Modelling Compressible Blood Flow with Slip in a Constricted Rectangular Flow Domain

The abnormal narrowing of blood vessels is known to affect the characterization of blood flow through these constricted regions. Both theoretical and clinical research has suggested that these changes in flow are associated with cardiovascular related diseases. Analytic, numerical, and particle based methods have been employed to solve the Navier-Stokes momentum integral equations associated with compressible, Newtonian fluid flow. In this thesis, the Karman-Pohlhausen method is used to transform a system of partial differential equations into a single second-order, non-linear differential equation in terms of the density. Numerical solutions are presented and important flow features, including the role of slip and compressibility, are discussed. The choice to use a symmetric rectangular channel, rather than a cylindrical one, is largely motivated by the opportunity to compare the numerical solutions with experimental data collected from a rectangular microchannel. The numerical results also indicate similar trends in the flow characteristics for the rectangular channel as compared to previous results using cylindrical models.

Modelling Compressible Blood Flow with Slip in a Constricted Rectangular Flow Domain

The abnormal narrowing of blood vessels is known to affect the characterization of blood flow through these constricted regions. Both theoretical and clinical research has suggested that these changes in flow are associated with cardiovascular related diseases. Analytic, numerical, and particle based methods have been employed to solve the Navier-Stokes momentum integral equations associated with compressible, Newtonian fluid flow. In this thesis, the Karman-Pohlhausen method is used to transform a system of partial differential equations into a single second-order, non-linear differential equation in terms of the density. Numerical solutions are presented and important flow features, including the role of slip and compressibility, are discussed. The choice to use a symmetric rectangular channel, rather than a cylindrical one, is largely motivated by the opportunity to compare the numerical solutions with experimental data collected from a rectangular microchannel. The numerical results also indicate similar trends in the flow characteristics for the rectangular channel as compared to previous results using cylindrical models.

Determining the leading-order contact term in neutrinoless double β decay

We present a method to determine the leading-order (LO) contact term contributing to the nn → ppe−e− amplitude through the exchange of light Majorana neutrinos. Our approach is based on the representation of the amplitude as the momentum integral of a known kernel (proportional to the neutrino propagator) times the generalized forward Compton scattering amplitude n(p1)n(p2)W+(k) →$$ p\left({p}_1^{\prime}\right)p\left({p}_2^{\prime}\right){W}^{-}(k) $$ p p 1 ′ p p 2 ′ W − k , in analogy to the Cottingham formula for the electromagnetic contribution to hadron masses. We construct model-independent representations of the integrand in the low- and high-momentum regions, through chiral EFT and the operator product expansion, respectively. We then construct a model for the full amplitude by interpolating between these two regions, using appropriate nucleon factors for the weak currents and information on nucleon-nucleon (NN) scattering in the 1S0 channel away from threshold. By matching the amplitude obtained in this way to the LO chiral EFT amplitude we obtain the relevant LO contact term and discuss various sources of uncertainty. We validate the approach by computing the analog I = 2 NN contact term and by reproducing, within uncertainties, the charge-independence-breaking contribution to the 1S0NN scattering lengths. While our analysis is performed in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme, we express our final result in terms of the scheme-independent renormalized amplitude $$ {\mathcal{A}}_{\nu}\left(\left|\mathbf{p}\right|,\left|\mathbf{p}^{\prime}\right|\right) $$ A ν p p ′ at a set of kinematic points near threshold. We illustrate for two cutoff schemes how, using our synthetic data for $$ {\mathcal{A}}_{\nu } $$ A ν , one can determine the contact-term contribution in any regularization scheme, in particular the ones employed in nuclear-structure calculations for isotopes of experimental interest.

Control of the motion of a circular cylinder in an ideal fluid using a source

The motion of a circular cylinder in an ideal fluid in the field of a fixed source is considered. It is shown that, when the source has constant strength, the system possesses a momentum integral and an energy integral. Conditions are found under which the equations of motion reduced to the level set of the momentum integral admit an unstable fixed point. This fixed point corresponds to circular motion of the cylinder about the source. A feedback is constructed which ensures stabilization of the above-mentioned fixed point by changing the strength of the source.

Parametrisation of the Pressure and the Momentum Integral for Inclined Sluicegates Flows

The flow under sluice gates is nowadays frequently still determined by empirical approaches, based on the Bernoulli equation and a specific discharge coefficient which depends on the geometry of the sluice gate. This discharge coefficient is determined from a selection of tables and charts, which are based on a variety of experimental series. In 2016 Malcherek developed a fundamentally new approach to describe hydraulic structures based on integral momentum balance instead of Bernoulli’s energy conservation principle. In this approach a flow is described as the result of the integral momentum balance including pressure forces on open boundaries as well as closed walls, momentum fluxes through open boundaries and gravitational and frictional forces. In this theoretical approach, the discharge under inclined sluice gates can be described as a result of the acting pressure forces and momentum fluxes. To apply the theory, the pressure integral at the sluicegate and under the sluice gate and also the momentum integral of the flow under the sluice gate have to be known. For the determination of these values, multiphase CFD simulations for different angles of inclination and waters levels upstream of the sluicegate were done by the authors in the paper “Theoretical and numerical analysis of the pressure distribution and discharge velocity in flows under inclined sluice gates” (AJKFLUIDS2019 5020). Using the values determined in this previous paper, parametrized model equations for the pressure and momentum integrals in dependency of the angle of inclination and upstream water levels were derived in this work. These polynomial approaches have been used to determine the three unknown physical quantities in the integral momentum balance: the pressure integral at the sluice gate, the pressure integral under the sluice gate and the momentum integral of the flow under the sluicegate. The polynomial approaches are shown in detail in this work.