Analysis of Shear Rate inside a Concrete Truck Mixer

Transcription

1 Analysis of Shear Rate inside a Concrete Truck Mixer Jon E. Wallevik 1, Olafur H. Wallevik 2 1 ICI Rheocenter, Innovation Center Iceland, Arleynir 2-8, IS-112 Reykjavik. 2 ICI Rheocenter, Reykjavik University & Innovation Center Iceland Abstract: In addition to the mixing energy applied to the fresh concrete (i.e. shearing during mixing), the shear history after mixing is also important. This applies especially for binder rich self-compacting concrete. This is due to the influence that the binder has on the overall concrete in terms of thixotropic- and structural breakdown behavior. In this work, the shear rate is analyzed inside a drum of a concrete truck mixer. The objective is to better understand the effect of transport of fresh concrete, from the ready mix plant to the building site. The shear rate analysis is done as a function of different drum charge volume and drum rotational speed. Also, the effect of yield stress and plastic viscosity is analyzed. Keywords: Truck mixer; Shear rate; Mixing energy; Drum charge volume; Bingham fluid; Drum rotational speed Introduction In addition to the mixing energy applied to the fresh concrete at the ready mix plant (i.e. shearing during mixing) [1-3], the shear history after mixing is also important. This applies especially for binder rich self-compacting concrete. This is due to the influence that the binder has on the overall concrete in terms of thixotropic- and structural breakdown behavior. The two processes, structural breakdown and thixotropic behavior are well explained in [4, 5]. In this work, the shear rate is analyzed inside a drum of a concrete truck mixer. It can be shown that the shear rate is closely related to the rate of thixotropic- and structural breakdown [4, 5]. Furthermore, the mixing energy, or rate in mechanical effort (also known as rate of work or power) is also closely related to shear rate. Thus, by analyzing the shear rate, one can better understand the potential effect of transport, from the ready mix plant to the building site, in terms of the concrete final rheological state (i.e. when it is cast from the truck mixer into the formwork). Higher K.H. Khayat, SCC th International RILEM Symposium on Self-Compacting Concrete, ISBN: RILEM

2 234 Jon E. Wallevik, Olafur H. Wallevik shear rate will imply higher mixing energy, more effective thixotropic- and structural breakdown and thus more flowable concrete during the casting phase. Lower shear rate will imply less effective mixing, increased thixotropic rebuild and thus stiffer concrete during casting. Here, the shear rate is analyzed as a function of drum rotational speed (0.03, 0.07, 0.11, 015, 019 and 0.23 rps revolutions per seconds) and drum charge volume (namely 2.6, 5.4 and 8.2 m 3 ). In addition to this, the effect of yield stress τ 0 and plastic viscosity μ is also analyzed. Figure 1. To the left: Computational mesh of the KARRENA 9/5 drum. To the right: Inside a KARRENA 9/5 drum (top); A concrete truck mixer (bottom). The concrete drum under consideration is the KARRENA 9/5. It is used for example at the premix plant Steypustöðin ehf in Reykjavik, Iceland. The KARRENA 9/5 has a geometrical drum volume of 15.7 m 3, but the max rated drum capacity is 9 m 3 (since a small end part of the actual drum is not included in the simulations, the drum volume in the computations is slightly less or 15 m 3 ). The range of drum speed is between 0 and 14 rpm (i.e. from 0 to 0.23 rps). The inclination of the drum relative to the horizontal is 11 degrees. In the left illustration of Fig. 1 is the computational mesh shown for the KARRENA 9/5 drum. The number of cell is about , but also a high resolution simulation has been done, which consists of about cells (not reported here). On this note, all analysis is done with the CFD simulation software OpenFOAM, version The simulations were performed on resources provided by the Nordic High Performance Computing (NHPC) on HP BladeCenter cluster, running Rocks. Experimental Programme

3 Analysis of Shear Rate inside a Concrete Truck Mixer 235 The software OpenFOAM is licensed under the GNU General Public License (GNU GPL) and is available at It is written in C++ and as such, an object-oriented programming approach is used in the creation of data types (fields) that closely mimics those of mathematical field theory [6]. OpenFOAM uses unstructured mesh system in Cartesian coordinate system. The no-slip boundary condition (i.e. the Dirichlet boundary condition) is used at all wall boundaries. This is not so unrealistic, as a used drum has usually rough surfaces due to older hardened concrete attached to the inside drum wall. An example of this is shown in the top right illustration of Fig. 1. Instead of physically rotating the computational mesh, the mesh is kept fixed and the gravity-field g is rather rotated at this rate. This means that instead of the drum is rotating on a stationary Earth surface, the drum is stationary and the Earth is rotating around the drum. In taking this step, the system (i.e. the computational domain) represents no longer an inertial reference frame [7] (i.e. is now a rotating reference frame). This means that the Coriolis force and the centrifugal force have to be included into the governing equation [7]. The constitutive equation used here, consists of the Generalized Newtonian Model [8], or in short GNM. An example of such model is the modified Bingham model. In [9], the benefit of the modified Bingham model is discussed for SCC. As such, in this work, it was programmed into the OpenFOAM framework. It should be noted that in this preliminary work, the so-called c-parameter is set equal to zero and thus in effect the traditional Bingham model is now used in this work. For 3D incompressible flow where the GNM is valid, it can be shown that the shear rate is calculated as γ = 2ε : ε [10].The term ε is the rate-of-deformation tensor [11,12]. In this work, the volume averaged shear rate is used. It is given by Eqn. (1). 1 ( t ) ( x, y, z, t) dx dy dz (1) V V The term V is the volume of the concrete sample inside the drum (i.e. the drum charge volume, either 2.6 m 3, 5.4 m 3 or 8.2 m 3 ) and the integration dv = dxdydz is over the same concrete sample. If the shear rate γ = 2ε : ε is constant within the concrete sample, the volume averaged shear rate Eqn. (1) would be the same as the shear rate γ = 2ε : ε. Data analysis

4 236 Jon E. Wallevik, Olafur H. Wallevik Figure 2 shows an example of the shear rate Eqn. (1) plotted as a function of time for the two cases of drum charge volume 2.6 m 3 (to the left) and 8.2 m 3 (to the right) and different drum speed. Above each plot is shown an example of drum with the corresponding quantity of concrete, in which the yellow color shows the surface of the concrete. In these top illustrations are cross sections of shear rate, where the shown color range is from 0 to 5 s -1 in shear rate γ = 2ε : ε, blue representing zero shear rate, while red shear rate at and above 5 s -1. With these cross sections, it is clear that the shear rate within the concrete is highly non-uniform, thus making the integration in Eqn. (1) most necessary to generate quantifiable values for analysis and comparison. Figure 2. Volume averaged shear rate Eqn. (1) plotted as a function of time. The results shown in Fig. 2, applies for the more computational challenging cases, namely when the yield stress is τ 0 = 300 Pa, and the plastic viscosity is μ = 75 Pa s. The density of the concrete samples is set as ρ = 2350 kg/m 3 in this figure and apply for all other cases in this work. At the start of each simulation in Fig. 2, the concrete sample is stationary and therefore the shear rate Egn. (1) begins at 0 s -1. With start of rotation, there are some wave generation occurring due to the fact that the concrete sample is interacting with the helix geometrical shape of the mixing blades inside the drum. Depending on Bingham parameters used τ 0, μ, drum charge volume V and drum rotational speed f, these wave phenomenon will differ (height and distance between the helix shaped blades and overall drum geometry will most certainly also influence the waves). In

5 Analysis of Shear Rate inside a Concrete Truck Mixer 237 some cases, the wave s will cease and the shear rate Eqn. (1) becomes a constant (more or less). For the lower drum speed like f = 0.03 rps, the simulation time of 20 seconds will only rotate the drum by the angle of (2 π f) 20 s = 260º, or just above half a circle. One might expect an incomplete shear rate result because of this. However, increasing the simulation in such manner that a complete rotation (and more) is achieved, did not change the outcome by any significance (see the lowest lines in Fig. 2). It did however increase the CPU cost and thus 20 s of simulation time was maintained for most cases. By time integrating Eqn. (1) as shown with Eqn. (2), only the latter part of the curves in Fig. 2 is utilized. The time integration starts at t = 10 s as shown with the vertical line in Fig. 2. The outcome of this approach (i.e. of Eqn (2)) is shown in Fig. 3. The outcome of this figure is also shown in Fig. 4d. 20s t ( t) 1 (20s 10s) (2) 10s dt Figure 3. Time averaged shear rate Eqn. (2) plotted as a function of drum speed. By starting the integration in Eqn. (2) at 10 seconds, and not at 0 seconds, is made due to the fact that equilibrium in shear rate is usually obtained at 10 seconds (see Fig. 2). The equilibrium value represents the condition in which the concrete is quickly in after start of its transport from the ready mix plant to the building site. Since all of the results presented in the remainder of this work will be in terms of Eqn. (2), which is a volume and time averaged shear rate, it will simply be referred to as shear rate from here on. Results

6 238 Jon E. Wallevik, Olafur H. Wallevik Figure 4 shows the shear rate as a function of different drum charge volume V, drum rotational speed f, yield stress τ 0 and plastic viscosity μ. The outcome shows how the shear rate increases with increased drum rotational speed f. The increase does not have to be linear as is clear for the most of the cases of drum charge V = 2.6 m 3. However, with increased volume of concrete (i.e. drum charge), the relationship between shear rate and drum speed becomes more linear. Figure 4. Shear rate Eqn. (2) as a function of drum speed for different conditions. Figure 5 shows the same data as presented in Fig. 4, however only using the three cases of f = 0.23 rps (Fig. 5a), 0.11 rps (Fig. 5b) and 0.03 rps (Fig. 5c). These results are plotted as a function of drum charge volume V instead of drum speed f. From Fig. 5, it is clear that the shear rate decreases in an exponential manner with increasing charge volume V. Thus, if an effective mixing (i.e., a high shear rate) is required during transport, it is important not to fill the drum up to capacity, since such would drastically reduce the concrete mixing energy. Rather, half full or less would be recommended. If it is indented to use the truck mixer as a ready mix plant (i.e. mix the concrete from its dry components and water), this would be especially important for the more difficult batches, like high powder concretes for its effective mixing. For case of zero yield stress τ 0 in Fig. 5, then by increasing the plastic viscosity μ from 25 Pa s to 75 Pa s will result in similar shear rate reduction as increasing the

7 Analysis of Shear Rate inside a Concrete Truck Mixer 239 volume of concrete from 2.6 to 5.4 m 3. Similar conclusion applies for the case of constant plastic viscosity μ = 25 Pa s and increasing the yield stress τ 0 from zero to 300 Pa. These are approximate conclusions as the relationship is quite non-linear as is clear with Fig. 5. For example, as the rotation speed of the drum decreases, the relative difference between each viscous case is reduced. Nevertheless, with the highest value of plastic viscosity μ and yield stress τ 0, the lowest shear rate is obtained for all cases, and the reverse is obtained with the lowest cases of μ and τ 0. Thus, depending on the drum rotational speed, the Bingham parameters will play a different role. But the dependency on the drum charge volume is always clear irrespective of drum speed. This is apparent with Fig. 5. Figure 5. Shear rate Eqn. (2) as a function of drum charge volume V. It should be clear that a certain amount of concrete material will go into feeding of the internal surface of the drum (just as does for concrete pipe flow, during pumping). The shear rate calculation Eqn (1) or (2) do not include concrete that is stuck on the surface, unless at the moment when it is part of the bulk concrete rotating inside the drum (i.e. the surface that it feeling the weight of the bulk concrete). Because of this, the volume of concrete for each analysis will slightly vary. This will depend on nominal quantity of concrete, on the yield stress τ 0 and plastic viscosity μ and on how much rotation is occurring within the 20 seconds of simulation. This slight variation is apparent in Fig. 5. Thus, the nominal mount of concrete volume, namely 2.6, 5.4 and 8.2 m 3 are average values, and the actual values can be slightly different (by at most, few percents).

8 240 Jon E. Wallevik, Olafur H. Wallevik Conclusions The increase in shear rate with increased rotational drum speed is not linear for the case V = 2.6 m 3 and low plastic viscosity case. This is possible due to the concrete interactions with the helix blade systems that generate different wave phenomenon, depending on rotational drum speed. However, with increased plastic viscosity (and thus, a more viscous dampening effects), a more linear relationship is obtained. The shear rate decreases in an exponential manner with increasing charge volume V. Thus, if an effective mixing is required to be maintained during transport of concrete in a truck mixer, then filling the drum up to its designated capacity would not be advisable. Rather, half full or less would be recommended. This is especially important if it is indented to use the truck mixer as a ready mix plant (i.e. mix the concrete from its dry components and water). Acknowledgments This work has been funded by The Icelandic Centre for Research (RANNIS) Grant Number , Norcem AS (Heidelberg Cement Group), ReadyMix Abu Dhabi, the Icelandic Road and Coastal Administration and Borregaard LignoTech. Also, in the early stages of this project, Steypustöðin ehf and the Housing Financing Fund, made contributions to this work. The simulations were performed on resources provided by the Nordic High Performance Computing (NHPC) nhpc.hi.is. References [1] Banfill, P.F.G. and Swift, D.S. (2004), The effect of mixing on the rheology of cement-based materials containing high performance superplasticizers, In: Annual Transactions of the Nordic Rheology Society, 12. [2] Orban, J., Parcevaux, P. and Guillot, D. (1986), Influence of shear history on the rheological properties of oil well cement slurries, In: Proc. 8th Int. Congress on the Chemistry of Cement, 6, [3] Banfill, P.F.G. (1992), Structural breakdown and the rheology of cement mortar, In Proc. XIth Int. Congress on Rheology, [4] Wallevik, J.E. (2009), Rheological properties of cement paste: thixotropic behavior and structural breakdown, Cement and Concrete Research, 39, [5] Wallevik, J.E. (2011); Particle Flow Interaction Theory - Thixotropic Behavior and Structural Breakdown, In: Proceedings of 36th Conference on our World of Concrete and Structures, th Agust, 103. Singapore.

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