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This paper reports a comprehensive set of hot-wire measurements of a round buoyant plume which was generated by forcing a jet of hot air vertically up into a quiescent environment. The boundary conditions of the experiment were measured, and are documented in the present paper in an attempt to sort out the contradictory mean flow results from the earlier studies. The ambient temperature was monitored to ensure that the facility was not stratified and that the experiment was conducted in a neutral environment. The axisymmetry of the flow was checked by using a planar array of sixteen thermocouples and the mean temperature measurements from these are used to supplement the hot-wire measurements. The source flow conditions were measured to ascertain the rate at which the buoyancy was added to the flow. The measurements conserve buoyancy within 10%. The results are used to determine balances of the mean energy and momentum differential equations. In the mean energy equation it is found that the vertical advection of energy is primarily balanced by the radial turbulent transport. In the mean momentum equation the vertical advection of momentum and the buoyancy force balance the radial turbulent transport. The buoyancy force is the second largest term in this balance and is responsible for the wider (and higher) velocity profiles in plumes as compared to jets. Budgets of the temperature variance and turbulent kinetic energy are also determined in which thermal and mechanical dissipation rates are obtained as the closing terms. Similarities and differences between the two balances are discussed. It is found that even though the direct effect of buoyancy in turbulence, as evidenced by the buoyancy production term, is substantial, most of the turbulence is produced by shear. This is in contrast to the mean velocity field where the effect of the buoyancy force is quite strong. Therefore, it is concluded that in a buoyant plume the primary effect of buoyancy on turbulence is indirect, and enters through the mean velocity field (giving larger shear production).

Supramolecular polymers are used in many applications such as adhesives, coatings, cosmetics, and printing. Characterizing the dynamics of such polymers is essential for tailoring user defined properties in products and applications. We present both linear and nonlinear rheological results for a model system of pure poly(n-butyl acrylate), PnBA, homopolymer and four PnBA-poly(acrylic acid), PnBA-PAA, copolymers with different number of AA side groups. The copolymers are synthesized via hydrolysis of the pure PnBA homopolymer. Therefore, all polymers studied have the same backbone length. The number of AA side groups (hydrogen bonding groups) after hydrolysis is determined from NMR measurements. We show that using the theoretical dependency * To whom correspondence should be addressed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 of modulus and reptation time on the packing length, we can account for the changes in linear viscoelasticity due to transformation of nBA side groups to AA along the backbone. Assuming superposition holds and subtracting out the linear chain rheology from LVE, the hydrogen bonding contribution to LVE is exposed. Hydrogen bonding affects linear viscoelasticity at frequencies below the inverse reptation time. More specifically, the presence of hydrogen bonds causes G and G as a function of frequency to shift to a power law scaling of 0.5. Furthermore, the magnitude of G and G scales linearly with the number of hydrogen bonding groups. The nonlinear extensional rheology shows extreme strain hardening. The magnitude of extensional stress has a strongly nonlinear dependence on the number of hydrogen bonding groups. These results are aimed at uncovering the molecular influence of hydrogen bonding on linear and nonlinear rheology to aid future molecular synthesis and model development.

Supramolecular polymers possess versatile mechanical properties and a unique ability to respond to external stimuli. Understanding the rich dynamics of such associative polymers is essential for tailoring user defined properties in many products. Linear copolymers of 2-methoxyethyl acrylate (MEA) and varying amounts of 2-ureido-4[1H]-pyrimidone (UPy) quadruple hydrogen-bonding side units were synthesized via free radical polymerization. Their linear viscoelastic response was studied via small amplitude oscillatory shear (SAOS). The measured linear viscoelastic envelope (LVE) resembles that of a well entangled polymer melt with a distinct * To whom correspondence should be addressed † Technical University of Denmark ‡ University of the Basque Country ¶ Drexel University 1 plateau modulus. Dielectric relaxation spectroscopy (DRS) was employed to independently examine the lifetime of hydrogen bond units. DRS reveals a high frequency α-relaxation associated with the dynamic glass transition, followed by a slower α * -relaxation attributed to the reversible UPy hydrogen bonds. This timescale is referred to as the bare lifetime of hydrogen bonding units. Using the sticky Rouse model and a renormalized lifetime, we predict satisfactorily the LVE response for varying amounts of UPy side groups. The deviation from the sticky Rouse prediction is attributed to polydispersity in the distribution of UPy groups along the chain backbone. We conclude that the response of associating polymers in linear viscoelasticity is general and does not depend on the chemistry of association, but rather on the polymer molecular weight (MW) and MW distribution, the number of stickers per chain, n s , and the distribution of stickers along the backbone.

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The effect of hub leakage flow on the performance of two high speed transonic rotors is investigated through numerical simulations and experiments. The leakage flow emanates from a small gap between the stationary and rotating parts of the hub flow path upstream of the rotor. Results of both the experiments and CFD simulations show that the introduction of a small leakage flow (0–25% of the main passage flow) can reduce the total pressure rise produced by the rotor across the entire span and generate a significant deficit in the total pressure profile near the hub. Numerical simulations done with a sinusoidal distribution of the leakage flow across the rotor pitch show that this deficit is present even when there is zero net leakage. Particle tracer studies of CFD simulations show that this deficit is due to the flow blockage produced by the radial migration of the low momentum leakage fluid. The performance degradation trends predicted by the simulations are qualitatively confirmed in the experimental investigation.

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A computational study is carried out to understand the physical mechanism responsible for the improvement in stall margin of an axial flow rotor due to the circumferential casing grooves. Computational fluid dynamics simulations show an increase in operating range of the low speed rotor in the presence of casing grooves. A budget of the axial momentum equation is carried out at the rotor casing in the tip gap in order to understand the physical process behind this stall margin improvement. It is shown that for the smooth casing the net axial pressure force at the rotor casing in the tip gap is balanced by the net axial shear stress force. However, for the grooved casing the net axial shear stress force acting at the casing is augmented by the axial force due to the radial transport of axial momentum, which occurs across the grooves and power stream interface. This additional force adds to the net axial viscous shear force and thus leads to an increase in the stall margin of the rotor.