Transition in inclined internally heated fluid layers

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

A micro gas turbines for UK domestic combined heat and power

Various micro-radial compressor configurations were investigated using one-dimensional meanline and computational fluid dynamics (CFD) techniques for use in a micro gas turbine (MGT) domestic combined heat and power (DCHP) application. Blade backsweep, shaft speed, and blade height were varied at a constant pressure ratio. Shaft speeds were limited to 220 000 r/min, to enable the use of a turbocharger bearing platform. Off-design compressor performance was established and used to determine the MGT performance envelope; this in turn was used to assess potential cost and environmental savings in a heat-led DCHP operating scenario within the target market of a detached family home. A low target-stage pressure ratio provided an opportunity to reduce diffusion within the impeller. Critically for DCHP, this produced very regular flow, which improved impeller performance for a wider operating envelope. The best performing impeller was a low-speed, 170 000 r/min, low-backsweep, 15° configuration producing 71.76 per cent stage efficiency at a pressure ratio of 2.20. This produced an MGT design point system efficiency of 14.85 per cent at 993 W, matching prime movers in the latest commercial DCHP units. Cost and CO2 savings were 10.7 per cent and 6.3 per cent, respectively, for annual power demands of 17.4 MWht and 6.1 MWhe compared to a standard condensing boiler (with grid) installation. The maximum cost saving (on design point) was 14.2 per cent for annual power demands of 22.62 MWht and 6.1 MWhe corresponding to an 8.1 per cent CO2 saving. When sizing, maximum savings were found with larger heat demands. When sized, maximum savings could be made by encouraging more electricity export either by reducing household electricity consumption or by increasing machine efficiency.

Transition in convective flows heated internally

The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.

Transition in plane parallel shear flows heated internally

The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0≤Pr≤100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635-642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory. © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.

Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

Convection induced by instabilities in the presence of a transverse seepage

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.

Development of a novel magnetic resonance imaging contrast agent for pressure measurements using lipid-coated microbubbles

The aim of this study was to prepare gas-filled lipid-coated microbubbles as potential MRI contrast agents for imaging of fluid pressure. Air-filled microbubbles were produced with phospholipid 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) in the presence or absence of cholesterol and/or polyethylene-glycol distearate (PEG-distearate). Microbubbles were also prepared containing a fluorinated phospholipid, perfluoroalkylated glycerol-phosphatidylcholine, F-GPC shells encompassing perfluorohexane-saturated nitrogen gas. These microbubbles were evaluated in terms of physico-chemical characteristics such as size and stability. In parallel to these studies, DSPC microbubbles were also formulated containing nitrogen (N2) gas and compared to air-filled microbubbles. By preventing advection, signal drifts were used to assess their stability. DSPC microbubbles were found to have a drift of 20% signal change per bar of applied pressure in contrast to the F-GPC microbubbles which are considerably more stable with a lower drift of 5% signal change per bar of applied pressure. By increasing the pressure of the system and monitoring the MR signal intensity, the point at which the majority of the microbubbles have been damaged was determined. For the DSPC microbubbles this occurs at 1.3 bar whilst the F-GPC microbubbles withstand pressures up to 2.6 bar. For the comparison between air-filled and N2-filled microbubbles, the MRI sensitivity is assessed by cycling the pressure of the system and monitoring the MR signal intensity. It was found that the sensitivity exhibited by the N2-filled microbubbles remained constant, whilst the air-filled microbubbles demonstrated a continuous drop in sensitivity due to continuous bubble damage.

Constant shear along a boundary of a flume

'I'he accurate rreasurement of bed shear stress has been extremely difficult due to its changing values until white propunded a theory which would give constant shear along the bed of a flume. In this investigation a flume has been designed according to White's theory and by two separate methods proven to give constant shearing force along the bed. The first method applied the Hydrogen Bubble Technique to obtain accurate values of velocity thus allowing the velocity profile to be plotted and the momentum at the various test sections to be calculated. The use of a 16 mm Beaulieu movie camera allowed the exact velocity profiles created by the hydrogen bubbles to be recorded whilst an analysing projector gave the means of calculating the exact velocities at the various test sections. Simultaneously Preston's technique of measuring skin friction using Pitot tubes was applied. Twc banks of open ended water manometer were used for recording the static and velocity head pressure drop along the flume. This tvpe of manometer eliminated air locks in the tubes and was found to be sufficiently accurate. Readings of pressure and velocity were taken for various types and diameters of bed material both natural sands and glass spheres and the results tabulated. Graphs of particle Reynolds Number against bed shear stress were plotted and gave a linear relationship which dropped off at high values of Reynolds number. It was found that bed movement occurred instantaneously along the bed of the flume once critical velocity had been reached. On completion of this test a roof curve inappropriate to the bed material was used and then the test repeated. The bed shearing stress was now no longer constant and yet bed movement started instantaneously along the bed of the flume, showing that there are more parameters than critical shear stress to bed movement. It is concluded from the two separate methods applied that the bed shear stress is constant along the bed of the flume.

Accommodation and intraocular pressure

The relationship between accommodation and intraocular pressure (lOP) has not been addressed as a research question for over 20 years, when measurement of both of these parameters was less advanced than today. Hence the central aim of this thesis was to evaluate the effects of accommodation on lOP. The instrument of choice throughout this thesis was the Pulsair EasyEye non-contact tonometer (NCT) due principally to its slim-line design which allowed the measurement of lOP in one eye and simultaneous stimulation of accommodation in the other eye. A second reason for using the Pulsair EasyEye NCT was that through collaboration with the manufacturers (Keeler, UK) the instrument's operational technology was made accessible. Hence, the principle components underpinning non-contact lOP measures of 0.1mmHg resolution (an order of magnitude greater than other methods) were made available. The relationship between the pressure-output and corneal response has been termed the pressure-response relationship, aspects of which have been shown to be related to ocular biometric parameters. Further, analysis of the components of the pressure-response relationship together with high-speed photography of the cornea during tonometry has enhanced our understanding of the derivation of an lOP measure with the Pulsair EasyEye NCT. The NCT samples the corneal response to the pressure pulse over a 19 ms cycle photoelectronically, but computes the subject's lOP using the data collected in the first 2.34 ms. The relatively instantaneous nature of the lOP measurement renders the measures susceptible to variations in the steady-state lOP caused by the respiratory and cardiac cycles. As such, the variance associated with these cycles was minimised by synchronising the lOP measures with the cardiac trace and maintaining a constant pace respiratory cycle at 15 breathes/minute. It is apparent that synchronising the lOP measures with the peak, middle or trough of the cardiac trace significantly reduced the spread of consecutive measures. Of the 3 locations investigated, synchronisation with the middle location demonstrated the least variance (coeflicient of variation = 9.1%) and a strong correlation (r = 0.90, p = <0.001) with lOP values obtained with Goldmann contact tonometry (n = 50). Accordingly lOP measures synchronised with the middle location of the cardiac cycle were taken in the RE while the LE fixated low (L; zero D), intermediate (I; 1.50 D) and high (H; 4 D) accommodation targets, Quasi-continuous measures of accommodation responses were obtained during the lOP measurement period using the portable infrared Grand Seiko FR-5000 autorefractor. The lOP reduced between L and I accommodative levels by approximately 0.61 mmHg (p <0.00 I). No significant reduction in IOP between L and H accommodation levels was elicited (p = 0.65) (n = 40). The relationship between accommodation and lOP was characterised by substantial inter-subject variations. Myopes demonstrated a tendency to show a reduction in IOP with accommodation which was significant only with I accommodation levels when measured with the NCT (r = 0.50, p = 0.01). However, the relationship between myopia and lOP change with accommodation reached significance for both I (r = 0.61, p= 0.003) and H (r = 0.531, p= 0.0 1) accommodation levels when measured with the Ocular blood Flow Analyser (OBFA). Investigation of the effects of accommodation on the parameters measured by the OBFA demonstrated that with H accommodation levels the pulse amplitude (PA) and pulse rate (PR) responses differed between myopes and emmetropes (PA: p = 0.03; PR: p = 0.004). As thc axial length increased there was a tendency for the pulsatile ocular blood flow (POBF) to reduce with accommodation, which was significant only with H accommodation levels (r = 0.38, p = 0.02). It is proposed that emmetropes arc able to regulate the POBF responses to changes in ocular perfusion pressure caused by changes in lOP with I (r = 0.77, p <0.001) and H (r = 0.73, p = 0.001) accommodation levels. However, thc relationship between lOP and POBF changes in the myopes was not correlated for both I (r = 0.33, p = 0.20) and H (r = 0.05, p = 0.85) accommodation levels. The thesis presents new data on the relationships between accommodation, lOP and parameters of the OBFA,: and provides evidence for possible lOP and choroidal blood flow regulatory mechanisms. Further the data highlight possible deficits in the vascular regulation of the myopic eye during accommodation, which may play a putative role in the aetiology of myopia development.