Numerical Solutions to the Partially Parabolized Navier-Stokes Equations for Developing Flow in a Channel

Chilukuri, R.; Pletcher, Richard H.

doi:10.1080/01495728008961753

Cited by 34 publications

(4 citation statements)

References 17 publications

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“…We use the fully parabolic flow approximation to the full three-dimensional momentum equations in our analysis. This approximation has often been used for flows in ducts (26)(27)(28)(29). It is valid for flows dominated by convection in one direction, becoming more accurate as the Reynolds number increases.…”

Section: Mathematical Modelmentioning

confidence: 99%

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Three‐Dimensional Flow Effects in Silicon CVD in Horizontal Reactors

Moffat

Jensen

1988

J. Electrochem. Soc.

156

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Numerical modeling of Si homoepitaxial deposition from SiH4 in the horizontal reactor has been undertaken employing the steady‐state, fully parabolic flow approximation for the heat, momentum, and mass‐transfer equations. Reactants are assumed to be dilute in their carrier gas. The resulting set of partial differential equations are discretized using finite elements and solved using the method of lines. The effect of a third dimension, the side temperature boundary conditions, and natural convection are explored. Given recent kinetics data on the silane decomposition and silylene insertion reactions, it is shown that a quasi‐thermodynamic equilibrium exists in the heated region above the surface, at least for hydrogen gas ambients. The combination of a fast silylene surface reaction and a slow silane surface reaction implies that the effective surface reaction rate is governed by the homogeneous thermodynamic equilibrium in the gas phase and diffusion through a thin mass‐transfer boundary layer near the surface. Examples of how tilting the susceptor contributes to growth uniformity are presented, and the effectiveness of similarity solution models at predicting this enhanced axial uniformity is tested.

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Section: Mathematical Modelmentioning

confidence: 99%

“…Chilukuri and Pletcher have examined the difference between flow profiles determined with the parabolic approximation and with the full treatment for the case of channel flow (28). Even for the relatively low Reynolds number of 10, the parabolic approximation is justified.…”

Section: Mathematical Modelmentioning

confidence: 99%

Three‐Dimensional Flow Effects in Silicon CVD in Horizontal Reactors

Moffat

Jensen

1988

J. Electrochem. Soc.

156

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“…He was one of the first to demonstrate the use of boundary-layer computational methods to compute flows in separated regions [1]. He has also been a leader in the application of viscous-inviscid interaction methods to flows with heat transfer [2], the application of preconditioning methods to compressible flows at low Mach numbers [3], the application of LES methods to turbulent flows with significant property variations [4][5][6][7], and the prediction of turbulent flows using the partially parabolized Navier-Stokes equations [8][9][10][11]. Professor Pletcher was also instrumental in employing a wide array of turbulence models to predict turbulent flows when this approach was at its infancy.…”

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confidence: 99%

In Memoriam: Professor Richard H. Pletcher (1935–2015), Who Advanced Computational Fluid Mechanics and Heat Transfer

Battaglia

Manglik

Sherif

2016

Journal of Fluids Engineering

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It is with great sadness that we share with you the loss of a dear colleague and friend, Dr. Richard H. Pletcher. He was one of the pioneers and an internationally renowned expert in computational fluid mechanics and heat transfer and was not only inspirational in directing the careers and lives of so many of us but also a mentor, who was extremely supportive and kind to all. Richard, or Dick, as we all personally and collegially addressed him, passed away on Saturday, Sept. 12, 2015, having been diagnosed with terminal cancer. His 80 years of life is marked with multifaceted contributions to engineering, as his work helped advance computational techniques to solve challenging problems in aerospace and mechanical engineering. Dick is remembered for his large body of work in heat transfer, fluid mechanics, buoyant jets and plumes, turbulence modeling, separated flows, viscous-inviscid interactions, computational fluid mechanics and heat transfer, and large-eddy simulation (LES) of complex turbulent flows. Richard was born in Elkhart, IN on May 21, 1935 to Raymond Harold Pletcher and Annabelle Mary Pletcher. He attended Purdue University and graduated with a Bachelor of Science in Mechanical Engineering in 1957. He married Carol Robbins on June 9, 1957 in Elkhart, and the couple soon thereafter moved to California so that he could report for active duty in the U.S. Navy. Dick proudly served as Ensign and Lieutenant (junior grade) for 3 years with amphibious forces in the Pacific. He served as an engineering officer of a landing craft utility division and assistant gunnery officer on a landing ship dock. After military service, Dick attended graduate school at the Cornell University where he received M.S. (1962) and Ph.D. (1967) degrees. During his doctoral studies, he was employed as an instructor by Cornell University for 3 years. He also worked as a senior research engineer in propulsion at the United Aircraft Research Laboratories in Hartford, CT (1965-1967), and subsequent to doctoral graduation, he joined the faculty in the Department of Mechanical Engineering at the Iowa State University (ISU), AMES, IA, in 1967. During Professor Pletcher's tenure at ISU, he left a legacy of affable collegiality, excellence in teaching, and path-breaking scholarship in computational modeling of complex fluid dynamics and heat transfer systems. His expertise centered on computational fluid dynamics (CFD), whereby he developed and taught courses for over 40 years in this new and emerging field. With Professor Dale Anderson and Professor John C. Tannehill in the Department of Aerospace Engineering at the ISU, a two-course sequence in computational fluid mechanics and heat transfer was developed in 1972. These courses were among the first in the U.S. in that specialty, which was born from the computer age. Papers based on numerical simulations carried out by Professor Pletcher appeared as early as 1965, a time when computer use for simulation in engineering was in an infant state. The early teaching activities in CFD were accompa...

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“…Chilukuri and Pletcher [25], Chilukuri [6], and Madavan [9] have reported solutions to the partially-parabolized Navier-Stokes equations for laminar incompressible flows. Chilukuri reported solutions of flow in the entry region of a channe l for Reynolds numbers in the range of 10-7500.…”

Section: Variations Of the Pratap And Spalding Approach We R E U Sed Bymentioning

confidence: 99%

A calculation procedure for the partially-parabolized Navier-Stokes equations in transformed coordinates for two-dimensional flow in channels of variable cross-section

Jorgenson

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Dimensionless pressure gradient t er ms derived from momentum equation s in~ and n directions, respective ly Pressure gradi ent t erms derive d from momentum equations in ~ and n directions, respective l y , lbm/ft sec Channel half height, ft Final channel half he i ght , ft Gridpoint index i n ~ direction Gridpoint index in n direction Total length of the channe l, ft Mass flow rate Number of gridpoint s in the n direction St atic pr essure, lbm/f t sec Dimensionless pr essure, p/p u;ef Reynolds number based on an equivalent height, p U:o / µ eq Reynolds number based on ini tial half height of channel, p Uh 0 / µ RMC RMl, RM2 s pj s cp .

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Numerical Solutions to the Partially Parabolized Navier-Stokes Equations for Developing Flow in a Channel

Cited by 34 publications

References 17 publications

Three‐Dimensional Flow Effects in Silicon CVD in Horizontal Reactors

Three‐Dimensional Flow Effects in Silicon CVD in Horizontal Reactors

In Memoriam: Professor Richard H. Pletcher (1935–2015), Who Advanced Computational Fluid Mechanics and Heat Transfer

A calculation procedure for the partially-parabolized Navier-Stokes equations in transformed coordinates for two-dimensional flow in channels of variable cross-section

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