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Mathematical modelling of selected problems in cryogenic fluid mechanics
Hodic, Jan ; La Mantia, Marco (advisor) ; Kreml, Ondřej (referee)
The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak ort he strong solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate properties of the solution.
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Spherically symmetrical thermal counterflow of superfluid helium
Novotný, Filip ; Schmoranzer, David (advisor) ; Kohout, Jaroslav (referee)
The principal aim of this Thesis was the investigation of quantum tur- bulence in superfluid helium in a special type of flow, spherically symmetric thermal counterflow. To this end, a new cell was designed and 3D-printed. Measurements of quantum turbulence were realized using the traditional technique of second sound attenuation, focusing both on steady state of tur- bulence and its temporal decay. The measured dependence of the quantized vortex line density L versus the counterflow velocity vns, where the data clearly show that L ∝ v3/2 ns , does not agree with the Vinen equation, which predicts L ∝ v2 ns. On the other hand, the dependence of vortex line density on time t obtained during the decay measurements L ∝ t−1 is paradoxically in close agreement with the Vinen equation. For the future, spherically sym- metrical thermal counterflow thus promises many interesting challenges and will remain an important topic of research. 1
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Steady state and decay of quantum turbulence generated in channel flows and detected by second sound attenuation
Varga, Emil ; Skrbek, Ladislav (advisor) ; Vinen, William Frank (referee)
Steady state and decay of quantum turbulence generated in channel flows and detected by second sound attenuation Bc. Emil Varga Abstract Quantum turbulence is studied in superfluid 4 He under classical flow condi- tions. Turbulence is generated by a flow through a 7 × 7 mm square channel with a flow conditioner either with an additional grid or without it. The flow is generated mechanically by squeezing a stainless steel bellows. Vortex line den- sity is measured by attenuation of second sound in both steady state and decay for a range of temperatures 1.17 - 2.16 K. In the steady state, temperature- independent scaling of the vortex line density with flow velocity of the form L ∝ V 3/2 is observed. In the decay the expected late-time behaviour L ∝ t−3/2 is observed. Explanation for both of these observations is based on a quasi- classical model of quantum turbulence, that allows the extraction of the effective kinematic viscosity νeff, which approximately agree with the values available in the literature. Two models based on counterflow theory are also explored and the effect of inhomogeneous vortex line distribution on the measurement tech- nique is studied.
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Mathematical modelling of selected problems in cryogenic fluid mechanics
Hodic, Jan ; La Mantia, Marco (advisor) ; Schmoranzer, David (referee)
The dynamics of low-temperature fluids, such as superfluid helium 4, is an open scientific problem. The experimental study of similarities and differences between quantum (superfluid) and classical (viscous) flows is specifically an active research field, which already led to significant progress in our phenomenological understanding of the underlying physics. It also revealed that a comprehensive theoretical description is still missing, as, for example, in the case of the observed behaviour of moving bodies in quantum flows. The work aim is to derive the existence theory for the weak solution of a relevant system of equations based on the Landau model of superfluid helium 4 and appropriate numerical schemes to solve these equations.
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Generation and detection of quantum turbulence in He II by second sound
Midlik, Šimon ; Schmoranzer, David (advisor) ; La Mantia, Marco (referee)
We have performed a study of quantum turbulence generated in oscillatory counterflow as a continuation of previous experiments on various channel flows of superfluid helium, in the form of coflow, thermal DC counterflow and pure superflow. We have investigated its development, steady state properties and temporal decay, as well as the effect of the resonant mode used to generate the turbulence at three different temperatures, 1.45 K, 1.65 K and 1.83 K. The attenuation of low amplitude second sound, orientated perpendicularly to the long axis of the resonator, was used to determine the amount of quantized vortices created. One of the main goals of this work was to characterize the critical parameters for the onset of instabilities in oscillatory counterflow and to determine their values. Decay measurements of the vortex line density allowed us to distinguish between Vinen-type and Kolmogorov- type decays of quantum turbulence.
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Quantum turbulence in superfluid helium studied by particle tracking velocimetry visualization technique
Duda, Daniel ; Skrbek, Ladislav (advisor) ; Chára, Zdeněk (referee) ; Skyba, Peter (referee)
❚✐t❧❡✿ ◗✉❛♥t✉♠ t✉r❜✉❧❡♥❝❡ ✐♥ s✉♣❡r✢✉✐❞ ❤❡❧✐✉♠ st✉❞✐❡❞ ❜② ♣❛rt✐❝❧❡ tr❛❝❦✐♥❣ ✈❡❧♦❝✐♠❡tr② ✈✐s✉❛❧✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ❆✉t❤♦r✿ ❘◆❉r✳ ❉❛♥✐❡❧ ❉✉❞❛ ❉❡♣❛rt♠❡♥t✿ ❉❡♣❛rt♠❡♥t ♦❢ ▲♦✇ ❚❡♠♣❡r❛t✉r❡ P❤②s✐❝s ❙✉♣❡r✈✐s♦r✿ ♣r♦❢✳ ❘◆❉r✳ ▲❛❞✐s❧❛✈ ❙❦r❜❡❦✱ ❉r❙❝✳ ❆❜str❛❝t✿ ❚❤❡ P❛rt✐❝❧❡ ❚r❛❝❦✐♥❣ ❱❡❧♦❝✐♠❡tr② ✈✐s✉❛❧✐③❛t✐♦♥ t❡❝❤♥✐q✉❡ ✉s✐♥❣ ♠✐❝✲ r♦♠❡t❡r s✐③❡ s♦❧✐❞ ❞❡✉t❡r✐✉♠ ♣❛rt✐❝❧❡s ❛s tr❛❝❡rs ❤❛s ❜❡❡♥ ❛♣♣❧✐❡❞ t♦ st✉❞② ♦s❝✐❧✲ ❧❛t♦r② ✢♦✇s ♦❢ ❍❡ ■■✱ ✇❤✐❝❤ ✐s ❛ q✉❛♥t✉♠ ✢✉✐❞ ✇✐t❤ q✉❛♥t✐③❡❞ ✈♦rt✐❝✐t②✱ ❛s ✇❡❧❧ ❛s ✢♦✇s ♦❢ ❍❡ ■✱ ✇❤✐❝❤ ✐s ❛ ❝❧❛ss✐❝❛❧ ✈✐s❝♦✉s ❧✐q✉✐❞✱ ❢♦❝✉s✐♥❣ ♦♥ t❤❡ s✐♠✐❧❛r✐t✐❡s ❛♥❞ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ q✉❛♥t✉♠ ❛♥❞ ❝❧❛ss✐❝❛❧ ✢♦✇s✳ ❚❤r❡❡ ❡①♣❡r✐♠❡♥ts ❛r❡ ❞❡s❝r✐❜❡❞✿ t❤❡ ✢♦✇ ♣❛st ❛ ❧❛r❣❡✲❛♠♣❧✐t✉❞❡ ❧♦✇✲❢r❡q✉❡♥❝② ♦s❝✐❧❧❛t✐♥❣ ♦❜st❛❝❧❡ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❛ ♣r✐s♠❀ t❤❡ st❡❛❞② str❡❛♠✐♥❣ ✢♦✇ ❞✉❡ t♦ ❛ s♠❛❧❧✲❛♠♣❧✐t✉❞❡ ❧❛r❣❡✲ ❢r❡q✉❡♥❝② ♦s❝✐❧❧❛t✐♥❣ q✉❛rt③ t✉♥✐♥❣ ❢♦r❦ ✲ ❛ ✇✐❞❡❧② ✉s❡❞ t♦♦❧ t♦ st✉❞② q✉❛♥t✉♠ t✉r❜✉❧❡♥❝❡❀ ❛♥❞ t❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❝❛✈✐t❛t✐♦♥ ✐♥ t❤❡ ✈✐❝✐♥✐t② ♦❢ ❛ ❢❛st✲♦s❝✐❧❧❛t✐♥❣ t✉♥✐♥❣ ❢♦r❦✳ ❚❤❡ ♠❛✐♥ ♦✉t❝♦♠❡ ✐s t❤❡ ♦❜s❡r✈❛t✐♦♥ t❤❛t t❤❡s❡ ✢♦✇s ❛r❡ s✐♠✐❧❛r ✐♥ ❍❡ ■ ❛♥❞ ✐♥ ❍❡ ■■ ❛t ❧❛r❣❡ ❧❡♥❣t❤✲s❝❛❧❡s✱ ✇❤❡r❡❛s ❛t s♠❛❧❧ s❝❛❧❡s✱ t❤❡② ❡①❤✐❜✐t t♦t❛❧❧② ❞✐✛❡r❡♥t st❛t✐st✐❝❛❧ ♣r♦♣❡rt✐❡s✳ ▼♦r❡♦✈❡r✱ ✐♥ ❍❡ ■■✱ t❤❡s❡ s♠❛❧❧ s❝❛❧❡ st❛✲ t✐st✐❝❛❧ ♣r♦♣❡rt✐❡s ❛r❡ ✉♥✐✈❡rs❛❧ ✐♥ t❤❛t t❤❡② ❞♦ ♥♦t ❞❡♣❡♥❞ ♦♥ t❤❡ t②♣❡ ♦❢ t❤❡ ✐♠♣♦s❡❞ ♠❡❛♥ ✢♦✇ ♦❢ t❤❡ s✉♣❡r✢✉✐❞ ❛♥❞ ♥♦r♠❛❧...
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Investigation of quantum turbulence using microresonators
Midlik, Šimon ; Schmoranzer, David (advisor) ; Kohout, Jaroslav (referee)
The principal aim of this Thesis is the construction of a cryogenic setup for the investigation of quantum turbulence in superfluid helium (He II) using microresonators and a to perform a study of the transition to turbulence in oscillatory flow of He II in the temperature range from 2.170 K down to 1.293 K. We have designed and constructed a setup consisting of a superconducting vibrating microwire and a so-called fountain pump, and, after initial testing and characterization, used it to probe the instabilities occurring in the flow of He II. Specifically, we were interested in the origin of the instabilities in the flow around the microwire and in the question whether they originate mostly from classical-like flow of the normal component, as is often the case with the well-known tuning forks, or whether they are related to the generation of quantized vortices in the superfluid component of He II. To distinguish between these two types of instabilities, we have derived from the Navier-Stokes equations scaling laws related to drag forces in classical oscillatory flow, which we have applied to the normal component of superfluid helium. This also enabled us to verify the validity of the high-frequency limit of oscillatory flow for the case of the microwire. Finally, we have examined the capability of the...
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Visualization of particle motions in superfluid helium flows
Švančara, Patrik ; La Mantia, Marco (advisor)
Flows of normal and superfluid 4 He (He I and He II, respectively) are investigated experimentally. Relatively small particles of solid hydrogen and deuterium are suspended in the experimental volume and their motions are tracked in both mechanically and thermally driven flows. A statistical study of the particle velocity and velocity increment distributions is performed at scales smaller and larger than the mean distance between quantized vortices, the quantum length scale of the investigated flows. We show that, at small scales, the observed particle dynamics in He II is greatly influenced by that of quantized vortices. We, additionally, report that this behavior is independent of the imposed large-scale flow. Instead, at large scales, we observe that particle motions are quasiclassical, that is, very similar to those reported to occur in turbulent flows of viscous fluids. The study reinforces therefore the idea of close similarity between viscous flows and large-scale (mechanically-driven) flows of He II, and simultaneously highlights the small-scale differences due to the presence of quantized vortices in He II.
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Spherically symmetrical thermal counterflow of superfluid helium
Novotný, Filip ; Schmoranzer, David (advisor) ; Kohout, Jaroslav (referee)
The principal aim of this Thesis was the investigation of quantum tur- bulence in superfluid helium in a special type of flow, spherically symmetric thermal counterflow. To this end, a new cell was designed and 3D-printed. Measurements of quantum turbulence were realized using the traditional technique of second sound attenuation, focusing both on steady state of tur- bulence and its temporal decay. The measured dependence of the quantized vortex line density L versus the counterflow velocity vns, where the data clearly show that L ∝ v3/2 ns , does not agree with the Vinen equation, which predicts L ∝ v2 ns. On the other hand, the dependence of vortex line density on time t obtained during the decay measurements L ∝ t−1 is paradoxically in close agreement with the Vinen equation. For the future, spherically sym- metrical thermal counterflow thus promises many interesting challenges and will remain an important topic of research. 1
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Visualization of particle motions in superfluid helium flows
Švančara, Patrik ; La Mantia, Marco (advisor)
Flows of normal and superfluid 4 He (He I and He II, respectively) are investigated experimentally. Relatively small particles of solid hydrogen and deuterium are suspended in the experimental volume and their motions are tracked in both mechanically and thermally driven flows. A statistical study of the particle velocity and velocity increment distributions is performed at scales smaller and larger than the mean distance between quantized vortices, the quantum length scale of the investigated flows. We show that, at small scales, the observed particle dynamics in He II is greatly influenced by that of quantized vortices. We, additionally, report that this behavior is independent of the imposed large-scale flow. Instead, at large scales, we observe that particle motions are quasiclassical, that is, very similar to those reported to occur in turbulent flows of viscous fluids. The study reinforces therefore the idea of close similarity between viscous flows and large-scale (mechanically-driven) flows of He II, and simultaneously highlights the small-scale differences due to the presence of quantized vortices in He II.
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