Ramin K. Rahmani

Numerical Simulation of Ablation for Reentry Vehicles

A computer program is developed for numerical simulation of ablation problems, taking into account in-depth pyrolysis; surface recession; nonequilibrium chemistry in the flow of pyrolysis gases through a variable porosity char; and thermal non-equilibrium between the char and the pyrolysis gases. The program provides a general and easy to use interface for coupling with a reacting flow solver and a radiation solver. The program is verified using available analytical solutions for heat conduction in non-receding and receding solids; the program will then be validated using available experimental data.

Numerical study of the heat transfer rate in a helical static mixer

In chemical processing industries, heating, cooling, and other thermal processing of viscous fluids are an integral part of the unit operations. Static mixers are often used in continuous mixing, heat transfer, and chemical reactions applications. In spite of widespread usage, the flow physics of static mixers is not fully understood. For a given application, besides experimentation, the modern approach to resolve this is to use powerful computational fluid dynamics tools to study static mixer performance. This paper extends a previous study by the authors on an industrial helical static mixer and investigates heat transfer and mixing mechanisms within a helical static mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer under both laminar and turbulent flow conditions. The turbulent flow cases were solved using k-ω model. The effects of different flow conditions on the performance of the mixer are studied. Also, the effects of different thermal boundary conditions on the heat transfer rate in static mixer are studied. Heat transfer rates for a flow in a pipe containing no mixer are compared to that with a helical static mixer.

Heat Flux Estimation in a Nonlinear Inverse Heat Conduction Problem With Moving Boundary

The estimation of heat flux in the nonlinear heat conduction problem becomes more challenging when the material at the boundary loses its mass due to phase change, chemical erosion, oxidation, or mechanical removal. In this paper, a new gradient-type method with an adjoint problem is employed to predict the unknown time-varying heat flux at the receding surface in the nonlinear heat conduction problem. Particular features of this novel approach are discussed and examined. Results obtained by the new method for several test cases are benchmarked and analyzed using numerical experiments with simulated exact and noisy measurements. Exceedingly reliable estimation on the heat flux can be obtained from the knowledge of the transient temperature recordings, even in the case with measurement errors. In order to evaluate the performance characteristics of the present inverse scheme, simulations are conducted to analyze the effects of this technique with regard to the conjugate gradient method with an adjoint problem and variable metric method with an adjoint problem. The results obtained show that the present inverse scheme distinguishably accelerates the convergence rate, which approve the well capability of the method for this type of heat conduction problems.

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase-change problems. Several isothermal phase-change cases are studied and comparisons are made to existing analytical solutions

Three-Dimensional Numerical Simulation and Performance Study of an Industrial Helical Static Mixer

In many branches of processing industries, viscous liquids need to be homogenized in continuous operations. Consequently, fluid mixing plays a critical role in the success or failure of these processes. Static mixers have been utilized over a wide range of applications such as continuous mixing, blending, heat and mass transfer processes, chemical reactions, etc. This paper describes how static mixing processes of single-phase viscous liquids can be simulated numerically, presents the flow pattern through a helical static mixer, and provides useful information that can be extracted from the simulation results. The three-dimensional finite volume computational fluid dynamics code used here solves the Navier-Stokes equations for both laminar and turbulent flow cases. The turbulent flow cases were solved using k-ω model and Reynolds stress model (RSM). The flow properties are calculated and the static mixer performance for different Reynolds numbers (from creeping flows to turbulent flows) is studied. A new parameter is introduced to measure the degree of mixing quantitatively. Furthermore, the results obtained by k-ω and RSM turbulence models and various numerical details of each model are compared. The calculated pressure drop is in good agreement with existing experimental data.

Numerical Simulation and Mixing Study of Pseudoplastic Fluids in an Industrial Helical Static Mixer

Static mixers are increasingly being used to perform a variety of mixing tasks in industries, ranging from simple blending to complex multiphase reaction systems. Use of static mixers to process non-Newtonian fluids is quite common. Data on the pressure drop of non-Newtonian fluids in static mixers and the degree of mixing of materials through the mixer are very useful in the design and engineering application of these tools. This paper extends a previous study by the authors on an industrial helical static mixer and illustrates how static mixing processes of single-phase viscous liquids can be simulated numerically. A further aim is to provide an improved understanding of the flow pattern of pseudoplastic liquids through the mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer. The flow velocities, pressure drops, etc., are calculated for various flow rates, using the Carreau and the power law models for non-Newtonian fluids. The numerical predictions by these two models are compared to existing experimental data. Also, a comparison of the mixer performance for both Newtonian and pseudoplastic fluids is presented. The effects of the Reynolds number of the flow and also properties of pseudoplastic fluids on the static mixer performance have been studied

Solution of Radiative Boundary Design Problems Using a Combined Optimization Technique

In this work, a novel combined strategy has been developed and verified for radiative boundary design problems. It is highly efficient and simple to implement and appears promising for obtaining appropriate results in practical applications. In the proposed approach, the determination of the unknown profile of heat flux through active constraints includes utilizing a new search optimization technique that is merged with the maximum entropy method (MEM). It is shown that use of the merged MEM algorithm minimizes both the occurrence of negative values for physically non-negative components, and the oscillatory profile of heat flux. A generalized computational grid based on finite-volume scheme is devised to solve the radiative transfer equation and sensitivity equations. Numerical simulations are conducted to evaluate the performance and accuracy of the present approach with regard to the classical methods involved in its derivation.

A Novel Methodology for Combined Parameter and Function Estimation Problems

This article presents a novel methodology, which is highly efficient and simple to implement, for simultaneous retrieval of a complete set of thermal coefficients in combined parameter and function estimation problems. Moreover, the effect of correlated unknown variables on convergence performance is examined. The present methodology is a combination of two different classical methods: The conjugate gradient method with adjoint problem (CGMAP) and Box-Kanemasu method (BKM). The methodology uses the benefit of CGMAP in handling function estimation problems and BKM for parameter estimation problems. One of the unique features about the present method is that the correlation among the separate unknowns does not disrupt the convergence of the problem. Numerical experiments using measurement errors are performed to verify the efficiency of the proposed method in solving the combined parameter and function estimation problems. The results obtained by the present approach show that the combined procedure can efficiently and reliably estimate the values of the unknown thermal coefficients.

Stefan Number-Insensitive Numerical Simulation of the Enthalpy Method for Stefan Problems Using the Space-Time CE/SE Method

An improvement is introduced to the conservation element and solution element (CE/SE) phase-change scheme presented previously. The improvement addresses a well-known weakness in numerical simulations of the enthalpy method when the Stefan number (the ratio of sensible to latent heat) is small (less than 0.1). Behavior of the improved scheme, at the limit of small Stefan numbers, is studied and compared with that of the original scheme. It is shown that high dissipative errors, associated with small Stefan numbers, do not occur using the new scheme.

A Numerical Study of the Global Performance of Two Static Mixers

The use of in-line static mixers has been widely advocated for an important variety of applications, such as continuous mixing, heat and mass transfer processes, and chemical reactions. This paper extends previous studies by the authors on industrial static mixers and illustrates how static mixing processes of single-phase viscous liquids can be numerically simulated. Mixing of Newtonian, shear-thinning, and shear-thickening fluids through static mixer, as well as thermal enhancement by static mixer is studied. Using different measuring tools, the global performance and costs of SMX (Sulzer mixer X) and helical static mixers are studied. It is shown that the SMX mixer manifests a higher performance; however, the required energy to maintain the flow across a SMX mixer is significantly higher.