Analytical investigations are carried out on pulsating laminar incompressible fully developed channel and pipe flows. An analytical solution of the velocity profile for arbitrary time-periodic pulsations is derived by approximating the pulsating flow variables by a Fourier series. The explicit interdependence between pulsations of velocity, mass-flow rate, pressure gradient, and wall shear stress are shown by using the proper dimensionless parameters that govern the flow. Utilizing the analytical results, the scaling laws for dimensionless pulsation amplitudes of the velocity, mass-flow rate, pressure gradient, and wall shear stress are analyzed as functions of the dimensionless pulsation frequency. Special attention has been given to the scaling laws describing the flow reversal phenomenon occurring in pulsating flows, such as the condition for flow reversal, the dependency of the reversal duration, and the amplitude. It is shown that two reversal locations away from the wall can occur in pulsating flows in pipes and channels and the reversed amount of mass per period reaches a maximum at a certain dimensionless frequency for a given amplitude of mass-flow rate fluctuations. These analyses are numerically conducted for pipe and channel flows over a large frequency range in a comparative manner.

Atomically thin flat sheets of carbon, called graphene, afford interesting opportunities to study the role of orientation in suspensions. In this work, we use general rigid bead-rod theory to arrive at general expressions from first principles for the complex viscosity of graphene suspensions. General rigid bead-rod theory relies entirely on suspension orientation to explain the elasticity of the liquid. We obtain analytical expressions for the complex viscosity of triangular and hexagonal graphene sheets of arbitrary size. We find good agreement with new complex viscosity measurements.

In this work a wastewater pump with a two-bladed prototype impeller and a specific speed of 0.68, referring to a well-established industrial design, was simulated in a commercial CFD solver, ANSYS CFX. Simulations of the impeller only and of the complete pump with spiral casing including a detailed analysis of the flow patterns were performed. A parameter study with around 25 new designs containing variations of the inlet angle and the wrap angle was carried out, leading to significant improvements of the flow pattern as well as of the hydraulic efficiency. Based on the optimum leading edge and wrap angle, the total head was improved by variation of the exit blade angle. Having set the better main dimensions, the effect of the blade shape, i.e. blade angle distribution, was investigated. Here it is shown that changing the blade angle distribution in such a way that the point of maximum blade angle is shifted to a bigger radius can lead to substantial improvements. One special focus in this whole study was also to describe and control the behavior of the relative eddy, which is directly related also to the slip factor. In the scope of this work it is shown how it is possible to influence and move the relative eddy to the best position, since due to the small relative velocities in the blade passage it is impossible to fully avoid it. A detailed analysis of these CFD results is presented as well as the recommendations for an efficient design of this special type of wastewater pump impellers.

Centrifugal pump impellers for wastewater applications have to be designed to meet additional requirements compared to clearwater pumps. Therefore these impellers usually have only one to three relatively thick blades and large width to diameter ratios. The presented study deals with the effect of trailing edge modifications, especially under-filing, to this class of impellers. Two wastewater pump impellers with different specific speeds have been investigated numerically and a detailed loss analysis has been made for the impellers with default and modified trailing edge configurations. In case of the impeller with lower specific speed the head but not the efficiency could be increased by trailing edge under-filing. For the impeller with higher specific speed, under-filing resulted in an significant increase in head and efficiency. The analysis of the losses showed how the losses in different sections of the impeller are affected by the trailing edge modifications and how and under what circumstances the efficiency can be increased in this way. Experiments on the test rig confirmed the numerical results and stated an increase in head of 7.7 percent at no increase in efficiency for the impeller with the lower specific speed and an increase in head of 11.7 percent at an efficiency gain of 1.7 percent at the design flow-rate and even 4.4 percent increase in maximum efficiency for the impeller with higher specific speed.