Masters Project LJ FINAL_2

7/27/2019 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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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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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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Dissipation rate

Eddy viscosity

k Model constant

Epsilon model constant

Model variable

Stress tensor

Kinematic viscosity

Dynamic viscosity

Density


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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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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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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. 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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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 to scale).

Significant length is provided for the inlet channel to ensure that the flow is fully

developed and does not contain any additional effects created by the flow source. The

significant length of the outlet channel ensures that the outlet condition does not affect

the flow near the step. The expansion ration, ER, is ratio of the outlet height over the

inlet height. For this case, ER = 1.942.

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

Height of inlet channel h 5.2

Height of outlet H 10.1Step height S 4.9

Inlet channel length Xe 200

Outlet channel length Xo 500

The Reynolds number is defined as,

Du =Re , where u is the inlet velocity, is the

kinematic viscosity, and D is the hydraulic diameter. The Reynolds number has been


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expressed differently throughout literature; D can be based on the inlet height, the outlet

height, or the step height. In agreement with Armaly et al., this study will use D=2h. It is

important to know how the Reynolds number was calculated when comparing data. Also

of importance is the method used to calculate the inlet velocity. The average velocity can

be used or one can use functions of the measured velocity profile, e.g., Armaly et al.

used 2/3 maximum measured inlet velocity. Another factor that may affect the

comparison of results is the turbulent intensity of the inlet velocity. Although inlet

velocity parameters have significant effect on the reattachment points (Badran and

Bruun), a relatively long inlet channel length should dissipate the discrepancies. Table 1

lists various constants used in this study.

Table 2 Miscellaneous reference values used in this study.

Density 1.225 3mkg

Dynamic viscosity 1.78945

10 smkg

Expansion Ratio ER 1.942 -

1.2 Previous research

The in-depth experimental data analysis performed by Armaly et al has provided the

majority of data used for comparison in the present study. Others, including Driver and

D. M., Seegmiller; D.E. Abbott and S.J. Kline; Denham. M. K. & Patrick; Etheridge,

D.W. & Kemp, have performed similar experiments and yielded similar results. These

experiments have provided useful data to compare with and validate numerical schemes.

In the following we can summarize the relationship between the location of the

separation point and Reynolds number. The two dimensional approximation is only valid

for Re 6600, for 400


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there is only one reattachment point for turbulent flow. For all flows, as ER increases the

distance that separation occurs increases.

The single reattachment point for turbulent flow has been observed to be

independent of the Reynolds number and depends only on geometry. Both Armaly et al.

and Abbot and Kline have determined experimentally that for turbulent flow (Re>6600)

the reattachment point 81 Sx at ER=1.94. The reattachment length decrease for

decreasing step heights; e.g., De Brederode and Bradshaw found the reattachment point

61 Sx at ER=1.2 and Moss et al. found the reattachment point 5.51 Sx at ER=1.1.

Backward-facing step flow research continues to be pursued as analysis methods

evolve. Lima et al. investigated two-dimensional laminar flow with Reynolds number

varying between 100 and 2500. Convergence could not be obtained using a steady state

segregated finite volume method (FVM); instead, an unsteady flow was analyzed for

very large time. Good agreement with Armaly et al. was found for x1 with Re


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2. Methodology

Flow over a backward-facing step is studied based on the numerical methods discussed

in Section 2.1 and the approach in Section 2.2. Compressibility and energy terms are

neglected. The following boundary conditions are used: non-slip walls, zero gaugepressure outlet, and constant normal inlet velocity that does not vary along the height of

inlet. The Reynolds number is varied from 50 to 1250 and the separation and

reattachment points are determined from minimum values of the coefficient of friction.

Reattachment points are also determined for various Reynolds numbers in the turbulent

region (Re>6600).

2.1 Theory

The governing equations for computational fluid dynamics (CFD) are based on

conservation of mass, momentum, and energy. FLUENT uses a finite volume method

(FVM) to solve the governing equations. The FVM involves descretization and

integration of the governing equation over the control volume. The following is a

summary of the theory involved in the FLUENT analysis and is based on the FLUENT

Users Manual, Bardina et al., and Anderson.

The basic equations for steady-state laminar flow are conservation of mass and

momentum. When heat transfer or compressibility is involved the energy equation is

also required. The governing equations are,

Continuity Equation:

Momentum equation:

where, , the stress tensor is,

Turbulent flow can be modeled using mean and fluctuating values for components,

such as velocity, iii uuu += . Substituting the mean and fluctuating value equations into


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the Navier-Stokes equations yields the Reynolds-averaged Navier-Stokes (RANS)

equations:

The k- model is semi-empirical two-equation turbulence model that is based on an

exact solution for the turbulent kinetic energy (k) and a model of the dissipation rate ().

To model the Reynolds stress, , in the RANS equations, the - model uses the

Bousinesq approximation to relate the Reynolds stresses to the mean velocity gradients.

Along with the Bousinesq approximation above, the following definition of the eddy

viscosity is used,

The realizable portion of the k- model is based on the following relationship, which

can be obtained by determining the point that the average normal stress becomes

negative. The realizable k- model coefficient,

C , is determined by equilibrium

analysis at high Reynolds numbers.

The realizable k- model is defined by the following two equations,

and

Gkrepresents the generation of turbulence kinetic energy due to the mean velocity

gradients and relies on the Boussinesq approximation.


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where the modulus of the mean rate-of-strain tensor,

and

+

=

i

j

j

iij

u

u

u

uS

2

1

The variable in the eddy viscosity is,

where,

and the model constants are,

where,

The following values are used for the remaining constants,


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2.2 Approach using FLUENT

The continuity and momentum equations, along with the realizable k- model with wall

enhancements and pressure gradients effects for turbulent flows, are solved using the

FVM in FLUENT. A pressure based solver is used since the flow is incompressible and

separation is caused by adverse pressure gradients. As demonstrated by Kim et al. the

realizable k- model with wall treatment performs well for boundary layers subject to

separation and is used.

A coupled pressure and velocity algorithm is used for laminar flows, which

solves the continuity and momentum equations in a simultaneous fashion and removes

the approximations associated with segregated algorithms where the momentum and

continuity equations are solved separately. The coupled algorithm is employed because

of convergence issues with segregated solvers on backward-facing step flows. The

coupled algorithm does not offer solution accuracy improvement over segregated

solvers; rather it provides improvement in stability and ability to converge. The semi-

implicit method for pressure-linked equations SIMPLE algorithm is a segregated

algorithm and is used for turbulent flow analysis in this study. The SIMPLE algorithm

solves the momentum equation first, then solves for pressure, and later corrects the

descretized solutions. The SIMPLE algorithm can offer increased convergence time due

to the smaller memory requirement over the coupled algorithm.

A convergence criterion of 5101 is used for continuity, x-velocity and y-velocity.

A convergence criterion of 3101 is used for k and . All solutions converged with

second order pressure and third order MUSCL (Monotone Upstream-centered Schemes

for Conservation Laws) momentum interpolation schemes for laminar flow. All

solutions converged with second order pressure, momentum, turbulent intensity, and

turbulent dissipation interpolation schemes for turbulent flow. Third order MUSCL

schemes did not provide significant accuracy for turbulent flow.

Adequate grid independence is satisfied with a quadrilateral mesh of 59251

nodes. The entire surface is meshed with 30151 nodes then adapted to 59251 nodes with

refinement only in the region of recirculation from the step (x=200) to 200 m

downstream from the step. Further adaptation to 174645 nodes in this region does not


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provide significant increase in the accuracy of the results. Shown below, Table 3 and

Figure 4 summarize the amount of grid adaptation used and the area of refinement.

Table 3 Number of nodes for grid reference number used to indicate amount of

mesh refinement in discussion section.

grid

number

number of

nodes

region

refinement

0 30151 no

1 59251 yes

2 174645 yes

Figure 4 Schematic showing region of grid refinement, 200m downstream from

step (to scale).


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3. Discussion

Laminar flow exists for Re


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not compare well with experimental data. The top reattachment point, x5, compares well

with data for Re1250). Oscillating residuals

were experienced and can be attributed to the use of a steady-state method. Numerical

unsteady analyses have obtained convergence for flows with three or more recirculation

zones, e.g., Lima et al. In this region, however, the flow is 3-D and numerical and

measured values do not agree.


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3.1 Laminar

The plot in Figure 6 below shows a closer view for Re


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Table 4 below. The first adaptation of the initial mesh 59251 nodes provided reasonable

accurate results and is used for all laminar Reynolds number. Adaptation was only

performed in the region between the step and 200 meters downstream (see Figure 4).


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Table 4 Effect of mesh refinement for Re=800.

gridnumber

4

x1/S x4/S x5/S

0 10.83 8.44 19.26

1 11.67 9.24 19.92

2 11.88 9.42 20.02

Table 5 below summarizes the values for separation and reattachment points at

Re=800 determined by various authors. The results of the present study are lower than

the average of values obtained by the various authors, but are still within the range of

data. The largest difference between present results and average literature value is the

upper reattachment point, x5/S=19.92; average is 20.62. This present result of

x5/S=19.92 is closer to the experimental value (Armly et al.) 19.33 than the average20.62.

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

ER=1.942 for various numerical studies.

x1/S x4/S x5/S (x5-x4)/S

Presentt study 11.67 9.24 19.92 10.68

Lima 11.97 9.51 20.40 10.89

Gartling 12.20 9.70 20.96 11.26

Lee and Mateescu 12.00 9.60 20.60 11.00

Barton 11.51 9.14 20.66 11.52Kim and Moin 11.90 - - -

Guj and Stella 12.05 9.70 20.20 10.50

Gresho et al. 12.20 9.72 20.98 11.26

Keskar and Lyn 12.19 9.71 20.96 11.25

Grigoriev and Dargush 12.18 9.70 20.94 11.24

Rogers and Kwak 11.48 - - -

Erturk 11.83 9.48 20.55 11.07

Average 11.93 9.55 20.62 11.07

Armaly et al.* 14.00 11.11 19.33 8.22

ER=2.0, * Experimental

A plot of the stream lines over the step for Re=800 is shown in Figure 7. The

fluid velocity at the step dissipates as slower recirculation region absorb some of the

momentum.

4See Table 2.


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Figure 7 Streamlines for Re=800; colored by velocity magnitude.

3.2 Turbulent

For turbulent flow (Re>6600) Armaly et al. and Abbot and Kline have determined

experimentally that the reattachment point, 81 Sx at ER=1.94. Table 6 below

summarizes the range of values obtained in the present study for the reattachment point

at various turbulent Reynolds numbers. The average value, x1/S=7.21, for the separation

point is lower than x1/S=8, the accepted value. The higher Reynolds numbers studied are

closer to the accepted value. For Re= 17799, x1/S=8.0, which is in agreement with the

accepted value.

Table 6 Separation points obtained for turbulent flow.

Re x1/S

7000 6.92

7476 6.61

7830 6.54

8000 6.80

11400 7.0117799 8.00

24480 8.60

average 7.21

A plot of the streamlines over the step is displayed in Figure 8 below. A second eddy

near the step corner is observed. The velocity of the recirculation zone is on the order of

magnitude lower than the velocity at the step.


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Figure 8 Plot of streamlines for Re=8000; colored by velocity magnitude.

Solving for turbulent flow required multiple levels of refinement to obtain an accurate

solution. Figure 9 shows a plot of the scaled residuals for the solution at Re=7470. Table7 provides the type of methods used to achieve each level of convergence displayed in

Figure 9.


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Figure 9 Scaled residuals for Re=7470.

RKE with mesh refinement provides significant accuracy over SKE with out wall

treatment. The third order MUSCL RKE with number 2 mesh refinement does not offer

significant increase in accuracy over second order RKE with number 1 mesh refinement.

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

Method Pressure

Momentum,Turbulent Kinetic

Energy, and turbulentdissipation rate

wallenhancementsand pressure

gradient effectsMeshrefinement

5 x1/S

SKE 1st order 1st order no 0 5.37

RKE 1st order 1st order yes 0 5.74

RKE 1st order 1st order yes 1 6.26

RKE 2nd order 2nd order yes 1 6.54

RKE 2nd order 3rd order MUSCL yes 1 6.59

RKE 2nd order 3rd order MUSCL yes 2 6.61

5See Table 2.


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4. Conclusion

The values for the separation and reattachment points obtained in this study compare

fairly well with published numerical data. The present results begin to differ from

experimental data at Reynolds numbers (Re>400) where three-dimensional effectsbecome important. The normalized values (x1/S~6.5) for the turbulent reattachment

points are less than accepted value (x1/S~8) for low turbulent Reynolds numbers

(Re~8000); however for higher Reynolds numbers (Re>15000), good agreement is

found. A general trend in the laminar results of this analysis is slightly lower values for

separation and reattachment points than compared with other numerical studies. This

difference with present results for laminar flow can be attributed to the range of methods

and grids used to perform the numerical calculations. Unsteady methods iterated over a

large time span are typically used for the laminar case because of convergence issues;

however, this study used a steady-state method with a coupled pressure-velocity

algorithm.


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5. References

Anderson, J.D. Jr., Computational Fluid Dynamics: The Basics with Applications,

McGraw Hill, 1995

Armaly, B.F., Durst, F., Pereira, J.C.F., and Schonung, B., Experimental and theoreticalinvestigation of backward-facing step flow, J. Fluid. Mech. 127 (1983), pp. 473496.

Badran, O.O., Bruun, H.H., Effect of inlet conditions on flow over backward facing step,

Journal of Wind Engineering and Industrial Aerodynamics, v 74-76, Apr-Aug,

1998, p 495-509.

Barber, B.W., Fonty, A., A numerical study of laminar flow over a confined backward-

facing step using a novel viscous-splitting vortex algorithm, 4th GRACMCongress on Computational Mechanics, Patras, 27-29 June 2002.

Bardina, J. E., Huang, P. G., Coakley, T. J., Turbulence Modeling Validation, Testing,and Development, AIAA-1997-2121, NASA Technical Memorandum 110446

Barton I.E., The entrance effect of laminar flow over a backward-facing step geometry,

Int J Numer Methods Fluids 1997, 25:63344.

Biswas, G., Breuer, M., Durst F., Backward-facing step flows for various expansion

reatios at low and moderate Reynolds numbers, Journal of Fluid EngineeringVol. 126, May 2004, 363-374.

De Brederode, V., Bradshaw, P., Three-dimensional flow in nominally two-dimensional

separation bubbles. I. Flow behind a rearward-facing step, Aero Report 72-19,Imperial College of Science and Technology (1972), London, England.

Denham. M. K. & Patrick, M. A. Laminar flow over a downstream-facing step in a two-

dimensional flow channel. Trans. Inst. Chem. Engrs 52 (1974), 361.

Driver, D. M., Seegmiller, H. L. and Marvin, J., Time-dependent behavior of areattaching shear layer, AIAA J. 25 (1987), 914-919.

Erturk E., Numerical solutions of 2-D steady incompressible flow over backward-facingstep, Part I: High Reynolds number solution, Computers & Fluids 37 (2008),

633-655.

Etheridge, D.W. & Kemp, P.H., Measurements of turbulent flow downstream of a

backward-facing step, J. Fluid Mech. 86 (1978), 545.

Fluent Inc, Users Guide, 6.3.26 version, 2006

Gartling D.K., A test problem for outflow boundary conditions flow over a backward-

facing step, Int J Numer Methods Fluids 1990, 11:95367.


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Gresho P.M., Gartling D.K., Torczynski JR, Cliffe KA, Winters KH, Garratt TJ, et al. Is

the steady viscous incompressible two-dimensional flow over a backward-facing

step at Re = 800 stable?, Int J Numer Methods Fluids 1993, 17:50141.

Grigoriev M.M., Dargush G.F., A poly-region boundary element method forincompressible viscous fluid flows, Int J Numer Methods Eng 1999, 46:112758.

Guj G., Stella F., Numerical solutions of high-Re recirculating flows in vorticityvelocity form, Int J Numer Methods Fluids 1988, 8:40516.

Keskar J., Lyn D.A., Computations of a laminar backward-facing step flow at Re = 800

with a spectral domain decomposition method, Int J Numer Methods Fluids

1999, 29:41127.

Kim J., Moin P., Application of a fractional-step method to incompressible Navier

Stokes equations, J Comp Phys 1985, 59:30823.

Kim, Ghajar, Tang, Foutchm Comparison of near-wall treatment methods for highReynolds number backward-facing step flow, International Journal of

Computational Fluid Dynamics, Vol. 19, No. 7 (2005), 493-500.

Lee, T. and Mateescu, D., Experimental and numerical investigation of 2-D backward-

facing step flow, Journal of Fluids and Structures (1998) 12, 703-716.

Lima, R.C., Andrade, C.R., and Zaparoli, E.L., Numerical study of three recirculation

zones in the unilateral sudden expansion flow, International Communications inHeat and Mass Transfer, Volume 35, Issue 9, November 2008, Pages 1053-1060.

Moss, Bakers, Bradburly, 1979 Measurements of mean velocity and Reynolds stresses in

some regions of recirculation flows, In Turbulent Shear Flows 1 (ed. F. Durst, B.

C. Launder, F. W. Schmidt & J. H. Whitelaw). Springer.

Rogers S.E., Kwak D., An upwind differencing scheme for the incompressible Navier

Stokes equations, Appl Numer Math 1991, 8:4364.

Simpson, R.L., Aspects of turbulent boundary-layer separation, Prog. Aerospace Sci.Vol 32 (1996), 457-521.


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6. Appendix

6.1 FLUENT Input

FLUENT

Version: 2d, dp, pbns, lam (2d, double precision, pressure-based, laminar)

Release: 6.3.26

Title:

Models

------

Model Settings

-------------------------------------

Space 2D

Time Steady

Viscous Laminar

Heat Transfer Disabled

Solidification and Melting Disabled

Species Transport Disabled

Coupled Dispersed Phase Disabled

Pollutants Disabled

Pollutants Disabled

Soot Disabled

Boundary Conditions

-------------------

Zones

name id type

---------------------------------------

fluid 2 fluid

outlet 3 pressure-outlet

inlet 4 velocity-inlet

top_wall 5 wall

bottom_wall 6 wall

default-interior 8 interior


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Boundary Conditions

fluid

Condition Value

---------------------------------------------------------------

Material Name air

Specify source terms? no

Source Terms ()

Specify fixed values? no

Fixed Values ()

Motion Type 0

X-Velocity Of Zone (m/s) 0Y-Velocity Of Zone (m/s) 0

Rotation speed (rad/s) 0

X-Origin of Rotation-Axis (m) 0

Y-Origin of Rotation-Axis (m) 0

Deactivated Thread no

Porous zone? no

X-Component of Direction-1 Vector 1

Y-Component of Direction-1 Vector 0

Relative Velocity Resistance Formulation? yes

Direction-1 Viscous Resistance (1/m2) 0

Direction-2 Viscous Resistance (1/m2) 0

Choose alternative formulation for inertial resistance? no

Direction-1 Inertial Resistance (1/m) 0

Direction-2 Inertial Resistance (1/m) 0

C0 Coefficient for Power-Law 0

C1 Coefficient for Power-Law 0

Porosity 1

outlet

Condition Value

-----------------------------------------------

Gauge Pressure (pascal) 0


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Backflow Direction Specification Method 1

X-Component of Flow Direction 1

Y-Component of Flow Direction 0

X-Component of Axis Direction 1

Y-Component of Axis Direction 0

Z-Component of Axis Direction 0

X-Coordinate of Axis Origin (m) 0

Y-Coordinate of Axis Origin (m) 0

Z-Coordinate of Axis Origin (m) 0

is zone used in mixing-plane model? no

Specify targeted mass flow rate no

Targeted mass flow (kg/s) 1

inlet

Condition Value

---------------------------------------------------

Velocity Specification Method 2

Reference Frame 0

Velocity Magnitude (m/s) 0.00028099999

X-Velocity (m/s) 0

Y-Velocity (m/s) 0

X-Component of Flow Direction 1

Y-Component of Flow Direction 0

X-Component of Axis Direction 1

Y-Component of Axis Direction 0

Z-Component of Axis Direction 0

X-Coordinate of Axis Origin (m) 0

Y-Coordinate of Axis Origin (m) 0

Z-Coordinate of Axis Origin (m) 0

Angular velocity (rad/s) 0

is zone used in mixing-plane model? no

top_wall

Condition Value

----------------------------------------------------------


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Wall Motion 0

Shear Boundary Condition 0

Define wall motion relative to adjacent cell zone? yes

Apply a rotational velocity to this wall? no

Velocity Magnitude (m/s) 0

X-Component of Wall Translation 1

Y-Component of Wall Translation 0

Define wall velocity components? no

X-Component of Wall Translation (m/s) 0

Y-Component of Wall Translation (m/s) 0

Rotation Speed (rad/s) 0

X-Position of Rotation-Axis Origin (m) 0

Y-Position of Rotation-Axis Origin (m) 0

X-component of shear stress (pascal) 0Y-component of shear stress (pascal) 0

Specularity Coefficient 0

bottom_wall

Condition Value

----------------------------------------------------------

Wall Motion 0

Shear Boundary Condition 0

Define wall motion relative to adjacent cell zone? yes

Apply a rotational velocity to this wall? no

Velocity Magnitude (m/s) 0

X-Component of Wall Translation 1

Y-Component of Wall Translation 0

Define wall velocity components? no

X-Component of Wall Translation (m/s) 0

Y-Component of Wall Translation (m/s) 0

Rotation Speed (rad/s) 0

X-Position of Rotation-Axis Origin (m) 0

Y-Position of Rotation-Axis Origin (m) 0

X-component of shear stress (pascal) 0

Y-component of shear stress (pascal) 0

Specularity Coefficient 0


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default-interior

Condition Value

-----------------

Solver Controls

---------------

Equations

Equation Solved

-----------------

Flow yes

Numerics

Numeric Enabled

---------------------------------------

Absolute Velocity Formulation yes

Relaxation

Variable Relaxation Factor

-------------------------------

Density 1

Body Forces 1

Linear Solver

Solver Termination Residual Reduction

Variable Type Criterion Tolerance

-----------------------------------------------------

Flow F-Cycle 0.1

Pressure-Velocity Coupling


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Parameter Value

---------------------------------------------

Type Coupled

Courant Number 200

Explicit Momentum Relaxation Factor 0.75

Explicit Pressure Relaxation Factor 0.75

Discretization Scheme

Variable Scheme

----------------------------

Pressure Second Order

Momentum Third-Order MUSCL

Solution Limits

Quantity Limit

---------------------------------

Minimum Absolute Pressure 1

Maximum Absolute Pressure 5e+10

Minimum Temperature 1

Maximum Temperature 5000

Material Properties

-------------------

Material: air (fluid)

Property Units Method Value(s)

----------------------------------------------------------------

Density kg/m3 constant 1.225

Cp (Specific Heat) j/kg-k constant 1006.43

Thermal Conductivity w/m-k constant 0.0242

Viscosity kg/m-s constant 1.7894e-05

Molecular Weight kg/kgmol constant 28.966

L-J Characteristic Length angstrom constant 3.711

L-J Energy Parameter k constant 78.6


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Thermal Expansion Coefficient 1/k constant 0

Degrees of Freedom constant 0

Speed of Sound m/s none #f

Material: aluminum (solid)

Property Units Method Value(s)

---------------------------------------------------

Density kg/m3 constant 2719

Cp (Specific Heat) j/kg-k constant 871

Thermal Conductivity w/m-k constant 202.4

Masters Project LJ FINAL_2

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