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Compressible plane Couette flow is studied with superposed small perturbations. The steady mean flow is characterized by a non-uniform shear-rate and a varying temperature across the wall-normal direction for an appropriate perfect gas model. The studies are broadly into four main categories as said briefly below. Nonmodal transient growth studies and estimation of optimal perturbations have been made. The maximum amplification of perturbation energy over time, G max, is found to increase with Reynolds number Re, but decreases with Mach number M. More specifically, the optimal energy amplification Gopt (the supremum of G max over both the streamwise and spanwise wavenumbers) is maximum in the incompressible limit and decreases monotonically as M increases. The corresponding optimal streamwise wavenumber, αopt, is non-zero at M = 0, increases with increasing M, reaching a maximum for some value of M and then decreases, eventually becoming zero at high Mach numbers. While the pure streamwise vortices are the optimal patterns at high Mach numbers (in contrast to incompressible Couette flow), the modulated streamwise vortices are the optimal patterns for low-to-moderate values of the Mach number. Unlike in incompressible shear flows, the streamwise-independent modes in the present flow do not follow the scaling law G(t/Re) ~ Re2, the reasons for which are shown to be tied to the dominance of some terms (related to density and temperature fluctuations) in the linear stability operator. Based on a detailed nonmodal energy anlaysis, we show that the transient energy growth occurs due to the transfer of energy from the mean flow to perturbations via an inviscid algebraic instability. The decrease of transient growth with increasing Mach number is also shown to be tied to the decrease in the energy transferred from the mean flow (E1) in the same limit. The sharp decay of the viscous eigenfunctions with increasing Mach number is responsible for the decrease of E1 for the present mean flow. Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for the uniform shear flow with constant viscosity. For a given M, the critical Reynolds number (Re), the dominant instability (over all stream-wise wavenumbers, α) of each mean flow belongs different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean-flow to perturbations. It is shown that the energy-transfer from mean-flow occurs close to the moving top-wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II”.For the Non-modal transient growth anlaysis, it is shown that the maximum temporal amplification of perturbation energy, G max,, and the corresponding time-scale are significantly larger for the uniform shear case compared to those for its non-uniform counterpart. For α = 0, the linear stability operator can be partitioned into L ~ L ¯ L +Re2Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t/Re) ~ Re2 . In contrast , the dominance of Lp is responsible for the invalidity of this scaling-law in non-uniform shear flow. An inviscid reduced model, based on Ellignsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and non-modal instability, the viscosity-stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow. Modal and nonmodal spatial growths of perturbations in compressible plane Couette flow are studied. The modal instability at a chosen set of parameters is caused by the scond least-decaying mode in the otherwise stable parameter setting. The eigenfunction is accurately computed using a three-domain spectral collocation method, and an anlysis of the energy contained in the least-decaying mode reveals that the instability is due to the work by the pressure fluctuations and an increased transfer of energy from mean flow. In the case of oblique modes the stability at higher spanwise wave number is due to higher thermal diffusion rate. At high frequency range there are disjoint regions of instability at chosen Reynolds number and Mach number. The stability characteristics in the inviscid limit is also presented. The increase in Mach number and frequency is found to further destabilize the unstable modes for the case of two-dimensional(2D) perturbations. The behaviors of the non-inflexional neutral modes are found to be similar to that of compressible boundary layer. A leading order viscous correction to the inviscid solution reveals that the neutral and unstable modes are destabilized by the no-slip enforced by viscosity. The viscosity has a dual role on the stable inviscid mode. A spatial transient growth studies have been performed and it is found that the transient amplification is of the order of Reynolds number for a superposition of stationary modes. The optimal perturbations are similar to the streamwise invariant perturbations in the temporal setting. Ellignsen & Palm solution for the spatial algebraic growth of stationary inviscid perturbation has been derived and found to agree well with the transient growth of viscous counterpart. This inviscid solution captures the features of streamwise vortices and streaks, which are observed as optimal viscous perturbations. The temporal secondary instability of most-unstable primary wave is also studied. The secondary growth-rate is many fold higher when compared with that of primary wave and found to be phase-locked. The fundamental mode is more unstable than subharmonic or detuned modes. The secondary growth is studied by varying the parameters such as β, Re, M and the detuning parameter.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

<p>The behavior of fibers suspended in a flow between two counter-rotating discs has been studied experimentally. This is inspired by the refining process in the papermaking process where cellulose fibers are ground between discs in order to change performance in the papermaking process and/or qualities of the final paper product.</p><p>To study the fiber behavior in a counter-rotating flow, an experimental set-up with two glass discs was built. A CCD-camera was used to capture images of the fibers in the flow. Image analysis based on the concept of steerable filters extracted the position and orientation of the fibers in the plane of the discs. Experiments were performed for gaps of 0.1-0.9 fiber lengths, and for equal absolute values of the angular velocities for the upper and lower disc. The aspect ratios of the fibers were 7, 14 and 28.</p><p>Depending on the angular velocity of the discs and the gap between them, the fibers were found to organize themselves in fiber trains. A fiber train is a set of fibers positioned one after another in the tangential direction with a close to constant fiber-to-fiber distance. In the fiber trains, each individual fiber is aligned in the radial direction (i.e. normal to the main direction of the train).</p><p>The experiments show that the number of fibers in a train increases as the gap between the discs decreases. Also, the distance between the fibers in a train decreases as the length of the train increases, and the results for short trains are in accordance with previous numerical results in two dimensions.Furthermore, the results of different aspect ratios imply that there are three-dimensional fiber end-effects that are important for the forming of fiber trains.</p>

Hot-wire measurements taken in the turbulent wake of a flat plate are presented. Symmetrical and antisymmetrical perturbations at various amplitudes and frequencies were introduced into the wake by small flap oscillations. As predicted by linear stability theory, the sinuous (antisymmetric) mode was observed to be more significant than the varicose (symmetric) mode. When the amplitude of the perturbation was low, the spatial development of the introduced coherent perturbation was predicted well by linear stability theory. At high forcing levels, the wake spreading showed dramatic deviations from the well known square-root behavior of the unforced case. Measured coherent Reynolds stresses changed sign in the neighborhood of the neutral point of the perturbation, as predicted by the linear theory. However, the linear theory failed to predict the disturbance amplitude and transverse shapes close to the neutral point. Some nonlinear aspects of the evolution of instabilities in the wake are discussed. Theoretical predictions of the mean flow distortion and the generation of the first harmonic are compared to experimental measurements. Given the unforced flow and the amplitude of the fundamental wave, the mean flow distortion and the amplitude of the first harmonic are predicted remarkably well.

This dissertation investigates spanwise periodic shear flow past two-dimensional bodies. The flow is assumed to be inviscid and incompressible. Using singular perturbation techniques, the solution is developed for ε = L/ℓ ≪ 1, where L represents body cross-sectional size, and ℓ the period of the oncoming flow U(z). The singular perturbation analysis involves three regions: the inner, wake and outer regions. The leading order solutions are developed in all regions, and in the inner region higher order terms are obtained. In the inner region near the body, the primary flow (U₀, V₀, P₀) corresponds to potential flow past the body with a local free stream value of U(z). The spanwise variation in U(z) produces a weak O(ε) secondary flow W₁ in the spanwise direction. As the vortex lines of the upstream flow are convected downstream, they wrap around the body, producing significant streamwise vorticity in a wake region of thickness O(L) directly behind the body. This streamwise vorticity induces a net volume flux into the wake. In the outer region far from the body, a nonlifting body appears as a distribution of three-dimensional dipoles, and the wake appears as a sheet of mass sinks. Both singularity structures must be included in describing the leading outer flow. For lifting bodies, the body appears as a lifting line, and the wake appears as a sheet of shed vorticity. The trailing vorticity is found to be equal to the spanwise derivative of the product of the circulation and the oncoming flow. For lifting bodies the first higher order correction to the inner flow is the response of the body to the downwash produced by the trailing vorticity. At large distances from the body, the flow takes on remarkably simple form.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Francesca De Siervi. / M.S.

Thesis (M.S.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Ocean Engineering; and the Woods Hole Oceanographic Institution), 1998. / Includes bibliographical references (p. 85-91). / by Alexandra Hughes Techet. / M.S.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Yolanda Leigh Hinton. / M.S.

Abstract not available