CarlosCoimbra

Carlos F. M. Coimbra

Multiphase Heat Transfer and Fluid Dynamics Group

Department of Mechanical and Aerospace Engineering

University of California

Irvine, CA 92697 - ccoimbra@eng.uci.edu

Professional Interests

Applied Mathematics in Fluid Mechanics, Heat and Mass Transfer; Computational Fluid Dynamics;

Mathematical Modeling of Dispersed Flows; Fractional Calculus in Diffusion Processes;

Energy and Thermodynamics; Eulerian-Lagrangian Computational Fluid Dynamics;

Turbulent Particle Dispersion; Combustion in Practical Systems and Industrial Equipment;

Pollutant Emissions from Combustion Equipment; Numerical Characterization of Utility Boilers;

Fossil Fuel Utilization; Environmental Impact of Combustion Technologies.

Academic Background

1998 Ph.D. Mechanical and Aerospace Engineering

University of California, Irvine, USA

1992 M. Sc. Mechanical Engineering / Energy

Instituto Superior Técnico, Technical University of Lisbon, Portugal

1990 B.Sc. Physics

University of Brasília, Brazil

1989 Mechanical Engineer

University of Brasília, Brazil

Current Lines of Research

The Unsteady Motion and Heat Transfer of Small Particles in Suspension

One of the most compelling reasons to justify orbital flights and the construction of a space station is that many manufacturing technologies would benefit from low-gravity environments. In order to be economically viable, the products of such manufacturing industries should concentrate high economic value per mass and per volume. Such conditions are met by the semiconductor and pharmaceutical industries, which would benefit from low-gravity to grow near-perfect crystals in space. The idea is that, in a zero-gravity environment, the growth of crystals approaches isotropic behavior in the macro-scale, regarded that the matrix fluid is kept unperturbed. The challenge in this case is to seek the most stable conditions for the matrix fluid, and to compensate for the inherent corrective motions of a space unit. In order to meet this challenges it is necessary to study the intricate relationship between the matrix fluid and the particles in suspension. In particular, one may retrieve information on slow-motion convection currents of the matrix fluid through study of the motion of small particles contained in it. In order to improve the quality of crystals manufactured under low-gravity conditions, and to assess the role of the induced convection caused by the growth of the crystals, the theoretical description of the diffusion and low-velocity convection phenomena becomes imperative.

The purpose of this research is to investigate the motion of small rigid particles of any density ratio in unsteady creeping flows. Applications of this problem may be found in the settling of particles in colloidal suspensions, in the motion of bubbles in liquid reservoirs, in the mechanical behavior of fluid markers, and in several other flows of engineering interest. The analytical description of the motion of small particles in creeping flows allows studying the inverse problem, which is the determination of the background flow patterns from a determined motion of suspended particles. The solution of the inverse problem is of fundamental importance to understand the phenomena related to crystal growth under low-gravity conditions, thus being a necessary step towards the improvement of crystal growth techniques.

The vast majority of the studies in the field of multiphase flows are conducted numerically, where the particle equation of motion is either solved through iterative schemes, or is simplified to allow for fast computations. In either situation, the outcome of the numerical studies is compromised, since computational costs need to be balanced against unrealistic solutions. The most commonly used strategy is to neglect troublesome terms in the equation of motion and solve exactly or numerically the remaining simplified equation. This option proves to be unsatisfactory for many important flows, especially when the unsteadiness of the flow field near the particle plays an important role on the balance of forces acting on the particle. In this work, we solve the particle equation of motion exactly, overcoming the most fundamental problems of computing particle velocities and trajectories in unsteady viscous flows.

The transient heat transfer from a spherical particle to a time-dependent surrounding temperature field is modified when compared to the quasi-steady formulation of the problem. The heat transfer modification is due to the developing temperature profile around the particle. This contribution is usually neglected in heat transfer analyses since it is common place to assume an average heat transfer coefficient that is independent of time. The contribution from the unsteadiness of the temperature profile in the near region of the particle is however not always negligible, and can account for significant modification of the quasi-steady temperature behavior. Due to the dispersed nature of the suspension under study in this work, the heat transfer problem is divided into two main problems: the unsteady diffusion heat transfer of a single particle, and the quasi-steady, linear radiation problem of a cloud of particles. The effects of both modes of heat transfer are combined to yield a formulation for the temperature response of the particles to time-dependent variations of the temperature of the surrounding medium.

Particle Motion in Unsteady Stokes Flows

The general solution to the particle momentum equation for unsteady Stokes flows is obtained analytically. The method used to obtain the solution consists on applying a fractional-differential operator to the first-order, integro-differential equation of motion in order to transform the original equation into a second-order, non-homogeneous equation, and then solving this last equation by the method of variation of parameters. The fractional differential operator consists of a three-time-scale, linear operator that stretches the order of the Riemann-Liouville fractional derivative associated with the history term in the equation of motion. In order to illustrate the application of the general solution to particular background flow fields, the particle velocity is calculated for three specific flow configurations. These flow configurations correspond to the gravitationally induced motion of a particle through an otherwise quiescent fluid, the motion of a particle caused by a background velocity field that accelerates linearly in time, and the motion of a particle in a fluid that undergoes an impulsive acceleration. The analytical solutions for these three specific cases are analyzed and compared to other solutions found in the literature.

Motion of Rigid Particles in Harmonic Stokes Flow

The particle momentum equation for harmonic Stokes flows is solved exactly in order to study the velocity response of rigid spherical particles. Fluid-to-particle density ratios varying from 0.001 to 1000 are studied to identify the proper scaling of the Virtual Mass, Stokes drag and History drag forces. The Fractional Calculus method used to render the governing integro-differential equation of motion analytically tractable is shown to be useful in determining the scaling of the above referenced forces. These forces scale as (a w )ⁿ, where a is the fluid-to-particle density ratio and w is the dimensionless forcing frequency. The power coefficient 'n' is the order of the derivative of the velocity potential that characterizes the force in question in the particle momentum equation. This coefficient is numerically equal to 0 for the Stokes drag, 1/2 for the History drag, and 1 for the Virtual Mass force. The ratio of the History drag and Virtual Mass forces to the Stokes drag is independent of the density of the particles, depending only on the radius of the particle and on the fluid characteristics and forcing frequency. The Virtual Mass force thus dominates the high-frequency response of light particles. The low-frequency response of heavy particles is dominated by the Stokes drag, and the intermediate frequency response is dominated by the Stokes drag for values of a less than 0.1, and by the Virtual Mass force for values of a larger than 10. The history drag contribution is maximum when the product aw = 2 and when the amplitude of oscillations are smaller than the radius of the particle.

Heat Transfer Analysis of Small Particles in a Homogenous Suspension

A theoretical formulation of the thermal response of particles subjected to time-dependent temperature perturbations in the surrounding medium is presented. The suspension of particles is considered homogeneous and dilute. The continuous medium containing the dispersion of particles is assumed to be weakly participating, having a small but non-zero absorption coefficient. The particles in suspension are small, so that the mechanisms of heat transfer between the particles and the continuous phase are of diffusive and radiative nature only. The general solution for the temperature response of the particles to time-dependent perturbations in the continuous phase is derived for the limit of small Biot and infintesimal Péclet numbers. The method used to derive the general solution consists of including the linearized radiation effects in the integro-differential equation that describes the temperature history of the particles. A fractional-differential operator that contains a Riemann-Liouville-Weyl half-derivative term is then applied to the radiation-diffusion equation in order to render the governing equation analytically tractable. The resulting equation is solved exactly by the method of variation of parameters for the temperature potential between the particles and the medium. Linear and harmonic perturbations are analyzed and discussed, and the radiative and history term contributions to the temperature response of the particles are studied.

List of Publications

Journal Papers

J.1) C.F.M. Coimbra, and R.H. Rangel (1998). "General Solution of the Particle Momentum Equation in Unsteady Stokes Flows" - Journal of Fluid Mechanics (370) pp. 53-72.

J.2) C.F.M. Coimbra, D.K. Edwards, and R.H. Rangel (1998). "Heat Transfer in a Homogeneous Suspension Including Radiation and History Effects" - AIAA Journal of Thermophysics and Heat Transfer (12) pp. 304-312.

J.3) C.F.M. Coimbra, J.S. Shirolkar and M.Q. McQuay (1998). "Modeling Particle Dispersion in a Turbulent, Multiphase Mixing Layer" - Journal of Wind Engineering and Industrial Aerodynamics (73) pp. 79-97.

J.4) C.F.M. Coimbra, P.J. Coelho, M.Q. McQuay and M.G. Carvalho (1996). "The Comparison of Two Comprehensive Combustion Codes to Simulate Large-Scale, Oil-Fired Boilers" - Combustion Science and Technology (120) pp. 55-81.

J.5) J.S. Shirolkar, C.F.M. Coimbra and M.Q. McQuay (1996). "Fundamental Aspects of Modeling Turbulent Particle Dispersion in Dilute Flows" - Progress in Energy and Combustion Science (22) pp. 363-399.

J.6) C.F.M. Coimbra and M. Queiroz (1995). "Evaluation of a Dimensionless Group Number to Determine Second-Einstein Temperatures in a Heat Capacity Model for All Coal Ranks" - Combustion and Flame (101) pp. 209-220.

J.7) C.F.M. Coimbra, J.L.T. Azevedo and M.G. Carvalho (1994). "3-D Numerical Model for Predicting NOx Emissions from an Industrial Pulverized Coal Combustor" - Fuel (73) pp. 1128-1134.

J.8) J.L.T. Azevedo, M.G. Carvalho, P.J. Coelho, C.F.M. Coimbra and M. Nogueira (1993). "Modeling of Combustion and NOx Emissions in Industrial Equipment" - Pure & Applied Chemistry (65), pp. 345-354.

Conference Papers

C.1) C.F.M. Coimbra, D.K. Edwards and R.H. Rangel (1997). "Particle Temperature Response to Transient Thermal Perturbations in a Dilute Suspension Including Radiation Heat Transfer" - Symposium on Dispersed Flows in Combustion, Incineration and Propulsion Systems - Dallas - USA.

C.2) C.F.M. Coimbra, P.J. Coelho, M.Q. McQuay and M.G. Carvalho (1995). " The Comparison of Two Comprehensive Combustion Codes to Simulate Large-Scale, Oil-Fired Boilers" - 3rd International Conference on Combustion Technologies for a Clean Environment - Lisbon - Portugal.

C.3) D.L. Black, C.F.M. Coimbra, and M.Q. McQuay (1995). "Experimental and Numerical Study on Combustion of Oil Sprays in Lab- and Industrial-Scale Reactors"- 9th ACERC Annual Technical Conference in Clean and Efficient Combustion of Fossil Fuels and Waste Materials - Provo - USA.

C.4) C.F.M. Coimbra and M.Q. McQuay (1995). "Numerical Characterization of Oil-Fired Industrial Boilers" - 4th ASME/JSME Thermal Engineering Joint Conference - Maui - USA.

C.5) C.F.M. Coimbra and M. Queiroz (1994). "CFD Modeling of Multiphase Oil Droplet Combustion in a 20 MW Industrial Boiler" - 5th Brazilian Thermal Science Meeting (V Encit) - São Paulo - Brazil.

C.6) C.F.M. Coimbra, M. Queiroz and A.M. Eaton (1994). "Eulerian-Lagrangian Computation of Oil Droplet Combustion in Industrial-Scale Boilers" - 8th ACERC Annual Technical Conference in Clean and Efficient Combustion of Fossil Fuels and Waste Materials - Provo - USA.

C.7) C.F.M Coimbra, J.L.T. Azevedo and M.G. Carvalho (1993). "3-D Numerical Model for Predicting NOx Emissions from a Pulverized Industrial Coal Combustor" - Coal Energy and the Environment - Orlando - USA.

C.8) J.L.T. Azevedo, J. Branco, M.G. Carvalho and C.F.M. Coimbra (1992). "NOx Emissions from a Front Wall-Fired, Pulverized Coal Boiler" - Energy Efficiency in Process Technology - Athens - Greece.

C.9) C.F.M. Coimbra and M.G. Carvalho (1992). "On the Development of a Numerical Code for Predicting 3-D Pulverized Coal Flames" - 4th Brazilian Thermal Science Meeting (IV Encit) - Rio de Janeiro, Brazil.

C.10) J.L.T. Azevedo, M.G. Carvalho, X.-Q. Chen, C.F.M. Coimbra and J.C.F. Pereira (1992). "Application of Stochastic Lagrangian Models to Dispersed Flows" - 29th European Two-Phase Flow Group Meeting - Stockholm - Sweden.

C.11) J.L.T. Azevedo, M.G. Carvalho, P.J. Coelho, C.F.M. Coimbra and M. Nogueira (1992). "Modeling of Combustion and NOx Emissions in Industrial Equipment (Invited Lecture)" - 4th International Seminar on Flame Structure - Novosibirsk - Russia.

C.12) A.F.P. Fortes, C.F.M. Coimbra and L.P.M. Costa (1990). "A Fluidized Solar Collector" -3rd Brazilian Thermal Science Meeting (III Encit) - Itapema - Brazil.

Teaching Experience

Summer/97 Thermodynamics (Undergraduate, TA)

Mechanical and Aerospace Engineering, UC Irvine

Spring/97 Thermodynamics (Undergraduate, TA)

Mechanical and Aerospace Engineering, UC Irvine

Winter/97 Engineering Analysis 2 (Graduate, Guest Lecturer, 1 lecture)

Topic of Lecture: Fractional Calculus in Diffusion Problems

Mechanical and Aerospace Engineering, UC Irvine

Spring/96 Thermodynamics (Undergraduate, TA)

Mechanical and Aerospace Engineering, UC Irvine

Winter/96 Viscous / Incompressible Inviscid Fluid Mechanics (Undergraduate, TA)

Mechanical and Aerospace Engineering, UC Irvine

Fall/95 Introduction to Fluid Mechanics (Undergraduate, TA)

Mechanical and Aerospace Engineering, UC Irvine

2nd Sem/89 Fluid Mechanics 2 (Undergraduate, TA)