Masters Project LJ FINAL_2

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    Numerical Study using FLUENT of the Separation and Reattachment

    Points for Backwards-Facing Step Flow

    byLuke Jongebloed

    An Engineering Project Submitted to the Graduate

    Faculty of Rensselaer Polytechnic Institute

    in Partial Fulfillment of the

    Requirements for the degree of

    Master of Engineering

    Major Subject: Mechanical Engineering

    Approved:

    _________________________________________

    Ernesto Gutierrez-Miravete, Project Adviser

    Rensselaer Polytechnic Institute

    Hartford, Connecticut

    December, 2008

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    ii

    CONTENTS

    Numerical Study using FLUENT of the Separation and Reattachment Points for

    Backwards-Facing Step Flow ....................................................................................... i

    LIST OF SYMBOLS ........................................................................................................ iii

    LIST OF TABLES............................................................................................................. v

    LIST OF FIGURES .......................................................................................................... vi

    ACKNOWLEDGMENT..................................................................................................vii

    ABSTRACT....................................................................................................................viii

    1. Background .................................................................................................................. 1

    1.1 Introduction ........................................................................................................ 1

    1.2 Previous research................................................................................................ 3

    2. Methodology ................................................................................................................ 5

    2.1 Theory ................................................................................................................ 5

    2.2 Approach using FLUENT .................................................................................. 8

    3. Discussion .................................................................................................................. 10

    3.1 Laminar ............................................................................................................ 12

    3.2 Turbulent .......................................................................................................... 15

    4. Conclusion ................................................................................................................. 18

    5. References.................................................................................................................. 19

    6. Appendix.................................................................................................................... 21

    6.1 FLUENT Input ................................................................................................. 21

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    iii

    LIST OF SYMBOLS

    A0 Model constant

    As Model variable

    C2 Model constantC Model variable

    D Hydraulic diameter of backwards step

    ER Expansion ratio

    Gk Turbulent generation term

    h Height of inlet channel

    H Height of outlet

    I Identity matrix

    i Sub index

    j Sub index

    k Turbulent kinetic energy

    k Sub index

    Re Reynolds number

    S Step height

    S Magnitude of mean strain

    Sij Mean strain tensor

    t Time

    u Fluid velocity

    U Characteristic velocity scale

    W Model variable

    x Direction vector

    x1 Reattachment point for 1st bottom recirculation zone

    x2 Separation point for 2st bottom recirculation zonex3 Reattachment point for 2nd bottom recirculation zone

    x4 Reattachment point for 1st top recirculation zone

    x5 Separation point for 2st top recirculation zone

    Xe Inlet channel length

    Xo Outlet channel length

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    iv

    Dissipation rate

    Eddy viscosity

    k Model constant

    Epsilon model constant

    Model variable

    Stress tensor

    Kinematic viscosity

    Dynamic viscosity

    Density

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    v

    LIST OF TABLES

    Table 1 Backward-facing step dimensions (all in meters).............................................. 2

    Table 2 Miscellaneous reference values used in this study. ........................................... 3

    Table 3 Number of nodes for grid reference number used to indicate amount of meshrefinement in discussion section. ............................................................................... 9

    Table 4 Effect of mesh refinement for Re=800. ........................................................... 14

    Table 5 Comparison of reattachment and separation points for Re=800 and ER=1.942

    for various numerical studies. .................................................................................. 14

    Table 6 Separation points obtained for turbulent flow. ................................................ 15

    Table 7 Comparison of methods used to obtain solution for Re=7470. ....................... 17

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    vi

    LIST OF FIGURES

    Figure 1 Schematic of backward-facing step turbulent-flow.......................................... 1

    Figure 2 Three recirculation zones for laminar flow. ..................................................... 2

    Figure 3 Schematic of backward-facing step geometry (not to scale). ........................... 2Figure 4 Schematic showing region of grid refinement, 200m downstream from step

    (to scale). .................................................................................................................... 9

    Figure 5 Comparison of separation and reattachment points for present analysis with

    experimental data collected by Armaly et al............................................................ 10

    Figure 6 Comparison of separation and reattachment points between present analysis

    and experimental data collected by Armaly et al. for Re

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    vii

    ACKNOWLEDGMENT

    I would like to thank my cat for sitting with me and providing support while I completed

    my school work.

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    viii

    ABSTRACT

    A numerical investigation is conducted on the affect of Reynolds number on the

    separation and attachment points for backward-facing step flow. Both turbulent and

    laminar flow is considered for two-dimensional viscous flow, neglecting compressibility,heat generation, and external body forces. A steady-state coupled pressure and velocity

    algorithm is used for laminar flow and a steady-state segregated pressure-velocity

    algorithm is used with a realizable k-wall-enhanced turbulence model. The expansion

    ratio of inlet height to outlet height is a 1.942. The results are compared to published

    experimental and numerical data. The present study agrees with published data for low

    Reynolds numbers (Re15000). Results exhibit

    behavior of published data, but are slightly lower in magnitude for 400

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    1

    1. Background

    1.1 Introduction

    A numerical analysis is performed using FLUENT to investigate backward-facing step

    flow for Reynolds numbers in the laminar and turbulent regions. Separation and

    reattachment lengths are determined for each Reynolds number and the results are

    compared to experimental data and numerical analyses found in literature.

    Flow over a backward-facing step produces recirculation zones where the fluid

    separates and forms vortices. For turbulent flow, the fluid separates at the step and

    reattaches downstream, as show below in Figure 1. Only a single recirculation zone

    develops for turbulent flow and the reattachment point is believed to be independent of

    the Reynolds number and depend only on the ratio of inlet height to outlet height.

    Figure 1 Schematic of backward-facing step turbulent-flow.1

    For laminar flow, various recirculation zones occur downstream from the step, as

    shown below in Figure 2. Separation occurs when adverse pressure gradients act on the

    fluid. As the Reynolds number increases from zero, the first region of separation occursat the step to x1 on the bottom wall. Next, the second region of separation occurs

    between x4 and x5 on the top wall. As the Reynolds number increases into the transition

    zone, a third separation region occurs between x2 and x3 on the bottom wall.

    1Figure from R.L. Simpson.

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    2

    Theoretically, recirculation zones will continue to develop downstream as the Reynolds

    number increases and the flow remains laminar; however, this has not been observed

    experimentally and the flow will eventually become turbulent.

    Figure 2 Three recirculation zones for laminar flow.

    The geometry for the backward-facing step used in this analysis is similar to that used by

    Armaly et al. Figure 3 and Table 1 provide the dimensions of the geometry.

    Figure 3 Schematic of backward-facing step geometry (not