Unsteady forcing of turbulence by a randomly actuated impeller array

We investigate the unsteady forcing of turbulent flow in a well-stirred reactor using opposing arrays of pitched-blade impellers which randomly and independently reverse rotation. We systematically explore the dependence of the large-scale motions and the homogeneity and isotropy of the turbulence upon the forcing. We identify three dimensionless control parameters: the source fraction (the fraction of time spent in clockwise motion), the dimensionless forcing period and an impeller Reynolds number. We find the timescale of unsteady motion corresponds to the forcing period T, the average period of impeller reversal, independently of the impeller angular speed $$\varOmega$$ Ω and source fraction. As in jet-stirred tanks, unsteady forcing substantially increases the unsteady kinetic energy, energy dissipation, integral length scale and Taylor microscale Reynolds number ($$R_\lambda$$ R λ ) and improves the homogeneity and isotropy of the flow, provided the source fraction is chosen optimally and the forcing period is sufficiently large ($$\varOmega T > 10^3$$ Ω T > 10 3 ); impeller Reynolds number has a relatively small influence. The forcing period must be matched to angular speed: decreasing the forcing period below this threshold results in a less intense, more inhomogeneous turbulent flow. Spectra of two-point velocity increments demonstrate that unsteady energy injection is dominated by axial shear generated across impellers and becomes less prominent at smaller scales. However, even at $$R_\lambda \approx 354$$ R λ ≈ 354 , the signature of this unsteady forcing can still be detected in near-dissipation-range statistics. These observations provide insight into optimisation of forcing and the mechanism of energy transfer when using unsteady forcing to generate turbulence in confined vessels. Graphical abstract

Thrust Force Generated by Heaving Motion of a Plate: The Role of Vortex-Induced Force

To understand the force acting on birds, insects, and fish, we take heaving motion as a simple example. This motion might deviate from the real one. However, since the mechanism of force generation is the vortex shedding due to the motion of an object, the heaving motion is important for understanding the force generated by unsteady motion. The vortices released from the object are closely related to the motion characteristics. To understand the force acting on an object, information about momentum change is necessary. However, in vortex systems, it is impossible to estimate the usual momentum. Instead of the momentum, the “virtual momentum,” or the impulse, is needed to generate the force. For calculating the virtual momentum, we traced all vortices over a whole period, which was carried out by using the vortex-element method. The force was then calculated based on the information on the vortices. We derived the thrust coefficient as a function of the ratio of the heaving to travelling velocity.

Optimal error estimate for a space-time discretization for incompressible generalized Newtonian fluids: the Dirichlet problem

In this paper we prove optimal error estimates for solutions with natural regularity of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the discretization. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semi-discrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions.

Fundamentals of the Theory of Power Pulse Device

The article discusses a mathematical model of a power impulse device, which allows you to select the characteristics of the ejected liquid jet, such as the velocity at the moment of ejection, the pressure created in the nozzle of the power impulse device, etc., by changing the parameters of the device. A feature of the proposed mathematical model, which significantly distinguishes it from the previously considered models, is that the model was considered for the case of unsteady motion. This state of the medium in a power impulse device is the most characteristic, therefore the results obtained are more general. It is shown that, in contrast to the steady motion of a liquid, in the case of unsteady motion, an additional term appears, which can be defined as a head having an inertial character. It can be seen from the proposed mathematical model that the presence of an inertial head leads to the appearance of a flow deceleration effect, which, in turn, leads to an increase in the total liquid head in the direction of the flow. The pressure generated in the barrel acts against the direction of the hydraulic resistance. All of the above is applicable only for a certain moment in time or for the case when the acceleration of the fluid is constant. If the acceleration changes, then the action of the heads along the fluid flow is a function of time. This circumstance makes it possible to apply the result obtained with unsteady motion to create devices that form a high-pressure jet. A distinctive feature of the considered model is that it analyzes the behavior of the fluid in the power impulse device for two cases: 1. the volume of fluid in the barrel of the power impulse unit is greater than the volume of the nozzle; 2. the volume of fluid in the barrel is less than or equal to the volume of the nozzle. The results of the analysis showed that in the first case, the initial velocity of liquid ejection significantly exceeds this velocity in the second case. That is, it is the first case that is of practical importance.

The dynamics of a laden skip of the shaft pneumatic winding plant during acceleration

Introduction. Ratios for calculating the laden skip acceleration and speed at the motion start are required to calculate skip pneumatic winding plant cycle components. The ratios are the solution to the skip dynamics equation which takes into account the relationship between the flow generated by a power unit and air pressure. Research methodology. The dynamics equation including the dependence of the pressure on the flow rate (aerodynamic characteristic) in a general form is compiled. In a special case of the unit’s physical model, a discharge unit with a linear aerodynamic characteristic is used. Research result. For a particular case, equations are obtained that allow to theoretically describe the kinematic parameters of a skip in the period of unsteady motion. It is established that the skip acceleration, velocity and displacement are asymptotic functions. The obtained expressions for kinematic parameters make it possible to theoretically determine the duration of the acceleration period and the path that the ISSN 0536-1028 «Известия вузов. Горный журнал», № 1, 2021 121 skip takes during this period. A method for calculating skip dynamics during acceleration is proposed, which contains approximating formula conclusion for the power unit aerodynamic characteristics, its substitution into the dynamics equation, and obtaining skip kinematic parameters by solving the dynamics equation. Conclusion. The obtained relations allow to calculate skip dynamics during acceleration taking into account power unit aerodynamic characteristics, which is necessary to determine the working cycle time of the pneumatic winding plant.