Flow around fishlike shapes studied using multiparticle collision dynamics

Empirical measurements of hydrodynamics of swimming fish are very difficult. Therefore, modeling studies may be of great benefit. Here, we investigate the suitability for such a study of a recently developed mesoscale method, namely, multiparticle collision dynamics. As a first step, we confine ourselves to investigations at intermediate Reynolds numbers of objects that are stiff. Due to the lack of empirical data on the hydrodynamics of stiff fishlike shapes we use a previously published numerical simulation of the shapes of a fish and a tadpole for comparison. Because the shape of a tadpole resembles that of a circle with an attached splitter plate, we exploit the knowledge on hydrodynamic consequences of such an attachment to test the model further and study the effects of splitter plates for objects of several shapes at several Reynolds numbers. Further, we measure the angles of separation of flow around a circular cylinder and make small adjustments to the boundary condition and the method to drive the flow. Our results correspond with empirical data and with results from other models.

Figure 1

The simulation setup. $W$ is the width of the channel, $L$ is its length (not to scale), and $D$ is the object diameter, measured along the width axis.

Figure 2

The separation angle ${\varphi }_i$. The four lines are estimates of the minimum and maximum separation angle on each side of the object.

Figure 3

(Color) Flow fields around a tadpole shape. (a) From Ref. [10], (b) in our model, and (c) in our model with added leglike protrusions. Color indicates flow speed, with high speed indicated by red and low speed by blue. Our simulations are at Reynolds numbers of approximately 105, based on the cross-channel size of the object. Figure (a) reproduced with permission of the Company of Biologists.

Figure 4

Results of simulations for basic shapes. (a) The recirculation length for the circular cylinder as a function of the Reynolds number. Data from Ref. [18] (○), this study (◼), and Ref. [27] $(\ast )$. Note that steady recirculation only occurs at Reynolds numbers below 45. (b) The drag coefficient for the square cylinder as a function of the Reynolds number. Data from Ref. [18] (○), and this study (◼). (c) The drag coefficient for the circular cylinder as a function of the Reynolds number. Data from Ref. [28] $(\ast )$, Ref. [18] (○), and this study (◼).

Figure 5

The separation angle for the circular cylinder as a function of the Reynolds number. Data from an overview of experimental data from Ref. [29] (gray area) and mean $\text{values}\pm \text{standard}$ error of this study (◼).

Figure 6

The drag coefficient of the circular cylinder as a function of the Reynolds number. Plotted values are for the cylinder with (●) and without (○) trailing splitter plate.

Figure 7

Streamlines for flat plate, circle, and square with and without splitter plate attached. The Reynolds number is approximately 80. Note that the flat plate and splitter plates are thicker than the mesh cell size $a_0$. The cross-channel diameter of the objects is the same in all cases.