Minimum drag profiles in infinite cavity flows

The problem considered is that of minimizing the drag of a symmetric plate in infinite cavity flow under the constraints of fixed arclength and fixed chord. The flow is assumed to be steady, irrotational, and incompressible. The effects of gravity and viscosity are ignored.

Using complex variables, expressions for the drag, arclength, and chord, are derived in terms of two hodograph variables, Γ (the logarithm of the speed) and β (the flow angle), and two real parameters, a magnification factor and a parameter which determines how much of the plate is a free-streamline.

Two methods are employed for optimization:

(1) The parameter method. Γ and β are expanded in finite orthogonal series of N terms. Optimization is performed with respect to the N coefficients in these series and the magnification and free-streamline parameters. This method is carried out for the case N = 1 and minimum drag profiles and drag coefficients are found for all values of the ratio of arclength to chord.

(2) The variational method. A variational calculus method for minimizing integral functionals of a function and its finite Hilbert transform is introduced, This method is applied to functionals of quadratic form and a necessary condition for the existence of a minimum solution is derived. The variational method is applied to the minimum drag problem and a nonlinear integral equation is derived but not solved.

The influence of freestream turbulence, freestream nuclei populations and a drag-reducing polymer on cavitation inception on two axisymmetric bodies

The influence upon the basic viscous flow about two axisymmetric bodies of (i) freestream turbulence level and (ii) the injection of small amounts of a drag-reducing polymer (Polyox WSR 301) into the test model boundary layer was investigated by the schlieren flow visualization technique. The changes in the type and occurrence of cavitation inception caused by the subsequent modifications in the viscous flow were studied. A nuclei counter using the holographic technique was built to monitor freestream nuclei populations and a few preliminary tests investigating the consequences of different populations on cavitation inception were carried out.

Both test models were observed to have a laminar separation over their respective test Reynolds number ranges. The separation on one test model was found to be insensitive to freestream turbulence levels of up to 3.75 percent. The second model was found to be very susceptible having its critical velocity reduced from 30 feet per second at a 0.04 percent turbulence level to 10 feet per second at a 3.75 percent turbulence level. Cavitation tests on both models at the lowest turbulence level showed the value of the incipient cavitation number and the type of cavitation were controlled by the presence of the laminar separation. Cavitation tests on the second model at 0.65 percent turbulence level showed no change in the inception index, but the appearance of the developed cavitation was altered.

The presence of Polyox in the boundary layer resulted in a cavitation suppression comparable to that found by other investigators. The elimination of the normally occurring laminar separation on these bodies by a polymer-induced instability in the laminar boundary layer was found to be responsible for the suppression of inception.

Freestream nuclei populations at test conditions were measured and it was found that if there were many freestream gas bubbles the normally present laminar separation was elminated and travelling bubble type cavitation occurred - the value of the inception index then depended upon the nuclei population. In cases where the laminar separation was present it was found that the value of the inception index was insensitive to the free stream nuclei populations.

Joule-Thomson coefficients of propane and n-butane

Experimental Joule-Thomson measurements were made on gaseous propane at temperatures from 100 to 280˚F and at pressures from 8 to 66 psia. Joule-Thomson measurements were also made on gaseous n-butane at temperatures from 100 to 280˚ and at pressures from 8 to 42 psia. For propane, the values of these measurements ranged from 0.07986˚F/psi at 280˚F and 8.01 psia to 0.19685˚F/psi at 100˚F and 66.15 psia. For n-butane, the values ranged from 0.11031˚F/psi at 280˚F and 9.36 psia to 0.30141˚F/psi at 100˚F and 41.02 psia. The experimental values have a maximum error of 1.5 percent.

For n-butane, the measurements of this study did not agree with previous Joule-Thomson measurements made in the Laboratory in 1935. The application of a thermal-transfer correction to the previous experimental measurements would cause the two sets of data to agree. Calculated values of the Joule-Thomson coefficient from other types of p-v-t data did agree with the present measurements for n-butane.

The apparatus used to measure the experimental Joule-Thomson coefficients had a radial-flow porous thimble and was operated at pressure changes between 2.3 and 8.6 psi. The major difference between this and other Joule-Thomson apparatus was its larger weight rates of flow (up to 6 pounds per hour) at atmospheric pressure. The flow rate was shown to have an appreciable effect on non-isenthalpic Joule-Thomson measurements.

Photographic materials on pages 79-81 are essential and will not reproduced clearly on Xerox copies. Photographic copies should be ordered.

Coulomb drag and tunneling studies in quantum Hall bilayers

The bilayer quantum Hall state at total filling factor ν_T=1, where the total electron density matches the degeneracy of the lowest Landau level, is a prominent example of Bose-Einstein condensation of excitons. A macroscopically ordered state is realized where an electron in one layer is tightly bound to a "hole" in the other layer. If exciton transport were the only bulk transportmechanism, a current driven in one layer would spontaneously generate a current of equal magnitude and opposite sign in the other layer. The Corbino Coulomb drag measurements presented in this thesis demonstrate precisely this phenomenon.

Excitonic superfluidity has been long sought in the ν_T=1 state. The tunneling between the two electron gas layers exihibit a dc Josephson-like effect. A simple model of an overdamped voltage biased Josephson junction is in reasonable agreement with the observed tunneling I-V. At small tunneling biases, it exhibits a tunneling "supercurrent". The dissipation is carefully studied in this tunneling "supercurrent" and found to remain small but finite.

Some properties of the coefficients of cyclotomic polynomials

An explicit formula is obtained for the coefficients of the cyclotomic polynomial F_n(x), where n is the product of two distinct odd primes. A recursion formula and a lower bound and an improvement of Bang’s upper bound for the coefficients of F_n(x) are also obtained, where n is the product of three distinct primes. The cyclotomic coefficients are also studied when n is the product of four distinct odd primes. A recursion formula and upper bounds for its coefficients are obtained. The last chapter includes a different approach to the cyclotomic coefficients. A connection is obtained between a certain partition function and the cyclotomic coefficients when n is the product of an arbitrary number of distinct odd primes. Finally, an upper bound for the coefficients is derived when n is the product of an arbitrary number of distinct and odd primes.

Friction and heat transfer coefficients in smooth and rough pipes with dilute polymer solutions

Measurements of friction and heat transfer coefficients were obtained with dilute polymer solutions flowing through electrically heated smooth and rough tubes. The polymer used was "Polyox WSR-301", and tests were performed at concentrations of 10 and 50 parts per million. The rough tubes contained a close-packed, granular type of surface with roughness-height-to-diameter ratios of 0.0138 and 0.0488 respectively. A Prandtl number range of 4.38 to 10.3 was investigated which was obtained by adjusting the bulk temperature of the solution. The Reynolds numbers in the experiments were varied from =10,000 (Pr= 10.3) to 250,000 (Pr= 4.38).

Friction reductions as high as 73% in smooth tubes and 83% in rough tubes were observed, accompanied by an even more drastic heat transfer reduction (as high as 84% in smooth tubes and 93% in rough tubes). The heat transfer coefficients with Polyox can be lower for a rough tube than for a smooth one.

The similarity rules previously developed for heat transfer with a Newtonian fluid were extended to dilute polymer solution pipe flows. A velocity profile similar to the one proposed by Deissler was taken as a model to interpret the friction and heat transfer data in smooth tubes. It was found that the observed results could be explained by assuming that the turbulent diffusivities are reduced in smooth tubes in the vicinity of the wall, which brings about a thickening of the viscous layer. A possible mechanism describing the effect of the polymer additive on rough pipe flow is also discussed.