Experimental Study Of Multi-Hole Cooling For Integrally-Woven, Ceramic Matrix Composite Walls For Gas Turbine Applications

In this paper, multi-hole cooling is studied for an oxide/oxide ceramic specimen with normal injection holes and for a SiC/SiC ceramic specimen with oblique injection holes. A special purpose heat transfer tunnel was designed and built, which can provide a wide range of Reynolds numbers (10(5)similar to 10(7)) and a large temperature ratio of the primary flow to the coolant (up to 2.5). Cooling effectiveness determined by the measured surface temperature for the two types of ceramic specimens is investigated. It is found that the multi-hole cooling system for both specimens has a high cooling efficiency and it is higher for the SiC/SiC specimen than for the oxide/oxide specimen. Effects on the cooling effectiveness of parameters including blowing ratio, Reynolds number and temperature ratio, are studied. In addition, profiles of the mean velocity and temperature above the cooling surface are measured to provide further understanding of the cooling process. Duplication of the key parameters for multi-hole cooling, for a representative combustor flow condition (without radiation effects), is achieved with parameter scaling and the results show the high efficiency of multi-hole cooling for the oblique hole, SiC/SiC specimen. (C) 2008 Elsevier Ltd. All rights reserved.

A CE/SE Scheme for Flows in Porous Media and Its Applications

In this paper, a new computational scheme for solving flows in porous media was proposed. The scheme was based on an improved CE/SE method (the space-time Conservation Element and Solution Element method). We described porous flows by adopting DFB (Brinkman-Forchheimer extended Darcy) equation. The comparison between our computational results and Ghia's confirmed the high accuracy, resolution, and efficiency of our CE/SE scheme. The proposed first-order CE/SE scheme is a new reliable way for numerical simulations of flows in porous media. After investigation of effects of Darcy number on porous flow, it shows that Darcy number has dominant influence on porous flow for the Reynolds number and porosity considered.

Heat Transfer of Aviation Kerosene at Supercritical Conditions

The heat transfer characteristics of China no. 3 kerosene were investigated experimentally and analytically under conditions relevant to a regenerative cooling system for scramjet applications. A test facility developed for the present study can handle kerosene in a temperature range of 300-1000 K, a pressure range of 2.6-5 MPa, and a mass How rate range of 10-100 g/s. In addition, the test section was uniquely designed such that both the wall temperature and the bulk fuel temperature were measured at the same location along the flowpath. The measured temperature distributions were then used to analytically deduce the local heat transfer characteristics. A 10-component kerosene surrogate was proposed and employed to calculate the fuel thermodynamic and transport properties that were required in the heat transfer analysis. Results revealed drastic changes in the fuel flow properties and heat transfer characteristics when kerosene approached its critical state. Convective heat transfer enhancement was also found as kerosene became supercritical. The heat transfer correlation in the relatively low-fuel-temperature region yielded a similar result to other commonly used jet fuels, such as JP-7 and JP-8, at compressed liquid states. In the high-fuel-temperature region, near and beyond the critical temperature, heat transfer enhancement was observed; hence, the associated correlation showed a more significant Reynolds number dependency.

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges

A continuation method is applied to investigate the linear stability of the steady, axisymmetric thermocapillary flows in liquid bridges. The method is based upon an appropriate extended system of perturbation equations depending on the nature of transition of the basic flow. The dependence of the critical Reynolds number and corresponding azimuthal wavenumber on serval parameters is presented for both cylindrical and non-cylindrical liquid bridges.

Large-eddy simulations of fully developed turbulent channel and pipe flows with smooth and rough walls

Studies in turbulence often focus on two flow conditions, both of which occur frequently in real-world flows and are sought-after for their value in advancing turbulence theory. These are the high Reynolds number regime and the effect of wall surface roughness. In this dissertation, a Large-Eddy Simulation (LES) recreates both conditions over a wide range of Reynolds numbers Re_τ = O(10²)-O(10⁸) and accounts for roughness by locally modeling the statistical effects of near-wall anisotropic fine scales in a thin layer immediately above the rough surface. A subgrid, roughness-corrected wall model is introduced to dynamically transmit this modeled information from the wall to the outer LES, which uses a stretched-vortex subgrid-scale model operating in the bulk of the flow. Of primary interest is the Reynolds number and roughness dependence of these flows in terms of first and second order statistics. The LES is first applied to a fully turbulent uniformly-smooth/rough channel flow to capture the flow dynamics over smooth, transitionally rough and fully rough regimes. Results include a Moody-like diagram for the wall averaged friction factor, believed to be the first of its kind obtained from LES. Confirmation is found for experimentally observed logarithmic behavior in the normalized stream-wise turbulent intensities. Tight logarithmic collapse, scaled on the wall friction velocity, is found for smooth-wall flows when Re_τ ≥ O(10⁶) and in fully rough cases. Since the wall model operates locally and dynamically, the framework is used to investigate non-uniform roughness distribution cases in a channel, where the flow adjustments to sudden surface changes are investigated. Recovery of mean quantities and turbulent statistics after transitions are discussed qualitatively and quantitatively at various roughness and Reynolds number levels. The internal boundary layer, which is defined as the border between the flow affected by the new surface condition and the unaffected part, is computed, and a collapse of the profiles on a length scale containing the logarithm of friction Reynolds number is presented. Finally, we turn to the possibility of expanding the present framework to accommodate more general geometries. As a first step, the whole LES framework is modified for use in the curvilinear geometry of a fully-developed turbulent pipe flow, with implementation carried out in a spectral element solver capable of handling complex wall profiles. The friction factors have shown favorable agreement with the superpipe data, and the LES estimates of the Karman constant and additive constant of the log-law closely match values obtained from experiment.

Boundary-layer transition on a slender cone in hypervelocity flow with real gas effects

The laminar to turbulent transition process in boundary layer flows in thermochemical nonequilibrium at high enthalpy is measured and characterized. Experiments are performed in the T5 Hypervelocity Reflected Shock Tunnel at Caltech, using a 1 m length 5-degree half angle axisymmetric cone instrumented with 80 fast-response annular thermocouples, complemented by boundary layer stability computations using the STABL software suite. A new mixing tank is added to the shock tube fill apparatus for premixed freestream gas experiments, and a new cleaning procedure results in more consistent transition measurements. Transition location is nondimensionalized using a scaling with the boundary layer thickness, which is correlated with the acoustic properties of the boundary layer, and compared with parabolized stability equation (PSE) analysis. In these nondimensionalized terms, transition delay with increasing CO₂ concentration is observed: tests in 100% and 50% CO₂, by mass, transition up to 25% and 15% later, respectively, than air experiments. These results are consistent with previous work indicating that CO₂ molecules at elevated temperatures absorb acoustic instabilities in the MHz range, which is the expected frequency of the Mack second-mode instability at these conditions, and also consistent with predictions from PSE analysis. A strong unit Reynolds number effect is observed, which is believed to arise from tunnel noise. N_Tr for air from 5.4 to 13.2 is computed, substantially higher than previously reported for noisy facilities. Time- and spatially-resolved heat transfer traces are used to track the propagation of turbulent spots, and convection rates at 90%, 76%, and 63% of the boundary layer edge velocity, respectively, are observed for the leading edge, centroid, and trailing edge of the spots. A model constructed with these spot propagation parameters is used to infer spot generation rates from measured transition onset to completion distance. Finally, a novel method to control transition location with boundary layer gas injection is investigated. An appropriate porous-metal injector section for the cone is designed and fabricated, and the efficacy of injected CO₂ for delaying transition is gauged at various mass flow rates, and compared with both no injection and chemically inert argon injection cases. While CO₂ injection seems to delay transition, and argon injection seems to promote it, the experimental results are inconclusive and matching computations do not predict a reduction in N factor from any CO₂ injection condition computed.

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.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Forced convection film boiling of subcooled water around a sphere

An experimental investigation was made of forced convection film boiling of subcooled water around a sphere at atmospheric pressure. The water was sufficiently cool that the vapor condensed before leaving the film with the result that no vapor bubbles left the film. The experimental runs were made using inductively heated spheres at temperatures above 740°C. and using inlet water temperatures between 15°C. and 27°C. The spheres used had diameters of 1/2 inch, 9/16 inch, and 3/8 inch and were supported by the liquid flow. Reynolds numbers between 60 and 700 were used.

Analysis of the collected non-condensables indicated that oxygen and nitrogen dissolved in the water accumulated within the vapor film and that hetrogeneous chemical reactions occurred at the sphere surface. An iron-steam reaction resulted in more than 20% by volume hydrogen in the film at wall temperatures above 900°C. At temperatures near 1100°C. more than 80% by volume of the film was composed of hydrogen. It was found that gold plating of the sphere could eliminate this reaction.

Material and energy balances were used to derive equations which may be used to predict the overall average heat transfer coefficients for subcooled film boiling around a sphere. These equations include the effect of dissolved gases in the water. Equations also were derived which may be used to predict the composition of the film for cases in which an equilibrium exists between the dissolved gases and the gases in the film.

The derived equations were compared to the experimental results. It was found that a correlation existed between the Nusselt number for heat transfer from the vapor-liquid interface into the liquid and the Reynolds number, liquid Prandtl number product. In addition, it was found that the percentage of dissolved oxygen removed during the film boiling could be predicted to within 10%.

Mass transfer from a cylinder to an air stream in axisymmetrical flow (an experimental study)

Mass transfer from wetted surfaces on one-inch cylinders with unwetted approach sections was studied experimentally by means of the evaporation of n-octane and n-heptane into an air stream in axisymmetrical flow, for Reynolds numbers from 5,000 to 310,000. A transition from the laminar to the turbulent boundary layer was observed to occur at Reynolds numbers from 10,000 to 15,000. The results were expressed in terms of the Sherwood number as a function of the Reynolds number, the Schmidt number, and the ratio of the unwetted approach length to the total length. Empirical formulas were obtained for both laminar and turbulent regimes. The rates of mass transfer obtained were higher than theoretical and experimental results obtained by previous investigators for mass and heat transfer from flat plates.

On the transport properties of fluid-particle flow

The hydrodynamic forces acting on a solid particle in a viscous, incompressible fluid medium at low Reynolds number flow is investigated mathematically as a prerequisite to the understanding of transport processes in two-phase flow involving solid particles and fluid. Viscous interaction between a small number of spherical particles and continuous solid boundaries as well as fluid interface are analyzed under a “point-force” approximation. Non-spherical and elastic spherical particles in a simple shear flow area are then considered. Non-steady motion of a spherical particle is briefly touched upon to illustrate the transient effect of particle motion.

A macroscopic continuum description of particle-fluid flow is formulated in terms of spatial averages yielding a set of particle continuum and bulk fluid equations. Phenomenological formulas describing the transport processes in a fluid medium are extended to cases where the volume concentration of solid particles is sufficiently high to exert an important influence. Hydrodynamic forces acting on a spherical solid particle in such a system, e.g. drag, torque, rotational coupling force, and viscous collision force between streams of different sized particles moving relative to each other are obtained. Phenomenological constants, such as the shear viscosity coefficient, and the diffusion coefficient of the bulk fluid, are found as a function of the material properties of the constituents of the two-phase system and the volume concentration of solid. For transient heat conduction phenomena, it is found that the introduction of a complex conductivity for the bulk fluid permits a simple mathematical description of this otherwise complicated process. The rate of heat transfer between particle continuum and bulk fluid is also investigated by means of an Oseen-type approximation to the energy equation.

Theoretical investigation of turbulent boundary layer over a wavy surface

The important features of the two-dimensional incompressible turbulent flow over a wavy surface of wavelength comparable with the boundary layer thickness are analyzed.

A turbulent field method using model equation for turbulent shear stress similar to the scheme of Bradshaw, Ferriss and Atwell (1967) is employed with suitable modification to cover the viscous sublayer. The governing differential equations are linearized based on the small but finite amplitude to wavelength ratio. An orthogonal wavy coordinate system, accurate to the second order in the amplitude ratio, is adopted to avoid the severe restriction to the validity of linearization due to the large mean velocity gradient near the wall. Analytic solution up to the second order is obtained by using the method of matched-asymptotic-expansion based on the large Reynolds number and hence the small skin friction coefficient.

In the outer part of the layer, the perturbed flow is practically "inviscid." Solutions for the velocity, Reynolds stress and also the wall pressure distributions agree well with the experimental measurement. In the wall region where the perturbed Reynolds stress plays an important role in the process of momentum transport, only a qualitative agreement is obtained. The results also show that the nonlinear second-order effect is negligible for amplitude ratio of 0.03. The discrepancies in the detailed structure of the velocity, shear stress, and skin friction distributions near the wall suggest modifications to the model are required to describe the present problem.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.