Compressible turbulence in a high-speed, high Reynolds number, supersonic free shear layer was studied. A two-dimensional free mixing layer was chosen to study turbulence rather than a wall bounded flow due to the experimental fact that the effects of compressibility become significant at lower Mach numbers. The mixing layer was generated by supersonic injection of air (M_s = 1.8, P_ts = 0.5 atm. T_ts= 295K. and Re/m = 7x10⁶) through a rearward facing tangential slot, into a supersonic free stream (M_∞ = 4.0, P_t∞ = 12.5 atm, T_t∞ = 290K, and Re/m = 70x10⁶). Flow visualization was accomplished by nanosecond Shadowgraph photography. The overall flow structure was documented with the Shadowgraph and conventional mean flow probes (Pitot pressure, cone-static pressure, and thermocouple probes). The turbulent structure of the flow field was also clearly depicted in the Shadowgraphs. Image processing techniques were developed in order to determine root-mean-square index of refraction (density) fluctuation levels from the Shadowgraph plates. Multiple overheat normal and cross-wire techniques were developed and/or improved for this study. The present research concentrated on the Reynolds averaged form of the Navier-Stokes equations. where the effects of compressibility are manifested through "apparent mass" terms (i.e. p′u′_i). These terms appear in all of the Reynolds averaged Navier-Stokes equations (continuity, momentum, and energy). A new turbulence transformation, coupled with innovative experimental methods. allowed the full compressible Reynolds shear stress (the typical incompressible term, pu′_iu′_j as well as the apparent mass terms) to be directly measured. The full compressible heat flux and apparent mass terms were also estimated from the cross-wire results. Profiles were obtained at four downstream stations which were strategically located to map different levels of development of the shear flow. The first station was very close to the injector, about one free stream boundary layer thickness downstream (x/δ_∞ ≈ 1), hence, it is in the initial region. The second station was located at x/δ_∞ ≈ 28, which was near the beginning of the fully developed zone. The third station, x/δ_∞ = 83, was just prior the shear layer and floor boundary layer merging. The last station was positioned just aft of the layer merging, x/δ_∞ = 106. Reynolds averaging of the compressible Navier-Stokes equations implies that the compressible turbulence affects all of the governing equations. It was found, experimentally, that the effects of compressibility on turbulence were more than significant accounting for about 75% of the total level of the Reynolds shear stress formulation for the present study (i.e. the apparent mass term multiplied by the axial velocity was about 3-4 times the typical incompressible shear term). For the present mean adiabatic flow, the compressible turbulence accounted for 100% of the turbulent heat flux. The apparent mass in the continuity equation was, by definition, only due to compressibility. These results led to the development of anew Compressible Apparent Mass Mixing Length Extension (CAMMLE) model that accounts for compressible turbulence in all of the governing equations (i.e. the turbulence terms in the continuity, momentum, and energy were all consistently formulated). The CAMMLE formulation is a generalization of the Situ-Schetz compressible mixing length formulation, which was developed to account for the apparent mass terms in the momentum equation. A total of seven turbulence models were experimentally evaluated, the CAMMLE model, the Prandtl incompressible and the Situ-Schetz compressible mixing length models, the Prandtl and Bradshaw turbulent kinetic energy (TKE) formulations, and two compressible TKE extensions that are based upon a newly defined compressible TKE formulation. The measured turbulence data was used to assess the various models, where the measured mean flow profiles were used in the model formulations. The incompressible formulations were generally successful in representing the measured incompressible part of the Reynolds shear stress. However, this term only accounted for about 25% of the total shear stress level. All of the compressible extensions provided accurate estimates of the full compressible Reynolds shear stress. In addition, the newly developed CAMMLE model was also successful in representing the apparent mass terms in the continuity equation. The CAMMLE model was also the only formulation to accurately predict the measured compressible turbulent heat flux in the energy equation. The CAMMLE, Situ-Schetz, and Prandtl incompressible mixing length models were all incorporated in to a 3-D finite volume Navier-Stokes code (GASP 2.0). The numerical simulations indicated that the new compressible apparent mass mixing length extension performed very well. The CFD results also enlightened a misuse with all of the current compressible turbulence models. With the exception of the new apparent mass formulation, all existing turbulence models neglect the compressible turbulence effects on the continuity equation and treat the energy equation in an ad hoc effective eddy viscosity and thermal conductivity fashion. The numerical and theoretical studies indicated that this led to poor prediction of the mixing layer width for cases where the free stream Mach number was significantly higher than the injection Mach number. / Ph. D.

The dependence of an airfoil stall behavior upon the acoustic l environment was experimentally investigated at a Reynolds number of 200,000. The Wortmann FX-63-137-ESM airfoil section was used for the model with an aspect ratio of 4. Some acoustic disturbances could alter the transition process in the shear layer of the separation bubble on the upper surface of the airfoil. These disturbances could delay the deep leading edge stall or hasten stall recovery in some cases. A good agreement was found with the Crabtree criterion to predict the leading edge stall. / Master of Science

A full three dimensional computational study was carried out using a finite-volume based solver for analyzing the performance of pin-fin based micro/meso scale heat exchangers with air as the working fluid. A staggered arrangement of cylindrical pin fins in rectangular channel geometry was used. Various configurations were considered consistent with a parallel experimental study being conducted based on a micro-wind tunnel setup. The pin/channel height used was 0.4 mm, and the pin diameters varied from 0.17-0.50 mm to give hydraulic diameters in the range of 0.13-0.78 mm. This gave volumetric area densities for the heat exchangers in the range of 5-15 mm2/mm3. Various heat exchanger configurations were simulated to determine performance characteristics such as the Nusselt number, friction factor, specific fluid friction power and Mach number in the Reynolds number regime for laminar flows. In addition a detailed numerical diagnosis was carried out to determine local behavior on the pin surfaces, end walls, etc to identify specific characteristics such as regions of high and low heat transfer, locations for possible shock formation, etc. The range of results obtained would be useful for future design of micro heat exchangers for use in small footprint, high heat flux dissipation applications like turbine blade and microelectronic systems.

This thesis has described a Reynolds Averaged Navier Stokes approach to modeling turbulence in the wake of a cylinder and airfoil. The mean flow, cross stresses, and two-point space time correlation structure was analyzed for an untripped cylinder with a Reynolds number based on the cylinder diameter and freestream velocity of 60,000. The same features were also analyzed using this approach for an untripped NACA 0012 airfoil with a Reynolds number based on the airfoil chord and freestream velocity of 328,000. These simulation results were compared to experimental and newly developed models for validation. The ultimate goal of this present study was to create the two-point space time correlation function of a cylinder and airfoil wake using RANS calculations which contributes to a larger study where the sound radiated by an open rotor due to ingestion of turbulence. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

There is currently growing interest in the field of Micro Air Vehicles (MAVs). A MAV is characterized by its low Reynolds numbers flight regime which makes lift and thrust creation a significant challenge. One possible solution inspired by nature is flapping flight, but instead of the large-amplitude low-frequency motion suited to the muscular actuators of nature, small-amplitude high-frequency motion may be more suitable for electrical actuators. In this thesis the effect of small-amplitude high-frequency motion is experimentally investigated focusing on three aspects: general performance improvement, deflected jets, and the effect of geometryResults presented herein demonstrate that using small-amplitude high-frequency plunging motion on a NACA 0012 airfoil at a post-stall angle of attack of 15° can lead to significant thrust production accompanying a 305% increase in lift coefficient. At low Strouhal numbers vortices form at the leading-edge during the downward motion and then convect into the wake. This ‘mode 1’ flow field is associated with high lift but low thrust. The maximum lift enhancement was due to resonance with the natural shedding frequency, its harmonics and subharmonics. At higher Strouhal numbers the vortex remains over the leading-edge area for a larger portion of the cycle and therefore loses its coherency through impingement with the upward moving airfoil. This ‘mode 2’ flowfield is associated with low lift and high thrust. At angles of attack below 12.5° very large force bifurcations are observed. These are associated with the formation of upwards or downwards deflected jets with the direction determined by initial conditions. The upwards deflected jet is associated with the counter-clockwise Trailing Edge Vortex (TEV) loitering over the airfoil and thereby pairing with the clockwise TEV to form a dipole that convects upwards. It therefore draws fluid from the upper surface enhancing the upper surface vortex leading to high lift. The downwards deflected jet is associated with the inverse. Deflected jets were not observed at larger angles of attack as the asymmetry in the strength of the TEVs was too great; nor at smaller amplitudes as the TEV strength was insufficient. To understand the effect of geometry comparable experiments were performed for a flat plate geometry. At zero degrees angle of attack deflected jets would form, as for the NACA 0012 airfoil, however their direction would switch sinusoidally with a period on the order of 100 cycles. The lift coefficient therefore also switched. At 15° angle of attack for Strouhal numbers up to unity the performance of the flat plate was comparable to the NACA 0012 airfoil. Above unity, the upper surface and lower surface leading-edge vortices form a dipole which convects away from the upper surface resulting in increased time-averaged separation and reduced lift.

Chan, Tak Shing = 粗糙表面的熱湍流對流的Nusselt數和雷諾數的測量 / 陳德城. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 63-67). / Abstracts in English and Chinese. / Chan, Tak Shing = Cu cao biao mian de re tuan liu dui liu de Nusselt shu he Leinuo shu de ce liang / Chen Decheng. / Table of Contents --- p.v / List of Figures --- p.xi / List of Tables --- p.xii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- What is turbulence ? --- p.1 / Chapter 1.2 --- Rayleigh Benard convection system --- p.3 / Chapter 1.2.1 --- Oberbeck-Boussinesq approximation and equations of Rayleigh- Benard system --- p.5 / Chapter 1.2.2 --- Some coherent structures of Rayleigh-Benard convection system --- p.7 / Chapter 1.3 --- Motivation --- p.8 / Chapter 2 --- Experimental methods and setups --- p.12 / Chapter 2.1 --- Convection cell --- p.12 / Chapter 2.2 --- Temperature measurement --- p.15 / Chapter 2.3 --- Experimental techniques --- p.16 / Chapter 2.3.1 --- Heat leakage prevention --- p.16 / Chapter 2.3.2 --- Water absorption of Dipropylene Glycol --- p.21 / Chapter 2.3.3 --- Particle Image Velocimetry --- p.22 / Chapter 3 --- Heat flux measurement --- p.25 / Chapter 3.1 --- Water Results --- p.26 / Chapter 3.1.1 --- Experimental procedures --- p.26 / Chapter 3.1.2 --- Heat leakage/ heat absorption estimation --- p.27 / Chapter 3.1.3 --- Results and discussions --- p.29 / Chapter 3.2 --- Dipropylene Glycol Results --- p.32 / Chapter 3.2.1 --- Experimental procedures --- p.32 / Chapter 3.2.2 --- Heat leakage/ heat absorption estimation --- p.33 / Chapter 3.2.3 --- Result and discussions --- p.34 / Chapter 3.3 --- More discussion --- p.41 / Chapter 4 --- Large scale circulation and Reynolds number measurement --- p.44 / Chapter 4.1 --- Flow pattern of turbulent Rayleigh-Benard convection over rough plates --- p.46 / Chapter 4.2 --- Reynolds number measurement --- p.48 / Chapter 4.2.1 --- Reynolds number determined from oscillation of temper- ature signals --- p.48 / Chapter 4.2.2 --- Reynolds number determined from velocity measurement near sidewall --- p.55 / Chapter 5 --- Conclusion --- p.61 / Chapter 5.1 --- Conclusion --- p.61 / Bibliography --- p.63

Ko, Tze Cheung = 均勻湍流對流殼模型內的熱傳送及雷諾數標度律 / 高子翔. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 76-78). / Abstracts in English and Chinese. / Ko, Tze Cheung = Jun yun tuan liu dui liu ke mo xing nei de re chuan song ji Leinuo shu biao du lü / Gao Zixiang. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Description of Rayleigh-Benard convection --- p.2 / Chapter 1.2 --- Interesting issues in turbulent Rayleigh-Benard convection --- p.3 / Chapter 2 --- Earlier studies of heat transport in Rayleigh-Benard convection --- p.6 / Chapter 2.1 --- Marginal stability arguments --- p.7 / Chapter 2.2 --- The Chicago mixing zone model --- p.8 / Chapter 2.3 --- Shraiman and Siggia theory --- p.10 / Chapter 2.4 --- Grossmann and Lohse theory --- p.12 / Chapter 2.4.1 --- Estimating the kinetic dissipation rates due to boundary layer and bulk --- p.13 / Chapter 2.4.2 --- Estimating the thermal dissipation rates due to boundary layer and bulk --- p.13 / Chapter 2.4.3 --- The four regimes --- p.15 / Chapter 2.5 --- The asymptotic limit of very high Ra --- p.17 / Chapter 3 --- The shell model used --- p.20 / Chapter 3.1 --- Background of shell models of turbulence --- p.20 / Chapter 3.2 --- The model used --- p.22 / Chapter 3.2.1 --- The Brandenburg model --- p.22 / Chapter 3.2.2 --- The requirement of a large scale drag term --- p.23 / Chapter 3.3 --- Previous work on the Brandenburg model --- p.24 / Chapter 4 --- "Definitions of Ra, Nu, and Re and two exact results" --- p.26 / Chapter 4.1 --- Heat transport study using shell model --- p.26 / Chapter 4.2 --- Two exact results --- p.28 / Chapter 5 --- Results and discussions --- p.29 / Chapter 5.1 --- Parameters used --- p.29 / Chapter 5.2 --- "Nu(Ra,Pr) and Re(Ra,Pr) scaling results" --- p.29 / Chapter 5.3 --- "Scaling results of ε, εdrag and x" --- p.32 / Chapter 5.4 --- Physical meaning of the drag term --- p.35 / Chapter 5.5 --- Understanding the dependence of ε on Re --- p.36 / Chapter 5.6 --- Understanding the dependence of x and εdrag on Re and Pr --- p.40 / Chapter 5.7 --- The form of the added drag term --- p.41 / Chapter 6 --- Possible changes of Nu and Re due to non-Boussinesq effects --- p.43 / Chapter 6.1 --- Background --- p.43 / Chapter 6.2 --- Method of study --- p.44 / Chapter 6.3 --- Effects due to the temperature dependence of kinematic viscosity --- p.45 / Chapter 6.4 --- Effects due to the temperature dependence of thermal diffusivity --- p.50 / Chapter 6.5 --- Effects due to the temperature dependence of volume expansion coefficient --- p.55 / Chapter 6.6 --- Understanding the scaling behavior under non-Boussinesq effects --- p.61 / Chapter 6.6.1 --- Scaling behavior of x on Re --- p.61 / Chapter 6.6.2 --- Scaling behavior of εtotai on Re --- p.65 / Chapter 6.6.3 --- Scaling behavior of Nu and Re on Ra --- p.66 / Chapter 6.7 --- Summary and future work --- p.68 / Chapter 7 --- Conclusion --- p.69 / Chapter A --- Height independence of Nu for homogeneous turbulent convection with periodic boundary conditions --- p.73 / Chapter B --- "Height independence of (uz)A,t for homogeneous turbulent convection with periodic boundary conditions" --- p.75 / Bibliography --- p.76

Abstract not available

A plane jet is a statistically two-dimensional flow, with the dominant flow in the streamwise (x) direction, spread in the lateral (y) direction and zero entrainment in the spanwise (z) direction respectively (see Figure 1). A plane jet has several industrial applications, mostly in engineering environments, although seldom is a jet issuing through a smooth contoured nozzle encountered in real life. Notably, the Reynolds number and boundary conditions between industrial and laboratory environments are different. In view of these, it is important to establish effects of nozzle boundary conditions as well as the influence of Reynolds number, on jet development. Such establishments are essential to gain an insight into their mixing field, particularly relevant to engineering applications. To satisfy this need, this thesis examines the influence of boundary conditions, especially those associated with the formation of the jet and jet exit Reynolds number, on the flow field of a turbulent plane air jet by measuring velocity with a hot wire anemometer. A systematic variation is performed, of the Reynolds number Re over the range 1,500≤Re ≤16,500, the inner-wall nozzle contraction profile r* over the range 0≤r*≤3.60 and nozzle aspect ratio AR over the range 15≤AR≤72 (see notation for symbols). An independent assessment of the effect of sidewalls on a plane jet is also performed. Key outcomes are as follows: (1) Effects of Reynolds number Re: Both the mean and turbulence fields show significant dependence on Re. The normalized initial mean velocity and turbulence intensity profiles are Re-dependent. An increase in the thickness of boundary layer at the nozzle lip with a decrease in Re is evident. This dependence appears to become negligible for Re ≥10,000. The centerline mean velocity decay and jet spreading rates are found to decrease as Re is increased. Furthermore, the mean velocity field appears to remain sensitive to Reynolds number at Re = 16,500. Unlike the mean velocity field, the turbulent velocity field has a negligible Re-dependence for Re ≥10,000. An increase in Reynolds number leads to an increase in the entrainment rate in the near field but a reduced rate in the far field. The centerline skewness and the flatness factors show a systematic dependence on Reynolds number too. (2) Effects of the inner-wall nozzle exit contraction profile r*: The inner-wall nozzle exit contraction profile r* influences the initial velocity and turbulence intensity profiles. Saddle-backed mean velocity profiles are evident for the sharp-edged orifice configuration (r* ≈ 0) and top hat profiles emerge when r* ≥1.80. As r* is increased from 0 to 3.60, both the near and the far field decay and the spreading rates of the plane jet are found to decrease. Hence, the sharp-edged orifice-jet (r* ≈ 0) decays and spreads more rapidly than the jet through a radially contoured configuration (r* ≈ 3.60). The asymptotic values of the center-line turbulence intensity, skewness and flatness factors of the velocity fluctuations increase as r* tends toward zero. The non-dimensional vortex shedding frequency of StH ≈ 0.39, is higher for the sharp-edged orifice nozzle (r*≈ 0), than for the radially contoured (r* ≈ 3.60) nozzle whose StH ≈ 0.24. Thus, the vortex shedding should be strongly dependent on flow geometry and on nozzle boundary conditions. (3) Effects of nozzle aspect ratio AR: The initial velocity and turbulence intensity profiles are slightly dependent on nozzle aspect ratio of the plane air jet. It is believed that a coupled influence of the nozzle aspect ratio and sidewalls produce changes in the initial flow field. The axial extent over which a statistically 'two-dimensional' flow is achieved, is found to depend upon nozzle aspect ratio. This could be possibly due to the influence of the evolving boundary layer on the sidewalls or due to increased three-dimensionality, whose influence becomes significantly larger as nozzle aspect ratio is reduced. A statistically two dimensional flow is only achieved over a very limited extent for AR = 15. In the self-similar region, the rates of centreline velocity decay, spreading of the mean velocity field and jet entrainment increase with an increase in nozzle aspect ratio. An estimate of the critical jet aspect ratio, where three-dimensional effects first emerge and its axial location is made. Results show that the critical aspect ratio increases with nozzle aspect ratio up to AR <30. For AR≥30, the critical aspect ratio based on jet half width, attains a constant value of about 0.15. Thus, it appears that when the width of the flow approximately equals the spacing between the sidewalls, the plane air jet undergoes a transition from 2-D to 3-D. A distinct hump of the locally normalized turbulence intensity at an axial distance between 10 to 12 nozzle widths downstream, characterizes the centerline turbulence intensity for all nozzle aspect ratios. This hump is smaller when nozzle aspect ratio is larger. (4) Effects of the sidewalls: A jet issuing from a nozzle of AR = 60 and measured at Re = 7,000 is tested with sidewalls, i.e. plane-jet and without sidewalls, i.e. free-rectangular-jet. It is found that the entire flow field behaves differently for the two cases. The initial velocity profiles are top hat for both jets. The free rectangular jet decays and spreads more rapidly in both the near and far field. It is found that the free rectangular jet behaves statistically two-dimensional up to a shorter axial distance (x/H = 70) as opposed to the plane jet whose two-dimensional region extends up to x/H = 160. Also noted are that the axial extent of the two-dimensional region depends strongly on nozzle aspect ratio. Beyond the 2-D region, the free rectangular jet tends to behave, statistically, like a round jet. The locally normalized centerline turbulence intensity also depend on sidewalls. Turbulence intensity for the plane jet asymptotes closer to the nozzle (around x/H = 30) whereas for the free rectangular jet, turbulence intensity varies as far downstream as x/H = 100, and then asymptotes. A constant StH of 0.36 is found for the free rectangular jet whereas an StH of 0.22 is obtained for the plane jet. It is noted that the effects of jet exit Reynolds number, inner-wall nozzle exit contraction profile, nozzle aspect ratio and sidewalls on the plane air jet are all non-negligible. The effect of viscosity is expected to weaken with increased Reynolds number and this may contribute to the downstream effects on the velocity field. Both the nozzle contraction profile and nozzle aspect ratio provide different exit boundaries for the jet. Such boundary conditions not only govern the formation of the initial jet but also its downstream flow properties. Hence, the initial growth of the shear layers and the structures within these layers are likely to evolve differently with different boundary conditions. Thus, the interaction of the large-scale structures with the surroundings seems to depend on nozzle boundary conditions and consequently, influences the downstream flow. In summary, the present study supports the notion that the near and far fields of the plane jet are strongly dependent on Reynolds number and boundary conditions. Therefore, the present thesis contains immensely useful information that will be helpful for laboratory-based engineers in selection of appropriate nozzle configurations for industrial applications. / Thesis (Ph.D.)--School of Mechanical Engineering, 2005.

Thesis (M.S.)--Baylor University, 2005. / Includes bibliographical references (p. 124-128).