was 2.5±1.5 Am2/kg This is significantly lower than Js of the Salten Skov I, that is 3.9 (1) Am2/kg (Nørnberg et al 2009) 56 Wind Tunnels and Experimental Fluid Dynamics Research SiO2 TiO2 Al2O3 Fe2O3 MnO MgO CaO Na2O K2O P2O5 VolaSum tiles % JSC-1 37.73 3.43 21.06 15.28 0.25 3.01 5.20 1.97 0.49 0.76 10.73 99.91 SS-1 16.10 0.29 < 63 µm 3.20 61.92 1.66 0.16 0.20 0.19 0.52 0.47 14.43 99.14 Table 2 Examples on chemical composition of silt size dust material 3 The one bar sand transport wind tunnels 3.1 The boundary layer wind tunnels Before dealing with flow in aeolian wind tunnels it is expedient to introduce a few concepts and assumptions Thus while the velocity field of flows in Nature is 3-dimensional (3-D) it is often simpler and described using a 2-D approximation in the wind tunnel Thus for a wind tunnel with a rectangular test section, we may assume a 2-D flow having average horizontal velocity component u parallel to the tunnel (x-)axis and average velocity component w in the vertical (z-)direction The corresponding fluctuating velocity components are u’ and w’ The boundary layer flow in the region immediately above the bed has shear stress τ defined as =  = − ∗ where u* is the friction speed The boundary layer has a logarithmic wind profile with u(z) given by ( )= ∗  with κ being the von Karmán’s constant (0.4) and z0 the aerodynamic roughness length The friction speed at which grains can be dislodged from the bed under fluid force is the threshold friction speed (u*t) while the equilibrium velocity of a particle settling through a fluid under gravity is the terminal speed (uF) Both u*t and uF are functions of particle diameter (see e.g Greeley and Iversen, 1987), and particle transport will take place if < ∗ while bedload (saltation or ∗ > ∗ Suspension will dominate for particles having > ∗ (Bagnold, 1941) creep) will be the dominant transport mode if A boundary layer wind tunnel designed for testing the physics of the windborne transport of sand and dust is often referred to as an aeolian wind tunnel Horizontal aeolian wind tunnels such as the primary wind tunnel at Aarhus University (figure 6) have been widely used to study in the laboratory processes related to sand drifting in the terrestrial as well as in planetary environments A variety of issues have been studied such as the threshold for initiation of movement (Bagnold, 1941; Chepil, 1959; Iversen and Rasmussen, 1994), effects of grain impact and inter-particle forces (Iversen et al, 1976; Iversen et al, 1987) and the interaction between wind flow and sand transport rate (Bagnold, 1941; Williams, 1964; Owen, 1964; Rasmussen and Mikkelsen, 1991; Iversen and Wind Tunnels for the Study of Particle Transport 57 Rasmussen, 1999) In nature, much sand transport (on sand dunes for example) takes place on sloping surfaces, but relatively few laboratory studies have been made in order to study the effects of slope Therefore a second wind tunnel of variable slope was built at the Aarhus University (figure 7) and this has been used to investigate threshold and mass transport characteristics for sands of different grain sizes Both wind tunnels at Aarhus University are primarily made of wood The horizontal aeolian wind tunnel (HW) is a 15 m long open circuit, suction type tunnel and the test section is 0.60 m wide and 0.90 m high A small bell-mouth, with a screen attach to it, is placed at the inlet in order to reduce the effect from low frequency fluctuations distorting the natural turbulence characteristics of the internal boundary-layer A sand feed mechanism follows one meter downwind of the inlet to maintain a constant transport rate downwind under the influence of a pre-designed boundary layer Sand transported in the HW is trapped in a sand collector in the downwind end of the tunnel, just in front of the fan and motor The working area is the section from 10-13 m downstream of the entry The side panels of the tunnel body consists of a set of gates (windows) that can swing up thus permitting access to the interior Another set of gates in the ceiling of the tunnel above the working section offer an alternative access to the working section The latter set of gates is primarily used to install instruments which must be operated partly from the outside or connected to an external power supply or recording system Fig 6 The horizontal wind tunnel with main sections indicated: 1 – entry with screen (S) and bell mouth (B); 2 – boundary layer modification with turbulence spires (T), roughness array (R) and sand feed (F); 3 – working section with laser Doppler (LD) and Pitot-static tube (P); 4 – expansion box (sand collector) with screens (S); 5 – fan (F) and exhaust The variable slope wind tunnel (VSW) is attached to the primary wind tunnel via a tower at the sand collector A pair of shutters can open or close either of the tunnels permitting that the sand collector and the motor-fan units are utilized for both tunnels The cross section of the VSW is smaller than that of the HW – only 0.35 m by 0.50 m The length of the VSW is only 6 meters which for the ± 25° variation of slope (upslope and downslope) uses the full height of the laboratory The front of the tower is covered with gates which, when moved one by one from below to above the tunnel (or vise versa), permits the slope of the tunnel to be varied in 5° bins A small bell-mount is placed at the inlet as in the primary tunnel The side panels of the tunnel is made of glass panes which cannot be opened Access to the interior of the tunnel is limited to gates placed almost continuously in the tunnel ceiling between the entry and the tower The working area is from 2 m to 5.5 m downstream of the 58 Wind Tunnels and Experimental Fluid Dynamics Research entry The VSW has a sand feed similar to that of the HW and sand is trapped in the common sand collector except during downslope experiments where most of the sand is trapped in a box at the bottom of the tower rather than in the sand collector Fig 7 Schematic diagram showing the sloping wind tunnel The exit tower permits the slope of the tunnel to be varied in 5" increments from - 25" to +25" The tunnel is suspended in the A-frame with a pivot point at the center of symmetry It is balanced by adjusting a counterweight with respect to its distance from the pivot point 3.2 Boundary layer modification in the tunnels When sand is introduced from the sand feed, it carries the momentum that is necessary for the chain reaction of saltating grains to create an equilibrium sand transport rate However, both the horizontal and the sloping tunnel are too short and too shallow to allow the development of a natural boundary layer which is sufficiently deep and has turbulence characteristics equivalent to those above a sand surface in Nature While the turbulent spectrum in a wind tunnel can never fully simulate that of the atmospheric boundary layer the average wind profile and the high frequency part of the spectrum can be artificially “designed” so that it makes a reasonable analogy to atmospheric surface layer flow Therefore immediately downwind of the entry we aim to construct a wind flow which will be in fair equilibrium with the saltation boundary that develops downstream of the sand feed (figure 6 and 7) Observations made in a previous, smaller wind tunnel indicated that for a high friction speed (u* ≈ 1 m/s) the aerodynamic roughness z0 will increase by a factor of thousand as compared to the quiescent surface For windblown quartz sand Rasmussen et al (1996) find that z0 typically falls in the range 4×10-5 to 1.1×10-3 m when friction speed ranges between 0.2 m/s to 0.75 m/s No single static roughness can therefore represent this enormous range in dynamic sand roughness It has thus been considered necessary to create, with turbulence spires and roughness blocks, a boundary layer which for some selected friction speeds matches the dynamic saltation layer roughness and required boundary layer in the test sections of the two wind tunnels We have selected nominal values of the friction speeds u* = 0.2, 0.3, 0.4, 0.6 and 0.7 m/s u* at which all experiments must be conducted, and in the Wind Tunnels for the Study of Particle Transport 59 next section we shall explain how spires and roughness blocks are used to control the state of the boundary layer Spires and roughness blocks A thick boundary layer which assures dynamic similitude with natural surfaces of drifting sand and which permits measurements of the velocity profile is created with triangular turbulence spires which are inserted in the flow immediately after the bell-mouth In our test section of height H0, the shape of the log-linear wind profile is determined at the entry by the spire geometry i.e spire height H, base width b and spacing Ls We have aimed for a boundary layer thickness δ ≈ 10 cm at approximately 1 m downwind of the entry and the single steps in the design follows the procedure summarized by Irwin (1981) A spire design corresponding to u* = 0.40 m/s is shown in fig 8 On the first 2.4 m of the test section between the spires and the fully developed saltation layer we control the boundary layer by an array of cubic roughness blocks, of block size h and spacing D Somewhat subjectively we have preferred to base the roughness arrays on 3dimensional roughness elements (Wooding, 1973) rather than 2-dimensional elements suggested by e.g Gartshore, 1973) Raupach et al (1991) have proposed that for sparse roughness arrays z0/h = λ (1) where λ is aspect ratio (frontal area/areal block density) They find that z0/h⏐max ≈ 0.1 Rather than using one block size for the entire set of nominal roughness values we use cubes with sizes of 10, 15, 20 and 25 mm placed in a cubic geometry and then control the particular roughness value by the λ-value An array design corresponding to u* = 0.40 m/s is shown in figure 8 One could point out, that Irwin's method gives higher values of the exponent n in the power law profile which is fitted to the boundary layer profile than suggested for example by Counihan (1975) but this is of minor importance because of the long working section Fig 8 Turbulence spires and roughness array for a nominal friction speed of 0.4 m/s 60 Wind Tunnels and Experimental Fluid Dynamics Research Fig 9 The sand feed system 3.3 Sand feed In order to avoid depletion of sand from the upstream part of the bed sand must be supplied continuously during experiments When the airflow is above the threshold of movement saltation is initiated through the collisional chain reaction governed by the splash function (Anderson and Haff, 1991) However, when the fetch is short, such as in a wind tunnel it is imperative that an external source initially supplies momentum to the saltation cloud in order to start the saltation process almost momentarily from nil to its fully saturated value Although the range of particle size in wind-blown sands is usually narrow it also appears that the sand feed is necessary to stimulate transport until the friction velocity is above its threshold value for almost the entire grain population (Rasmussen and Mikkelsen, 1991) Otherwise the coarser grains in the sample will slowly armour the bed and reduce or even stop saltation transport The sand feed used for the VSW is only 350 mm wide while for the HW it is 600 mm (figure 9) However, the cross section of the two sand feeds is the same Sand is stored in the upper funnel from where it drops into the grooves of a rotating drum which then carries the sand to the lower funnel The lower funnel is divided into five chambers from where the sand slides into a 10 mm steel tube and then into the wind tunnel (visible above the roughness array on Fig 8) Depending on the wind flow (friction speed) in the tunnel the tubes stop at 0.4 m above the wind tunnel floor (u* < 0.5 m/s), at 0.2 m (0.5 < u*